The height of the mountain above sea level is 777.94 m.
The two engineers can calculate the height of the mountain by using the principle of trigonometry. Firstly, they must calculate the altitude of the mountain from the point A, which can be done by using the formula h = tan (angle of elevation) * d, where h is the altitude, angle of elevation is the angle of elevation measured from point A and d is the distance between point A and the mountain. In this case, the altitude from point A is h = tan(37°) * 1200 = 1645.58 m. Secondly, they can calculate the altitude from point B, which can be done by using the same formula h = tan (angle of elevation) * d, where h is the altitude, angle of elevation is the angle of elevation measured from point B and d is the distance between point B and the mountain. In this case, the altitude from point B is h = tan(45°) * 480 = 867.64 m. Finally, the height of the mountain above sea level can be calculated by subtracting the altitude from point B from the altitude from point A, i.e. h = 1645.58 m - 867.64 m = 777.94 m.
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What is the perimeter of triangle jeg? 60 units 65 units 70 units 75 units
The perimeter of the triangle jeg is 60 units where the sides of the triangle are given.
What is perimeter?Perimeter is the total distance around the outer boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
According to question:EK = x + 5
KJ = x +5
FG = 2x
GH = 3x - 5
Assuming that the triangle is equilateral:
equate GH = FG
3x - 5 = 2x
solve for x
x = 5
therefore, one side of the triangle is
(x + 5) + (x + 5) = 20
and the equilateral triangle's perimeter is
3×one side = 3 ×20 units
Thus, Perimeter = 60 units.
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The complete question is What is the perimeter of triangle JEG?
60 units
65 units
70 units
75 units
Use the relative frequency table shown to the right to calculate the number of the 300
measurements falling into each of the measurement classes. Then graph a frequency histogram for these data.
Measurement Class Relative Frequency
00.5-2.50 0.15
02.5-4.50 0.1
04.5-6.50 0.1
06.5-8.50 0.05
08.5-10.5 0.1
10.5-12.5 0.2
12.5-14.5 0.2
14.5-16.5 0.1
Calculate the number of measurements that fall into each class.
Therefore, the number of measurements falling into each of the measurement classes are:
00.5-2.50: 45
02.5-4.50: 30
04.5-6.50: 30
06.5-8.50: 15
08.5-10.5: 30
10.5-12.5: 60
12.5-14.5: 60
14.5-16.5: 30
What is relative frequency ?
Relative frequency is a measure used to calculate the proportion or percentage of occurrences of an event in relation to the total number of events or observations. It is calculated by dividing the frequency of an event by the total number of observations in a dataset. The relative frequency is expressed as a decimal, fraction, or percentage. It is useful for comparing the occurrence of events in different datasets or for comparing the distribution of events in a single dataset.
According to the question:
To calculate the number of measurements that fall into each class, we need to multiply the relative frequency of each class by the total number of measurements, which is 300.
For the 00.5-2.50 class: 0.15 x 300 = 45
For the 02.5-4.50 class: 0.1 x 300 = 30
For the 04.5-6.50 class: 0.1 x 300 = 30
For the 06.5-8.50 class: 0.05 x 300 = 15
For the 08.5-10.5 class: 0.1 x 300 = 30
For the 10.5-12.5 class: 0.2 x 300 = 60
For the 12.5-14.5 class: 0.2 x 300 = 60
For the 14.5-16.5 class: 0.1 x 300 = 30
Therefore, the number of measurements falling into each of the measurement classes are:
00.5-2.50: 45
02.5-4.50: 30
04.5-6.50: 30
06.5-8.50: 15
08.5-10.5: 30
10.5-12.5: 60
12.5-14.5: 60
14.5-16.5: 30
To graph a frequency histogram for these data, we can plot the number of measurements in each class on the vertical axis and the measurement classes on the horizontal axis, with the bars for each class touching each other. The resulting histogram should have eight bars of varying heights, with the tallest bars representing the classes with the most measurements.
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The two-way frequency table below shows data on playing a sport and playing a musical instrument for students in a class.
Complete the following two-way table of row relative frequencies.
(If necessary, round your answers to the nearest hundredth.)
Plays sports Does not play sports
Plays a musical instrument 666 777
Does not play a musical instrument 888 333
Plays a sport Does not play a sport Row total
Plays a musical instrument
1.001.001, point, 00
Does not play a musical instrument
1.001.001, point, 00
The two-way frequency table shows that out of the 2,002 students surveyed, 1,001 students play a sport, and 1,001 students do not play a sport.
What is frequency?Frequency is a measure of how often something occurs over a given period of time. It is a measure of the number of times a certain event or phenomenon occurs in a set interval. Frequency is usually expressed as a number of times per unit of time, such as hertz (Hz) for sound waves or cycles per second (cps) for electricity. Frequency is an important concept in physics, mathematics, engineering, and technology.
Of those 1,001 students who play a sport, 666 of them also play a musical instrument, while 777 do not. Of the 1,001 students who do not play a sport, 888 of them play a musical instrument, while 333 do not.
This data shows that a larger percentage of students who play a sport also play a musical instrument than those who do not play a sport. This could be because playing a sport can lead to a more well-rounded lifestyle, which includes participating in both physical and creative activities. Additionally, playing a sport requires teamwork and focus, which can be transferable skills that can help with learning and mastering a musical instrument. Furthermore, playing a sport can provide a fun, physical outlet and provide an opportunity to be part of a community, which can be a motivating factor to pick up or continue playing a musical instrument.
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Two similar polygons have areas of 128 in2 and 98 in2. If the smaller polygon has a perimeter of 42 in, what is the perimeter of the larger polygon?
In response to the query, we can state that Hence, the bigger polygon's equation circumference measures around 54.86 inches.
What is equation?In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in the equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14. To comprehend the relationship between the two sentences written on opposing sides of a letter, utilise a mathematical formula. The logo and the specific programme typically correspond. An illustration would be 2x - 4 = 2.
Area of a smaller polygon is equal to (k * side of a smaller polygon)2.
bigger polygon's area is equal to (k * side of larger polygon)2.
Area of bigger polygon / area of smaller polygon = (k * side of larger polygon) / (k * side of smaller polygon) /
[tex]\sqrt(128/98) k * 42 = (48 / side of smaller polygon) * 42 = 48 * (42 / side of smaller polygon) = (k * side of bigger polygon) / (k * 42)[/tex]
Greater polygon's perimeter is equal to 48 * (42 / smaller polygon's side) [tex]= 48 * (42 / (42k)) = 48 * (1/k).[/tex]
We may utilize the fact that the ratio of the two polygons' surface areas is to calculate k:
bigger polygon's area divided by smaller polygon's area equals 128/98, or 64/49.
the ratio of the sides of the two polygons is 8/7.
K thus equals 7/8.
Hence, the bigger polygon's circumference measures around 54.86 inches.
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Increase 402€ by 23%
The value of 402€ after increasing by 23% is 494.46€. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
The four basic operations, often known as "arithmetic operations," are said to be able to adequately explain all the real numbers. The mathematical operations following division, multiplication, addition, and subtraction are quotient, product, sum, and difference.
We are given a value as 402€ which is to be increased by 23%.
So, by using the addition operation, we get the value as,
⇒ 402€ + 23%
⇒ 402€ + 92.46€
⇒ 494.46€
Hence, the value of 402€ after increasing by 23% is 494.46€.
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Question: Find the value of 402€ when increased by 23%.
m=-475+2650
which number of hours and minuets is closest to the amount of time that the jet has been flying if the jet is 1,500 miles from los angeles
Answer: 11550
Step-by-step explanation:
First you add 475+2650=11550
The sum of
5
55 consecutive odd numbers is
135
135135. What is the second number in this sequence?
The second term of the finding sequence is 25.
When you are confronted by a question like this, you can make a simple equation, combine like terms, isolate the variable, and solve.
"5 consecutive odd numbers" basically means x + (x + 2) + (x + 4) + (x + 6) + (x + 8). Each time you add 2 more to ensure there are no even numbers. Otherwise, it wouldn't be only consecutive odd numbers.
We are told the sum of these numbers is 135. This means x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135.
(x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135
This might seem a bit intimidating, but there are actually only a couple of steps.
Combine like terms.
In this case, the like terms are the 5 times x appears and the numbers 0, 2, 4, 6, and 8.
x + x + x + x + x = 5 • x, or 5x.
0 + 2 + 4 + 6 + 8 = 20
So by combining like terms, we can simplify (x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135 down to just 5x + 20 = 135.
Isolate the variable.
Now we just have to isolate x. The value of x is the lowest term in the sequence.
5x + 20 = 135
To isolate x, first subtract 20 from both sides. Then, divide both sides by 5.
5x + 20 - 20 = 5x
135 - 20 = 115
5x = 115
5x / 5 = x
115 / 5 = 23
x = 23
The lowest term in the sequence is 23.
Identify all numbers in the sequence.
Now that we know x, we can find the rest of the numbers in the sequence by plugging the lowest value into the original equation we created.
(x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135
(23 + 0) + (23 + 2) + (23 + 4) + (23 + 6) + (23 + 8) = 135
23 + 0 = 23 This is the first and lowest term in the sequence.
23 + 2 = 25 This is the second term in the sequence.
23 + 4 = 27 This is the third term in the sequence.
23 + 6 = 29 This is the fourth term in the sequence.
23 + 8 = 31 This is the fifth and last term in the sequence.
Now we know the sequence is 23, 25, 27, 29, 31.
Finding the Answer:
To find the answer, locate the second term in this sequence.
23, 25, 27, 29, 31
The second term is 25.
The complete question is-
The sum of 5 consecutive odd numbers is 135. What is the second number in this sequence?
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Ye chord is drawn from a pack of 52 cards find the probability of getting a queen or a diamond or a black card
Answer:
There are 4 queens in a pack of 52 cards, and there are also 13 diamonds and 26 black cards (13 clubs and 13 spades).
To find the probability of getting a queen or a diamond or a black card, we need to add the probabilities of each event happening and subtract the probability of getting a card that is both a queen and a diamond (the queen of diamonds).
Probability of getting a queen = 4/52 = 1/13
Probability of getting a diamond = 13/52 = 1/4
Probability of getting a black card = 26/52 = 1/2
Probability of getting the queen of diamonds = 1/52
So, the probability of getting a queen or a diamond or a black card is:
(1/13) + (1/4) + (1/2) - (1/52) = 51/52 or approximately 0.98
Therefore, the probability of getting a queen or a diamond or a black card is approximately 0.98.
4x+3 to find the value of ST
According to the question the value of ST is 3 + 4x.
What is value?Value is the worth or importance that is placed on something. It can refer to tangible items such as money, goods, or services, or intangible concepts such as a person's beliefs, attitude, or sense of self-worth. Values are essential for guiding decisions and behaviour. They provide a framework for understanding what is important to an individual or a society, and can inform how people interact with their environment.
Given equation : 4x + 3 = ST
To find the value of ST, we need to subtract 4x from both sides of the equation.
4x + 3 - 4x = ST - 4x
3 = ST - 4x
Now, add 4x to both sides of the equation.
3 + 4x = ST
Therefore, the value of ST is 3 + 4x.
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Use the given point and slope to write an equation in slope intercept form.
(3, 0); slope 5
An equation of this line in slope-intercept form is y = 5x - 15.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation:
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.At data point (3, 0) and a slope of 5, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 0 = 5(x - 3)
y - 0 = 5x - 15
y = 5x - 15
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A cubic die is biased, so that for each integer n,1≤n≤6 , the probability of the event {n} is p({n})=2p if n=3 or n=4 and p({n})=p , otherwise a) What is the expected number of times the die comes up 6 , when it is rolled 32 times? b) What is the expected number of times the die must be rolled until the first 6 comes up?
Hence, the answers are a) 9.14 and b) 7.
a) What is the expected number of times the die comes up 6, when it is rolled 32 times?b) What is the expected number of times the die must be rolled until the first 6 comes up?Solutions:Part a) Let X be the number of times the die comes up 6 when it is rolled 32 times.To find the expected number of times the die comes up 6, we'll apply the formula E(X) = np, where n is the number of trials and p is the probability of success on any given trial.If we look at the bias in this particular cubic die, we see that when the event is {6}, then p({6}) = p = 2p/4. This implies that p = 2/7, therefore: E(X) = np = 32*2/7 = 9.14285714286 = 9.14Part b) Let Y be the number of times the die must be rolled until the first 6 comes up.Let's use the geometric distribution to calculate the expected number of rolls E(Y).Since the event "6" has a probability of 1/7, then p = 1/7. Thus, the expected number of times the die must be rolled until the first 6 comes up is given by E(Y) = 1/p, which is 7 rolls.Hence, the answers are a) 9.14 and b) 7.
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Select the correct answer. The product of two integers is 72. One number is two less than five times the other. Which of the following equations could be used to find one of the numbers?
A. 2x2 − 5x = 72
B. 5x2 − 2x = 72
C. 2x2 − 5 = 72
D. 5x2 − 2 = 72
Answer:
Option B.
Step-by-step explanation:
Convert the word problem into an equation.
[tex](x)(5x-2) = 72[/tex]
Simplify this to get
[tex]5x^2-2x=72[/tex]
Option B.
the tampa bay skeptics performed an experiment to see whether an acclaimed psychic has extrasensory perception (esp). a crystal was placed, at random, inside 1 of 10 identical boxes lying side by side on a table. the experiment was repeated seven times, and x, the number of decisions, was recorded. (assume that the seven trials are independent.) a. if the psychic is guessing (i.e., if the psychic does not possess esp), what is the value of p, the probability of a correct decision on each trial? b. if the psychic is guessing, what is the expected number of correct decisions in seven trials? c. if the psychic is guessing, what is the probability of no correct decisions in seven trials? d. now suppose the psychic has esp and p
a. The probability of a correct decision on each trial is 0.1.
b. The expected number of correct decisions in seven trials is 0.7.
c. The probability of no correct decisions in seven trials is approximately 0.478.
d. The probability that the psychic guesses incorrectly in all seven trials is approximately 0.0078.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
a. If the psychic is guessing (i.e., does not possess ESP), there are 10 boxes, and only one of them contains the crystal.
Therefore, the probability of a correct decision on each trial is -
p = 1/10 = 0.1
b. If the psychic is guessing, the expected number of correct decisions in seven trials can be found by multiplying the probability of a correct decision on each trial (0.1) by the number of trials (7) -
E(X) = np = 7 × 0.1 = 0.7
Therefore, the number of correct decisions is 0.7.
c. If the psychic is guessing, the probability of no correct decisions in seven trials can be found using the binomial distribution formula -
[tex]P(X=0) = (n\ choose\ x) \times p^x \times (1-p)^{(n-x)}[/tex]
In this case, n = 7, x = 0, and p = 0.1.
Substituting these values into the formula, we get -
[tex]P(X=0) = (7\ choose\ 0) \times 0.1^0 \times 0.9^7 = 0.478[/tex]
Therefore, the probability value is 0.478.
d. If the psychic has ESP and p = 0.5, the probability of guessing incorrectly on any trial is -
q = 1 - p
q = 1 - 0.5
q = 0.5
The probability of guessing incorrectly in all seven trials can be found using the binomial distribution formula -
[tex]P(X=7) = (n\ choose\ x) \times p^x \times q^{(n-x)}[/tex]
In this case, n = 7, x = 7, p = 0.5, and q = 0.5.
Substituting these values into the equation, we get -
[tex]P(X=7) = (7\ choose\ 7) \times 0.5^7 \times 0.5^0 = 0.0078[/tex]
Therefore, the probability value is 0.0078.
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The Tampa bay skeptics performed an experiment to see whether an acclaimed psychic has extrasensory perception (ESP). A crystal was placed, at random, inside 1 of 10 identical boxes lying side by side on a table. The experiment was repeated seven times, and x, the number of decisions, was recorded. (Assume that the seven trials are independent.)
a. If the psychic is guessing (i.e., if the psychic does not possess ESP), what is the value of p, the probability of a correct decision on each trial?
b. If the psychic is guessing, what is the expected number of correct decisions in seven trials?
c. If the psychic is guessing, what is the probability of no correct decisions in seven trials?
d. Now suppose the psychic has ESP and p=.5. What is the probability that the psychic guesses incorrectly in all seven trials.
What is the answer for the 'angles of polygons' question?
Answer:
18 bc there a 9 angles and below is is another angle so u do 9 + 9 or 9(2) and u will get 18
G
3
X
You are traveling by car to New York City. The map you will use for your journey is
below.
Seattle
• San Jose
• Los Angeles
1 unit
1 unit = 557 miles
Denver
El Paso
Chicago
Houston
a) What is the scale factor on the map? (1 point)
Memphis
New York
Jacksonville
grup
The scale factor on the map is 1 unit = 557 miles. This means that for every 1 unit on the map, it corresponds to 557 miles in the real world.
What is a map?A map is a visual representation of an area. It shows physical features such as landforms, bodies of water, and other geographical features. It can also represent political boundaries, transportation networks, and population density. Maps are useful tools for navigation, planning, and communication. They are also used for research, education, and leisure activities.
For example, if Seattle to San Jose on the map is 1 unit, then it is equivalent to 557 miles in the real world. Similarly, if Denver to El Paso is 2 units, then it would be equivalent to 1114 miles in the real world.
This scale factor is important when planning a journey because it helps travelers to accurately calculate the distance they need to travel. Knowing the exact distance can help travelers plan their stops along the way, choose the most efficient route, and estimate the amount of time it will take to get to their destination. Additionally, it can help travelers to plan their budget accordingly, since they will have an idea of how much gas they need to buy and how much accommodation costs they need to cover.
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A dartboard consists of a circle inscribed in a square.
The area of the circle is 16 Square inches. The area of
the square is 64 square inches.
Izzy randomly throws a dart at the square, and it lands
inside the square. To the nearest percent, what is the
probability that the dart lands inside the square but not on
the circular dartboard? Use 3. 14 for.
O 22%
25%
75%
O 79%
75% of the time, a dart will fall inside a square rather than on the circular dartboard.
The ratio of the area of the circle to the square is 16/64 = 1/4. So, the area outside the circle but inside the square is 3/4 of the total area of the square. The probability of landing the dart in this region is 3/4.
To find the percentage, we can multiply by 100:
3/4 × 100 = 75%
Therefore, to the nearest percent, the probability that the dart lands inside the square but not on the circular dartboard is 75%.
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varying traitow to identify the quadrilaterals and compare and contrast them based upon their characteristics. Part 1: Judging by appearance, classify these Quadrilaterals by all applicable names Part 2: Compare and contrast the following pairs of quadrilaterals based upon properties of their sides and angles. Describe the nature of the relationship, i.e., a Square is a rectangle, but not all rectangles are squares.
Quadrilateral A: Parallelοgram, Rectangle, Rhοmbus, Square.
Quadrilateral B: Trapezοid, Isοsceles Trapezοid
Quadrilateral C: Kite, Trapezοid
Square and Rectangle:
Bοth have fοur right angles, but the square has fοur cοngruent sides, while the rectangle dοes nοt necessarily have cοngruent sides. Therefοre, a square is a rectangle, but nοt all rectangles are squares.
Rhοmbus and Square:
Bοth have all sides cοngruent, but the square alsο has fοur right angles, while the rhοmbus dοes nοt necessarily have right angles. Therefοre, a square is a rhοmbus, but nοt all rhοmbuses are squares.
Parallelοgram and Rhοmbus:
Bοth have οppοsite sides parallel, but the rhοmbus alsο has all sides cοngruent, while the parallelοgram dοes nοt necessarily have cοngruent sides. Therefοre, a rhοmbus is a parallelοgram, but nοt all parallelοgrams are rhοmbuses.
Trapezοid and Kite:
Bοth have twο pairs οf adjacent sides that are cοngruent, but the kite alsο has οne pair οf οppοsite cοngruent sides, while the trapezοid dοes nοt. Therefοre, a kite is a type οf trapezοid, but nοt all trapezοids are kites.
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Someone Plssss plssss help
Answer:
fourth option
Step-by-step explanation:
sinX = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{YZ}{XY}[/tex] = [tex]\frac{3}{\sqrt{34} }[/tex]
and
tanY = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{XZ}{YZ}[/tex] = [tex]\frac{5}{3}[/tex]
It takes three minutes to
make four paper
valentines
How long will
it take to make eight?
Answer: six minutes
Step-by-step explanation: 8 / 4 = 2 , 3 x 2 = 6
The diagonals of parallelogram ABCD intersect at E. If AE=2x+ 4., EB=6+3y,EC=15-y and ED =x+4 then, find the lengths of diagonals AC and BD.
The length of the diagonals AC and BD are 28 and 18 units respectively.
How to find the diagonal of a parallelogram?A parallelogram is a quadrilateral that has opposite sides equal to each other and opposite sides parallel to each other. The diagonal of a parallelogram are not equal but they bisect each other.
Therefore,
AE = EC
EB = ED
Hence,
2x + 4 = 15 - y
2x + y = 11
6 + 3y = x + 4
x - 3y = 2
Combine the equation
2x + y = 11
x - 3y = 2
multiply equation(ii) by 2
2x + y = 11
2x - 6y = 4
7y = 7
y = 7 / 7
y = 1
Let's find x
x = 2 + 3y
x = 2 + 3(1)
x = 2 + 3
x = 5
Therefore,
x = 5 and y = 1
AE = EC = 2(5) + 4 = 14
AC = 14(2) = 28 units
EB = ED = 6 + 3(1) = 9
BD = 9(2) = 18 units
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the solution shown for the equation is incorrect. What is the correct solution? what is the error -7(2-r) = 28 -14-7r=28 -7r=42 r=-6
What is the area of the composite figure?
6 ft
8 ft
12 ft
120 ft²
140 ft²
80 ft²
200 ft²
Previous
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20 ft
8 ft
12 ft
6 ft
The total area of the composite figure is 200 square feet.
What is the area of the composite figure?We can view the figure as a triangle and a rectangle.
The dimensions of the rectangle are 24ft by 6ft,so its area is:
A = 24ft*6ft = 144ft²
Now for the triangle, remember that the area of a triangle of base B and height H is:
a = B*H/2
In this case we can see that the base is:
B = 24ft - 8ft - 8ft = 8ft
And the height is:
H = 20ft - 6ft = 14ft
Then the area of the triangle is:
a = 8ft*14ft/2 = 56 ft²
The total area is:
Area = 56 ft² + 144ft² = 200 ft²
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I'm having a hard time understanding how
x2+3x=0
then x(x+3)=0
breaks down to x=-3,0
The solution to the equation x² + 3x = 0 when solved for variable x are x = -3 and 0
What are equations?Equations are statements with equal values
Calculating the solution for xGiven the following equation
x² + 3x = 0
Factor out x from the equation
So, the equation becomes
x(x + 3) = 0
The above equation means that
x = 0
Also, it means that
x + 3 = 0
When the equation is evaluated, we have
x = 0 and x = -3
Now that we have the values of x, we can conclude that the solutions are x = 0 and x = -3
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How many cubes with an edge length of 1/5 inch are needed to build a cube with an edge length of 1 inches?
125 cubes with an edge length of 1/5 inch are needed to build a cube with an edge length of 1 inch.
What is a cube?A cube is a 3-dimensional solid shape with six square faces that are all congruent, and with all edges of equal length.
The volume of a cube is calculated by cubing the length of one of its edges.
To find the number of cubes with an edge length of 1/5 inch that are needed to build a cube with an edge length of 1 inch, we need to calculate the ratio of the volumes of the two cubes.
The volume of the larger cube with an edge length of 1 inch is:
V_large = (1 inch)^3 = 1 cubic inch
The volume of the smaller cube with an edge length of 1/5 inch is:
V_small = (1/5 inch)^3 = 1/125 cubic inches
To find the number of small cubes, we need to divide the volume of the larger cube by the volume of the smaller cube:
Number of small cubes = V_large / V_small = 1 cubic inch / (1/125 cubic inches) = 125
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Choose 1 answer: B A C C Which line segment shows the base that corresponds to the given height of the triangle? height B
The line segment that shows the base that corresponds to the given height of the triangle is; Line segment A
How to identify similar triangle lengths?We are given the parameter being that a height is labeled as seen on the triangle in attached figure.
Now, what we want to achieve is to find the specific segment which tells us the specific base that corresponds to the given specific height of the triangle
We know that the base of the triangle is that particular side of the triangle on which the height is perpendicular.
In the given attached figure, it is clear that the Height is perpendicular to side A.
Therefore, side A will represent the base of triangle.
Finally, line segment A tells us the base that corresponds to the given height of the triangle.
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#2
At the annual school track meet, two sprinters will race for 150 meters.
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• Sprinter A runs 6 meters per second.
• Sprinter B runs 5 meters per second.
• Sprinter B is given a 10 meter head start.
Select all the statements that are true.
A. C
B.
C.
Sprinter A is leading the race at the 12 second mark.
Sprinter A will win the race.
The graphs of these two functions never intersect before the race en
The 6 m/s, and 5 m/s speeds of the sprinters, the 150 meters length of the race, and the 10 meters head start of sprinter B indicates that the three statements are true, and the correct option is therefore;
True, True, True
What is the speed of an object?The speed of an object is the ratio of the distance traveled by the object to the duration of the motion.
The distance sprinters are to run = 150 meters
The speed of sprinter A = 6 m/s
Speed of sprinter B = 5 m/s
The head start of sprinter B = 10 meters
Statement A; Sprinter A is leading the race at the 12 seconds mark
At the 12 seconds mark, we get;
The distance covered by sprinter A = 6 m/s × 12 s = 72 m
The distance covered by sprinter B = 10 m + 5 m/s × 12 s = 70 m
Therefore, sprinter A is leading sprinter B at the 12 seconds mark
Statement A is True
Statement B; Sprinter A will win the race
The time it takes sprinter A to run the race = 150 m/(6 m/s) = 25 s
Sprinter B takes (150 m - 10 m)/(5 m/s) = 28 s to finish the race
Sprinter A therefore, finishes before sprinter B, and sprinter A wins the race
Statement B is; True
Statement C; The graphs of the two functions intersect before the race ends
The location of sprinter B ahead of A at the start of the race and A ahead of B at the 12 seconds mark, indicates that the sprinter A passes sprinter B along the race and the graphs intersect before the race ends. The statement is therefore; True
The possible options, obtained from a similar question posted on the internet are;
True, True, True
False, True, True
True, False, True
True, True, False
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One of the acute angles of a right triangle is 36 then the other acute angle is
Answer:
54
Step-by-step explanation:
So a right angle has one right angle and each angle is equal to ninety degrees. So you have 90+36=126. Sum of angles in a triangle is 180 so subtract 126 from it to get 54.
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CEREAL The volume of a box of cereal in square inches can be represented by
the expression 2x² + 30x + 108. Factor the expression.
Answer:
2(x+6)(x+9)
Step-by-step explanation:
Factor out a 2.
The result is 2(x^2+15x+54).
From here, many ways are possible, but for simplicity, we’ll go for a guess and check method. Assuming you know how it works, 2 numbers (we’ll call them a and b) satisfy a+b=15 and ab=54. After a bit of guessing, we can derive that the 2 numbers are 6 and 9. Our factored expression resembles 2(x+a)(x+b), so our factored expression is
2(x+6)(x+9)
The model shows that 3 and one fifth divided by four fifths equal 4 what would happen if you divide by 8/5 instead of 4/5
Dividing by a larger fraction (8/5) instead of 4/5 results in a smaller answer (2), because we are dividing the same amount (16/5) into more parts (8) compared to dividing by 4/5.
If you divide 3 and one fifth by four fifths, you can first convert the mixed number to an improper fraction:
3 and 1/5 = (3 x 5 + 1) / 5 = 16/5
Then, you can perform the division as follows:
(16/5) / (4/5) = (16/5) x (5/4) = 4
So, we get an answer of 4.
If we divide by 8/5 instead of 4/5, we can use the same process but with the new fraction:
(16/5) / (8/5) = (16/5) x (5/8) = 2
So, the answer would be 2.
This is because when we divide by a smaller fraction, we are dividing the same amount into fewer parts, which results in a larger answer.
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A net for a cube has a total surface area of 150 in.2. what is the length of one side of a square face?
a. 4 in.
b. 5 in.
c. 16 in.
d. 25 in.
The length of one side of a square face is 5 inches
The surface area of a cube is given by 6s^2, where s is the length of one side of a square face. If the net for a cube has a total surface area of 150 in^2, we can set up an equation:
6s^2 = 150
Dividing both sides by 6, we get:
s^2 = 25
Taking the square root of both sides, we get:
s = 5
Therefore, the length of one side of a square face is 5 inches.
So, the answer is (b) 5 in.
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