The points on line segment in Question 1 is C (52, 3)( 5 2 , 3) and the answer to Question 2 is A (112, 3)( 11 2 , 3).
What is a line segment?
A line segment is a straight line that is bounded by two distinct endpoints. It is the shortest distance between two points and is usually represented by an arrow. Line segments are an essential part of geometry, as they form the basis for many shapes, such as triangles and rectangles.
A line segment can be divided into two parts in a given ratio if the difference of the coordinates of the end points of the line segment is divided in the same ratio.
For Question 1, the ratio of the line segment is 1:3. To find the point on the line segment, we will divide the difference of the coordinates of the end points of the line segment into the ratio 1:3. The coordinates of the end points of the line segment PQ are (10,2) and (14,6). The difference of the coordinates of the end points of the line segment PQ is (14-10, 6-2) = (4,4). The difference of the coordinates (4,4) is divided into the ratio 1:3. After dividing the difference of the coordinates into the ratio 1:3, we get the coordinates of the point on the line segment PQ as (52,3).
For Question 2, the ratio of the line segment is 3:1. To find the point on the line segment, we will divide the difference of the coordinates of the end points of the line segment into the ratio 3:1. The coordinates of the end points of the line segment PQ are (10,2) and (14,6). The difference of the coordinates of the end points of the line segment PQ is (14-10, 6-2) = (4,4). The difference of the coordinates (4,4) is divided into the ratio 3:1. After dividing the difference of the coordinates into the ratio 3:1, we get the coordinates of the point on the line segment PQ as (112,3).
In conclusion, the point on the line segment PQ that divides the line segment into the ratio of 1:3 is C (52, 3)( 5 2 , 3) and the point on the line segment PQ that divides the line segment into the ratio of 3:1 is A (112, 3)( 11 2 , 3).
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cara buys a crystal vase priced at 855 if the sales tax 10% how much tax will cara pay
Answer: 85.5
Step-by-step explanation: divide 855 by ten or move the decimal to the left one place for every zero
Ella's buys a computer for $785. Her local tax rate is 7%. How much does Ella pay for the computer, including tax?
Answer:
$839.95
Step-by-step explanation:
To get the amount of tax Ella would have to pay for, multiply the price of the computer by the tax rate
785 x .07 = 54.95
Then add the computer price and tax to get how much she paid for in total
785 +54.95= $839.95
Help with the question
In this case, the population is children from 6 to 18 years old who had nonlethal scorpion sting; on the other hand, the sample is the 245 children selected.
How to identify the population and the sample?In a research study, the population is considered as the group of individuals being studied. However, as this number is often high, researchers often select a small random percentage that should be representative of the population, which is known as the sample.
Based on this, the population can be children from 6 to 18 years old who had nonlethal scorpion sting, while the sample are those children selected (245) to carry out the research study.
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may you please help me with this
Answer:
C). 8/9n - 1 1/3
Step-by-step explanation:
Answer:
[tex]\frac{8}{9} n - 1\frac{1}{3}[/tex]
Step-by-step explanation:
Using the distributive property [tex]\frac{4}{9}[/tex] times 2 equals [tex]\frac{8}{9}[/tex] and [tex]\frac{4}{9}[/tex] times 3 equals [tex]\frac{4}{3}[/tex] which simplifies to [tex]1\frac{1}{3}[/tex]
What is the binomial is a factor to this trinomial:
4x^2+20x-24
[tex]4x^2+20x-24 = 4x^2-4x+24x-24 = 4x(x-1)+24(x-1) = (4x + 24)(x-1)\\[/tex]
[tex]= 4(x+6)(x-1)[/tex]
"which describes the translation of f(x) to g(x)?"
The translation of f(x) to g(x) is described by - translation of 4 units up.
Explain about the translation of coordinates?As you translate a figure, you slide it left, right, up, or down. This implies that the coordinates for such vertices of the figure will alter on the coordinate plane. Apply the identical modification to every point in order to graph a translation. The variations in a reflection's coordinates can be used to identify it.As you translate a figure, you slide it left, right, up, or down. This implies that the coordinates for such vertices of the figure will alter on the coordinate plane.
Apply the identical modification to every point in order to graph a translation.
As there is the shift of coordinates on y axis upward by 4 units units.
Thus, the translation of f(x) to g(x) is described by - translation of 4 units upward.
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The variance will reach a maximum in a binomial distribution when
Answer:
Third choice
π = 1/2 and 1 - π = 1/2
Step-by-step explanation:
Formula for binomial distribution is
[tex]P(x) = \dfrac{n!}{x!(n-x)!} \pi^x (1-\pi)^{n-x}[/tex]
where
x is the number of successes
n = number of trials
π = probability of success on a single trial
The variance of the binomial distribution is
[tex]\sigma^2 = n \cdot \pi(1-\pi)[/tex]
The maximum variance occurs when
[tex]\pi = (1- \pi) = 1/2[/tex]
Hence the correct choice is the third choice
π = 1/2 and 1- π = 1/2
Solve for x.
Enter your answer in the box.
According the Question the value οf x will be 6.
What is circumference οf a circle?The measurement οf the circle's bοundaries is called as the circumference οr perimeter οf the circle. whereas the circumference οf a circle determines the space it οccupies. The circumference οf a circle is its length when it is οpened up and drawn as a straight line. Units like cm οr unit m are typically used tο measure it.
The circle's radius is cοnsidered while calculating the circumference οf the circle using the fοrmula. As a result, in οrder tο calculate the circle's perimeter, we must knοw the radius οr diameter value.
The side οf the circle JH . JG = JK . JM
JM = 7*16/8 = 14
X = 14-8 =6
Hene the value οf x will be 6.
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Help immediately please!! Lots of points :)
The quotient gives (f/g)(4) = -16/3 and the value that is not in the domain is x = 1.
How to find the quotient between the functions?Here we know that:
f(x) = (x + 4)(x - 6)
g(x) = x - 1
And we want to find the quotient between these functions:
(f/g)(4)
So first let's find the values of the functions when x = 4.
f(4) = (4 + 4)*(4 - 6) = 8*-2 = -16
g(4) = 4 - 1 = 3
Then the quotient is:
(f/g)(4) = -16/3
Now, the values that are not in the domain of f/g are the values that make the denominator equal to zero, because we can't divide by zero.
g(x) = 0 = x - 1
1 =x
The denominator is zero for x = 1, so that value is not in the domain.
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(ANSWER ASAP!! GIVING BRAINLIEST AS SOON AS AVAILABLE! )
It took 22.2 gallons to fill Pedro's car with gasoline. There are approximately 3.8 liters in 1 gallon. Which measurement is closest to the number of liters of gasoline it took to completely fill Pedro's car with gas?
A: 20 L
B: 84.58L
C: 90L
D: 18.4 L
Answer: The answer is B!
Step-by-step explanation:
If you multiply 22.2 by 8.3, you get 84.36 (if you move the decimal point one space, otherwise you'd get 843.6.) Then if you estimate it, you would get 84.58.
Zoey needs to create a linear graph. Her graph will show the time on the x-axis and temperature (in °F) on the y-axis. Which set of data should Zoey use?
A the hourly temperature of a lake for six monthsthe hourly temperature of a lake for six months
B the temperature of an oven every minute until it reaches 350°the temperature of an oven every minute until it reaches 350°
C the average daily temperature of a town for a yearthe average daily temperature of a town for a year
D the temperature of a water sample increasing 2° every hour
The set of data that Zoey should use for the linear graph is given as follows:
D the temperature of a water sample increasing 2° every hour.
How to obtain the set of data for the graph?The graph represents a linear function, meaning that the rate of change of the output variable relative to the input variable must be constant.
The input and output variables of the graph are given as follows:
Input variable -> Time.Output variable -> Temperature.As the rate of change must be constant, the correct option is given by option d, which has a rate of change of 2º every hour. For the other options, the rate of change is not constant.
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I NEED THIS EXTREMELY FAST
Answer:
4[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
Answer:
4 3/8
Step-by-step explanation:
4*8=32 35-32=3
From 2014-2015 to 2024-2025, the number of students enrolled in an associate degree program is projected to increase by 21.5%. If the enrollment in associate degree programs in 2014-2015 is 6,500,000 , find the increase and the projected number of students in an associate degree program in 2024-2025.
By solving the increase in percentage, the projected number of students in an associate degree program in 2024-2025 is approximately 7,897,500.
What is an increase in percentage?
An increase in percentage is a measure of the change in a quantity expressed as a percentage of the initial value. It is calculated by subtracting the initial value from the final value, dividing the result by the initial value, and then multiplying the quotient by 100 to express the result as a percentage. The formula for calculating the percentage increase is:
percentage increase = (final value - initial value) / initial value * 100
To find the increase in the number of students enrolled in an associate degree program from 2014-2015 to 2024-2025, we can first calculate the amount of increase as a percentage of the initial enrollment:
Increase = 21.5% * 6,500,000 = 1,397,500
Therefore, the increase in the number of students is approximately 1,397,500.
To find the projected number of students in an associate degree program in 2024-2025, we can add the increase to the initial enrollment:
Projected enrollment = 6,500,000 + 1,397,500 = 7,897,500
Therefore, the projected number of students in an associate degree program in 2024-2025 is approximately 7,897,500.
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The angle measurements in the diagram are represented by the following expressions.
\qquad \blueD{\angle A=7x + 24^\circ}∠A=7x+24
∘
start color #11accd, angle, A, equals, 7, x, plus, 24, degrees, end color #11accd \qquad \greenD{\angle B=3x + 92^\circ}∠B=3x+92
∘
start color #1fab54, angle, B, equals, 3, x, plus, 92, degrees, end color #1fab54
Solve for xxx and then find the measure of \blueD{\angle A}∠Astart color #11accd, angle, A, end color #11accd:
\blueD{\angle A} =
The measure of the angles is 143°
Lines and anglesFrom the given diagram, the given measures are alternate exterior angles and they are equal.
Given the following parameters
∠A =7x + 24
∠B = 3x + 92
Equate
7x + 24 = 3x + 92
7x - 3x = 92 - 24
4x = 68
x = 17
Determine the measure of the angles
∠A = ∠B = 7x + 24
∠A = ∠B = 7(17) + 24
∠A = ∠B = 143 degrees
Hence the measure of the angles is 143°
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find the 9th term of the geometric sequence whose common ration is 2/3 and whose first term is 6.
Answer:
To find the 9th term of a geometric sequence, we can use the formula:
an = a1 * r^(n-1)
where:
an = the nth term of the sequence
a1 = the first term of the sequence
r = the common ratio of the sequence
n = the term number we want to find
In this case, we are given that the common ratio is 2/3, the first term is 6, and we want to find the 9th term. So we can plug in those values and get:
a9 = 6 * (2/3)^(9-1)
Simplifying the exponent, we get:
a9 = 6 * (2/3)^8
Using a calculator, we can evaluate the exponent:
a9 = 6 * 0.015625
Multiplying, we get:
a9 = 0.09375
Therefore, the 9th term of the geometric sequence is 0.09375.
Step-by-step explanation:
here's a step-by-step explanation:
We are given the first term of the geometric sequence, a1 = 6, and the common ratio, r = 2/3. We need to find the 9th term, which we can do using the formula:
an = a1 * r^(n-1)
where n is the term number we want to find.
Step 1: Substitute the given values into the formula
a9 = 6 * (2/3)^(9-1)
Step 2: Simplify the exponent
a9 = 6 * (2/3)^8
The exponent 9-1 simplifies to 8.
Step 3: Evaluate the exponent
a9 = 6 * 0.015625
We can use a calculator to evaluate (2/3)^8, which is 0.015625.
Step 4: Multiply to find the 9th term
a9 = 0.09375
Multiplying 6 by 0.015625 gives us the 9th term of the geometric sequence, which is 0.09375.
Therefore, the 9th term of the geometric sequence whose common ratio is 2/3 and whose first term is 6 is 0.09375.
Use the graph of the function to answer the following question.
Which of the following statements about the function is TRUE?
A.The function has a maximum value of 0.
B.As x approaches ∞, the function approaches ∞.
C.The function is always decreasing.
D.The function is positive on the interval (- 1, 1).
The function is positive on the interval (-1, 1)," is the only answer that is accurate. Due to the fact that the function accepts positive values for x between -1 and 0, accepts 0 at x = 0, and then accepts positive values.
A function on an interval is what exactly?When a function is specified at each point along an interval without any gaps, leaps, or interruptions, the interval is said to be continuous for that function.
When we examine the function's graph, we can observe that:
Because the function accepts negative values for x > 1 and positive values for x -1, it does not have a maximum value of 0.
The function does not approach as x approaches. Instead, as x rises, the function alternates between positive and negative values.
There are times when the function increases. Rather, it is rising on the interval (1, ) and falling on the intervals (-, 1). At x = -1, it has a local minimum, while at x = 1, it has a local maximum.
Due to the fact that it accepts negative values for x between -1 and 0, the function is not positive on the range (-1, 1).
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What is the (backwards y looking thing) (∠FNL)
According to the given information, measure of angle FNL is given by 234 - 13x.
What is angle ?
In geometry, an angle is a figure formed by two rays, or line segments, that share a common endpoint, called the vertex of the angle. The two rays are called the sides or legs of the angle.
line FN || line EM || line DL,
line FD and line NL intersects line FN,line EM and line DL at pts F,E,D and N,M,L respectively
FE = ED ,NM = ML
angle FNL = (9x-40)deg
angle FDL = (4x-14)deg
Since line FN is parallel to line EM, we have:
angle FNM = angle FEL (corresponding angles)
Since line FN is parallel to line DL, we have:
angle FNL = angle FLD (alternate interior angles)
Similarly, since line FD intersects line FN and line EM at points F and E, we have:
angle FEL + angle FED = 180 degrees (linear pair)
Since FE = ED, we have:
angle FEL = angle FED (opposite angles of a parallelogram are equal)
Combining the above equations, we get:
angle FNL = angle FLD = angle FED = 180 - angle FEL
Also, since NM = ML, we have:
angle NML = angle MLM
Now, applying the angle sum property in triangle FNL, we get:
angle FNL + angle FLD + angle FEL = 180 degrees
Substituting the given values, we get:
(9x-40) + (4x-14) + (180 - angle FEL) = 180
Simplifying, we get:
13x - 54 + 180 - angle FEL = 180
13x - angle FEL = 54
Solving for angle FEL, we get:
angle FEL = 13x - 54
Substituting this value in the equation we derived earlier, we get:
angle FNL = angle FLD = angle FED = 180 - angle FEL
= 180 - (13x - 54)
= 234 - 13x
Therefore, measure of angle FNL is given by 234 - 13x
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Simba Travel Agency arranges trips for climbing Mount Kilimanjaro. For each trip, they charge an initial fee of
$
100
$100dollar sign, 100 in addition to a constant fee for each vertical meter climbed. For instance, the total fee for climbing to the Shira Volcanic Cone, which is
3000
30003000 meters above the base of the mountain, is
$
400
$400dollar sign, 400.
Let
y
yy represent the total fee (in dollars) of a trip where they climbed
x
xx vertical meters.
Complete the equation for the relationship between the total fee and vertical distance.
y
=
The equation for the relationship between the total fee and vertical distance is: y = 100 + x/3000.
What does vertical distance mean?Vertical distance is the measurement of the straight line distance between two points in a vertical plane. It is the difference between the higher and lower altitudes of two points and is measured in a straight line from the highest point to the lowest point.
This equation can be explained as follows. The total fee for a trip to climb Mount Kilimanjaro is split into two parts. The first part is the initial fee of $100, which is a fixed cost independent of the distance climbed. The second part is the cost per vertical meter, which is calculated by dividing the vertical distance climbed (x) by 3000 (the constant fee for each vertical meter climbed) and then multiplying the result by the constant fee. Therefore, the equation for the relationship between the total fee and vertical distance is y = 100 + x/3000.
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hii
what's the best way to recreate the incident as it happened and to picture
hii
what's the best way to recreate the incident as it happened and to picture
HELP ILL MARK BRAINLIEST (the first answer choice i am not sure if right)
Answer: is mature enough to vote
Step-by-step explanation: the second drop box is asking about the opposing claim, which is the one that the professor gives.
Answer:
the last option, " is mature enough to vote".
Step-by-step explanation:
Professor Steinberg believes that 16 old can vote as their brains are mature enough to make informed decisions like voting.
7. A ball is dropped from a height of 80 cm. After each bounce it rebounds to 70% of its previous
maximum height.
c Find the total vertical distance travelled by the ball before it stops bouncing
d State one limitation with the model.
Through the given statement we can say that the vertical distance travelled by the ball is 84 m.
One limitation of this model is that it assumes that the ball rebounds to the same percentage of its previous maximum height after every bounce.
What is the vertical distance formula?The formula for vertical distance from the earth is y = - 1 2 g t 2 y = - frac 1 2 g t 2 y=-21gt2, where g is the acceleration of gravity and h is an elevation.
So :
C) the required total vertical distance that the given dropped ball travels until its bouncing stops:
= (12 m) + 2*(12 m)*(3/4)*[1 + 3/4 + (3/4)^2 + (3/4)^∞] [the factor 2 is for equal distance being covered up and down after each bounce of the ball]
= (12 m) + (24 m)*(3/4)*
(sum of an infinite GP series whose 1st term is 1 and common ratio is 3/4)
= (12 m) + (24 m)*(3/4)*[1/(1 - 3/4)]
= (12 m) + (24 m)*(3/4)*4
= (12 m) + (72m) = 84 m
D) This model's assumption that the ball will always bounce back to a certain proportion of its maximum height is one of its limitations. In fact, the rebound height can differ from one bounce to the next due to factors like air resistance, the ball's elasticity, and the surface it bounces on.
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The table shows the number of yearbooks sold and the price needed to cover the costs of printing. What function models the data?
The data modelling function is Price required to recoup printing expenses is equal to 0.1 * (numbers of yearbooks sold) + 45.
What is an annual?A yearbook is a collection of images and text that is issued by an organisation once a year to remember and highlight the happenings at a particular school during the previous academic year. Yearbooks were used in elementary, middle, high, and college and university settings throughout the 20th century.
Using the information in the table,
[tex]n = 5[/tex]
Σ[tex]x = 1175[/tex]
Σ[tex]y = 145[/tex]
Σ[tex](xy) = 41000[/tex]
Σ[tex](x^2) = 287500[/tex]
When these values are inserted into the formula,
[tex]m = (541000 - 1175145) / (5*287500 - 1175^2)[/tex]
[tex]= -0.1[/tex]
Therefore, the slope of the linear function is [tex]-0.1[/tex].
[tex]b = y - mx[/tex]
where we can use any of the data points. Let's use[tex](250, 20)[/tex]
[tex]b = 20 - (-0.1*250)[/tex]
[tex]= 45[/tex]
Therefore, the y-intercept of the linear function is [tex]45[/tex].
[tex]y = -0.1x + 45[/tex]
Therefore,
Price needed to cover the costs of printing [tex]= -0.1*[/tex](number of yearbooks sold) [tex]+ 45[/tex].
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A hot air balloon is at an altitude of 113.2 meters. The balloon's altitude decreases by 10.8 meters every minute. Which equation can you use to find the number of minutes m until the balloon is 70 meters?
Answer: 113.2 - 10.8x=70
Step-by-step explanation:
If anybody sees this can they help me out
The trees in a forest are being cut down at a monthly rate of 3.2%. This situation can be modeled by an exponentia function. The forest contained 5,500 trees when cutting began. Which function can be used to find the number of trees in the forest at the end of m months?
A) t(m) -5,500(0.032)m
B) t(m) - 5,500(1.968)m
C) t(m) -5,500(1.032)m
D) t(m) -5,500(0.968)m
Answer:
B
Step-by-step explanation:
The function that models the situation is an exponential decay function of the form:
t(m) = a(1 - r)^m
where:
t(m) is the number of trees after m months
a is the initial number of trees (5,500 in this case)
r is the monthly rate of decrease (3.2% or 0.032 as a decimal)
Substituting the values given in the options, we get:
A) t(m) = 5,500(0.032)^m
B) t(m) = 5,500(1-0.032)^m = 5,500(0.968)^m
C) t(m) = 5,500(1.032)^m
D) t(m) = 5,500(1-0.968)^m = 5,500(0.032)^m
Option B is the correct answer as it correctly models the situation with exponential decay with a starting value of 5,500 trees and a monthly rate of decrease of 3.2%.
Answer: The formula for exponential decay is given by:
t(m) = a(1-r)^m
where
a = initial value
r = decay rate
Here, the initial value is 5,500 and the monthly decay rate is 3.2% or 0.032. So the function that can be used to find the number of trees in the forest at the end of m months is:
t(m) = 5,500(1 - 0.032)^m
t(m) = 5,500(0.968)^m
Therefore, the answer is (D) t(m) = 5,500(0.968)^m.
Your welcome (;
3.2 3.3 34 Determine the mean number (rounded to the nearest whole number) of water tanks that were supplied to the construction site in March 2022 during weekdays. What type of numerical data was recorded on the calender in ANNEXURE A by the contractor? Determine the modal number of water tankers that were supplied to the construction site in June 2022. Records of the number of water tankers that were supplied to the construction site appear in the calender on ANNEXURE A. The water tanker has a fuel capacity of 460 litres.. The rate of fuel consumption of the Mercedes water tanker averages 5 km/t. The prices of fuel per litre in March and June 2022 appear below. MARCH 2022 FUEL PRICES DIESEL 50 ppm COST R19,55 JUNE 2022 FUEL PRICES DIESEL 50 ppm Source: COST R24,14 (3) (2) (2)
Answer:
Step-by-step explanation:
To determine the mean number of water tanks supplied to the construction site in March 2022 during weekdays, we need to add up the number of tanks supplied during weekdays and divide by the number of weekdays in March 2022:
March 2022 had 23 weekdays.
From the information given, we don't know the number of tanks supplied during weekdays in March 2022. Therefore, we cannot calculate the mean number of tanks supplied during weekdays in March 2022.
The numerical data recorded on the calendar in ANNEXURE A by the contractor was the number of water tankers supplied to the construction site on each day of the month.
To determine the modal number of water tankers that were supplied to the construction site in June 2022, we need to find the number that appears most frequently in the data:
From the information given, we don't have the data on the number of water tankers supplied to the construction site in June 2022. Therefore, we cannot determine the modal number of water tankers supplied in June 2022.
Given that the water tanker has a fuel capacity of 460 litres and the rate of fuel consumption of the Mercedes water tanker averages 5 km/l, we can calculate the distance traveled on a full tank of fuel:
The distance traveled on a full tank of fuel is 460 litres x 5 km/l = 2,300 km.
Finally, we are given the prices of fuel per litre in March and June 2022:
In March 2022, the price of diesel 50 ppm was R19.55 per litre.
In June 2022, the price of diesel 50 ppm was R24.14 per litre.
I will mark you brainiest!
What is the area of the polygon shown?
A) 22 cm2
B) 38 cm2
C) 44 cm2
D) 50 cm2
Therefore, the area of the polygon is 22 cm². The correct answer is A) 22 cm².
Provide an area example.Another option is to plot the shape on a grid and count the squares: The rectangle's surface area is 15. Example: If each square is one meter in size, the area is 15 m2 (15 square meters).
To find the area of the polygon, we need to use the formula:
Area = (1/2) x Base x Height
We are given that the base of the polygon is 11 cm and the height is 4 cm. Therefore, we can substitute these values in the formula to get:
Area = (1/2) x 11 cm x 4 cm
Area = 22 cm²
Therefore, the area of the polygon is 22 cm². The correct answer is A) 22 cm².
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Brittany's W-2 reported total Medicare withholding based on wages of as $117,676. She contributed
$72.07 biweekly to her FSA and 10% of each paycheck to her retirement plan. She received a 1099 from
her bank for interest and dividends of $2,404 and a 1099 form in the amount of $4,600 from an employer
for whom she did some consulting work. What is Brittany's adjusted gross income?
Answer:
Step-by-step explanation
I:
Juli is going to launch a model rocket in her back yard. When she launches the rocket, the function h(t)=−16t2+76t model the height, h, in feet of the rocket above the ground as a function of time, t, measured in seconds. When will the rocket hit the ground? When will the rocket be 70 feet above the ground?
the rocket will be 70 feet above the ground after 1.25 seconds and again after 3.5 seconds.
Define factorizationFactorization, also known as factoring, is the process of expressing a mathematical object (such as a number, polynomial, or matrix) as a product of simpler objects.
To determine when the rocket hits the ground, we need to find the value of t when the height, h, is equal to 0. We can set h(t) = 0 and solve for t:
-16t²+ 76t = 0
-16t(t - 4.75) = 0
So either -16t = 0 or t - 4.75 = 0. The first equation has no solutions, so we solve the second equation:
t - 4.75 = 0
t = 4.75
Therefore, the rocket will hit the ground after 4.75 seconds.
To determine when the rocket is 70 feet above the ground, we need to find the value of t when h(t) = 70. We can set h(t) = 70 and solve for t:
-16t² + 76t = 70
-16t²+ 76t - 70 = 0
We can simplify this equation by dividing each term by -2:
8t² - 38t + 35 = 0
We can factor this equation:
(4t - 5)(2t - 7) = 0
So either 4t - 5 = 0 or 2t - 7 = 0. Solving these equations gives:
4t - 5 = 0
t = 1.25
2t - 7 = 0
t = 3.5
Therefore, the rocket will be 70 feet above the ground after 1.25 seconds and again after 3.5 seconds.
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Help me! I need help with my homework
Answer:
1065.09 square meters
Step-by-step explanation:
The inner circle has a diameter of 21.4 cm
Its radius is half that = 21.4/2 = 10.7 m
Area of the inner circle = π (10.7)² = 114.49π m²
The outer circle has a radius
= radius of inner circle + 10.6
= 10.7 + 10.6
= 21.3 m
Therefore the area of the outer circle
= π(21.3)² = 453.6π m²
Area of shaded region
= Area of outer circle - Area of inner circle
= 453.6π - 114.49π
= 339.2 π
Taking π = 3.14
Area of shaded region
= 339.2 x 3.14
= 1,065.088 m²
= 1065.09 m² (rounded to nearest hundredth)
Graph the equation shown below by transforming the given graph of the parent
function.
The answer of the question based on graph function is given below, graph is a reflection of the parent function y = x² about the x-axis, horizontally compressed by a factor of 2, and vertically shifted downward by 4 units.
What is Graph?A graph is visual representation of data or functions. It is way to display information in visual format, usually with use of coordinates and shapes.
The given equation is:
y = (-1/4 x)² - 4
To transform the graph of the parent function y = x², we can apply the following transformations:
Horizontal compression by a factor of 2: This will compress the graph horizontally, making it wider and shorter. The coefficient -1/4 in front of the x² indicates this compression.
Reflection across the x-axis: This will flip the graph of y = x² upside down. The negative sign after the x² in the equation indicates this reflection.
Vertical shift downward by 4 units: This will shift the entire graph downward by 4 units. The constant -4 at the end of the equation indicates this shift.
Using these transformations, we can graph the equation as follows:
Start with the graph of the parent function y = x²:
Apply the horizontal compression by a factor of 2 by multiplying the equation by -1/4:
y = (-1/4 x)²
Apply the reflection across the x-axis by negating the equation:
y = -(1/4 x)²
Apply the vertical shift downward by 4 units by subtracting 4 from the equation:
y = -(1/4 x)² - 4
The resulting graph is a reflection of the parent function y = x² about the x-axis, horizontally compressed by a factor of 2, and vertically shifted downward by 4 units.
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