The width of the rectangle is 13 cm and the dimension is 26 cm x 13 cm
Given data ,
Let the length be L and width be W
Now , the width is 1/2 of the length, so we can write:
W = (1/2)L
The area of a rectangle is given by the formula:
Area = Length x Width
Given that the area is 338 square centimeters, we can write:
338 = L × W
Substituting W with (1/2)L, we have:
338 = L × (1/2)L
To solve this equation, we can multiply both sides by 2 to eliminate the fraction:
676 = L²
Taking the square root of both sides, we find:
L = √676
L = 26
So the length of the rectangle is 26 centimeters.
Substituting this value back into the equation for the width, we have:
W = (1/2)L
W = (1/2)(26)
W = 13
Hence , the dimensions of the rectangle are length = 26 centimeters and width = 13 centimeters
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Need the answer quickly!
What’s the total liquid measure of the punch
The correct option is B, the total volume is 6 gallons, 2 quarts, and 1 pint.
What’s the total liquid measure of the punch?Here we just need to add all the volumes that are in the question, we have.
1 gallons, 2 quarts, 3 pints of orange juice.1 gallons, 3 quarts, 7 pints of pineapple juice.1 gallons, 3 quarts, 3 pints of ginger ale.So there are:
3 gallons.
8 quarts.
13 pints.
Now let's do the changes of units, we know that:
8 pints = 1 gallon
4 quarts = 1 gallon
1 quart = 2 pints
then:
13 pints = 1 gallon and 5 pints
8 quarts = 2 gallons
5 pints = 2 quarts and 1 pint
Then the total volume is:
6 gallons, 2 quarts, and 1 pint.
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Is 4.1 less than or greater than 4.10 
Answer:
4.1 = 4.10
Step-by-step explanation:
Extra 0 at the end of 4.10 doesn't change the quantity of the number, so 4.1 is equal to 4.10
) Assume that a simple random sample has been selected from a normally distributed population and test the given claim at α = 0.05. State the claim mathematically. Identify the null and alternative hypotheses, test statistic, critical region(s), and the decision regarding the null hypothesis. State the conclusion that addresses the original claim. A local group claims that police issue at least 60 speeding tickets a day in their area. To prove their point, they randomly select two weeks. Their research yields the number of tickets issued for each day. The data are listed below. 70 48 41 68 69 55 70 57 60 83 32 60 72 58
We cannot conclude that there are more than 70,000 defined words in the dictionary.
To test the claim that there are more than 70,000 defined words in the dictionary, we can set up the null and alternative hypotheses as follows:
Null Hypothesis (H0): The mean number of defined words on a page is 48.0 or less.
Alternative Hypothesis (H1): The mean number of defined words on a page is greater than 48.0.
So, sample mean
= (59 + 37 + 56 + 67 + 43 + 49 + 46 + 37 + 41 + 85) / 10
= 510 / 10
= 51.0
and, the sample standard deviation (s)
= √[((59 - 51)² + (37 - 51)² + ... + (85 - 51)²) / (10 - 1)]
≈ 16.23
Next, we calculate the test statistic using the formula:
test statistic = (x - μ) / (s / √n)
In this case, μ = 48.0, s ≈ 16.23, and n = 10.
test statistic = (51.0 - 48.0) / (16.23 / √10) ≈ 1.34
With a significance level of 0.05 and 9 degrees of freedom (n - 1 = 10 - 1 = 9), the critical value is 1.833.
Since the test statistic (1.34) is not greater than the critical value (1.833), we do not have enough evidence to reject the null hypothesis.
Therefore, based on the given data, we cannot conclude that there are more than 70,000 defined words in the dictionary.
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In your drawer you have 10 white socks and 14 black socks. You choose one sock from the drawer and then a second sock (without replacement.)
Event A: You choose a black sock.
Event B: You choose a black sock.
Tell whether the events are independent or dependent. Explain your reasoning.
The events A and B are dependent events.
The probability of event B will be different from the initial probability of selecting a black sock (event A).
Two events are considered independent if the outcome of one event does not affect the probability of the other event.
The outcome of event A (choosing a black sock) directly affects the probability of event B (choosing a black sock again).
To explain further, let's consider the initial scenario:
You have 10 white socks and 14 black socks in your drawer.
The total number of socks is 24.
The first sock, there are two possibilities:
Either it is a black sock or a white sock.
If event A occurs and you select a black sock, the total number of black socks in the drawer decreases to 13, while the total number of socks decreases to 23.
If event B to occur (selecting a black sock again), the probability is now influenced by the fact that you have one less black sock and one less sock in the drawer.
The probability of event B will be different from the initial probability of selecting a black sock (event A).
The outcome of event A affects the probability of event B, the two events are dependent.
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NO LINKS!! URGENT HELP PLEASE!!!
O is the center of the regular decagon below. Find its perimeter. Round to the nearest tenth if necessary.
Answer:
65 units
Step-by-step explanation:
solution Given:
apothem(a)=10
no of side(n)= 10
First, we need to find the length of one side (s).
We can find the length of one side using the following formula:
[tex]\boxed{\bold{s = 2 * a * tan(\frac{\pi}{n})}}[/tex]
substituting value:
[tex]\bold{s = 2 * 10 * tan(\frac{\pi}{10})=6.498}[/tex] here π is 180°
Now
Perimeter: n*s
substituting value:
Perimeter = 10*6.498= 64.98 in nearest tenth 65 units
Therefore, the Perimeter of a regular decagon is 65 units.
Answer:
65.0 units
Step-by-step explanation:
A regular decagon is a 10-sided polygon with sides of equal length.
To find its perimeter, we first need to find its side length (s).
As we have been given its apothem, we can use the apothem formula to find an expression for side length (s).
[tex]\boxed{\begin{minipage}{5.5cm}\underline{Apothem of a regular polygon}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]
Given the apothem is 10 units and the number of sides is 10, substitute a = 10 and n = 10 into the formula and solve for s:
[tex]10=\dfrac{s}{2 \tan \left(\dfrac{180^{\circ}}{10}\right)}[/tex]
[tex]10=\dfrac{s}{2 \tan \left(18^{\circ}\right)}[/tex]
[tex]s=20 \tan \left(18^{\circ}\right)[/tex]
The perimeter (P) of a regular polygon is the product of its side length and the number of sides. Therefore, the perimeter of the given regular decagon is:
[tex]P=s \cdot n[/tex]
[tex]P=20 \tan \left(18^{\circ}\right) \cdot 10[/tex]
[tex]P=200 \tan \left(18^{\circ}\right)[/tex]
[tex]P=64.9839392...[/tex]
[tex]P=65.0\; \sf units\;(nearest\;tenth)[/tex]
Therefore, the perimeter of a regular decagon with an apothem of 10 units is 65.0 units, to the nearest tenth.
3(x + 4) pleeeeeeeeeeeeaaaase
Answer:
3x + 12
Step-by-step explanation:
Using the distributive property, multiply 3 by x and get 3x. Then multiply 3 by 4 and get 12. Put it together and get 3x + 12
Given l ∥ m ∥ n, find the value of x.
Answer:
-x = 17
Step-by-step explanation:
Given m||n we can write the following equation:
(5x - 23)° + (7x - 1)° = 180° because the these angles are supplementary angles.
Add like terms.(12x - 24)° = 180°
Add 24 to both sides.(12x)° = 204°
Divide both sides with 12.x = 17
100 Points! Algebra question. Graph the function. Photo attached. Thank you!
The graph of the piecewise function g(x) is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
The definitions to the function in this problem are given as follows:
Horizontal line at y = -1 to the left of x = 0.Linear function from x = 0 to x = 3, with a line connecting the points (0,0) and (3,6).Horizontal line at y = 6 to the right of x = 3.Hence the graph of the piecewise function g(x) is given by the image presented at the end of the answer.
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if a population function x has mean M(x)=2 and M(x^2)=8 ,find its standard deviation
The standard deviation of the population function x is 2.
We have,
To find the standard deviation of the population function x, we need the mean M(x) and the mean of the squared values M(x²).
So,
Standard Deviation = √[M(x²) - (M(x))²]
Given that M(x) = 2 and M(x²) = 8, we can substitute these values into the formula:
Standard Deviation = √[8 - (2)²]
Standard Deviation = √[8 - 4]
Standard Deviation = √4
Standard Deviation = 2
Therefore,
The standard deviation of the population function x is 2.
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Find the product of (3x + 4)(x − 1). 3x2 + 7x − 4 3x2 + 7x − 3 3x2 − x − 4 3x2 + x − 4
Hello !
Answer:
[tex]\boxed{\sf (3x + 4)(x - 1)=3x^2+x-4}[/tex]
Step-by-step explanation:
We will have to use the distributive property to expand this expression.
Let's remember :
[tex]\sf (a+b)(c+d)=ab+ad+bc+bd)[/tex]
Let's apply this property to our expression :
[tex]\sf (3x + 4)(x -1)\\=3x\times x+3x\times(-1)+4\times x+4\times(-1)[/tex]
Now let's calculate and combine like terms :
[tex]\sf 3x^2-3x+4x-4\\\boxed{\sf =3x^2+x-4}[/tex]
Have a nice day ;)
The equation of the hyperbola that has a center at (3, 10), a focus at (8, 10), and a vertex at (6, 10), is
Int he above expression, A = 3 (distance from the vertex to the center)
B = 4
C = 3 (distance from focus to center)
D = 10
How is this so?Since the center of the hyperbola is (3,10), we have C=3 and D=10.
The distance from the center to the vertex is A, so we have A= 6-3
A = 3.
The distance from the center to the focus is given by c, so we have c=8-3=5.
We can use the relationship a² + b² = c² to solve for B:
a = 6 - 3 = 3 (distance from vertex to center)
c = 5 (distance from focus to center)
b = ?
b² = c² - a²
b² = 5² - 3²
b² = 16
b = 4
Therefore, the equation of the hyperbola is
((x-3)²/3²) - ((y-10)²/4²) = 1
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Full Quesitn:
The equation of the hyperbola that has a center at (3, 10), a focus at (8, 10), and a vertex at (6, 10), is
((x-C)²/A²) - ((y-D)²)/B²) = 1
Where A = ?
B = ?
C = ?
D = ?
PLEASE HELP ASAP, IM CONFUSED
The transformation of Δ ABC to ΔADE is a dilation by a scale factor of 1/2 and then 180 degrees rotation about the origin.
We have,
In ΔABC,
The coordinates of each point are:
A = (0, 0)
B = (0, -6)
C = (8, -6)
And,
ΔADE,
A = (0, 0)
D = (0, 3)
E = (4, 3)
Now,
We can see that,
If we use a scale factor 1/2 on each the coordinates of A, B, and C and rotated to 180 degrees about the origin.
We get,
A = (0, 0) = (0, 0)
B = (0, - 6) = (0, -3) = (0, 3)
C = (8, -6) = (4, -3) = (4, 3)
Thus,
The transformation of Δ ABC to ΔADE is a dilation by a scale factor of 1/2 and then 180 degrees rotation about the origin.
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if f(x)=-2x, g(x)=3x-7, and h(x)=2x^2-10, fill in the following chart
The values of Composite function are:
f(g(-1)) = 20
h[g(4)] = 40
g[f(5)] = -37
f[h(-4)] = -44
g[g(7)] = 35
h[f(1/2)] = -8
We have, f(x) = -2x, g(x) = 3x-7 and h(x)= 2x² -10
f(g(-1)):
First, substitute -1 into g(x): g(-1) = 3(-1) - 7 = -3 - 7 = -10.
Next, substitute the result into f(x): f(-10) = -2(-10) = 20.
Therefore, f(g(-1)) = 20.
h[g(4)]:
First, substitute 4 into g(x): g(4) = 3(4) - 7 = 12 - 7 = 5.
Next, substitute the result into h(x): h(5) = 2(5^2) - 10 = 2(25) - 10 = 50 - 10 = 40.
Therefore, h[g(4)] = 40.
g[f(5)]:
First, substitute 5 into f(x): f(5) = -2(5) = -10.
Next, substitute the result into g(x): g(-10) = 3(-10) - 7 = -30 - 7 = -37.
Therefore, g[f(5)] = -37.
f[h(-4)]:
First, substitute -4 into h(x): h(-4) = 2(-4²) - 10 = 2(16) - 10 = 32 - 10 = 22.
Next, substitute the result into f(x): f(22) = -2(22) = -44.
Therefore, f[h(-4)] = -44.
g[g(7)]:
First, substitute 7 into g(x): g(7) = 3(7) - 7 = 21 - 7 = 14.
Next, substitute the result into g(x) again: g(14) = 3(14) - 7 = 42 - 7 = 35.
Therefore, g[g(7)] = 35.
h[f(1/2)]:
First, substitute 1/2 into f(x): f(1/2) = -2(1/2) = -1.
Next, substitute the result into h(x): h(-1) = 2(-1²) - 10 = 2(1) - 10 = 2 - 10 = -8.
Therefore, h[f(1/2)] = -8.
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(-4,4) is the center and (-2,4) is a point on the circle. What is the equation?
The equation of the circle with center (-4, 4) and passing through (-2, 4) is [tex](x + 4)^2 + (y - 4)^2 = 4.[/tex]
We have,
To determine the equation of a circle, we need the center coordinates and the radius. The center coordinates are given as (-4, 4), and we have a point on the circle as (-2, 4).
The distance between the center (-4, 4) and the point on the circle (-2, 4) represents the radius of the circle.
Using the distance formula.
[tex]radius = √[(x_2 - x_1)^2 + (y_2 - y_1)^2]\\= \sqrt{(-2 - (-4))^2 + (4 - 4)^2}\\= \sqrt{2^2 + 0^2}\\= \sqrt{4}\\= 2[/tex]
Now that we have the center coordinates (-4, 4) and the radius 2, we can write the equation of the circle in standard form:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Substituting the values:
[tex](x - (-4))^2 + (y - 4)^2 = 2^2\\(x + 4)^2 + (y - 4)^2 = 4[/tex]
Therefore,
The equation of the circle with center (-4, 4) and passing through (-2, 4) is [tex](x + 4)^2 + (y - 4)^2 = 4.[/tex]
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Part C. Jack also likes to collect buttons. He has 5 bags of button The fewest number of buttons in a bag is 21. The greatest number of buttons in a bag is 29 The mean number of buttons in the bags is 27. There are two modes for the number of buttons in each bag. How many buttons are in each of Jack's five bags?
To find the number of buttons in each of Jack's five bags, we can use the information given to us and solve for the unknowns. Let's start by finding the total number of buttons:
Total number of buttons = Mean number of buttons × Number of bags
Total number of buttons = 27 × 5
Total number of buttons = 135
Since we know the fewest and greatest number of buttons in a bag, we can find the range:
Range = Greatest number of buttons - Fewest number of buttons
Range = 29 - 21
Range = 8
Now, we can set up two equations to find the two modes:
Mode 1 + Mode 2 + 3 × 27 = 135 (sum of all bags)
Mode 2 - Mode 1 = 8 (difference between the two modes)
Solving these equations simultaneously, we get:
Mode 1 = 23
Mode 2 = 31
Therefore, the number of buttons in each of Jack's five bags is:
Bag 1: 21 buttons
Bag 2: 23 buttons
Bag 3: 25 buttons
Bag 4: 27 buttons
Bag 5: 29 buttons
Write the equation of a parabola whose directrix is x = -2 and has a focus at (8,-8).
The equation of the parabola is (x - 3)² = 20(y - k)
Given data ,
To write the equation of a parabola given its directrix and focus, we can use the standard form for a parabola with a vertical axis of symmetry:
(x - h)² = 4p(y - k)
where (h, k) represents the vertex of the parabola, and the distance between the vertex and the focus is equal to the distance between the vertex and the directrix.
In this case, the directrix is x = -2 and the focus is located at (8, -8). Since the directrix is a vertical line, the parabola has a horizontal axis of symmetry.
And , the vertex lies on the axis of symmetry, which is the line equidistant between the directrix and the focus. In this case, the axis of symmetry is the vertical line x = (8 + (-2)) / 2 = 3.
So, the vertex of the parabola is (3, k), where k is yet to be determined
Next, we need to find the value of p, which represents the distance between the vertex and the focus. Since the focus is at (8, -8), and the vertex is at (3, k), the distance between them is given by
p = 8 - 3 = 5
Now, substituting the values into the standard form equation, we have:
(x - 3)² = 4(5)(y - k)
Simplifying further:
(x - 3)² = 20(y - k)
Hence , the equation of the parabola is (x - 3)^2 = 20(y - k), where k is the y-coordinate of the vertex
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You have one red apple and three green apples in a
bowl. You randomly select one apple to eat now and
another apple for your lunch. Use a sample space to
determine whether randomly selecting a green apple
first and randomly selecting a green apple second are
independent events.
Answer: vvvvv
Step-by-step explanation:
Let R1 and G1 represent the red and green apples available for the first selection, respectively. Similarly, let R2, G2a, and G2b represent the red and two green apples available for the second selection, respectively. Then, the sample space for the two selections is:
{(R1, R2), (R1, G2a), (R1, G2b), (G1, R2), (G1, G2a), (G1, G2b)}
Out of these six outcomes, only two involve selecting a green apple first: (G1, R2) and (G1, G2a). And out of these two outcomes, only one involves selecting a green apple second: (G1, G2a).
Therefore, since the probability of selecting a green apple second changes based on whether a green apple was selected first, the events of selecting a green apple first and selecting a green apple second are dependent.
10-
Next O
Post Test: Linear Equations
10
Select all the correct answers
Which lines in the graph have a slope greater than 1 but less than 27
line 1
line 2
line 3
line 4
line 5
3 4
5
The slope of the straight line in the graph that expresses proportional relationship indicates that the lines in the graph that have a slope greater than 1 but less than 2 are;
Line 3Line 4What is the slope of a graph of a straight line?The slope of the graph of a straight line is the ratio of the rise to the run on the line.
The slope of a graph with a slope of 1 has an increase in the y-value of 1 for each increase in the x-value of 1
Slope = 1 = Δy/Δx
When the slope is greater than 1, we get;
Δy/Δx > 1, therefore Δy is larger than 1 when Δx is 1.
Similarly, the slope of a graph with a slope of 2 has an increase in the y-value of 2 for each increase in the x-value of 1
Slope = 2 = Δy/Δx
When the slope is less than 1, we get;
Δy/Δx < 2, therefore Δy is less than 2 when Δx is
The lines in the graph that have a slope greater than 1 but less than 2 are therefore the graphs with the coordinates;
Line 3; (0, 0), (4, 6); Slope = 6/4 = 3/2, therefore; 1 < slope = 3/2 < 2
Line 4; (0, 0), (5, 6); Slope = 6/5, therefore; 1 < Slope < 2
The line 5 has a slope of 1, and the line 1, has a slope of 3, line 2 has a slope of 2
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4. Determine the lateral and total surface area of the rectangular pyramid. 6 cm 8 cm 6 cm Lateral Surface Area Total Surface Area 6.5 cm
The lateral and the total surface area of the rectangular pyramid are 182 square cm and 278 square cm
Determining the lateral and total surface area of the rectangular pyramid.From the question, we have the following parameters that can be used in our computation:
Length = 6 cm
Width = 8 cm
Height = 6.5 cm
The lateral surface area of the rectangular pyramid is calculated as
LA = 2 *(L + W)H
So, we have
LA = 2 *(6 + 8) * 6.5
Evaluate
LA = 182
The total surface area of the rectangular pyramid is calculated as
TA = 2 * (LW + LH + HW)
So, we have
TA = 2 * (8 * 6 + 8 * 6.5 + 6.5 * 6)
Evalaute
TA = 278
Hence, total surface area of the rectangular pyramid is 278 square cm
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A sphere and its dimension are shown in the diagram 15 inches
The measurement that is closest to the volume of the sphere is given as follows:
1,767.1 in³.
What is the volume of an sphere?The volume of an sphere of radius r is given by the multiplication of 4π by the radius cubed and divided by 3, hence the equation is presented as follows:
[tex]V = \frac{4\pi r^3}{3}[/tex]
From the image given at the end of the answer, we have that the diameter is of 15 units, hence the radius of the sphere, which is half the diameter, is given as follows:
r = 0.5 x 15
r = 7.5 units.
Then the volume of the sphere is given as follows:
V = 4/3 x π x 7.5³
V = 1,767.1 in³.
Missing InformationThe sphere is given by the image presented at the end of the answer.
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Drag each number to a box to complete the table. Each number may be used once or not at all
Each number should be dragged to a box to complete the table as follows;
Kilometers Meters
1 1,000
2 2,000
3 3,000
5 5,000
8 8,000
What is a conversion factor?In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.
Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;
Conversion:
1 kilometer = 1,000 meters
2 kilometer = 2,000 meters
3 kilometer = 3,000 meters
4 kilometer = 4,000 meters
5 kilometer = 5,000 meters
6 kilometer = 6,000 meters
7 kilometer = 7,000 meters
8 kilometer = 8,000 meters
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
need help can someone help me need it to pass math
The measure of segment HI is given as follows:
HI = 7.
How to obtain the measure of segment HI?The measure of segment HI for this problem are obtained considering the triangle midsegment theorem, which states that the length of the midsegment of the triangle is equals to half the length of the base, hence the base has the length that is twice the midsegment.
The lengths are given as follows:
Midsegment HI = -9x + 70.Base EF = -21 + 5x.Hence the value of x is obtained as follows:
EF = 2HI
-21 + 5x = 2(-9x + 70)
-21 + 5x = -18x + 140
23x = 161
x = 7.
Hence the length HI is given as follows:
HI = -9(7) + 70
HI = 7.
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I need help!!!!!!!!!
Answer:
its b4 + 7b3 + 4b2 + b5 + 7b4+ 4b3= b5+8b4+11b3+4b2
Answer:
When multiplying, add the exponents, (example) remember if there is "7b" the exponent is one.
Multiply b^2 * b^3 = b^5 (add the exponent 2 + 3 = 5)
Multiply 7b * b^3 = 7b^4 (the exponent of 7b is one, add 1 + 3 for the exponent to become 4)
Multiply 4 * b^3 = 4b^3 (4 doesn't have a variable, the exponent will be 3)
b^2 * b*2 = b^4 (add exponents)
7b * b^2 = 7b^3 (add the exponents 1 + 2)
4 * b^2 = 4b^2
b^2 + 7b + 4
b^3 b^5 + 7b^4 + 4b^3
+
b^2 b^4 + 7b^3 + 4b^2
b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2
[tex]b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2[/tex]
b^5 + 8b^4 + 11b^3 + 4b^2find the indicated side of the right triangle. 45 degrees, 45 degrees, 6, y, x, x = ?
3√2 and 3 are the values of x and y respectively from the figure.
Trigonometry identitiesThe given diagram is a right triangle with an acute angle of 45 degrees
We need to determine the values of variables x and y.
Applying the trigonometry identity, we will have:
sin 45 = opposite/hypotenuse
sin45 = 3/x
x = 3/sin45
x = 3/(1/√2)
x = 3√2
Similarly:
tan 45 = opposite/adjacent
tan 45 = 3/y
1 = 3/y
y = 3
Hence the values of x and y from the figure is 3√2 and 3 respectively
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The base of the mountain is 6,500 feet above sea level and lineAB measures 230 feet across. Given that the measurements for angleQAP is 20° and angleQBP is 35°, how far above sea level is peak P? Express your answer to the nearest foot.
The required measure of point P above the sea level is 6717.22 feet.
Given that,
A is known to be 6,500 feet above sea level; AB = 230 feet.
And, The angle at A looking up at P is 20°.
The angle at B looking up at P is 35°.
Since, These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here,
Let the horizontal distance between A and Q be x and the vertical distance between P and Q be h.
Now,
tan20 = h / x
034x = h
Now,
tan35 = [230 + h]/x
0.7x = 230 + 0.34x
x = 636.89
Now,
h = 0.34 x 636.89
h = 217.2
Now,
The measure of peak P above sea level = 217.2 + 6500 = 6717.22
Thus, the required measure of point P above the sea level is 6717.22 feet.
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sin( 3pi/4 ) =
O A. 1/2
OB. -√2/2
O C. √3/2
O D. √2/2
Answer:
D
Step-by-step explanation:
sin ( 3pi / 4 )
= sin ( pi - pi / 4 )
= sin ( pi / 4 )
= 1/root(2)
= root(2) / 2
Use the associative law of multiplication to write an equivalent expression
(12x)y
Using the associative law of multiplication we get this two solution of the given expression: (12x)y = (12 * x) * y , (12x)y = 12 * (x * y)
The associative law of multiplication states that when multiplying three or more numbers, the product is the same regardless of the order in which the numbers are grouped. In other words, it doesn't matter which numbers we multiply first, the result will be the same.
Using the associative law of multiplication, we can group the factors in any way we like. Therefore, we can write an equivalent expression to (12x)y by changing the grouping of factors.
One way to group the factors is to group the two numerical coefficients (12 and y) together.
Another way to group the factors is to group the variable x and the coefficient y together.
Both of these expressions are equivalent to (12x)y and they all follow the associative law of multiplication.
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If a wheelchair access ramp has to have an angle of elevation no more than 4.8 degrees and it has to rise 18 inches above the ground, how long must the ramp be?
The wheelchair access ramp must be 216.09 inches long.
To find the length of the wheelchair access ramp, we can use trigonometry.
The tangent function relates the angle of elevation to the ratio of the opposite side (height) to the adjacent side (length of the ramp).
Let's denote the length of the ramp as "x".
The height of the ramp is given as 18 inches.
Using the tangent function:
tan(angle of elevation) = height/length of the ramp
tan(4.8 degrees) = 18/x
To solve for x, we can rearrange the equation:
x = 18 / tan(4.8 degrees)
Using a calculator to evaluate the tangent of 4.8 degrees:
x = 18 / 0.08331
x= 216.09
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What are three consecutive multiples of 3 if 2/3
of the sum of the first
two numbers is 1 greater than the third number?
The three consecutive multiples of 3 are 15, 18 and 21
To solve this problem
First, let's determine three successive multiples of 3:
The subsequent two would be "x+3" and "x+6" if we call the initial number "x".
Since we are aware that the third number (x+6) is one more than the first two numbers (x + x+3), we can write the following equation:
2/3(x + x+3) = (x+6) + 1
Simplifying this equation, we get:
2/3(2x+3) = x+7
Multiplying both sides by 3, we get:
2(2x+3) = 3(x+7)
Expanding and simplifying, we get:
4x + 6 = 3x + 21
Subtracting 3x and 6 from both sides, we get:
x = 15
Therefore, the three consecutive multiples of 3 are 15, 18 and 21
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