The volume of this triangular prism is 1,170 cubic feet. What is the value of m?

1. The difference of two supplementary angles is 70° which is the larger angle?

A/ 135°

B/145

C/55

The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:

πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:

A = (πr^2)/2 + rh

To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:

r = (9 - 2h)/(π)

Now we can rewrite the area function in terms of h only:

A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)

Simplifying this equation, we get:

A = (1/2)(9h - h^2/π)

To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:

dA/dh = 9/2 - h/π = 0

Solving this equation, we find:h = 9π/2

Substituting this value of h back into the area function, we get:

A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4

Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.

Learn more about area here:

https://brainly.com/question/2607596

#SPJ8

Answer: C

Step-by-step explanation:

The function exists at all points on the interval with no discontinuities (such as jump discontinuities).

Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C).

The given functions are f(x) = 3x² and g(x) = -2².

To understand the difference between their graphs, let's examine the characteristics of each function individually:

Function f(x) = 3x²:

The coefficient of x² is positive (3), indicating an upward-opening parabola.

The graph of f(x) will be symmetric with respect to the y-axis, as any change in x will result in the same y-value due to the squaring of x.

The vertex of the parabola will be at the origin (0, 0) since there are no additional terms affecting the position of the graph.

Function g(x) = -2²:

The coefficient of x² is negative (-2), indicating a downward-opening parabola.

The negative sign will reflect the graph of f(x) across the x-axis, resulting in a vertical flip.

The vertex of the parabola will also be at the origin (0, 0) due to the absence of additional terms.

Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C). This means that g(x) is obtained by taking the graph of f(x) and flipping it vertically. The reflection occurs over the x-axis, causing the parabola to open downward instead of upward.

Therefore, the correct answer is option C: g(x) is a reflection of f(x) over the x-axis.

For more such questions on functions visit:

https://brainly.com/question/25638609

#SPJ8

Answer:

x ≈ 77.79 ft

Step-by-step explanation:

using the sine ratio in the right triangle

sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{50}{x}[/tex] ( multiply both sides by x )

x × sin40° = 50 ( divide both sides by sin40° )

x = [tex]\frac{50}{sin40}[/tex] ≈ 77.79 ft ( to the nearest hundredth )

Answer:

Step Reason

∠NYR and ∠RYA form a linear pair

∠AXY and ∠AXZ form a linear pair Given

∠RYA≅∠AXY Given

∠NYR and ∠RYA are supplementary Definition of Linear Pair

If two angles form a linear pair, then they are supplementary angles Definition of Linear Pair

∠NYR and ∠AXY are supplementary Transitive Property of Equality

m∠NYR+m∠RYA=180

m∠AXY+m∠AXZ=180 Definition of Supplementary Angles

m∠NYR+m∠RYA=m∠AXY+m∠AXZ Substitution Property of Equality

m∠NYR+m∠RYA=m∠NYR+m∠AXZ Substitution Property of Equality

m∠RYA=m∠AXZ Subtraction Property of Equality

∠NYR and ∠AXY are supplementary Definition of Supplementary Angles

m∠NYR+m∠AXY=180

m∠NYR+m∠RYA=m∠NYR+m∠AXY Substitution Property of Equality

m∠RYA=m∠AXY Subtraction Property of Equality

∠NYR≅∠AXY Definition of Congruent Angles.

Answer:

The number is 16

Step-by-step explanation:

This follows a multiplication rule,

4 times 1 = 4

4 times 2 = 8

4 times 3 = 12

4 times 4 = 16

So, the number is 16

0.612 can be rewritten as the simplified fraction 153/250.

Question: Rewrite as a simplified fraction. 0.612
To rewrite 0.612 as a simplified fraction, we need to convert the decimal into a fraction.
Step 1: Count the number of decimal places.
In this case, 0.612 has three decimal places.
Step 2: Write the decimal as a fraction with the decimal part as the numerator and the denominator as the place value of the rightmost digit.
Since there are three decimal places, the denominator will be 1000 (10 raised to the power of 3).
0.612 = 612/1000
Step 3: Simplify the fraction.
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. In this case, both the numerator and denominator are divisible by 4.
612/1000 = (612 ÷ 4) / (1000 ÷ 4) = 153/250

Fore more such questions on simplified fraction

https://brainly.com/question/78672

#SPJ8

The point A divides the line segment AB into the ratio 3:1, while the point B divides it into the ratio 1:3.

1. To find the ratio in which each point divides AB, we need to calculate the distances from each endpoint to the dividing point.

2. Let's calculate the distance from point A to the dividing point. The x-coordinate of point A is -7, and the y-coordinate is -14. Similarly, the x-coordinate of point B is 5, and the y-coordinate is 10.

3. We'll use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:

  distance = sqrt((x2 - [tex]x1)^2 + (y2 - y1)^2)[/tex]

4. Applying the distance formula, we find the distance from point A to the dividing point:

[tex]distance_A[/tex] = sqrt((5 -[tex](-7))^2 + (10 - (-14))^2)[/tex]

             = sqrt((5 + [tex]7)^2 + (10 + 14)^2)[/tex]

             = sqrt([tex]12^2[/tex] + [tex]24^2[/tex])

             = sqrt(144 + 576)

             = sqrt(720)

             = 12√5

5. Similarly, let's calculate the distance from point B to the dividing point:

[tex]distance_B[/tex] = sqrt((-7 - [tex]5)^2 + (-14 - 10)^2)[/tex]

             = sqrt((-[tex]12)^2 + (-24)^2)[/tex]

             = sqrt(144 + 576)

             = sqrt(720)

             = 12√5

6. The dividing ratio can be determined by comparing the distances from each endpoint to the dividing point. Since distance_A:distance_B = 3:1, we conclude that point A divides the line segment AB into the ratio 3:1, and point B divides it into the ratio 1:3.

Thus, the endpoints A and B divide the line segment AB into the ratios 3:1 and 1:3, respectively.

For more such questions on ratio, click on:

https://brainly.com/question/12024093

#SPJ8

Answer:

the ratio for point C is 1 : 2.

the ratio for point D is 3 : 1.

the ratio for point E is 2 : 1.

Step-by-step explanation:

I just got it right on the test

The transformation that moves the shape is (a) translation

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have:

This means that the only transformation is translation

So, the transformation is (a) translation

Read more about transformation at

brainly.com/question/4289712

#SPJ1

Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

Answer:

31

Step-by-step explanation:

you add the hats to get the total number of hats then divide the answer by

No, it is much too high. Then the correct option is B.

An equation is a statement of equality between two expressions consisting of variables and/or numbers.

Given the question above, we need to find if the hats is to high or low.

Calculating the total numbers of hats made, we have

[tex]21 + 29 + 12 = 62 \ \text{hats}[/tex]

If Edna wants to split 62 hats evenly between two hospital, then each hospital will get

[tex]\dfrac{62}{2} = 31 \ \text{hats}[/tex]

Therefore, if Edna works out that each hospital gets 62 hats, No it is too high, as that is the total of all the hat that is available

Hence, the correct option is B.

Learn more on equations at:

https://brainly.com/question/29657983

Edna just joined a group that makes hats for babies in the hospital. Two weeks ago they made 21 hats. Last week they made 29 hats. This week they made 12 hats. All these hats will be split evenly between 2 nearby hospitals. Edna works out that's 62 hats for each hospital. Does that sound about right?

A. Yes

B. No, it is much too high

C. No, it is much too low

Answer:  Choice C.   [tex]\displaystyle \boldsymbol{-\frac{\sqrt{5}}{3}}[/tex]

===================================================

Work Shown:

Part 1

[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\cos^2(\theta) = 1-\sin^2(\theta)\\\\\cos(\theta) = -\sqrt{1-\sin^2(\theta)} \ \ \text{ ..... cosine is negative in Q2}\\\\\cos(\theta) = -\sqrt{1-\left(\frac{2}{3}\right)^2}\\\\\\cos(\theta) = -\sqrt{1-\frac{4}{9}}\\\\[/tex]

Part 2

[tex]\cos(\theta) = -\sqrt{\frac{9}{9}-\frac{4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{9-4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{5}{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{\sqrt{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{3}\\\\[/tex]

For accelerated motion, changes in distance compare with equal changes in velocity as follows:

B. Distance increases faster than time.

A reason why a person will not compute a slope for the accelerated motion graph is that it graphed as a straight line.

Accelerated motion is a form of motion in which the motion is not equal and the object moving does not complete the same distances in the same intervals of time.

The graph formed in the case of an accelerated motion is not a straight line. So, a reason why a person would not compute a slope for the accelerated motion is that it graphed as a straight line.

Learn more about accelerated motion here:

https://brainly.com/question/25876659

#SPJ1

Answer:

would this not be a converse statement?

Step-by-step explanation:

triangle ABC is the hypothesis and it's conclusion is triangle DEF

I agree with both Priya's and Han's equations.

To determine if either Priya or Han equation is correct, we can substitute the coordinates of the given point (1,2) into each equation and check if the equation holds true.

For Priya's equation, y - 2 = (1/3)(x - 1), substituting x = 1 and y = 2:

2 - 2 = (1/3)(1 - 1)

0 = 0

The equation holds true, so Priya's equation is correct.

For Han's equation, 3y - x = 5, substituting x = 1 and y = 2:

3(2) - 1 = 5

6 - 1 = 5

5 = 5

The equation also holds true, so Han's equation is correct.

Both Priya's and Han's equations are valid equations of the line with a slope of 1/3 passing through the point (1,2). The equations have different forms, but they are algebraically equivalent and represent the same line. Therefore, I agree with both Priya's and Han's equations.

For more questions on coordinates, click on:

https://brainly.com/question/31293074

#SPJ8

Answer: The statement that correctly describes the data is:

The typical value is 17. Most values are close to 17, except 4, which is an extreme value.

This is because the value 17 appears most frequently in the data set, making it the mode or the typical value. The value 4 is an extreme value as it is the minimum value in the data set. The maximum value of 18 is not the typical value because it is not as representative of the overall distribution of ages in the data set as the mode, which is 17.

Step-by-step explanation:

Answer:

a) r = .1880

b) a = .1186

c) r² = .0353

d) b = 3.6780

The equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.

To form a system of equations that has an infinite number of solutions when graphed with the given equation, we need to find an equation that represents the same line or is a multiple of the given equation.

The given equation is: y + 4x - 1 = 0

To find an equation with an infinite number of solutions, we can multiply the given equation by a non-zero constant.

Let's multiply the given equation by 2:

2(y + 4x - 1) = 2(0)

2y + 8x - 2 = 0

The equation 2y + 8x - 2 = 0, when graphed with the given equation y + 4x - 1 = 0, will form a system that has an infinite number of solutions. The two equations represent the same line, just with different coefficients.

Therefore, the equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.

Learn more about equation at https://brainly.com/question/29174899

#SPJ1

The calculated length of the arc JK is 7π

From the question, we have the following parameters that can be used in our computation:

Central angle = 140 degrees

Radius, IJ = 9 inches

Using the above as a guide, we have the following:

JK = Central angle/360 * 2 * π * Radius

Substitute the known values in the above equation, so, we have the following representation

JK = 140/360 * 2 * π * 9

Evaluate

JK = 7π

Hence, the length of the arc is 7π

Read more about arc lengths at

brainly.com/question/16552139

#SPJ1

Answer: 0.3464 (correct upto 4 decimal places )

Step-by-step explanation:

[tex]\sqrt{3/25}[/tex]= [tex]\sqrt{3} /\sqrt{25\\}[/tex]     (as the square root of 25 is 5)

=1.73205/5

=0.3464

Answer: 2 1/2 pounds of more clay

Step-by-step explanation:

To calculate how much more clay Ms. Garcia needs, we need to add up the clay requirements for each grade level and then subtract the amount she already has.

For the sixth graders:

Number of students: 25

Clay required per student: 3/4 pound

Total clay required for sixth graders: 25 * (3/4) = 75/4 = 18 3/4 pounds

For the seventh graders:

Clay required for sculptures: 20 pounds

Total clay required for both grade levels: 18 3/4 + 20 = 38 3/4 pounds

Clay leftover from last year: 5 2/5 pounds

To find out how much more clay Ms. Garcia needs, we subtract the clay she already has from the total required:

38 3/4 - 5 2/5 = 38 3/4 - 27/5 = 38 3/4 - 27/5 = (155 - 108 + 3)/20 = 50/20 = 5/2 = 2 1/2 pounds

Therefore, Ms. Garcia needs an additional 2 1/2 pounds of clay.

Answer:

C

Step-by-step explanation:

x ≥ 25

Because this inequality has an equal sign, it will be a close circle. x ≥ -25 meaning the x go to the right of -25.

So, the answer is C

Answer:

(a) To find the average cost in 2011, substitute 11 for x in the function.

g(11) = -1,736.7 + 1,661.6 ln 11 = $2,247.64

The average cost in 2011 was $2,247.64.

(b) Using the graphing calculator, graph the function in the viewing window

[6, 15] by [1,000, 3,000].

The correct graph is B.

(c) A. The average cost increases at a slower rate as time goes on.

Answer:

(- 4, - 4 )

Step-by-step explanation:

x - 5y = 16 → (1)

4x - 2y = - 8 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x

- 4x + 20y = - 64 → (3)

add (2) and (3) term by term to eliminate x

(4x - 4x) + (- 2y + 20y) = - 8 - 64

0 + 18y = - 72

18y = - 72 ( divide both sides by 18 )

y = - 4

substitute y = - 4 into either of the 2 equations and solve for x

substituting into (1)

x - 5(- 4) = 16

x + 20 = 16 ( subtract 20 from both sides )

x = - 4

solution is (- 4, - 4 )

Answer:   D

Step-by-step explanation:

Similar means that if you multiplied all of the sides by the same number it would proportionally be that much larger.

D)    4x2=8

       12x2=24

       15x2=30      All sides were multiplied by 2 so D is similar

Answer:

D)

Step-by-step explanation:

Figure D is similar in all mesurements .

...

The exact volume of a cone with the same dimensions is 9428.57 cubic inches

From the question, we have the following parameters that can be used in our computation:

The cylinder

The volume of the cone with the same dimensions is calculated as

Volume = 1/3 * Volume of cylinder

So, we have

Volume = 1/3 * 22/7 * (30/2) * (30/2) * 40

Evaluate

Volume = 9428.57

Hence, the exact volume of a cone with the same dimensions is 9428.57 cubic inches

Read more about volume at

https://brainly.com/question/30849227

#SPJ1

Answer:

  4

Step-by-step explanation:

You want the sum of digits of the largest number that divides 1305, 4665, and 6905 with the same remainder.

We can look at 4665/1305 ≈ 3.57 and 6905/1305 ≈ 5.29 for a clue as to the divisor of interest. These quotients tell us that one possibility is the value that would give quotients of 4 and 6 after the remainder is subtracted from each of the numbers.

For 1305 and 4665, if r is the remainder, we require ...

  4(1305 -r) = 4665 -r

  5220 -4665 = 4r -r

  555/3 = r = 185

If 185 is the remainder in this scenario, then 1305 -185 = 1120 is the divisor. Checking the remainder with 6905, we find ...

  6905/1120 = 6 r 185

The sum of digits of this divisor is 1 + 1 + 2 + 0 = 4.

The sum of the digits in N is 4.

The vertex and the x-intercepts of the quadratic equation are:

The vertex is (-1, -4)

The x-intercepts are -3 and 1.

To express the quadratic equation [tex]y = x^2 + 2x - 3[/tex]in vertex and intercept form, we need to complete the square to find the vertex and rewrite the equation in terms of the x-intercepts.

First, let's complete the square to find the vertex. We can do this by taking half the coefficient of x, squaring it, and adding/subtracting it to both sides of the equation:

[tex]y = x^2 + 2x - 3\\y = (x^2 + 2x + 1) - 1 - 3\\y = (x + 1)^2 - 4[/tex]

Now we have the equation in the form [tex]y = a(x - h)^2 + k[/tex], where the vertex is at the point (-h, k). The vertex is (-1, -4).

Next, let's find the x-intercepts by setting y = 0:

[tex]0 = x^2 + 2x - 3\\0 = (x + 3)(x - 1)[/tex]

The x-intercepts are -3 and 1.

In vertex and intercept form, the equation is:

[tex]y = (x + 1)^2 - 4[/tex]

The vertex is (-1, -4)

The x-intercepts are -3 and 1.

This form allows us to easily identify the vertex and the x-intercepts of the quadratic equation.

For more such questions on Vertex

https://brainly.com/question/29638000

#SPJ8