y = 40 (1.25) Does this equation represent exponential growth
or
decay?

Answer: n= 6  x= 38.7427    f= 4.618802    h= 9.237604

Step-by-step explanation:

for the first one:

there are 2 45 90 triangles. Since the sides of a 45 90 triangle are n for 45 and \(n\sqrt{2}\) for the 90 degrees, that means that if \(6\sqrt{2} = n\sqrt{2}\) then n is 6.

Second one:

You have to split the x into two parts.

Starting on the first part use the 30 60 90 triangle with given with the length for the 60°

60 = \(n\sqrt{3}\)

so \(30=n\sqrt{3}\)

n = 17.320506

so part of x is 17.320506

For the next triangle you would use Tan 35 = \(\frac{15}{y}\)

this would equal 21.422201

adding both values up it would be 38.742707

Third question:

There is two 30 60 90 triangles

The 60° is equal to 8 which means \(8=n\sqrt{3}\)

Simplifying this \(n=4.618802\)

h = 2n.      which is h= 9.237604

f=n             f is 4.618802

Answer:

1) Ratio of angles: 45: 45: 90

  Ratio of sides: 1: 1: √2

Sides are n, n, n√2

  The side opposite to 90° = n√2

           n√2 = 6√2

                \(\boxed{\sf n = 6}\)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2) Ratio of angles: 30: 60: 90

  Ratio of side: 1: √3: 2

Sides are m, m√3, 2m.

Side opposite to 60° = m√3

     m√3 = 30

           \(m = \dfrac{30}{\sqrt{3}}\\\\\\m = \dfrac{30\sqrt{3}}{3}\\\\m = 10\sqrt{3}\)

Side opposite to 30° = m

          m = 10√3

In ΔABC,

          \(Tan \ 35= \dfrac{opposite \ side \ of \angle C }{adjacent \ side \ of \angle C}\\\\\\~~~~~~0.7 = \dfrac{15}{CB}\\\\\)

       0.7 * CB = 15

                \(CB =\dfrac{15}{0.7}\\\\CB = 21.43\)

x = m + CB

   = 10√3 + 21.43

  = 10*1.732 + 21.43

  = 17.32 + 21.43

  = 38.75

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3) Ratio of angles: 30: 60: 90

    Ratio of side: 1: √3: 2

Sides are y, y√3, 2y.

Side opposite to 60° = y√3

         \(\sf y\sqrt{3}= 8\\\\ ~~~~~ y = \dfrac{8}{\sqrt{3}}\\\\~~~~~ y =\dfrac{8*\sqrt{3}}{\sqrt{3}*\sqrt{3}}\\\\\\~~~~~ y =\dfrac{8\sqrt{3}}{3}\)

    Side opposite to 30° = y

              \(\sf f = y\\\\ \boxed{f = \dfrac{8\sqrt{3}}{3}}\)

 Side opposite to 90° = 2y

           h = 2y

          \(\sf h =2*\dfrac{8\sqrt{3}}{3}\\\\\\\boxed{h=\dfrac{16\sqrt{3}}{3}}\)    

Answer:

there are 100 centigrams in a gram

Step-by-step explanation:

The correct answer is: D.

The system has only one solution, and it is viable because it results in positive side lengths.

Let x be the shorter leg of the triangle, and y be the area. The longer leg is 4 + 6x, and the area of the triangle is y = (1/2) * x * (4 + 6x).

For the rectangle, the width is 5 + x, the length is 3, and its area is also y = (5 + x) * 3.

The system of equations is:

y = (1/2) * x * (4 + 6x)

y = (5 + x) * 3

Substitute equation (2) into equation (1) and solve for x:

(5 + x) * 3 = (1/2) * x * (4 + 6x)

30 + 6x = 4x + 6x^2

6x^2 - 2x - 30 = 0

Using the quadratic formula, we find two solutions for x:

x1 ≈ 2.62

x2 ≈ -1.95

Since x represents the length of the shorter leg, we discard the negative solution. Thus, there is only one viable solution for x: x ≈ 2.62. Now find y using equation (2): y ≈ 22.86.

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A carpenter is creating two new templates for his designs. One template will be in the shape of a right triangle, where the longer leg is 4 inches more than six times the shorter leg.

The second template will be in the shape of a rectangle, where the width is 5 inches more than the triangle’s shorter leg, and the length is 3 inches.

The carpenter needs the areas of the two templates to be the same. Write a system of equations to represent this situation, where y is the area, and x is the length of the shorter leg of the triangle. Which statement describes the number and viability of the system’s solutions?

A.

The system has two solutions, but only one is viable because the other results in negative side lengths.

B.

The system has two solutions, and both are viable because they result in positive side lengths.

C.

The system has only one solution, but it is not viable because it results in negative side lengths.

D.

The system has only one solution, and it is viable because it results in positive side lengths.

Answer: yes

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

First of all we know b is a parrellogram, so it is b.

But also other reasons:

It can't be A because they are next to each other, in fact supplementary angles. It can't be C because it doesn't make any sense and same thing for E.

Answer:

B

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

So quadratic formulas help

Answer:

A regular dodecagon has 12 sides and rotational symmetry. This means that if you rotate it by a certain angle about its center, it will look the same as before the rotation. The angle of rotation that would carry a regular dodecagon onto itself is equal to 360 degrees divided by the number of sides.

In this case, 360 degrees / 12 sides = 30 degrees.

So a regular dodecagon can be rotated onto itself by any multiple of 30 degrees. Out of the options you provided, only option 3 (330 degrees) is a multiple of 30 degrees. Therefore, an angle of rotation of 330 degrees would carry a regular dodecagon onto itself.

Answer:

She would need 11.1 liters of gas.

Answer:

.25

Step-by-step explanation:

hundredth's is the second place over so you look the the 3rd number. 4 or less it stays the same 5 or more you add one

Answers:

x > 9

Graph has open circle

Arrow points to the right

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

Reason:

Add 7 to both sides to go from the original inequality to 9 < x, which is the same as x > 9

The graph will involve an open circle at 9. We don't include this endpoint because there isn't "or equal to" in the inequality sign.

We shade to the right due to the "greater than"

This visually shows all values larger than 9.

All of the equations that are equivalent to n − 9 = 12 include the following:

A. n - n - 9 = 12 - n

D. n - 9 - n = 12 - n

In this exercise, you are to determine the equations that are equivalent to the given equation (mathematical expression). This ultimately implies that, the left-hand side (LHS) of the given equation (mathematical expression) must be equal to the left-hand side (LHS) of the given equation (mathematical expression).

By substracting the variable n from both sides of the given equation (mathematical expression), we have the following:

n - 9 - n = 12 - n (equivalent)

By collecting terms and rearranging the equation (mathematical expression), we have the following:

n - n - 9 = 12 - n (equivalent).

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Answer:

key food has the better deal

Step-by-step explanation:

19.95/5 = 3.99 per pound and 18/5 = 4.50 per pound

Answer:

C

Step-by-step explanation:

Answer:

11.4

Step-by-step explanation:

Answer:

11.4

Step-by-step explanation:

Answer:

the answer would be 25

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

5(x – 10) = 30 – 15x

Distribute

5x -50 = 30-15x

Add 15x to each side

5x+15x – 50 = 30 – 15x+15x

20x-50 = 30

Add 50 to each side

20x-50+50 = 30+50

20x = 80

Divide by 20

20x/20 = 80/20

x =4

Answer:

The answer is D. 1 cubic foot.

Step-by-step explanation:

To solve for the volume of a cube, use the formula V= \(a^{3}\). This is the formula because the volume of a cube formula equals length times width times height. Since the length, width, and height are all the same values, the simplest volume of a cube formula is \(a^{3}\).

Next, plug in the information from the question into the formula, which will look like V= \(1^{3}\). Then, solve the equation, and the final answer will be 1 cubic foot.

Answer:

$75,867

Step-by-step explanation:

that will be the answer

Answer:

25 students and 40%

Step-by-step explanation:

Answer:

Robin’s median score is 107. Evelyn’s median score is 138. The medians are the same as the means, so the same conclusion would be reached that Robin is winning

Step-by-step explanation:

Answer:

Robin’s median score is 107. Evelyn’s median score is 138. The medians are the same as the means, so the same conclusion would be reached that Robin is winning.

the answer is $15.21

Answer:

The total cost of the lunch, including the tip and without tax, is $15.21.

Step-by-step explanation:

We know that the tip is calculated as 17% of the cost of the lunch, without tax.

1. convert percentage into a decimal

17% = 0.17 because 17/100 = 0.17

2. calculate the tip amount

tip = 0.17  * 13

tip = $2.21

3. find the total cost of the lunch

total cost = cost of lunch + tip

total cost = $13 + $2.21

total cost = $15.21

Therefore, the total cost of the lunch, including tip and without tax is $15.21.

Answer:

x∠15 or 15 is greater than x The x being the amount of money Jonathan has in his bank account.

Step-by-step explanation:

Sorry if this is not what you are looking for.

(a) the Riemann sum using left endpoints and n equals 4 is L₄ = 1620.

(b) the Riemann sum using right endpoints and n equals 4 is R₄ = 2916.

What is riemann sum?

A Riemann sum is a method used in calculus to approximate the area under a curve or the value of an integral. It involves dividing the region under the curve into smaller subintervals and approximating the area of each subinterval using a specific rule.

To find the Riemann sum using left endpoints and n equals 4, we need to divide the interval [2, 14] into four equal subintervals. The width of each subinterval, denoted as Δx, is calculated as (b - a) / n, where b is the upper limit (14) and a is the lower limit (2).

So, Δx = (14 - 2) / 4 = 12 / 4 = 3.

Now, we evaluate the function at the left endpoint of each subinterval and multiply it by the width (Δx).

The left endpoints for n = 4 are: x₀ = 2, x₁ = 5, x₂ = 8, x₃ = 11.

The Riemann sum using left endpoints is given by:

L₄ = f(x₀) Δx + f(x₁) Δx + f(x₂) Δx + f(x₃) Δx.

Now, let's substitute the given function f(x) = 2x² + 4x + 2 into the Riemann sum equation:

L₄ = (2x₀² + 4x₀ + 2) Δx + (2x₁² + 4x₁ + 2) Δx + (2x₂² + 4x₂ + 2) Δx + (2x₃² + 4x₃ + 2) Δx.

L₄ = (2(2)² + 4(2) + 2) (3) + (2(5)² + 4(5) + 2) (3) + (2(8)² + 4(8) + 2) (3) + (2(11)² + 4(11) + 2) (3).

L₄ = (8 + 8 + 2) (3) + (50 + 20 + 2) (3) + (128 + 32 + 2) (3) + (242 + 44 + 2) (3).

L₄ = (18)(3) + (72)(3) + (162)(3) + (288)(3).

L₄ = 54 + 216 + 486 + 864.

L₄ = 1620.

Therefore, the Riemann sum using left endpoints and n equals 4 is L₄ = 1620.

To find the Riemann sum using right endpoints and n equals 4, the process is similar. However, this time we evaluate the function at the right endpoint of each subinterval.

The right endpoints for n = 4 are: x₁ = 5, x₂ = 8, x₃ = 11, x₄ = 14.

The Riemann sum using right endpoints is given by:

R₄ = f(x₁) Δx + f(x₂) Δx + f(x₃) Δx + f(x₄) Δx.

Substituting the function into the Riemann sum equation:

R₄ = (2x₁² + 4x₁ + 2) Δx + (2x₂² + 4x₂ + 2) Δx + (2x₃² + 4x₃ + 2) Δx + (2x₄² + 4x₄ + 2) Δx.

R₄ = (2(5)² + 4(5) + 2) (3) + (2(8)² + 4(8) + 2) (3) + (2(11)² + 4(11) + 2) (3) + (2(14)² + 4(14) + 2) (3).

R₄ = (50 + 20 + 2) (3) + (128 + 32 + 2) (3) + (242 + 44 + 2) (3) + (392 + 56 + 2) (3).

R₄ = (72)(3) + (162)(3) + (288)(3) + (450)(3).

R₄ = 216 + 486 + 864 + 1350.

R₄ = 2916.

Therefore, the Riemann sum using right endpoints and n equals 4 is R₄ = 2916.

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1 standard deviation =  8 inches. the answer is OPTION E

We know that 99.7% of American men have heights between 5'0" and 7'0". Since height is normally distributed, we can use the empirical rule to estimate the standard deviation.

According to the empirical rule, 99.7% of the data falls within 3 standard deviations of the mean. Therefore, we can say that the range of heights from 5'0" to 7'0" is 3 standard deviations.

We can use this information to estimate the standard deviation as follows:

Range of heights = 7'0" - 5'0" = 2 feet

3 standard deviations = 2 feet

1 standard deviation = 2/3 feet

1 foot = 12 inches

Therefore, 1 standard deviation = 2/3 * 12 inches = 8 inches

So, our estimate of the standard deviation of the height of American men is 8 inches. Therefore, the answer is OPTION E in the given options.

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Complete question

If the heights of 99.7% of American men are between 5'0"

and 7'0", what is your estimate of the standard deviation of

the height of American men? (Assume the heights of

American Men are Normally Distributed).

A.) 1"

B.) 2"

C.) 4"

D.) 6"

E.) 8"

Answer:

Step-by-step explanation:

1/4 (g + 2) = 8

g + 2 = 8 (4)

g = 32 - 2

g = 30

The solution to the linear programming problem is:

Maximum value of z = 120

x₁ = 0, x₂ = 6

To solve the given linear programming problem using the graphical method, we first need to plot the feasible region determined by the constraints and then identify the optimal solution.

The constraints are:

x₁ + x₂ ≥ 12

x₁ + x₂ ≤ 6

x₁, x₂ ≥ 0

Let's plot these constraints on a graph:

The line x₁ + x₂ = 12:

Plotting this line on the graph, we find that it passes through the points (12, 0) and (0, 12). Shade the region above this line.

The line x₁ + x₂ = 6:

Plotting this line on the graph, we find that it passes through the points (6, 0) and (0, 6). Shade the region below this line.

The x-axis (x₁ ≥ 0) and y-axis (x₂ ≥ 0):

Shade the region in the first quadrant of the graph.

The feasible region is the overlapping shaded region determined by all the constraints.

Next, we need to find the corner points of the feasible region by finding the intersection points of the lines. In this case, the corner points are (6, 0), (4, 2), (0, 6), and (0, 0).

Now, we evaluate the objective function z = 15x₁ + 20x₂ at each corner point:

For (6, 0): z = 15(6) + 20(0) = 90

For (4, 2): z = 15(4) + 20(2) = 100

For (0, 6): z = 15(0) + 20(6) = 120

For (0, 0): z = 15(0) + 20(0) = 0

From the evaluations, we can see that the maximum value of z is 120, which occurs at the corner point (0, 6).

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The standard form equation for the hyperbola is 80x^2 - y^2 = 80. This equation represents a hyperbola centered at the origin, with a horizontal transverse axis and a vertical conjugate axis.

To find the standard form equation for a hyperbola, we need the coordinates of the vertices and an additional point on the hyperbola. In this case, the vertices are given as (4, 0) and (-4, 0), and the point on the hyperbola is (6, 20).

The standard form equation for a hyperbola centered at the origin is:

(x^2 / a^2) - (y^2 / b^2) = 1

where a represents the distance from the center to the vertices along the x-axis, and b represents the distance from the center to the co-vertices along the y-axis.

First, let's find the value of a. The distance between the x-coordinates of the vertices gives us the value of 2a, which is equal to 4 - (-4) = 8. Therefore, a = 4.

Next, we need to find the value of b. To do this, we can use the point (6, 20) that lies on the hyperbola. Substituting the x- and y-coordinates into the equation, we get:

(6^2 / 4^2) - (20^2 / b^2) = 1

36 / 16 - 400 / b^2 = 1

Simplifying further:

9/4 - 400 / b^2 = 1

9 - 400 / b^2 = 4

400 / b^2 = 5

b^2 = 400 / 5

b^2 = 80

Now, we have the values of a = 4 and b^2 = 80. Plugging them into the standard form equation, we get:

(x^2 / 4^2) - (y^2 / √80^2) = 1

Simplifying:

x^2 / 16 - y^2 / 80 = 1

Multiplying both sides by 80 to eliminate fractions:

80x^2 - y^2 = 80

Thus, the standard form equation for the hyperbola with vertices at (4, 0) and (-4, 0) that passes through the point (6, 20) is 80x^2 - y^2 = 80.

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