The polygons to the right are similar. Find the value of each variable.

X?
Y?

Two questions about systems aaa and bbb, the given system is:

System aaa: x = -1/3 and y = -7/3
System bbb: x = -1/3 and y = -7/3

To answer two questions about systems aaa and bbb, let's first clarify the given system:

System aaa:
x - 4y = 9

System bbb:
2x + y = -3

Question 1: Solve system aaa.
To solve system aaa, we'll use the method of substitution:

Step 1: Solve one equation for one variable.
From the first equation in system aaa, we can isolate x:
x = 4y + 9

Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for x in the second equation of system aaa:
2(4y + 9) + y = -3

Step 3: Simplify and solve for y.
8y + 18 + y = -3
9y + 18 = -3
9y = -3 - 18
9y = -21
y = -21/9
y = -7/3

Step 4: Substitute the value of y into the expression for x.
Using the first equation in system aaa:
x - 4(-7/3) = 9
x + 28/3 = 9
x = 9 - 28/3
x = (27 - 28)/3
x = -1/3

Therefore, the solution to system aaa is x = -1/3 and y = -7/3.

Question 2: Solve system bbb.
To solve system bbb, we'll use the method of substitution:

Step 1: Solve one equation for one variable.
From the second equation in system bbb, we can isolate y:
y = -2x - 3

Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for y in the first equation of system bbb:
x - 4(-2x - 3) = 9

Step 3: Simplify and solve for x.
x + 8x + 12 = 9
9x + 12 = 9
9x = 9 - 12
9x = -3
x = -3/9
x = -1/3

Step 4: Substitute the value of x into the expression for y.
Using the second equation in system bbb:
y = -2(-1/3) - 3
y = 2/3 - 3
y = 2/3 - 9/3
y = -7/3

Therefore, the solution to system bbb is x = -1/3 and y = -7/3.

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Answer:

y=2x-4

Step-by-step explanation:

slope=mx+b

8x-4y=16

-4y=-8x+16

-4y/-4=y

(-8x+16)/-4=2x-4

y=2x-4

Hope this helps! :)

Using the t-distribution, as we have the standard deviation for the sample, it is found that it can be concluded that the holes are being punched an average of 1. 84 cm.

At the null hypotheses, it is tested if the mean is of 1.84 cm, that is:

\(H_0: \mu = 1.84\)

At the alternative hypothesis, it is tested if the mean is different of 1.84 cm, that is:

\(H_1: \mu \neq 1.84\)

The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

The parameters are:

Considering the hypothesis and the given sample, it is found that the parameters are as follows:

\(\overline{x} = 1.85, \mu = 1.84, s = 0.0235, n = 12\).

Hence, the test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{1.85 - 1.84}{\frac{0.0235}{\sqrt{12}}}\)

\(t = 1.47\)

Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.1 and 12 - 1 = 11 df, the critical value is of \(|t^{\ast}| = 1.7959\)

Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis and it can be concluded that the holes are being punched an average of 1. 84 cm.

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There are 3 cases to consider when determining horizontal asymptotes:

1) Case 1: if: degree of numerator < degree of denominator. then: horizontal asymptote: y = 0 (x-axis)

2) Case 2: if: degree of numerator = degree of denominator.

3) Case 3: if: degree of numerator > degree of denominator.

Answer:

Step-by-step explanation:

i think 45 because a square could be broken up into 4s

Answer:

\(90^{\circ}\)

Step-by-step explanation:

Take any square and try rotating it.

Answer:

First situation

More than 3 hours

At least 10

15

75

Step-by-step explanation:

Let x be the number of hours

The equation will be

\(5x>15\\\Rightarrow x>\dfrac{15}{5}\\\Rightarrow x>3\)

So, she needs to work more than 3 hours in order to make more than $15.

The situation that represents \(5x>15\) is the first one.

Let x be the additional number of cans

The inequality will be

\(x+5\geq15\\\Rightarrow x\geq 15-5\\\Rightarrow x\geq 10\)

So, the additional number of cans to be bought is at least 10.

Let x be the number of comic books Clarice has.

\(x>15\)

So, Clarice needs to have more than 15 comic books.

Let x be age of Elizabeth

The equation will be

\(x=5\times 15\\\Rightarrow x=75\)

So, Elizabeth is 75 years old.

Answer:

-11

Step-by-step explanation:

let (2,1)be x1 and y1 respectively

(3,-10) be x2 and y2 respectively

From,slope= (y2-y1)/(x2-x1)

=(-10-1)/(3-2)

= -11/1

= -11

Step-by-step explanation:

integral from 0 to 2pi of cos3x

(sin3x)/3 from 0 to 2 pi

sin 6pi /3 - sin 0 /3 = 0

Answer:

21

Step-by-step explanation:

you gave me free points why thank you

Answer:

The probability that the next spin will land on blue is 0.12.

Step-by-step explanation:

The result of the several spins are as follows:

Color           Frequency

Red                  18

Blue                   9

Green               18

Yellow              19

Purple               12

TOTAL             76

Compute the probability that the next spin will land on blue as follows:

\(P(Blue)=\frac{n(Blue)}{N}\\\\=\frac{9}{76}\\\\=0.1184211\\\\\approx 0.12\)

Thus, the probability that the next spin will land on blue is 0.12.

The probability that the next spin will land on blue as a decimal to the nearest hundredth is 0.12 and this can be determined by using the given data.

Given :

A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple.

The spinner is spun several times, and the results are recorded below:

Colour                               Frequency

Red                                         18

Blue                                         9

Green                                      18

Yellow                                     19

Purple                                      12

So, the total frequency is = 18 + 9 + 18 + 19 + 12

                                          =  76

Based on the above given results, the probability that the next spin will land on blue is given by:

\(\rm P = \dfrac{n}{N}\)

\(\rm P = \dfrac{9}{76}\)

P = 0.1184

P \(\approx\) 0.12

So, the probability that the next spin will land on blue as a decimal to the nearest hundredth is 0.12.

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Answer:

Large boxes are 18.25 kg

Small boxes are 15.25 kg

Step-by-step explanation:

This is a system of equations. You need to set up each equation first.

I am assigning x to be big boxes and y to be small boxes.

5x + 3y = 137

2x + 6y = 128

To solve, you will need to eliminate a variable. That means you will have to multiply one of the equations by a number to make it so a variable will be eliminated. I will be multiplying the top equation by -2.

-2 ( 5x + 3y = 137)

    2x + 6y = 128

Distribute the -2 to everything in the parentheses in the first equation.

-10x - 6y = -274

2x + 6y = 128

Notice the 6y will go away because -6y + 6y = 0. Now add the equations together. The remaining equation is:

-8x = -146

Solve for x by dividing by -8.

x = 18.25

Now plug that into one of the original equations.

2(18.25) + 6y = 128.

36.5 + 6y = 128                Subtract 36.5 from each side

-36.5            -36.5

6y = 91.5                          Divide by 6 to solve

y = 15.25

To show that β=3α, where β represents the volumetric thermal expansion coefficient and α represents the linear thermal expansion coefficient, we can calculate the infinitesimal change in volume (dv) of a cube with sides of length l when the temperature changes by dt.

The linear thermal expansion coefficient α is defined as the fractional change in length per unit change in temperature. Similarly, the volumetric thermal expansion coefficient β is defined as the fractional change in volume per unit change in temperature.

Let's consider a cube with sides of length l. The initial volume of the cube is \(V = l^3\). Now, when the temperature changes by dt, the sides of the cube will also change. Let dl be the infinitesimal change in length due to the temperature change.

The infinitesimal change in volume, dv, can be calculated using the formula for differential calculus:

\(\[dv = \frac{{\partial V}}{{\partial l}} dl = \frac{{dV}}{{dl}} dl\]\)

Since \(V = l^3,\) we can differentiate both sides of the equation with respect to l:

\(\[dV = 3l^2 dl\]\)

Substituting this back into the previous equation, we get:

\(\[dv = 3l^2 dl\]\)

Now, we can express dl in terms of dt using the linear thermal expansion coefficient α:

\(\[dl = \alpha l dt\]\)

Substituting this into the equation for dv, we have:

\(\[dv = 3l^2 \alpha l dt = 3\alpha l^3 dt\]\)

Comparing this with the definition of β (fractional change in volume per unit change in temperature), we find that:

\(\[\beta = \frac{{dv}}{{V dt}} = \frac{{3\alpha l^3 dt}}{{l^3 dt}} = 3\alpha\]\)

Therefore, we have shown that β = 3α, indicating that the volumetric thermal expansion coefficient is three times the linear thermal expansion coefficient for a cube.

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Answer:

10

Step-by-step explanation:

Answer:

divide 20 by two lol

Step-by-step explanation:

The volume of the solid generated by revolving the region R bounded by

y = \(e^{-2x}\), y = 0, x = 0, x = ln 9 around x-axis = 0.25 cubic units

Given the region R bounded by y = \(e^{-2x}\), y = 0, x = 0, x = ln 9.

We will find the volume of the solid obtained by revolving this region around the x-axis through disc integration method.

The disc integration method is used to find the volume of a solid obtained by revolving a region around an axis parallel to x-axis.

Then, volume, V = \(\int\limits^0_{ln9} {y^2} \, dx\)

                            = \(\int\limits^0_{ln9} {(e^{-2x})^2} \, dx\)

                            = \(\int\limits^0_{ln9} {e^{-4x}} \, dx\)

                            = \(\frac{e^{-4x}}{-4} |_{x=0\ to \ x=ln9}\)

                            = \(\frac{e^{-4 ln9}}{-4} +\frac{1}{4}\)

                            = \(\frac{9^{-4}+1}{4}\) ≈ 0.25 cubic units

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Answer:

B) 174

Step-by-step explanation:

30+6*2 because she already has 30 made and 2 dozen per 6 hours. So to find how any dozen in the 6hrs you do 2*6 = 12. So 12 dozen in 6hrs. 1 dozen is 12 cookies. To find how much cookies in 12 dozen you do 12*12 = 144. Now you do 144+30 because she bakes 30 earlier and she will bake 144 in those 6 hours. 144+30 = 174. So Frida will have 174 cookies. So the answer is B) 174.

The probability that Diesel will win her 6th game on the 18th game is approximately 0.000568, or 0.0568%.

The probability that Diesel will win her 6th game on the 18th game is calculated using the binomial distribution formula.

Let's define the following terms:
- n = number of trials (games played) = 18
- k = number of successes (games won by Diesel) = 6
- p = probability of success (Diesel winning a game) = 1/4
- q = probability of failure (Daisy winning a game) = 1 - p = 3/4

The formula for the probability of exactly k successes in n trials is:

P(k) = (n choose k) * p^k * q^(n-k)

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes out of n trials. It can be calculated as:

(n choose k) = n! / (k! * (n-k)!)

Plugging in the values, we get:

P(6) = (18 choose 6) * (1/4)^6 * (3/4)^12
= 18! / (6! * 12!) * (1/4)^6 * (3/4)^12
= 18564 * 0.00000244 * 0.0122
= 0.000568

Therefore, the probability that Diesel will win her 6th game on the 18th game is approximately 0.000568, or 0.0568%.

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The approximate circumference of spaceship Earth is 160m

The formula for calculating the volume of a sphere is given as;

V = 4/3 πr³

Given that;

Now, substitute the values

65417 = 1. 3 ×3.14r³

Multiply the values

65417 = 4. 082r³

Make r the subject

r³ = 16025. 722

Find the cube root

r = 25. 2m

The circumference is expressed as;

Circumference = 2πr

Substitute the values, we have;

Circumference = 2× 3.14 × 25.2

Circumference = 160 m

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Answer:

w(t-4)=t^2-9t+20

Step-by-step explanation:

w(t)=t^2-t

w(t-4)=(t-4)^2-(t-4)

w(t-4)= t^2-8t+16-t+4

w(t-4)=t^2-9t+20

The angle x in the diagram is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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1. The area of the scale drawing of the park is 146,880 square inches (Option J).

2. The perimeter of the park is 126 feet (Option D).

3. The length of the south side of the park is 40% of the length of the north side (Option F).

1. To find the area of the scale drawing of the park, we need to calculate the area of the trapezium. The formula for the area of a trapezium is (base1 + base2) * height / 2.

Using the scale, the lengths of the bases (parallel sides) in feet would be:

Base1 = 28 inches * 1.5 feet/inch = 42 feet

Base2 = 40 inches * 1.5 feet/inch = 60 feet

Plugging in the values into the formula, we have:

Area = (42 + 60) * 16 / 2 = 1020 square feet

Since the answer options are in square inches, we need to convert the area back to square inches:

Area = 1020 square feet * 144 square inches/square foot = 146880 square inches

Therefore, the area of the scale drawing of the park is 146880 square inches.

2. The perimeter of the park can be calculated by summing up the lengths of all sides.

The lengths of the sides in feet would be:

Side1 = 28 inches * 1.5 feet/inch = 42 feet

Side2 = 40 inches * 1.5 feet/inch = 60 feet

Side3 = 16 inches * 1.5 feet/inch = 24 feet

Adding up all sides, we have:

Perimeter = Side1 + Side2 + Side3 = 42 feet + 60 feet + 24 feet = 126 feet

Therefore, the perimeter of the park is 126 feet.

3. To find the percentage length of the south side compared to the north side, we can calculate:

Percentage = (South Side Length / North Side Length) * 100

Using the scale, the length of the south side in feet would be:

South Side Length = 16 inches * 1.5 feet/inch = 24 feet

The length of the north side is already given as 40 inches * 1.5 feet/inch = 60 feet.

Plugging in the values, we have:

Percentage = (24 feet / 60 feet) * 100 = 40%

Therefore, the length of the south side of the park is 40% of the length of the north side.

Complete Question:

Mikea, an intern with the Parks and Recreation Department, is developing a proposal for the new trapezoidal Springdale Park. The figure below shows her scale drawing of the proposed park with 3 side lengths and the radius of the merry-go-round given in inches. In Mikea's scale drawing, 1 inch represents 1.5 feet.

1. What is the area, in square inches, of the scale drawing of the park? 448 544 H. 640 672 K. 1.088

2. Mikea's proposal includes installing a fence on the perimeter of the park. What is the perimeter, in feet, of the park? A. 84 B. 88 C. 104 D. 126 E 156

3. The length of the south side of the park is what percent of the length of the north side? F. 112% G. 1245 H. 142 J. 1754 K. 250%

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Answer:

2.35

Step-by-step explanation:

Make sure to remember that the meaning of slope is the gradient of the equation.

Hence the slope of the equation is 2.35.

Answer: The answer is 2

Step-by-step explanation:

Given A and B are vertical angles with m ∠A = 20x + 10 and m ∠B =30x - 10, the value of x is 2

From the Vertical angle theorems, we have that

Two opposite vertical angles formed when two lines intersect each other are always equal to each other.

Now, from the question, we are given that A and B are vertical angles

That means

A = B

Also, from the question

measure of angle A = 20x + 10 and measure of angle B = 30x - 10

To determine the value of x, we will equate the two equations to each other  

A = 20x + 10

B = 30x - 10

Since, A = B

∴ 20x + 10 = 30x - 10

To solve for x,

20x + 10 + 10 = 30x - 10 +10

We get

20x + 20 = 30x

20x - 20x + 20 = 30x - 20x

20 = 10x

That is,

10x = 20

∴ x = 20 ÷ 10

x = 2

Hence, given A and B are vertical angles with m ∠A = 20x + 10 and m ∠B =30x - 10, the value of x is 2

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The resistance between the adjustable contact and the upper-end terminal of a 1M linear potentiometer, when the contact is set at 1/4 of full rotation from the lower-end terminal, can be calculated as follows:

The resistance of a linear potentiometer is distributed evenly along its entire length. Since the potentiometer has a total resistance of 1M (1 megohm), the resistance between the adjustable contact and the upper-end terminal can be determined by finding the proportion of the total resistance.

When the contact is set at 1/4 of full rotation from the lower-end terminal, it means that the adjustable contact has traveled 1/4 of the total length of the potentiometer track. Thus, the resistance between the adjustable contact and the upper-end terminal would be 1/4 of the total resistance.

Therefore, the resistance between the adjustable contact and the upper-end terminal of the 1M linear potentiometer, in this case, would be 1/4 of 1M, which is 250k ohms (or 250,000 ohms).

When the adjustable contact of a 1M linear potentiometer is set at 1/4 of full rotation from the lower-end terminal, the resistance between the adjustable contact and the upper-end terminal is 250k ohms. This can be calculated by considering the proportion of the total resistance based on the position of the adjustable contact along the potentiometer track.

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Answer: 100% increase

Step-by-step explanation:

Answer:

500 + (100 x 5) = 1000

Step-by-step explanation:

If you cut off one of the corners of a rectangular prism, you would get a triangle.

The rectangular prism is a solid that possesses six rectangular surfaces constituting its three-dimensional shape. If you excise any of the corners of this structure, it will create an opening intersecting through a plane that runs across three neighboring edges converging at the apex.

Owing to the orientation and configuration of the three planes colliding beneath the inaccessible edge, which form right angles with one another as per the shape's design, a resultant triangle displays an exact angle when fused to the original prism with proportions depending on the respective dimensions of the rectangular prism.

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This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,

Remember that a vertical translation of N units is:

g(x) = f(x) + N

if N < 0 the translation is down.

if N > 0 the translation is up.

And a horizontal translation of N units is:

g(x) = f(x + N)

If N > 0 the translation is to the right.

if N < 0 the translation is to the left.

Here we have the transformation:

f(x) = x²

g(x) = (x + 2)² + 5

So this is a translation of 2 units to the left and 5 units up.

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