the polygons in each pair are similar. find the missing side length. ​

Answer:

20

Step-by-step explanation:

to eliminate the variable y

we have steps are,

1) Divide the second equation by 2. then add the result to the first equation

or

2) Multiply the first equation by 2. then add the result to the second equation

or

3) Multiply the first equation by 4 and the second equation by 6, then subtract the resulting equations.

so the answer is the first three options.

Answer:

This is an equation of a line in standard form. The "C" is the constant of the equation

Step-by-step explanation:

The evaluated double integral is (ln(2)) * (2 * e^3 - 1).

To evaluate the double integral of (x * e^x) / y over the region R = [0, 3] x [1, 2], follow these steps:

1. Set up the double integral: ∬(x * e^x) / y dA, where dA = dy dx (since the region is given in terms of x and y).

2. Integrate with respect to y first: ∫(∫(x * e^x) / y dy) dx. The limits for y are from 1 to 2.

3. Calculate the inner integral:
∫(x * e^x * (ln(y))) | from y=1 to y=2 dx.

4. Substitute the limits for y:
∫(x * e^x * (ln(2) - ln(1))) dx.

5. Simplify the expression:
∫(x * e^x * ln(2)) dx, with limits for x from 0 to 3.

6. Integrate with respect to x:
(ln(2)) * (∫x * e^x dx), from x=0 to x=3.

7. Use integration by parts for ∫x * e^x dx, with u=x and dv=e^x dx:
du = dx and v = e^x.

8. Apply integration by parts formula:
uv - ∫v du = x * e^x - ∫e^x dx.

9. Integrate the remaining term:
x * e^x - e^x, evaluated from x=0 to x=3.

10. Substitute the limits for x:
(ln(2)) * ((3 * e^3 - e^3) - (0 * e^0 - e^0)).

11. Simplify the expression:
(ln(2)) * (2 * e^3 - 1).

The evaluated double integral is (ln(2)) * (2 * e^3 - 1).

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Therefore, the integral of xe^x / y da r = [0,3] x [1,2] is 60.2565...

The integral of xe^x / y da r = [0,3] x [1,2] is:∫∫(xe^x / y) dA = ∫1²∫0³(xe^x / y) dxdy = ∫1²(∫0³(xe^x / y) dx) dy

Integration with respect to x:∫0³(xe^x / y) dx = (xe^x / y) |0³ = (3e³ / y) - (0 / y) = 3e³ / y

Thus,∫1²∫0³(xe^x / y) dxdy = ∫1²(3e³ / y) dy= 3e³[ln(y)] |1²= 3e³(ln(2) - ln(1))= 3e³ln(2) - 3e³ln(1)= 3e³ln(2) = 3 * 20.0855...= 60.2565...

Therefore, the integral of xe^x / y da r = [0,3] x [1,2] is 60.2565...

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Answer:

\(\displaystyle m=\frac{6}{5}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (4, 6)

Point (-16, -18)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

The square mil area for a 2 inch wide by 1/4 inch thick copper busbar is 500 square mils.

To find the square mil area for a 2 inch wide by 1/4 inch thick copper busbar, we need to multiply the width and thickness of the busbar in mils.

1 inch = 1000 mils

So, the width of the busbar in mils = 2 inches x 1000 mils/inch = 2000 mils

And, the thickness of the busbar in mils = 1/4 inch x 1000 mils/inch = 250 mils

Therefore, the square mil area of the copper busbar = width x thickness = 2000 mils x 250 mils = 500,000 square mils.

Hence, the square mil area for a 2 inch wide by 1/4 inch thick copper busbar is 500,000 square mils.

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The probability that a single marble chosen at random from the jar is yellow or green is 7/10, or 0.7.

The probability that a single marble chosen at random from the jar is yellow or green can be found by adding the probability of choosing a yellow marble to the probability of choosing a green marble.

There are a total of 1 + 3 + 2 + 4 = 10 marbles in the jar. The probability of choosing a yellow marble is 4/10 = 2/5, and the probability of choosing a green marble is 3/10. Therefore, the probability of choosing a yellow or green marble is:

P(yellow or green) = P(yellow) + P(green) = 4/10 + 3/10 = 7/10

So the probability that a single marble chosen at random from the jar is yellow or green is 7/10, or 0.7.

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Answer:

001,23,83,88,112,132,667

Step-by-step explanation:

Are you kidding me that you need help on this?

The missing lengths  in the triangles are h = 3/2√2 and b = 4√3

Triangle a and b

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

A special right triangle

For a right triangle with an angle of 45 degrees

The measure of the leg is

h = Hypotenuse/√2

So, we have

h = 3/√2

Evaluate

h = 3/2√2

For the other triangle, we have

sin(60) = b/6

So, we have

b = 6/sin(60)

Evaluate

b = 4√3

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Answer: 6 cm

Step-by-step explanation:

Given: The ratio of the areas of two similar  parallelograms is 4:9.

To find : The height of the  bigger one if the smaller is of height 4 cm.

Let h be the height of the  bigger one.

Since the areas of similar figures are proportional to the square of their corresponding sides.

Then, \(\dfrac{4^2}{h^2}=\dfrac{4}{9}\)

\(\dfrac{16}{h^2}=\dfrac{4}{9}\\\\\Rightarrow\ h^2=\dfrac{9}{4}\times16\\\\\Rightarrow\ h^2=36\\\\\Rightarow\ h= 6\ cm\ \ \ \ \text{[ height cannot be negative.]}\)

Hence, the height of bigger parallelogram = 6 cm

a stack of 31 sheets of aluminum is approximately 7.099 inches thick.

To find the thickness of a stack of 31 sheets, you can multiply the thickness of one sheet by 31.

Thickness of one sheet = 0.229 inches

Thickness of 31 sheets = 31 x 0.229 inches

Thickness of 31 sheets = 7.099 inches (rounded to three decimal places)

what is thickness?

Thickness refers to the distance between two opposite surfaces of an object, typically measured in units of length, such as inches, centimeters, or millimeters. It is a physical property that is used to describe the size of an object in the dimension perpendicular to its surface. Thickness is often an important consideration in manufacturing and construction, as it can affect the strength, durability, and overall performance of a material or structure. In the case of the example given, thickness is being used to describe the distance between the two surfaces of a sheet of aluminum.

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Answer:

Step-by-step explanation:

Vertices of the given quadrilateral are A(-4, 3), B(2, -1), C(2, -5) and D(-4, -1)

Since, slope of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by,

Slope = \(\frac{y_2-y_1}{x_2-x_1}\)

Slope of AB = \(\frac{3+1}{-4-2}\)

                    = \(-\frac{2}{3}\)

Slope of AD = \(\frac{3+1}{-4+4}\)

                    = Not defined (Parallel to y-axis)

Slope of DC = \(\frac{-5+1}{2+4}\)

                     = \(-\frac{2}{3}\)

Slope of BC = \(\frac{-1+5}{2-2}\)

                   = Not defined (Parallel to y-axis)

Slope of AB = slope of DC = \(-\frac{2}{3}\)

Slope of BC = slope of AD = Not defined (parallel to y-axis)

As per property of a parallelogram,

"Opposite sides of a parallelogram are parallel and equal in measure"                  

Therefore, ABCD is a parallelogram.

Maggie needs to save for at least 4.5 weeks (or 5 weeks, since she cannot save for a fraction of a week) to be able to purchase the hoodie.

Let's denote the number of weeks Maggie needs to save as "w".

Every week she adds $10 to her bank account, so after "w" weeks, she will have saved:

10w

If we add this to the initial amount she had in her account, we get her total savings:

30 + 10w

For Maggie to be able to purchase the hoodie, her savings must be greater than or equal to $75, so we can write:

30 + 10w ≥ 75

To solve for "w", we can start by subtracting 30 from both sides of the inequality:

10w ≥ 45

Next, we can divide both sides by 10 to isolate "w":

w ≥ 4.5

To graph this inequality on a number line, we can plot a closed circle at the point 4.5 and shade to the right of it, since any value of "w" greater than or equal to 4.5 would satisfy the inequality.

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The solutuion to the given differntial equation is: f(t) = -1/4 e^(2t) + t e^(2t) + 3/4 sin(t)

ℒ{f(t)}(s) = 1/(s^2 - 4s + 5)

We can factor the denominator of the fraction to obtain:

s^2 - 4s + 5 = (s - 2)^2 + 1

Using the partial fraction decomposition, we can write:

1/(s^2 - 4s + 5) = A/(s - 2) + B/(s - 2)^2 + C/(s^2 + 1)

Multiplying both sides by the denominator (s^2 - 4s + 5), we get:

1 = A(s - 2)(s^2 + 1) + B(s^2 + 1) + C(s - 2)^2

Setting s = 2, we get:

1 = B

Setting s = 0, we get:

1 = A(2)(1) + B(1) + C(2)^2

1 = 2A + B + 4C

Setting s = 1, we get:

1 = A(-1)(2) + B(1) + C(1 - 2)^2

1 = -2A + B + C

Solving this system of equations, we get:

A = -1/4

B = 1

C = 3/4

Therefore,

1/(s^2 - 4s + 5) = -1/4/(s - 2) + 1/(s - 2)^2 + 3/4/(s^2 + 1)

Taking the inverse Laplace transform of both sides, we get:

f(t) = -1/4 e^(2t) + t e^(2t) + 3/4 sin(t)

Therefore, the solution to the given differential equation is:

f(t) = -1/4 e^(2t) + t e^(2t) + 3/4 sin(t)

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Answer:

30 miles

Step-by-step explanation:

Step-by-step explanation:

f(x)=(30x-2)

then,

f(3)=(30×3-2)

=90-2

=88 hope so,

Answer:

If we’re asked for f(3), we will place 3 instead of x

30×3=90

So,

90-2=88

f(x)=88

Step-by-step explanation:

I hope this helps, please give me brainliest

Answer:

The increase is 53,57%.

Step-by-step explanation:

This problem is solved by the rule of 3. It's necessary verify the proportionality. On the both sides it's directly propose, so it's necessary multiply crossed:

2800 _____> 100%

4300 _____> x

2800 * x = 4300 * 100

x = (4300 * 100)/2800

x = 153,57%

153,57% - 100% = 53,57%, that's the answer

Answer:

736in²

Step-by-step explanation:

8+10+8+10=36

36x16=576

10x8x2=160

576+160=736in²

Given: RS and TS are tangents to the circle V at R and T, respectively, and intersect at the exterior point S.Prove: m∠RST= 1/2(m(QTR)-m(TR))

Let us consider a circle V with two tangents RS and TS at points R and T respectively as shown below. In order to prove the given statement, we need to draw a line through T parallel to RS and intersects QR at P.As TS is tangent to the circle V at point T, the angle RST is a right angle.

In ΔQTR, angles TQR and QTR add up to 180°.We know that the exterior angle is equal to the sum of the opposite angles Therefore, we can say that angle QTR is equal to the sum of angles TQP and TPQ. From the above diagram, we have:∠RST = 90° (As TS is a tangent and RS is parallel to TQ)∠TQP = ∠STR∠TPQ = ∠SRT∠QTR = ∠QTP + ∠TPQThus, ∠QTR = ∠TQP + ∠TPQ Using the above results in the given expression, we get:m∠RST= 1/2(m(QTR)-m(TR))m∠RST= 1/2(m(TQP + TPQ) - m(TR))m ∠RST= 1/2(m(TQP) + m(TPQ) - m(TR))m∠RST= 1/2(m(TQR) - m(TR))Hence, proved that m∠RST = 1/2(m(QTR) - m(TR))

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The value of the 500cm expressed in the unit of meter is 0.5 m

A conversion factor is a ratio or proportion that can be calculated mathematically to change one unit of measurement into another. It enables you to change the units in which a quantity is expressed without altering its value.

The equivalency between two dissimilar units of measurement yields conversion factors.

We know that;

1000 cm makes 1 m

500 cm = 500 cm * 1 m/1000 cm

= 0.5 m

Thus in the unit of meters we are going to have 0.5 m

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Step-by-step explanation:

What you do pretty much is combine the parts with f and combine the regular numbers

\( - 2.6f + 0.3f = - 2.3f\)

\( - 15 - 4 = - 19\)

\( - 2.3f - 19\)

Answer:four eighth notes

Step-by-step explanation:

Juan can expect to win about 83 cents for his $2 raffle ticket. However, it's important to note that this is just an average, and he may win more or less than this amount depending on the luck of the draw.

The expected value of Juan's ticket can be calculated by multiplying the probability of winning each prize by the amount of money that is won for that prize, and then adding up the products. There are 8 total prizes, so the probability of winning each prize is:
- 5/300 for the $5 prize
- 2/300 for the $50 prize
- 1/300 for the $100 prize
To calculate the expected value, we can use the following formula: (expected value) = (probability of winning prize 1) x (amount won for prize 1) + (probability of winning prize 2) x (amount won for prize 2) + ... + (probability of winning prize 8) x (amount won for prize 8)
So, the expected value for Juan's ticket would be: (expected value) = (5/300) x $5 + (2/300) x $50 + (1/300) x $100 - $2
(expected value) = $0.83

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Answer:

\( = > 10 \times 5 \times 13\)

\( = > 50 \times 13\)

\( = > 650\)

First pump can fill the tank in 4 hours. So, In 1 hour it fill 1/4 of the tank.

Second pump 1/3

Third one, 1/4

If three pumps are used at the same time, then in 1 hour they will fill

1/4 + 1/3 + 1/4 = 5/6

Therefore tank will be full = 1 ÷ 5/6 = 1.2 hours or 1 hour and 12 minutes

Using the appropriate arithmetic operations, the amount of change Travis is entitled to is :$6.50

Total cost of paper back books :

Total cost of hardcover books :

Total cost = $7.50 + $6.00 = $13.50

Change = $20 - $13.50 = $6.50

Therefore, Travis will get a change of $6.50

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Answer:(8x+24)(2x+1)

Step-by-step explanation: I dont know if im right but i think if the equation was 8(x-3)(2x+1) so if I distributed then the answer turnt out to be (8x+24)(2x+1) so im guessing thats the answer.............(8x+24)(2x+1) equals 16x^2+56x+24

Answer:

(8x+24)(2x+1)

Step-by-step explanation:

Answer:

The answer is C. 6ft 2

Step-by-step explanation:

The area of the rectangle having the dimension 3 feet by 2 feet is 6 square feet. Then the correct option is C.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.

A rectangle is 3 feet wide and 2 feet high.

Then the area of the rectangle will be

Area = Length × Width

Area = 3 × 2

Area = 6 ft²

The area of the rectangle is 6 square feet.

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