In ΔKLM, l = 820 cm, m = 560 cm and ∠K=169°. Find the length of k, to the nearest centimeter.

Answer:

The answer is C, 40.32

Step-by-step explanation:

If you put 6.25 in your calculator times 40.32% you get 2.52. Then you add the 2.52 to 6.25 to get 8.77.

Here we have a problem of rates of work, we want to know how long will take the 3 ants to build an ant hill if they work together.

We will find that working together, they need to work for 8 hours.

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Let's start by defining the variables that we will use:

Now let's see the given information:

"Aran and Beatrice can build an ant hill in 10 hours"

This can be written as:

(A + B)*10 h = 1 ant hill

"Aran and Charlie can build the ant hill in 12 hours"

This can be written as:

(A + C)*12 h = 1 ant hill

"Beatrice and Charlie can build the ant hill in 15 hours"

This can be written as:

(B + C)*15 h = 1 ant hill.

Then we have 3 equations:

[tex](A + B)*10 h = 1[/tex]

[tex](A + C)*12 h = 1[/tex]

[tex](B + C)*15 h = 1[/tex]

Where for commodity, I removed the "ant hill" unit.

Now we need to solve this system of equations, to do it, we need to isolate one variable in one of the equations and then replace it on another equation.

I will isolate A in the first equation:

[tex]A = \frac{1}{10h} - B[/tex]

Now we can replace it in the second equation to get:

[tex](\frac{1}{10h} - B + C)*12h = 1[/tex]

Now we can isolate C in the last equation to get:

[tex]C = \frac{1}{15h} - B[/tex]

Replacing that in the above equation we get:

[tex](\frac{1}{10h} - B + \frac{1}{15h} - B)*12h = 1\\\\\frac{1}{6h} - \frac{1}{12h}= 2*B\\\\\frac{1}{2}*\frac{1}{12h} = \frac{1}{24h} = B[/tex]

This means that Beatrice alone would construct the hill in 24 hours.

Now that we know the value of B, we can use:

[tex]C = \frac{1}{15h} - B = \frac{1}{15h} - \frac{1}{24h} = \frac{1}{40h}[/tex]

This means that Charlie needs 40 hours to finish the hill alone.

Finally, we can use [tex]A = \frac{1}{10h} - B[/tex] to find the value of A:

[tex]A = \frac{1}{10h} - B = \frac{1}{10h} - \frac{1}{24h} = \frac{7}{120h}[/tex]

Now if the 3 ants work together, the total rate at which they work is:

[tex](A + B + C) = (\frac{7}{120h} + \frac{1}{40h} + \frac{1}{24h} ) = 0.125 h^{-1}[/tex]

This means that they need to work for the inverse of that rate

[tex]\frac{1}{0.125h^{-1}} = 8h[/tex]

Working together, they need to work for 8 hours to complete an ant hill

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Answer:

Step-by-step explanation:

Answer:

= 2 and 5

Step-by-step explanation:

( 4 - 7x ) + ( 2x - 2 ) = 0

4 - 7x = 2x - 2 = 0

-7x -2x - 2 + 4 = 0

  -5x   - 2   = 0

-5 x = 0                  or             -2 = 0

x = 5                                       x = 2

Answer:

2223

Step-by-step explanation:

We need to find the value of 2021-2223+2425.

Firstly subtract 2223 from 2021.

2021-2223 = -202

Now add -202 and 2425. So,

2425 +(-202) = 2223

So, the value of 2021-2223+2425 is 2223. Hence, this is the required solution.

Answer:

A notebook at the dollar store costs between 1-2 dollars

Answer:

A

Step-by-step explanation:

Answer:

AA~

Step-by-step explanation:

These triangles are similar but not congruent. One triangle is bigger than the other, meaning none of the side lengths are the same. On the triangles, two angles are given, a 53 degree and a 90 meaning that you would us the AA rule to determine if they are similar. Which they are.

The two triangles are similar triangles using AA postulate.

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".

Given one of the angles in both the triangles is equal to 53°, the other angle is 90°, which are also the vertical angles to each other. As shown below.

Hence, the two triangles are similar triangles using AA postulate.

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Answer:

The solution to the system of equations is:

[tex]x=10,\:y=4[/tex]

Step-by-step explanation:

Given the system of equations

[tex]\begin{bmatrix}5x-4y=34\\ -x+8y=22\end{bmatrix}[/tex]

Multiply -x+8y=22 by 5:  -5x+40y=110

[tex]\begin{bmatrix}5x-4y=34\\ -5x+40y=110\end{bmatrix}[/tex]

so adding the equations

[tex]-5x+40y=110[/tex]

[tex]+[/tex]

[tex]\underline{5x-4y=34}[/tex]

[tex]36y=144[/tex]

solve 36y = 144 for y:

[tex]36y=144[/tex]

divide both sides by 36

[tex]\frac{36y}{36}=\frac{144}{36}[/tex]

Simplify

[tex]y=4[/tex]

For 5x-4y=34 plug in y=4

[tex]5x-4\cdot \:4=34[/tex]

[tex]5x-16=34[/tex]

Add 16 to both sides

[tex]5x-16+16=34+16[/tex]

Simplify

[tex]5x=50[/tex]

Divide both sides by 5

[tex]\frac{5x}{5}=\frac{50}{5}[/tex]

Simplify

[tex]x=10[/tex]

Therefore, the solution to the system of equations is:

[tex]x=10,\:y=4[/tex]

Answer:

1. 18

2. 370

3. 65

Step-by-step explanation:

1. 180/10=18

2. 370 add a zero

3. tens means ·10 so 650/10=65

Answer:

1.)18

2.)370

3.)65 tens yw(:

Answer:

17 students

Step-by-step explanation:

If he started with 37 and ended with 3 we have to subtract those three first so that we know how many we are actually working with so, 37-3=34. 34 balls is the amount distributed among the class. 34/2 is 17.

Answer:

y=-15

.2020202020charactersneeded

Answer:

0.08522

Step-by-step explanation:

Answer: x=-6 1/4

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:

Candy bars: $13

Step-by-step explanation:

$3 magazine + $13 total of candy bars = $19

Answer:

-2

Step-by-step explanation:

-4-(-2) = -2

-6-(-4) = -2

The perimeter of the rectangle is 70cm.

Perimeter is the total length of the sides of a two-dimensional shape.

Perimeter of the square is given by

P = 4a

where,

a is the side length of the square.

P is the perimeter of the square.

Perimeter of the rectangle is given by

P = 2( l + b)

Where,

l is the of the rectangle

b is the breadth of the the rectangle

According to the given question.

We have the perimeter of the square is 20cm.

⇒ 4a = 20

⇒ a = 5cm

⇒ Each side length of the square is 5cm

And a rectangle made of 10 squares.

⇒ length of the rectangle = 5×5 = 25cm

and the breadth of the rectangle = 2 × 5 = 10cm

Therefore, the perimeter of the rectangle = 2(25 + 10) = 2 × 35 = 70cm

Hence, the perimeter of the rectangle is 70cm.

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Answer:

26x2,

52xπ

Step-by-step explanation:

The perimeter of this semi-circle with a radius of 26 cm will be 81.64 cm.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let 'r' be the radius of the circle. The circumference of the circle will be

C = 2πr units

The radius of the semicircle is given as,

r = 26 cm

Then the circumference of the semicircle is half of the circle. Then we have

C = 1/2 x 2πr

C = πr

At r = 26 cm, then we have

C = 3.14 x 26

C = 81.64 cm

The perimeter of this semi-circle with a radius of 26 cm will be 81.64 cm.

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Answer:

y = 3x -2

Step-by-step explanation:

The general equation form is;

y = mx + b

where m is the slope and b is the y-intercept

For the equation given;

y = 3x -5

the slope from here is 3

If two lines are parallel, they have equal slopes

This mean that the slope of the line we want to calculate too is 3

Now we can use the point slope format to get the correct equation

y-y1 = m(x-x1)

y+ 5. = 3(x+ 1)

y = 3x + 3 -5

y = 3x -2

Answer:

56 screws

Step-by-step explanation:

So, first we can find how many screws he needs.

So,  if he uses 2 steps for 8 screws, and has 14 steps, that means he puts screws in 7 steps ( 14÷2)

then, if he uses 8 screws, each with 8 steps, we can do 8 times 7, which is 56 screws

The screws does Jonathan need is  56 screws.

It is required to find how many screws does Jonathan need.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Jonathan uses 8 screws for every 2 steps. If there are 14 steps.

So, first we can find how many screws he needs.

According to given question we have

So,  if he uses 2 steps for 8 screws, and has 14 steps, that means he puts screws in 7 steps ( 14÷2)

then, if he uses 8 screws, each with 8 steps, we can do 8 times 7, which is 56 screws.

Therefore, the screws does Jonathan need is  56 screws.

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Answer:

Train A is 287 tons

Train B is 94 tons

Step-by-step explanation:

My method of solving it may have been a bit different from how you were taught. I divided 381 by 2 to give both trains an equal weight of 190.5 tons. I then divided the difference, 193, by 2 to get 96.5 tons. I subtracted the new difference from the weight of Train B and added it to train A. To double check, you can grab a calculator and see that their weights are equal to 381.

Answer:

12

Step-by-step explanation: 18/3=6 6(2)= 12

To find the equation of a perpendicular line, you first need to find the negative reciprocal of the slope given. The slope is -1/3, so the slope of the perpendicular line will be 3

Now we just need to find the y intercept using the point (3, 2) and you can plug the coordinates in and then solve for b. Let's see what that looks like.

y=3x+b

2=3*(3)+b

2=9+b

-7=b  So now we know the y-intercept and slope. We just put them together now

y=3x-7

Answer:

Say you have y=2x. That is direct variation and will always pass through the origin when graphed. When x is multiplied by a number, the y value will also be changed by that number. If you add a y-intercept and change y=2x to, for example, y=2x+2, the x and the y will no longer be related by a constant ratio.

Step-by-step explanation:

Answer:

A. President Millard Fillmore