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3 years ago

The diagram to the right shows a reflection across a line. Find the value of each variable.

Mathematics

2 answers:

puteri [66]3 years ago

7 0

From the diagram, we can conclude that 5x = 15, 4y = 8, and 2z - 1 = 24.From that, we solve and get x = 3, y = 2, and z = 12.5

Hope this helps!

nydimaria [60]3 years ago

4 0

5x = 15

x = 3 <===== x is here

4y = 8

y = 2 <===== y is here

2z - 1 = 24

2z = 25

z = 12.5 <===== z is here

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44 is equal to 8 times a number minus 4. what is the number?

postnew [5]

Answer:

Step-by-step explanation:

Let "a number" = x

44 = 8x - 4

Simplify. Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First add 4 to both sides:

44 (+4) = 8x - 4 (+4)

44 + 4 = 8x

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Isolate the variable, x. Divide 8 from both sides:

(48)/8 = (8x)/8

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6 is your answer.

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3 years ago

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The value of U.S exports to China increased from $1480 million in 2011 to $2768 million

aliya0001 [1]

The percentage of increase was 87.027... %

Explanation

The value of U.S exports to China increased from $1480 million to $2768 million.

Suppose, the percentage of increase is $x\%$

So, the amount of increase = $x\%$ of 1480 $=1480*\frac{x}{100}=14.8x$

Thus, the equation will be......

$14.8x= 2768-1480\\ \\ 14.8x=1288\\ \\ x= \frac{1288}{14.8}=87.027....$

So, the percentage of increase was 87.027... %

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3 years ago

One leg of a right triangle is 28 inches longer than the other leg, and the hypotenuse is 52 inches. Find the lengths of the leg

katovenus [111]

Step-by-step explanation:

Let x represent the missing sides measurement.

x+x+28=52

combine like terms

2x + 28 = 52

subtract 28 from both sides

2x + 28 = 52

- 28 - 28

2x = 24

divide both sides by 2

x = 12

plug it back in

one leg is 12 inches

the other leg is 40 inches

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2 years ago

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2 years ago

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What is the length of EF in the triangle? Show your work. HELP!

Zinaida [17]

The length of EF in the given triangle is 8.80 m.

Step-by-step explanation:

Step 1:

In the given triangle, the opposite side's length is 16.2 m, the adjacent side's length is x m while the triangle's hypotenuse measures 16.2 m units.

The angle given is 90°, this makes the triangle a right-angled triangle.

So first we calculate the angle of E and use that to find x.

Step 2:

As we have the values of the length of the opposite side and the hypotenuse, we can calculate the sine of the angle to determine the value of the angle of E.

$sinE = \frac{oppositeside}{hypotenuse} =\frac{13.6}{16.2} = 0.8395.$

$E = sin^{-1} (0.8395), E = 57.087.$

So the angle E of the triangle DEF is 57.087°.

Step 3:

As we have the values of the angle and the hypotenuse, we can calculate the cos of the angle to determine x.

$cos E = \frac{adjacentside}{hypotenuse} = \frac{x}{16.2} .$

$cos(57.087) = 0.5433, x = 16.2 (0.5433) = 8.8014.$

Rounding this off to the nearest hundredth, we get x = 8.80 m.

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3 years ago