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Nataly [62]
2 years ago
9

Please help! If the two triangles are similar, which equation represents the value of side x?

Mathematics
1 answer:
madam [21]2 years ago
5 0

x=\frac{p q}{m} equation represents the value of side x.

Solution:

The two triangles are similar.

<em>If two triangles are similar, then the corresponding sides are in proportional.</em>

$\Rightarrow \frac{m}{p} =\frac{q}{x}

Do cross multiplication.

$\Rightarrow mx=pq

Divide by m on both sides.

$\Rightarrow \frac{mx}{m} =\frac{pq}{m}

$\Rightarrow x =\frac{pq}{m}

Therefore, x=\frac{p q}{m} equation represents the value of side x.

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The solution to the system -2x+5y=-15 and 5x+2y=-6 is what
cupoosta [38]

Step-by-step explanation:

−2x+5y=−15 and 5x+2y=−6

Rewrite equations:

−2x+5y=−15;5x+2y=−6

Step: Solve−2x+5y=−15for x:

−2x+5y=−15

−2x+5y+−5y=−15+−5y(Add -5y to both sides)

−2x=−5y−15

−2x−2=−5y−15−2(Divide both sides by -2)

x=52y+152

Step: Substitute52y+152forxin5x+2y=−6:

5x+2y=−6

5(52y+152)+2y=−6

292y+752=−6(Simplify both sides of the equation)

292y+752+−752=−6+−752(Add (-75)/2 to both sides)

292y=−872

292y292=−872292(Divide both sides by 29/2)

y=−3

Step: Substitute−3foryinx=52y+152:

x=52y+152

x=52(−3)+152

x=0(Simplify both sides of the equation)

Answer:

x=0 and y=−3

8 0
2 years ago
Jacob decided to ride his bicycle across the country during his 2-month summer vacation. the route he took from washington, dc t
Artist 52 [7]

Step 1: Assign variable for the unknown that we need to find.

Let ' x ' be the number of miles traveled by Jacob so far (His distance from starting point)

Step 2: Use the sentence given to set up an equation

Sentence 1: "His distance from his starting point was exactly 100 miles more than three times the distance remaining until the finishing point"

Total distance is 2800 miles, if his distance from the starting point is 'x', then remaining distance can be represented by 2800 - x.

Using the sentence we can write the below equation...

x = 100 + 3(2800 - x)

Distributing 3 in the right side of the equation, we get...

x = 100 + 8400 - 3x

Adding 3x on both sides of the equation, we get...

x+3x = 8500

Combine like terms in the left side of the equation, we get...

4x=8500

Dividing 4 on both sides of the equation, we get...

\frac{4x}{4} =\frac{8500}{4}

Simplifying the fraction on either side of the equation, we get...

x=2125miles

Conclusion:

Out of the 2800 miles, Jacob travelled a distance of 2125 miles and remaining miles that he need to cover will be <u>675 miles</u>.

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