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3 years ago

PQ= 2x +1 and QR= 5x - 44; find PQ

Mathematics

2 answers:

Lena [83]3 years ago

6 0

2x+1=5x-44 that would be your equation

next start to simplify

subtract 1 from both sides so you are left with 2x=5x-45

then subtract 5x from both sides and you have -3x=-45

then finally divide -3 from -45 to get x=15

vova2212 [387]3 years ago

6 0

Answer:

$PQ=31\ units$

Step-by-step explanation:

we know that

In this problem Q is the midpoint of PR

$PQ=QR$

we have

$PQ=2x+1$ -----> equation A

$QR=5x-44$ -----> equation B

equate equation A and equation B

$2x+1=5x-44$

solve for x

$5x-2x=1+44$

$3x=45$

$x=15$

Find the value of PQ

$PQ=2x+1$ ------> $PQ=2(15)+1=31\ units$

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Ymorist [56]

By solving the quadratic equation using completing the square method we got that Penelope should have added 4 to both sides instead of adding 1.

<h3>What is quadratic equation ?</h3>

Any equation of the form $ax^2+bx+c=0$ where x is variable and a, b, and c are any real numbers where a ≠ 0 is called quadratic equation .

Given work of Penelope is

$\begin{aligned}&f(x)=4 x^{2}+8 x+1 \\&-1=4 x^{2}+8 x \\&-1=4\left(x^{2}+2 x\right) \\&-1+1=4\left(x^{2}+2 x+1\right) \\&0=4(x+2)^{2} \\&0=(x+2)^{2} \\&0=x+2 \\&-2=x\end{aligned}$

Now we can see that Penelope determined the solutions of the quadratic function by completing the square. so he must have been done as following

$\begin{aligned}&f(x)=4 x^{2}+8 x+1 \\&-1=4 x^{2}+8 x \\&-1=4\left(x^{2}+2 x\right) \\&-1+4=4\left(x^{2}+2 x+1\right) \\&3=4(x+2)^{2} \\&\frac{3}{4} =x+2)^{2} \\&\frac{\pm\sqrt3}{2} =x+2 \\&\frac{-2\pm\sqrt3}{2} =x\end{aligned}$

By solving the quadratic equation using completing the square method we got that Penelope should have added 4 to both sides instead of adding 1.

To learn more about quadratic equations visit : brainly.com/question/1214333

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