what value in place of the question mark makes the polynomial below a perfect square trinomial? 9x2+?x+49

Mathematics

2 answers:

Alchen [17]3 years ago

3 0

the missing number should be the square root of the last number times 2 for a perfect trinomial

so square root of 49 = 7

7*2 =14

so the missing number should be 14

swat323 years ago

3 0

U take the sqrt of the first term, which happens to be 3x...then u take the square root of the 3rd term, which is 7, then u multiply that product by 2....
3x * 7 = 21x.....21x * 2 = 42x

lets check..
9x^2 + 42x + 49 = (3x + 7)^2...correct

so ur middle term will be 42x

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Please help Find the measure of UT 65° 51° 70° 55°

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$\huge\boxed{55^\circ}$

First of all, we know that $\angle Q=95^{\circ}$ because of its vertical angle. $\angle Q$ is also equal to $\dfrac{\widehat{RS}+\widehat{UT}}{2}$ because it's an interior angle.

$\begin{aligned}\angle Q&=\frac{\widehat{RS}+\widehat{UT}}{2}\\95^\circ&=\frac{135^\circ+\widehat{UT}}{2}&&\qquad&&\textsf{Substitute in the known values.}\\190^\circ&=135^\circ+\widehat{UT}&&\qquad&&\textsf{Multiply both sides by $2$.}\\55^\circ&=\widehat{UT}&&\qquad&&\textsf{Subtract $135^\circ$ from both sides.}\\\widehat{UT}&=\boxed{55^\circ}&&\qquad&&\textsf{Switch the sides of the equation to show our answer.}\end{aligned}$