<img src="https://tex.z-dn.net/?f=%20%7B16x%7D%5E%7B2%7D%20%20%20%20%2B%208x%20%2B%201" id="TexFormula1" title=" {16x}^{2} +

timurjin [86]

3 years ago

8x + 1" alt=" {16x}^{2} + 8x + 1" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

Musya8 [376]3 years ago

4 0

${16x}^{2} + 8x + 1 = (4x + 1)(4x + 1) = (4x + 1)^2$

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What is the product of all constants $k$ such that the quadratic $x^2 + kx +15$ can be factored in the form $(x+a)(x+b)$, where

Setler79 [48]

Answer:

$k=-16,k=-8,k=8,k=16$

Step-by-step explanation:

We are given quadratic equations as

$x^2+kx+15$

and it can be factored as

$=(x+a)(x+b)$

now, we can multiply factor term

$(x+a)(x+b)=x^2+(a+b)x+ab$

now, we can compare

$x^2+(a+b)x+ab=x^2+kx+15$

so, we get

$k=a+b$

$ab=15$

we are given that

'a' and 'b' are integers

so, we can find all possible factors

$15=(-1\times -15),(1\times 15)$

$15=(-3\times -5),(3\times 5)$

so, we can find k

At $(-1\times -15)$ :

$k=a+b$

we can plug values

$k=-1-15$

$k=-16$

At $(1\times 15)$ :

$k=a+b$

we can plug values

$k=1+15$

$k=16$

At $(-3\times -5)$ :

$k=a+b$

we can plug values

$k=-3-5$

$k=-8$

At $(3\times 5)$ :

$k=a+b$

we can plug values

$k=3+5$

$k=8$

So, values of k are

$k=-16,k=-8,k=8,k=16$

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The sum of the measures of angle Y and angle Z is 180 degrees. Angle Y measures (3x + 20) degrees and Angle Z measures x degrees

Minchanka [31]

A)
The question tells us that
y + z = 180
And
y=3x+20
z=x

So we put them in the first formula:

y + z = 180
(3x + 20) + x = 180

Add and get x to one side:
4x + 20 = 180
4x + 20 - 20 = 180-20
4x = 160
Divide both sides by 4
x = 40

B)
Put x back in to equation to get size of each angle:

Y =3x +20
Y=3(40)+20
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Z=x
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Verify: y+z=180
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