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Leno4ka [110]
2 years ago
7

What is the expression in factored form x^2+13x+42

Mathematics
2 answers:
omeli [17]2 years ago
8 0
The correct answer is (x+6)(x+7). Great job.
Sveta_85 [38]2 years ago
8 0

we have

x^{2} +13x+42

Find the factors

Equate the equation to zero

x^{2} +13x+42=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

x^{2} +13x=-42

Complete the square. Remember to balance the equation by adding the same constants to each side

x^{2} +13x+6.5^{2}=-42+6.5^{2}

x^{2} +13x+42.25=-42+42.25

x^{2} +13x+42.25=0.25

Rewrite as perfect squares

(x+6.5)^{2}=0.25

Square root both sides

(x+6.5)=(+/-)\sqrt{0.25} \\ \\x+6.5=(+/-)0.50 \\ \\x=-6.5(+/-) 0.50

x1=-6.5+0.50=-6

x2=-6.5-0.50=-7

therefore

<u>the answer is</u>

(x+6)(x+7)

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Convert the fraction to higher terms. Enter the value of the missing numerator. 3/11= /77?
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What is the interest rate of each investment if The annual interest on a $17,000 investment exceeds the interest earned on an $8
Butoxors [25]

<u>Solution-</u>

Let's assume, the rate of interest of $8000 is x%,

then the rate of interest of $17000 is (x+0.3x) =1.3x%

Interest earned by $8000,

i_1=\frac{8000\times x\times 1}{100} =80x

Interest earned by $17,000,

i_2=\frac{17000\times 1.3x\times 1}{100} =221x

According to the question,

\Rightarrow i_1=i_2+276

\Rightarrow 221x=80x+276

\Rightarrow 221x-80x=276

\Rightarrow 141x=276

\Rightarrow x=1.96

∴ Rate of interest of $8000 is 1.96% and rate of interest of $17000 is (1.3×1.96) =2.55%

3 0
2 years ago
Please help ( the function table)
Norma-Jean [14]
Hope this will help

8 0
3 years ago
The water reaches a max height when the horizontal distance from the firefighter to the building is approximately __m. Round to
elena-s [515]

The horizontal distance from the firefighter at which the maximum height of water occurs is 10.83m

<u>Explanation:</u>

Given:

h(x) = -0.026x² + 0.563x + 3

where,

h(x) is the height of the water

Initial speed, u = 14m/s

angle, θ = 30°

(a)

Horizontal distance = ?

h(x) = ax² + bx + c

the vertex is found at x = -b/2a

where,

x = distance to the maximum height

As compared to the equation given:

a = -0.026

b = 0.563

Thus,

x = \frac{-0.563}{2 X -0.026} \\\\x = \frac{0.563}{0.052}\\ \\x = 10.83m

Therefore, horizontal distance from the firefighter at which the maximum height of water occurs is 10.83m

3 0
3 years ago
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