Let f(x) = ax³ + 9x² + 4x – 10
g(x) = 0⇒x - 3 = 0
⇒ x = 0 + 3
⇒ x = 3
On dividing f(x) by x - 3, it leaves a remainder 5.
Now keeping, f(3) = 5
⇒a(3)³ + 9(3)² + 4(3) - 10 = 5
⇒ a × 27 + 9 × 9 + 4 × 3 - 10 = 5
⇒ 27a + 81 + 12 - 10 = 5
⇒ 81 + 12 - 10 - 5 = 27a
⇒ 81 + 12 - 15 = 27a
⇒ 93 - 15 = 27a
⇒ 78 = 27a
⇒ a = 27/78
⇒ a = 0.3461
We know the algebraic rule
A polynomial having degree n has n no of zeros .
As her the degree is 1 the function has 1 zeros and is linear
Option A
Let's find the value
7-3(2x-4)=-29
Answer: 210 beats
Step-by-step explanation:
Given: A song has 28 beats in 4 seconds.
To find the rate of beats in song we need to divide 28 by 4, we get
⇒ Beats in each second of song=![\frac{28}{4}=7\text{ beats}](https://tex.z-dn.net/?f=%5Cfrac%7B28%7D%7B4%7D%3D7%5Ctext%7B%20beats%7D)
To find the number of beats in 30 seconds, we need to multiply 30 to the rate of beats, we get
⇒Beats in 30 seconds of song=![7\times30=210\text{ beats}](https://tex.z-dn.net/?f=7%5Ctimes30%3D210%5Ctext%7B%20beats%7D)
Hence, there are 210 beats in 30 seconds of song.
Answer:
The height of the prism is 5 inches
Step-by-step explanation:
The rule of the lateral area of the rectangular prism is
L.A = 2(L + W) × H, where
- L is the length of the base of the prism
- W is the width of the base of the prism
- H is the height of the prism
∵ A rectangular prism has a length of 9 inches and a width of 8 inches
∴ L = 9 inches
∴ W = 8 inches
∵ The lateral area of it is 170 square inches
∴ L.A = 170 square inches
→ Substitute them in the rule above to find the height of the prism
∵ 170 = 2(9 + 8) × H
∴ 170 = 2(17) × 5
∴ 170 = 34 × H
→ Divide both sides by 34 to find H
∴ 5 = H
∴ The height of the prism is 5 inches.
Answer: f(x) and g(x) are inverses of each other
<u>Step-by-step explanation:</u>
To find the inverse of a function, swap the x's and y's and then solve for "y"
f(x) = 5x + 2
y = 5x + 2
Swap:
x = 5y + 2
<u> -2 </u> <u> - 2 </u>
x - 2 = 5y
<u>÷5 </u> <u>÷5 </u>
![\dfrac{x-2}{5}=y](https://tex.z-dn.net/?f=%5Cdfrac%7Bx-2%7D%7B5%7D%3Dy)
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![g(x)=\dfrac{x-2}{5}\\\\y=\dfrac{x-2}{5}\\\\\text{Swap:}\\x=\dfrac{y-2}{5}\\\\\\(5)x=\dfrac{y-2}{5}(5)\\\\\\5x=y-2\\\\5x+2=y](https://tex.z-dn.net/?f=g%28x%29%3D%5Cdfrac%7Bx-2%7D%7B5%7D%5C%5C%5C%5Cy%3D%5Cdfrac%7Bx-2%7D%7B5%7D%5C%5C%5C%5C%5Ctext%7BSwap%3A%7D%5C%5Cx%3D%5Cdfrac%7By-2%7D%7B5%7D%5C%5C%5C%5C%5C%5C%285%29x%3D%5Cdfrac%7By-2%7D%7B5%7D%285%29%5C%5C%5C%5C%5C%5C5x%3Dy-2%5C%5C%5C%5C5x%2B2%3Dy)