Construct a polynomial function with the following properties: fifth degree, 2 is a zero of multiplicity 4, −2 is the only other zero, leading coefficient is 3.

First, you should simplify the function expression.

3(x2 + 10x + 5) - 5(x-k) = 3x2 + 30x + 15 - 5x + 5k = 3x2 +15x +15 +5k

In order for the polynomial to be divisible by x, all terms need to divide by x with no remainder.  The first two terms clearly divide by x.  However, the last two do not.  In order for this to work out where k is constant, 5k would have to cancel out the  +15 term, leaving nothing to divide by x.

So: 15 + 5k = 0

5k = -15

k = -3

The intensity of sound which the decibel level of the sound measures 156 is 3.981 × 10³ W/m²

Decibel level, dB = 10log₁₀(I/I₀) where dB = decibel level = 156, I = intensity at 156 dB and I₀ = 10⁻¹² W/m².

Since we require I, making I subject of the formula, we have

dB/10 = log₁₀(I/I₀)

[tex]\frac{I}{I_{0} } = 10^{\frac{dB}{10} } \\I = I_{0} 10^{\frac{dB}{10} }[/tex]

Substituting the values of the variables into the equation, we have

[tex]I = I_{0} 10^{\frac{dB}{10} }\\I = 10^{-12} 10^{\frac{156}{10} }\\I = 10^{-12} 10^{15.6}\\I = 10^{15.6-12} \\I = 10^{3.6} W/m^{2}[/tex]

I = 3981.072W/m²

I = 3.981 × 10³ W/m²

So, the intensity of sound which the decibel level of the sound measures 156 is 3.981 × 10³ W/m²

Learn more about intensity of sound here:

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26

the number line ticks count by 2

hope this helped :)

Answer:

3.657 and 7.657 to the nearest thousandth.

Step-by-step explanation:

x - y = 4

x^2 + y^2 = 72

From equation 1

x = y + 4 so

(y + 4)^2 + y^2 = 72

y^2 + 8y + 16 + y^2 - 72 = 0

2y^2 + 8y - 56 = 0

y^2 + 4y - 28 = 0

y = 3.657.

so x = 7.657.

Answer:

A Least Square Regression Line is the best thing to use for this because there is inconsistencies and no direct equation to be able to fill all of these points. They may be outliers and therefore we should use a calculator for a Regression Line to be calculated to find the residual.

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

8×3²

=8×9

=72

so it is the answer

Answer:

d. -6x + 2 = -15

Answer:

$32.50

Step-by-step explanation:

The equation for simple interest is

Simple Interest=P×r×n

where:

P=Principal amount

r=Annual interest rate

n=Term of loan, in years

​so

P=200

r=0.0325

n=5

so 200*0.0325*5=32.5

Answer:

Domain: (0,1,23)

Range: (0.35,1.35,2.35)

Step-by-step explanation: The domain is the set of all the first components of the ordered pairs, and the range is the set of all the second components of the ordered pairs.

Answer:

y=0x+2

Step-by-step explanation:

Answer:

the answer based on the information provided is c + 8

Step-by-step explanation:

8 added to C is c + 8, since they are unlike terms

Step- by - Step Explanation:

Area of a circle=πr²

=3.14...×6²

=113.0973355292325

Approximately ≈113.1cm²

Please mark BRAINLIEST if I'm right.

Answer:

C) Little Rock’s temperature < Lincoln’s temperature

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

The answer would be C.

Little Rock's temperature is less than Lincoln's temperature.

66 < 82

Answer:

F(x)=(x+6)^2

Step-by-step explanation:

Hope this helps!

Answer:

7°

Step-by-step explanation:

simple arithmetic duh

[tex]y = -\frac{1}{9}(x - 1)^2 - 6[/tex]

Step-by-step explanation:

The vertex form of the equation for a parabola is given by

[tex]y = a(x - h)^2 + k[/tex]

where (h, k) are the coordinates of the parabola's vertex. Since the vertex is at (1, -6), we can write the equation as

[tex]y = a(x - 1)^2 - 6[/tex]

Also, since the parabola passes through (4, -7), we can use this to find the value for a:

[tex]-7 = a(4 - 1)^2 - 6 \Rightarrow -7 = 9a - 6[/tex]

or

[tex]a = -\frac{1}{9}[/tex]

Therefore, the equation of the parabola is

[tex]y = -\frac{1}{9}(x - 1)^2 - 6[/tex]

Answer:

24

Step-by-step explanation:

You're given a side and a hypotenuse in a right triangle, so you're able to use the Pythagorean Theorem.

[tex]a^{2} + b^{2} = c^{2}\\\\a^{2} + (7)^{2} = (25)^{2}\\[/tex]

Now isolate a on one side and solve for a.

[tex]\\a^{2} = (25)^{2} - (7)^{2}\\\\a = \sqrt{(25)^{2} - (7)^{2}} \\\\a = 24[/tex]

4x + 3 = -5x + 21

9x + 3 = 21

9x = 18

x = 2

Hope this helps!! :)

Answer:

x=2

Step-by-step explanation:

4x + 3 = -5x + 21

Answer:

hey man i need a screenshot or something

Step-by-step explanation:

Lotion - Liquid

Suspension - semisolid

Capsule - solid

hope this helps: )

Answer:

ITS D GOOD LUCK WITH YOUR HMK

Answer:

=2691

Step-by-step explanation:

=2700+35−44

=2735−44

=2691

Answer:

your answer is 3/15

Step-by-step explanation:

if im wrong pls let me know

We want to find a graph that represents Noah's average speed.

We define the average speed as the quotient between the distance moved and the time it takes to move that distance, then in this case we will have:

s = 12ft/6s = 2ft/s

Then we can define a linear equation:

y = (2ft/s)*x

As the distance that Noah travels in x seconds.

The graph of the given linear function can be seen below, and that is the graph with the slope that best represents Noah's average speed.

If you want to learn more, you can read:

https://brainly.com/question/11897796

Answer:

9000

Step-by-step explanation:

Answer:

8:36

Step-by-step explanation:

if you sharpened 8 pencils out of 44 that means 8 pencils are sharpened and the other 36 aren't

Answer:

< 2 = 35 degrees and

<3 = 55 degrees

Step-by-step explanation:

<3 = 90-35

= 55 degrees

<1 = 90 degrees

<2 = 180 - 90 - 55

= 35 degrees