9514 1404 393
Answer:
p(x) = 3(x -2)^4(x +2) . . . in factored form
p(x) = 3x^5 -18x^4 +24x^3 +48x^2 -144x +96 . . . in standard form
Step-by-step explanation:
When a polynomial has a zero at x=p, it has a factor of (x -p). The exponent of the factor is the multiplicity of the zero. The product of factors can be multiplied by 3 to make the leading coefficient be 3.
p(x) = 3(x -2)^4(x -(-2))
= 3(x^4 +4(-2)x^3 +6(-2)^2x^2 +4(-2)^3x +(-2)^4)·(x +2)
= 3(x^4 -8x^3 +24x^2 -32x +16)(x +2)
= 3(x^5 -6x^4 +8x^3 +16x^2 -48x +32)
p(x) = 3x^5 -18x^4 +24x^3 +48x^2 -144x +96
Noah’s remote control car moved 12 feet in 6 seconds. Which graph has a slope that best represents Noah’s car’s average rate of speed?
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
after spending 5/6 of his January salary on paying school fees, Bikila was left with ksh 1500. how much money did he earn that month?
Answer:
9000
Step-by-step explanation:
equation of the parabola in vertex form that passes through (4,-7) and has a vertex of (1,-6)
[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]
can anyone heelp me pls pls
Lotion - Liquid
Suspension - semisolid
Capsule - solid
hope this helps: )
Estimate a 15% tip on a dinner bill of $39.42 by first rounding the bill amount to the nearest ten dollars.
Once the high temperature was 30°F. Then at night the temperature dropped by 23 degrees. does the expression 30 + (-23) mean the temperature at night? explain.
Answer:
7°
Step-by-step explanation:
simple arithmetic duh
What is the length of ef in the right triangle below?
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]
solve pls branliest !
Answer:
72
Step-by-step explanation:
8×3²
=8×9
=72
so it is the answer
Suppose z varies directly with x and inversely with the square of y . If z=18 when x=6 and y=5 , what is z when x=11 and y=10?
1/2 : 10 = 2 12 : x
What is the value of x
Joseph takes his little brother to the local frozen yogurt shop. he doesn't want his brother to spoil his dinner, so he can get no more than three ounces bought. the function consists only of the ordered pairs (0, 0.35), (1,1.35), (2,2.35) and (3,3.35) what is the domain and range of the function?
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.
HELP SOLVE PLEASEEE
Answer:
d. -6x + 2 = -15
p(x) = 3(x + 10x + 5) - 5(x - k)
In the polynomial p(x) defined above, k is a
constant. If p(x) is divisible by x, what is the value
of k?
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
a positive real number is 4 less than anther of the sum of the squares of the two numbers is 72 then find the numbers.
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.
C increased by 8 can I get help
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
find the value of x 4x + 3 = -5x + 21
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
add 5x on both sideswhich will get u to 9x +3 = 21subtract 3 from both sideswhich will get u to 9x = 18divide 9 from both sides and the answer is x = 2NEED HELP ASAP RIGHT ANSWER ONLY 69 POINTS
In two or more complete sentences, determine the appropriate model for the given data and explain how you made your decision.
(2,−1), (3,0.5), (6,1.5),
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:
If measure angle 4 is equal to 35 degrees, find the measure angle 2 and measure angle 3.
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
A student bought 44 pencils for school. if he sharpened 8 of the pencils before school, what is his ratio of unsharpened pencils to sharpened pencils
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
OMG I NEED HELP WITH THIS ANSWER RN
The temperature in Little Rock, Arkansas, is 66°F, and the temperature in Lincoln, Nebraska, is 82°F. Which of the following is true?
A.
Little Rock's temperature > Lincoln's temperature
B.
Little Rock's temperature = Lincoln's temperature
C.
Little Rock's temperature < Lincoln's temperature
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
50×54+35-44
Simplification
no spam
steps must
Answer:
=2691
Step-by-step explanation:
=2700+35−44
=2735−44
=2691
pls help I will put brainliest
26
the number line ticks count by 2
hope this helped :)
Given that [tex]I_0 = 10^-12[/tex] watts/[tex]meters^2[/tex], what is the intensity of a sound for which the decibel level of the sound measures 156? Round off your answer to three decimal places.
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:
https://brainly.com/question/4431819
Which of the following fractions is equivalent to 4/20? 1/10
3/15
3/19
2/12
Answer:
your answer is 3/15
Step-by-step explanation:
if im wrong pls let me know
I need help with this math problem
Answer:
F(x)=(x+6)^2
Step-by-step explanation:
Hope this helps!
A line that includes the point (3, 2) has a slope of 0. What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y=0x+2
Step-by-step explanation:
You deposit $200 in a savings
account that pays a simple
interest rate of 3.25% per year.
How much interest will you earn
after 5 years?
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
Please help I’ll give brainliest
Answer:
ITS D GOOD LUCK WITH YOUR HMK
Find the area of the circle.
Step- by - Step Explanation:
Area of a circle=πr²
=3.14...×6²
=113.0973355292325
Approximately ≈113.1cm²
Please mark BRAINLIEST if I'm right.
Write and simplify an expression for the difference between the perimeters of the rectangle and the hexagon
Answer:
hey man i need a screenshot or something
Step-by-step explanation: