Given:
[tex]f(x)=4x^3-5x^2-3x+2[/tex]
[tex]g(x)=x-3[/tex]
To find:
The remainder when f(x) is divided by g(x).
Solution:
According to remainder theorem, if f(x) is divides by (x-c), then remainder is f(c).
Using remainder theorem, if [tex]f(x)=4x^3-5x^2-3x+2[/tex] is divides by [tex]g(x)=x-3[/tex], then remainder is f(3).
Substitute x=3 in f(x).
[tex]f(3)=4(3)^3-5(3)^2-3(3)+2[/tex]
[tex]f(3)=4(27)-5(9)-9+2[/tex]
[tex]f(3)=108-45-7[/tex]
[tex]f(3)=56[/tex]
Therefore, the required remainder is 56.
Using the following conversions between the metric and U.S. systems, convert the measurement. Round your answer to the nearest tenth as needed
There are 8 fluid ounces in a cup, 2 cups in a pint, 2 pints in a quart,
and 4 quarts in a gallon.
1L ~ 0.26 gallons
9 fl oz _____ mL
Answer:
266.162 ml
Step-by-step explanation:
A serving of rice is 2/5 of a cup. How many servings are there in a 1 3/5-cup bag of rice?
Need Help. ( Look at the picture). Will Mark Brainliest. Graph the step function over the interval. And you can just write the steps out also. Working on it now but really need help please asap.
Answer:
x = -3
Step-by-step explanation:
f(x) = x + 3
0 = x + 3
-x = 3
x = -3
Ms. Smith bought a 5 pound bag of candy for her 6 grade classroom. She gave away 2 pounds of candy to her students during the first unit of
instruction and ate 6 ounces of candy during planning.
How many ounces of candy does Ms. Smith still have in her bag?
Note: (1 pound = 16 ounces)
A 38 ounces
o
B. 42 ounces
O c. 48 ounces
D. 54 ounces
Answer:
42 ounces or B
Step-by-step explanation:
5 pounds - 2 pounds=3 pounds
3 pounds=48 ounces
48 ounces-6 ounces=42 ounces
Where is the vertex of f(x) = -2x - 3| +6.4?
The radius of a circle is 2 inches. What is the circle's area?
Answer:
A= 12.57 inches squared
Step-by-step explanation:
The formula for the area of a circle is A=πr2. Substitute 2 for r, square it, and multiply it by pi (3.14.) The answer is 12.57 inches squared.
Answer:
[tex]\boxed {\tt a\approx 12.57 \ in^2}[/tex]
Step-by-step explanation:
The area of a circle can be found using the following formula.
[tex]a= \pi r^2[/tex]
The radius of the circle is 2 inches.
[tex]r= 2 \ in[/tex]
Substitute the value into the formula.
[tex]a=\pi ( 2 \ in)^2[/tex]
Evaluate the exponent.
(2 in)²= 2 in * 2 in = 4 in²[tex]a= \pi(4 \ in^2)[/tex]
Multiply.
[tex]a=12.5663706 \ in^2[/tex]
Round to the nearest hundredth. The 6 in the thousandth place tells us to round the 6 to a 7.
[tex]a\approx12.57 \ in^2[/tex]
The area of the circle is about 12.57 square inches.
Caroline is baking pies to the teachers lunch at her school she plans to give every teacher 1/8 of a pie she decides to bake 12 pies Each pie takes 26.5 minutes to bake if coraline bakes 1 pie at a time how many total minutes is it
Answer:
It will take her 318 minutes.
Step-by-step explanation:
26.5 times 12 equals 318
How do you find what p is?
Answer:
p > -3
Step-by-step explanation:
This is an alternating p-series. It is absolutely convergent if│an│converges. 1 / nᵖ⁺³ converges if the exponent is greater than 1.
p + 3 > 1
p > -2
The series is conditionally convergent if │an│diverges. 1 / nᵖ⁺³ diverges if the exponent is greater than 0 and less than or equal to 1.
0 < p + 3 ≤ 1
-3 < p ≤ -2
Combining these two, we get p > -3.
Which two numbers add to -10 and multiply to 9
Answer:
The two numbers are negative 1 and negative 9 which is -1 and -9
A triangle has a base length of 10 inches and a height of 4 inches.
What is the area of the triangle?
Answer:
No, The answer is 20. Remember area of triangle equals 1/2bh (or half of base and height multiplied.)
The area of triangle that has a base length of 10 inches and a height of 4 inches is 20 square inches.
What is area of a triangle?
The area of a triangle is one half the product of its base multiplied by height. Mathematically -
Area [Δ] = 1/2 x base x height
Given is a triangle (Δ) has a base length of 10 inches and a height of 4 inches.
We can write -
Base Length [B] = 10 inches
Height of triangle [H] = 4 inches
Area of triangle (Δ) = 1/2 x B x H
A(Δ) = 1/2 x B x H
A(Δ) = 1/2 x 10 x 4
A(Δ) = 20 square inches
Therefore, the area of triangle that has a base length of 10 inches and a height of 4 inches is 20 square inches.
To solve more questions on Triangles, visit the link below-
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g Statesville population in 2010 was about 24,700, and was growing by about 1% each year. If this continues, what will Statesville population be in 2018? [Round to the nearest person.]
Answer:
26,676population
Step-by-step explanation:
Population in 2010 = 24,700
If it grows yearly by 1%, increment per year is expressed as:
1% of 24,700
= 1/100×24700
= 247 populations
After 8years, population increase will be 247×8 = 1976 population
Statesville population in 2018 will be expressed as;
Population in 2010+increase after 8years
= 24700+1976
= 26,676 population
Hence statesville population in 2018 will be 26,676population
what equation is modeled by the graph below?
Answer:
B. -5/12
Step-by-step explanation:
Answer:
B.5/12
Step-by-step explanations:
There are 60 animal exhibits at the local zoo. What percent of the zoo's exhibits does each animal class represent?
Answer:
30+15+12+3= 60
for mammal 30/60=0.50%
reptile 15/60=0.25%
fish 12/60= 0.20%
bird 3/60=0-05%
i hope that helps
When Alexander moved into a new house, he planted two trees in his backyard. At
the time of planting, Tree A was 36 inches tall and Tree B was 21 inches tall. Each
year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per
year. Let A represent the height of Tree At years after being planted and let B
represent the height of Tree Bt years after being planted. Write an equation for each
situation, in terms of t, and determine which tree is taller after 3 years.
Answer:
The equations for each situation are
A = 36 + 6t
B = 21 + 9t
After 3 years, Tree A is taller.
Step-by-step explanation:
From the question,
Tree A was 36 inches tall and Tree B was 21 inches tall at the time of planting; and
Tree A grew by 6 inches per year and Tree B grew by 9 inches per year after planting.
For Tree A,
Given a period of t years after planting, the height would have increased by 6t
∴ A = 36 + 6t
For Tree B,
Given a period of t years after planting, the height would have increased by 9t
∴ B = 21 + 9t
To determine, which tree is taller after 3 years,
t = 3
For Tree A
A = 36 + 6t
A = 36 + 6(3)
A = 36 + 18
A = 54 inches
For Tree B
B = 21 + 9t
B = 21 + 9(3)
B = 21 + 27
B = 48 inches
Hence, After 3 years, Tree A is taller.
I need to find the missing angles of this triangle
Answer:
it is 90 degrees
Step-by-step explanation:
All you have to do is add the sides that you know and triangles total is 180 so add 32+58 and u get 90 degrees then u will have to subtract 180 from 90 and it equals 90 which is your missing angle
Find three nonzero vectors a, b, and c such that a × b = a × c != 0 but b != c.
9514 1404 393
Answer:
a = {1, 2, 3}, b = (2, 4, 7}, c = (-3/14, -3/7, 5/14}
Step-by-step explanation:
For the above vectors, ...
a × b = a × c = (2, -1, 0)
__
Here, c is found to be a scaled version of (a×(a×b)).
Question 5
Here are four cards.
4 5 0.
Use each card once to make the largest number that is less than 10
Here are four cards.
4 5 0 .
Use each card once to make the largest number that is less than 10
Answer:
9 by adding all the three cards
The Census Bureau wants to conduct a survey to determine the percentage of adults that buy clothing online. How many adults do they need to survey in order to be confident that the sample proportion is in error by no more that 2 percentage points.
Answer and explanation:
Please find attached answer and explanation
Please help ASAP.
Will mark brainliste
Answer:
i think its c but it could also be d sorry if im wrong T-T
Step-by-step explanation:
find a formula for the nth partial sum of each series 4+(4/3)+(4/9) and use it to find the series’ sum of the series converges.
Answer:
We can see that:
a₀ = 4
a₁ = 4/3
a₂ = 4/9.
We easily can see that the n-th therm of this will be:
aₙ = 4/3^n.
Now, the denominator increases as n increases, then for a really large n, aₙ will tend asymptotically to zero. This means that this summation converges.
We can write this summation as:
4*∑(1/3)^n.
The sum for the first N-th therms is:
We know that for a summation:
1 + r + r^2 + r^3 + ... + r^N = (1 - r^(N + 1))/(1 - r)
4 + 4*(1/3) + 4*(1/3)^2 + ... + 4*(1/3)^N = 4*( 1 - (1/3)^(N + 1))/(1 - (1/3))
Now, for the complete sum we have that:
n = {0, 1, 2, ...}
We know that for a summation:
∑a*r^n
with n = {0, 1, ...}
the sum is = a/(1 + r).
in this case we have:
a = 4, r = 1/3.
Then the sum is:
S = 4/(1 - 1/3) = 4/(2/3) = 3*2 = 6
Given z1 = StartRoot 2 EndRoot (cosine (StartFraction 3 pi Over 4 EndFraction) + I sine (StartFraction 3 pi Over 4 EndFraction) ) and z 2 = (Cosine (StartFraction pi Over 2 EndFraction) + I sine (StartFraction Pi Over 2 EndFraction) ) , what is the value of z1 – z2?
cos(0) + isin(0)
cos(0) – isin(0)
cos(Pi) + isin(Pi)
cos(Pi) – isin(Pi)
Answer: C. cos(Pi) + isin(Pi)
Step-by-step explanation:
The value of subtraction of two given complex numbers z₁ and z₂ is cos(π) + isin(π).
What are complex numbers?A complex number is an element of a number system that includes real numbers and a specific element labeled i sometimes known as the imaginary unit, and which obeys the equation i² = 1. Furthermore, every complex number can be written as a + bi, where a and b are both real values.
How to solve this problem?We know that cos(π - x) = - cosx, sin(π - x) = sinx, cos(π/4) = 1/√2 = sin(π/4), cos(π/2) = 0, sin(π/2) = 1, cos(π) = - 1, sin(π) = 0.
Given that z₁ = √2[cos(3π/4) + isin(3π/4)] = √2[cos(π - π/4) + sin(π - π/4)] = √2[- cos(π/4) + sin(π/4)] = √2[- 1/√2 + 1/√2] = √2[0] = 0
and z₂ = cos(π/2) + isin(π/2) = 0 + i × 1 = 1
Now, z₁ - z₂ = 0 - 1 = - 1 = - 1 + i × 0 = cos(π) + isin(π)
Therefore, the value of subtraction of two given complex numbers z₁ and z₂ is cos(π) + isin(π).
Learn more about complex numbers here -
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$11000 is compounded semiannually at a rate of 8% for 19 years. What is the total amount in the compound interest account?
Answer:
all really all you have to do is do 8 divided by 19 and then whatever that number that you get from that attractive from your highest number that you have in your question which is 11000
6. The store paid $2.50 for a book and sold it for $5.25. What is the profit as a percent?
4 tens + 14 ones = 5 tens + ___ ones
Answer:
4 becuase 40+14 = 54 so 50+4= 54 too
Step-by-step explanation:
HOPE THIS HELPS :)what does 3 to the -2 power equal
Answer:
[tex]\frac{1}{9}[/tex]
PLZ HELP !!
Max deposited $1,300 into an account that pays 4.5% interest, compounded daily. At end of six years he has a balance of ?
Answer:
The final balance is $1,692.94.
The total compound interest is $392.94.
Step-by-step explanation:
1,300 x 0.045=___ x 6
14/18 in decimal form
Answer:
.77
Step-by-step explanation:
the 7 is repeating so you can put a dash above the second 7
Hassan predicted that he would sell 178 postcards. He actually sold 142 postcards. What are the values of a and b in the table below?
Percent Error
Item
Approximate value
Exact value
Error
Absolute error
Ratio
Percent error
Postcards
178
142
a
b
a = negative 36; b = negative 36
a = negative 36; b = 36
a = 36; b = negative 36
a = 36; b = 36
Answer:
its b
Step-by-step explanation:
took the test on edge
Giving out brainlst to whoever can answer this
show that 5x²+2x-3
can be written in the
form |x+1/5| < 4/5 Hence, solve
the inequality
5x²+2x-3< 0
5x² + 2x - 3 < 0
5x² + 2x < 3
x² + 2/5 x < 3/5
Complete the square on the left side:
x² + 2/5 x + 1/25 - 1/25 < 3/5
(x + 1/5)² - 1/25 < 3/5
(x + 1/5)² < 16/25
Take the square root of both sides, keeping in mind that √(x²) = |x| for all x.
√((x + 1/5)²) < √(16/25)
|x + 1/5| < 4/5
This means
-4/5 < x + 1/5 < 4/5
-1 < x < 3/5