Product of two polynomials can be done by distribution of multiplication over addition. The product of [tex](4x -3)(2x^2 -7x + 1)[/tex] is [tex]8x^3 - 34x^2 + 25x - 3[/tex]
What is distributive property of multiplication over addition?Suppose a, b and c are three numbers. Then we have:
[tex]a(b + c) = a\times b + a\times c[/tex]
(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)
The product result of the given expression is obtained as:
[tex](4x -3)(2x^2 -7x + 1) = 4x(2x^2 - 7x + 1) -3(2x^2 - 7x + 1)\\(4x -3)(2x^2 -7x + 1) = 8x^{1 + 2} - 28x^2 + 4x - 6x^2 + 21x - 3\\(4x -3)(2x^2 -7x + 1) = 8x^3 + (-28-6)x^2 + (4 + 21)x - 3\\(4x -3)(2x^2 -7x + 1) = 8x^3 - 34x^2 + 25x - 3[/tex]
Thus,
The product of [tex](4x -3)(2x^2 -7x + 1)[/tex] is [tex]8x^3 - 34x^2 + 25x - 3[/tex]
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Brett's fish tank can hold up to 10.5 gallons of water before it overflows. Brett has poured 9 gallons of water into his fish tank so far.
Let x represent how many more gallons of water Brett can pour into his fish tank. Which inequality describes the problem?
Answer:
x=1.5
Step-by-step explanation:
A bag is filled with marbles. Three fifths of the bag consists of 27 red marbles. The rest of the bag is filled with yellow marbles.
How many yellow marbles are in the bag?
Answer:
There are 18 yellow marbles in the bag.
Step-by-step explanation:
Let total marble be x,
3/5 of x = 27
or, 3x = 135
so, x = 45
Total = 45
Now,
yellow marbles = 45 - 27 = 18
Answer:
18 yellow marbles.
Step-by-step explanation:
what is [tex]4\sqrt{16}[/tex]?
Solve for the letter x:
Mike has an adjusted gross income of $85,643. He claims two exemptions and can deduct $896 for state income tax, $2,145 for charitable donations, and $3,473 for medical expenses. If the standard deduction is $5,700 and exemptions are each worth $3,650, what is Mike’s total taxable income? a. $72,643 b. $75,479 c. $71,829 d. $66,129 Please select the best answer from the choices provided A B C D.
Answer:
The answer would be C. $71,829
Hope this helped :D
The net salary after all deductions will be $66,129 and can be calculated by subtraction of gross salary from all deductions thus option (d) is correct.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.
The group's total number of items decreases or becomes lower when we subtract from it.
Gross income = $85,463
Deductions are,
Income will be $896
Exemptions is 2 x $3,650
Charitable donations is $2,145
Exemptions is 2 x $3,650 expenses is $3,473
Add all above the deduction to find out the total deduction,
$896 + $2,145 + $3,473 + 2 x $3,650 = $13,814
Thus, net income will be as by subtraction,
$85,463 - $13,814 = $66,129
Hence "The net salary after all deductions will be $66,129 and can be calculated by subtraction of gross salary from all deductions".
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Tom the painter is painting window frames on a house. He knows that the angle his ladder should make with the ground should be between 55° and 35° in order to be safe. Tom's ladder is 8m and he wishes to paint a window frame 6.3m above the ground.
Is Tom's ladder safe to use?
Answer:
Tom should use a ladder that is smaller or at the the same height of the window frame. Here it says that he is using a ladder that is taller than the window frame, and this can be very uncomfortable for the person who is using the ladder, so it would be recommendable for Tom to use a smaller ladder, probably a ladder that is only a few inches smaller or taller than the window frame. Using a ladder that is like this should be safe to use.
Step-by-step explanation:
Hope this helps =)
If Michael and Lmani go out to eat and their food costs 25.30 and there is a 8% meals tax how much is the meal?
Answer:
I believe the answer is $27.32
What is the product?
Answer:
It refers to the result of one or more multiplication.
Help fast
Select the function table that matches the equation below.
y=1/4x+6
Answer:
It is number 3
Step-by-step explanation:
bc i said so
A student has some $1 and $5 bills in his wallet. He has a total of 11 bills that are worth $31. How many of each type of bill does he have? The student has enter your response here $1 bills and enter your response here $5 bills.
Answer:
6 $1 bills, 5 $5 bills
Step-by-step explanation:
Say the student has x $1 bills.
Then they have 11 - x $5 bills.
31 = 1 * x + (11 - x) * 5 = 55 - 4x
4x = 55 - 31 = 24
x = 6
So, they have 6 $1 bills and 11 - 6 = 5 $5 bills
Answer:
5, 5, 5, 5, 5, 1, 1, 1, 1, 1, 1. As you see those are eleven numbers/bills so your answer may be, The student has 5, 5$ bills and 6, 1$ bills. which makes up 31$.
Step-by-step explanation:
d) x + y = 42 X-6 = 5 (-6)
Answer: X = -24 Y = 66
Step-by-step explanation:
5(-6) = -30
X = 6 - 30 = -24
Y = 42 + 24 = 66
Hello there, Today we will solve your math problem
[tex]{\huge{\boxed{\mathfrak{{Question}}}}[/tex]
[tex]x+y=42\\x-6=5(-6)[/tex]
________________
First off let's isolate [tex]x[/tex]
after doing that we can substitute [tex]x[/tex] for [tex]-12[/tex]
Here is our equation
[tex]-12+y=4[/tex]
solve for [tex]y[/tex] and we get that [tex]y=16[/tex]
________________
[tex]{\huge{\boxed{\mathfrak{{Answer}}}}[/tex]
[tex]{\boxed{x=-12}}[/tex][tex]{\boxed{y=16}}[/tex]Have a good day!Number 13 please.it’s the answe.r
acks father drives to work in 30 min when driving at his usual speed. When traffic is bad, he drives 30mph slower and the trip takes one hour longer. How far is Jacks Fathers work from home in miles
me give brainliest
Answer:
Jack's fathers work is 1350 miles away from home
Step-by-step explanation:
Equation for trip 1:
Usual speed=x
Time=30 minutes
Formula for distance: d=st
d=30x
Equation for trip 2:
Speed= x-30
Time=90 minutes
d=90(x-30)
Now we solve for x using simultaneous equations:
30x=90(x-30)
x=45
Now to find d we sub in our new found value into one of the two equations (it doesn't matter which one)
d=30(45)
d=1350 miles
solve for me the slop
Answer: -1
Step-by-step explanation:
Take 2 random coords from the graph to find the slope
(0,4) and (2,2)
(4-2)/(0-2) = -1
Slope
Pick two points on the line
[tex]\tt slope=\dfrac{\Delta Y}{\Delta X}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
point 1: -4,5
point 2: 0,3
[tex]\tt slope=\dfrac{5-3}{-4-0}=\dfrac{2}{-4}=-\dfrac{1}{2}[/tex]
Can anyone help please
Answer:
7
Step-by-step explanation:
love is = 4, because love + love = 8 meaning its 4+4
heart is = 5, because heart - 4(love) = 1
bird is = 3, because bear is = 9 since 5(heart) + 4(love) is bear, and 3 birds make a bear.
Answer:
17
8 ÷ 2 = 4. love = 4.
heart - 4 = 1. heart = 5.
love 4 + heart 5 =9. bear =9
9÷3=3. birds = 3.
HELP NEEDED PLEASE!!!!
Answer:
B√134
Step-by-step explanation:
the answer is B(√134)
hope it helps
Answer:
B
Step-by-step explanation:
The distance from A to D is 2 and 5/6km.
AB is 4/5km more than BC
CD is 2/3 less than BC
Calculate the distance from C to D.
2/15
but iam not sure check with other guy
Find the value of x.
Answer:
25
Step-by-step explanation:
(2x+15)+x+90=180
3x=75
x=25
An app brought in $2 million in revenue before giving 10% of its revenue to pay for the reward prizes. How much revenue did the app earn the store after paying for the reward prizes?
Answer:
$1,800,000 dollars
Step-by-step explanation:
Given the following question:
10% of 2,000,000
An app brought in $2 million in revenue before giving 10% of that revenue to pay for prizes. We need to find how much revenue did the app earn AFTER the store paid for the reward prizes.
[tex]\frac{10\times2000000}{100} =10\times2000000=20000000\div100=200000[/tex]
10% of 2 million is 200,000.
[tex]2000000-200000=1800000[/tex]
The app earned "$1.8 million" after paying for the reward prizes.
Hope this helps.
The average resident of Metro City produces 630 pounds of solid waste each year, and the standard deviation is approximately 70 pounds. Use Chebyshev's theorem to find the weight range that contains at least of all residents' annual garbage weights.
The weight range that contains at least 75% of all residents' annual garbage goes between 420 pounds and 787.5 pounds.
AveragesGiven that the average resident of Metro City produces 630 pounds of solid waste each year, and the standard deviation is approximately 70 pounds, to determine the weight range that contains at least 75% of all residents' annual garbage weights, the following calculation must be performed:
630 - 70 = 560630 + 70 = 700560 x 0.75 = 420630 x 1.25 = 787.5Therefore, the weight range that contains at least 75% of all residents' annual garbage goes between 420 pounds and 787.5 pounds.
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For the following right triangle, find the side length X. Round your answer to the nearest hundredth
Answer:
x = 7.48
Step-by-step explanation:
You need to use the Pythagorean theorem to solve this problem.
leg^2 + leg^2 = hypotenuse^2
a^2 + b^2 = c^2
5^2 + x^2 = 9^2
25 + x^2 = 81
subtract 25 from both sides.
x^2 = 81 - 25
x^2 = 56
Square root both sides.
x = sqroot(56)
x = 7.48
If f(1) = 0, what are all the roots of the function f (x) = x cubed 3 x squared minus x minus 3? Use the Remainder Theorem.
Remainder theorem tells about the remainder of division of a polynomial with x - a. The roots of given function are: 1, -1, -3
What is remainder theorem for polynomials?If there is a polynomial p(x), and a constant number 'a', then
[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]
where g(x) is a factor of p(x)
For the given case, we've got:
[tex]f(x) = x^3 + 3x^2 -x - 3[/tex]
and
f(1) = 0
Thus, for a = 1, from remainder theorem, we get:
[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)\\\\\dfrac{f(x)}{(x-1)} = g(x) + f(1)\\\\\dfrac{x^3 + 3x^2 - x - 3}{(x-1)} = g(x) + 0\\\\ \dfrac{x^2(x+3) -1(x+3)}{x-1} = \dfrac{(x^2-1)(x+3)}{(x-1)} = g(x)\\\\(x+1)(x+3) = g(x)[/tex]
Thus, the other factor of f(x) is g(x) = (x+1)(x+3)
And we have:
[tex]\dfrac{f(x)}{x-1} = g(x)\\\\f(x) = (x+1)(x+3)(x-1)[/tex]
Putting it equal to 0, we get:
[tex]f(x) = 0\\(x+1)(x+3)(x-1) = 0\\x = 1, -1, -3[/tex]
Thus,
The roots of given function are: 1, -1, -3
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Answer:
A
Step-by-step explanation:
got it right on Edge 1943 whilst fighting the German Forces in Northern Italy while my friends were on the beaches of Normandy.
I NEED HELP PLZ ASAP , I AM SO STUCK ON THIS.
Function
d. 4f(t)
=4(t²+9)
=4t²+36
e. (f(t))²+8
=(t²+9)² + 8
= t⁴+18t²+81+8
= t⁴+18t²+89
In triangle RST, TU bisects angle T. If U is a point on RS, RU = 6,
RT = 9, and ST = 12, find RS.
Answer:
14.
Step-by-step explanation:
1. RS=RU+US, - US is unknown yet;
2. the property of bisector is:
RU/US=RT/ST;
3. according to the property above:
US=RU*ST/RT; US=12*6/9=8;
4. RS=RU+US; ⇒ RS=6+8=14.
the price paid for a 83.50 dollar chair with an 8 percent sales tax
Answer:
$90.18 dollars
Step-by-step explanation:
Given the following question:
Original cost = $83.50
Sales tax = 8%
In order to find the price paid for the chair, we find 8 percent of the original price. Then we add that number to the $83.50 for the chair and then we will have our answer.
[tex]\frac{8\times83.5}{100} =8\times83.5=668\div100=6.68[/tex]
Sales tax of the chair is $6.68.
[tex]83.50+6.68=90.18[/tex]
Total cost of the chair after an 8 percent sales tax is "$90.18 dollars."
Hope this helps.
Calculate the average speed for the following sections on the graph.
Answer:
A to B = 2000 m/s
C to D = 30,000m/s
Step-by-step explanation:
A to B is 10secs and the distance is 200m so you multiply them and you get 2000m/s
C to D is 60secs and the distance is 500m so you multiply and you get 30,000m/s
Answer:
a to b is 20m/s I'm in k12 and I got the same question but I don't know for c to d yet
Step-by-step explanation:
A =0
B=200
T=10s
200 divided by 10 is 20m/s
and for the question at the bottom, the answer is c bc c to d is accelerating
2. Kira's skateboard is 71 centimeters long. What is the length of her skateboard in millimeters? Show your work. Answer:
Answer:
710
Step-by-step explanation:
1 centimeter = 0.1 mi millimeter so 71 centimeters= 710 millimeters
i'm in k12 and i just took the test too
hope this helps have a good day ^ω^
The length of Kira's skateboard in millimetres is 710 mm
What is unit conversion?A unit conversion expresses the same property as a different unit of measurement.
Given that, Kira's skateboard is 71 centimetres long.
1 cm = 10 mm
Converting the units,
71 cm = 10×71 = 710 mm
Hence, the length of Kira's skateboard in millimetres is 710 mm
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A farmer keeps a record of the weekly milk yield of his herd of seven cows over a period of six months. He finds that the mean yield is 24 litres. He buys another cow that he is told will produce 28 litres of milk a week. Work out the effect this will have on the mean milk yield of his cows.
Answer:
A farmer keeps a record of the weekly milk yield of his herd of seven cows over a period of six months. He finds that the mean yield is 24 liters. He buys another cow that he is told will produce 28 liters of milk a week. Work out the effect this will have on the mean milk yield of his cows.
Step-by-step explanation:
Hope it helps<3
Answer:
24.5 liters/week
Step-by-step explanation:
24 liters/week for 7 cows is 168 liters/week
Add 1 cow that produces 28 liters/week
The new total is 196 liters/week for 8 cows
(196 liters/week for 8 cows)/(8 cows) = 24.5 liters/week is the new mean.
The difference of two numbers is 8. When twice the first number is added to three times the second number, the result is 51. What are the two numbers?
А. 12 and 4
B. 15 and 7
C. 20 and 12
D. 23 and 15
Is square root of 0.49 a rational number?
Answer:
yes it is a rational number because the square root of 0.49 is 0.7
Step-by-step explanation:
Hope that helps!