Product of two polynomials can be done by distribution of multiplication over addition. The product of [tex](x+5)^2[/tex] is [tex]x^2 + 10x + 25[/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)
What is a polynomial?They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.
Example:
[tex]x^3 + 4x + 3[/tex]
is a polynomial.
Using both above facts, as the given expression is [tex](x+5)^2[/tex]
Its product result is obtained as
[tex](x+5)^2 = (x+5)(x+5) = x(x+5) + 5(x+5) = x^{1+1} + 5x + 5x + 25\\\\(x+5)^2 = x^2 + (5+5)x + 25 \text{\:(Addition of coefficients of like terms)}\\\\(x+5)^2 = x^2 + 10x + 25[/tex]
It is a fact that result of a polynomial product is polynomial. Thus, the obtained product is a polynomial since x + 5 was a polynomial.
Thus,
The product of [tex](x+5)^2[/tex] is [tex]x^2 + 10x + 25[/tex]
Learn more about polynomial product here;
https://brainly.com/question/9106484
Scores on an exam follow an approximately normal distribution with a mean of 76. 4 and a standard deviation of 6. 1 points. What percent of students scored above 75 points?.
Using the normal distribution, it is found that 59.09% of students scored above 75 points.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is [tex]\mu = 76.4[/tex].The standard deviation is [tex]\sigma = 6.1[/tex].The proportion of students who scored above 75 points is 1 subtracted by the p-value of Z when X = 75, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75 - 76.4}{6.1}[/tex]
[tex]Z = -0.23[/tex]
[tex]Z = -0.23[/tex] has a p-value of 0.4091.
1 - 0.4091 = 0.5909
0.5909 = 59.09% of students scored above 75 points.
You can learn more about the normal distribution at https://brainly.com/question/24663213
2 km
Find the volume of the sphere. Show
your work.
Answer:
See answer below
Step-by-step explanation:
[tex]V = \frac{4}{3} \pi r^3[/tex] 2km = radius
[tex]V=\frac{4}{3}\pi (2)^3[/tex]
[tex]V = \frac{4}{3}\pi (8)[/tex]
[tex]V = \frac{4}{3}(8)\pi[/tex]
[tex]V =\frac{32}{3}\pi[/tex] [tex]\pi =3.14[/tex]
[tex]V = \frac{32}{3}(3.14)[/tex]
[tex]V = 33.493[/tex]
V≈ 33.49
Using π on the calculator
[tex]V = \frac{32}{3} \pi[/tex]
[tex]V = 33.510[/tex]
V ≈ 33.51
3 Claudia draws four cards with integers on them.
She must choose two of the integers to multiply.
The cards that should be chosen by Claudia from the integers in order to make the greatest product will be 0 and 3.
How to solve the integersFrom the complete question, it should noted that the number on the cards are -3, -2, 3, and 0.
In this case, she needs the card that will give her the greatest product. Therefore, the cards that should be chosen will be 0 and 3 which gives 0 unlike others that will give a negative value.
Learn more about integers on:
https://brainly.com/question/17695139
In an arithmetic sequence, the first term,
a1, is equal to 9, and the sixth term, a6, is
equal to 34. Which number represents the
common difference of the arithmetic
sequence?
Answer:
See below
Step-by-step explanation:
Add 5 to each preceding number
[tex]a_{n}[/tex] = ([tex]a_{n-1}[/tex])+5
1 9 9
2 14 [9+5]
3 19 [14+5]
4 24 [19+5]
5 29 [24+5]
6 34 34 [29+5]
I really need some help
Answer:
CEFA
Step-by-step explanation:
1. [tex]p=2(2x)+2(3x+2)=4x+6x+4=10x+4[/tex]
2. [tex]p=2(x)+2(4x+1)=2x+8x+2=10x+2[/tex]
3. [tex]p=2(7)+2(x+5)=14+2x+10=2x+24[/tex]
4. [tex]p=2(5)+2(4x-3)=10+8x-6=8x+4[/tex]
Hope this helps
Can somebody please help and try to answer this word problem and showing your work while doing it, thank you!!!
WILL MARK BRAINLIEST FOR ANYONE WHO CAN ANSWER THIS QUICKLY AND CORRECTLY!! :DDD
Answer:
Do you understand?
Step-by-step explanation:
you gained 23 (14+9)
and lost 7 yards(23-7=16)
so you will still have gained 16yds in total
16 yards was the overall gain.
Need help solving for X
Answer:
x = 9
Step-by-step explanation:
1: Make an equation
[tex]180 = 54 + 6x + 8 + 180 - (11x + 17)[/tex]
2: factor the -1
[tex]180 = 54 + 6x + 8 + 180 -11x - 17[/tex]
2: move x to one side
[tex]11x - 6x = 54 + 8 + 180 - 17 - 180[/tex]
3: simplify
[tex]5x = 45[/tex]
4: solve for x
[tex]x=9[/tex]
96 stickers on 8 pages = _____ stickers per page.
[tex] \tt \to \dfrac{96}{8} [/tex]
[tex] \\ \\ [/tex]
[tex] \tt \to \: 12 \: stickers[/tex]
Verify:-
12 × 8 = 96
hope it helped u!
Answer:
96/8
I promise you that it os
Question on Image
Deanne is out shopping and finds a $135.00 bike that was marked down by 25%.
How much was the item originally?
Answer:
168.75
Step-by-step explanation:
135.00 + 25% is 168.75
168.75 - 25% is 135.00
Find the measures of each numbered angles
Answer:
∠ 1 = 109° , ∠ 2 = 29° , ∠ 3 = 71°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , then
∠ 1 + 35° + 36° = 180°
∠ 1 + 71° = 180° ( subtract 71° from both sides )
∠ 1 = 109°
-------------------
∠ RVU and ∠ 1 are adjacent angles on a straight line and sum to 180° , then
∠ RVU + ∠ 1 = 180°
∠ RVU + 109° = 180° ( subtract 109° from both sides )
∠ RVU = 71°
In Δ RVU
∠ 2 + 80° + 71° = 180° ( sum of angles in triangle )
∠ 2 + 151° = 180° ( subtract 151° from both sides )
∠ 2 = 29°
-------------------------
∠ 3 and ∠ RVU are vertically opposite angles and are congruent , then
∠ 3 = 71°
Δ UVT has: ∠V₁ = 180⁰ - ∠TUV - ∠VTU = 180⁰ - 35⁰ - 36⁰ = 109⁰
We have: ∠RVU = ∠V₃ = 180⁰ - ∠V₁ = 180⁰ - 109⁰ = 71⁰
ΔRVU has: ∠U₂ = 180⁰ - ∠URV - ∠ RVU = 180⁰ - 80⁰ - 71⁰ = 29⁰
Answer:
∠V₁ = 109⁰∠U₂ = 29⁰∠V₃ = 71⁰Ok done. Thank to me :>
The sum of the measures of three adjacent angles is 150∘. The measures of the angles are in the ratio of 1:2:3. What is the measure, in degrees, of the largest angle?
Answer:
75°
Step-by-step explanation:
1:2:3
so there are a total of 6 parts. Then, each part would be:
=) 150÷6= 25
The largest angle is 3 parts. so, if 1 part is 25, 3 parts is 25×3= 75
The largest angle is is 75°
Hope this helps!
What’s the answers and now would I work this out ?
Answer:
15 cm²
Step-by-step explanation:
To find the volume of a prism you multiply the area of the end face (pentagon in this example) by the length (9 cm). Here you would reverse that and divide the volume by the length to find the area. 135/9 is 15 so the area of the pentagon is 15 cm².
In equation form would be:
V=A×L [V=volume A=area L=length]
So if you do inverse operations you would divide the volume by the length to get the area.
V/L=A
What is the equation of the line through (4, 2) and (0, -2)?
3 of 5 QUESTIONS
O y=x+2
O y=-x-2
O y=x-2
O y=-x+2
SUBMIT
Answer:
y=x-2
Step-by-step explanation:
set up in y1-y2/x1-x2
2 - (-2)/4 - 0
4/4 = 1
so x=1 and the y intercept is -2
so the answer is C
Find the area of the parallelogram.
4 in
4 in
A =
in 2
Answer:
16
Step-by-step explanation:
The area of a parallelogram can be found with the formula: A=bh (area equals base times height)
The base of this shape is 4, we multiply this by the height which is four.
Four times four equals 16
So that's the answer, 16.
You are welcome ahhahahehehehe.
Is this function linear or nonlinear? Why?
X^4+x^2=y
Is this function linear or nonlinear? Why?
2x+3y-x-y=4
Is this function linear or nonlinear? Why?
X=y=45
Is this function linear or nonlinear? Why?
Y=5x-10
Is this function linear or nonlinear? Why?
Y=56
Is this function linear or nonlinear? Why?
X^2+y=45
Is this function linear or nonlinear? Why?
Y=3x^5+4x^3
Is this function linear or nonlinear? Why?
Y=3x^5+4x^3
Is this function linear or nonlinear? Why?
Y=\|~11x+3
Answer:
1: No, x is raised to a power
2: Yes, can be solved in the form of y = mx + b
3: If this is supposed to be x + y = 45, then yes because it can be solved in the form of y = mx + b
4: Yes, it is in the form of y = mx + b
5: Yes, it is in the form of y = mx +b, it has a slope of zero and will be a horizontal line, which will pass the vertical line test
6: No, x is raised to a power.
7: No, x is raised to a power.
8: No, x is raised to a power
9: Is that supposed to be pi? If so, yes, it is in the form of y = mx + b
Step-by-step explanation:
Name the three different types of proofs you saw in this lesson. Give a description of each.
One type of proof is a two-column proof. It contains statements and reasons in columns. Another type is a paragraph proof, in which statements and reasons are written in words. A third type is a flowchart proof, which uses a diagram to show the steps of a proof.
You already have the answer. It is "One type of proof is a two-column proof. It contains statements and reasons in columns. Another type is a paragraph proof, in which statements and reasons are written in words. A third type is a flowchart proof, which uses a diagram to show the steps of a proof." which looks correct to me.
Gwen measured a kitchen and made a scale drawing. The scale she used was 11 inches : 5 feet. If a countertop in the kitchen is 22 inches long in the drawing, how long is the actual counter?
In right triangle ABC below, CD is the altitude to hypotenuse AB. If CD=6 and the ratio of AD to AB is 1:5, determine and state the length of BD.
Step-by-step explanation:
the altitude makes a right angle at hypotenuse
cd^2+ ad^2 = ac^2
36+ (h/5)^2 = ac^2
ad/ab = 1/5; ad/h = 1/5; ad=h/5
similarly
bd^2+cd^2 = bc^2
(4/5)^2+ 36 = bc^2
ac^2+bc^2 = ab^2
36+h^2/25+ 16/25h^2+36 = h^2
h= 15
bd/ab = 4/5
bd= .8*15=12
This relationship is not a function. Choose the sentence or
sentences that explain why.
10
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1
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2
8
6
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x=1
6
8
10
2
0
N
4
The graph is a line.
The graph intersects
the x-axis.
The input x-1 has
many outputs.
The graph is a
vertical line.
Answer:
The input x = 1 has many outputs.
The graph is a vertical line.
Step-by-step explanation:
Hi there!
A function is defined as a relation that only gives one output for every given input. For every x-value, there is only one y-value.
Because the x-value of 1 gives us an infinite number of y-values, this is therefore not a function.
More generally, no vertical line is a function for this reason.
I hope this helps!
ILL GIVE BRAINLIEST FOR CORRECT SIMPLIFYED ANSWERS QUESTIONS 1-8
Answer:
1. 7x + 2 3/5
2. 2x-6.3
3. 27t + 36b
4. 3.5a - 9.1p
5. 8(x+7)
6. 3(x+19)
7. y= -8.9
8. n = -18
Step-by-step explanation:
1. combine like terms
2. Keep change change then combine like terms
3. distribute
4. distribute
5. have 8 in common
6. have 3 in common
7. subtract 1.6 from -7.3
8. multiply both sides by -2/3
the table shows the last holiday destination of 60 people
Answer:
Use your protractor to draw the lines
Step-by-step explanation:
You worked out the angles, so using the centre point as the middle and the line underneath France as your starter line, do 108° sector for Spain, then a 90° for Greece and a 12° for Others
A line passes through the point (7, -2) and has a slope of -1
Write an equation in point-slope form for this line
Answer:
is there any others?
Step-by-step explanation:
I need the answer to 3/4÷1/5
Answer:
The answer is 15/4
………………………………
You have to write each expression in expanded form
Answer:
1) 12 2) 2y 3) 12+2y 4) 12+2y
Step-by-step explanation:
Can you please help with this problem
= 48cm²
To work out the area you must firstly multiply 8 by 12.
1) 8 x 12 = 96
Now you have to divide it by 2.
2) 96 / 2 = 48
⭐ Answered by Foxzy0⭐
⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐
⭐ If you have questions, leave a comment, I'm happy to help! ⭐
Answer:
area for this rhombus: 48 units²
Explanation:
area of rhombus: [tex]\boxed{\frac{1}{2} * diagonal.1* diagonal.2}[/tex]
Here diagonal.1 is 8 units and diagonal.2 is 12 units
Using the formula:
→ [tex]\frac{1}{2} * diagonal.1* diagonal.2[/tex]
→ [tex]\frac{1}{2} * 8 * 12[/tex]
→ [tex]48[/tex] units²
Isaac parents paid $3,200 per month to rent an office space for their own business. Of this amount, $325 was for the utilities. What percent of their rental cost was for the utilities?
Answer:
10.2%
Step-by-step explanation:
($325) / ($3,200) = 0.102 x 100 = 10.2%
Divide the amount for utilities by the total amount of rent.
24 as the product of 2 factors
Answer:
1 × 24 = 24 1, 24
2 × 12 = 24 2, 12
3 × 8 = 24 3, 8
4 × 6 = 24 4, 6
6 × 4 = 24 6, 4
8 × 3 = 24 8, 3
12 × 2 = 24 12, 2
24 × 1 = 24 24,1
Step-by-step explanation:
Hi!
I can help you with joy!
Remember, the product of means we multiply 2 numbers.
There are lots of ways we can write 24 as a product of 2 factors:
1×24
2×12
3×8
4×6
And the other way around as well:
6×4
8×3
12×2
24×1
Hope it helps!
Enjoy your day!
~Misty~
Help! Please answer quickly and accurately or I'll report your answer.
Nora rings up an item that costs $86.25. After sales tax, the total is $91.08. What is the sales tax percentage?
Write your answer as a decimal using a percent sign (%). For example, 0.5% or 12.7%
Answer:
The sales tax is equal to 5.6%
Step-by-step explanation:
To solve first we have to subtract the item's cost before sales tax from the total due. 91.08 - 86.25 = 4.83.
Next we take the amount we payed as tax and divide it by the pre-tax price. 4.83/86.25 = 0.056
Lastly we take 0.056 and convert it to a percentage. This can be accomplished by moving the decimal sign to 2 times to the left or multiplying the tax rate by 100.
The sales tax percentage is equal to 5.6%
Hope this helps you out :)
Britney made a proportional copy of a figure by multiplying each side length by 1/4. drag numbers to complete the table
Answer:
Side Original length Copy length
a 4 1 =4
b 6 1.5 =4
c 20 5 =4
d 16 4 =4
PLS HELP CAN’T FIGURE OUT HOW TO FIND b OR c ASAPPPPPPPPP
Answer:
b = 0.35 ; c = 2.03
Step-by-step explanation:
tan = opposite/hypotenuse
Therefore, tan (10) = b/2
b = 2 tan (10) = about 0.35
Use the Pythagorean theorem to find that c = 2.03