Answer:
(1) -4n-5
(2) 15r
(3) 12x-9
(4) 12r-20
(5) 10n-13
(6) 42n^2+21n
(7) 10a^2-100ab
(8) 3n^3-18n^2+15n
(9) 9v^2+24v-15
(10) 9v^2u^2 + 9uv^3- 45v^4
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A. Simplifying an algebraic expression means combining any like terms, which are terms that have the same variable and exponent. In these problems, we are asked to simplify the expressions by combining like terms.
1. n + 4 − 9 − 5n = n - 5n + 4 - 9 = -4n - 5
The first step is to combine the like terms which are n and -5n, we get -4n then we combine -9 and 4 and we get -5.
2. 12r + 5 + 3r – 5 = 12r + 3r + 5 - 5 = 15r
The first step is to combine the like terms which are 12r and 3r, we get 15r then we combine 5 and -5 and we get 0
3. −3x − 9 + 15x = 15x - 3x - 9 = 12x - 9
The first step is to combine the like terms which are 15x and -3x, we get 12xthen we combine -9 and 0 and we get -9
4. 12r - 8 - 12 = 12r - 12 - 8 = 12r - 20
The first step is to combine the like terms which are 12r and -12, we get 12r-12 then we combine -8 and 0 and we get -20
5. n - 10 + 9n - 3 = n + 9n - 10 - 3 = 10n - 13
The first step is to combine the like terms which are n and 9n, we get 10n then we combine -10 and -3 and we get -13
B. In these problems, we are asked to multiply the expressions.
6. 7n(6n + 3) = 42n^2 + 21n
In this example we have 7n multiplied by the expression 6n + 3, the distributive property is used to multiply 7n by each term in the parenthesis (6n and 3)
7n * 6n = 42n^2
7n * 3 = 21n
7. 10a( a − 10b) = 10a^2 - 100ab
In this example we have 10a multiplied by the expression a - 10b, the distributive property is used to multiply 10a by each term in the parenthesis (a and -10b)
10a * a = 10a^2
10a * -10b = -100ab
8. 3n( n2 − 6n + 5) = 3n^3 - 18n^2 + 15n
In this example we have 3n multiplied by the expression n^2 − 6n + 5, the distributive property is used to multiply 3n by each term in the parenthesis (n^2, -6n and 5)
3n * n^2 = 3n^3
3n * -6n = -18n^2
3n * 5 = 15n
9. 3(3v^2 + 8v - 5) = 9v^2 + 24v - 15
In this example we have 3 multiplied by the expression 3v^2 + 8v - 5, the distributive property is used to multiply 3 by each term in the parenthesis (3v^2, 8v and -5)
3 * 3v^2 = 9v^2
3 * 8v = 24v
3 * -5 = -15
10. v^2( u^2 + uv − 5v^2) = 9v^4 + 9
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When a point is reflected across a line of reflection, it remains the same distance from the line.True or False
Answer:
True
Step-by-step explanation:
To answer this question, I will use the following illustrations.
Assume a point (x,y) is reflected across the x-axis.
Using reflection rule, the new point will be: (x,-y)
On a coordinate plane, the x-axis is represented as: (x,0)
So, we will calculate the distance between (x,y) and (x,0) and also calculate the distance between (x,-y) and (x,0) using the following distance formula.
[tex]D= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Distance between (x,y) and (x,0)
[tex]D= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]D= \sqrt{(x - x)^2 + (0 - y)^2}[/tex]
[tex]D= \sqrt{(0)^2 + (- y)^2}[/tex]
[tex]D= \sqrt{0 + y^2}[/tex]
[tex]D= \sqrt{y^2}[/tex]
[tex]D = y[/tex]
Distance between (x,-y) and (x,0)
[tex]D= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
[tex]D= \sqrt{(x - x)^2 + (0 - (-y))^2}[/tex]
[tex]D= \sqrt{(0)^2 + (0+y)^2}[/tex]
[tex]D= \sqrt{0 + y^2}[/tex]
[tex]D= \sqrt{y^2}[/tex]
[tex]D = y[/tex]
See that the calculated distance are equal.
Hence, the given statement is true
if p is the smallest of four integers, what is their sum interms of P
Answer:
If p is the smallest of n consecutive integers of the same sign than we have p , p+1 , p+2 , … , p+(n−1) ,
So the sum is
∑k=0n−1(p+k)=∑k=0n−1p+∑k=0n−1k=np+n2−n2
Here n=4
So we have 4p+6
And checking
p+(p+1)+(p+2)+(p+3)=4p+6
Note if p=−v
Than you have the same thing as if p=v−n+1 just negative for example 3 consecutive integers the smallest is −5 so the sum is −5+(−4)+(−3)=3×−5+32−32=−15+3=−12
On the other hand:
−(3+4+5)=−(3×3+32−32)=−(9+3)=−12
If p=−v the sum of next v+1 integers is −(∑k=0vk)=−(v2+v2)
Than needs an other v integers to bring it up to 0 again. From there it is
∑k=0hk=h2+h2
Where h=n−(2v+1) .
So recap if p is the smallest of n consecutive integers their sum is
p+(p+1)+(p+2)+…+(p+(n−1))=⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪np+n2+n2−(n|p|+n2+n2)((n−|p|)2+(n−|p|)2)−(|p|p+|p|2+|p|2)((n−|p|)2+(n−|p|)2)n≥0p<0∧n<|p|+1p<0∧|p|<n<2|p|+1p<0∧n>2|p|+1
Step-by-step explanation:
50 points for this helpppp plzz
Answer:
ok
Step-by-step explanation:
Answer:
srry I needed the points hope u don\t mind
Step-by-step explanation:
what is the equivalent Ratios to 18:15
Answer:
6:5 in simplest form
Step-by-step explanation:
Answer:
6:5
Step-by-step explanation:
The greatest common factor, and only shared factor is 3. Use three and divide on both sides to get 6 and 5
I NEED HELP PLEASE. I WILL GIVE BRAINLIST IF RIGHT!
Answer:
Shift f up by 1 unit
Step-by-step explanation:
The email address lol
find the missing measure
Answer:
Step-by-step explanation:
A number cube is rolled and a marble is selected at random from a bag containing 2 green marbles, 2 yellow marbles, 2 red marbles, 1 purple marble, and 1 blue marble. Find each probability. Show your work. 1. P(1 and red) 2. P(3 and purple) 3. P(even and yellow) 4. P(odd and not green) Give me all the answer thanks.
Answer:
total number of marble=8
p(of green marble)=2/8=1/4
p(of yellow marble)=2/8=1/4
p(of red marble)=2/8=1/4
p(of purple marble)=1/8
p(of blue marble)=1/8.
The greatest common factor(GCF) of LaTeX: x^7,\:x^3,\:x^5\:is\:_{ }__________.
Answer:
x^3Step-by-step explanation:
We are to find the greatest common factor of x^7, x^3 and x^5
x^7 = x^3 * x^4
x^3 = x^3 * 1
x^5 = x^3 * x^2
From both factors, we cam see that x^3 is common to the three, hence the GCF is x^3
the graph of y=-3x+2, state the domain and the range
Answer:
Domain: (-∞,∞)
Range: (-∞, ∞)
Hope this helps.
one hundred twenty-three and thirty hundreths. in decimal form
Answer:
0.2330
Step-by-step explanation:
what is the slope of this line? -2x + 3y =-6
Answer:
Slope: 2/3
Step-by-step explanation:
You have to first write the equation into slope-intercept form...
y = mx + b
So...
-2x + 3y = -6
becomes...
3y = 2x - 6
y = 2/3x - 2
Which means...
2/3 is the slope
Hope this help :)
Let me know if there are any mistakes!!
Kim got to the store at 11:19 in the morning. She spent 24 minuets in the store how many minuets after she got to the store and left?
Answer:
11:43 am
Step-by-step explanation:
Given data
Time of arrival= 11:19 am
We are told that she spent 24 minutes in the store
Based on this, we can estimate the time she left the store
The time she left
=11:19+ 24
=11:43 am
Hence she left 11:43 am
pls help me it is important to me
Answer:
no
Step-by-step explanation:
can someone please help me??
Answer:
There is only one solution and it is the point of intersection
Step-by-step explanation:
Nathan Reynolds bought a car for $15,000. He made a down payment of $3,000. Nathan secured a loan for the balance of the purchase price at 8 percent interest for four years.
determine the monthly payment and total interest
Answer:
1) The monthly payment is approximately $292.96
2) The total interest is approximately $2,061.84
Step-by-step explanation:
1) The financing method Nathan Reynolds applied to buy the car is given as follows;
The purchase price of the car = $15,000
The down payment made for the car = $3,000
The
The interest on the loan he took for the balance of the purchase price, R = 8%
The number of years for which he took the loan, n = 4 years = 48 months
We have;
The balance of the purchase price = (The purchase price of the car) - (The down payment made for the car)
∴ The balance of the purchase price = $15,000 - $3,000 = $12,000
The balance of the purchase price = $12,000 = The loan Nathan secured
The monthly payment on a loan is given by the following formula
[tex]A = P \times \dfrac{r \cdot (1 + r)^n}{(1 + r)^n - 1}[/tex]
Where;
A = The payment amount made monthly
P = The principal or loan amount = $12,000
r = The interest rate divided by 12 = R/12 = 8/12 = 2/3
n = The number of months the monthly payment will be made = 48 months
By plugging in the variable values, we get;
[tex]A = 12,000 \times \dfrac{\dfrac{2}{300} \times \left (1 + \dfrac{2}{300} \right ) ^{48}}{ \left (1 + \dfrac{2}{300} \right )^{48} - 1} = 292.955068099 \approx 292.96[/tex]
Therefore, the payment amount made monthly, A ≈ $292.96
2) The total payment made in the 48 months = A × 48 = 292.955068099 × 48 ≈ 14,061.84
The total payment made in the 48 months ≈ $14,061.84
The total interest = (The total payment made in the 48 months) - (The loan amount)
∴ The total interest = $14,061.84 - $12,000 ≈ $2,061.84
11x + x = 60
full answer pls
Answer:
Step-by-step explanation:
Which sentence can represent the inequality 3.5 x greater-than-or-equal-to 7?
A The sum of 3.5 and a number is greater than 7.
B The sum of 3.5 and a number is greater than or equal to 7.
C The product of 3.5 and a number is greater than 7.
D The product of 3.5 and a number is greater than or equal to 7.
Answer:
c
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
hope it helps
7.1 as a percentage
Answer:
its 710%
Step-by-step explanation:
710% hope it helps!
A = 5x^2+3xy-7y^2 B = -x^2+2xy+8y^2 B, minus, A, equals
I WILL GIVE BRAINLYIST!!!!!!!!!!! Help!!!!!
Answer: -6x^2-xy+15y^2
Step-by-step explanation:
The value of B-A is -6x²-xy+15y² .
What is an Equation ?A statement where the algebraic expressions are equated with an equal sign with each other is called an Equation.
It is given that
A = 5x²+3xy-7y²
B = -x²+2xy+8y²
To calculate is B - A
B- A = ² (-x²+2xy+8y²) - (5x²+3xy-7y² )
B-A = -x²+2xy+8y² - 5x²- 3xy +7y²
B-A = -6x²-xy+15y²
Therefore the value of B-A is -6x²-xy+15y² .
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15) Dan is putting a fence around his circular swimming pool. If the pool
has a diameter of 13.5 feet and fencing costs $6 per foot, how much will
he spend?
Answer: 2
Step-by-step explanation:
Answer:
2.25
Step-by-step explanation:
You have to divide 13.5 and 6 to get your answer
A cake recipe calls for 2 1/4 cups of flour. Mrs Allen measured 3/4 cup of whole wheat flour and plans to use bleached flour for the remainder. How much bleached flour should she use?
Answer:
she should use 1 2/4 cups of bleached flour
A typical person takes about 24000 breaths each day. Write an equation you can use to find the number of breaths a typical person takes each minute.
Step-by-step explanation:
Welp if a typical person takes 24000 breaths each day that's means
24000÷24=1000
so that's means 1000 per hour
if a hour take 60 Min that's mean
1000÷60=16.6666667 don't tell me I'm not sure about this answer and not really good at this :p
A store sold 281 dresses last year. The store makes a profit of $35 for each dress sold.
How much did the store make from selling the dresses?
Answer:
9,835
Step-by-step explanation:
PLEASE HELP ME WITH THIS I HATE SCHOOL
Answer:
B.)[tex]\sqrt{245}[/tex]
Step-by-step explanation:
[tex]\sqrt{245}[/tex]=15.65
7[tex]\sqrt{5}[/tex]=15.65
Hope this helps! :)
Answer:
its is B
Step-by-step explanation:
I just put 7/5 and put the answers below in my calculator and got whatever went with the answer when I put 7/5 (I dont have the square root sign)
Can someone help me in this math problem? It’s a picture of the problem if you can!
Hello! I'm gettin' rekt right now, and I need help.
1st Question: How do you find the average of a number on a number line?
2nd Question: How do you find the average of 2 numbers on a number line?
Answer:
Step-by-step explanation:
Hm. I'm not sure what your asking, but I'll try my best.
To find an average, you would add all the numbers up, and then divide how many numbers there are.
Let me explain: If you wanted to find a average on a number line, that means you want to find one number on the number line. On this case, you would just take the number on the number line, and then divide it by 1.
2nd question: This question is the same as the first, except theres two numbers now, instead of 1. For this one, you would add up the 2 numbers, and then divide it by 2.
Hope this helps!
Calculate the unit price of the following item:
Chocolate chip cookies cost $2.79 per package and
there are 30 cookies inside. What is the price per
cookie? *
Consider the inequality -20.2 > 0y. Which of the following must be true? Check all that apply.
You cannot divide by zero.
The inequality is equivalent to -20.2 > 0, which is false.
The solution is y > 0.
The solution is 0 > y.
The solution is y = 0.
I think the answer is 0>y
Answer:
option 1 and 2
Step-by-step explanation:
edge 2021
The standard form of y = 5(x + 4)(x + 5) is
Answer:
mark me as brainliest plz
Answer:
21 is Correct answer hope you will like it
Can i get the answers i need them or else i fail