Step-by-step explanation:
So how is the distributive property used to expand expressions? Let's use your example.
We have 2(x + 3) = 30
It seems like we're stuck, we cannot add a variable by a real number, can we? This is when the distributive property comes into play, we will use the 2 outside of the parenthesis to multiply x and 3.
2(x) + 2(6) = 30
We multiply the number inside the parenthesis since we can't solve the inside of it, therefore causing it to expand.
4(x + 5) = 43
4(x) + 4(5) = 43
^^^ Another example
Each month a tax is deducted from lucy's earnings. Which best describes the tax that is deducted from her pay check
F sales tax
G payroll tax
H property tax
J not here
Answer:
h property tax
Step-by-step explanation:
write the equation of the line in standard form passing through (2,-4) with a slope of -7
Answer:
7x+Y=-2
Step-by-step explanation:
(y-y1)=m(x-x1)
(Y+4)=-7(x-2)
Y+4=-7x+2
Y+7x=2-4
7x+Y=-2
Which is the better buy?
3,805 pounds of cement for $266.35 or
5 tons of cement for $1,400.00
Answer:
3,805 pounds of cement for $266.35 is a better buy
Step-by-step explanation:
3,805 pounds of cement for $266.35
266.35 : 3,805= 0.07
check your work: 3,805 x 0.07 = 266.35
so for the first offer you will be paying $0.07 per pound
5 tons of cement for $1,400.00
1 ton = 2000 pounds
5 tons = 10000 pounds
1,400.00 : 10000 = 0.14
for the second offer you will be paying $0.14 per pound of cement. 3,805 pounds of cement for $266.35 is a better buy because you will be paying half of the price for each pound.
hope this helps!
Look at the subtraction expression below.
Which number line models this expression?
A.
B.
C.
D.
Answer:
A
Step-by-step explanation:
I took the quiz
Answer:
The Answer IS {A} just did the test!!
Step-by-step explanation:
Given that for an arithmetic sequence, the first term is q and the second term is qz.
(a) Find the common difference d the general term Tn and the sum of the first n terms. Answer must
be in terms of q and z.
(b) Hence, find the sum of the first 10 terms in terms of q and z.
Answer:
[tex]d = q(z-1)[/tex]
[tex]S_n = \frac{nq}{2}(2 + (n-1)(z-1))[/tex]
[tex]S_{10} = 5q(9z -7)[/tex]
Step-by-step explanation:
Given
[tex]T_1 = q[/tex]
[tex]T_2 = qz[/tex]
Solving (a1): The common difference (d)
d is calculated as
[tex]d = T_2 - T_1[/tex]
This gives:
[tex]d = qz - q[/tex]
Factorize:
[tex]d = q(z-1)[/tex]
Solving (a2): Sum of n terms
This is calculated using:
[tex]S_n = \frac{n}{2}(2*T_1 + (n-1)d)[/tex]
Substitute values for T1 and d
[tex]S_n = \frac{n}{2}(2*q + (n-1)q(z-1))[/tex]
[tex]S_n = \frac{n}{2}(2q + q(n-1)(z-1))[/tex]
Factorize:
[tex]S_n = \frac{n}{2}(q(2 + (n-1)(z-1)))[/tex]
[tex]S_n = \frac{nq}{2}(2 + (n-1)(z-1))[/tex]
Solving (b): Sum of first 10.
In this case, n = 10
So:
[tex]S_n = \frac{nq}{2}(2 + (n-1)(z-1))[/tex]
becomes
[tex]S_{10} = \frac{10 * q}{2}(2 + (10-1)(z-1))[/tex]
[tex]S_{10} = 5 * q(2 + 9(z-1))[/tex]
[tex]S_{10} = 5q(2 + 9(z-1))[/tex]
[tex]S_{10} = 5q(2 + 9z-9)[/tex]
[tex]S_{10} = 5q(2 -9+ 9z)[/tex]
[tex]S_{10} = 5q(-7+ 9z)[/tex]
[tex]S_{10} = 5q(9z -7)[/tex]
Given that the first term and the second term of an arithmetic sequence is q and qz respectively, therefore:
a. Common difference (d) = [tex]\mathbf{d = q(z - 1)}[/tex]
Sum of the first n terms is: [tex]\mathbf{S_n = \frac{qn}{2}[2 + (n - 1)(z - 1)]}[/tex]
b. [tex]\mathbf{S_{10} = 5q(9z - 7)}[/tex]
Recall:
The common difference (d) of an arithmetic sequence = difference between the next term and the previous termSum of n terms, [tex]S_n[/tex] of arithmetic sequence = [tex]\frac{n}{2}[2a + (n - 1)d][/tex]Given:
First term, [tex]T_1 = q[/tex] (this is also "a")Second term, [tex]\\\\T_2 = qz[/tex]a. Common difference (d) = [tex]T_2 - T_1[/tex]
Substitute[tex]d = qz - q\\\\\mathbf{d = q(z - 1)}[/tex]
Sum of n terms:
[tex]T_n = \frac{n}{2}[2a + (n - 1)d][/tex]
Substitute by plugging in the value of d and a[tex]S_n = \frac{n}{2}[2(q) + (n - 1)q(z - 1)]\\\\S_n = \frac{n}{2}[2q + q(n - 1)(z - 1)]\\\\S_n = \frac{qn}{2}[2 + 1(n - 1)(z - 1)]\\\\\mathbf{S_n = \frac{qn}{2}[2 + (n - 1)(z - 1)]}[/tex]
b. Sum of the first 10 terms:
Substitute n = 10 into [tex]S_n = \frac{qn}{2}[2 + (n - 1)(z - 1)][/tex][tex]S_{10} = \frac{q(10)}{2}[2 + (10 - 1)(z - 1)][/tex]
Simplify[tex]S_{10} = 5q[2 + (9)(z - 1)]\\\\S_{10} = 5q(2 + 9z - 9)\\\\[/tex]
Add like terms[tex]\mathbf{S_{10} = 5q(9z - 7)}[/tex]
In summary, given that the first term and the second term of an arithmetic sequence is q and qz respectively, therefore:
a. Common difference (d) = [tex]\mathbf{d = q(z - 1)}[/tex]
Sum of the first n terms is: [tex]\mathbf{S_n = \frac{qn}{2}[2 + (n - 1)(z - 1)]}[/tex]
b. [tex]\mathbf{S_{10} = 5q(9z - 7)}[/tex]
Learn more here:
https://brainly.com/question/14311840
{−2x+7y=−7
−5x+14y=−7
Answer: x=7, y=2
Step-by-step explanation:
1. -2(-2x+7y=-7) -> 4x-14y=14
2. 4x-14y=14
-5x+14y=-7
3. -x = 7, x=7
4. -5(7)+14y=-7
5. -35+14y=-7
6. 14y=28, y=2
Answer: [tex]x=-7[/tex], [tex]y=-3[/tex]
Step-by-step explanation:
[tex]\left \{ {-2x+7y=-7} \atop {-5x+14y=-7} \right.[/tex]
multiply 2 at [tex]-2x+7y=-7[/tex]
[tex]-4x+14y=-14[/tex]
subtract [tex]-4x+14y=-14[/tex] and [tex]-5x+14y=-7[/tex]
[tex]x=-7[/tex]
put [tex]x=-7[/tex] at [tex]-2x+7y=-7[/tex]
[tex]7y=-21, y=-3[/tex]
5+5 100 points please help I'm in 8th grade and my teacher wants me to answer this
if i have 1000 dollars and lose 1000 dollars how much do i have left 100 points
The mathematical answer would happen to be... 0
Answer:
0
Step-by-step explanation:
I needs help, I’ll give brainliest !!
Answer:
(4,-5)
Step-by-step explanation:
Can you help with the 2 that are not correct?
Answer:
MPO=MNO
NPO=MNP
Step-by-step explanation:
MPO=MNO because MPO opposite angles of a parallelogram are congruent.
MNO is the top right angle of the parallelogram and so the opposite side of that is MPO or OPN whatever way you want to write it.
NPO=MNP because they are alternate interior angles. (If you don't understand what that means I can come back and explain it)
Solve for the roots: x3-2x2+3x-6
Answer:
x = 2, i[tex]\sqrt[]{3}[/tex], -i [tex]\sqrt{3}[/tex]
x^3 - 2x^2+ 3x - 6 = 0
Hint: Solve by grouping.
How can you rewrite the problem so that the divisor is a whole number?
0.21 divided by 17.66
Answer: 21 divided by 1766
Step-by-step explanation:
just try to remove the decimal points which mean 0.21 to 21 and 17.66 to 1766
PLEASE I NEED HELPP !!
Which situation leads to a unit cost of $8 per softball ticket?
A. $6 paid for 2 softball tickets
B. $6 paid for 6 softball tickets
C. 6 softball tickets for $24
D. 9 softball tickets for $72
Answer:
D 9 softball tickets for $72
Step-by-step explanation:
72/9=8
Answer:
The answer is D.
Step-by-step explanation:
You divide 72 by 9. Hope this helps!!! Please mark me brainliest and have a good rest of your day!!!
85% of a number is added to 24, the result is the same number find the number.
Answer:
160
Step-by-step explanation:
Help please! I’ll give brainliest!
d+g/h for d=35, g=19 and h=6
A. 9
B. 2.7
C. 7.3
D. 8
Answer:
PLZ MARK ME AS BRAINLIST
Step-by-step explanation:
THE CORRECT ANSWER IS 9...
HOPE IT HELPS...
DNDNDNDN
SNSNDNDN
SBSNDNXN D DXBNXF D XNXJXNXN
SNDNXNDBDNZJXNXDNSKSKDN
DNDNDN
NDNDSNSNSNSND
SNDNDNDN
Please help quick!!!
Answer:
Investigation 1
Step-by-step explanation:
Temperature change reveals a chemical reaction.
PLEASE HELP ASAP I WILL GIVE BRAILY AND 25 POINTS... write an expression equivalent to 4x + 12 using the distributive property
Answer:4x + 12 = 2 ( 2x + 6)
Step-by-step explanation:
#13 Easton is planning on buying a new pair of cowboy boots. When he
went to Eastern Outfitters last week they costs $60 on the black Friday
sale. This week, they aren't on sale anymore and they cost $85. What is the
percent of change on the boots? *
O 25%
O 45%
O 55%
75%
What is the scale factor and center of dilation?
A bag contains 150 marbles. Some are blue, and the rest are white. There are 21 blue marbles for every 4 white marbles. . How many blue marbles are in the bag
Ty takes 1 hour to read 35 pages, 2 hours to read 70 pages, and 3 hours to read 105 pages.
Answer: There are 210 pages that ty read in 6 hours.
Step-by-step explanation:
a package of 5 pairs of insulated socks cost $34.95. what is the unit price of the pair of socks?
Answer:$6.99
Step-by-step explanation:
DO
$34.95/5=6.99
Answer:
$6.99
Step-by-step explanation:
you have to divide the 2 numbers above
Decide whether the statement is true or false. If angle1= angle2 and angle2= angle3 , then angle1= angle3 .
Answer:
Step-by-step explanation:
Hope this helps
Answer: true
Step-by-step explanation: let’s take angle 1 as 5
angle 1 = angle 2
5=5
we know angle 2 = 5
angle 2 = angle 3
5=5
now we know able 3= 5
angle 1 = angle 3
5=5
Write the equation of a line perpendicular to 5x - 7y =-6 that passes through the point (-5,6)
9514 1404 393
Answer:
7x +5y = -5
Step-by-step explanation:
You can find the perpendicular line by swapping the x- and y-coefficients, and negating one of them. The new constant can be found by using the given point.
7x +5y = 7(-5) +5(6) = -5
The perpendicular line through (-5, 6) is ...
7x +5y = -5
Find the measure of angle J
Answer:
Step-by-step explanation:
Equals 23x
Veronica's family is getting ready for
a huge go-kart race. They only brought
15 gallons of gasoline, though. If each
cart needs 2 and 1/3 gallons of gas, how many
go-karts can be filled for the race?
Answer:
6.5
Step-by-step explanation:
15gallons ÷ 2.3 gallons per car = 6.5 cars so filled would be 6
If v varies inversely with w and v = 18 when w =3
find the equation that relates v and w.
Answer:
V= 6/w
Step-by-step explanation:
Which statement is true about the equation shown below?
10 – 2 (4x – 3) = 2x + 7 – 10x
A.The only solution to the equation is x=9/16
B.The only solution to the
equation is x=9/20
C.The equation has infinite
solutions.
D.The equation has no solution.
Answer: C.The equation has infinite
solutions.
Invalid data.
23. 6) Word Problem:
Bill makes $30.00 per day. He makes twice as much as Jack makes before
Jacks's salary was doubled. How much does Jack make now?
24. 7) A purchase of $0.73 is made by a customer. The customer hands you a $10.00 bill.
How much change should you give back?
25. 8) A customer buys 3 items at $0.25 each, 2 items at $0.55 each, and 1 other item for
$0.15. Assuming the tax rate on a dollar is 2%, how much will the total transaction be?
26. 9) How many nickels are there in a $2.00 roll?
Answer:
23.6) $30.00
24.7) $9.27
25.8) I'm not sure
26.9) 40 nickles
Step-by-step explanation:
