In multiplication, the exponents add up.
5.5²=5¹.5²=5³
Note:
In the extraction ,the exponents remove.
5¹⁰÷5³=5⁷
Answer:
5³
Step-by-step explanation:
Using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
Given
5 × 5²
= [tex]5^{1}[/tex] × 5²
= [tex]5^{(1+2)}[/tex]
= 5³ ← in index form
= [ 125 ]
Burt's grandparents started a savings account for him when he was born. They invested
$1250 in an account that pays 7.5% interest every year. How much money is in the
account on Burt's 18th birthday?
Answer:
4594.76 USD will be in the account on Burt's 18th birthday.
Step-by-step explanation:
Since interest rate is constant in time, we can use the definition of composite interest to determine how much money will be on Burt's 18th birthday, that is:
[tex]C = C_{o}\cdot \left(1+\frac{r}{100} \right)^{t}[/tex] (1)
Where:
[tex]C_{o}[/tex] - Initial amount, measured in US dollars.
[tex]C[/tex] - Current amount, measured in US dollars.
[tex]r[/tex] - Annual interest rate, measured in percentage.
[tex]t[/tex] - Time, measured in years.
If we know that [tex]C_{o} = 1250\,USD[/tex], [tex]r = 7.5[/tex] and [tex]t = 18[/tex], then the money in the savings account on Burt's 18th birthday is:
[tex]C = (1250\,USD)\cdot \left(1+\frac{7.5}{100} \right)^{18}[/tex]
[tex]C = 4594.76\,USD[/tex]
4594.76 USD will be in the account on Burt's 18th birthday.
f(x) = 2\3x -6 identifiy 0
A system of two linear equations is graphed. The lines have the same slope, but different intercepts. How many solutions does the system have?. A. 0. B. 1. C. 2. D. infinite
Answer:
D
Step-by-step explanation:
I hope this is correct and have a great day
interest 600$ invested at6% compounded annually for 7 years
Answer:
The interest earned is $302.18
Step-by-step explanation:
Compound Interest
It occurs when the interest is reinvested rather than paying it out. Interest in the next compound period is earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
The investment described in the question is of P=$600 at a rate of r=6%=0.06 for t=7 years compounded annually. The compounding period coincides with the time of interest rate, thus n=1.
Applying the formula:
[tex]{\displaystyle A=600\left(1+{\frac {0.06}{1}}\right)^{1*7}}[/tex]
[tex]{\displaystyle A=600\left(1.06}\right)^{7}}[/tex]
A = $902.18
The interest is:
I = A - P = $902.18 - $600 = $302.18
The interest earned is $302.18
Is this correct and if not can you please help me?
Answer:
No problems here!
Great Job!
Step-by-step explanation:
Jason can travel 23 3/4 miles in 2/3 of an hour. what is his speed in mph
Answer:
I agree buster. I can't even run that far.
Step-by-step explanation:
The Great Pyramids of Giza are named the Pyramid of Menkaure, the Pyramid of Khafre and the Pyramid of Khufu. The height and base of each of these pyramids are: 65.5 m by 103.4 m2, 136.4 m by 215.25 m2, 138.8 m by 230.4 m2 respectively. What is the volume of each of the Great Pyramids of Giza?
Step-by-step explanation:
The volume of a pyramid is equal to one third the product of the area of the base and the height.
Pyramid of Menkaure
Area of Base, B = 103.4 m2
Height, H = 65.5 m
Volume = 1/3 * BH
Volume = 1/3 * 103.4 * 65.5 = 2257.56 m3
Pyramid of Khafre
Area of Base, B = 215.25 m2
Height, H = 136.4 m
Volume = 1/3 * BH
Volume = 1/3 * 215.25 * 136.4 = 9786.7 m3
Pyramid of Khufu
Area of Base, B = 230.4 m2
Height, H = 138.8 m
Volume = 1/3 * BH
Volume = 1/3 * 230.4 * 138.8 = 10598.4 m3
solver r=1/2m2p for p
Answer:
p= 2r/m^2
Step-by-step explanation:
Find tan A ( write as a decimal rounded to the three decimal places) FIRST ANSWER GETS BRAINIEST
Answer:
[tex]tanA = \frac{28}{21 } = 1.333[/tex]
a worker can complete the assembly of 15 chairs in 6 hours. At the rate,how many can the worker complete in a 40-hour work week?
Answer:
ooo
Step-by-step explanation:
oooo
—5 + 3x + 2 = 12
Solve for x
Answer:
x=5
Step-by-step explanation:
Answer:
x=5
Step-by-step explanation:
The area of a rectangle is represented by the expression 16m - 24. Which expression shows a factored version of the Area, one that shows the length and the width.
A | 8(2m+3)
B | 8(2+3m)
C | 8(2-3m)
D | 8(2m-3)
Answer:
The espression 8(2m - 3) shows the length and the width of the rectangle ⇒ D
Step-by-step explanation:
Let us find the greatest common factor of 16 and 24
∵ 16 = 1 × 16, 2 × 8, 4 × 4
∴ The factors of 16 are 1, 2, 4, 8, 16
∵ 24 = 1 × 24, 2 × 12, 3 × 8, 4 × 6
∴ The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
→ Find the common factors of 16 and 24
∵ The common factor of 16 and 24 are 1, 2, 4, 8
∵ The greatest one is 8
∴ The greatest common factor of 16 and 24 is 8
→ Take 8 as a common factor from 16m and 24
∵ 16m ÷ 8 = 2m
∵ 24 ÷ 8 = 3
∴ 16m - 24 = 8(2m - 3)
∴ The espression 8(2m - 3) shows the length and the width of
the rectangle
a company that makes hair care products had people try a new shampoo of the 200 people 20 had a mild allergic reaction. what percent of the people had mild allergic reaction?
Answer:
4%
Step-by-step explanation:
8 divided by 200 equals 0.04
0.04 times 100 equals 4
Therefore 4 percent of the people had a mild allgergic reaction.
Can someone help mean I know this is easy but it’s not to me lol
Answer:
I. Not a function
II. Not a function
III. Yes, function
IIII. Yep!
(I messed up the numbering in the explanations, sorry 3 is 4 and 4 is 3)
Step-by-step explanation:
Hi!
For a function, every x value must have exactly 1 y value.
f(2) can't equal both 0 and 10. It can only equal 0 or 10. So, because of this, we have a test called the vertical line test. Basically, you drag a line through a graph, and if there is any x value that goes to two (or more) different y-values, then that graph is not the graph of the function.
Let me try to give a practical explanation.
I.
In this graph, everything looks fine until we reach x=6. (I'm assuming the graph goes by ones). Do you see the problem? Yep! x has two different y values.
y= 4 and y= 6.
So, this isn't a function. Why? Because there are two y values for each x value (aka, this doesn't pass the V.L.T)
II.
(1,2), (2,5) , (3,8) , (2,-5) (1,-2)
We have two groups of problem points.
(2,5) and (2,-5) and (1,2) and (1,-2)
Here, each x value goes to a different y value. Therefore, this isn't a function
III. y=x^2
This is your typical parabola. See the graph that I attached.
Notice that -2 and 2 both go to 4. Two different x-values going to the same y-value is fine, but one x can't go to to different y values.
IIII.
(-4,1) , (0,3) , (4,5) , (6,6)
Check 1: Does any x-value go to multiple y values? Nope! So, this is a function.
Given angle FGH - angle LMN, which must be true?
Answer:
A, B, C and E are true. Only D is false.
Step-by-step explanation:
Find "x" so that a line drawn through the given points has the given slope. (Sketching the
problem may be helpful.)_
Given: A(x,6) B(2,4)
m=1/3
Answer:
x = 8Step-by-step explanation:
Slope is expressed as shown;
m = y2-y1/x2-x1
Given
m = 1/3
Coordinates A(x,6) B(2,4)
Substitute and get x
1/3 = 4-6/2-x
1/3 = -2/2-x
Cross multiply
2-x = 3(-2)
2-x = -6
-x = -6-2
-x = -8
x = 8
Hence the value of x is 8
POSSIBLE POINTS 100
A video rental store charges a $20 membership fee and $2.50 for each video rented. Write a linear equation (y=mx++) to model this situation
y = 20x + 25
y = 2.5x + 20
y = 2.5x + 20
y = -20x + 25
y = 20 + 2.5x
have to write more or I cant post this
Simplify 2 root 1/2 - 6 root 1/8 - 10 root 4/5
Answer:
0.70710678 is 2 root 1/2 simplified
Step-by-step explanation:
How much cheaper per ounce is purchasing 6 ounces for $6.72 compared to purchasing 3 ounces for
$3.48
Answer:
1.60
Step-by-step explanation:
:)
I’m giving 20 points and will give brainliest.
Answer:
Express 5 72 in simplest radical form:
Factorize the 72 in your expression:
5√72 = 5√(2*2*2*3*3)
take a pair of two's and a pair of three's out of the radical sign:
5√72 = 5*2*3√2 = 30√2
this is the simplest radical form
Step-by-step explanation:
Answer: Express 5 72 in simplest radical form:
Factorize the 72 in your expression:
5√72 = 5√(2*2*2*3*3)
take a pair of two's and a pair of three's out of the radical sign:
5√72 = 5*2*3√2 = 30√2
this is the simplest radical form
Step-by-step explanation:
HOPE I HELPED
A test has 10 questions worth 100 points in total. The test consists of multiple choice questions, which at worth 4 points each, and open-response questions, which are worth 12 points each. How many multiple choice questions are on the test
Given:
A test has 10 questions worth 100 points.
Points of each multiple choice question = 4
Points of each open-response question = 12
To find:
The number of multiple choice questions.
Solution:
Let x be the number of multiple choice questions and y be the open-response questions.
According to the question,
Total question : [tex]x+y=10[/tex] ...(i)
Total points : [tex]4x+12y=100[/tex] ...(ii)
Form (i), we get
[tex]y=10-x[/tex] ...(iii)
Putting this in (ii), we get
[tex]4x+12(10-x)=100[/tex]
[tex]4x+120-12x=100[/tex]
[tex]-8x=100-120[/tex]
[tex]-8x=-20[/tex]
Dividing both sides by -8, we get
[tex]x=\dfrac{-20}{-8}[/tex]
[tex]x=2.5[/tex]
Since x is the number of multiple choice questions, so it cannot be a faction value.
Therefore, the number of multiple choice questions in test are either 2 or 3.
If 3x−y=12, what is the value of
8x.2y? Explain.
A) 212
B) 44
C) 82
D) The value cannot be determined from the information given.
Answer:
A
Step-by-step explanation:
use the equation x=4+y/3 to find out.
8x + 2y = 24
2y = -8x + 24
y = -4x + 12.....so the slope is -4, and the y int is 12 or (0,12)
to find the x int, sub in 0 for y and solve for x....in either the original equation or the slope intercept equation
8x + 2y = 24
8x + 2(0) = 24
8x = 24
x = 24/8
x = 3.....so the x int is 3 or (3,0)
now plot ur intercepts (3,0) and (0,12)......now start at ur y int (0,12)...and since ur slope is -4, u come down 4 spaces, then to the right 1 space, then down 4, and to the right 1...keep doing this and u should cross the x axis at (3,0)
Answer:
Step-by-step explanation:
A)212
The diagram below shows the start and finish diagrams of a construction using a compass and straightedge.
Start
Finish
X
F
W
х у
Which of the following statements are true about this construction? Select all that apply.
The construction is of a line perpendicular to FG from a point not on FG
The first step of the construction is to draw a circle with center X
The first step of the construction is to draw the perpendicular bisector of WY.
The second step of the construction is to draw the perpendicular bisector of FG.
O The second step of the construction is to draw the perpendicular bisector of WY.
Answer:
1st and 4th
Step-by-step explanation:
Find the unit rate: 6 children from 2 families.
2 children per family
1/2 children per family
3 children per family
1/6 children per family
Answer:
The answer is 3 children per family.
Step-by-step explanation:
This is a fraction equal to
6 children ÷ 2 familys =3 children per family.
Just took the quiz.
Question 2 What is the length of segment BC? a:4 b:5 c:6 d:7
Answer:
a
Step-by-step explanation:
solve the following-
4y + 2+y= 2(2y + 3)
-4
4
-8
8
Answer:
y=4
Step-by-step explanation:
4y+2+y=4y+6
4y-4y+y=6-2
y=4
hope it helps
Answer:
4
Step-by-step explanation:
Which statement is true about the numbers marked on this horizontal number line?
A.
0.25 < -0.25
B.
0.25 > -0.25
C.
-0.25 = 0.25
D.
-0.25 > 0.25
Answer:
B.
Step-by-step explanation:
Answer:
The answer to this issssssss surely B
PLEASE HELP...
A car is bought at the price of $20,000. The value decreases at the rate of .20 every year (t). The exponential expression 20,000(0.80)t describes this situation. Find the price of the car after 3 years.
Question 2 options:
A)
$10,240
B)
$11,874
C)
$5,892
D)
$9,399
Answer:
$10,240
Step-by-step explanation:
y = 20,000 (.80)^t
y = 20,000 (0.80)^3
0.8^3 = 0.512
0.512 x 20,000 = 10240
Your answer would be A. $10,240.
It's timed plzzz help!!!
Answer:
2A/p
the last option
Step-by-step explanation:
gl!!!
It will cost a total of $7,740 for 18 students to go to New York City for Spring Break. The cost for each student is the same. What is the cost for each student?
$430.00
Step-by-step explanation:
[tex]7740 \div 18 = 430[/tex]