Expressions a, b, and d are equivalent to 5^3. They all follow the laws of exponents, resulting in the same value of 5^3, or 125.
Explanation:The question is asking which expressions are equivalent to 5^3. Let's break down each option:
a. 5^7 x 5^-4: Utilizing the law of exponents, we add the exponents when multiplying the same base, hence we get 5^3. b. 5^12/5^9: According to the law of exponents, we subtract the exponent of the denominator from the exponent of the numerator, which gives us 5^3. c. 5^1 + 5^2: This equals 5 + 25, which is not equal to 5^3 (125). d. 5^0 x 5^3: Any number raised to the power 0 is 1, therefore this equals 5^3. e. 5^3 - 5^0: This equals 125 – 1, which is not equal to 5^3 (125).
So, options a, b, and d are equivalent to 5^3.
Learn more about Equivalent Expressions here:https://brainly.com/question/32827451
#SPJ1
If A varies directly as b and A=6, when b=1/3, find the equation that relates A and b.
Answer:
A = 18b
Step-by-step explanation:
A = kb
6 = k(⅓)
k = 6×3
k = 18
A = 18b
Answer:
a = 18b
Step-by-step explanation:
Given that a varies directly as b then the equation relating them is
a = kb ← k is the constant of variation
To find k use the condition that a = 6 when b = [tex]\frac{1}{3}[/tex] , thus
k = [tex]\frac{a}{b}[/tex] = [tex]\frac{6}{\frac{1}{3} }[/tex] = 18
a = 18b ← equation of variation
A data set consists of the following data points:
(2,4),(4,7), (5, 12)
The line of best fit has the equation y = 2.5x - 1.5. What does this equation
predict for a value of x = 7?
0
O A. 16
O B. 19
O C. 20.5
O D. 175
0 0 0
Answer: when x=7 the answer is 16
Step-by-step explanation:
The sum of Rodney and his sister is 31 his sister is five years less than three times Rodney’s age what is the difference in age between Ronnie and his sister
Answer: The difference in their ages is 13.
Step-by-step explanation: We shall start by assigning letters to represent the age of each one of them, that is the unknown variables. So, we shall call Rodney’s age r, and his sister’s age we shall call t. If the sum of Rodney and his sister’s age is 31, then we can write this as an expression,
r + t = 31
Also three times Rodney’s age can be written as 3 times r, or simply put, 3r. So five years less than three times Rodney’s age is equal to 3r - 5. Hence his sister’s age is equal to 3r - 5, or simply put,
t = 3r - 5
What we now have is a pair of simultaneous equations
r + t = 31 ————(1)
t = 3r - 5 ————(2)
We shall use the substitution method here. From equation (2), t = 3r - 5. So we shall substitute for the value of t into equation (1).
r + t = 31 now becomes
r + 3r - 5 = 31
4r - 5 = 31
Add 5 to both sides of the equation
4r -5 + 5 = 31 + 5
4r = 36
Divide both sides of the equation by 4
r = 9.
That means Rodney’s age is 9.
If from equation (1) r + t = 31, we can now insert the value of r in order to find t.
r + t = 31
9 + t = 31
Subtract 9 from both sides of the equation
t = 22.
That means his sister’s age is 22 while Rodney’s age is 9.
Therefore the difference in age between Rodney and his sister is
22 - 9 which equals 13.
Averi was trying to factor 4x2 + 20x - 16. She found
that the greatest common factor of these terms was 4
and made an area model:
What is the width of Averi's area model?
Answer:
The width will be [tex]x^{2} +5x-4[/tex]
Step-by-step explanation:
Thinking process:
Let the model be:
[tex]4x^{2} +20x-16[/tex]
factoring out 4 gives:
[tex]4(x^{2} +5x-4)[/tex]
Factorizing the expression in the parentheses gives:
[tex]4(x^{2} +5x-4)[/tex]
Therefore, since the expression in the parentheses cannot be factorized further, the expression is:
[tex]length = 4 units\\width = x^{2} +5x-4[/tex]
The width of the area model is x^2 + 5x - 4
How to determine the width?The area model is given as:
Area = 4x^2 + 20x - 16
Factor out 4 from the expression
Area = 4(x^2 + 5x - 4)
Express as product
Area = 4 * (x^2 + 5x - 4)
4 represents the length.
So, the width of the area model is x^2 + 5x - 4
Read more about areas at:
https://brainly.com/question/24487155
To make the sum or difference of 3/4+1/3
Answer:
13/12 or 1 1/12
Step-by-step explanation:
First, I like to line up the fractions like this:
3/4
1/3
You can't add them yet because they have different denominators, so we have to get them to the same denominator first. What is a number 3 and 4 can be multiplied by? Let's use 12. So, we want both of their denominators to be 12. How do we do that? 4 times what equals 12? 3. However, whatever you multiply the denominator by, you have to do to the numerator as well. Here is what we have:
3/4 x 3
1/3
3x3 equals 9, so your first fraction is 9/12. Then, do the second fraction. 3 times what equals 12? 4. So, multiply the numerator, 1, by 4 to get 4. So, your second fraction is 4/12. Now, you have to add them together, 9+4 = 13. The denominator stays the same. So, your sum is 13/12. If you want to, you can also simplify it to a mixed number into 1 1/12.
If Sarah rents a washer and dryer for $52 per month for 13 months how much will she pay for 13 months?
Answer:
$676
Step-by-step explanation:
52x13= 676
Answer:
She would pay $676
Step-by-step explanation:
marvin has a standard deck of cards, what is the probability of 5?
Answer: 4/52
Step-by-step explanation:
Because thwre are 4, fives in a normal deck so the probability would be 4/52 not simplifyed
Machine 1 can complete a task in x hours while an upgraded machine (machine 2) needs 9 fewer hours. The plant mana
knows the two machines will take at least 6 hours, as represented by the inequality
Which answer choice includes all solutions to the inequality and identifies which interval(s) contain viable completion time
machine 12
(0.31 U 9.18] both contain viable times for machine 1
(0 3] U9,18]; only (9.18) contains viable times for machine 1
(-00U13,9 UL18,co), no interval contains viable times for machine 1
(-0,0) U(39) U (18,co), but only [18,00) contains viable times for machine 1
Answer:
its B
Step-by-step explanation:
after you find the intervals. you also need to consider that the plant manager knows the two machines will take at least 6 hours, so (0, 3] is taken out of the picture leaving you with B
The correct answer choice is:
(-0,0) U (3,9) U (18,∞), but only the interval [18,∞) contains viable times for machine 1.
Here, we have,
The given inequality represents the condition that the task should take at least 6 hours to complete.
Let's analyze the answer choices:
(0.31 U 9.18] both contain viable times for machine 1:
This answer choice includes the interval (0.31, 9.18], which contains values less than 6.
Therefore, it does not satisfy the condition of at least 6 hours.
(0, 3] U (9,18]; only (9, 18] contains viable times for machine 1:
This answer choice includes the intervals (0, 3] and (9, 18].
Both of these intervals contain values less than 6, so they do not satisfy the condition of at least 6 hours.
(-∞,0) U (13,9) U (18,∞), no interval contains viable times for machine 1:
This answer choice does not include the interval (0, 3] where viable times for machine 1 exist.
(-0,0) U (3,9) U (18,∞), but only [18,∞) contains viable times for machine 1:
This answer choice includes the intervals (0, 3] and (18,∞), which contain viable times for machine 1. However, the interval [18,∞) specifically represents viable completion times for machine 1.
Therefore, the correct answer is (-0,0) U (3,9) U (18,∞), but only the interval [18,∞) contains viable times for machine 1.
To learn more about the inequality visit:
brainly.com/question/24372553
#SPJ4
A manufacturing plant is looking at units shipped for a 3-year period. In 2005, the plant shipped 12,500 units. In 2008, the
plant shipped 16,000 units. Find the rate of change of units shipped over the 3-year period.
A. 3,500/
2,008
B. 3,500/
2,005
C. 3,500/3
D. 9,500
Option C - 3500/3
Step-by-step explanation:
Step 1 :
Number of units shipped in the year 2005 = 12,500 units
Number of units shipped in the year 2008 = 16,000 units
Time period = 3 years
We have to determine the rate of change of units over the 3 year period. This is obtained by dividing the difference in units by the time period.
Step 2:
The difference in units over the 3 year period = 16000 - 12,500 = 3500 units.
Hence the required change rate over the 3 year period = 3500/3
Option C is the answer.
a square green rug has a yellow square in the center. The side of the yellow square is x inches the width of the green band that surrounds the yellow square is 7 inches. What is the area of the green band?
Answer:
28x +196 in^2
Step-by-step explanation:
The outside dimension of the square green rug is (x+14), so its area is (x+14)^2. The area of the green band will be the difference between this and the area of the yellow square, (x^2).
green band area = (x +14)^2 -(x^2) = x^2 +28x +196 -x^2
green band area = 28x +196 . . . . square inches
9. Jady got a job at Yogurt land. She makes $17 per hour as a store manager. On Friday she worked 6 hours, on Sunday
she worked 4 hours and on Wednesday she worked 5 hours. When she picked up her paycheck her mom reminded her
that she owed her $65 for a pair of shoes she bought her. How much money did she have left after paying back her
mom (before taxes)?
steps ?
Answer:
190$
Step-by-step explanation:
6+4+5=15 (Hours per day she worked)
15*17=255 (The money Jady got from her paycheck)
255-65=190 (The money Jady owes her mom)
What is the perimeter of the figure
Answer:
Option A.
[tex]P=73.4\ units[/tex]
Step-by-step explanation:
see the attached figure with letters to better understand the problem
In this problem we have a triangle with a circle inscribed in it
so
[tex]A.F=A.B\\C.B=C.D\\E.F=E.D[/tex]
step 1
Find the length side B.C
[tex]C.B=A.C-A.B[/tex]
substitute the given values
[tex]C.B=23-14=9\ units[/tex]
step 2
Find the length side C.D
Remember that
[tex]C.D=C.B[/tex]
therefore
[tex]C.D=9\ units[/tex]
step 3
Find the length side E.D
we know that
[tex]E.D=E.C-C.D[/tex]
substitute the given values
[tex]E.D=22.7-9=13.7\ units[/tex]
step 4
Find the length side E.F
Remember that
[tex]E.F=E.D[/tex]
therefore
[tex]E.F=13.7\ units[/tex]
step 5
Find the length side A.F
Remember that
[tex]A.F=A.B[/tex]
therefore
[tex]A.F=14\ units[/tex]
step 6
Find the perimeter
[tex]P=23+22.7+13.7+14[/tex]
[tex]P=73.4\ units[/tex]
What is the algebraic way to solve 2000 (X -0.03)= 6000 by using the dividing each side first method
To solve the equation 2000 (X - 0.03) = 6000, divide both sides by 2000 to get X - 0.03 = 3, and then add 0.03 to each side to find X = 3.03.
Explanation:To solve the algebraic equation 2000 (X - 0.03) = 6000 using the divide each side method, we can follow these steps:
Divide both sides of the equation by 2000 to isolate the term with the variable X.This simplifies the equation to X - 0.03 = 3.Add 0.03 to both sides to solve for X.This gives us X = 3.03 as the solution.Now X has been isolated, and we have found the value that satisfies the equation.
What points names the ordered -4 -2
which of the following is not a congruence transformation
A) Translating
B) Stretching
C) Rotating
Answer:
B) Stretching is not a congruence transformation because when the shape is stretched its size can change causing that shape to not be congruent.
Alice has 800 MB of data. Bob has 1500 MB of data. Jack has 750 MB of data. Will it all fit on Alice's 4 GB thumb drive?
Answer:
Ill walk you through
Step-by-step explanation:
How many MBs are in a GB??
Remember that 1000 MB = 1 GB.
Start by adding together all the MB values.
800 MB + 1500 MB + 750 MB = 3050 MB.
Next, convert to GB by dividing by 1000.
3050 MB / 1000 = 3.05 GB
Since 3.05 < 4, YES. It will all fit in Alice's 4 GB thumb drive.
Is parallelogram HIJK a square?
Answer:
Yes
Step-by-step explanation:
Do you need an explanation?
a value of 6000 is increased by 15% find the new value
Answer:
6900
Step-by-step explanation:
[tex] = 6000 \times \frac{115}{100} = 6900[/tex]
KINDERGARTENER ASSIGNMENT
Can anyone describe me the OVERALL of this house in super SIMPLE sentenceS (without including whats inside the rooms)..???? I’ll translate it to Spanish after.
Answer:
Name the rooms in basement, ground floor and the attic.
Step-by-step explanation:
The house has 3 levels: basement, ground floor and the attic.
In the basement there's basement study and a laundry room.
On the ground floor there's a kitchen, a dining room and a living room.
In the attic there is a bathroom and two bedrooms: one for children and the other one for the parents.
Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots
are located
x2 + 3x -4 = 0
Answer:
x = 1 and x = -4
Step-by-step explanation:
Step 1: Factor and find the roots
x^2 + 3x - 4 = 0
(x - 1)(x + 4)
x - 1 + 1 = 0 + 1 and x + 4 - 4 = 0 - 4
x = 1 and x = -4
Answer: x = 1 and x = -4
Graph Below:
3.) Jada takes out a loan for $6000 to start a business after hig
8% interest for the loan. After 5 years how much interest will be added?
Answer:
$2,400
Step-by-step explanation:
1) lets use the i=prt formula
where i=interest
p=principal
r=rate
t=time
the principal here is $6000(starting amount)
rate is 0.08
and time is 5
so
I=0.08*5*6000
I=2400
you will gain an interest of $2400
Order this fraction from largest to smallest
1/4, 1/2, 1/5, 2/3, 1/6
For the same numerator, bigger denominators mean smaller fractions (if everything's positive). 2/3 is bigger than all the other ones , which are 1/2 or less.
Answer: 2/3, 1/2, 1/4, 1/5, 1/6
Before lunch, Carol hiked 3 5/8 miles. After lunch, she hiked another 2 7/8 miles. How far did she hike altogether?
6 6/8 or 6 3/4 simplified
Step-by-step explanation:
First, add 5/8 and 7/8
Next, divide the sum of 5/8 and 7/8 (which is 1 4/8)
Lastly, add the wholes and 1 from 4/8
what value of x makes the equation true?
x+41=-90
i need help
Answer:
Step-by-step explanation:
x+41=-90 (original problem)
-41 -41 (you must get rid of the common factors by doing the opposite on both sides)
x= -132 (add -90 and -41 to get -132)
16k + 24, can you show work?
Answer:yes
Step-by-step explanation:
Answer:
k = -1.5
Step-by-step explanation:
Step 1: Solve for k
16k + 24 - 24 = 0 - 24
16k / 16 = -24 / 16
k = -3/2
k = -1.5
Answer: k = -1.5
1220000 scientific notation
Answer:
1.22 x [tex]10^{6}[/tex]
Step-by-step explanation:
1,220,000 would be...
1.22 x 10^6
Answer:
you could do this 1.22E+6 or 1.22 x 10⁶
Step-by-step explanation:
2. If you know the volume of a cube, how do you find its
edge length?
nel
[tex]\huge\boxed{\sqrt[3]{\text{V}}}[/tex]
The volume of a cube is found by cubing the edge length — or multiplying it by itself twice.
In other words, the volume of a cube is as follows:
[tex]V=e*e*e[/tex]
Simplified:
[tex]V=e^3[/tex]
To find the edge length from the volume, you'd have to do the opposite, which is to find the cubic root.
(Two-Step Equations - Integers)
Sheet 3
1
The bartender of a poolside bar prepares 96 fluid Ounces of mocktail by blending
the juice of cranberries and oranges. He uses three times the amount of cranberry
juice than orange juice to prepare the mocktail. He also adds 24 ounces of lemon
extract. How many fluid Ounces of orange juice was used in all?
Cloubt 1tbe ofroncorn
Answer:
18
Step-by-step explanation:
cranberries, oranges and lemon extracts makes =96 fluid Ounces of mock-tail
i.e cranberries+oranges+lemon extracts=96 fluid Ounces of mock-tail....... (1)
let fluid ounces of orange=xthen fluid ounces of cranberry=3x; \\ because it is three times of orangeand lemon extract is given as 24 ounces.putting these values in (1), we get
[tex]3x+x+24=96[/tex]
[tex]4x+24=96\\4x=96-24\\4x=72\\x=\frac{72}{4}\\ x=18[/tex]
fluid Ounces of orange juice was used in all=18
Final answer:
To find the amount of orange juice used in the mocktail, we set up an equation and solve for 'x'. We find that the bartender used 18 fluid ounces of orange juice in the mocktail.
Explanation:
To find the number of fluid ounces of orange juice used, we need to set up an equation. Let's say the amount of orange juice used is represented by 'x'. According to the problem, the amount of cranberry juice used is three times the amount of orange juice, so it can be represented as '3x'.
We know that the total amount of mocktail prepared is 96 ounces, and the lemon extract added is 24 ounces. So, we can set up the equation: x + 3x + 24 = 96. Simplifying this equation, we get 4x + 24 = 96.
Next, we need to isolate 'x'. Subtracting 24 from both sides of the equation, we get 4x = 72. Dividing both sides by 4, we find that x = 18.
Therefore, the bartender used 18 fluid ounces of orange juice in the mocktail.
Suppose a population of 50 crickets doubles in size every 4 months. How many crickets will there be after 5 years?
1,500 crickets
1,600 crickets
2,000 crickets
1,638,400 crickets
Answer:
Starting population of crickets is 50. It doubles in size every 4 months.
5 years = 60 months
60 : 4 = 15
The equation is:
f ( x ) = 50 * 2^x ( an exponential function )
f ( 15 ) = 50 * 2^15 = 50 * 32,768
f ( 15 ) = 1,638,400
Answer: A ) 1,638,400
Determine the distance around a cherry pie crust with a 7 inch radius. Round to the nearest tenth.
Answer:
The circumference is 43.98
or 44 inches rounded, maybe
Step-by-step explanation: