Mathematics Middle School

Which is the simplified form of the expression (2^-2) (3^4)^-3 x (2^-3) (3^2) ^2?


A: 1/ 2^36 3^48

B: 1/ 3^8

C: 3^8

D:2^36 3^48

Answers

Answer 1
[tex](2^{-2})(3^4)^{-3}\times(2^{-3})(3^2)^2=(2^{-2})(2^{-3})\times(3^4)^{-3}(3^2)^2\\\\=2^{-2+(-3)}\times(3^{4\cdot(-3)})(3^{2\cdot2})=2^{-5}\times(3^{-12})(3^4)\\\\=2^{-5}\times3^{-12+4}=2^{-5}\times3^{-8} =\dfrac{1}{2^5\cdot3^8}\\\\\text{used:}\\\\a\cdot b=b\cdot a\\\\a^n\cdot a^m=a^{n+m}\\\\(a^n)^m=a^{n\cdot m}[/tex]
Answer 2

The answer is D

Just took the test

Related Questions

A rectangle has a perimeter of 34 cm in an area of 52 cm squared it's length is 5 more than twice its width write and solve the system of equations to find the dimensions of the rectangle

Answers

L+W=17 W=4 is the answer.

Let [tex] l [/tex] be the length and [tex] w [/tex] be the width of the rectangle.

Given perimeter of the rectangle

[tex] 2(l+w)=34 \; l+w=17[/tex]

Area of the rectangle is

[tex] lw=52 [/tex]

Also length is 5 more than twice its width,

[tex] l=2w+5 [/tex]

From the above equations

[tex] (l-w)^2=(l+w)^2-4lw=17^2-4*52=81\\
l-w=9,\; since \; l>w [/tex]

Now [tex] 2l=9+17=26\;,l=13,w=4 [/tex]

The dimensions of the rectangle are length [tex] l=13 [/tex], and width [tex] w=4 [/tex].


which is cheaper 6x8 tiles for 1.29 or 4x4 tiles for .99

Answers

- 48 = 1.29

- 16 = .99

16 × 3 = 48
 
3 × 0.99 = 2.97

That equals:

48 = 1.29

48 = 2.97

The cheaper one is 6×8 tiles for $1.29

Hope this helped☺☺

Final answer:

After calculating the cost per square inch for both tiles, the 6x8 tile at $0.026875 per square inch is less expensive than the 4x4 tile at $0.061875 per square inch. Thus, the 6x8 tiles are cheaper.

Explanation:

To determine which tile is cheaper, you need to calculate the cost per square inch for each tile, and then compare them. The 6x8 tile has an area of 48 square inches (6 inches x 8 inches), and it costs $1.29. To find the cost per square inch, divide $1.29 by 48 square inches.

Cost per square inch for 6x8 tile: $1.29 / 48 = $0.026875

The 4x4 tile has an area of 16 square inches (4 inches x 4 inches), and it costs $0.99. To find the cost per square inch, divide $0.99 by 16 square inches.

Cost per square inch for 4x4 tile: $0.99 / 16 = $0.061875

Comparing these two amounts, the 6x8 tile at $0.026875 per square inch is less expensive than the 4x4 tile at $0.061875 per square inch. Therefore, the 6x8 tiles are cheaper than the 4x4 tiles.

For several months, a restaurant manager collected data on the number of people at a table (p) and the total bill, in dollars (d). She found that there is a positive linear association between p and d that is best modeled by the equation
d = 15.7p + 2.0.

What statement is true?


The model predicts that the average total bill for a table is $15.70.

The model predicts that for each additional 2 people at a table, the total bill increases by $15.70.

The model predicts that the average bill for any table with 2 people is $15.70.

The model predicts that for each additional person at a table, the total bill increases by $15.70.

Answers

The second to last answer would be correct
i believe it should be c

Sara hiked down a mountain for 4 hours. Each hour her elevation decreased by 8 meters. Compute her change in elevation to her starting point.

Answers

In order for me to figure out the answer I need the "starting point" all I get from this is how much she decreased in total, which is 32.
Final answer:

Sara's change in elevation is calculated by multiplying 4 hours by -8 meters/hour. This gives a total change in elevation of -32 meters, which shows that Sara descended 32 meters from her starting point.

Explanation:

The subject of your question is math, specifically dealing with the concept of multiplication. To determine Sara's change in elevation, we have to know how much the elevation decreases each hour. It's important to note that the decrease in elevation is the same as saying Sara is descending, thus the change will be represented by a negative number.

In this case, for every hour Sara hiked, her elevation decreased by 8 meters. Therefore, the total change in elevation after 4 hours would be 4 hours multiplied by -8 meters/hour. The calculation for this is:

4 hours * -8 meters/hour = -32 meters

Therefore, Sara hiked down a total of 32 meters from her starting point on the mountain.

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the radius of a golf ball is 2.1 centimeters find the volume of the golf ball to the nearest tenth

Answers

Final answer:

The volume of the golf ball, rounded to the nearest tenth, is approximately 13.8 cm^3.

Explanation:

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.

In this case, the radius of the golf ball is given as 2.1 centimeters. So, substituting the value of the radius into the formula, we can find the volume.V = (4/3)π(2.1)^3 = 4.4π cm^3. To find the volume to the nearest tenth, we substitute π with its approximate value of 3.14 and calculate V = 4.4 * 3.14 = 13.816 cm^3.

Rounded to the nearest tenth, the volume of the golf ball is approximately 13.8 cm^3.

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A ladder is leaning on a fence and it reaches up a wall 20 feet high. The fence is 10 feet from the wall and the base of the ladder is 12 feet from the fence. How tall is the fence, in feet?

Answers

Answer:

10.9 feet

Step-by-step explanation:

The wall, fence and ladder form similar right triangles as pictured

Use the ratio of corresponding sides to solve for x, the fence height

x/12 = 20/(10+12)x/12=20/22x/12 = 10/11x = 12*10/11x = 10.9 feet

The fence is 10.9 feet tall

use the law of cosines to find the measure of BC?

Answers

x^2= 17^2+28^2-2(17)(28)cos91 
x=33.00

The length of side CB is 33 unit using Law of Cosines.

Thus, option (D) is correct.

Given:

AB = 28 unit

<A = 81

AC = 17 unit

According to Law of Cosines

the lengths of the sides of a triangle to the cosine of one of its angles.

The Law of Cosines states:

[tex]c^2 = a^2 + b^2 - 2ab * cos(C)[/tex]

Where:

c  = side opposite angle C

a and b = lengths of the other two sides

< C= opposite side c

Now, using Law of Cosines

CB² = AC² + AB² - 2 . AC. AB COS (91)

       = (17)² + (28)² - 2 (17)(28) COS (91)

       = 289 + 784 - 476 (-0.01745)

       = 1,081.3062

So, CB = √ (1,081.3062)

CB = 32.883

CB = 33 unit.

Thus, the value of CB is 33 unit.

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PLEASE HELP ASAP!!!!!

Answers

accute hope this helps
the answer is scalene. hope this helps : )

Sarah bought a 16 ounce jar of strawberry jam for $3.20. What is the unit price

Answers

Divide 16 by 3.20$. You would get 50 cents per ounce of strawberry jam
Well, the unit price is how much does 1 ounce cost. Since 16 ounces of strawberry jam costs $3.20, divide 3.20 by 16 to find the unit price.
3.20/16=0.2, so the unit price is $0.20.
I hope this helps!
-Raiden

DF bisects EDG find the value of x

Answers

DF bisects <EDG 
so EF = FG
5x + 24 = 9x
4x = 24
  x = 6

answer
D. last one
6

9x squared= -18x+7
[tex]9x {}^{2} = - 18 + 7[/tex]

Answers

[tex]-9x^2=-18x+7\ \ \ |+9x^2\\\\9x^2-18x+7=0\\\\a=9;\ b=-18;\ c=7\\\\\Delta=b^2-4ac\to\Delta=(-18)^2-4\cdot9\cdot7=324-252=72\\\\\sqrt\Delta=\sqrt{72}=\sqrt{36\cdot2}=\sqrt{36}\cdot\sqrt2=6\sqrt2\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a};\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\x_1=\dfrac{18-6\sqrt2}{2\cdot9}=\dfrac{9-3\sqrt2}{9}=\dfrac{3-\sqrt2}{3}\\\\x_2=\dfrac{3+\sqrt2}{3}[/tex]

The cost of a taxi is $2.75 plus $0.40 per half mile.write an equation to find the cost of a taxi ride that is m miles long How much would it cost you to travel 45 miles m=#miles c=#cost
1.C stand for ____.
a.cost
b.circle
2.what is the equation?
a.c=-0.4m+2.75
b.c=0.4m+2.75
3.what is the solution?
a.$6.35
b.$6.25

Answers

1) It tells you in the question c = cost, so cost would be the answer

2) 2.75 is the fixed rate so we would keep it as is. C is the cost which would the total, so c = ?m + 2.75
0.40 per half mile so you put 0.40m because it varies depending on the amount of miles
That makes the equation c = 0.40m + 2.75

3) Now to find how much it costs for 45 miles, you plug 45 for m
c = 0.4 * 45 + 2.75
c = 20.75
Not sure why it isn't an option

Alice paid $17.00 for 2 beads for her bracelet. Then she paid $42.50 for 5 more of the same kind of beads for her bracelet. Which is the price of one bead?

Answers

Your answer should be 8.5! if thats not one of your answer choices then round it then your answer would be 9! I hope this helped.

Answer:

Step-by-step explanation:

Jackson goes to the gym 0, 2, or 3 days per week, depending on work demands. The expected value of the number of days per week that Jackson goes to the gym is 2.05. The probability that he goes 0 days is 0.1, the probability that he goes 2 days is , and the probability that he goes 3 days is .

Answers

For a probability distribution the expected value is the summation of product of probabilities with their respective data values. Let x be the probability that Jackson goes gym for 2 days and y be the probability that he goes gym for 3 days.

For the given case we have following values and their probabilities:

0 : 0.1

2 : x

3 : y

So the expected value will be = 0(0.1) + 2(x) + 3(y)

Expected value is given to be 2.05. So we can write the equation as:

2x + 3y = 2.05 (Equation 1)

Also for a probability distribution, the sum of probabilities must always equal to 1. So we can set up the second equation as:

0.1 + x + y = 1

x + y = 0.9 (Equation 2)

From Equation 2 we can write the value of x to be x = 0.9 - y. Using this value in equation 1, we get:

2(0.9 - y) + 3y = 2.05

1.8 - 2y + 3y = 2.05

1.8 + y = 2.05

y = 0.25

Using the value of y in equation 2 we get value of x to be 0.65

Therefore we can conclude that:

The probability that Jackson goes to gym for 2 days is 0.65 and the probability that he goes to gym for 3 days is 0.25

He goes to the gym 0, 2, or 3 days per week.  

Let's assume P(0 days)=p, P(2 days)=q, and P(3 days) = r.

So, p+q+r = 1

E(X)= E(x=0)*P(0 days) + E(x=2)*P(2 days) + E(x=3)*P(3 days)

E(X) = 0*p + 2*q + 3*r = 2q + 3r

Given is the value of P(0 days) = p = 0.1

Given is the expected value of number of days is E(X) = 2.05

Therefore, we have 0.1 + q + r = 1 and 2q + 3r = 2.05

Or, q + r = 0.9 and 2q + 3r = 2.05

Solving the two equations :-

(2q+3r)-2*(q+r) = 2.05-2(0.9)

r = 0.25

q = 0.65

Therefore, P(2 days) = 0.65 and P(3 days) = 0.25

What is QR to the nearest tenth

Answers

The answer is 36.0 because

An event is three times as likely as its complement. What is the probability of the event?

Answers

E = some event
C = complement of event E
Since the events are complementary, this means P(E)+P(C) = 1

We know that P(E) = 3*P(C) since "an event is three times as likely as its complement"

So we can replace P(E) with 3*P(C) and then isolate P(C)
P(E) + P(C) = 1
3*P(C) + P(C) = 1
4*P(C) = 1
P(C) = 1/4

The probability of the complementary event is 1/4
So the probability of the original event is 3/4 (three times 1/4)

Answer: 3/4

note: in decimal form, 3/4 = 0.75

how do you solve for x and y

Answers

Given that the length of the bigger triangle is 2 times the length of the smaller triangle :
⇒ Ratio of the smaller triangle : larger triangle = 1 : 2

x = 34 x 2 = 68 units

Angles in a triangle sum up to 180:
y = 180 - 76 - 41 = 63°

Answer : x = 68 units, y = 63°




Explain how the segment addition postulate can be modeled using a real-world object.

Answers

To determine the length of AB, one must subtract BC from AC. If the length of AC is 18 and the length of BC is 4, then using this formula yields 18 - 4 = 14, so the length of AB is 14.This postulate also allows a line segment that has only two known points to be broken into two line segments with the addition of a third point in between the endpoints. This is useful for proofs in geometry and analysis.

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Dadas las funciones f(x) = x + 3, g(x)= x(cuadrada)+ 5x + 6,r(x) = x+2, s(x) = x(cuadrada) - 3x - 10

Determina (g(x)) (s(x))

Answers

so the answer is D hope this would help you

A truck is transporting 6 cars to a dealership. Each car weighs 1 ton 1,400 pounds. What is the total weight in pounds of the cars the truck is transporting?

Answers

1 ton= 2000 pounds

STEP 1:
Convert each car's weight to pounds:

= 2000 pounds + 1400 pounds
= 3400 pounds per car


STEP 2:
multiply each car's weight in pounds by the total number of cars

= 3400 pounds * 6 cars
= 20,400 pounds total


ANSWER: The truck is transporting 20,400 pounds.

Hope this helps!  :)

The Eiffel Tower is about 301 m tall Cooper is making a scale model of the using the scale 750 meters : 1 meter to the nearest 10th of a meter, what will be the height of the scale model

Answers

Assuming the scale is 750:1, you can set up the following proportion:

[tex] \frac{301}{x} = \frac{750}{1} [/tex]

Cross multiply the values.

750x = 301

Divide both sides by 750 to solve for x.

x = [tex] \frac{301}{750} [/tex]

Converted to a decimal and rounded to the nearest tenth, the scale model will be 0.4 meters tall.

maths question help plz

Answers

using the Pythagorean theorem:
x = sqrt(5.1^2 + 2.5^2)

x = sqrt ( 26.01 + 6.25)

x = sqrt(32.26)

x = 5.679
rounded off: X = 5.68 mm

help please 38 points

Answers

I’m confused on the same question :(

Alan drew a polygon with four sides and four angles. All four sides are equal.None of the angles are right angles.What figure did Alan draw

Answers

Alan drew a rhombus, all four side are equal but none of the angles are right.

Organizers of an outdoor concert will use 320 feet of fencing to fence off a rectangular VIP section. What is the maximum area that they can fence off? A) 3,200 square feet B) 6,400 square feet C) 12,800 square feet D) 24,000 square feet

Answers

2(l+w)=320

l+w= 160

l=160-w

lw=A

160w-w²= A

w²-160w+A=0


w max= -b/(2a)= 160/2= 80 ft


Max A = 160(80)-(80)²= 6400 ft²

So  B is correct

Answer:

B

Step-by-step explanation:

A map has a scale of 1/2 inch to 4 miles. The shortest distance between two cities on the map measures 8 inches. If d represents the shortest distance between the two cities, what is d?

A. 16 mi.

B. 32 mi.

C. 64 mi.

D. 72 mi.

Answers

The answer would be C because for every 1 inch, would be 8 miles, so we then multiply the inches by 8 to get to 8 inches, so we then multiply the miles by 8 and we get 64 miles.

D = 64 mi.

Answer:

C

TOOK SAME TEST ON EDGE 2021

The ___ is the collection of all possible individual outcomes for a chance process. The total probability of all the possible individual outcomes is ____.

Choices for first blank: probability model; relative frequency; sample space; probability


Choices for second blank: 0.5; 0; 1; 100

Answers

Answer:

1. sample space

2. 1

Step-by-step explanation:

9. Find the constant of variation, k, for y= –8 when x = 12.

show your work

Answers

The answer to this question depends on whether x and y are directly or inversely related.

Since you have not provided the relation between the two variables, I will provide the answer in both cases.

1- In case x was directly proportional to y:
This means that as x increases, y increases and vice-versa.
Translating this into an equation, we would get the following:
y = kx
where k is the constant of proportionality.
Now, we are given that:
y = -8 at x = 12
Substitute with these givens in the above equation to get k as follows:
-8 = k * 12
k = -8/12
k = -2/3

2- In case x was inversely proportional to y:
This means that as x increases, y decreases and vice-versa.
Translating this into an equation, we would get the following:
y = k / x
where k is the constant of proportionality.
Now, we are given that:
y = -8 at x = 12
Substitute with these givens in the above equation to get k as follows:
-8 = k / 12
k = -8*12
k = -96

Hope this helps :)

$7800 increased by 22.5%

Answers

First you must divide 22.5 by 100. 

22.5 / 100 = .225

Then add 1.

.225 + 1 = 1.225

Finally times 7800 with 1.225

7800(1.225) = 9555

$9555 is the answer.

Evaluate 2^5/2^3

A 1

B 2^8

C 4

D 8

Answers

Hello!

When you divide two exponents with the same base you can subtract the exponents

2^5 / 2^3 = 2^2

2^2 = 4

The answer is C) 4

Hope this helps!
Hello there i really need brainliest so,

to evaluate division you do subtraction with the exponents

2^5/2^3 = 2^2= 2 x 2 = 4

So your answer is C) 4

Hope this helps,
QueenBeauty666
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