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Answer:

Equivalent Expression:  [tex]\displaytext\mathsf{\frac{a^7}{b^8}}[/tex]

Step-by-step explanation:

Given the exponential expression,  [tex]\displaystyle\mathsf{\frac{a^{12}\:b^{-3}}{a^{5}\:b^{5}}}[/tex]:

We could use the Quotient Rule of Exponents where it states that:

[tex]\displaystyle\mathsf{\frac{a^m}{a^n}\:=\:a^{(m\:-\:n)}}[/tex]

Since we have the variables, a and b as the base, we could simply apply the Quotient Rule and subtract their exponents.

[tex]\displaystyle\mathsf{\frac{a^{12}\:b^{-3}}{a^{5}\:b^{5}}\:=\:a^{(12\:-\:5)}\:b^{(-3\:-\:5)}}[/tex]

[tex]\displaytext\mathsf{=\:a^{7}\:b^{-8}}[/tex]

Next, we must transform the negative exponent of base, b, into positive by applying the Negative Exponent Rule, where it states that:

[tex]\large\text{$ a^{-n}\:=\:\frac{1}{a^{n}} $}[/tex]

Applying the Negative Exponent Rule will result in the following exponential expression:

[tex]\LARGE\text{$ a^{7}\:b^{-8}\:=\:[a^{7}\:\times\:\frac{1}{b^8}]\:=\:\frac{a^7}{b^8} $}[/tex]

Therefore, the equivalent expression is:  [tex]\LARGE\text{$ \frac{a^7}{b^8} $}[/tex].

Answer:

28000

Step-by-step explanation:

You multiply 4 and 700.

Answer:

525 students

Step-by-step explanation:

There will be 175 chaperones on the trip.

All you need to do is find 1/4 of 700 which is the number of chaperones.

Then subtract it by 700 to find the number of students.

I hope this helps!!

Answer:

Linear

Step-by-step explanation:

This is linear because using the data you have provided we can work out that the equation is y= -5x+27

y= mx+ c (c is the gradient)

This equation shows that the line is straight (also shown in the picture) and therefore must make it a linear graph.

For the graph to be non linear, the graph would be curved but this would mean the equation would have to be a quadratic - which it isn't.

Hope this helps!

Answer:

after 13 hours

Step-by-step explanation:

Since the monthly fee is $4.25

so

● $4.25 + ( 2.75 × Number of hours) = 40

● ( 2.75 × Number of hours) = $40 - $4.25

● 35.75/ 2.75 = 13

The size of angle x from the figure is 16 degrees

The sum of the interior angle of a triangle is 180 degrees, hence to get the value of X, we will take the sum of all the given angles and equate them to 180 degrees.

127 + 37 + X = 180

164 + x = 180

Subtract 164 from  both sides

164 + x - 164 = 180 - 164

x =16 degrees

Hence the size of angle x from the figure is 16 degrees

Learn more on angles here: https://brainly.com/question/16281260

Answer:

As we know that the sum of interior angles of triangle is 180⁰.

Accounting to the question :

[tex]\implies[/tex] Sum of angles = 180⁰

[tex]\implies[/tex] 127⁰ + 37⁰ + X = 180⁰

[tex]\implies[/tex] 164⁰ + X = 180⁰

[tex]\implies[/tex] X = 180⁰ - 164⁰

[tex]\implies[/tex] X = 16⁰

Hence, the size of angle is 16⁰.

[tex]\rule{300}{1.5}[/tex]

Answer: C

Step-by-step explanation: Depositing is the act of putting money inside the bank account usually to gain interest.

If John started with $75, you add his deposit ($7) which comes out to 82. Then add 82+7 which equals 89 and so on.

75+7= 82

82+7= 89

89+7= 96

96+7= 103

Answer: is the C

Step-by-step explanation:

bank account: 75$

1st week:75

2nd week:82

3rd week:89

4th week:96

5th week:103

Answer: 10%

Step-by-step explanation:

Answer:

Step-by-step explanation:

P(B|A)=[P(A and B)]/[P(A)]

0.86=[P(A and B)]/0.43

P(A and B)=0.86×0.43=0.3698≈0.340

Answer:

Step-by-step explanation:

To solve this, what you first should do is make one of the variables equal, that way you can eliminate that variable and only have to solve one of them. Let's eliminate y, since that one is easier. As you can see, the y in the first equation is 3 times less than the y in the second, so you would multiply everything the first equation by 3 to help eliminate y. After doing this, you would have -6x + 3y = 48, with which you will add to the second equation, which leaves you with -10x = 50. Since you have a negative x, multiplying both sides by a negative sign will make it much easier to find x's value, which gives you -5 as x's value, so x = -5. Now keep this aside, because it will help you solve.

     Now that you have the value of x (-5), you should replace one of the equations with x's value, so let's just do this to the second equation. Now you have 20 - 3y = 2. Here, you should take the 20 to the right side to isolate 3y from the numbers, which leaves you with -3y = -18. This gives tells you, after simplifying, that y = 6.

     And since the order pair is always (x,y), your answer would be (-5, 6). STILL EDITING ANSWER!

Answer:

Step-by-step explanation:

To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y. For example, lets find the intercepts of the equation y = 3 x − 1 \displaystyle y=3x - 1 y=3x−1. To find the x-intercept, set y = 0 \displaystyle y=0 y=0.

1.To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y.

2.To find the x-intercept, set y = 0 \displaystyle y=0 y=0.

3.To find the y-intercept, set x = 0 \displaystyle x=0 x=0.

Answer:

d

Step-by-step explanation:

range means y values so automatically a and b aren't right

there's no limits for y since it's linear, so it's D

that R sign basically means "all real numbers"

Answer:

y - 1 =  -2(x - 3)

Step-by-step explanation:

Given the point, (3, 1) and the slope of –2:

Let  (x₁, y₁) = (3, 1)

slope: m = -2

Substitute these values into the following point-slope form:

y - y₁ = m(x - x₁)

y - 1 = -2(x - 3)  ⇒ This is the point-slope form.

Answer:

You haven't shown the graph image but here is what the graph looks like if the equation is y=3/4x -3

Step-by-step explanation:

Answer:

0.75x-3

Step-by-step explanation:

914 1404 393

Answer:

  24% of 24 is not a whole number

Step-by-step explanation:

24% of Mrs. Cho's students is ...

  0.24 × 24 = 5.76 . . . students

This is not a whole number. The number of students must be a whole number. There cannot be part of a student in the play.

Answer:

all squares are quadrilaterala

Step-by-step explanation:

it has 4 sides and I just remember.

Answer:

All squares are quadrilaterals.

Step-by-step explanation:

Squares are defined as quadrilaterals with four right angles and four congruent sides.

Answer:

63°

Step-by-step explanation:

Angle sum property = 180°

=> 19 + 98 + x = 180

=> x = 180 - 117 = 63°

Answer:

Step-by-step explanation:

Given,

Measurement of one angle of a triangle = 19°

Measurement of 2nd angle of the triangle = 98°

Let,

The third angle be = x

As we know,

Sum of all the angles of a triangle is 180°

Therefore,

By the problem,

=> 19° + 98° + x = 180°

=> x = 180 - 98 - 19

=> x = 63

Hence,

The measurement of 5he third angle of the triangle is 63° (Ans)

If Athlete J continues at that speed, it will take 12 minutes to run 1 mile

It will take Athlete J 60 minutes to run 5miles

Since the speed of Athlete H is greater than that of J, hence Athlete H runs faster.

The formula for calculating the speed of the athlete is expressed as:

Speed = Distance/Time

1) If Athlete J runs 2/3 of a mile in 8 minutes, this can be expressed as:

2/3 miles = 8 minutes

If the athlete runs for 1 mile, then;

1 mile = x

Divide both expressions

2/3 = 8/x

2x = 24

x = 12 minutes

Hence If Athlete J continues at that speed, it will take 12 minutes to run 1 mile

2) if athlete J run 5 miles, the time taken will be expressed as;

2/3(5) = 8/x

2/15 = 8/x

2x = 120

x = 60minutes

Hence it will take Athlete J 60 minutes to run 5miles

3) If Athlete H runs 2 3/4 miles in 1/2 hour, then the speed of athlete H will be expressed as:

Speed = (2 3/4)/0.5

Speed = 2.75/0.5

Speed = 5.5miles/hr

For Athlete J;

Speed = 5/1

Speed = 5 miles/hr

Since the speed of Athlete H is greater than that of J, hence Athlete H runs faster.

Learn more here: https://brainly.com/question/13262646

Answer: 8

Step-by-step explanation:

Rewriting input as fractions if necessary:

1/8, 1/4

For the denominators (8, 4) the least common multiple (LCM) is 8.

LCM(8, 4)

Therefore, the least common denominator (LCD) is 8.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

1/8 = 1/8 × 1/1 = 1/8

1/4 = 1/4 × 2/2 = 2/8

Step-by-step explanation:

you need to be careful when writing/copying the text.

I assume this one here is actually

(3/5)m > -30

then

3m > -150

m > -50

Answer: m > -50

Step-by-step explanation: Got correct on test

Answer its 5982

Step-by-step explana

Answer:

2x - y = - 8

Step-by-step explanation:

y - 4 = 2(x + 2) ← distribute

y - 4 = 2x + 4 ( subtract y from both sides )

- 4 = 2x - y + 4 ( subtract 4 from both sides )

- 8 = 2x - y , that is

2x - y = - 8 ← in standard form

with A = 2, B = - 1 and C = - 8

Answer:

1 pack = 16

128 dollars will get you 128/16 which is 8

so 128 dollars will give you 8 packs

Answer:

8

Step-by-step explanation:

128 divided by 16

Answer:

There are 719,115.8179kg of fuel stored in the external tank

Step-by-step explanation:

102619.377 + 616496.4409 = 719,115.8179

Answer:

4b<30

Step-by-step explanation:

product means multiply so 4•b or 4b

less than so<

Step-by-step explanation:

addition means the sum of 2 numbers

so.....b+4 <30

b <30-4

B <26

Height: 4 units

Width 2√/2

Explanation:

Start by sketching y = 6 - ². Then draw a rectangle beneath it. You will notice that the width is 2x and the height is 6 ². Area is given by length - times width, so the area function will be A=2x (6 - x²) = 12x - 2x³.

Now you differentiate to find the maximum.

A' = 12 - 6x²

Find critical numbers by setting A' to 0.

x = ± √/2

The derivative is negative at x = 2 and positive at x = 1, which justifies that the rectangle with width of √2 has maximal area.

The height will be y (√2) = 6 – (√2)²) = 4

Answer:

i dont know

Step-by-step explanation:

Step-by-step explanation:

Absolute value is the positive of a number.

Ex: -2 absolute value is 2

So -62 would have an absolute value greater than 50.

Answer:

-62

Step-by-step explanation:

Answer:

....................... what is the queston

Step-by-step explanation:

Answer:

8x + 4y

Step-by-step explanation:

3(x + y) + 5x + y

3x + 3y + 5x + y....... distribute 3 to both variables in the parenthesis

8x + 4y....................... combine like terms

Answer

8x+4y

Step-by-step explanation:

First you expand the 3(x+y) by multiplying 3 with x+y

So it becomes 3x+3y

Now your new expression will be 3x+3y+5x+y

After that, you combine the like terms, 3x and 5x are like terms, 3y and y are like terms.

So it will become 3x+5x+3y+y

You can add the like terms up, so 3x+5x=8x and 3y+y =4y

The simplified expression will be 8x+4y