What are the slope and y-intercept of the line?

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:

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:

Option D

Step-by-step explanation:

Given the inequality statement: 5 + 8x < 3(2x + 4):

We must solve for the solution of the given inequality statement.

First, distribute 3 into the parenthesis:

5 + 8x < 3(2x + 4)

5 + 8x < 6x + 12

Next, subtract 6x from both sides:

5 + 8x - 6x < 6x - 6x + 12

5 + 2x < 12

Then, subtract 5 from both sides:

5 - 5 + 2x < 12 - 5

2x < 7

Divide both sides by 2 to solve for x:

[tex]\displaystyle\mathsf{\frac{2x}{2}<\:\frac{7}{2}}[/tex]

[tex]\displaystyle\mathsf{x<\:\frac{7}{2}}[/tex]  

Since  [tex]\displaystyle\mathsf{\frac{7}{2}}[/tex] = 3.5, and that the inequality symbol is "<," then it means that   [tex]\displaystyle\mathsf{\frac{7}{2}}[/tex] or 3.5 is not included as an endpoint.  This corresponds to an empty circle on the 3.5 mark on the number line, pointing towards the left (indicating that the values must be less than 3.5).

Therefore, the correct answer is Option D.

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:

Step-by-step explanation:

how do I rewrite this using the distinctive property

6(-4)

Answer:

14+29=43

Step-by-step explanation:just add it

The antecedent is They had a guard dog and the consequent is No one would trust pass on their property.

The proposition given contains a conditional, whose form is [tex]p \implies q[/tex], representing a causal relationship, where:

(Antecedent) [tex]p:[/tex] They had a guard dog.

(Consequent) [tex]q:[/tex] No one would trust pass on their property.

Hence, the antecedent is They had a guard dog and the consequent is No one would trust pass on their property.

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Answer:

Z and X is incorrect

Answer:

Step-by-step explanation:

For the first throw the probability that it does not land on four should be .35 not .25

On the top for the second throw the probabilities should be swapped (so land on 4= .65 and not land on four =.35)

Answer: C. an increase in prices for domestically produced watermelons.

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:

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:

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)

Answer:

Step-by-step explanation:

Old weight = 60 pound

New weight = 80 pound

Finding:

Percent of increase in weight

Therefore:

Percent of expansion in weight = [(New weight - old weight)/Old weight]100

Percent of expansion in weight = [(80 - 60)/60]100

Percent of expansion in weight = [(20)/60]100

Percent of expansion in weight = 33.33% Approx.

Answer:

$1200

Step-by-step explanation:

Since he's paying $100 on a 12 month plan, you do

100 * 12 = 1200

In total he's paying $1,200.

Answer: 1200

Step-by-step explanation: Hope this helps :)

Answer:

9.51

Step-by-step explanation:

9 x 1 is equal to 9

5 x 1/10 is equal to 5/10 which is also 0.5

1 x 1/100 is equal to 1/100 which is also 0.01

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:

A.25×5×8=960

B.15×7×14=1610

C.5x39×8=1290

D.12×20×4=1124

Step-by-step explanation:

yan po hirap

Answer:

ñ

Step-by-step explanation:

ñ

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

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.

The given quadratic function for the restaurant sales indicates that the sale first reduces then increases.

Reasons:

The function for the sales in the restaurant is y = 3·x² + 3.2·x + 514

Where;

y = Sales in billions of dollars

x = Number of years since 2008

Required:

The year in which the restaurant industry food and drink sales will be $1212 billion.

Solution:

When the food and drink sale is $1212 billion, we have;

1212 = 3·x² + 3.2·x + 514

Which gives;

3·x² + 3.2·x + 514 - 1212 = 0

3·x² + 3.2·x - 698 = 0

Factorizing with a graphing calculator gives;

(x + 15.796)·(x - 14.729) = 0

x = -15.796, or x = 14.729

The time will have a natural number value, therefore the positive value of x

= 14.729 is used.

Therefore, the number years since 2008 at which the restaurant sales will

be $1212 billion is approximately 15 years.

The year at which the sales will be $1212 billion = 2008 + 15 = 2023

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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!!

The length of the zipline is found using Pythagoras's theorem, which gives

the length of the hypotenuse side of a right triangle.

Reasons:

Height at which the zipline will be tied to one of the trees = 42 feet

Height at which the zipline will be tied to the other tree = 3 feet

The distance between the trees = 60 feet

Required:

The length of the zipline

Solution:

The length of the zipline is found as follows;

Taking one of the trees to be at the origin, the coordinates of one of the tying point = (0, 42)

The coordinates of the other tying point = (60, 3)

The in the imagined right triangle formed by the zipline and the distance

between the trees, the length of the zipline is given by Pythagoras theorem

as follows;

Length of zipline = [tex]\sqrt{(60 - 0)^2 + (3 - 42)^2} = 3 \cdot \sqrt{569}[/tex] ≈ 71.56

Length of the zipline ≈ 71.56 ft.

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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

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

Answer:

1/345 or 0.00289855 (for 1/5 / 69)

I feel like you're most likely talking about 69 / 1/5 which is 345

Try looking at the problem you are doing again :)

Answer:

0.00289855072

Step-by-step explanation:

1÷5 = 0.2

0.2 ÷ 69 = 0.00289855072

Answer:

1st one

Step-by-step explanation:

:) pls mark brainliest