Which expressions simplify to a rational answer?

Select each correct answer.

The cost for a year is cheaper in the Gym A than Gym B. The value of k for the cheaper membership would be; $10.

An equation is an expression that shows the relationship between two or more numbers and variables. A linear equation is an equation that increases at a constant rate.

An equation in the form y = kx is called a linear equation.

In the equation of form y = kx

y = dependent variable which is the total cost

x = number of months

k = constant of proportion / cost per month

Thus k = y/x

The Cost per month at Gym A = $50 / 5 = $10

The Cost per month at Gym B = $40 / 3 = $13.33

The Membership cost at Gym A for a year = $10 x 12 = $120

The Membership cost at Gym B for a year = $13.33 x 12 = $160

Hence, The cost for a year is cheaper in the Gym A than Gym B. The value of k for the cheaper membership would be; $10.

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Answer: 25 + 12.5v ≥ 170

Step-by-step explanation:

We already have the 25 reward points; it also gives the information that she gets 12.5 points for each visit. Because we don't know the amount she has gone to the theater or will go we have to use a variable; 12.5v. When we add them, we get 25 + 12.5v. The inequality we use is ≥ because it says "at least". When this is used that means it has to be equal to or greater and that is why use that sign and get the full equation;

5 + 12.5v ≥ 170

Answer:

55

Step-by-step explanation:

-119

1) Let's evaluate that polynomial when y=4, note that to evaluate is to find out the corresponding value when we plug into that another one:

2) Hence, the answer is -119

Answer:

The answer to your question is: 6 units

Step-by-step explanation:

Data

A (-4, 0)

B (-3,1)

C (0,-2)

D (-1,-3)

Formula

d = √((x2 - x1)² + (y2 - y1)²)

Process

dAB = √((x2 - x1)² + (y2 - y1)²)                 dAC = √((0 + 4)² + (-2 + 0)²)

      = √((-3 + 4)² + (1 - 0)²)                      dAC = √((4)² + (-2)²)

      = √((1)² + (1)²)                                    dAC = √(16 + 4)

      = √1 + 1                                             dAC = √20

dAB = √2  = dCD

dAD = √((-1 + 4)² + (-3 - 0)²)                    

dAD = √((3)² + (-3)²)

dAD = √9 + 9

dAD = √18 = dBC

reactangle's area = base x height = √18 x √2 = √18 x 2 = √36

                                                       = 6 units

Class rings are sold by a nearby jewelry store, which buys them for $60 each. The amount of markup is y=204.

Given that,

Class rings are sold by a nearby jewelry store, which buys them for $60 each. The ring has a name and date engraved on it, and the retailer markup it up by 340% before selling it.

We have to find the equation that can be used to find the amount of markup y.

So,

We can write the equation as

Amount of markup=340% of the purchases amount

Taking amount of the markup as y and purchases amount is $60.

y=340%×60

y=340/100×(60)

y=34×6

y=204

Therefore, The amount of markup is y=204.

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Answer:

y = -1/2x + 6.

Step-by-step explanation:

The line perpendicular to y = 2x + 3 has slope of - 1/2 so we can write it as

y = -1/2x + c

When x = -4, y = 8 so we substitute:

8 = -1/2 (-4) + c

8 = 2 + c

c = 8-2 = 6

So, the answer is

y = -1/2x + 6.

Answer:

y = -1/2x + 6.

Step-by-step explanation:

It is a completely randomized design.

What is completely randomized design ?

Completely randomized designs are used in experiment design to explore the effects of a single primary factor without taking additional nuisance variables into account. This article describes single-factor, entirely randomized designs. On the basis of the various levels of that primary factor, the experiment compares the values of a response variable. The levels of the main factor are given at random to the experimental units in fully randomized designs.

Objects or subjects are assigned to groups in a completely random design at random. Labeling each subject before choosing from the labeled participants in a table of random numbers is one common practice for allocating subjects to treatment groups. Computers can be used to accomplish this as well.

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Step-by-step explanation:

[tex] \frac{5}{6} (a) - 3 = \frac{5}{8} \\ lcd = 48 \\ \\ \frac{5}{6} (a)(48) - 3(48) = \frac{5}{8} (48) \\ 40a - 144 = 30 \\ 40a = 30 + 144 \\ 40a = 174 \\ \frac{40a}{40} = \frac{174}{40} \\ a = 4\frac{14}{40} \\ a = 4 \frac{7}{20} [/tex]

I FIRST FOUND THE LCD AFTER THAT MULTIPLY EACH AND EVERY TERM IN THE EQUATION BY IT TO HET RID OF THE FRACTIONS AND SOLVE FOR a.

Answer:

5;3

Step-by-step explanation:

Answer:

3 5/14 (second choice)

Step-by-step explanation:

c = -3 1/7

d = 6.5 (6 1/2 as fraction)

-3 1/7 as improper fraction: -22/7

6 1/2 as improper fraction: 13/2

Now put both fractions into a common denominator

-22/7 = -44/14

13/2 = 91/14

Now add:

-44/14 + 91/14 = 47/14

Change 47/14 back to fraction

47/14 = 3 5/14

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given exponential function

STEP 2: Compare with the standard exponential function to determine whether it shows growth or decay.

If a is positive and b is greater than 1 , then it is exponential growth.

If a is positive and b is less than 1 but greater than 0 , then it is exponential decay.

Hence, the given function shows an exponential decay.

STEP 3: Graph the values by using a table of values

We generate a table of values first

STEP 4: Plot the graph of the data values

The equation that represents the value of d is d = b + kc

The graph that completes the question is added as an attachment

The equation of the graph is given as

y = kx

Because the graph shows a direct variation, the equation can be illustrated as

y = mx

Where m represents the slope of the line

By comparing the equation y = mx and y = kx, we can conclude that

m = k

This means that the slope of the equation y = kx is k

From the graph, we have the points

(x, y) = (a, b) and (a + c, d)

The slope of a line is calculated using

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

Slope = k

(x₁, y₁) = (a, b) and (x₂, y₂) = (a + c, d)

So, we have

k = (d - b)/(a + c - a)

Evaluate the like terms

k = (d - b)/(c)

Multiply both sides by c

d - b = kc

Add b to both sides

d = b + kc

Hence, the value of d is d = b + kc

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By solving the equation we can conclude that Andre (36,000 steps) walks more than Priya (35,400 steps).

So, the distance that Andre traveled.

He demonstrated his ability to take 6000 steps in 50 minutes.

The pace at which Andre can walk is:

The 5 hours in minutes conversion: 5  × 60 minutes = 300 minutes

Then,

The distance traveled by Andre is:

Where x represents the number of minutes and y is the number of steps.

The formula to convert 5 hours to minutes is:

Replace x with its value in the equation:

35400 steps are taken by Priya.

Therefore, by solving the equation we can conclude that Andre (36,000 steps) walks more than Priya (35,400 steps).

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The correct question is given below:

Andre and Priya are tracking the number of steps they walk. Andre records that he can walk 6000 steps in 50 minutes. Priya writes the equation y=118x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andre and Priya each walked for a total of 5 hours. Who walks more steps?

Our strategy to win $200 is to use $100 in just one chance. It is the best bet for winning $200.

Given that we start with $100 at a casino and can bet any amount of that particular money to play a game to any amount of times where we have a 40% chance of winning in each game. If we win, we will gain the amount we bet and return the amount that we bet. If we lose, we will lose our bet.

It has been asked that what should be our strategy to win get $200.

We can write from the given information that:

Probability of wining = 40 % = 0.4

Probability of losing = 1 - 0.4 = 0.6

The best bet to win $200 is to bet $100 in one go itself.

For the above bet chance of winning $100 is 0.4

But let us assume that we are betting $50 two times,

Then L-Lose and W-Win

There will be 4 rational possible cases (WW,WL,LW,LL)

Probability of all the 4 above given cases will be as follows:

Probability of (WW) = 0.4 X 0.4 = 0.16

Probaility of (WL) = 0.4 X 0.6 = 0.24

Probability of (LW) = 0.6 X 0.4 = 0.24

Probability of (LL) = 0.6 X 0.6 = 0.36

Now for winning $100 we need to win both the bets of $50.

But the probability of winning both the bets = 0.16 ( very less than 0.4)

Hence the best bet would be to use $100 in one chance itself.

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Our strategy to win $200 is to use $100 in just one chance. It is the best bet for winning $200.

It has been asked that what should be our strategy to win get $200.

We can write from the given information that:

Probability of wining = 40 % = 0.4

Probability of losing = 1 - 0.4 = 0.6

The best bet to win $200 is to bet $100 in one go itself.

For the above bet chance of winning $100 is 0.4

But let us assume that we are betting $50 two times,

Then L-Lose and W-Win

There will be 4 rational possible cases (WW,WL,LW,LL)

Probability of all the 4 above given cases will be as follows:

Probability of (WW) = 0.4 X 0.4 = 0.16

Probability of (WL) = 0.4 X 0.6 = 0.24

Probability of (LW) = 0.6 X 0.4 = 0.24

Probability of (LL) = 0.6 X 0.6 = 0.36

Now for winning $100 we need to win both the bets of $50.

But the probability of winning both the bets = 0.16 ( very less than 0.4)

Hence the best bet would be to use $100 in one chance itself.

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Answer:

6.5°

Step-by-step explanation:

We know that both XYZ and LMN are complementary angles.

Complementary angles add up to 90°.

So,

we can simply add both of the expressions and set it equal to 90 (degrees).

(3x+14) + (5x+24) = 90

-> add the variables and constants

8x+38=90

-> subtract the 38 from both sides (90-38)

8x=52

-> divide out the coefficient to isolate the variable

x=6.5

So, the answer is 6.5 degrees.

Hope this helped :)

Answer:

[tex]\sf 12-5x+6x=4[/tex]  (Given)

[tex]\sf 12+x=4[/tex]  (Combine like terms)

[tex]\sf x=-8[/tex]  (Subtraction property of equality)

--------------------------------------------------

Hope this is what you're looking for!

Answer:

1. given

2. combine like terms,

3. subtraction property of equality

Step-by-step explanation:

Answer: the measure of H is 39 the measure of G is 51

Step-by-step explanation:

6x-15+3x+6=90

9x-9=90

9x=99

x=11

6(11)-15=51

3(11)+6=39

Two day growth factor for the height of the sun flower is 1.1449

Take the current number and subtract it from the prior value to determine the growth rate. The growth rate is then expressed as a percentage by multiplying the difference by the previous number and dividing by 100.

A height increases by 7% per day

So the growth factor for height of sun flower is  107/100 =1.07

For 2.7 days - 12 inch

3.74 days increase by 7% by day

⇒ 12 + 7/100 x 12

⇒ 12 ( 107/100 )

⇒ 12.84 inches

3.74 days 12.84 inches

4.74 days increase by 7 % by day

⇒ 12.84 + 7/100 x 12.84

⇒ 12.84 x 107/100

⇒ 13.73 inches

Two days growth factor

⇒ 107/100 x 100/107

⇒ 1.1449

Hence Two day growth factor for the height of the sun flower is 1.1449

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In an observational study, we measure or survey members of a sample without trying to affect them. In an experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.

This is clearly an observational study

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The unknown angles are as follows:

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, linear angles, alternate angles etc.

Therefore,

∠1 = 110 degrees

∠2 = 180 - 110 (sum of angles on a straight line)

∠2 = 70°

∠3 = ∠1 (vertically opposite angles)

Vertically opposite angles are congruent. vertically opposite angles share the same vertex

Therefore,

∠3 = 110°

∠2 = ∠4 (vertically opposite angles)

∠4 = 70°

∠1 = ∠5 (corresponding angles)

Corresponding angles are congruent

∠5 = 110°

∠6 = ∠4(alternate angles)

Alternate angles are congruent.

∠6 = 70°

∠1 = ∠7 (alternate exterior angles)

∠7 = 110°

∠2 = ∠8(alternate exterior angles)

∠8 = 70°

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The measure of the acute angles in the triangle are 7.5 and 82.5

From the question, we have the following parameters:

One acute angle is 11 times the measure of the other acute angle.

Let the acute angles be x and y

Such that

y = 11x

The sum of the acute angles in a right triangle is 90

So, we have

x + y = 90

This gives

x + 11x = 90

So, we have

12x = 90

Divide by 12

x = 7.5

Recall that y = 11x

So, we have

y = 11 x 7.5

Evaluate

y = 82.5

Hence, the acute angles are 7.5 and 82.5

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The new function that can be formed after f(x) transforms horizontally 4 units to the right and then vertically 7 units upwards is
H(x) = h(x) = x² + 11x + 37.

How to shift an equation horizontally?
For a function, f; a brand new function d(x) = f(x - h), where h is a constant, is a horizontal shift of the function f; for positive 'h' the graph shifts right and for negative 'h' the graph shifts left.
How to shift an equation vertically?
For a function, f; a brand new function d(x) = f(x) + k, where k is a constant, is a vertical shift of the function f; for positive 'h' the graph shifts up and for negative 'h' the graph shifts down.

Given, the equation is f(x) = x² + 3x + 2
The new equation formed will be = h(x)
Also, the function horizontally shifts 4 units to the right.
Therefore, h(x) = f(x + 4) = (x + 4)² + 3(x + 4) + 2 = x² + 11x + 30
Again, the function formed in h(x) vertically shifts up by 7 units.
Thus, new equation for h(x) is = h(x) + 7 = x² + 11x + 37
Therefore, the required equation for H(x) = h(x) = x² + 11x + 37

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Answer:

it would be 89

Step-by-step explanation:

Height of the ladder on the wall in decreasing at the rate of ≈ 6m/s

Finding a function's derivative, or rate of change, is the process of differentiation in mathematics. The practical approach of differentiation can be performed utilizing only algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.

let ym be the height of wall at  which ladder touches

Also let the foot of ladder be xm away from the wall

then by the pythagoras theorem we have ,

[tex]x^{2} +y^{2} =[/tex] 64 [ length of ladder = 8 m ]

⇒ y = [tex]\sqrt{64 - x^{2} }[/tex]

then , the rate of change of height (y) with respect to time (t) is given by

[tex]\frac{dy}{dt}=\frac{-x}{\sqrt{64 - x^{2} }} . \frac{dx}{dt}[/tex]

it is given that [tex]\frac{dx}{dt}[/tex] = 5 m/s

∴ [tex]\frac{dy}{dt}=[/tex] [tex]\frac{-5x}{\sqrt{64 - x^{2} }}[/tex]

now when x = 6m , we have :

[tex]\frac{dy}{dt} = \frac{-5 * 6}{\sqrt{64 - 6^{2} }}[/tex]

  = -30 / 5 .3

  = -5.660377358490566

therefore height of the ladder on the wall in decreasing at the rate of ≈ 6m/s

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1. The unit price of apple in store A is $4

2. The unit price of apple in store B is $2

3. The unit price of apple in store C is $3

4. The store with the lowest unit price is store B

1. How to determine the unit price at store A

We can obtain the unit price at store A by doing the following:

3 pounds of apples cost $12.

Therefore,

1 pound will cost = (1 × pound $12) / 3 pounds = $4

Thus, the unit price is $4

2. How to determine the unit price at store B

We can obtain the unit price at store B by doing the following:

y = 2x

y = 2x

y = 2 × 1

y = $2

Thus, the unit price is $2

3. How to determine the unit price at store C

We can obtain the unit price at store C by obtaining the slope of the graph. This can be obtaioned as follow:

m = (y₂ – y₁) / (x₂ – x₁)

m = (9 – 3) / (3 – 1)

m = 6 / 2

m = 3

Thus, the unit price is $3

4.How todetermine the store with the lowest unit price

From the above, we can conclude that store B has the lowest unit price

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The cost of the bag of cat food is $6.22

What is cost prize ?

The prize at which the good and services have been bought is known as cost prize.

here, the given information is :

Cost of a container of cat liter = $13.75

Cost of a bag of cat food = X dollars

Total amount of money required to purchase the items = $20.80

Percentage of sales tax that had to be given = 4%

Then,

Amount of sales tax given = (4/100) * 20.8 dollars

                                            = 20.8/25 dollars

                                            = 0.83 dollars

Then the total purchase price for the two items = 20.80 - 0.83 dollars

                                                                               = 19.97 dollars

Now we can easily find the cost of the cat food by subtracting the cost of the liter from the total purchase amount :

Cost of the cat food = 19.97 - 13.75 dollars

                                = 6.22 dollars

Therefore, the cost of the bag of cat food is $6.22

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The number of hours ago was the temperature 0 degrees is 6 hours.

Temperature simply means the degree if hotness and coldness in a body.

In this case, the temperature has been dropping 2 1/2 degrees every hour. Let the number of hours be h.

This will be illustrated as:

-15 = -2.5h

where h = number of hours

Divide

h = -15 / -2.5

h = 6

Therefore, the correct option is 6 hours.

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The volume of the building in the shape of a square pyramid is 252720 m³

In terms of geometry, a square pyramid is a pyramid with a square base and four lateral faces. A pyramid is a type of polyhedron with three or more triangle faces that meet above its base (the apex).

The building is in the shape of a square pyramid.

The base of the building is 54 meters long.

The height of the building is 260 meters.

The volume of the right square pyramid is given as:

V = ( 1/3)a²h

Where a is the base and h is the height.

Now we have,

a = 54 meters and h = 260 meters

Then the volume of the building is:

V = ( 1/3)a²h

V = ( 1/3 ) × ( 54 )² × 260

V = ( 1/3 ) × 54 × 54 × 260

V = 758160/3

V = 252720 m³

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Problem

Juanita wants to buy a computer. She needs to earn at least 400 dollars. If she makes 9 dollars an hour and has already saved 40 dollars, how many hours does she need to work?

Solution

Let x the number of hours required we can set up the following inequality:

40 + 9x > 400

And now we can solve for x we can subtract 40 and we got:

9x > 360

And then we got:

x> 40

So then Juanita needs to work at least 40 hours

And the graph of the inequality is given by: