Mary’s backyard vegetable garden measures 20 ft by 30 ft, so its area is 20*30=600 ft 2. She decides to make it longer, as shown in the figure, so that the area increases to A=20(30+x). Which property of real numbers tells us that the new area can also be written A=600+20x?

28 quarts are equivalent to 7 gallons

The table represents a proportional relationship or proportional linear function

A proportional linear function is represented as

y = kx

Where

k represents the proportionality constant

y represents the number of quarts

x represents the number of gallons

When x = 14 and y = 56, we have:

56 = 14k

Divide by 14

k = 4

Substitute k = 4 in y = kx

y = 4x

When x = 7, we have

y = 4 * 7

Evaluate

y = 28

Hence, 28 quarts are equivalent to 7 gallons

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Answer:

A. A reflection over the line x = 6

Step-by-step explanation:

You can see in the picture if you follow the line every edge has the same

Number x=6

Answer:

The value of b would be $25 since it's the initial amt. The value of m would be $8. The equation would be y=8x+25

Answer: B': (-3, 4)

C': (-3, 0)

D': (-2, 0)

E': (-2, 4)

Step-by-step explanation:

270 degrees counterclockwise=

(360-270) degrees clockwise=90 degrees clockwise

In a 90 degree clockwise rotation about the origin for this rectangle, the x and y coordinates of the rectangle's edges are swapped, but the y-coordinates are negated. This is because the transformation is happening over the x-axis, where the y-values will be changing signs while the x-values will still have the same signs.

B: (-4, -3) ==> (-3, -4) ==> B': (-3, 4)

C: (0, -3) ==> C': (-3, 0)

D: (0, -2) ==> D': (-2, 0)

E: (-4, -2) ==> (-2, -4) ==> E': (-2, 4)

Answer:

[tex]\frac{63}{4}[/tex]

Step-by-step explanation:

[tex]\frac{42}{1} x \frac{3}{8}[/tex]

Cross out common factors 42 & 8;

[tex]21 * \frac{3}{4}[/tex]

Write as a single factor.

[tex]\frac{21*3}{4}[/tex]

21*3= 63

[tex]\frac{63}{4}[/tex]

Answer: a) 5

Step-by-step explanation:

Answer:

A:5

Step-by-step explanation:

I say 5 times because you said '1 green cube and 2 whites' it is very possible you can get green 5 times but 10, 15, and 20 times seems a bit lucky is maybe the word i'm looking for but overall i say 5 because 5 is possible. Virtual smile ; )

I really hope i helped

We get the perimeter 8 √ 5 units as and the area as 10 units² .

We are given that a square has side lengths that measure 2√5 units.

We know that, the perimeter of square is:

P = 4 × side units

P = 4 × 2 √ 5 units

P = 8 √ 5 units

We also know that the area of square is:

A = side²

A = ( 2 √ 5 units ) ²

A = 2 × 5 units²

A = 10 units²

Therefore, we get the perimeter 8 √ 5 units as and the area as 10 units² .

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Your question was incomplete. Please find the content below.

A square has side lengths that measure 2√5 units. Find perimeter and area.

The company must sell 400 radios to break even, i.e, when the revenue function and cost function is same.

The sum of the units sold times the price per unit is the revenue. Multiply the output level by the pricing function to get the revenue function.

The cost function is the total cost of production of the item which includes the cost of raw materials, labor, transport and establishment costs.

The cost function and the revenue function is given as:

Cost function is C(x) =5000 + 7.5x

And the revenue function is R(x) = 20x

a)In the break even point cost will be equal to revenue

so, C(x)=R(x)

or,5000+7.5x=20x

or,12.5x=5000

or, x=5000÷12.5

or, x=400

The number of radios produced to break even is 400.

(b)When the company breaks even then x=400

∴R(200)=200×20=8000

So the amount of money is dollars that is coming in or going out is given by 8000.

(c)We know that the profit=Revenue - cost

So the required profit function is given by:

p(x)=R(x)-C(x)

or, p(x)=20x-5000-7.5x

or,p(x)=12.5x-5000

(d)The company sells 500 radios

Therefore profit will be given by

p(500)=12.5×500-5000

or,p(500)=6250-5000

or, p(500)=1250

So on selling 500 radios the company will earn $1875.

Disclaimer: The revenue and cost function of the equation are  

C(x) =5000 + 7.5x and  R(x) = 20x .

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Graph with points x=3 and y =1.5

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Answer:

1576

Step-by-step explanation:

The arithmetic sequence goes up by 16 each term. So if you are trying to find the 98th term, multiply 16 by 98. This results in the number 1568. Now because the arithmetic sequence starts at 8, simply add 8 to the number, and the answer is 1576

Answer:

Step-by-step explanation:

First you need to know how much is the sales tax

Then add the sales tax to the value of the vaccum cleaner

Answer

Answer:

No

Step-by-step explanation:

Following pemdas (parentheses exponents multiplication addition subtraction) you would do division first so 6/2 equals 3 then 14+3=17 divided by 2 equals 8.5

Leta has $24 in her account in august;

Amount of money in Leta's Account in may=$ 45

If leta has not spent a penny till august,and not added a penny in her account, then amount of money in leta's account = $45

Money in Leta's account in June = $45 - $17 = $28

Money in Leta's account in July = $28 - $22 = $6

Money in Leta's account in August = $6 + $18 = $24

Amount, sum, sum of money; "he borrowed a considerable sum," "the amount he had in cash was insufficient." Gain is the difference between a company's revenue and operating expenses. The whole amount of income before any deductions is referred to as gross, receipts, or revenue.

The amount of money you have accessible in your checking or savings account is known as your account balance in the world of banking. The net amount remaining in your account after all deposits and credits have been balanced against any charges and debits is your account balance.

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The distance between the two points is approximately 19.18 units

The length of the line segment connecting any two points is referred to as their distance. In coordinate geometry, the distance formula is usedto calculate the distance between two points.

In 1731, the distance formula itself was first made public. Pythagorean distance is another name for Euclidean distance. The Pythagoras is used to derive the distance formula.

If two point are given as A [tex](x_1,y_1)[/tex] and B [tex](x_2,y_2)[/tex] then the distance between the two points or the length of AB is calculated using the formula:

[tex]AB = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

The co ordinates of the two points are given as [tex](5\sqrt{3},7\sqrt5 )[/tex] and [tex](-\sqrt{3},-\sqrt{5} )[/tex].

Therefore distance between the points will be given by:

[tex]=\sqrt{(5\sqrt{3} - \sqrt{3} )^2 + (7\sqrt{5} -(-\sqrt{5} )^2}\\=\sqrt{(4\sqrt{3})^2+(8\sqrt{5})^2 }\\=\sqrt{48+320}\\=\sqrt{368}\\\approx19.18[/tex]

The distance between the two points is approximately 19.18 units.

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Answer:

C

Step-by-step explanation:

We can go through the process of elimination to solve the question.

A is incorrect because they are only running for a minute and the variation between time and heart rate cannot be measured.

B is incorrect because there are too many variables to account for and they are both running for the same amount of time.

D is incorrect because there are too many variables to account for and it is not a fair test as he is running at many different speeds (you can only change the independent variable which is the time).

Hence, C is the answer. It is a fair test as he is running at different speeds and keeping everything else the same.

Step-by-step explanation:

The area of the rectangle = 338 square units

The co-ordinate plane has two axes X and Y.

The points in the co-ordinate plane is given as U(4, -6) to V(-8, -11).

i.e., (x₁, y₁) = (4, -6) and (x₂, y₂) = (-8, -11)

The distance between these points are considered as a side of a rectangle.

Distance between U(4, -6) and V(-8, -11) =  [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

                                                               = [tex]\sqrt{(-8-4)^2+(-11--6)^2}[/tex]

                                                               = [tex]\sqrt{(-12)^2+(-5)^2}[/tex]

                                                               = √169

                                                               = 13 units

So the length of one side of rectangle, l = 13 units

Let 'w' be the width of the rectangle.

Also perimeter of the rectangle = 78 units

⇒  2(l +w) = 78

⇒ l +w = 39

⇒ w = 39 -l

⇒ w = 39 - 13

⇒ w = 26 units

Area of the rectangle = length x width

                                    = l x w

                                    = 13 x 26

                                    = 338 square units

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The given statement about when next they visit the restaurant that the meals will be free is an example of; inductive reasoning.

Inductive reasoning is a type of reasoning that involves forming general theories from specific observations. Observing something happen repeatedly and concluding that it will happen again in the same way is an example of inductive reasoning.

Deductive reasoning is a type of reasoning that involves forming specific conclusions from general premises. An example is; Everyone in this class is an English major; Jesse is in this class; therefore, Jesse is an English major.

Now, from the given question, it was observed that Every Tuesday that Yolanda's family has visited a specific local restaurant, the Nids meals have been free. Now, using that to conclude that when next he visits the restaurant that the meals will be free is an example of inductive reasoning.

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Answer: 1/6

Step-by-step explanation:I hope i have helped u have a wonderful day or night!

Answer:

B. y=|x+6|-3                                            

Answer:

it is C because If you subtract 48 from 42 and then you ad 1 you get 7.5

Answer:x=60 y=61

Step-by-step explanation:

lmk if you want an explanation

By writing an exponential equation, we can conclude that the initial deposit is of $606.22

Here we know that we have an annual rate of 6%, so if you deposit an initial amount of A, the amount of money that the account has after t years is:

M(t) = A*(1 + 6%/100%)^t = A*(1.06)^t

Now, you know that after 8 years you earn (in interest) $360, then we can write:

M(8) - A = 360

A*(1.06)^8 - A = 360

Now we can solve that equation for A.

A*( (1.06)^8 - 1) = 360

A =  360/( (1.06)^8 - 1) = 606.22

The initial deposit is of $606.22

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Answer:

a)  9 days

b)  47 days

Step-by-step explanation:

Given information:

[tex]\begin{array}{|c|r|c|r|}\cline{1-4} \sf Day & \sf Height\:{(ft) & \sf Night & \sf Height\:(ft) \\\cline{1-4} 1 & 5 & 1 & 5 - 3 = 2\\\cline{1-4} 2 & 2 + 5 = 7 & 2 & 7 - 3 = 4 \\\cline{1-4} 3 & 4 + 5 = 9 & 3 & 9 - 3 = 6 \\\cline{1-4} 4 & 6 + 5 = 11 & 4 & 11 - 3 = 8 \\\cline{1-4} 5 & 8 + 5 = 13 & 5 & 13 - 3 = 10 \\\cline{1-4} 6 & 10 + 5 = 15 & 6 & 15-3=12\\\cline{1-4} 7 & 12 + 5 = 17 & 7 & 17 - 3 = 14 \\\cline{1-4} 8 & 14 + 5 = 19 & 8 & 19-3=16\\\cline{1-4} 9 & 16 + 5 = 21 &&\\\cline{1-4}\end{array}[/tex]

On the first day the worm climbs 5 ft, but slips back 3 ft during the first night.

On the second day the worm climbs a further 5 ft, so is now at 7 ft, but slips back 3 ft during the second night.  Therefore, it starts the third day at a height of 4 ft.

The progression continues this way so that the worm starts the 9th day at a height of 16 ft. As it climbs 5 feet during the day, it will reach the height of 20 ft during the 9th day, and so will climb out of the ravine before it sleeps for the night.

Therefore, it will take 9 days for the worm to crawl up a 20 ft ravine.

This can be modeled as an arithmetic sequence:

[tex]y=a+(x-1)d[/tex]

where:

Therefore:

[tex]\implies y=5+(x-1)2[/tex]

[tex]\implies y=5+2x-2[/tex]

[tex]\implies y=3+2x[/tex]

To calculate how long it will take the worm to crawl up the ravine if it is 97 ft high, substitute y = 97 into the equation and solve for x:

[tex]\implies 3+2x=97[/tex]

[tex]\implies 3+2x-3=97-3[/tex]

[tex]\implies2x=94[/tex]

[tex]\implies \dfrac{2x}{2}=\dfrac{94}{2}[/tex]

[tex]\implies x=47[/tex]

Therefore, it will take 47 days for the worm to crawl up a 97 ft ravine.

The expression for the volume of the pool is given by (25 d³ + 225 d² + 350 d) feet³.

We have:

We are given that the depth of the pool is = d feet

Width of the pool is 10 feet greater than five times it’s depth

Width of the pool = 10 + 5 d feet

length of the pool is 35 feet greater than five times its depth

Length of the pool = 35 + 5 d

We know that:

Volume = l b h

Volume = (d) × (10 + 5 d) × (35 + 5 d)

Volume = (10 d + 5 d²) (35 + 5 d)

Volume = 350 d + 175 d² + 50 d² + 25 d³

Volume = (25 d³ + 225 d² + 350 d) feet³

Therefore, we get that, the expression for the volume of the pool is given by (25 d³ + 225 d² + 350 d) feet³.

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Answer:

14+15=29 or 14x15=210

Step-by-step explanation:

.

Answer:

The common difference equals: 6

The sum of the sequence equals: 176

The explicit formula of this sequence is:  a_n=1+(n-1)*6

The recursive formula of this sequence is: a_n=a_((n-1))+6

1,7,13,19,25,31,37,43,49,55,61...

Step-by-step explanation:

nice :0

Answer:

Step-by-step explanation:

Simplifying

3 + -4x = 23

Solving

3 + -4x = 23

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.

3 + -3 + -4x = 23 + -3

Combine like terms: 3 + -3 = 0

0 + -4x = 23 + -3

-4x = 23 + -3

Combine like terms: 23 + -3 = 20

-4x = 20

Divide each side by '-4'.

x = -5

Simplifying

x = -5