BUILDING A horse farm is developing a new indoor arena in a rectangular building. They want the width of the building to be 3y feet and the length to be 4y+9 feet. Write an expression in simplest form to represent the area A of the building in terms of y.

A= ____

Answer:

Step-by-step explanation:

Givens

Length = a

Width = a + 3

Formulas

P = 2L + 2w

Area = L * w

Solution

Perimeter

P = 2L +  2w

P = 2*a + 2(a + 3)             Remove the Brackets

p = 2a + 2a + 6                Combine

P = 4a + 6

Area

Area = L * w

Area = a (a + 3)

Area = a^2 + 3a

Answer:

2x+4

Step-by-step explanation:

Trust me

The domain of the logarithm function is (0, ∞) and the range of the logarithm function will be (-∞, ∞)

The domain means all the possible values of the x and the range means all the possible values of the y.

The table is shown below.

Let the logarithm function with the variables x and y. Then we have

y = logₐ x

At x = 25, the value of y will be 2. Then the value of a will be

2 = logₐ 25

2 = 2 logₐ 5

1 = logₐ 5

Then 1 can be written as

1 = log₅ 5

Then on comparing, the value of a will be

a = 5

Then the logarithm function will be

y = log₅ x

Then the domain of the logarithm function is (0, ∞) and the range of the logarithm function will be (-∞, ∞)

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[tex]x=10[/tex]

[tex]y=20[/tex]

Note:

(sin, cos, tan) Formulas:

[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]

[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]

[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]

To find the value of [tex]x[/tex]

1) Using [tex]tan[/tex] formula

[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]

[tex]tan(60°)=\dfrac{10\sqrt{3}}{x}[/tex]

2) Multiply both sides by [tex]x[/tex]

[tex]xtan(60°)=\dfrac{10\sqrt{3}}{x}\times x[/tex]

[tex]xtan(60°)=10\sqrt{3}[/tex]

3) Divide both side by [tex]tan(60°)[/tex]

[tex]\dfrac{xtan(60°)}{tan(60°)}=\dfrac{10\sqrt{3}}{tan(60°)}[/tex]

4) Calculate

[tex]x=\dfrac{10\sqrt{3}}{tan(60°)}[/tex]

[tex]x=10[/tex]

To find the value of [tex]y[/tex]

1) Using [tex]cos[/tex] formula

[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]

[tex]cos(60°)=\dfrac{10}{y}[/tex]

2) Multiply both sides by [tex]y[/tex]

[tex]ycos(60°)=\dfrac{10}{y}\times y[/tex]

[tex]ycos(60°)=10[/tex]

3) Divide both side by [tex]cos(60°)[/tex]

[tex]\dfrac{ycos(60°)}{cos(60°)}=\dfrac{10}{cos(60°)}[/tex]

4) Calculate

[tex]y=\dfrac{10}{cos(60°)}[/tex]

[tex]y=20[/tex]

The missing values in the diagram given that figure ABCD is a dilation of figure KLMN, are:

AB = 4

LM = 20

∠B = 98.87°

∠N = 141.87°

Dilation is a form of transformation whereby a new figure is formed by enlarging or reducing an original figure by a scale factor. After dilation, the corresponding sides of both figures are proportional, while the corresponding angles of both figures are congruent to each other.

Find AB:

AB/KL = DC/NM

Plug in the values

AB/10 = 4/10

AB(10) = 4(10)

AB = 40/10

AB = 4

Find LM:

BC/LM = DC/NM

Plug in the values

8/LM = 4/10

8(10) = 4(LM)

LM = 80/4

LM = 20

∠B = ∠L = 98.87°

∠N = ∠D = 141.87°

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Answer:

The bottom graph on the right, check the image below:

Explanation:

Substitute the x value with 1,

f(1)=1(1+2)=3

f(2)=2(2+2)=8

f(-1)=-1(-1+2)=-1

f(-2)=-2(-2+2)=0

Answer:

e

Step-by-step explanation:

the sum of 24 and 7 is 24 + 7 and multiplying this by 5 gives

5 × (24 + 7)

Answer:

e.

Step-by-step explanation:

24 + 7 = 31

5 * 31 = 155.

Answer:

D

Step-by-step explanation:

114 hundredths

Answer:

42 hundredths

Step-by-step explanation

Normally do 34+8 then add the hundredths since 34 hundredths is the bigger value

Answer:

363

Step-by-step explanation:

11x11=121

((11x11)÷2)x4=11x11x2=121x2=242

121+242=363

Answer:

From inspection of the diagram, the pattern is:

Step 1:      1² + 1

Step 2:    2² + 2

Step 3:    3² + 3

Let x = step number

Let y = total number of squares

Therefore, the equation that represents the relationship is:  

y = x² + x

x² relates to the large square made up of small squares (top part of the image of each step)

x relates to the rectangle of small squares (bottom part of the image of each step)

y is the total number of small squares in the image of each step.

The pattern is

More simply

So for an integer n

#b

n² is pair of boxes at top side

n is boxes underneath

Answer:

adjacent exterior angles

x equals 80

63 cm2

hope it helps

you

63 CM answer

Answer:

the half liter

Step-by-step explanation:

200 mL :

4,000 mL in 4 liters.

4,000/200=20

20x1.19=23.8

half liter :

4x2=8

8x2.86=22.88

A factor of the polynomial f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35 is 2x - 7

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the polynomial:

f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35

The polynomial can be further simplified to:

f(x) = (2x - 7)(3x³ - 2x + 5)

A factor of the polynomial f(x) = 6x⁴ - 21x³ - 4x² + 24x - 35 is 2x - 7

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Answer:

2x-7

Step-by-step explanation:

TLDR verified answer, correct on edge 2023

Answer:

5/8

Step-by-step explanation:

1/5 x 5

1

1/8 x 5

5/8

Answer:

65 times in 75 seconds

Step-by-step explanation:

52 × 75 = 3,900

3,900 ÷ 60 = 65

Answer: The answer you selected in the picture is correct.

Step-by-step explanation:

There will be no heat transfer from the nickel to the water in the glass since heat transfer is purely a function of temperature difference.

there will be no transfer of heat from the nickel to the water in the glass

Answer:

Where is the quadrilateral? You haven't inserted a picture.

The solution set of the inequality is represented as [911,∞)

let

x be the number of cans collected by Shane.

Therefore,

Since,  Abha collected 178 more cans than Shane did.

Therefore,

Abha  = 178 + x

Hence,

Also, Shane and Abha earned a team badge that required their team to collect no less than 2000 cans for recycling.

Therefore,

x + 178 + x ≥ 2000

2x + 178 ≥ 2000

2x ≥ 2000 - 178

2x ≥ 1822

x ≥ 1822 / 2

x ≥ 911

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Answer:

y = 4, x = 0

y = 1, x = -1

Step-by-step explanation:

[tex]y = 3 {x}^{2} + 6x + 4[/tex]

[tex]y = - 3 {x}^{2} + 4[/tex]

[tex] \: [/tex]

Since both of them are equal to y, we can just equate them and solve.

[tex] \: [/tex]

[tex]3 {x}^{2} + 6x + 4 = - 3 {x}^{2} + 4[/tex]

[tex]3 {x}^{2} + 6x + 4 + 3 {x}^{2} - 4 = 0[/tex]

[tex]6 {x}^{2} + 6x = 0[/tex]

[tex]6x(x + 1) = 0[/tex]

[tex]6x = 0[/tex]

[tex]x = 0[/tex]

[tex] \: [/tex]

[tex]x + 1 = 0[/tex]

[tex]x = - 1[/tex]

[tex] \: [/tex]

[tex]for \: x = 0[/tex]

[tex]y = 3( {0})^{2} + 6(0) + 4[/tex]

[tex]y = 4[/tex]

[tex] \: [/tex]

[tex]for \: x = - 1[/tex]

[tex]y = 3( { - 1})^{2} + 6( - 1) + 4[/tex]

[tex]y = 1[/tex]

[tex] \: [/tex]

[tex]values \: of \: x \: and \: y \: for \: the \: system \: of \: equations \: are[/tex]

y = 4, x = 0

y = 1, x = -1

The system of equations has been solved and the solution set of the equation are (-1,1) and (0,4).

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

The first equation given as,

y = 3x² + 6x + 4

The second equation given as,

y = -3x² + 4

Equate the value of y from both equation as,

3x² + 6x + 4=-3x²+4

3x²+3x²+6x+4-4=0

6x²+6x=0

6x(x+1)=0

x=0:x=-1

Put these values of x, in first equation,

y = 3(-1)^2 + 6(-1) + 4

y = 3 - 6 + 4

y=1

Put 0 on the place of x,

y = 3(0)^2 + 6(0) + 4

y = 0 +0+ 4

y=4

Thus, the system of equations has been solved and the solution set of the equation are (-1,1) and (0,4).

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Inequality are expressions that are not separated by an equal sign. The solution to the given system of equation is x > 4

Inequality are expressions that are not separated by an equal sign.

Given the inequality

8x+2 > 34

Subtract 2 from both sides

8x + 2 - 2 > 34 - 2

8x > 32

Divide both sides by 8

8x/8 = 32/8
x > 4

Hence the solution to the given system of equation is x > 4

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Answer:

y = 4"x +2

Step-by-step explanation:

We choose negative 4 because the graph lies below the asymptote and we chose positive 2 because the horizontal asymptote is on the positive section of the y axis

The equation in slope-intercept form is y = (5/4)x + 7.

We have,

The slope-intercept form of a linear equation is given by y = mx + b, where "m" is the slope and "b" is the y-intercept.

To write the equation 12y - 15x = 84 in slope-intercept form, simplify the fractions and solve for y:

12y = 15x + 84

y = (15x + 84) / 12

y = (5x + 28) / 4

y = (5/4)x + 28/4

y = (5/4)x + 7

Thus,

The equation in slope-intercept form is y = (5/4)x + 7.

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Answer:

196 in^3

Step-by-step explanation:

Volume of pyramid = 1/3 base * height

                = 1/3  (7x7) (12) = 196  in^3