The length of a rectangle is 2 yards less than 3 times the width.The perimeter is 68 yards. Find the width

Answer:

C.  Every integer is a rational number

Step-by-step explanation:

Integers are whole numbers which could be positive or negative and zero. Examples of integers are 330, 21, 10,052, 0, -425, -879, etc. Fractions are not integers.  Rational numbers are numbers that are expressed as the ratio of two integers. So numbers that have integers as their numerators and denominators can be rightly said to be rational numbers. Examples are, 5/7, 10,111/880, -365/15.

Since both the numerators and denominators are whole numbers, the entire figures can be said to be rational numbers. So, fractions are rational numbers.    

Answer:

(x - 6)(x + 4)(x - 2)

Step-by-step explanation:

since x = 6 is a root then (x - 6) is a factor

x³ - 4x² - 20x + 48 ÷ (x - 6)

= (x - 6)(x² + 2x - 8)

= (x - 6)(x + 4)(x - 2) ← factors of f(x)

By using the Remainder Theorem, all the factors of the function are,

⇒ (x - 6) (x + 2) (x - 4)

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

One root of function f (x) = x³ -4x² -20x + 48 is,  x = 6.

Hence, (x - 6) is divide the function  f (x) = x³ -4x² -20x + 48 as;

(x - 6) ) x³ -4x² -20x + 48 ( x² + 2x - 8

           x³ - 6x²

         --------------

                 2x² - 20x

                 2x² - 12x

                 -----------------

                         - 8x + 48

                         - 8x + 48

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

                                      0

Hence, We get;

f (x) = x³ -4x² -20x + 48

f (x) = (x - 6) (x² + 2x - 8)

⇒ f (x) = (x - 6) (x² - 4x + 2x - 8)

⇒ f (x) = (x - 6) (x(x - 4) + 2(x - 4))

⇒ f (x) = (x - 6) (x + 2) (x - 4)

Thus., By using the Remainder Theorem, all the factors of the function are,

⇒ (x - 6) (x + 2) (x - 4)

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Answer:

5t

Step-by-step explanation:

Answer:

m = -4

Step-by-step explanation:

m - 4 = 2m

Switch sides.

2m = m - 4

Subtract m from both sides.

m = -4

Answer:

-4

Step-by-step explanation:

cause mafs

Answer:

I'm pretty sure it's c and d

Step-by-step explanation:

-12 = v + 8

v + 8 = -12

v = -12 - 8

v = -20

The values of the given function when x = -3, 0, and 5 are 13, 4, and -11 respectively

From the question,

The given function is g(x) = 4 - 3x

We are to evaluate the function for the given values of x

put the value x = -3 into the function

That is,

g(x) = 4 - 3x becomes

g(-3) = 4 - 3(-3)

g(-3) = 4 + 9

g(-3) = 13

Put the value x = 0 into the function

That is,

g(x) = 4 - 3x becomes

g(0) = 4 - 3(0)

g(0) = 4 - 0

g(0) = 4

Put the value x = 5 into the function

That is,

g(x) = 4 - 3x becomes

g(5) = 4 - 3(5)

g(5) = 4 - 15

g(5) = -11

Hence, the values of the given function when x = -3, 0, and 5 are 13, 4, and -11 respectively

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Answer:

(8,8)

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

5^4 x 5^3/5^5

5^(3+4)/5^5

5^7/5^5

5^(7-5)

5^2

25

Answer:

5 to the power of 2.

Step-by-step explanation:

Answer:

y = (2-3d)/(7+c)

Step-by-step explanation:

-cy + 2 = 3d + 7y

To solve this equation in terms of y, we must first move all of the terms containing a y to one side of the equation and move all of the other terms to the other side.

Our first step is going to be to add cy to both sides of the equation.

- cy + cy + 2 = 3d + 7y + cy

2 = 3d + 7y + cy

Next, we can subtract 3d from both sides of the equation.

2 - 3d = 7y + cy

Next, we can factor out a y from the right side of the equation.

2 - 3d = y (7 + c)

Finally, we can divide both sides by the quantity (7+c) to get the y alone on the right side of the equation.

(2-3d)/(7+c) = y

Therefore, your answer is y = (2-3d)/(7+c).

Hope this helps!

Answer:

second option

Step-by-step explanation:

Given

A = 4xy ( to isolate x divide both sides by 4y )

[tex]\frac{A}{4y}[/tex] = x , that is x = [tex]\frac{A}{4y}[/tex]

Answer:

-7

Step-by-step explanation:

Since we are losing something, it is reasonably assumptive that we have to have a negative.

So a loss of 7 yards would be an integer of -7.

Answer:

20

Step-by-step explanation:

Answer:

[See Below]

Step-by-step explanation:

✦ First change the improper fractions to decimals:

  ✧ ⁵⁄₄ = 1.25

  ✧ -⁹⁄₅ = -1.8

✦ Then divide:

  ✧ 1.25 ÷ -1.8 = -0.69

So x would be -0.69 in decimal form.

~Hope this helps Mate. If you need anything feel free to message me.

Answer:

m=14

n=32

p=64

Step-by-step explanation:

B=M, so 154=11m

m=154/11

m=14

E=P, so 118=n+86

n=118-86

n=32

A=L, so 116=180-p

p=180-116

p=64

Answer:

C. 51.84 cm³

Step-by-step explanation:

Volume of traingular prism = Base Area * height of prism

Base Area = ½*base(b)*height(h)

Where, b = base of traingular base = 5.4 cm

h = height of triangular base = 3.2 cm

Base Area = ½*5.4*3.2 = 8.64 cm²

Height of prism is given as 6 cm

Therefore, volume of triangular prism =

8.64*6 = 51.84 cm³

Volume is C. 51.84 cm³

Answer:

-4.

Step-by-step explanation:

The bracket should be (-4) as AD which is height +2 has been shifted down to EF which is height -2.

Answer:

350 miles

Step-by-step explanation:

Let x represent the miles driven

The cost with the first plan will be represented by 0.40x + 70

The second plan will be represented by 0.60x

Set these 2 expressions equal to each other and solve for x:

0.40x + 70 = 0.60x

70 = 0.20x

350 = x

So, Susan will have to drive 350 miles for the cost to be the same

Answer:

4^-2

Step-by-step explanation:

Answer:

[tex] 2^{-2} [/tex]

Step-by-step explanation:

1/4 is between 0 and 1/2.

[tex] \dfrac{1}{4} = \dfrac{1}{2^2} = 2^{-2} [/tex]

Answer:

95

Step-by-step explanation:

80+(200 divided by 2)+(420 divided by 4)=285

285 divided by 3=95

Answer:

9.85

Step-by-step explanation:

you can use the Pythagoras theorem

[tex]a^2+b^2=c^2[/tex]

with c the hypotenuse

[tex]9^2+4^2=c^2\\\\81+16=c^2\\\\97=c^2\\\\c=\sqrt{97}[/tex]

which is aprox

9.85

ups sorry :(

Answer:

Remeber that

[tex]A^{2}+ B^{2} =C^{2}[/tex]

so

[tex]4^{2}+9^{2}=C^{2}[/tex]

16+81 = [tex]C^{2}[/tex]

97 = [tex]C^{2}[/tex]

Take the square root of both sides

[tex]\sqrt{97} = \sqrt{C^{2} }[/tex]

9.85 = C

Step-by-step explanation:

X2+ax+b=(x-9)(x+9)

X2+ax+b=x2-9x+9x-81

X2+ax+b=x2-81

therefore,a=0,b=(-81)

Then , ab = 0×-81 = 0

Answer:

Step-by-step explanation:

x² + ax + b = (x – 9)(x + 9)

x² + ax + b = x² – 9x + 9x – 81

x² + ax + b = x² + 0x – 81

x²=x²      +ax = +0x        +b = -81

                    a = 0            b = -81

ab = 0(-81) = 0    

Answer:

3(2a+4b+7)+6a = 12a+12b+21

Step-by-step explanation:

5/(x + 2) + 3/(x - 4) = 2

5(x - 4) + 3(x + 2) = 2(x + 2)(x - 4)

5x - 20 + 3x + 6 = 2x^2 - 4x - 16

8x - 14 = 2x^2 - 4x - 16

4x - 7 = x^2 - 2x - 8

x^2 - 6x - 1 = 0

By using the quadratic formula, x = (-6 +/-√40)/2.

Answer:

hrheje

Step-by-step explanation:

bdhsjsiskskdkdhdhennsjss

Answer:

2c + 15 = 25

Step-by-step explanation:

The total he wants to earn is $25, so we know the equation must be an expression that equals 25.

____ = 25

He earns a fixed $15. He also earns $2 per customer.

The total he earns is the sum of the fixed amount ($15) and the amount he earns per customer. Let the number of customers be c. The amount he earns from the number of customers is 2c.

fixed amount + amount per customer = 25

15 + 2c = 25

2c + 15 = 25

Answer: 2c + 15 = 25

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the angles ∠ABF=8s-6, ∠ABE = 2(s + 11), we are to find the angle ∠EBF. The following expression is true for the three angles;

∠ABF = ∠ABE + ∠EBF

Substituting the given angles into the equation to get the unknown;

8s-6 = 2(s + 11)+ ∠EBF

open the parenthesis

8s-6 = 2s + 22+ ∠EBF

∠EBF = 8s-6-2s-22

collect the like terms

∠EBF = 8s-2s-22-6

∠EBF = 6s-28

factor out the common multiple

∠EBF = 2(3s-14)

Hence the measure of angle ∠EBF is 2(3s-14)

Answer:

first option

Step-by-step explanation:

To find the product, that is

(4x + 1)(x² - 5)

Each term in the second factor is multiplied by each term in the first factor, that is

4x(x² - 5) + 1(x² - 5) ← distribute both parenthesis

= 4x³ - 20x + x² - 5

= 4x³ + x² - 20x - 5