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Vikentia [17]
4 years ago
7

The length of a rectangle is 2 inches more than its width. The perimeter of the rectangle is 24 inches. The equation 2x + 2(x +

2) = 24, where x is the width in inches, represents this situation.
The value of x from the set {1, 3, 5, 7} that holds true for the equation is ___ . So, the width of the rectangle is ___ inches and its length is ___ inches
Mathematics
1 answer:
alexandr1967 [171]4 years ago
7 0
2x + 2(x + 2) = 24
2x + 2x + 4 = 24
4x = 24 - 4
4x = 20
x = 20/4
x = 5

The value of x that holds true for the equation is : x = 5.
So the width of the rectangle is 5 inches and the length is (x + 2 = 5 + 2) = 7 inches
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dsp73
The base, 1.74, represents 100% of the original number of hits plus the percent increase, 0.74=74%, daily.
8 0
3 years ago
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Which of the following pairs of functions are inverses of each other?
natta225 [31]

Answer:

The pair which are inverse of each other are:

Option: C

f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}

Step-by-step explanation:

Two functions f(x) and g(x) are said to be inverse of each other if:

fog(x)=gof(x)=x

i.e. the composition of two functions give identity no matter what the order is.

A)

f(x)=\dfrac{x}{12}+15 and g(x)=12x-15

Now we calculate fog(x):

fog(x)=f(g(x))\\\\fog(x)=f(12x-15)\\\\fog(x)=\dfrac{12x-15}{12}+15\\\\fog(x)=x-\dfrac{15}{12}+15\\\\fog(x)=x-\dfrac{55}{4}\neq x

Hence, option: A is incorrect.

B)

f(x)=\dfrac{3}{x}-10\ and\ g(x)=\dfrac{x+10}{2}

Now we calculate fog(x):

fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+10}{3})\\\\fog(x)=\dfrac{3}{\dfrac{x+10}{3}}-10\\\\fog(x)=\dfrac{9}{x+10}-10\neq x

Hence, option: B is incorrect.

D)

f(x)=9+\sqrt[3]{x}\ and\ g(x)=9-x^3

Now we calculate fog(x):

fog(x)=f(g(x))\\\\fog(x)=f(9-x^3)

fog(x)=9+\sqrt[3]{9-x^3}\neq x

Hence, option: D is incorrect.

C)

f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}

Now we calculate fog(x):

fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+4}{11})

fog(x)=11\times (\dfrac{x+4}{11})-4\\\\fog(x)=x+4-4\\\\fog(x)=x

Similarly,

gof(x)=g(f(x))\\\\gof(x)=g(11x-4)\\\\gof(x)=\dfrac{11x-4+4}{11}\\\\gof(x)=\dfrac{11x}{11}\\\\gof(x)=x

Hence, option: C is the correct option.

6 0
3 years ago
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What is the quotient to 3/4 divided by 2?
ikadub [295]

3/4 divided by 2 would equal 3/8.

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3 years ago
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81. What is the distance between (-5, 2) and (-9,-4)?
swat32

Answer:

Use the distance formula to determine the distance between the two points.

Distance

=

√

(

x

2

−

x

1

)

2

+

(

y

2

−

y

1

)

2

Substitute the actual values of the points into the distance formula.

√

(

4

−

(

−

5

)

)

2

+

(

9

−

2

)

2

Simplify.

Tap for more steps...

√

130

The result can be shown in multiple forms.

Exact Form:

√

130

Decimal Form:

11.40175425

…

image of graph

([)]|√>≥

789÷<≤

456/×

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3 years ago
How do you factor: x^3 - 8 (x cubed minus 8)
Firlakuza [10]
x^3 - 8 =x^3-2^3 = (x-2) (x^2 + 2x + 2^2)=(x-2) (x^2 + 2x + 4)\\ \\ \\a^3 - b^3 = (a - b) (a^2 + ab + b^2)


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3 years ago
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