38°
24 in
A restaurant owner plans to install this bicycle rack in front of her restaurant. In order to meet city safety requirements, the base
of the bicycle rack cannot exceed 20 inches so as to not obstruct pedestrians. Will this bicycle rack be approved by the city?

Answer:

∠S = 151

Step-by-step explanation:

The figure shown is a pentagon

The angles in a pentagon add up to equal 540

Thus, ∠Q + ∠P + ∠T + ∠S + ∠R = 540

Or 10x - 3 + 5x + 2 + 7x - 11  + 13x - 31 + 8x - 19 = 540

This is the equation we will use to solve for x

Step 1 combine like terms

10x = 5x + 7x + 13x + 8x = 43x

-3 + 2 - 11 - 31 - 19 = -62

We now have 540 = 43x - 62

Step 2 add 62 to each side

-62 + 62 cancels out

540 + 62 = 602

we now have 602 = 43x

Step 3 divide each side by 43

43x / 43 = x

602 / 43 = 14

we're left with x = 14

Finally we plug in 14 for x in the given expression for ∠S

∠S = 13x - 31

* substitute 14 for x *

∠S = 13 ( 14 ) - 31

∠S = 13 * 14 = 182

182 - 21 = 151

Thus, ∠S = 151

The measure of ∠S is equal to 151°.

In mathematics, shapes define the perimeters or contours of an object. The forms can be categorized into numerous groups according to their individual traits. A border or outline made up of points, lines, curves, etc. frequently surrounds the forms.

As per the given data:

We are given the diagram of a shape and all its internal angles.

As the given shape is having 5 sides, it will be a pentagon.

The sum of all internal angles in a pentagon is equal to 540°.

∴ ∠P + ∠Q + ∠R + ∠S + ∠T = 540°

⇒ 10x - 3 + 5x + 2 + 7x - 11 + 13x - 31 + 8x - 19 = 540

= 43x - 62 = 540

= 43x = 602

x = 14

To find the measure of ∠S.

∠S = 13x - 31

∠S = 13(14) - 31

∠S = 151°

The measure of ∠S is equal to 151°.

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Answer:

s = 4π    Exact answer

s = 12.56   Decimal approximation

Step-by-step explanation:

cicrumference  = πd

s = (∅/360)(πd)

s = (60/360)(π * 24)

s = 4π    Exact answer

s = 4 * 3.14

s = 12.56   Decimal approximation

Answer: [tex]3x^{-2.5}[/tex]

Step-by-step explanation:

Given

Expression is

[tex]\dfrac{12\sqrt{x}}{4x^3}[/tex]

Using exponent property [tex]x^a\cdot x^b=x^{a+b}[/tex]

Writing expression in the form of [tex]k\cdot x^n[/tex]

[tex]\Rightarrow \dfrac{12\sqrt{x}}{4x^3}=\dfrac{3\times 4}{4}\times \dfrac{x^{0.5}}{x^3}\\\\\Rightarrow \dfrac{3\times 4}{4}\times x^{0.5-3}\\\\\Rightarrow 3x^{-2.5}[/tex]

The screenshot is the correct answers

The table modeling the inverse of function f is,

  [tex]x[/tex]                  [tex]f^{-1}(x)[/tex]

-28                  -2

-9                   -1

-2                     0

 -1                     1

  0                    2

"A function g is the inverse of a function f if whenever y = f(x) then x = g(y)"

For given question,

We have been given a table modeling function f.

 x             f(x)

-2            -28

-1              -9

 0              -2  

 1               -1

 2              0

We need to complete the table modeling the inverse of function f.

We know that the inverse of function y = f(x) is [tex]x=f^{-1}(y)[/tex]

For given function f(x), we find inverse of f(x)

  [tex]x[/tex]                  [tex]f^{-1}(x)[/tex]

-28                  -2

-9                    -1

-2                    0

 -1                     1

  0                   2

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Answer:

True

Step-by-step explanation:

Equivalent fractions are fractions with different numbers representing the same part of a whole.

Answer:

.01 + .3 = 0.31

Step-by-step explanation:

Answer:

15 plates

Step-by-step explanation:

450 divided by 30 = 15, meaning 30 x 15 would be 450 mg. This also means that if the weight of some plates was 450 mg, there would be 15 plates.

Answer:

15

Step-by-step explanation:

Your units are a little confused.

The mass (total ) is 450 mg

1 plate weighs 30 mg

1 plate / 30 mg  =  x plates / 450 mg             Cross multiply

1 * 450 = 30x                                                   Divide by 30

450 / 30 = x

x = 15

There are 15 gold plates.

Answer:

0.8k +14

Step-by-step explanation:

See the steps below:)

Answer:

The average rate of change of the function over the interval is of 6.

Step-by-step explanation:

Average rate of change:

The average rate of change of a function h(x) over an interval [a,b] is given by:

[tex]A = \frac{h(b)-h(a)}{b-a}[/tex]

In this question:

Over the interval [-9,-2], so [tex]a = -9, b = -2, b - a = -2 -(-9) = 7[/tex]

The function is:

[tex]h(x) = -x^2 - 5x + 14[/tex]

[tex]h(-9) = -9^2 -5(-9) + 14 = -81 + 45 + 14 = -22[/tex]

[tex]h(-2) = -2^2 -5(-2) + 14 = -4 + 10 + 14 = 20[/tex]

Then

[tex]A = \frac{h(-2)-h(-9)}{7} = \frac{20-(-22)}{7} = \frac{42}{7} = 6[/tex]

The average rate of change of the function over the interval is of 6.

GE = 26

Step-by-step explanation:

OP = 16 + 9 = 25

PE - OG = 7

Using Pythagorean theorem,

(GE)^2 = (OP)^2 + (PE - OG)^2

=(25)^2 + (7)^2

= 625 + 49

= 674

or

GE = √674 = 25.96 or 26

Answer:

∠A and ∠G is the pair of vertical angles.

Step-by-step explanation:

From the figure attached,

Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.

Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."

Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ∠F are the vertical angles.

From the given options,

∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.

Answer:

∠A and ∠G

Step-by-Step Explaination:

I did it on

E

D

G

E

N

U

I

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Y

this is the answer on edmentum

The matching will be given below.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The value of sin C will be

sin C = 3 / 5

The value of sin D will be

sin D = 4 / 5

The value of cos C will be

cos C = 4 / 5

The value of cos D will be

cos D = 3 / 5

The value of tan C will be

tan C = 3 / 4

The value of tan D will be

tan D = 4 / 3

The product of sin D and cos D will be

sin D × cos D = (4 / 5) × (3 / 5)

sin D × cos D = 12 / 25

The product of tan C and tan D will be

tan C × tan D = (3 / 4) × (4 / 3)

tan C × tan D = 1

The product of cos C and tan D will be

cos C × tan D = (4 / 5) × (4 / 3)

cos C × tan D = 16 / 15

Then the matching will be given below.

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Multipuly po ba (15;000 7%)

Answer:

Step-by-step explanation:

-4<n≤5

Answer:

7 socks were sold

Step-by-step explanation:

7*8=56

11-7=4

4×11=44

56+44=100

This proves the answer of 7 to be correct

Answer:

8

Step-by-step explanation:

[tex]\angle RPS = 3x + 12,\ \angle QPR = 7x + 88\ =>\ \angle QPS = 3x + 12 + 7x + 88 = 180[/tex]

[tex]3x + 12 + 7x + 88 = 180[/tex]

[tex]10x + 100 = 180[/tex]

[tex]10x = 80[/tex]

[tex]x = 8[/tex]

Answer:

Area= 90

Step-by-step explanation:

triangle area: (b x h) / 2

(12 x 15) / 2

(180) / 2

a= 90