Maria scored 20 goals in 4 soccer games
last season. Approximately how many
points did Maria average per game?

Answer:

Step-by-step explanation:

$38, 20% off = $30.40

$30.40, 10% off = $27.36

$27.36 is the final price of the shirt

The inverse of the function f(x) = 4(x - 3) is f⁻¹(x)=(x+12)/4.

A function that "undoes" another function is known as an inverse in mathematics. In other words, if f(x) generates y, then y entered into f's inverse creates x. x . Invertible refers to a function that has an inverse, which is represented by the symbol f1.

Inverse functions are functions that "reverse" one another in the broadest sense. If f, for instance, goes from a to b, then its inverse, f 1 f -1 f 1f, start superscript, minus 1, end superscript, must go from b to a.

Make f a function. Any horizontal line that crosses the f graph more than once indicates that f lacks an inverse. F has an inverse if there are no horizontal lines that cross the graph of f more than once.

Let f(x)=y

f(x)=4(x-3)

f(x)=y

y=4(x-3)

x=4(y-3)

x=4y-12

4y=x+12

y=(x+12)/4

Therefore, f⁻¹(x)=(x+12)/4

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The expression |ab^3| if a>0 and b>0 is even.

What is Parity Definition?

Even Function: A function is even if f(-x)=f(x) for all [tex]$x \in \mathbb{R}$[/tex] Odd Function: A function is odd if f(-x)=-f(x) for all [tex]$x \in \mathbb{R}$[/tex]

[tex]f(a): \quad|a|\left|b^3\right|[/tex]

[tex]f(-a): \quad|a|\left|b^3\right|[/tex]

[tex]-f(a):-|a|\left|b^3\right|[/tex]

Check parity of [tex]$|a|\left|b^3\right|$[/tex]

Check if Even: True

Check if Odd: False

Even

The expression |ab^3| if  b>0

[tex]$$\begin{aligned}& f(a): \quad|a| b^3 \mid \\& f(-a): \quad|a|\left|b^3\right| \\& -f(a): \quad-|a| b^3 \mid\end{aligned}$$[/tex]

Check parity of [tex]$|a|\left|b^3\right|$[/tex]

Check if Even: True

Check if Odd: False

Even

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Answer:

14

Step-by-step explanation:

To find g(f(3)), you will need to first find f(3) and then substitute that value into the function g(x).

To find f(3), substitute 3 for x in the equation for f(x):

f(3) = 3(3) - 2 = 9 - 2 = 7

Now substitute the value of f(3) into the equation for g(x):

g(f(3)) = g(7) = 2(7) = 14

Therefore, g(f(3)) = 14

Answer:

f(3)=7  g(3)=6

Step-by-step explanation:

f(x)=3x-2

f(3)=3(3)-2

f(3)=9-2

f(3)=7

g(x)=2x

g(3)=2(3)

g(3)=6

The value of k will be equal to 4/3 and there will be two real and different roots.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given that the equation is k + 4/x +3/x² =0. The value of k will be calculated as,

k + 4/x +3/x² =0.

kx² + 4x + 3 = 0

b² - 4ac =0

4² = 4 x k x 3

16 = 12k

k = 4/3

Therefore, the value of k will be equal to 4/3 and there will be two real and different roots.

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The equation of line s is y + 7 = -7/6(x - 7).

What is slope of a line?

A line's steepness and direction are measured by the line's slope. A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates,  Δy, Δx respectively. Consequently, it is possible to write the change in y coordinate with respect to the change in x coordinate as m = Δy/Δx

Given equation of line r is y = 6/7x+1.

The slope of line r is m = 6/7

The slope of the line that is perpendicular to line r is -1/m = - 7/6.

The equation of line that passes through the point (x₁, y₁) with slope m is y - y₁ = m(x - x₁).

Putting m = - 7/6, x₁ = 7 and y₁ = -7 in y - y₁ = m(x - x₁):

y - (-7) = - 7/6(x - 7)

y + 7 = - 7/6(x - 7)

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a) Equation for length and width of the rectangular rug be [tex]x^{2}[/tex] + 8x - 42 = 0

b) Width of the rectangular rug be 3.5 feet

c) Diagonal of the rectangle is 12.5 feet

What is the area of the rectangle?

The area of ​​a rectangle is the area occupied by the rectangle within its four sides or boundaries.

The area of ​​a rectangle depends on its sides. Basically, the formula for area is equal to the product of the length and width of a rectangle. The perimeter of a rectangle is equal to the sum of all its four sides

It is given that area of a rectangular rug id 42 square feet. The rug is 8 feet longer than its wide

a) Let the width of the rectangular rug be x feet

Length of the rectangular rug = (x+8) feet

area of rectangular rug = Length × width = x × (x + 8) = [tex]x^{2}[/tex] + 8x

area of rectangular rug = 42

[tex]x^{2}[/tex] + 8x = 42

[tex]x^{2}[/tex] + 8x - 42 = 0

Therefore, equation for length and width of the rectangular rug be [tex]x^{2}[/tex] + 8x - 42 = 0

b) If the length of the rectangle is 12 feet

Area of rectangle = 42 square feet

length × width = 42 square feet

12 × width = 42 square feet

width = 42/12 = 3.5

Therefore, width of the rectangular rug be 3.5 feet

c) Length of the diagonal of the rectangle = [tex]\sqrt{length^2+width^2}[/tex]

= [tex]\sqrt{12^2+3.5^2}=\sqrt{144+12.25}=\sqrt{156.25}= 12.5[/tex]

Therefore, diagonal of the rectangle is 12.5 feet

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The cost of each DVD as per the given data will be 20.08  without tax.  and 21.35 with sales tax.

Cost of DVD,

with sales tax

(40.15 + 2.55) / 2

= 42.70/2

= 21.35 per DVD

without sales tax

40.15 / 2

= 20.08 per DVD

Sales taxes are a type of tax that is paid to a governing body when goods and services are sold. Sales tax is an indirect tax that is often assessed at the time that certain taxable products are purchased or exchanged. It is assessed as a percentage of the item's retail price.

The government in power and the specific rules it enforces determine the sales tax, which is typically easy to calculate and collect. The sales tax can be thought of simply as an additional sum of money paid while buying products or services.

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Answer:

Below

Step-by-step explanation:

Sum of interior angles for the uppr right triangle = 180

52 + 90 + '2' = 180

'2' =38°

Answer:

4

Step-by-step explanation:

First we need to get some definitions out of the way

Definition of a turning point

Definition of degree of polynomial

The expected value of these outcomes are  $262.5, $496 and $648 respectively

You should know that the expected value are the proportion of the values when valued with the percentages

The given values are $210, $320 and $540

The given percentages are 25%, 55% and 20%

The expected values are

0.25*210 = $52.5+210=$262.5

0.55*320=176+320=$496

0.20*540=108+540=$648

Therefore the projected values of the project are  $262.5, $496 and $648 respectively

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The angle of CAE is 22

A line known as a perpendicular bisector cuts a specified line segment precisely in half, creating a 90° angle at the junction. The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler. On both sides of the line segment being divided, it forms a 90° angle.

Perpendicular bisector of ABC's side AB crosses BC at point E and side AB at point D. Additionally, m CAB = 82 and m C = 68.

Adopt A E.

In ABC, the triangle's angle sum property is A+B+C=180°.

82°+∠B+68°=180°

∠B= 180°-150°

∠B=30°

AD=B DDE is a perpendicular bisector in A DE and B DE.

If ADE=BDE=90°

DE is common.

Δ A DE ≅ Δ E DB→→[S AS]

∠DEB=∠D A E→→[CPCT]----(1)

In Δ DBE

∠EDB + ∠DBE+∠BED=180°→→Angle sum property of Triangle.

90° +30°+∠BED=180°

∠BED=180°-120°

∠BED=60°

So, ∠BAE=∠BED=60°------[using (1)]

∠CAE=∠CAB - ∠BAE

= 82°-60°

= 22°

Therefore the angle CAE is 22

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Given that x is in quadrant 3, its value for tan x=1/2 will be 206.565°, and its value for cos(206.565°) will be -0.894.

Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry. The sine, cosine, and tangent are the three fundamental trigonometric operations. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical concepts are built.

Here,

Tan x=1/2

π<x<3π/2

x=tan⁻¹/²(1/2)

x=26.565°

As the x is in quadrant 3,

=180+26.565°

=206.565°

cos(206.565°)=-0.894

The value of x for tan x=1/2 will be 206.565° as x is in quadrant 3 and for the same value of x, cos(206.565°) will be -0.894.

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Answer:

-sqrt 5 - 2 sqrt 5/10

Step-by-step explanation:

Edge 2023

Answer:56.6%

Step-by-step explanation:

30 - 13 = 17

17 /30 x 100 = 56.6 %

An equation of line having slope 1/6 and passes through the point (0,-3) is y = 1/6x - 3

We know that the slope-point form of line is:

(y - y1) = m(x - x1)

Here, we need to find an equation of line having slope 1/6 and passes pae through the point (0,-3)

let (x1, y1) = (0, -3)

and m = 1/6

substitute values in above formula,

(y - (-3)) = 1/6 (x - 0)

y + 3 = 1/6 (x)

y = 1/6x - 3

which is slope-intercept form of line (y = mx + b)

Therefore, equation of line is y = 1/6x - 3

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Answer:

6 + 2x

Step-by-step explanation:

5 + 5x - 3x + 1

add 5 + 1

6 + 5x - 3x

collect like terms 5x -3x

6 + 2x

Step-by-step explanation:

Please follow me the answer is 6+2x

or 2x+6

Answer:

4.

y = -1/6 * x - 7/3

Step-by-step explanation:

We can just check:

1.

y =  -1/6 * x

this doesn't work for x = -2 and y = -2 (first point) because we get

-2 = -1/6 * -2 = 1/3

this is nonsense

2.

y = -6x - 3/7

this doesn't work for x = -2 and y = -2 (first point) because we get

-2 = -6 * -2 - 3/7 = 12 - 3/7 = 11 + 4/7

this is nonsense

3.

y = -6x

this doesn't work for x = -2 and y = -2 (first point) because we get

-2 = -6 * -2 = 12

this is nonsense

4.

y = -1/6 * x - 7/3

this works for x = -2 and y = -2 because

-2 = -1/6 * -2 - 7/3 = 2/6 - 7/3 = 1/3 - 7/3 = -6/3 = -2

it also works for x = 4 and y = -3 because

-3 = -1/6 * 4 - 7/3 = -4/6 - 7/3 = -2/3 - 7/3 = -9/3 = -3

As per the congruency theorem, the two triangles are congruent.

Congruency theorem:

Congruency theorem states that "if all the three sides of one triangle are equal to all the three sides of another triangle, then both the triangles are congruent to each other."

Given,

Here we need to prove that  congruency theorem can be used to prove that △wut ≅ △vtu.

Let us consider triangles WUT and VTU.

And in these triangles:

=> WU≅VT

And in those one, ∠T≅∠U,

Therefore, m∠T = m∠U = 90°

Here the side TU is common.

Now, we have to note that triangles WUT and VTU are right triangles, because m∠T = m∠U = 90°.

Then the side TU is common leg and sides WU and VT are hypotenuses.

Therefore, the HL theorem states: if the hypotenuse (WU) and one leg  (TU) of a right triangle (ΔWUT) are congruent to the hypotenuse (VT) and one leg (TU) of another right triangle (ΔVTU), then the triangles are congruent.

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Answer: HL

Step-by-step explanation:

The total area of the shaded region is solved to be 154.93 cm²

The diameter is solved using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 8² + 15²

x² = 289

x = √289

x = 17

Work out the area of the triangle using the formula

= 1/2 *  base * height

base = hypotenuse or diameter

height = radius = diameter/2

= 0.5 * 17 * 8.5

= 72.25 cm²

Area of the circle

= Π * radius²

= 22/7 * 8.5²

= 226.98 cm²

shaded portion

= Area of the circle - area of the triangle

= 226.98 - 72.25

= 154.93 cm²

the area of the shaded portion is 154.93 cm²

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The bus is covering a distance of 42 miles in 1 hour 30 minutes then the speed of the bus will be 28 mph.

The overall distance the object covers in a given amount of time is its average speed. The scalar quantity represents the average speed. It does not have direction; it is represented by magnitude.

As per the given data provided in the question,

Total distance traveled by bus = 42 miles

Total time is taken by the bus = 1 hour 30 minutes = 1.5 hours.

Then the average speed of the bus will be,

[tex]Average\ Speed(S) = Total\ Distance/Total\ Time[/tex]

S = 42/1.5

S = 28 mph.

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Answer: 50 existing members

If the pond now contains 320 gallons of water, number of weeks it has been since the pond was at full capacity is 5 week.

Given that, a full pond containing 625 gallons of water begins losing its water at a rate of 20% per week.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here, number of gallons water being used for x weeks is

625-320=305 gallons

Now, number of gallons of water used in a week= 20% of 305

= 20/100 ×305

= 0.2 ×305

= 61 gallons

So, number of weeks = x=305/61

= 5

Therefore, if the pond now contains 320 gallons of water, number of weeks it has been since the pond was at full capacity is 5 week.

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Answer:

5

Step-by-step explanation:

Look that guys answer is better

Answer:

53 degrees

Step-by-step explanation:

This is a transversal question (look at attached). Because the lines are parallel, g will equal to 180(a straight line is 180 degrees) - a. Then, because g + f + e = 180 (since it is a straight line), substitute the values that we know and solve. (61) + f +(66) = 180. f = 53

Cutting perfect slices of pie can be tricky. Crusts can crumble, bottoms can buckle and fillings can spill over, but there are a lot of tricks for a good slice.

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American adults believes in alien for the  given 95% confidence interval and sample surveyed is in the interval range of ( 0.66 , 0.78 ).

As given in the question,

Sample of American adults surveyed 'n' = 200

Percent of people believes in aliens are success  'p'= 72%

                                                                                      = 0.72

Percent of people who don't believes (failure) in aliens ' 1 - p'  = 1 - 0.72

                                                                                          = 0.28                                                                                    

95% Confidence interval that represents Americans adults who believes in aliens

value of z - score for 95% confidence interval = ± 1.96

Margin of error 'MOE'= (z-score)√p ( 1- p) /n

                                   = ( 1.96)√(0.72 × ( 1 - 0.72 )/ 200

                                   = 1.96 ( √0.2016 / 200)

                                   = 1.96 ×√0.001008

                                   = 0.063

Lower limit = p - MOE

                 = 0.72 - 0.063

                 = 0.66

Upper limit =  p + Margin of error

                 = 0.72 + 0.063

                 = 0.78

Therefore, 95% confidence interval with sample size of the Americans adults who believes in alien are in the interval of ( 0.66 , 0.78 ).

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Answer:

-133.16472

Step-by-step explanation:

N/A

Answer:

-133.16472

Step-by-step explanation:

Answer:

EP = GP

GP = HP

angle EFH = 45

Think these 3 are the right answers, hope it helps.

Answer:

a and f are 14°

Angles b, c, d, and e are all 166°

Step-by-step explanation:

Alternate interior angles are congruent

x + 9 = 4x - 6  Subtract x from both sides

9 = 3x - 6    Add 6 to both sides

15 = 3x  Divide both sides by 3

5 = x

Plug this back into the equation for find the angles measurements

x + 9

5 + 9

14

or

4x _ 6

4(5) -6

20 - 6

14

angles a and f are vertical angles so they are congruent and equal to 14

B ,c , d and e are all supplements to the found angles

180-14 = 166