What is the slope-intercept form of the function described by this table?



x 0 1 2 3
y 3 8 13 18

Enter your answer by filling in the boxes.

y =
x +

Answer:

C.

Step-by-step explanation:

The answer is C (-1, 1/2)

In a market economy, option C. all consumers collectively have a great influence on the price of goods and services.

A market economy is an economic system in which goods and services are traded in a market, and prices are determined by supply and demand. The decisions of individual consumers and producers, operating through the market mechanism, determine what goods and services are produced and how they are distributed.

Therefore, the correct answer is as given above. It could be concluded that market economy allow individuals to influence the price of goods and services

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Answer:x=1

Step-by-step explanation:

For this, you will need to use substitution.

we know that a²+b²=c²

plug it in

[tex]x^2+3^2=y^2[/tex]

simplify to find

[tex]x^2+9=y^2[/tex]

[tex]y=\sqrt{x^2+9}[/tex]

repeat with the other side

[tex](x+8)^2+3^2=z^2[/tex]

[tex]x^2+16x+73=z^2[/tex]

[tex]z=\sqrt{x^2+16x+73}[/tex]

plug these in for the larger triangle

[tex]y^2+z^2=(2x+8)^2[/tex]

[tex]x^2+9+x^2+16x+73=4x^2+32x+64[/tex]

[tex]2x^2+16x+82=4x^2+32x+64[/tex]

set equal to 0 and simplify

[tex]-2x^2-16x+18=0[/tex]

pull out a -2

[tex]x^2+8x-9=0[/tex]

factor

[tex](x-1)(x+9)=0[/tex]

x=-9,1

x cannot be negative since it a measurement so x=1

The value of sin A is, 7/25.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

The terminal side of angle A goes through the point (−24/25,7/25) on the unit circle.

Now, By definition we get;

⇒ cos A = - 24/25

⇒ Sin A = 7/25

Thus, The value of sin A is, 7/25.

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For the first function, the domain and the range are given as follows:

For the second function, the domain and the range are given as follows:

The domain of a function is the set that contains all the input values that can be assumed by the function, hence it is given by the set that contains all the values of x in the graph of the function.

The range of a function is the set that contains all the output values that can be assumed by the function, hence it is given by the set that contains all the values of y in the graph of the function.

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The size of the crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route is 44000 people.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, the size of a crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route,

The number of people that can fit comfortably in a 6 feet by 6 feet area = 10

The ratio of the number of people per unit area = 10/(6 × 6) = 10/36

The area, A, occupied by the crowd = 5 feet × 3 mile × 2

3 miles = 15840 feet

∴ A = 5 feet × 15840 feet × 2 = 158400 ft²

We then have;

Number of people / 158400 = 10/36

Number of people = 44000

Hence, the size of the crowd that is 5 feet deep on both sides of the street along a 3-mile section of a parade route is 44000 people.

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Answer:

1 quarter, 3 dimes, 1 nickel, 1 penny

Step-by-step explanation:

25c + 10c+10c+10c+5c+1c =61c

Answer:

50

Step-by-step explanation:

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=8 \end{cases}\implies S=180(8-2)\implies S=1080 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{just one angle is}}{\cfrac{1080}{8}\implies 135^o}\hspace{5em}\stackrel{\textit{for six angles}}{(6)(135)\implies \boxed{810^o}}[/tex]

The correlation between the amount of rain (mm) in the summer and the amount of water (m2) used for watering the lawn is directly proportion to each other

Based on the grain size, the classification of rain is divided into four, namely:

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The properties are used to manipulate equations in order to isolate a variable, find a solution, or simplify the equation

What are the properties of equality?

The "division property of equality" states that if you divide both sides of an equation by the same non-zero number, the two sides will remain equal.

The "simplification" step is used to simplify an expression by combining like terms, reducing fractions, or performing other operations to simplify the expression.

The "multiplication property of equality" states that if you multiply both sides of an equation by the same non-zero number, the two sides will remain equal.

The "addition property of equality" states that if you add the same number to both sides of an equation, the two sides will remain equal.

The "subtraction property of equality" states that if you subtract the same number from both sides of an equation, the two sides will remain equal.

These properties are used to manipulate equations in order to isolate a variable, find a solution, or simplify the equation.

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The volume of the sculpture is 92.316 feet³.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is (1/3)πr²h.

We have,

Cone-shaped sculpture:

Height = 5 feet

Base circumference = 26.376

This means,

2πr = 26.376

r = 26.376/(2 x 3.14)

r = 4.2 feet

Now,

The volume of the sculpture.

= 1/3 x 3.14 x 4.2 x 4.2 x 5

= 92.316 feet³.

Thus,

92.316 feet³ is the volume of the sculpture.

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Answer:

At an x-intercept

Step-by-step explanation:

y = sin x

y = sin 0

y = 0

(0,0) is an x-intercept but not it's maximum or minimum.

The value of function for f(5) is 3125.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given that, f(1) = 5 and f(n) = 5f(n − 1)

Now, for finding the the 5th term we have to find the remaining four term before the 5th term.

So, n=2

f(2) = 5f(1)

f(2)=  5(5)

f(2)=  25

Now, n=3

f(3) = 5f(2)

f(3)=  5(25)

f(3)=  125

Now, n=4

f(4) = 5f(3)

f(4)=  5(125)

f(4)=  625

Now, n=5

f(5) = 5f(4)

f(5)=  5(625)

f(5)=  3125

Hence, the value of function for f(5) is 3125.

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Answer: A baker needs to make a dessert for a party. The recipe calls for 1 3/4 cups of sugar, but the baker only has 1/2 cup measuring cups. How many measuring cups does the baker need to measure out the sugar for the recipe?

We can start by converting the mixed number 1 3/4 into an improper fraction: 1 3/4 = 7/4. Then, we can divide 7/4 by 1/2:

7/4 ÷ 1/2 = 7/4 * 2/1 = 14/4 = 3 1/4

The baker needs 3 1/4 measuring cups to measure out the sugar for the recipe.

[Image: Three and a quarter measuring cups filled with sugar]

Step-by-step explanation:

The solution of the system of equations is (0, 1).

Here we want to solve the system of equations:

12x - 3y  = -3

6x + y = 1

To use the elimination method, we can take the difference between the first equation and two times the second one, then we will get:

12x - 3y - 2*(6x + y) = -3 - 2*1

12x - 3y - 12x - 2y = -5

-5y = -5

y = -5/-5 = 1

Now we know the value of y, we can replace it in one of the equations ot find the value of x.

6x + y = 1

6x + 1 = 1

6x =  1 - 1 = 0

x = 0

The solution is (0, 1)

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Answer: 241

300 / 3 = 100

321 / 3 = 107

241 / 3 = 80.333

8.910 / 3 = 2.97

Answer:

17

degree

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Step-by-step explanation:

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On solving the provided question, we can say that by solving the interest  the amount after his 21st birthday =  $ 10,806

Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.

P = $6000

Rate=  4 %

Time, t= 12 years  

Formula of Compound Interest

[tex]A = P(1+R/100)^T\\A = 6000(1+4/100)^{12}\\A = 9606.19332[/tex]

On his 19 th birthday

[tex]A = P(1+R/100)^T\\A = 6000(1+4/100)^{13}\\A = 9990. 44106[/tex]

After 21st year S. I is

S. I =  10390.058700 × 4/100

S. I = 415.602348

A= 415.602348 + 10390.058700

A = $ 10,805.661.

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Probability that the shopper selected at random was satisfied with the service they received is 845 / 1522.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Total number of customers = 1522

Out of these,

Number of customers made a purchase = 624

Number of customers not made a purchase = 898

Number of customers who purchased satisfied with the service = 130

Number of customers who does not purchase satisfied with the service = 715

Total number of customers who are satisfied with the service = 130 + 715 = 845

Probability that the randomly selected shopper satisfied with the service = 845 / 1522

Hence the probability is 845 / 1522.

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The function rule for this situation is f(n) = 1/36n

From the question, we have the following parameters that can be used in our computation:

The length of a string in yards is a function ƒ(n) of the length n in inches.

The conversion of yards to inches is

Yard = 1/36 * Inches

When represeted as a function, we have

f(n) = 1/36n

Hence, the function is f(n) = 1/36n

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Han should expect to pay $90 for the ticket if he buys it the day of the game.

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 "%".

Han should expect to pay $90 for the ticket if he buys it the day of the game

The current ticket fee = $30

The markup = 200%

The markup = 200% of the current price

Markup = 200/100 ×30

= $60

The ticket fee on the game day = The current fee + The markup

The ticket fee on the game day = $30  +  $60

The ticket fee on the game day = $90

Hence, Han should expect to pay $90 for the ticket if he buys it the day of the game.

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The number of fifty dollars with the manager are 31.

Two or more expressions with an Equal sign is called as Equation.

Given that a convention manager finds that she has $1370, made up of twenties and fifties.

20x+50y=1370

She has a total of 46 bills.

x+y=46

x=46-y

Now we have to plug in x value in equation 1

20(46-y)+50y=1370

920-20y+50y=1370

920+30y=1370

Subtract 920 on both sides

30y=450

Divide both sides by 30

y=15

Now plug in y value in x+y=46

x+15=46

Subtract 15 on both sides

x=46-15

x=31

Hence, the number of fifty dollars with the manager are 31.

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the number of sides of the polygon​ 12 sides

An interior angle is a shape's internal angle. The closed shape with sides and vertices is a polygon. All of the inner angles of a regular polygon are equal to one another. For instance, a square has interior angles that are all exactly right angles, or 90 degrees.

In a regular polygon, all internal angles are equal. Interior angle of a polygon = sum of interior angles number of sides is the formula for determining the amount of an interior angle.

The n-sided polygon's inner angle total equals (n-2).

180°, thus as follows:

140°+160°+ (n-2)150 = (n-2)180°

or, 300° = (n-2)(180° - 150°).

or, 300° = (n-2) 30°

or, 10= n - 2.

alternately, n = 10 + 2 = 12 sides.

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The answers to each part is given above.

Given is that when an object is thrown upward with an initial velocity of v{0}, then its approximate height is given by this quadratic function -

S = - 4.9t² + [tex]$v_{o} ^{t}[/tex] + h

The approximate height is given by this quadratic function -

S = - 4.9t² + [tex]$v_{o} ^{t}[/tex] + h

{ 1 } - For the maximum height :

dS/dt = 0                                        ... Eq{ 1 }

dS/dt = -9.8t + [tex]$3.1^{t}[/tex] log(3.1) + 0 = 0

- 9.8t + [tex]$3.1^{t}[/tex] log(3.1) = 0

Refer to the graph attached. At t = 3.8 {possible value}, the function is 0.

So we get -

t = 3.8 s                                         ... Eq{ 2 }  

Maximum height achieved -

h{max} = - 9.8t + [tex]$3.1^{t}[/tex] log(3.1) + 15

h{max} = - 9.8 x 3.8 + [tex]$3.1^{3.8}[/tex] log(3.1) + 15

h{max} =  - 37.24 + 73.65 x 0.50 + 15

h{max} =  14.585 m

{ 2 } -

0 = 3.1 t + 9.8/2 t²

0 = 3.1 t + 4.9 t²

Solving graphically, we get -

|t| = 0.6 s

Total time taken to reach ground -

T = 2 x 3.8 + 0.6

T = 8.2 seconds                                       ... Eq{ 3 }

Therefore, the answers to each part is given above.

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the slope of the line means in this situation "a. The cost is $4 per T-shirt".

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, Seth owns a printing shop that makes customized T-shirts.

Since The cost to make T-shirts is proportional to the number of T-shirts he makes.

Thus,

The y-intercept of the line will be 0 cause the line is passing through the origin point.

The general formula of the equation of a line:

y=mx+b,

where m is the slope

b is the y-intercept

since, slope = (y - y')/(x -x')

In our case,

b = 0

m = (8 - 4)(2-1)

m = 4

And m represents The cost is $4 per T-shirt.

therefore,  the slope of the line means in this situation "a. The cost is $4 per T-shirt".

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The piecewise function for the Tax due on an income of x dollars are:

From the case, we know that there are 3 scenariois for filling tax due based on an individual's income, where:

To construct the piecewise function for the Tax due, we need to translate the given conditions into mathematical formulation.

We assume that:

T(x) = tax due

x = $ amount of taxable income

For taxable income between $0 until $15,000, the tax is 3.5% of taxable income; then:

T(x) = 3.5% x

T(x) = 0.035x

For taxable income between $15,000 until $30,000, the tax is $525 plus 6.25% of excess over $15,000. Then:

T(x) = 525 + 6.25% (x - 15,000)

T(x) = 525 + 0.0625 (x- 15,000)

Please note that the additional 6.25% only will be counted based on the remaining of the taxable income deducted by $15,000.

For taxable income over than $30,000, the tax is $1462.50 plus 6.8% of excess over $30,000. Then:

T(x) = 1462.50 + 6.8% (x - 30,000)

T(x) = 1462.50 + 0.068 (x - 30,000)

Please note that the additional 6.8% only will be counted based on the remaining of the taxable income deducted by $30,000.

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a) The measure of <ABC is 131 degree.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle.

The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle.

Given:

a) As <ACD= 90

and Triangle BCD is an equilateral triangle then each of its angle measure 60 degree.

So, <ACD= 90

<ACB + <BCD = 90

<ACB = 90 - 60

<ACB = 30

and, <BAC = 19

Using Angle sum property in Triangle ACB

19 + <ABC + 30 = 180

<ABC = 180 - 49

<ABC = 131 degree.

b) Bow, In Triangle HEF using Angle sum property

<E + <F + <EHF = 180

<EHF = 180 - (69+ 40)

<EHF = 71 degree.

Then, <GHE + <EHF + <FHI

= 72 + 71 + 37

= 180, which forms on straight line.

Thus, GHI is a straight line.

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