The points in the table lie on a line. Find the slope of the line.

x: 1, 3, 5, 7
y: 2, 10, 18, 26

Answer:1.44

Step-by-step explanation:

Answer:

  a) 23.1 million

  b) year 2013

Step-by-step explanation:

Given a population in millions is modeled by A = 23.1e^(0.0152t) for t years after 2000, you want to know the population in year 2000, and the year in which the population is 28.3 million.

When t=0, the exponential factor is 1. The population is given by the coefficient of that factor: 23.1

The population in 2000 was 23.1 millions.

We can solve for t to find the year the population is 28.3 million:

  28.3 = 23.1e^(0.0152t)

  28.3/23.1 = e^(0.0152t) . . . . .divide by 23.1

  ln(28.3/23.1) = 0.0152t . . . . . take natural logs

  t ≈ 13.36

The population will reach 28.3 million in the year 2013.

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answer:

step by step explanation:

(4,8); y = 2x — 4 = ?

A pyramid is a solid shape with a specified shaped base. The required answer is 8.67 cubic feet.

A pyramid is a solid shape with a specified shaped base. While a square based pyramid is a type of pyramid which has its base to be a square.

Volume of a square based pyramid = [tex]\frac{1}{3}[/tex] x base area x height

Also, are of a square = length x length

So that,

i. For the first pyramid;

volume =  [tex]\frac{1}{3}[/tex] x (2 x 2) x 6

            = 8 cubic feet

The volume of the first pyramid is 8 cubic feet.

ii. For the second pyramid, we have;

height = 8 feet

base side = 2.5 feet

So that.

Volume =  [tex]\frac{1}{3}[/tex] x (2.5 x 2.5) x 8

             = 16.6667

Volume = 16.67 cubic meters

The volume of the second pyramid is 16.67 cubic meters.

Therefore, the volume of the second pyramid is greater than the volume of the first pyramid by;

volume of the second pyramid - volume of the first pyramid = 16.67 - 8.0

                                              = 8.67 cubic feet

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Answer:

y = - [tex]\frac{5}{4}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0-5}{4-0}[/tex] = [tex]\frac{-5}{4}[/tex] = - [tex]\frac{5}{4}[/tex]

the line crosses the y- axis at (0, 5 ) ⇒ b = 5

y = - [tex]\frac{5}{4}[/tex] x + 5 ← equation of line

Answer:D

beacuse it is correct  just trust me i have done this class and its correct

Answer: 2x+y=5

Step-by-step explanation:

The standard form of a linear equation is

ax+by=c

Move all terms containing variables to the left side of the equation.

2x+y=5

Answer:

2x + y = 5

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\$Ax+By=C$\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are constants. \\ \phantom{ww}$\bullet$ $A$ must be positive.\\\end{minipage}}[/tex]

Given equation:

[tex]y=-2x+5[/tex]

To write the given equation in standard form, collect the terms with variables on one side of the equation, ensuring the term in x is positive.

Add 2x to both sides:

[tex]\implies y+2x=-2x+5+2x[/tex]

[tex]\implies y+2x=5[/tex]

[tex]\implies 2x+y=5[/tex]

Answer:

1/4

Step-by-step explanation:

1/2 divided by 2 would be 0.25, and since that's a quarter it would be 1/4.

The location of G is (3, 0).

Given question in that we have a number line.

A number line goes from negative 5 to positive 10.

Point D is at negative 2 and point F is at positive 7.

A line is drawn from point D to point F.

So we can write coordinate of point D as (-2,0) and point F as (7,0).

line segment from D to  F divides as point G as in ratio of 5:4

Consider two points P(x1, y1) and Q(x2, y2). We have to find the coordinates of the point R which divides PQ in the ratio m : n

x = [tex]m*x2+n*x1/(m + n)[/tex]

[tex]y = m*y2+n*y1/(m + n)[/tex]

so here in our question m =5 n=4

x1=-2 x2=7 y1=0 y2=0

x = 5*7+4*(-2)/9

x = 3

y = 5*0+4*0/9 = 0

So the location of G is (3, 0)

Given Question is incomplete complete question here.

What is the location of point G, which partitions the directed line segment from D to F into a 5:4 ratio? A number line goes from negative 5 to positive 10. Point D is at negative 2 and point F is at positive 7. A line is drawn from point D to point F.

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If the ratio of band members in group 1 to band members in group 2 is 1 to 3, then for every 3 band members in group 2, there will be 1 band member in group 1.Therefore, group 2 will have 11 band members.

Comparing two numbers or quantities results in a ratio. Usually, it is expressed in the form "a:b" or "a/b," with a and b standing for the two quantities under comparison. Contrarily, a percentage is an equation that states that two ratios are equal. Alternatively said, a proportion is a claim that one ratio is equal to another.

For example, if the ratio of apples to oranges in a basket is 2:3, this implies that there are three oranges per each two apples. We may alternatively state that the ratio of apples to total number of fruits in the basket is 2:5, because 2 + 3 = 5. The two ratios (2:3 and 2:5) are proportionate in this instance. Also, ratio of band members in group 1 to band members in group 2 to be 1 to 3

How to solve?

If the director wants to divide 44 band members into two groups, with this ratio, then the number of band members in group 2 will be 44 / (1 + 3) = 44 / 4 = 11 band members.

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The independent variable in the given function is h.

The Independent variables are those variable whose value does not depend on any other variable. And it causes the change in other variables.

The dependent variable is those variables whose value is not independent and change in this variable is dependent on the change of the independent variable.

Given the function p(h)=20h−50, which represents Lamont works for a company that pays him $20 per hour(h), but $50 each week is deducted from his pay for insurance.

Now, in the given function since the amount that Lamont will get depends upon the number of hours for which he is working.
Therefore, the h is the independent variable and p is the dependent variable.

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200 rides does it take to break even.

What are the many sorts of cost?

Fixed and variable costs are the two main categories of expenses incurred by enterprises. While variable costs fluctuate with output, fixed costs do not.

                 Sometimes, fixed costs are referred to as overhead costs. They must be paid whether a company produces 100 or 1,000 widgets.

The cost function is given by

C(x ) = 15x + 1000

It is also given that it costs $25 per ride.

so,

Revenue function for x number of rides be

 R(x) = 20x

For break even:-

The cost must be equal to the Revenue i.,e

       C(x) = R(x)

  15x + 1000 = 20x

     1000 = 20x - 15x

     1000 =  5x

        x = 1000/5

        x = 200

Therefore, 200 rides does it take to break even.

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The converse of the conditional statement is “If dangerous to your health then walking in front of a moving car”.

The inverse of the conditional statement is “If not dangerous to your health then not walking in front of a moving car”.

The contrapositive of the conditional statement is “if not walking in front of a moving car then not dangerous to your health."

The conditional statement is defined as the two fundamental components that make up a conditional statement Hypothesis (if) and Conclusion (then).

The given conditional statement is "walking in front of a moving car is dangerous to your health."

The converse of the conditional statement is “If dangerous to your health then walking in front of a moving car”.

The inverse of the conditional statement is “If not dangerous to your health then not walking in front of a moving car”.

The contrapositive of the conditional statement is “if not walking in front of a moving car then not dangerous to your health."

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The slope of the line that passes through the points (10, 3)(10,3) and (7, 0)(7,0)= 1.

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line.

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, respectively.

Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-

P1 = (x1, y1) and P2 = (x2, y2)

According to our question-

The slope m using the slope formula

m = y2-y1/x2-x1

with (x₁, y₁ ) = (10, 3 ) and (x₂, y₂ ) = (7, 0 )

-3/-3 = 1

Hence, the slope is = 1.

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Answer:

[tex]x=59[/tex]

Step-by-step explanation:

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]\implies x=180-48-73=59[/tex]

Th length of the enclosed area of the scale model in inches is 32 inches.

Joseph and Raquel are building a scale model of the Alamo Mission for their Texas history project using a scale in which 2 inches represents 30 feet.

The enclosed area of the Alamo Mission was 480 feet long and 160 feet wide.

The length of the enclosed area of the scale model in inches can be calculated as follows:

30 feet = 2 inches

480 feet = ?

cross multiply

length of the enclosed area = 480 × 2 / 30

length of  the enclosed area = 960 / 30

length of the enclosed area = 32 inches

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Answer:

The answer is B

Step-by-step explanation:

I took the test and got it right,(also i have a pic) brainiest pls!!

Answer:

-2.25x = 30

Step-by-step explanation:

I hope this helps!

Based on the unit rate of the table, the missing values that shows the cost and the number of tickets are:

$32 and 9 tickets.

To calculate the missing values in the table shown in the attachment below, we have to find the unit rate, which is the cost of 1 ticket.

Given that 3 tickets will cost $12, therefore:

Unit rate = 12 / 3 = $4 per ticket.

Using this rate, find the missing values as explained below.

For 8 tickets, we will have the following cost:

8 × $4 = $32

For $36, we will have the following tickets:

$36/$4 = 9 tickets

Thus, the missing values that will complete the table will be:

$32 and 9 tickets.

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Answer:

648

Step-by-step explanation:

An easy way to do this is to multiply all sides, then divide by 2.

8 × 9 × 18 = 1296

Now divide that by 2:

1296 ÷ 2 = 648

The area of the triangle is 648.

Let X be the number of hours it takes Paige to sort the toys alone.

It takes Madison X + 6 hours to sort the toys alone.

Together, it takes them X + (X + 6) = 4 hours to sort the toys.

Combining like terms, we get 2X = 4

Dividing both sides by 2, we get X = 2

Therefore, it takes Paige 2 hours to sort the toys alone.

It takes Madison 2 + 6 = 8 hours to sort the toys alone.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The value of x is 1.

The value of y is 4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 9 = 5 is an equation.

We have,

-4.5x - 2y = -12.5 ____(1)

3.25x - y = -0.75 _____(2)

From (1) we get,

-4.5x + 12.5 = 2y

y = (-4.5x + 12.5) / 2 _____(3)

Now,

3.25x - y = -0.75

Putting (3) in (2) we get,

3.25x - (-4.5x + 12.5) / 2 = -0.75

6.5x + 4.5x - 12.5 = 2 x -0.75

11x - 12.5 = -1.5

11x = -1.5 + 12.5

11x = 11

x = 1

Now,

From (3) we get,

y = (-4.5x + 12.5) / 2

y = (-4.5 x 1 + 12.5) / 2

y = (-4.5 + 12.5) / 2

y = 8/2

y = 4

Thus,

The value of x is 1.

The value of y is 4.

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The smallest integer out of the three integers is 109

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.

A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.

Three consecutive integers:

x, x+1, x+2

The sum of the integers,

x+(x+1)+(x+2) = 330

3x + 3 = 330

3x= 327

x= 327/3

x= 109

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Answer: To find out how long it takes the paddle wheel to complete 100 full revolutions, we need to calculate the circumference of the paddle wheel and divide that by the speed at which the fins along the outer edge are traveling.

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference and r is the radius of the circle.

The radius of the paddle wheel is 2 feet (the diameter of 4 feet divided by 2), so the circumference is:

C = 2π * 2 = 8π feet

To find out how long it takes the paddle wheel to complete 100 full revolutions, we divide the number of feet traveled in one revolution (the circumference of 8π feet) by the speed at which the fins are traveling (1.3 feet per second):

100 * 8π feet / 1.3 feet per second = 615.38 seconds

Rounded to the nearest second, it takes approximately 615 seconds for the paddle wheel to complete 100 full revolutions.

Answer:

∠AFB

Step-by-step explanation:

Vertical angles are opposite to one another and share the same vertex or endpoint. ∠DFE is ∠AFE both share the point F, and they are opposite to each other, so they are also vertical to each other.

Answer:

Step-by-step explanation:

(2, 0), (3, 4)

(4 - 0)/(3 - 2)= 4/1 = 4

The required solutions are x = 2-i and x = 2+i to the given quadratic function.

The quadratic function is defined as a function containing the highest power of a variable is two.

We have been given that quadratic function as

-2x² + 8x - 10 = 0

Compare the given function to the standard quadratic function f(x) = ax² + b x + c.

We get a = -2, b = 8 and c = -10

Using the quadratic formula to solve the above quadratic function

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\dfrac{-8\pm \sqrt{8^2-4\left(-2\right)\left(-10\right)}}{2\left(-2\right)}[/tex]

[tex]x=\dfrac{-8\pm \:4i}{2\left(-2\right)}[/tex]

[tex]x=\dfrac{-8+4i}{2\left(-2\right)},\:x=\dfrac{-8-4i}{2\left(-2\right)}[/tex]

x = 2-i, x = 2+i

Thus, the required solutions are x = 2-i and x = 2+i to the given quadratic function.

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