Write an expression that is equivalent to
5(3r-8). State the property that justifies
your answer.

Answer:

1. T, W, E, G

2. C, B, D, A

Step-by-step explanation:

For question 1:

G passes through (2, 3) and (0, -1). So, the slope is [tex]\frac{-1-3}{0-2}[/tex] = 2.

T passes through (0, 3) and (4, 4) so the slope is (4-3)/(4-0) = [tex]\frac{1}{4}[/tex].

E has a slope of [tex]\frac{5}{3}[/tex] because the equation is y = mx+b where m is the slope.

W has a slope of  [tex]\frac{1}{3}[/tex]  since slope is increase in y divided by increase in x.

The order of these from least to greatest is [tex]\frac{1}{4}[/tex], [tex]\frac{1}{3}[/tex], [tex]\frac{5}{3}[/tex], and 2.

Therefore, the answer is T, W, E, G.

For question 2:

A passes through (0, -1) and (2, 2), so the slope is (2- -1)/(2-0) = [tex]\frac{3}{2}[/tex].

B passes through (2, 0) and (4, 1), so the slope is (1-0)/(4-2) = [tex]\frac{1}{2}[/tex].

C has a slope of [tex]\frac{1}{4}[/tex] since the equation is y=mx+b where m is the slope.

D has a slope of [tex]\frac{3}{4}[/tex] since the slope is increase in y divided by increase in x.

The order of these from least to greatest is [tex]\frac{1}{4}[/tex], [tex]\frac{1}{2}[/tex], [tex]\frac{3}{4}[/tex], and [tex]\frac{3}{2}[/tex].

Therefore, the answer is C, B, D, A.

I hope this helps! :)

Didn't understand something? Some important formulas/things to remember that I used:

The equation of a linear function can be written as y=mx+b. m represents the slope.

The slope is the change/increase (decrease, in some cases), in y, divided by the change/increase in x.

The formula for the slope is [tex]\frac{Y2 - Y1}{X2 - X1}[/tex], where Y2 is the y coordinate of the second point, Y1 is the y coordinate of the first point, X2 is the x coordinate of the second point, and X1 is the x coordinate of the first point.

The rate of change of the linear function is the third option which is -3.

The linear function runs through the points (-3,14) and is specified in question (2,-1).

The function's rate of change must be determined.

Having said that,

The slope of a linear function determines how quickly it changes.

A line's slope

By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

In light of this, the slope of a line passing through the points (-3,14) and (2,-1) is

(-1-14)/(2-(-3)) = -15/5 = -3.

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The right triangle Short leg: 14 feet and  Long leg: 85 feet.

Because you have a right triangle,  and you know the hypotenuse, you can use the Pythagorean Theorem:

x2 + y2 = 852

You are told the difference between the 2 sides:

x = y + 71

Now you have 2 equations.  Use the expression for x in the 2nd equation, and substitute into the first:

(y + 71)2  + y2  = 852

Originally known as a rectangle triangle , a right triangle or right-angled triangle  is a triangle in which one angle is a right angle (that is, a 90-degree angle), i.e., It has two perpendicular sides.

The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

The hypotenuse is the side that is opposite the right angle (side c in the figure). Legs are the sides that are close to the correct angle (or catheti, singular: cathetus).

The side b that is adjacent to angle B and opposite to angle A is known as side a, while the side a that is adjacent to angle A and opposite to angle B is known as side b.

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The value of the short leg of the right angle triangle is 14 feet while the value of the long leg will be 85 feet.

You may apply the Pythagorean Theorem since you have a right triangle and know the hypotenuse:

x^2 + y^2 = 852

You are told the difference between the 2 sides:

x = y + 71

Now we have 2 equations.  

Now, we will use the expression for x in the 2nd equation, and substitute into the first:

Thus we will get it as:

(y + 71)^2+y^2=852

A right triangle, also known as a right-angled triangle, is a triangle with one angle that is a right angle (that is, a 90-degree angle), i.e., it has two perpendicular sides.

The connection between the sides and angles of a right triangle is the basis of trigonometry.

The hypotenuse is the opposite side of the right angle.

Legs are the sides that are nearly at the right angle

The side b that is adjacent to angle B and opposite to angle A is known as side a, while the side a that is adjacent to angle A and opposite to angle B is known as side b.

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a) The graph of the parabola opens downwards.

b) The point for axis of symmetry is x = -3.

c) The points of vertex for the parabola is (-3,-3).

d) There is no x-intercept and only one y-intercept, y = - 7.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

The graph of a parabola is given.

a) The parabola is starting from -∞ and is rising and then it is falling downwards towards the +∞.

Therefore, the parabola opens downwards.

b) The vertical line that passes through a parabola's vertex is the axis of symmetry, making the parabola's left and right sides symmetric. This line divides the graph of a quadratic equation into two mirror representations in order to make things simpler.

The parabola is symmetrical about x = -3.

Therefore, the axis of symmetry is x = -3.

c) There is a pivotal point in every parabola. To put it another way, it has a turning point where it either goes from "growing" to "decreasing" or vice versa. The vertex of the parabola is the name given to that pivotal point.

Here, the parabola turns at point (-3,-3).

Therefore, the points of vertex is (-3,-3).

d) The x-intercept is when the graph of parabola crosses the x-axis. In this case the parabola is drawn below the x-axis so there is no x-intercept.

The y-intercept is when the graph of parabola crosses the y-axis. In this case the parabola crosses the y-axis once at y = -7.

Therefore, the y-intercept is y = -7.

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Answer:2216 feet

Step-by-step explanation:

Badwater Basin is below sea level, so already we know that the 284 should be a negative number since it is below sea level. Mount McKinley is above sea level, so that number stays as a positive number. Now we can put these two number into an equation to solve, which would be 2,500 + (-284).

Note that the parenthesis are only there so you know that the number is negative, you don't need to solve anything.

Since adding a negative to a positive number is the same as subtraction, we can simplify it to look a little less confusing. You only need to solve 2,500 - 284 , which then equals 2216 ft.

Hope this helps you!

To go from the first town to the second town, you must drive 137.5 miles.

What is an proportion?

A proportion is a mathematical equation that compares two ratios. It is usually written as two equal fractions or ratios, one on each side of the equation. A proportion can be used to compare the relationship between different quantities, such as measurements, rates, or even time.

We can use proportion to solve this problem. The proportion relates the map scale to the actual distance:

0.75 inch / 50 miles = x / distance

where x is the actual distance we want to find.

We can cross-multiply and solve for x:

0.75 inch * distance = 2.75 inches * 50 miles

x = (2.75 inches * 50 miles) / 0.75 inch

x = (137.5 miles)

To go from the first town to the second town, you must drive 137.5 miles.

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36 pounds is equal to 16.344 kilograms.

Given that we need to convert 36 pounds to kilograms.

We have 1 pound = 0.454 kilogram,

To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.454 kilogram.

Given that we have 36 pounds, we can multiply this value by the conversion factor to find the equivalent weight in kilograms:

36 pounds x 0.454 kilogram/pound = 16.344 kilograms

Therefore, 36 pounds is equal to 16.344 kilograms.

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Answer:

To find the slope of a line, we can use the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Given the points (0,-10) and (-4,-11), we can plug these coordinates into the formula:

slope = (-11 - (-10)) / (-4 - 0) = -1 / -4 = 1/4

So, the slope of the line that passes through the points (0,-10) and (-4,-11) is 1/4.

Step-by-step explanation:

The expression for the area of a rectangle is A = L * W, where L is the length and W is the width.

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The school need to hire additional teacher to get 1:18 ratio is 20.

The teacher and student ratio in a school is 1:30,

let the number of teachers in a school=x,

then the number of students in school=30x,

total number of students in school=900

So, the number of teachers in school x=900÷30

                                                                x=30.

We want to take ratio of students and teachers =1:18

So, according to this ratio number of students=18x

and the number of required teachers x= 900 ÷ 18

                                                                x=50,

the school required 50 teachers,

Hence, the school need to hired teachers = 50-30=20

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Total cost c as a function of x is $94000 + 11.2x.

A company invests $94,000 for equipment to produce a new product. each unit of the product costs $11.40 and is sold for $17.98.

let x be the number of units produced and sold.

now,

Number of units = x

so,

c(x)= $94000 + 11.2x

Equation

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

Function

A function relates an input to an output. It is like a machine that has an input and an output. And the output is related somehow to the input.

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Answer:

To solve the equation (4x - 24) + x = 14, we can start by combining like terms on the left side of the equation:

4x - 24 + x = 14

Next we'll add the x terms together and the constants together:

5x - 24 = 14

Then we'll add 24 to both sides to get all the x terms on one side:

5x = 38

Finally we'll divide both sides by 5 to find the value of x:

x = 7.6

So the solution to the equation is x = 7.6

The last temperature will be 73.2 degrees Fahrenheit.

The parameter f(m) 15.2m+58 in the straight capability addresses the rate at which the water temperature increments over the long haul. In particular, it addresses the number of degrees Fahrenheit that the water temperature increments for each 1 moment of warming. So assuming the water has been warming for 2 minutes, its temperature will have expanded by 2 * 15.2 = 30.4 degrees Fahrenheit.

Parameter 58 in the linear function addresses the underlying temperature of the water when it begins warming. It is estimated in degrees Fahrenheit. So on the off chance that the water begins at a temperature of 58 degrees Fahrenheit and is warmed for 1 moment, its last temperature will be 15.2 + 58 = 73.2 degrees Fahrenheit.

Subsequently, The last temperature will be 73.2 degrees Fahrenheit.

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The inequality that describes that Trina must spend at least 45 minutes studying for her test at x ≥ 45 min.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions.

Trina is to spend at least 45 minutes studying for her test which means that she can either spend 45 minutes studying, or more than 45 minutes.

The inequality for this is therefore:

x ≥ 45

Assuming that the minutes she spends studying is x.

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Full question is:

Trina must spend at least 45 minutes studying for her math test. (find the inequality)

Answer:

Step-by-step explanation:

Ahh hell nah

The straight line distance between the northbound and eastbound cars is 5.7 kilometres.

The movement of cars and straight line connecting them forms a right angled triangle. The straight line will be hypotenuse will the eastbound and northbound distance will be perpendicular and base of the triangle. Thus, using Pythagoras theorem to find the distance between the two cars.

Distance between the two cars = ✓4² + 4²

Taking square of the numbers

Distance between the two cars = ✓16 + 16

Performing addition

Distance between the two cars = ✓32

Taking square root

Distance between the two cars = 5.66

Round to nearest tenth = 5.7

Thus, the distance is 5.7 kilometres.

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Answer:

a = not viable

b = 265

c = 0

good?

Answer: a = not viable b= 265 c = 0

Step-by-step explanation:

Answer: 108 mph

Step-by-step explanation: 378 divided by 3.5= 108mph

Answer: 108mph

Step-by-step explanation: 378 divided by 3.5= 108mph

By using the combination theorem, it can be concluded that the value of m + n = 125

Combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.

nCr = n! / (n - r)! r!

Let's denote the number of rectangles as r, and the number of squares as s:

r = ⁹C₂ x ⁹C₂

 = (9! / (9 - 2)! 2!) x (9! / (9 - 2)! 2!)

 = (9! / 7! 2!)   x   (9! / 7! 2!)

 = 36 x 36

 = 1296 rectangles

s = 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8²

  = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64

  = 204 squares

Then we get the ratio of s : r as follows:

s / r = 204 / 1296

      = 17 / 108

Since m represents the horizontal lines and n represents the vertical lines, then m + n = 17 + 108 = 125.

Thus, it can be concluded that the value of m + n = 125

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We must sell 625 loaves of bread to break even.

If it is a solution of equations, fill all the information of your solution into the equations you are working on to ensure that all equations are satisfied by your solution. And then, solve these equations to find the answer to your problem.

Let N be the number of loaves you sell.

Your cost would be,

C = 500 + 0.2N

Your revenue would be,

R = 1. N

Now, find out when is C = R  

⇒500 + 0.2N = N

⇒500  = 0. 8 N

⇒N = 500/0. 8

⇒N = 625

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15 + 6t >= 63

t >= (63 - 15) / 6

t >= 4.5

t >= 5 (since t must be a whole number of minutes)

So the possible numbers of minutes Kaitlin could add water are 5, 6, 7, 8, ... (any whole number greater than or equal to 5). This can be written as t >= 5.

0.3 pounds of oranges are left and this can be calculated by following steps :

Convert the 8 2/5 oranges to pounds.

8 2/5 oranges = 8.4 oranges

1 orange = 0.5 pounds

8.4 oranges x 0.5 pounds = 4.2 pounds

Subtract the amount of oranges eaten (4 5/8 pounds) from the total amount of oranges (4.2 pounds).

4.2 pounds - 4 5/8 pounds = 0.3 pounds

Answer: 0.3 pounds of oranges are left.

One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction. Removal of items from a collection is represented by the operation of subtraction.

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Answer:

Your answer is 9x^6*y^2π

Step-by-step explanation:

The formula for a circle is πr^2, with r as the radius.

Since 3x^3*y is the radius, you put that value in to get the equation:

(3x^3*y)^2*π

Once simplified, you get 9x^6*y^2π.

You can simplify further using the value of π, but it depends if the questions wants you to or not, mostly it doesn't.

I hope this was helpful.

The least expensive will be the lowest cost among the cost greater than $13.

i.e $13.5

If the cost of the favors is:

$13.5 < $14 < $15 < $20

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

All of the party favors cost more than $13.

This means,

Cost = x

x > 13

Now,

If the following are the cost of the favors:

$13.5, $14, $15, and $20

The least expensive will be the lowest cost among the cost greater than $13.

i.e $13.5

13.5 < 14 < 15 < 20

Thus,

The least expensive will be the lowest cost among the cost greater than $13.

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The predicted demand of a bobblehead that has price of $6.00 is given as follows:

49.093 units.

The function in the context of this problem is defined as follows:

y = -0.227x + 50.445.

In which:

For a price of $6.00, the predicted demand is obtained with the numeric value at x = 6, replacing the lone instance of x by 6, hence:

y = -0.227(6) + 50.445

y = 49.093 units.

Meaning that the second option is the correct option.

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Answer:

9

Step-by-step explanation:

make them equal to each other

15x = 14x + 9

x = 9

La ecuación de la fuerza resultante es el vector R = F · cos 234.689° i + F · sin 234.689° j.

Los vectores se caracterizan por tener magnitud y dirección, sea F la magnitud de la fuerza resultante del avión (nótese que la magnitud es un valor no negativo por regla general), cuya fórmula es la siguiente:

R = F · cos θ i + F · sin θ j

Donde:

La dirección del vector se determina mediante la siguiente función trigonométrica inversa:

θ = tan⁻¹ (Fy / Fx)

Donde:

Si sabemos que Fx = - 17 km y Fy = - 24 km, entonces la ecuación de la fuerza resultante es:

θ ≈ 234.689°

R = F · cos 234.689° i + F · sin 234.689° j

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The proportional relationship is option D. The graph of the relationship is given below.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

A relationship is proportional if y = kx, for some constant k.

Consider the last table.

x −2   1   2   3

y −6   3  6   9

When x = -2, y = -2 × 3 = -6

When x = 1, y = 1 × 3 = 3

When x = 2, y = 2 × 3 = 6

When x = 3, y = 3 × 3 = 9

So this is a proportional relationship with constant of proportionality k = 3.

Hence the table shown in the last option is the proportional relationship.

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The answer is the fourth one: Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.

Answer: To find the number of students, you can multiply the number of teachers by the number of students per teacher.

3,461 teachers * 28 students/teacher = 96,668 students

So, there are 96,668 students in the school district.

Step-by-step explanation: