4.
Consider the following diagram:
What is the value of m?
56°
m
68°

The simple interest that Oliver needs to pay is $ 90

Simple interest is nothing but interest on a loan at a rate. The formula for Simple interest is given below

Simple interest, I = ptr

where p = principal amount

t = time period in years

r = rate of interest in decimals

Here we have

Oliver borrowed $1,500 to purchase a riding lawn mower  

The rate of interest r = 12%

=> 12/100 = 0.12 (in decimals )

The time period given = 6 months = 0.5 years   [ 6/12 = 0.5 ]  

From the above formula,

The simple interest, I = ptr

=> I = $1,500(0.12) (0.5) = $ 90

Therefore,

The simple interest that Oliver needs to pay is $ 90  

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An equation modeling the population, p, of Ohio given the year, t is,

p = 0.04t + 10.98.

What is population?

The term "population" refers to all citizens who are either permanently residing in a country or who are just passing through. This indicator reveals how many people typically reside in a certain area. Growth rates are the population changes that occur each year as a result of births, deaths, and net migration.

Given: In the year 2000, the population of Ohio was 11.03 million people. By the year 2017 the population of Ohio was 11.66 million people.

From this we get, two points (0, 11.03) and (17, 11.66).

First to find the slope using the above two points.

[tex]m=\frac{11.66 - 11.03}{17-0} = \frac{0.63}{17} = 0.04[/tex]

Now to find the equation,

Consider,

p - 11.66 = 0.04(t - 17)

p - 11.66 = 0.04t - 0.68

          p = 0.04t - 0.68 + 11.66

          p = 0.04t + 10.98

Therefore, the equation modeling the population, p, of Ohio given the year, t is, p = 0.04t + 10.98

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Answer:Answer: SAS

Step-by-step explanation:

The average monthly increase in net worth for the 6-month period is $1832.16.

Given:

A business started the year with a net worth of $4,873. During the first six months of the year, the business recovered and increased its net worth to a value of $15,866.

Six months net worth = 15,866 - 4873

= 10,993

Average monthly increase in net worth =  six month net worth / 6

= 10,993/6

= $1832.16.

Therefore The average monthly increase in net worth for the 6-month period is $1832.16.

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The graph that beast describes the slope of -2/3 passing through points (-1, 0) is in option c

Information given in the question include

a linear function graph

The data is plotted as a linear function

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m = -2/3

negative slopes slants from top left to bottom right as in a and c

from the graph, option c has points (-1, 0) and (0, -2/3)

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

m = (-2/3) / (0 + 1)

m = -2/3

This matches with option C

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Answer:

7 in

Step-by-step explanation:

If 12 inches of wire can be bought for $0.48, we can set up the following ratio:

[tex]\frac{12\text{ in}}{\$0.48}[/tex]

Then, to determine how many inches of wire can be bought for $0.28, set up equivalent fractions, as such:

[tex]\frac{12\text{ in}}{\$0.48}=\frac{x}{\$0.28}[/tex]

Then, cross-multiply and solve for [tex]x[/tex]:

[tex]\$0.48x=(\$0.28)(12)[/tex]

[tex]\$0.48x=\$3.36[/tex]

[tex]x=\frac{\$3.36}{\$0.48}[/tex]

[tex]x=7[/tex]

The slope of the line x = 3 is undefined

How to describe the slope of the line

The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

Mathematically, the slope is the change in y divided by the change in x. That is:

Slope = y2-y1 / x2-x1

Let's pick any two convenient points on the line:

(3, 9) and (3, -9) = > x1 = 3, y1 = -9 and  x2 = 3, y2 = 9

Slope = 9-(-9) / 3-3  = 18/0

The denominator here is 0, if you evaluate this using a calculator you will a maths error. So we say the slope is undefined

Notice that: There is no change in x i.e. x1 = x2

Therefore, the slope of x = 3 is undefined because x = 3 is a vertical line

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The slope of the line that is parallel to the line -7x-5y=-6 is -7/5

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope of lines in a coordinate plane can aid in anticipating whether the lines are parallel, perpendicular, or none at all without actually using a compass.

Any two unique places along the line may be used to determine the slope of any line. When two different places on a line are considered, the slope of a line formula compares the vertical change to the horizontal change in each case. We shall comprehend how to discover the slope in this piece, along with some of its uses.

Given, line is -7x-5y=-6

We have to write the given line in slope-intercept form

Then, y= (-7/5)x+(6/5)

The slope-intercept form is y= mx +c

By using the slope-intercept form,

Slope=(-7/5)

The lines that are parallel to y= (-7/5)x+(6/5) have the same slope of -7/5

Therefore, the slope of the line that is parallel to the line -7x-5y=-6 is -7/5

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Answer:

(∞,-3) and (1,-∞)

Step-by-step explanation:

Decreasing means going down or in math terms, going toward the negatives.

When you are talking intervals in math, you only want to use the x-axis for the interval points. We write the interval as if it was a coordinate point though.

Looking at the graph it looks like it is going from infinity to -3 or written as (∞,3) and from 1 to negative infinity or written as (1, -∞)

The interval(s) for which the function shown below is decreasing are (∞,-3) and (1,-∞).

A function is a relationship between two sets of values in mathematics where each input value (or "argument") corresponds to a certain output value.

In most cases, the input values come from a set referred to as the function's domain, while the output values come from a set referred to as the function's range.

Declining is the mathematical phrase for decreasing or moving towards the negatives.

Mathematicians only use the x-axis to represent interval points when discussing intervals. Yet, we express the interval as if it were a coordinate point.

If you look at the graph, it appears to be traveling from infinity to -3, which is written as (,3), and from one to negative infinity, which is written as (1, -).

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The y-intercept of the equation y = (x - 4) is -4

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

y --(x - 4)

Rewrite the equation properly

So, we have the following representation

y = (x - 4)

To calculate the y-intercept, we set x to 0

So, we have the following representation

y = 0 - 4

Evaluate the difference

y = -4

Hence, the y-intercept is -4

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Answer:

265 is the snakiest number

Step-by-step explanation:

If price p(x) =26(4)^{-x/5}, the revenue when 15 units are sold is equal to $6.09.

From the information provided, the amount of revenue with respect to price that's being generated in this scenario can be calculated by using the following function (expression):

R(x) = x × P(x)

Where:

Since the revenue function, we would simply substitute the value of the unit price and evaluate as follows:

Revenue, R(x) = x × 26(4)^{-x/5}

Substituting the given parameters into the formula, we have;

Revenue, R(x) = 15 × 26(4)^{-15/5}

Revenue, R(x) = 15 × 26(4)^{-3} or (15 × 26)/4³

Revenue, R(x) = 15 × 26(0.015625) or 390/64

Revenue, R(x) = 6.09375 ≈ $6.09.

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Complete Question:

The revenue function is given by R(x)=x⋅p(x) dollars where x is the number of units sold and p(x) is the unit price. If p(x)=26(4)^{-x/5}, find the revenue if 15 units are sold. Round to two decimal places.

Answer:

33 degrees

Step-by-step explanation:

The square in the corner of these two vectors signifies that this is a right angle, which will always equal 90 degrees, so if you subtract angle 2's value of 57 degrees, you will be left with angle 1 as 33 degrees.

The first table A shows the relationship between the number of sets of markers bought by the teacher and the total cost of the markers.

From given question, the cost per set of markers = $3

The teacher had a $2-off coupon to use toward the total cost of the markers bought.

It is given that the number of sets of markers bought by the teacher is x, and y is the total cost of the markers.

so, we get a linear equation as:

3x - 2 = y

From table A we can see that the data satisfied the given equation,

3x - 2 = y

when x = 3, y = 3(3) - 2 = $7

when x = 9, y = 3(9) - 2 = $25

when x = 12, y = 3(12) - 2 = $34

when x = 24, y = 3(24) - 2 = $70

Therefore, the first table A shows the relationship between the number of sets of markers bought by the teacher and the total cost of the markers.

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Answer: f^-1(x)= - 1/5x - 4/5

Step-by-step explanation:

substitute y for f(x):              y= -5x-4

interchange x and y:            x=-5y-4

swap the sides:                     -5y-4=x

move the constant                -5y=x+4

divide both sides by 5          y= - 1/5x - 4/5

substitute f^-1(x) for y          f^-1(x)= - 1/5x - 4/5

Answer:

[tex]y+17=-2(x-14)[/tex]

Step-by-step explanation:

The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].

The volume of the flower box is 7560 cubic inches

The given parameters in the question are:

Length = 5 ft

Upper and lower bases = 18 inches and 10 inches

Height  = 9 inches

The volume of the box can be calculated using the following volume equation

Volume = 0.5 * Height * Length * (Sum of the bases)

Substitute the known values in the above equation So, we have the following equation

Volume = 0.5 * 9 inches * 5 feet * (18 inches + 10 inches)

Convert feet to inches

Volume = 0.5 * 9 inches * 60 inches * (18 inches + 10 inches)

Evaluate

Volume = 7560 cubic inches

Hence, the volume is 7560 cubic inches

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Answer:

Step-by-step explanation: a square x b square

Answer:

given point is (-3,-2)

The rule for a rotation by 270° about the origin is (x,y)→(y,−x).

So,

(-3,-2)==============(-2,3).

there fore,

(-2,3) is the image point of (-3,-2)after the transformation r(x-axis) and rotation 270°.

Answer: 16

Step-by-step explanation:

Usando una relación trigonometrica veremos que la anchura del rio es 66.4 pies.

Podemos ver la situación como si trabajaramos con un triangulo rectangulo, donde la torre de 50 pies es un cateto y la anchura del rio es el otro cateto. (la imagen de este triangulo se puede ver en la imagen al final)

Usando la relacion:

tan(a) = (cateto opuesto)/(cateto adjacente)

Podemos escribir:

tan(37°) = 50ft/x

Resolviendo para x, la anchura del rio:

x = 50ft/tan(37°) =66.4 ft

El rio tiene un ancho de 66.4 pies.

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Answer: y= 3 times 2 to the power x. Second answer

Step-by-step explanation:

if you plug in 0 for x, y= 3x 1= 3

if you plug in 1 for x y= 3 x 2 = 6

Look at the x values and y values

(0,3) and (1, 6) on the graph. It matches answer number 2. Remember, 2 raised to the power 0 = 1 and 3 times 1 = 3. And 2 raised to the power 1 =2 and 3 times 2 = 6.

Answer:

Use AAA congurency rule

Step-by-step explanation:

1 angle=52

2 angle=58

3 angle=78

A factor is a number that divides another number, leaving no remainder

Step-by-step explanation:

first you have to multiply 4 with 3 and add with 2 and do same as in second .

then do lcm