Kelly reads an advertisement for a zero finance charge installment planwhen a new riding lawn mower is paid in full within 8 months. She goes tothe store offering the promotion and finds out that the mowers are $1,017.The minimum payment that must be made each month is $54. If Kelly onlypays the minimum payment for 7 months, how much must she pay on theeighth payment to avoid finance charges? Do not include a dollar sign inyour answer.

The smallest angle of the equilateral triangle is 60 degrees

If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.

To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.

For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:

Smallest angle \(= \frac{180}{3} = 60\)\) degrees.

Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).

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For the given:  linear function: y = 3x and quadratic function: y = 7x², the graph is plotted.

f(x) = ax² + bx + c, where such a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.

Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.

Given functions:

y = 3x and y = 7x²

For the linear function:

y = 3x

Put x = 1, y = 3*1 = 1 ; (1,3)

Put x = 2 , y = 3*2 = 6 ; (2,6)

For the quadratic function: y = 7x²

Put x = 1; y = 7(1)² = 7 ; (1, 7)

Put x = 2 ; y = 7(2)² = 28; (2,28)

Plot the obtained points on the graph;

The graph for the given function is obtained using the graphing tool.

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Correct question:

Sketch the region enclosed by y = 3x and y = 7x². Find the area of the region.

The graph of the cost function is

Cost function refers to the functional relationship between cost and output. It studies the behavior of cost at different levels of output when technology is assumed to be constant.

Given: There are two companies Cronus and Zeus. Cronus charges a flat rate of $8 per GB of data. Zeus charges $3 per GB of data in addition to a monthly $10 fee that everyone pays. You expect to use between 0 GB and 8 GB of data each month.

Let y be the cost for data consumed.

Let x be Gb of data consumed.

Cost function of Cronus is y = 8x

Cost function of Zeus is y = 10+3x

Graph of both the companies is

where green line denotes the graph for Cronus and red line denotes the graph for Zeus.

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Answer:

s = 2 1/3 + 1/2

t = 2/3 + 3/2

We have to find the sum of both s and t.

2 1/3 + 1/2 = 2 2/6 + 3/6 = 2 5/6

2/3 + 3/2 = 4/6 +  9/6 = 13/6 = 2 1/6

If we look at the number lines, we can see that c matches with both points.

They spend $5.88 on a gift, but there is not enough money left over to spend $3.25 on a card, if Samuel and Jason spent 3/4 of their combined earnings from 100 by gift.

A formula that expresses the connection between two expressions on each side of a sign is called equation. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2.

Given,

Samuel and Jason spent 3/4 of their combined earnings from 100 by gift.

Samuel and Jason's profits as of Wednesday are as follows:

Earnings for Samuel:

12.5 x 40  

$5.

Earnings for Jason are

7.1 x $0.40

$2.84.

The total revenue for Wednesday is:

Samuel's and Jason's combined incomes are equal.

Earnings totaled

$5 + $2.84 = $7.84

The money that was spent is:

Total income multiplied by 34 equals spent income.

Earnings spent = 7.84 x 1/4

Earnings spent =  $5.88

The remainder is:

Equation

Leftover = Total Earnings - Spent Earnings

7.84 - 5.88 =  $1.96 in leftovers.

They spend $5.88 on a gift, but there is not enough money left over to spend $3.25 on a card.

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To find the slope of the table, we need to use the next formula:

Replace taking two points from the given table.

Then, P1(0,-3) and P2(1,-7):

Now, we can use the next equation to get the slope- intercept form:

Relace using P(0,-3) and m-4.

Therefore:

Finally, we get the slope-intercept form y=mx+b.

Where b represents the y-intercept.

The y-intercept is -3.

In conclusion:

Slope = -4

y-intercept b= -3

Formula h(x) = -4x-3

Answer:

.49 if you're dividing them.

Step-by-step explanation:

Answer:

22 degrees

Step-by-step explanation:

Just do arccos(0.9272) on your calculator or just do 90 minus 68.

The degree solutions of the equation are 51.82 degrees and 128.17 degrees

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

cos² (x) + cos (x) − 1 = 0

Let y = cos(x)

So, we have

y² + y - 1 = 0

When solved graphically, we have

y = ±0.618

This means that

cos(x) = ±0.618

Take the arccos of both sides

x = cos-1(±0.618)

Evaluate

x = 51.82 degrees and 128.17 degrees

Hence, the angles are 51.82 degrees and 128.17 degrees

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Answer:

An amortization schedule is a complete table of periodic loan payments, showing the amount of principal and the amount of interest that comprise each payment until the loan is paid off at the end of its term.

Step-by-step explanation:

Answer:

Step-by-step explanation:

An amortization schedule is a complete table of periodic loan payments, showing the amount of principal and the amount of interest that comprise each payment until the loan is paid off at the end of its term\

Solving a system of equations we can see that each pound of trail mix costs $3.50, and each pound of jelly beans costs $1.50

Let's define the variables:

Then we can write a system of equations so we will get:

5x + 3y = 22

2x + 12y = 25

To solve this, we can subtract 4 times the first equation fom the second one:

2x + 12y - 4(5x + 3y) = 25 - 4*22

2x + 12y - 20x - 12y = -63

-18x = -63

x = -63/-18

x = 3.5

That is the cost of each pound of trail mix, and replacing that in one of the equations:

2*3.5 + 12y = 25

y = (25 - 2*3.5)/12

y = 1.5

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Answer:

\(a>6\)

Step-by-step explanation:

1) Subtract 1 from both sides.

\(a>7-1\)

2) Simplify 7 - 1 to 6.

\(a>6\)

Therefor, the answer is a > 6.

Answer:

a > 6.

Step-by-step explanation:

Move all terms not containing a to the right side of the inequality.

Inequality Form:

a > 6.

The linear velocity expression of the given problem is: 8π/7 feet per second

Angular velocity is defined as the time rate at which an object rotates, or revolves, about an axis, or at which the angular displacement between two bodies changes.

We are given the angular velocity as:

ω = π/7

The formula that shows the relationship between angular velocity and linear velocity is:

v = ωr

Thus:

v = (π/7) * 8

v = 8π/7 feet per second

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So, the equation of the axis of the segment AB is (A) y = 1/2 - x/2.

What is slope?

In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.

The slope of the line passing through points A and B can be calculated as follows:

slope = (change in y) / (change in x) = (1-0) / (1-0) = 1/1 = 1

The equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

To find the y-intercept, we can use point A (0,0) and substitute the slope value.

y = mx + b

0 = 1(0) + b

b = 0

Therefore, the equation of the line passing through points A and B is:

y = 1x + 0

Simplifying, we get:

y = x

So, the answer is (A) y = 1/2 - x/2. However, this is not one of the given answer choices. We can also write the equation in point-slope form as y - y1 = m(x - x1) using point A, which gives:

y - 0 = 1(x - 0)

y = x

This confirms our earlier answer.

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The dimensions of a rectangle with an area of 12 ft.² and a diagonal of 5 feet are 4 feet and 3 feet.

From the information, we are given that the dimensions of a rectangle with an area of 12 ft.² and a diagonal of 5 feet.

It should be noted that the number will be:

= 4 × 3 = 12 ft²

It should be noted that 4² + 3² = 25 and the square root will give 5 which is also the diagonal.

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Answer:

Area of part 1: 3 * \(5\sqrt{2}\) = \(15\sqrt{2}\)

Area of part 2: \(3\sqrt{2} * 5\sqrt{2}\)\(=30\)

Area of entire rectangle: \(30 + 15\sqrt{2}\)

Step-by-step explanation:

The area of a rectangle can be found by using formula : length * width.

The area of part 1 can be simplified to this:

3 * \(5\sqrt{2}\) = \(15\sqrt{2}\)

Area of part 2:

\(3\sqrt{2} * 5\sqrt{2}\)\(=30\)

The area of the entire rectangle can simply be added from part 1 and part 2.

For area 2, remember multiplying the square root of 2 twice nullifies the square root. So it becomes 15 * 2, which is equal to 30.

What are the areas of each smaller rectangle and the large rectangle?

Drag each tile to the correct location on the image. Not all tiles will be used.

i took the test thing

Answer: 3 ≤ 47

Step-by-step explanation:

The inequality given is 3 ≤ 47.

To determine the solutions to this inequality, we need to find the values of x that satisfy the inequality.

Looking at the options provided:

x = 24: This is not a solution because 24 is less than 47.

x = 51: This is a solution because 51 is greater than or equal to 47.

x = 6: This is not a solution because 6 is less than 47.

x = 99: This is a solution because 99 is greater than or equal to 47.

Therefore, the solutions to the inequality 3 ≤ 47 are x = 51 and x = 99.

The method that you find important to enhance the strong number sense is  the use of manipulatives and hands-on activities.

Example:

Illustrating numbers and executing mathematical operations through block representations can assist students in visualizing addition, subtraction, and multiplication.

Using manipulatives and interactive activities, numerical concepts can be grasped more tangibly, as learners physically engage with these objects, thereby developing a concrete understanding of mathematics.

Students can enhance their comprehension of measurement and units by employing measurement instruments such as rulers and measuring tapes.

Through participation in these tasks, students cultivate a profound sense of intuition in regard to numbers, operations, and their interconnections, thereby establishing a firm groundwork.

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The answer is:

Work/explanation:

To evaluate f(x) = 5x - 10 for f(4), we need to plugin 4 for x:

f(4) = 5(4) - 10

     = 20 - 10

    = 10

Answer:

\(C = 25.1 \text{ cm}\)

Step-by-step explanation:

We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:

\(C = \pi d\)

Note: This formula can also be written as \(C = 2\pi r\) because \(2r = d\).

↓ plugging in the given radius

\(C = 8\pi \text{ cm}\)

↓ rounding to the nearest tenth

\(\boxed{C = 25.1 \text{ cm}}\)

Answer:

Step-by-step explanation:

Given set:

We observe that:

Each term can be shown as 3ⁿ, where n is natural number between 0 and 3.

Set builder notation:

Here let's observe

So set builder form:-

\(\\ \sf\longmapsto E=\{x|x=3^n,n\in N,0\leqslant n\leqslant 3\}\)

A tangent and a radius of a circle meet to form a 90 angle is a true statement about a tangent and a radius.

The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary use, it also refers to the length of such line segments.

A tangent is a line that very slightly touches the circumference of a circle. The angle between a radius and a tangent is always exactly 90 degrees if the radius and circumference are drawn at the same location.

Hence the correct option is B

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The domain of the function, is : Domain → (- ∞ , + ∞) and the inverse of the function is y = 3 + √x.

Domain is the set of {x} - values for which a function {y - values} exists. It is one of the important parameter while defining the characteristics of a function.

Given is the function as -

f(x) = (x - 3)²

{ 1 } -

The domain of the function f(x) = (x - 3)².

The function has no undefined points. So, we can write the domain as -

Domain → (- ∞ , + ∞)

{ 2 } -

The inverse of the function f(x) = (x - 3)².

We have -

f(x) = (x - 3)²

y = (x - 3)²

x = (y - 3)²

y - 3 = √x

y = 3 + √x

Therefore, the domain of the function, is : Domain → (- ∞ , + ∞) and the inverse of the function is y = 3 + √x.

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Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

B

Step-by-step explanation:

First isolate the variable, x. To do this, use inverse operations. The inverse operation of -4 is +4. So, add 4 on both sides of the equals sign. The positive 4 cancels out the negative 4 on the left side. Add 4 to the other side, -18, for -14. You are left with 7x = -14. Now to get rid of the coefficient, 7. The inverse of x7 is ÷7. So divide 7x by 7 to completely isolate x. On the right side, -14 is divided by 7 to get -2. You are left with x = -2. Wow that was a ted talk :P Anyway, hope this was helpful ^^ lmk if I need to clarify about anything :D Good day man