Letters a, b, c, and d are angle measures. Which should equal 105° to prove that fll g? Фа Ob n b 75° 0 d g f Mark this and return Save and Exit Next Submit

The inequality representing the amount of money, m. Derrick's football team needs to raise is D. m>$520

In mathematics, Inequality is part of equations solved with the use of the some special type of equality signs. The signs used inequality calculations are

Given that:

Derrick's football team needs to raise at least $1,000

The team collected 480

To solve the given problem we have the inequality in the form

at least $1,000 ≡ greater than or equal to 1000

m > $1000

having collected $480 so far. The amount collected is subtracted from the $1000

m > $1000 - $480

m > $520

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Total Sales = 14910

8% on 5000

10% on 5500

15% on

14910 - 10500 = 4410

So,

15% on 4410 [this is the excess of 10,500]

Converting percentages to decimal:

8% = 8/100 = 0.08

10% = 10/100 = 0.1

15% = 15/100 = 0.15

Total Commission

Given:

Ben, Claire, and Devon are swimming one mile.

Ben swam 0.77 of the mile before stopping.

So, the distance Ben swam = 0.77 x 1 = 0.77 mile

Claire swam 3/5 of the mile.

So, the distance Claire swam = 3/5 x 1 = 3/5 = 0.6 miles

Devon swam 82% of the mile before stopping.

So, the distance Devon swam = 82% of 1 mile = 0.82 x 1 = 0.82 miles

Arrange the distances in order from the largest to the least:

0.82, 0.77, 0.6

So, the answer will be:

The farthest distance is for Devon = 0.82 miles

The shortest distance is for Claire = 0.6 miles

From the question, we have the given information.

We will use the formula below to solve the question

Therefore;

Since the Amount = 13797.71, we can get the interest by using the formula below.

Answer: Interest =$1497.71

Given the function:

Where A is the amount of money (in dollars) Diane has left in her account after t trips on the toll roads.

(a)

After 8 trips on the toll roads (t = 8):

(b)

If her account is empty:

Solving the equation for t:

Answer : 1500 miles

According to the distance time relationship

Distance = Rate x time

From the figure given, the hawk flies 500 miles in 5 days

We can find our rate using the above parameters

Since, distance = rate x time

Rate = distance / time

Rate = 500 / 5

Rate = 100 miles / day

Since, the rate remains constant

How far the hawk can fly in 15 days can be calculated as follows

Time = 15 days

Rate = 100

Distance = ?

Disatnce = rate x time

Distance = 100 x 15

Distance = 1500 miles

The Hawk can fly 1500 miles in 15 days

The form of the linear equation is

m is the slope

b is the y-intercept

The given equation is

Let us compare the given equation with the form above, then

and the value of b is

The slope of the line is the coefficient of x

The y-intercept is the numerical term

The slope = -2/3

The y-intercept = 1

The right answer is D the last answer

In any question like that, put the equation in the form

y = m x + b

m is the slope

b is the y-intercept

Prior to multiplying the result by 100, divide the finance charge by the total amount funded. The finance charge per $100 of the financed amount is the end outcome of credit.

Step 1

Loan Amount(p)= 3600

Number of Payments per year(n)= 12

Time in Years (t)=4

Installment Payment (m)=83.81

Total amount paid in 48 installments= 4022.88

Amount Paid - Amount Financed = 4022.88 - 3500 = 522.88 in finance charges.

To determine the annual percentage rate. Prior to multiplying the result by 100, divide the finance charge by the total amount funded. The finance charge per $100 of the financed amount is the end outcome.

Finance Charge​/ Amount financed × 100= 522.88/ 3600× 100= 14.5

To use Table , look for 48 in the far left-hand column under the heading Number of Payments. Then move across to the right until you find the value closest to 14.5. In this case, 14.5 is in the table. The value 7 is at the top of this column. The yearly percentage rate is therefore around 7. Monthly payments are 83.81. After 12 payments have been made, 30 payments remain. Therefore, P = 83.81 and n = 30. Use the APR table to calculate V . In the Number of Payments column, find the number of remaining payments, 30, and then look to the right until you reach the column headed by 7%, the APR. intersect at 9.30. Thus, V = 9.30.

:[tex]u=nPV/100+V\\u=30*83.81*9.30/100+9.30=213[/tex]

Total due amount = Total remaining payment including interest- saving on interest + 12th monthly payment= 2514.3- 213.934+ 83.81= 2384.17

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The height of the building is 38.85 ft.

Given;

length of the ladder, x = 39 ft

the angle between the ground and the ladder, θ = 85°

let the height of the building be h.

Construct this triangle, the ladder forms the hypotenuse side of the right angle triangle, the height of the triangle is the opposite side of the triangle while the base of the triangle is the adjacent side of the triangle.

Apply the following trig ratio to determine the height of the triangle;

sin(θ) = opposite/hypotenuse

sin(85°) = h/39

h = 39sin(85°)

h = 38.85 ft

Therefore, the height of the building is 38.85 ft (approx.).

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According to the given graph, we have the following:

1) The graph represents a plane descending.

2) The line is slanting downwards and therefore has a negative slope.

3) It takes the plane 15 seconds to touch the ground.

4) The plane starts at 3 kilometers in the sky.

5) Graph does not touch the origin (0,0).

The given graph shows a decreasing line, starting at y = 3, and reaching y = 0 when x = 15.

we can see the interval is between -2 and 1. but the -2 isn't included (you can notice by the white circle) and the 1 is included, so in interval notation you get:

(-2,1]

Rotation 90° about the origin.

First, choose a point from triangle A.

For example: (-2,2)

For any point (x,y) rotated 90° =(-y,x)

So:

(-2,2) becames = (-2,-2)

Triangle D

The factors of 99 are: 1, 3, 9, 11, 33 and 99.

Given:

Required:

to show which graph is correct for the inequality.

Explanation:

Given graph is correct for the equation.

Required answer:

The given graph is correct.

2+7x=15

Explanation

Step 1

Let

x represents the number

seven times a number = 7x

two more = +2 or 2+, you need to add 2

is = "="

Step 2

replace,

"Two more than seven times a number is fifteen"

I hope this helps you

Answer:

Step-by-step explanation:The line parallel to y = -2x + 5 that passes through the point(1,1)

Has the same slope, m but a different y intercept (0,b)

So lets start by using the given point (1, 1) and the slope intercept form of the line to calculate b

y = mx + b

m = -2

1 = -2(1) + b

1 = -2 + b

Add 2 to both sides of the equation to solve for b

1 + 2 = b

3 = b

The line is

y = -2x + 3

The Solution:

Let the outcomes when two dice are tossed be as summarized in the picture attached below:

The point that belongs to the solution set is A( 4, 4)

Inequalities are defined as mathematical relations involving an unequal comparison between two numbers, elements or other arithmetic expressions.

They are mostly used to compare two numbers on the number line on the basis of their sizes.

Given the inequalities;

Make 'x' the subject from equation 1, we have;

x > 6 - y

substitute the value into equation 2, we have;

3( 6 - y) - 5y  ≤ 2

expand the bracket

18 - 3y - 5y ≤ 2

collect like terms

- 8y ≤ 2 - 18

- 8y ≤ -16

Make 'y' the subject of formula

y ≤ 2

Substitute the value in equation 3

x > 6 - 2

x > 4

Hence, the point is A( 4, 4)

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We want to graph the following inequality system

First, we need to solve both inequalities. To solve the first one, we subtract 8 from both sides

To solve the second one, we multiply both sides by 7.

Now, our system is

We can combine those inequalities into one.

The number x is inside the interval between 1 and 7. Graphically, this is the region between those numbers(including them).

Number of chaperones for a trip defined by function f(x) = (1/4)x+2 then,

a. If the parents is reduced to 0 then the graph passes through origin (0,0).

b. If the number of teachers is raised to 1 for every 3 students then line cut x-axis at (-6,0) .

As given in the question,

Given conditions:

Field trip must include 1 teacher for every 4 students and add 2 parents in total.

Number of chaperones for a trip defined by function f(x) = (1/4)x+2

a. If the parents is reduced to 0 then the changes seen in the graph are as follow:

f(x) =  (1/4)x+2 passes through the point (0,2)

when parents changes to 0 then graph passes through (0,0).

b.  If the number of teachers is raised to 1 for every 3 students then the changes seen in the graph are as follow:

For f(x) = (1/4)x+2 the graph cut axis at (-8,0)

When for every 1 teacher there are 3 students then graph cut x-axis at (-6,0).

Therefore, number of chaperones for a trip defined by function f(x) = (1/4)x+2 then,

a. If the parents is reduced to 0 then the graph passes through origin (0,0).

b. If the number of teachers is raised to 1 for every 3 students then line cut x-axis at (-6,0) .

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Step 1

Find the resultant of the vectors

There are a total of 50 numbers that are between 1 and 50. Halft of these numbers are even (divisible by 2 ) and half of then odd.

There are 25 integers that are not even and in total there are 50 integers; thereofre, the probablity of finding an even integer is

25/50 = 1/2

The height reached by the projectile is 784 feet.

The projectile experiments an uniformly accelerated motion due to gravity, whose height is represented by the quadratic equation:

h(t) = - 16 · t² + 224 · t

Where t is the time, in seconds.

In this problem we need to find the maximum height reached by the projectile, which can be found by finding the vertex form of the quadratic equation:

h(t) = - 16 · (t² - 14 · t)

h(t) - 16 · 49 = - 16 · (t² - 14 · t + 49)

h(t) - 784 = - 16 · (t - 7)²

The maximum height of the projectile is 784 feet.

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Answer: g(f(5)) = 352

Step-by-step explanation:

The question being asked is the same as finding g(f(5)).

What this means is to find f(5), and then plug that value into g(x) as x and solve.

f(5) = 4(5) + 1 = 20 + 1 = 21

g(f(5)) = g(21) = 21^2 - 4(21) - 5 = 441 - 84 - 5 = 357 - 5 = 352

Note: You could also find g(f(x)), and then plug 5 in as x and solve.

Start by plugging f(x) into g(x) such that you get g(x = f(x))

g(f(x)) = (4x + 1)^2 - 4(4x + 1) - 5

Now, replace x with 5 and solve to get g(f(5)).

g(f(5)) = (4(5) + 1)^2 - 4(4(5) + 1) - 5 = 352

Based on the fact that Home Liquidators marked up their merchandise by 35% on cost, the company equivalent markup on selling price is 26%.

The equivalent markup by Home Liquidators on the selling price can be found by the formula:
= Percentage markup / Percentage selling price x 100%

The percentage markup  = 35%

Percentage selling price = (100% + 35%) = 135%

The equivalent markup by Home Liquidators is therefore:

= 35% / 135% x 100%

= 26%

In conclusion, the Home Liquidators has an equivalent markup of 26% on selling price.

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Solution

- Let the length of the rectangle be x

- Let the width of the rectangle be y.

- Thus, we can interpret the lines of the question as follows:

- Now, let us solve these two equations simultaneously.

- We shall proceed by solving the system of equations graphically.

- Wherever the graphs of Equation 1 and Equation 2 intersect represents the solution to the system of equations

- The plot of the equations is given below

- Observe that the graphs cross at two points. The first point is positive and the other, negative.

- Since we cannot have negative lengths (x) or width (y), we can discard the negative coordinates.

- Thus, the length (x) and width (y) are given below:

Final Answer

The length of the rectangle is 156 feet

you can find the slope taking two points of a graph or function,

identify the rightmost point and apply this equation

where (x2,y2) is the rightmost point and (x1,y1) is the other point

If i have two points (3,4) and (6,2)

the rigthmost point is (6,2) because 6 is greater than 3 and these two numbers are x, the place where I can locate myself horizontally or left or right

so, apply the equation

So, the slope is

A person who watches TV 11.5 hours can do 36 sit-ups.

Define Regression Analysis

Regression analysis is a mathematical measure of the average relationship between two or more variables in terms of the original units of the data

Given,

y = ax +b

a = -1.073

b = 27.069

r² = 0.434281

r = -0.659

No. of hours TV watched = 11.5 hours

we have , y = ax + b

where, a = 1.073 , b = 27.069 and x = 11.5 hours

put this value in given equation,

y = 1.073 * 11.5 + 27.069

After calculating, we get

y = 39.4085 or 39

Therefore, a person who watches TV 11.5 hours can do 36 sit-ups.

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The given system of inequality is

At first, we must draw the lines to represent these inequalities

Let x = 0, then find y

The first point is (0, 4)

Let y = 0

The second point is (-6, 0)

We will do the same with the second line

Let x = 0

The first point is (0, -2)

Let y = 0

The second point is (-2, 0)

Since the sign of the first inequality is >, then the line will be dashed

Since the sign of the second inequality is >=, then the line will be solid

Let us substitute x, y by the origin point (0,0) in both inequalities to find the shaded part of each one

Since the inequality is true then the point (0, 0) lies on the shaded area

Since the inequality is true, then point (0, 0) lies in the shaded area

Let us draw the graph

The red line represents the first inequality

The blue line represents the second inequality

The area of two colors is the area of the solution

Point (0, 0) lies in this area, then it is a solution for the given system of inequalities

We want to know if (x-sqroot(6)) is a factor of (x^4 - 36)

That's mean:

Where P(X) is a polinomial.

In this case, if x = sqroot(6) the polinomail (x^4 - 36) must be zero, that's mean sqroot(6) is a root (or a zero) of (x^4-36).

So, if we evaluate (x^4 - 36) in x=sqroot(6):

So, the answer is true.