Ivan is a software salesman. His base salary is $2400, and he makes an additional $110 for every copy of History is Fun he sells.
Let P represent his total pay (in dollars), and let N represent the number of coples of History is Fun he sells. Write an equation relating P to N. Then use this
equation to find his total pay if he sells 24 coples of History is Fun.

Answer:

Angle B is 30 degrees

Step-by-step explanation:

Vertical angles are always congruent

Vertical angles are always of same measure. The measure of angle B in this case is evaluated as: [tex]m\angle B = 30^\circ[/tex]

Each of the pairs of the opposite angles made by two intersecting lines are called vertical angles.

They are always of same measure.

We can think about this fact as: "there were two lines overlaying on each other. Then, there was a finite point chosen, from where both decided to rotate by a certain degree. Since angle is measure of rotation, and as vertically opposite sides were equally rotated, so they get same measure:"

Its diagram is attached below. The vertical angles are congruent (denoted by ≅) (which is another way to say that they are of same measure)

Since the angle A and angle B specified in this case are pair of vertical angles, and since measure of angle A = 30 degrees, thus, angle B is also of measure 30 degrees.

The measure of an angle is written by writing small m in its left as:  [tex]m\angle B = 30^\circ[/tex]

Therefore, the measure of angle B in this case is evaluated as: [tex]m\angle B = 30^\circ[/tex]

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Answer:

166

Step-by-step explanation:

1) the area of triangles on the left and right sides: 2*13

2) the area of triangles on top and bottom sides: 10*12

3) the area of the rectangle in the middle: 10*2

4) Altogether: 2*13+10*12+10*2=166

Answer:

360

Step-by-step explanation:

60 divided by 15=4

90 x 4 =360

Answer:

720 miles

Step-by-step explanation:

This is assuming the train continues to move at the same speed.

You can think about the problem in the following way:

The 2 hour journey is split up into x number of 15 minute segments.

2 hours = 120 minutes

120/15 = 8

Therefore, x = 8.

If the journey can be split into 8 15 minute segments, and each 15 minute segment carries it 90 miles, the total distance traveled is given by:

8 * 90 miles = 720 miles

Atlernatively, you can calculate the average speed of the train.

Speed = Distance/Time

So: Speed = 90 miles/15 minutes = 6 miles/minute.

Reusing the above formula, substituting in speed = 6 miles/minute and time = 120

Answer: 31.5

Step-by-step explanation:

6.3 x 5

hope this helps :)

Graph of given system of equations is shown in figure with intersection point (2, 4).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equation is,

⇒ 2x + y = 8

⇒ - x + 2y = 6

By solving both equation , we get;

⇒ (x, y) = (2, 4)

Thus, The graph of system of equation intersect on point (2, 4).

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Therefore, we can rationalize the denominator of a fraction containing a radical by taking the methods outlined above.

Components of fractions are the numbers in the numerator and denominator (and ratios). The denominator, which is the smallest number, represents the greatest possible number of parts that can be put together to create a whole. You can tell how many parts you have by looking at the numerator, which is the greatest number. It might not be the whole thing! If the denominator is 0, that is bad. Division by zero is prohibited. If the denominator is a 1, our fraction is actually an integer.

Here,

we can rationalize a radical-containing fraction's denominator by doing the following:

Step 1: In order to eliminate the radical from the denominator, multiply the numerator and denominator by a radical.

Verify in step two that all radicals have been streamlined.

Step three is to simplify the fraction, if necessary.

Therefore, we can rationalize the denominator of a fraction containing a radical by taking the methods outlined above.

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Answer:

6 Passwords

Step-by-step explanation:

718, 781, 817, 871, 178, 187

(Hope this helped! Please comment any questions) :)

Answer:

The idiot that sent the link just got taken down so I'll just answer with my comment.

Step-by-step explanation:

"I believe it is 6"

Answer:

50.24

Step-by-step explanation:

The formula for solving circumference is 2 x pi x r

first the radius is 8 (divide 16 by 2 and get radius)

( pi can be 22/7 or 3.14. but I’m taking 3.14 )

second, we have all values, now we just have to substitute them!

Pi = 3.14

R = 8

so when we do 2x 3.14 x 8 = 50.24

I hope this helped!

Answer: The area of the circle is 64π cm

Step-by-step explanation:

d=16→r=8

A= π⋅8 ^2

A= π⋅64

A=64π

Answer:

50.05 cm^2

Step-by-step explanation:

Ok so first lets find the area of the rectangle before finding the attached triangle. You have to imagine a line separating this shape into a triangle and rectangle.

The rectangle's size is 6.5x5.5=35.75 cm^2

The rectangle's size is 11.7-6.5 to get the base length, which is 5.2

The height is 5.5

So it's 5.2*5.5/2=14.3 cm^2

14.3+35.75=50.05 cm^2

Answer:

sector area = [central angle / 360] * PI * radius²

central angle = sector area * 360 / [PI * radius²]

central angle = 9 cm² * 360 / [3.14159 * 6²]

central angle = 28.6479139544 degrees

Source: http://www.1728.org/radians.htm

Step-by-step explanation:

Answer:

ITS 64 degrees

Step-by-step explanation:

Answer:

116

Step-by-step explanation:

hope this helps:)..........

A system that has no solution is classified as inconsistent.

A system that has one and only one solution is classified as  independent

The system of equation graphed is consistent and independent.

The equations given by the graph are expressed as;

3x - 4y = 32

3x + 5y = 24

Now, if we subtract eq 1 from eq 2, we will get;

5y - (-4y) = 24 - 32

9y = -8

y = -8/9

Put 8/9 for y in eq 2 to get;

3x + 5(8/9) = 24

3x = 24 - 40/9

3x = 176/9

x = 176/27

Now, to classify solution to equations, we say that;

1) When there is no solution, it is inconsistent.

2) When there is one and only one solution, it is independent

Since we have a solution and only one solution, then we can say that the system of equation graphed is consistent and independent.

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Answer:

Step-by-step explanation:Its actually 102, not 110

The inverse of f(x) = 3/(x-1) is f^-1(x) = 3/x - 1.

So the correct answer is  f ^ - 1 * (x) = 3/x - 1

The inverse of a function, denoted f^-1(x), is a function that "undoes" the original function. To find the inverse of a function, we need to switch the roles of x and y and then solve for x.

Given the function f(x) = 3/(x + 1), we can find its inverse by:

y = 3/ (x + 1)

Multiply with (x + 1) and divide by y

y(x + 1)/ y = (3/ (x + 1))×(x + 1)/ y

x + 1 = 3/ y

x = 3/ y - 1

Switching the roles of x and y:

y = 3/ x - 1

Thus f^(-1)(x) = 3/ x - 1

It's worth noting that in order for a function to have an inverse function it must be a one-to-one function. This means that for every y value there is only one x value.

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Answer:

x = A/7

Step-by-step explanation:

Given that the screen is rectangular, recall that the area A of a rectangle whose length is L and width is W is given as

A = L * W

Hence if the width is 7 inches and the length is x inches then the area which is A square inches is connected to both sides as

A = x * 7

Divide both sides by 7

x = A/7 inches

Answer:

45.7 inches

Step-by-step explanation:

The perimeter uses 3 sides of the square, so 3 x 10 = 30. We'll add that later.

Then we need to find the circumference of the half-circle. We know the diameter is 10, because that's the side of a square.

Circumference = pi x diameter

C = 3.14 x 10 = 31.4

But that's for the whole circle. We only have a half.

31.4 /2 = 15.7 is the perimeter for the half circle. Add this to the 3 sides of the square

30 + 15.7 = 45.7

Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day

Two or more expressions with an Equal sign is called as Equation.

The billing cycle for the month = 28 days

Current beginning balance = x

Annual percentage rate (APR) = 24%

Monthly percentage rate (MPR) = 2% (24% ÷ 12)

Purchase on the last day = $1,400

Total finance charge for the month = $51

Finance charge for the last-day purchase = $1 ($1,400 x 2% x 1/28)

Finance charge for the beginning balance = $50 ($51 - $1)

The current beginning balance, x = $2,500 ($50 ÷ 2%)

Equation for current beginning balance, x = 51 - 1 ÷ 0.02

Total finance charge for the last-day purchase = $28 ($1,400 x 2%)

Savings in finance charge by purchasing on the last day = $27 ($28 - $1)

Hence, Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the last day of the billing cycle instead of on the first day.

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Answer:

55555555546776546567

Answer:

0.26.  This is the fraction of states that do not use wind energy.  

Step-by-step explanation:

There are 50 states total.  If 37 use wind energy, then 50 - 37, or 13, do not.

13/50 = 0.26.  This is the fraction of states that do not use wind energy.  

To calculate the percent change of two numbers such as 99 to 71, you use the Percent Change Formula, where a is the start value and b is the end value. When we insert a = 99 and b = 71 in the formula above, then we get the following that we can simplify and solve to get the percent change from 99 to 71.

Change ≈ -28.2828%

50-50-80 is a Isosceles acute triangle.

An isosceles acute triangle is a triangle in which all three angles are less than 90°, and at least two of its angles are equal in measurement. One example of the angles of an isosceles acute triangle is 50°, 50°, and 80°.

Properties of Isosceles Acute Triangle

It is easy to point to an isosceles acute triangle if we know its properties. The properties of the isosceles acute triangle are noted below:

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The p-value of the test statistic is calculated as follows:

0.6386.

At the null hypothesis, it is tested if the mean is actually of 48.3 miles per gallon, that is:

[tex]H_0: \mu = 48.3[/tex]

At the alternative hypothesis, it is tested if the mean is different of that, hence:

[tex]H_1: \mu \neq 48.3[/tex]

The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.

The equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 48.2, \mu = 48.3, \sigma = \sqrt{6.76} = 2.6, n = 150[/tex]

Hence the test statistic is obtained as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{48.2 - 48.3}{\frac{2.6}{\sqrt{150}}}[/tex]

z = -0.47.

The p-value is found using a z-distribution calculator, with a two-tailed test, as we are testing if the mean is different of a value, with z = -0.47, hence it is of:

0.6386.

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Answer:

Isosceles trapezoid has congruent base angles:

∠A ≅ ∠D and ∠B ≅ ∠C

Answer:

x = 16 degrees

y = 28 degrees

Step-by-step explanation:

1.) ∠A ≈ ∠D since they are base angles: so;

5x = 80

=> divide 5 on both sides:

x = 16 degrees

2.) Now Substitute 16 in for the x-value

5x ⇒ 5(16) = 80,

3.) Since we know the measure of the sum of interior angles is 360° we can say that:

(4y - 12) + 100 + 5(16) + 80 = 360

=> 4y - 12 + 100 + 80 + 80 = 360

=> 4y + 248 = 360

Subtract 248 on both sides of "="

=> 4y = 112

Divide 4 on both sides of "="

=> y = 28

Hope this helps!

Answer:

1)  23x + 6y

2) 8x  - 4y

3)  4x - x² + 7

Step-by-step explanation:

Simplify:

Multiply each term of (3x + 6y) by 5 and multiply each term of (2x - 6y) by 4.

5(3x + 6y) + 4 (2x - 6y)  = 5*3x + 5*6y + 4*2x - 4*6y

                                       = 15x + 30y + 8x - 24y

Now, combine like terms. Like terms have same variable with same power.

                                         = 15x + 8x + 30y - 24y

                                           = 23x + 6y

2) 3(4x - 2y) - 2*(2x -y) = 3*4x + 3*(-2y) + (-2)* 2x + (-2)*(-y)

                                     = 12x - 6y - 4x + 2y

                                     = 12x - 4x - 6y + 2y

                                    =  8x - 4y

3) f(x) = 3x + 2

To find f(x +1),  replace x with (x +1)

f(x +1) = 3*(x + 1) + 2

          = 3*x + 3*1 + 2

          = 3x + 3 + 2

          =3x + 5

f(2x) = 3*(2x) + 2

        = 6x + 2

f(2x) + h(x) = 6x + 2 - x² - 2x + 5

                 = 6x - 2x - x² +2 + 5

                 = 4x - x² + 7

By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.

Expressions are polynomials, but expressions that equal zero are polynomial equations.

A polynomial may be written as the sum of a finite number of terms, where each term is the product of one or more variables raised to a positive integer exponent and a constant coefficient (or power).

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

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Answer: its hard to give an answer but read explanation

Step-by-step explanation: so the first number (1/3x) is your slope and the second number is the y-intercept (5). so for example, you're going to put positive 5 on the y-axis and because you slope is a fraction, rise/run will make you go 3 to the right and 1 up. Then you do the same with the second equation except, the slop is negative and you'll have to go down.

Answer:

the amount spent on petrol is Rs 9,676

Step-by-step explanation:

Given that

The tax driver filled the car petrol with 54 liters on Saturday

On sunday, he filled his tank with 64 liters

And, the petrol cost is Rs 82 per liter

We need to find out the amount of money spent

SO,

= (54 liters + 64 liters) × Rs 82

= Rs 9,676

Hence, the amount spent on petrol is Rs 9,676

Therefore, the inequality problem solution is even if Guliskhan runs for 60 seconds and cycles for 90 seconds, she will not be able to travel the required distance.

Both formulae and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,≥,≤, or.<

Here,

R should stand for Guliskhan's running seconds, and B should stand for her bicycling seconds.

Guliskhan is said to bike at a pace of 7 meters per second, hence the distance (in meters) that he covers in B seconds will be 7B.

An inequity of 3R + 7B 1000 has been handed to us.

We can observe that 7B reflects the cycling distance covered by Gulkishan in meters in B seconds.

Guliskhan covers a distance of 3R meters in the number of seconds she runs for, where R is the number of seconds she runs for.

Guliskhan moves at a steady pace of 3 meters per second because of this.

B. Since Gulkiskhan 3R plus 7B has traveled a total distance greater than or equal to 1000 meters, her minimum intended distance is 1000 meters.

C. Let's replace R=60 and B=90 in our inequality to see if Guliskhan is capable of traveling this minimum distance.

=>3*60 + 7*90 ≥ 1000

=>180 + 630 ≥ 1000

=>810 ≠> 1000

Therefore, even if Guliskhan runs for 60 seconds and cycles for 90 seconds, she will not be able to travel the required distance.

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