Which equation models the following word problem?Find three consecutive odd integers such that the sum of 3 times thesmaller and 5 times the largest is 770.

x - 1 < -10

add 1 to both sides

x - 1 + 1 < -10 + 1

x < -9

For solving our problem we have to divide our total which is $8425 by the hourly charge $10.25

$8425 / $10.25 = 821,95

The rounded answer is 822 hours.

the perimeter is equal to the sum of all the sides, therefore:

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The area of a rectangle is given by:

Problem

Melissa has reached her credit card limit of $ 6,500. Since Melissa has poor credit history, the annual interest rate on her credit card is 19%. Using an online calculator, Melissa determined that if she pays $ 220 per month and does not make any additional purchases with her credit card, it will take her 41 months to pay off the credit card. Which of the follow represents the total interest Melissa will pay when her credit card is paid off?

Solution

For this case we can start the amount of money paid by Mellissa with this operation:

220$/month *41 months = $9020

And since the credit card limit is $6500 we can calculate the interest paid with this difference:

$9020- $ 6500=$2520

And the best answer for this case would be $2520

To solve this problem, we multiply and divide the given expression by 2-i:

Recall that:

Therefore:

Finally, multiplying the factors in the numerator, we get:

Finally, simplifying the above result, we get:

the equation that represents the number line below is:

Let x be an even integer then x+2 is the next consecutive even integer.

We need to look at [tex](x+2)^2 - x^2[/tex], since that's the difference between the squares of any two consecutive even integers.

[tex](x+2)^2 - x^2 = x^2 + 4x + 4 - x^2[/tex]

                     [tex]=4x+4[/tex]

                     [tex]=4(x+1)[/tex]

Since that difference is 4 times something, it is a multiple of 4.

In order to find the missing coordinate, start graphing the three points given

then, ubicate the point where a 90° angle is formed in the missing corner, keeping the x-coordinate from the point below and the y-coordinate from the point to the left.

1727.88 cm³/sec is the volume of the cone .

How much volume do a cone and a cylinder have?

Volume of cone V = 1/3πr²h

               r/h = 15/20 = 3/4

            V = 1/3πr²h

dv/dt = 1/3 [π[r²dh/dt + 2rhdr/dt]

   dr/dt = dh/dt = 2cm/sec

   r = 15 cm  h = 20 cm

 dv/dt = π/3[15² × 2 + 2 × 15 × 20 × 2 ]

   550π  = 1727.88 cm³/sec

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Monthly revenue:

As the monthly revenue is given by a quadratic equation, the number of units that must be sold each month maximize the revenue and the maximum revenue are the coordinates of the vertex for the parabola that correspond to the given function.

x is the number of units

y is the maximum revenue

To find the x coordinate of the vertex, use the next formula:

Use the x-coordinate in the function to find the y-coordinate (R(600)):

Answer

The height of the plane at that time is 1.1 miles

The distance of the plane's path is 10.1 miles

Explanation

The situation models a right angle triangle as shown below

Using trigonometric ratio,

tan 6° = opposite / adjacent

The opposite side of the triangle is the height of the plane. The distance traveled horizontally is the adjacent side. Therefore,

The height of the plane at that time ≈ 1.1 miles

The hypotenuse of the triangle formed is the distance of the plane path.

Therefore, this distance can be calculated using Pythagoras rule as follows:

The distance of the plane's path = 10.1 miles

We have a set of points and we have to calculate the least squares line that fits the data.

total money she has is 32 $

now after buying she has left only with 20$

so she spent 32 - 20 = 12 $

she spent 12 $ for buying 9 packs of noisemaker,

9 Pack cost = 12 $

1 pack cost = 12 / 9

= 4/3 = 1.3333 $

so cost of each pack of noise is 1.33 $

The difference of squares identity can be expressed as

this is because when expanding the expression on the left the term ab needs to be cancelled like this

Answer:

28.27 inches squared

Step-by-step explanation:

A = π r²

A = π (3)²

A = π 9

π*9 = 28.2743338823

A = 28.27

Let's begin by identifying key information given to us:

We are given 8 interior angles & which are listed below:

Reading the value of the protractor, we will get the following angle for KDC = 130 degrees.

Angle DC = 50 degrees (Alternate Interior Angles with LDC)

Angle LDC = 50 degrees (Supplementary Angle with KDC)

Angle DCH = 130 degrees (Alternate Interior Angles KDC)

Angle MEF = 50 degrees (Corresponding Angle with DC)

Angle HEF = 130 degrees (Corresponding Angle with CDH)

Angle EFJ = 50 degrees (Alternate Interior Angles with MEF)

Angle EF = 130 degrees (Supplementary angle with EFJ)

First, we need to solve for θ:

But, since the cosine is a function that takes the same values every 3π/2, if we add this to the solution:

Thus, the two solutions are:

Solution:

Given:

The domain of a function is the set of input values that make the function real and defined.

Hence, we need to find the singularity or undefined points of the function.

The function H(x) will be undefined when the denominator is 0.

Thus, singularity exists at;

The function is therefore defined at all other values except at the undefined points.

Hence,

Therefore, the domain of the function H(x) is;

Step 1:

Probability formula

Step 2:

Number of possible outcomes

Quarters = 3

Dimes = 5

Nickels = 2

Total possible outcomes = 10

Step 3:

Final answer

The probability he will pull two quarters in a row from his pocket without replacement = 1/15

Solution

By definition of similar figures:

Similar figures are two figures having the same shape

The polygons that are similar to poly gone 1 are

Polygon 3 and Polygon 4

The significant figures are the digits of the number that provide information about the measurement that number represents.

In this case, all the digits has to be included because all of them are giving information about the measurement.

According to the given data we have the following:

Whitney earns 312 in 26 hours of work

Andrew earns 451 in 41 hours of work

Lena earns 10 per hour

In order to calculate who earns the most money per hour we would have to calculate the rate of money per hour of Whitney and Andrew and the compare it with Lena.

So, money per hour of whtiney=312/26

money per hour of whtiney=12 per hour

money per hour of Andrew=451/41

money per hour of Andrew=11 per hour

Therefore, Whitney is the person that earns most money per hour.

The standard form of the equation is 9y = 5x + 40

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y. The values of x and y represent the coordinates of the point on the line represented in the coordinate plane

The given points are (-8, 0) and (1,5)

We find the slope first,

Slope(m) = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

Where [tex]y_{1}[/tex] = 0, [tex]x_{1}[/tex] = -8 and [tex]y_{2}[/tex] = 5 and [tex]x_{2}[/tex] = 1

slope(m) = [tex]\frac{5 - 0}{1 - - 8}[/tex]

slope = 5/9

But equation o line is y = mx + c

To find c, take values of x = -8 and y = 0

so that the equation y = mx + c  becomes

0 = 5/9(-8) + c

c = 40/9

substitute for the values of m and c into y = mx + c

y = 5/9x + 40/9

Multiply through by 9, we have

9y = 5x + 40

writing it in standard form, 9y -5x - 40 = 0

In conclusion, the equation of the line in standard form is 9y -5x - 40 = 0

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Answer:

-2

Step-by-step explanation:

y^3=-8.

y=cube root of -8 = -2

SOLUTION:

Step 1:

In this question, we are given the following:

9/10 - 5/6

Write your answer as a fraction in simplest fraction in simplest form.

Step 2:

The details of the solution are as follows:

CONCLUSION:

The final answer is:

Answer: A=56/5 ft^2

Step-by-step explanation:

A=Area of triangle. b=base. h=height

A=1/2 * b * h

A=1/2 * (5+3/5) * 4

A=1/2 * (25/5 + 3/5) * 4

A=1/2 * 28/5 * 4

A=28/10 * 4

A=28*4/10

A=112/10

A=56/5 ft^2

The slope of the line perpendicular to the segment AB is 1/4

The slopes of perpendicular lines are negative reciprocals of each other.

Given the endpoints A(-8.1, 4.9) and B(-7.6, 2.9), the slope of this line is as follows:

(2.9 - 4.9)/[-7.6 - (-8.1)]

= (2.9 - 4.9)/(-7.6 + 8.1)

= -2/0.5

= -4

The negative reciprocal of -4 is 1/4

Therefore, the slope of the line perpendicular to the segment AB is 1/4

the last three pictures have at least 1 pair of perpendicular sides

1) Considering that the sum of the interior angles of a triangle is 180º, i.e., what the triangle angle-sum theorem means

2) Let' solve for y

y+27°+4y+113=180 Combine like terms

5y +140 = 180 Subtract 140º from both sides.

5y = 40 Divide both sides by 5

y=8

2) Hence y = 8

The shape is polygon if it closed by by finite number of side.

So circle is not a polygon.

The polygon is convex if all the interior angle of polygon is less than 180 degree and polygon is concave if any one angle is greater than 180 degree.

The second shape is closed by finite number of side and all the interior angles are less tha 180 degree so it is conved polygon.

The third shape is also closed by finite number of side but two of interior angle is more than 180 degree so shape 3 is concave polygon.

Answers:

Shape 1: Not a polygon.

Shape 2: Convex polygon

Shape 3" Concave polygon.