Match each problem to its solution.32672.72671.7216Jeff wants to buy a new guitar that costs$1,701.04. Currently, he has 51,029.32How many more dollars does he need tobuy the guitar?Rose walks 3.2 miles every day. How manymiles will she have walked in 5 days?Christie was on a road trip. She traveled320.95 miles on day one, 231.45 miles onday two, and 120.32 miles on day three.How many miles did she travel duringher three-day trip?Hugh drove 774.4 miles. His car averaged24.2 miles per gallon of gas. How manygallons of gas did the car use?No

well, the midpoint of segment AB is the center of the circle, so

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 -2}{2}~~~ ,~~~ \cfrac{ 9 +1}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 10 }{2} \right)\implies \stackrel{center}{(2~~,~~5)}[/tex]

now since we know AB is the diameter, so half that distance AB is its radius, so

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}[/tex]

[tex]AB=\sqrt{(~~6 - (-2)~~)^2 + (~~9 - 1~~)^2} \implies AB=\sqrt{(6 +2)^2 + (9 -1)^2} \\\\\\ AB=\sqrt{( 8 )^2 + ( 8 )^2} \implies AB=\sqrt{ 64 + 64 } \implies AB=\sqrt{ 128 } \\\\\\ AB=8\sqrt{2}\hspace{5em}\stackrel{\textit{half that is the radius}}{\cfrac{8\sqrt{2}}{2}\implies 4\sqrt{2}\implies \sqrt{32}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{2}{h}~~,~~\underset{5}{k})}\qquad \stackrel{radius}{\underset{\sqrt{32}}{r}} \\\\\\ (x-2)^2~~ + ~~(y-5)^2~~ = ~~(\sqrt{32})^2\implies {\large \begin{array}{llll} (x-2)^2~ + ~(y-5)^2~ = ~32 \end{array}}[/tex]

The probability of choosing a painting random and it is British is 0.50.

Given,

The total number of paintings = 30

Then,

T = Painting from 20th century

B = British paintings

We have to find the probability of choosing a painting random and it is British.

Here,

Probability = British/ Its from 20th century

Probability = n (B and T) / n(T)

                  = x / (x + x(x-2))

                  = 3 / (3 + 3(3 - 2))

                  = 3 / (3 + 9 - 6)

                  = 3 / 6 = 1/2 = 0.5

Here, the probability of choosing a painting random and it is British is 0.50.

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The slope intercept form of equation that models $20 startup fee and $5 monthly fee is y = 5x +20 , y is total fee and x is number of months

The slope intercept form of an equation is y = mx + c

where y is y coordinate, x is x coordinate, m is the slope of the line and c is y intercept.

Let the total fee after x months be y

Then y is sum of startup fee and sum of all month's fee

For x months total monthly fees = 5(x)

Therefore the total fee after x months , y = 5x +20 which is same as slope intercept form y=mx+c

when x= 0 ⇒ y = 20 , startup fee

Thus, the equation in slope intercept form is  y = 5x +20 ,where y is total fee and x is number of months.

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Answer:

See below

Step-by-step explanation:

Point slope form

y - - 8 = (-1)(x -3)      re-arrange

y + 8 = -x+3

y = -x - 5

Answer:

The answer would be 7 times 12
Eric will spend $84
I calculated it by seeing how much each of the pizzas cost-$7 the I figure out how many pizzas he need-12 Now what we need to do is multiply 7 and 12 because if one pizza is $7 (Stated in the written problem) then I know that it would be 7+7+7+7+7+7+7+7+7+7+7+7 12 times, one time for each pizza needed. The simpler version would be 7 time 12 which then we would get a value of $84.

Step-by-step explanation:

Hope this helps!!

Answers to all the subparts using equations are:

So, the answers to all the subparts are as follows:

(A) Equation that can be formed is:

(B) Cost of 12 pizzas:

Let, x = 12.

(C) Total cost can be calculated easily by substituting the number of pizzas bought which is 12 in this case in the place of x.

Therefore, answers to all the subparts using equations are:

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Correct question:

Eric is buying food for an upcoming holiday party. He can get pizzas for $7 each using a coupon he found online, and he wants to figure out the cost of buying 12 pizzas so he can plan his budget. Please provide answers to each of the following questions:

(A) What is the direct variation equation that represents this situation? (worth 2

points)

(B) How much will Eric spend if he buys 12 pizzas? (worth 2 points)

(C) Explain how you calculated his total cost for pizzas. (worth 2 points)

The variable y is shown with no exponent. Any term with no exponent is understood to have an exponent of 1, so y has an exponent of 1.

Answer: The cost of her phone is $1,820.

45*12=540 per year

540*3=1,820 every 3 years.

She would have had the phone between 2 and 3 years if she had spent 1,500.

Answer: x = 65

Step-by-step explanation:

1) First find the mini triangles, left and right angles

We will be calling the left one A and the right one B.

2) Next use triangle sum to find B.

62 + 50 + b = 180

b = 68

3) Use triangle sum again to find A.

53 + 80 + a = 180

a = 47

4) Use triangle sum to find the top mini angle.

47 + 68 + c = 180

c = 65

5) Since x is in the vertical angle of c, they are equal

c = x

65 = x

The constant of proportionality when the restaurant is placing an order for paper towels is 12.

It should be noted that the constant of proportionality simply means the ratio that is important to show the proportional relationship between the two given values.

This will be illustrated as:

y = kx

y = Number of paper roll

x = Number of cases ordered

From the table, this will be:

y = kx

12 = k × 1

k = 12

Therefore, the constant of proportionality is 12.

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Answer:

-2

Step-by-step explanation:

f(x) = -2 (1/2)^x

you find the y-intercept where x = 0

= -2 (1/2)^0

= -2 *1

= -2

The polynomial is x³ + 2x

If the zeros or roots of the polynomial are given, then the standard form of the polynomial can be found.

That is, a, b and c are roots of the polynomial, then  the polynomial will be of degree 3 since 3 zeros are there and the factors of the polynomial will be , x-a, x-b and x- c.

Then the polynomial is, (x-a)(x-b)(x- c) = x³-(a+b+c)x-abc

Here the zeros of the polynomial are x = 0, x = i√2 and x = -i√2.

So the factors of the polynomial are (x-0), (x - i√2) and (x +i√2).

Hence the polynomial is , (x-0) (x - i√2)(x +i√2) = x(x²+2) = x³ + 2x

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Answer:

plane

Step-by-step explanation:

The plane is flat like a wall or the floor. It has infinite length and infinite width but has no thickness (as thick as a line--which has no thickness) basically a line is one-dimensional and a plane is two-dimensional.

See image.

Answer:

x = 60

Step-by-step explanation:

(2x + 15)° and 135° are corresponding angles and are congruent , then

2x + 15 = 135 ( subtract 15 from both sides )

2x = 120 ( divide both sides by 2 )

x = 60

Answer:

x = 60

Step-by-step explanation:

The two angles are corresponding. This means that both of the angles are congruent (same). So, you set both of them equal to each other. That means to do 2x + 15 = 135. You do basic algebra and then you get 60 for x. Hope this helps!

Answer:

176 yd

Step-by-step explanation:

UNSHADED REGION (white rhombus): A=(s1+s2)/2 * H

s1=7

s2=1+7=8

H=6

A=(7+8)/2*6=45

SHADED + UNSHADED REGION (big parallelogram): area of parallelogram A=B*H

B=17

H=7+6 = 13

A=17*13=221

SHADED REGION: big parallelogram area - rhombus area

221 - 45 =176 yd

The coordinates of the orthocenter of triangle DEF are given as follows:

(6.67,  -2).

The orthocenter of a triangle is the point of intersection of the three altitude lines of the triangle.

Hence, we need to find two of the lines, and them find the intersection point between them, as the third line will necessarily intersect these lines at this point.

The midpoint of segment DE is:

(6, 1).

Which is the mean of the coordinates.

Vertex F is at point (8, -8), hence the slope of the line with these two points is:

m = (-8 - 1)/(8 - 2) = -9/2 = -4.5.

Hence:

y = -4.5x + b.

When x = 6, y = 1, hence we can find b as follows:

1 = -4.5(6) + b

b = 28.

Hence one line is:

y = -4.5x + 28.

The midpoint of segment EF is:

(8, -1.5).

Which is the mean of the coordinates.

Vertex D is at point (4, -3), hence the slope of the line with these two points is:

m = (-1.5 - (-3))/(8 - 4) = 0.375.

Hence:

y = 0.375x + b.

When x = 8, y = -1.5, hence we can find b as follows:

-1.5 = 0.375(8) + b

b = -4.5.

Hence the two lines that we have to find the intersection point is:

Then the x-coordinate of the orthocenter of the triangle is:

-4.5x + 28 = 0.375x - 4.5

4.875x = 32.5

x = 32.5/4.875

x = 6.67.

The y-coordinate of the orthocenter of the triangle is:

y = 0.375(6.67) - 4.5 = -2.

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Answer:

5 7/10

Step-by-step explanation:

first you multiply five by the three, then add the eleven. so now you have a improper fraction, 26/5 plus 1/2. find the Least common denominator which is 10, and whatever you do to the denominator you do to the numerator which makes 57/10 simplify and you'll get 5 7/10

Answer:

Step-by-step explanation:

1. Find the lcm(least common denominator)

(5 x 2 = 10)

2. Multiply the numerators by the same number as the denominator(you multiplied 5 by 2 to get 10 so you multiply 311 by 2. You multiplied 2 by 5 to get 10 so you multiply 1 by 5.)

311 x 2 = 622

1 x 5 = 5

3. Add

622/10 + 5/10 = 627/10

4. Simplify

627 ÷ 10 = 62 [tex]\frac{7}{10}[/tex] (it can also be written as: 62.7)

The solution for the given inequality is p < -2.2. The graph that represents the solution is attached below.

From the question, we are to determine the graph for the solution set for the given inequality

The given inequality is p - 3.6 < -5.8

First, we will solve the inequality

Solving the inequality

p - 3.6 < -5.8

Add 3.6 to both sides

p - 3.6 + 3.6 < -5.8 + 3.6

p < -2.2

The solution is p < -2.2

The graph of the inequality is shown below

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Answer: number line with an open circle on point negative 2.2 and arrow shaded to the left

Step-by-step explanation:

If this guy is correct

In accordance with analytic geometry, the equation that represents the line is y = - (1 / 4) · x - 6.

Herein we find the representation of a line set on a Cartesian plane. According to analytic geometry, line are represented by equations of the form y = m · x + b, where m, b are the slope and the y-intercept, respectively.

Both the values of the slope and the y-intercept can be found by knowing the location of two points lying on the line. If we know that (x₁, y₁) = (0, - 6) and (x₂, y₂) = (4, - 7), then we find the following system of linear equations:

b = - 6                                    (1)

4 · m + b = - 7                        (2)

By (1) in (2):

4 · m - 6 = - 7

4 · m = - 1

m = - 1 / 4

The equation that represents the line is y = - (1 / 4) · x - 6.

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Algebraic equations are mathematical equations that consist of unknown variables. These unknown variables can be represented with any letter of the alphabet.

The cost of 2 pounds(lb) of the first type of candy is $8

Note that: x represents the cost per pound (lb) of the first type of candy

The Algebraic equation for the above statement is given as:

2lb × $x + 3 Ib × $1.50 = $2.50(2lb + 3lb)

2x + 4.5 = 12.5

Collect like terms

2x = 12.5 - 4.5

2x = 8

Divide both sides by 2

2x/2 = 8/2

x = 4

The cost of the 1 pound of first type of candy is $4

The cost of 2 pounds(lb) of the first type of candy is calculated as:

2 x $4

= $8

hope it will be helpful

The coordinates of A"B"C" are as follows :

A = 1 1/2,3

B = 1 1/2,0

C = -4 1/2, 3.

Using one or more numbers, or coordinates, a coordinate system in geometry establishes a unique way to locate points or other geometrical objects on a manifold, such Euclidean space. a group of numbers representing a precise place. On graphs, there are typically two numbers: the first one indicates the length along, and the second one indicates the length up or down. For instance, the value of the point (12,5) is 12 units. In general, alphanumeric characters are used to express GPS coordinates, which are a distinctive identifier of a certain geographic location on the globe. Points of intersection in a grid system are referred to as coordinates in this context. Typically, the latitude and longitude coordinates are used to represent GPS coordinates.

Five units up and along.

90degrees clockwise is x, y, y, -x.

A = 1,2

B = 1,0

C = -3, 2.

Times everything by 3/2 now.

A = 1 1/2,3

B = 1 1/2,0

C = -4 1/2, 3.

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Answer:

You've gotta be kidding me...It's easy come on

-2 is the answer

Step-by-step explanation:

f(x)= -x-1        JUST SUBSTITUTE 1 FOR X

f(1)= -(1)-1

f(1)= -2

Answer:

y=x^2+3x-10

Step-by-step explanation:

.........

Using simple linear equations we calculate that the change left will be $6.24 .

The equals sign is used to indicate that two expressions on each side of the equal sign are equal in the many mathematical formulas that are utilized to form an equation.

Let the change received be x.

Therefore let us construct an equation for the situation

cost of game + tax + change = 20

or, 12.98 + 0.78 + x = 20

or, 13.76 + x = 20

or, x = 6.24

Therefore he will receive   6.24 after solving the equation.

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The number sentence that is true is 1/3 x (-2/5)=-2/15 . Option A

A fraction is simply defined as the subset of a whole set or the part of a whole element.

The several types of fractions includes;

Examples of simple fractions: 1/2, 1/8

Examples of proper fractions: 3/4, 8/10

Examples of mixed fractions: 3 1/6, 2 1/8

Examples of improper fractions: 7/4, 8/5

Given the fraction;

a. 1/3 x (-2/5)

The product of the fraction is = - 2/15

b. -1/3 x 2/5 = 2/15

The product is = -2/15

c. -1/3 x (-2/5)

The product is 2/15

d. 1/3 x 2/3

The product is 2/9

Hence, the sentence is option A

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