(SHOW WORK NEED IT BY TONIGHT! )Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.


Nick, a caterer, is investing some money in equipment and employees to help grow his business. Recently he spent $47 on equipment and hired a server who makes $15 per hour. Nick is hoping to make up these expense at the next job that is scheduled, which pays a base of $54 in addition to $14 per hour that the server works. In theory, this event could pay enough to cancel out Nick's expenditures. How much would the job pay? How long would the job have to be?



The expenditures and pay would both be $_ if the job lasted for _ hours.

Answer:

Number of photographs Bob has can be represented as ⇒ [tex]11p[/tex]

Step-by-step explanation:

Given:

Alan has 11 photographs.

Bob has [tex]p[/tex] times as many photographs as Alan.

To find the expression representing the number of photographs Bob has.

Solution:

Since Bob has [tex]p[/tex] times as many photographs as Alan has so, in order  to find the number of photographs Bob has, we will multiply [tex]p[/tex] with number of photographs Alan has.

Alan having 11 photographs, Bob will have as much as:

⇒ [tex]11\times p[/tex]

⇒ [tex]11 p[/tex] photographs

Answer:

all work is shown and pictured

The solution of the expression is,

⇒ c = 10/3

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expression is,

⇒ 5/2c = 8 1/3

Now,

We can simplify the expression is,

⇒ 5/2c = 8 1/3

⇒ 5/2c = 25/3

⇒ c = 25/3 × 2/5

⇒ c = 10/3

Thus, The solution of the expression is,

⇒ c = 10/3

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Answer:

Hence after solving the given equation we get x = 13/20.

Step-by-step explanation:

Given:

-3 x + 0.1 + 10 x = x + 4

-3 x + 10 x - x = 4 - 0.1

6 x = 3.9

x = [tex]\frac{3.9}{6}[/tex]

x = [tex]\frac{1.3}{2}[/tex]

x = [tex]\frac{13}{20}[/tex]

Answer:

There is no picture

Step-by-step explanation:

Answer:

$240

Step-by-step explanation:

i = prt

i = $2,000 x 0.03 x 4

i = $240

The amount of interest Antonia will earn in 4 years is $240.

Answer:

see below

Step-by-step explanation:

Answer:

The first answer is the correct choice.

Step-by-step explanation:

For this, there are two initial options. A cake or a shake. This means that there are two different trees that need to exist. One for Cakes and one for shakes.

Each of these trees needs to have the options of having vanilla and strawberry.

The first answer is the only one that follows this criteria

Answer:

1st one is correct.

Step-by-step explanation:

Answer:

Answer to #1: -44.21

Answer to #2: 1.2

:)

8.27 - 52.48 = -44.21

7.38 - 6.18 = 1.2

Number of adult tickets sold is 100 and number of children tickets sold is 150

Solution:

Let "c" be the number of childrens ticket sold

Let "a" be the number of adult tickets sold

Cost of 1 children's musical ticket = $ 2.00

Cost of 1 adult musical ticket = $ 3.50

Given that 250 tickets were sold

number of childrens ticket sold + number of adult tickets sold = 250

c + a = 250 ---- eqn 1

250 tickets were sold for a total of 650

So we can frame a equation as:

number of childrens ticket sold x Cost of 1 children's musical ticket + number of adult tickets sold x Cost of 1 adult musical ticket = 650

[tex]c \times 2.00 + a \times 3.50 = 650[/tex]

2c + 3.50a = 650 ---- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "a" and "c"

From eqn 1,

c = 250 - a ----- eqn 3

Substitute eqn 3 in eqn 2

2(250 - a) + 3.50a = 650

500 - 2a + 3.50a = 650

1.5a = 150

From eqn 1,

c = 250 - 100

Thus number of adult tickets sold is 100 and number of children tickets sold is 150

Answer:

B

Step-by-step explanation:

x² - 10x -24 = (x + 2) (x - 12)  ....(1)

x² - 3x - 108 = (x + 9) ( x - 12) ....(2)

(1) / (2)     formula (2) can't be 0 ∴ x ≠ -9 and x ≠ 12

(1) / (2) = (x + 2) / (x + 9)

answer is (B)

Answer:

The expression is  [tex]a_{10}[/tex] = 100+(10 - 1)50 .

Step-by-step explanation:

Given as :

The amount of money added as prize money =  $50

The amount that first caller will win =  [tex]a_{1}[/tex] = $100

Let The amount that 10th caller win = $A

∴ common difference for the callers amount = $50

Now, According to question

The given statement is in arithmetic expression

So, For A.P , The nth term is written as

nth term = first term  + (n - 1) × common difference

I.e [tex]a_{10}[/tex] = [tex]a_{1}[/tex] +  (n - 1) × common difference

Here n = 10

Or, A = $100 +  (10 - 1) × 50

So, The expression =  [tex]a_{10}[/tex] = 100+(10 - 1)50

Hence, The expression is  [tex]a_{10}[/tex] = 100+(10 - 1)50 . Answer

Answer:

The answer is A.

Step-by-step explanation:

a10=100+(10-1)50

Got it correct in the quiz.

Answer: 50%

Step-by-step explanation:

12x1.5=18

Answer:

50% increase

Step-by-step explanation:

Percentage change = increase/original × 100

[tex]change = \frac{(18 - 12)}{12} \times 100[/tex]

[tex]change = \frac{6}{12} \times 100[/tex]

[tex]change = 0.5 \times 100[/tex]

[tex]change = 50\%[/tex]

Answer:

x = 1 , y = 2

Step-by-step explanation:

Solve the following system:

{5 x + 2 = 7 | (equation 1)

y = x + 1 | (equation 2)

Express the system in standard form:

{5 x+0 y = 5 | (equation 1)

-x + y = 1 | (equation 2)

Add 1/5 × (equation 1) to equation 2:

{5 x+0 y = 5 | (equation 1)

0 x+y = 2 | (equation 2)

Divide equation 1 by 5:

{x+0 y = 1 | (equation 1)

0 x+y = 2 | (equation 2)

Collect results:

Answer: {x = 1 , y = 2

Answer: 71300000

Step-by-step explanation:

Answer:

7.13 x 10^7.

Step-by-step explanation:

2.3x10^-5)(3.1x10^12

= 2.3x3.1 x 10^-5 x 10^12

= 7.13 x 10^(-5+12)

= 7.13 x 10^7.

Final answer:

The area of Triangle B is two times greater than the area of Triangle A, due to the height of Triangle B being twice that of Triangle A with the base remaining constant.

Explanation:

The question pertains to the comparison of the areas of two triangles that share the same base. The height of Triangle B is twice the height of Triangle A. To find the area of a triangle, we use the formula 1/2 × base × height. Given that both triangles have the same base, if we call the height of Triangle A 'h', then the height of Triangle B is '2h'.

So, the area of Triangle A is (1/2 × base × h), and the area of Triangle B is (1/2 × base × 2h). Simplifying the expression for the area of Triangle B, we find it is equal to 2 × (1/2 × base × h), which means it's exactly twice the area of Triangle A. Thus, the area of Triangle B is two times greater than the area of Triangle A.

If one triangle's height is double the other's, its area is four times greater, with same base.

let's break it down step by step.

1. Area of a Triangle Formula: The area of a triangle is calculated using the formula:

[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

2. Given Information:

  - Both Triangle A and Triangle B have the same base.

  - The height of Triangle B is twice the height of Triangle A.

3. Comparing the Areas:

  - Let's denote the base of both triangles as [tex]\( b \).[/tex]

  - Let the height of Triangle A be [tex]\( h_A \)[/tex] and the height of Triangle B be [tex]\( h_B \).[/tex]

4. Area of Triangle A [tex](A_A)[/tex]:

  - Using the area formula, the area of Triangle A is:

   [tex]\[ A_A = \frac{1}{2} \times b \times h_A \][/tex]

5. Area of Triangle B [tex](A_B)[/tex]:

  - Triangle B has double the height of Triangle A, so the height of Triangle B is [tex]\( 2h_A \).[/tex]

  - Using the area formula, the area of Triangle B is:

   [tex]\[ A_B = \frac{1}{2} \times b \times (2h_A) = b \times h_A \][/tex]

6. Comparing the Areas:

  - Since both triangles have the same base [tex](\( b \)),[/tex] and the height of Triangle B [tex](\( 2h_A \))[/tex] is twice the height of Triangle A [tex](\( h_A \)),[/tex] the area of Triangle B is [tex]\( b \times h_A \)[/tex] which is exactly the same as Triangle A.

7. Conclusion:

  - The area of Triangle B is not just greater, it's exactly the same as Triangle A.

So, if the base and one of the heights are doubled, the area of the triangle also doubles. This is because the area of a triangle is directly proportional to its height when the base is constant.

The right answer is: g(x)  is translated 2 units up from  f(x)

Step-by-step explanation:

Given functions are:

[tex]f(x) = 4x\\g(x) = 4x+2[/tex]

In order to shift the functions upward or downward, an integer is added or subtracted from the original function's output.

We can see by comparing both functions that 2 can be added to f(x) to make function g.

As 2 is added to the function, not the input, it is a vertical shifting.

As the integer is positive, the shift is upward.

So,

The right answer is: g(x)  is translated 2 units up from  f(x)

Keywords: Functions, shifting

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Answer:

x=-3, y=-6. (-3, -6).

Step-by-step explanation:

-4x+y=6

-5x-y=21

--------------

-9x=27

x=27/-9

x=-3

-5(-3)-y=21

15-y=21

y=15-21

y=-6

Answer:

$2.80 (rounded from 2.796)

Step-by-step explanation:

13.98*0.2

Answer:

$2.80

Step-by-step explanation:

Multiply $13.98 by 0.2 (0.2 = 20%):

[tex]13.98*0.2=2.796[/tex]

Since you can't tip less than a cent, round to the nearest cent (hundredth of a dollar):

[tex]2.80[/tex]

20% tip on a bill of $13.98 is $2.80.

Answer:

Step-by-step explanation:

substitute x = - y - 2 in 0.5x + y = 1

0.5(- y - 2) + y = 1

-0.5y-1+y=1

0.5y=2

y=4

x=- y - 2

x=-4-2

x=-6

Answer:

x=4; x=-6

Step-by-step explanation:

The ordered pair solution of y = (2/5)x + 2 corresponding to -5 is (x, y) = (-5, 0)

Solution:

Given that we have to find the ordered pair solution of [tex]y = \frac{2}{5}x + 2[/tex] corresponding to -5

Let us find the ordered pair corresponding x = -5

Ordered pairs are often used to represent two variables

The number which corresponds to the value of x is called the x-coordinate and the number which corresponds to the value of y is called the y-coordinate

Substitute x = - 5 into the function and evaluate for y

[tex]y = \frac{2}{5}x + 2\\\\y = \frac{2}{5}(-5) + 2\\\\y = 2(-1) + 2\\\\y = -2 + 2\\\\y = 0[/tex]

Therefore the ordered pair is x = -5 and y = 0 which is (x, y) = (-5, 0)

Answer: They are skew and will never instersect.

Step-by-step explanation: First of all, they will never instersect because they are in the parallel planes. They are also skew because in the 3 dimensional geometry, they are also not parallel because they can be different directions.

Answer:

Step-by-step explanation:

WE know that lines are in different planes which are parallel, this means that those planes have the same angle of direction.

If planes are parallel, then all lines inside them are skew, that is,  line a and line b will never intersect and they aren't necessarily has to be parallel.

For example, imagine you are in a apartment, parallel planes are the roof and the floor, they are parallel, that is, the will never intersect each other. So, if you have a ruler attached to the roof and another ruler on the floor, you will see that those rulers are not necessarily parallels, and they won't intersect each other because, they have the same angle of direction.

Therefore, the right answer is "They are skew and will never intersect"

Answer:

[tex]y = - \frac{3}{4}x - 7[/tex]

Step-by-step explanation:

We have to find the equation of the straight line which has the slope equal to [tex]- \frac{3}{4}[/tex] and passes through the point (-4,-4).

As the slope of the equation is [tex]- \frac{3}{4}[/tex], hence by slope-intercept form the equation of the straight line will be given by  

[tex]y = - \frac{3}{4}x + c[/tex] .......... (1), where c is any constant which we have to evaluate from the given point on the line (-4,-4).

So, the point (-4,-4) satisfies the equation (1) and hence,

[tex]- 4 = - (\frac{3}{4}) \times (- 4) + c[/tex]

⇒ - 4 = 3 + c

⇒ c = - 7

Therefore, the equation of the straight line will be  

[tex]y = - \frac{3}{4}x - 7[/tex] (Answer)

Answer:veg students: 50

Step-by-step explanation:

The slope of the line that passes through the pair of point (5, 7), (2, 1) is 2

Solution:

Given that line that passes through the pair of point (5, 7), (2, 1)

To find: slope of the line

The slope of line is given as:

For a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] slope is given as:

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

Here in this problem,

[tex]\left(x_{1}, y_{1}\right)=(5,7) \text { and }\left(x_{2}, y_{2}\right)=(2,1)[/tex]

Substituting the values in above formula,

[tex]m=\frac{1-7}{2-5}=\frac{-6}{-3}=2[/tex]

Thus the slope of given line is 2

Answer:

The solution is the ordered pair (3,2)

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y=\frac{1}{3}x+1[/tex] -----> equation A

[tex]x+y=5[/tex] ----> equation B

Solve by graphing

Remember that

The solution of the system of equations is the intersection point both lines

using a graphing tool

The intersection point is (3,2)

see the attached figure

therefore

The solution is the ordered pair (3,2)

A system of equation can be solved in several ways, which includes the use of graphs

The solution to the system of linear equations is (3,2)

The system of equations is given as:

[tex]y=\frac 13x+1[/tex]

[tex]x+y=5[/tex]

See attachment for the graphs of  [tex]y=\frac 13x+1[/tex]  and [tex]x+y=5[/tex].

From the attachment, the point of intersection of the lines of both equations is (3,2)

Hence, the solution to the system of linear equations is (3,2)

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Answer:

I DONT KNOW

Step-by-step explanation:

I DO NOT KNOW

Answer: roberts wire  = 5.71

              Marias wire.  = 4.29

Step-by-step explanation:

Robert wire : y

Marias wire: x

y/2=2/3x

3y=4x

y=4/3x

x+y=10

x+4/3x=10

3x+4x=30

7x=30

x=30/7

X=4.29 feet

Y=4.29*4/3=5.71

To find out how much longer Robert's wire is than Maria's, we need to determine their respective lengths. Let's assume that Maria's wire is x feet long. Then we can set up an equation to solve for the length of Maria's wire and the length of Robert's wire.

To find out how much longer Robert's wire is than Maria's, we need to determine their respective lengths. It is given that half of Robert's wire is equal to 2/3 of Maria's wire, and the total length of their wires is 10 feet.

Let's assume that Maria's wire is x feet long. According to the given information, half of Robert's wire would be x/2 feet long. And since half of Robert's wire is equal to 2/3 of Maria's wire, we can set up the following equation: x/2 = (2/3) * x

We can solve this equation to find the length of Maria's wire. Once we have that, we can find the length of Robert's wire by doubling it (since it is given that half of Robert's wire is equal to x/2).

After finding the lengths of their wires, we can subtract Maria's wire length from Robert's wire length to determine how much longer Robert's wire is than Maria's.

Answer: 14. The three consecutive numbers are 12, 14 and 16.

15. An example of equation whose solution is 5 is given below

2X — 20 = X — 15

Step-by-step explanation: please see attachment for explanation.

Answer:

The smaller one measures 80 degrees.

Step-by-step explanation:

We are given:

[tex]a+b=180[/tex]

[tex]\frac{a}{b}=\frac{5}{4}[/tex]

So we have a system to solve.

I'm going to solve the bottom equation for [tex]a[/tex] by multiplying [tex]b[/tex] on both sides:

[tex]a=\frac{5}{4}b[/tex].

Let's plug this into the first equation: [tex]a+b=180[/tex]:

[tex]\frac{5}{4}b+b=180[/tex]

[tex]\frac{5}{4}b+\frac{4}{4}b=180[/tex]

[tex]\frac{9}{4}b=180[/tex]

Multiply both sides by 4/9:

[tex]b=\frac{4}{9} \cdot 180[/tex]

[tex]b=\4 \cdot \frac{180}{9}[/tex]

[tex]b=4 \cdot 20[/tex]

[texb=80[/tex].

This means [tex]a=\frac{5}{4} \cdot 80=5 \cdot \frac{80}{4}=5 \cdot 20=100[/tex].

We do have [tex]100+80=180 \text{ and } \frac{100}{80}=\frac{5}{4}[/tex].

So the smallest of the two angles is the one that measures 80 degrees.

The one that is the larger of the two is the one that measures 100 degrees.

Final answer:

The measure of the smaller angle, which is part of a pair of supplementary angles in a 5:4 ratio, is 80 degrees.

Explanation:

Supplementary angles are two angles that add up to 180 degrees. When two angles are in the ratio of 5:4, we can find the measure of the smaller angle by first adding the parts of the ratio together, which gives us 5+4=9 parts. Since the total is 180 degrees, each part is equal to 180 ÷ 9 = 20 degrees. Therefore, the smaller angle, which is 4 parts of the ratio, is 4 x 20 degrees = 80 degrees.