Find the equation of line that passes through the points (-2,2) and (10,4)

For the given function, we have that:

The domain of a function is the set that contains all possible input values for the function. In a graph, it is the set that contains all the values of x of the function.

Hence, the domain is [-4,4] for the given function.

The zeros of a function are the values of x for which f(x) = 0, on the graph they are the values of x when the function crosses the x-axis.

For this problem, the function does not cross the x-axis, hence it has no zeros.

Looking at the graph of the function, we have that:

Hence, for the function in the given graph:

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The type of the compound inequality 3|y+7| - 16 > 5 is an intersection

The compound inequality is given as

3|y+7| - 16 > 5

Add 16 to both sides of the inequality

So, we have

3|y+7| > 21

Divides both sides by 3

So, we have

|y+7| > 3

When the above inequality is solved, the region between the boundaries are shaded

This represents an intersection

Hence, the type of the compound inequality 3|y+7| - 16 > 5 is an intersection

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Answer:The answer is disjunction !!

Step-by-step explanation:

I took the test and got this correct.

Answer: i think it is d but im not sure

Step-by-step explanation:

Answer: 7(x-2(112/8))= 7(x-28)= 7x - 28*7

7x = 28*7

x=28

The value of y in the given equation is 19/20

From the question, we are to determine the value of y in the given equation

The given equation is

3 1/3(y + 1 1/8) = 6 11/12

First, convert the the fractions into improper fractions

10/3(y + 9/8) = 83/12

Multiply both sides of the equation by 3/10

3/10× 10/3(y + 9/8) = 3/10× 83/12

y + 9/8 = 3/10× 83/12

y + 9/8 = 83/40

y = 83/40 - 9/8

y = (83 - 45)/40

y = 38/40

y = 19/20

Hence, the value of y in the given equation is 19/20

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The value of y when x= 2 and z= 1/4 is y = 4

In this question, we have been given y varies jointly with x and z.

This means y is directly proportional to x and z.

y = 16 when x = 4 and z = 1/2

We need to find the value of y when  x= 2 and z= 1/4

From y = 16 when x = 4 and z = 1/2 we can compute the equation as,

y = 8xz

16 = 8(4)(1/2)

16 = 8 × 2

16 = 16

So, the equation is y = 8xz

Now for x= 2 and z= 1/4,

y = 8xz

y = 8 × 2 × (1/4)

y = 2 × 2

y = 4

Therefore, the value of y when x= 2 and z= 1/4 is y = 4

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Step-by-step explanation:

This is a simple system of equations problem, with our equation being:

[tex]\frac{4}{7}x+9=x[/tex]

We know this as her dogs (x) is equal to 4/7 of her dogs (x) plus 9. Now all we must do is solve for x:

[tex]\frac{4}{7}x+9=x\\\\\frac{4}{7}x=x-9\\\\\frac{4}{7}x=\frac{7}{7}x-9\\\\\frac{-3}{7}x=-9\\\\x=21[/tex]

Answer:

The weight of gold in the alloy is 32 g.

Answer:

The weight is 32 grams

Step-by-step explanation:

Answer: (83 + 91 + 82 + 95) / 4

Step-by-step explanation:

        The information given tells us how to complete the question. We will be finding the average.

       Add all the scores together, and divide by the number of tests.

(83 + 91 + 82 + 95) / 4

       Since this question asks for an expression, we will end here. If it asked us to solve, we would do the following;

(83 + 91 + 82 + 95) / 4

(351) / 4

87.75

By solving a system of equations, we conclude that they sold 30 of the same-day tickets and 15 of the advance tickets.

Let's define the variables that we will be using:

We can write the system of equations:

x + y = 45

x*35 + y*20 = 1125

Isolating x on the first equation we get:

x = 45 - y

Repacing that in the other equation we get:

(45 - y)*35 + y*20 = 1125

1,575 - y*15 = 1125

1,575 - 1125 = y*15

(1,575 - 1125)/15 = y = 30

Then:

x = 45 - y = 45 - 30 = 15

We conclude that they sold 30 of the same-day tickets and 15 of the advance tickets.

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The number of teaspoons of key lime zest to make 30 cupcakes is

35/8 or 4 3/8

Given,

Margaret uses 1 3/4 teaspoon of key lime zest to make 12 cupcakes.

She wants to make 30 cupcakes.

We need to find how much key lime zest will Margaret use.

Example:

1 bag = N mango

Then to find the number of mangoes in 5 bags we need to multiply 5 on both sides.

5 bags = 5 x N mangoes.

We have,

1 3/4 teaspoons of key lime zest = 12 cupcakes

7/4 teaspoons of key lime zest = 12 cupcakes

7/4 = 12 cupcakes

Multiply 30 on both sides.

7/4 x 30 = 30 x 12 cupcakes

Divide both sides by 12.

7/4 x 30/12 = 30 cupcakes

35 / 8 = 30 cupcakes

or

4 3/8 = 30 cupcakes

This means,

35/8 or 4 3/8 teaspoons of key lime zest to make 30 cupcakes.

Thus the number of teaspoons of key lime zest to make 30 cupcakes is

35/8 or 4 3/8.

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Answer: 6.2

Step-by-step explanation:

2.9/1.3 +4.0=

2.23 + 4.0=

2.2 + 4.0=6.2

The given information is,

→ (2.9/1.3) + 4.0

Let's solve the problem,

→ (2.9/1.3) + 4.0

→ 2.23 + 4 = 6.23

Thus, the answer is 6.23.

Answer:

this makes no sense but I think the answer is 38 inches

Step-by-step explanation:

Expression best shows above condition is -5-3+3

What is an expression?

Expression in mathematics is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here, it is given that while playing board game we pick a card that sends us back five spaces. On our next turn, we must move back three more spaces. On our third turn, we get to move forward three spaces.

and, expression best shows how we could find our new spot on the game board will be :

for first move, five spaces back means = -5

for second move, three spaces back means = -3

and for third move, three spaces move forward = +3

combining all the three terms we get :  -5-3+3

Therefore, expression best shows above condition is -5-3+3

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Answer: 13 goats and 21 geese

Step-by-step explanation:

     Since we know some are goats, which have four feet, and some are geese, which have two feet, we will set up an equation.

           Let x be goats and y be geese.

4x + 2y = 94

     Next, we know both animals [usually] only have one head.

x + y = 34

     Lastly, we will solve this as a system of equations.

➜ I graphed the equations, see attached, but you can also solve by substitution or other methods.

➜ When graphing, the point of intersection is the solution. This means there are 13 goats and 21 geese.

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Using simple linear equations, we can calculate that Andy has 3 quarters.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Let the number of quarters Andy has = x

number of dollars Andy has = 20 - x

value of quarter = 0.25x

value of dollars = 0.5(20 - x)

Total value = $9.25

⇒ 0.25x + 0.5(20 - x) = 9.25

⇒ 0.25x + 10 - 0.5x = 9.25

⇒ - 0.25x = 9.25 - 10

⇒ - 0.25x = - 0.75

⇒   x = 3

Andy has quarter = 3

He has dollars = 20 - 3 = 17

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The quadratic equation that contains (0, 7), (2, 15) and (3, 10) is y = - 3 · x² + 10 · x + 7.

Quadratic functions are polynomials of the form y = a · x² + b · x + c, where a, b, c are real coefficients. To determine the coefficients, we need at least three distinct points on Cartesian plane. A solution that is algebraic exact only need three points, then we must resolve this system of linear equations:

c = 7                                      (1)

4 · a + 2 · b + c = 15              (2)

9 · a + 3 · b + c = 10              (3)

The solution to this system of linear equations is (a, b, c) = (- 3, 10, 7).

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Answer: 5578

Step-by-step explanation:

1058 + 4520 = 5578

Answer:

Average salary 13.16 120 + 18 + 20/12

Mars is half as big as Earth and that they each have an equal amount of dry land surface to determine by how much the circumference of the Earth is larger than that of Mars.

we need D(Earth) / D(Mars).

D(Earth) / D(Mars) = 1.2763 x 10⁴km/6.8  x 10³ km ≈ 1.9

D(Earth) / D(Mars) ≈ 1.9

The fifth-largest planet in our solar system by radius, the Earth has a circumference of 3,959 miles.

The other seven planets are joined by Earth and Mars. These two planets in our solar system share some geological characteristics, such as the fact that  Mars, the seventh-largest planet in our solar system, has a radius of 2,106 miles. There are a few distinctions between Mars and Earth, though.

Hence, these planets differ in terms of their sizes, atmospheres, and temperatures.

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The numbers are 4 units from -2 on this number lines are -6, 2 and 6.

A number line is a horizontal line that has equally spread number increments.

The numbers included on the line will determine how the number on the line can be marked.

According to the question,

Firstly, we will add the two numbers.

4 + (-2) = 4 - 2 = 2

Then, we will subtract the two numbers.

4 - (-2) = 4 + 2 = 6

-2 - 4 = -6

The numbers 2, 6 and -6 are represented on the number line.

Therefore, the numbers are 4 units from -2 on this number lines are -6, 2 and 6.

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Based on the fact that both workers received the same number of hours, the minimum number of hours that each employee will be assigned is 60 hours.

One worker gets 15 hours shifts and the other gets 6 hour shifts.

If they will have the same number of working hours, the minimum number of hours for these workers will be the lowest common multiple of 6 and 15.

Multiples of 15:

Multiples of 6:

The minimum number of hours is therefore 60 hours.

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Answer: 60

Step-by-step explanation:

LCM of 6 & 15

15

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

15

30

45

60

75

90

105

6

---------

6

12

18

24

30

36

42

48

54

60

LCM of 6 & 15 is 60

The equation of the linear function in slope intercept form is given as y = -2x + 1

An equation is an expression that shows the relationship between two or more numbers and variables.

From the table, the linear function contains the points (0, 1) and (2, -3), hence:

y - 1 = [(-3 - 1)/(2 - 0)](x - 0)

y = -2x + 1

The equation of the linear function in slope intercept form is given as y = -2x + 1

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Annual interest rate on $4800 for 2 years is 5.6%.

An interest rate indicates how expensive borrowing is or how lucrative saving is. Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount.

Given,

The principal amount = $4800

Time period = 2 years

Interest rate = $537.60

I = P × R × T / 100

where P = principal amount,

R = rate of interest,

T = Time period

537.60 = 4800 × R ×2 / 100

⇒ R = 537.60 ×100 / 4800 × 2

⇒ R = 5.6%

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The balance in dollars and cents in Yolanda's account at the end of 4 years is $5,355.29

What is the future value of an ordinary?

An ordinary annuity is the one where the monthly deposit occurs at the end of each month rather than at the beginning of the months such its future value based on 5.5% annual interest rate can be determined thus:

FV=PMT*(1+r)^N-1/r

FV=balance in dollars and cents in Yolanda's account at the end of 4 years=unknown

PMT=monthly deposit=$100

r=monthly interest rate=5.5%/12=0.00458333333333333

N=number of monthly deposits in 4 years=4*12=48

FV=$100*(1+0.00458333333333333)^48-1/0.00458333333333333

FV=$5,355.29

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Missing question:

What was the balance in dollars and cents in Yolanda's account at the end of 4 years?

Answer:

b

Step-by-step explanation:

Teresa in 3 years will owe $12.520, of which she borrowed $8,000 at the rate of 15.5% compounded semiannually.

So, Teresa borrowed $8,000 at a rate of 15.5%:

(Refer to the table given below)

Therefore, Teresa in 3 years will owe $12.520, of which she borrowed $8,000 at the rate of 15.5% compounded semiannually.

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Airline A will pay $28 million in taxes based on the EBIT of $100 million

The increase in interest expenses by $20 million means that the  income tax expense decreases by $7 million.

What is the taxable earnings for company A?

The fact that company A has debt and would pay interest expenses of $20 million means that its taxable income is the earnings before interest and tax minus the interest expense

taxable income=$100 million-$20 million

taxable income=$80 million

taxes=taxable income*tax rate

tax rate=35%

company A's taxes=$80 million*35%

company A's taxes=$28 million

It should be noted that the higher the increase in interest expenses, the higher the tax savings that Airline A would achieve, hence, adding an additional borrowing which costs an extra $20 million in interest means that the company's taxes can be computed as shown below:

taxable income=$100 million-$20 million-$20 million

taxable income=$60 million

taxes=taxable income*tax rate

tax rate=35%

company A's taxes=$60 million*35%

company A's taxes=$21 million

In other words, Airline A would achieve a $7 million savings in taxes since the increase in interest expenses means that taxes decrease from $28 million to $21 million

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Joe worked for 14 hours at Job A and for 16 hours at Job B.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Now it is given that,

Joe works two part-time jobs for a total of 30 hours a week.

Let x be the number hours that Joe worked at job A in a week.

and y be the number hours that Joe worked at job B in a week.

⇒ x + y = 30        ...(i)

Now Job A pays $5.90 per hour,

Therefore,

Amount receive from Job A = 5.9x

And Job B pays $7.20 per hour

Therefore,

Amount receive from Job B = 7.20y

Also it is given that, he work at each job the week that he made $197.80

Therefore,

5.90x + 7.20y = 197.8   ....(ii)

Now multiplying equation (i) by 5.9 we get,

5.90x + 5.90y = 177      ....(iii)

Subtracting equation (ii) and equation (iii) we get,

1.3y = 20.8

Dividing both the side by 1.3 we get,

1.3y/1.3 = 20.8/1.3

Solving we get,

y = 16

Putting the value of y in equation (i) we get,

x + 16 = 30

Subtracting both the side by 16 we get,

x + 16 - 16 = 30 - 16

Solving we get,

x = 14

Thus, we get

x = 14

y = 16

Hence,

Number hours that Joe worked at job A in a week = 14 hours

and,

Number hours that Joe worked at job B in a week = 16 hours

Thus, Joe worked for 14 hours at Job A and for 16 hours at Job B.

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