The y-intercept of the line y=-4 x-7 is
a. -7
c. 4
b. -4
d. 7
B
A
D
C

Gavin already had 12 rolls of towels, and he is buying 3 rolls per week.

Slope tells us the change between two points given, and is shown by  the change in the y coordinate divided by the corresponding change in the x coordinate.

Given that, Gavin is stocking up on paper towel rolls. He already has some at his house, and begins buying more every week at a constant rate. The line y = 3x + 12 represents this scenario.

Here the equation is y = 3x+12

When comparing with standard equation of the line, y = mx+c where m is slope, we get,

m = 3 and c = 12

Therefore, the change is 3, that means, he is buying 3 rolls per week,

and the constant is 12 that tells that he already have 12 rolls in stock.

Hence, a) he is buying 3 rolls every week, b) he has 12 rolls in stock.

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The slope of the equations is equal. Then the lines are parallel to each other.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

y = 2x + 1        ....1

2x - y = 3

y = 2x - 3         ....2

The slope of both equations is 2.

The slope of the equations is equal. Then the lines are parallel to each other.

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Answer:

b=12

Step-by-step explanation:

Answer: (-1,1)

Step-by-step explanation:

since y is equal to 2x+3  you can sub 2x+3 into the y value of 12x+4y=-8

12x+4(2x+3)=-8

Multiply the numbers inside the parentheses using the distributive property

12x+8x+12=-8

Combine like terms

20x+12=-8

Isolate x by moving all other numbers to the right side

Subtract 12 on both sides

20x+12-12=-8-12

20x=-20

divide both sides by 20 to isolate and get the value of x

x=-1

Now that we know the x value substitute the value of x in any of the above equations. I am using y=2x+3

y=2(-1)+3

Multiply the numbers inside the parentheses

y=-2+3

y=1

The x value is -1, and the y value is 1.

Use them as coordinate points

(x,y)

(-1,1)

The solution to the given system of equations is the point (-1, 1) which is determined by the substitution method.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The system of equations is given as:

12x + 4y = −8

y = 2x + 3

To solve this system of equations using the substitution method, you can substitute the second equation into the first equation to eliminate one of the variables.

Substituting y = 2x + 3 into the first equation gives:

12x + 4(2x + 3) = -8

12x + 8x + 12 = -8

20x + 12 = -8

20x = -20

x = -1

Substituting this value of x back into the second equation gives:

y = 2(-1) + 3

y = -2 + 3

y = 1

Therefore, the solution to the system of equations is the point (-1, 1).

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Answer:

Step-by-step explanation:

ok this is hella easy what kind of geometry is this

ok on to the answers

statement 1: angle 1 is a right angle, angle 2 is a right angle

reason 1: given

statement 2: angle 1 is congruent to angle 2

reason 2: all right angles are congruent theorem

second problem

statement 1: angle 1 and angle 2 are vertical angles

reason 1: either say given or shown in diagram (id do both if ur teacher is picky)

statement 2: angle 1 is congruent to angle 2

reason 2: vertical angles are congruent theorem

Here is the two column proof:

    Statement                                        Reason                                              

===================================================

    Statement                                        Reason                                              

Answer:

To simplify the given equation, we can start by using the rules of algebra to rearrange the terms and combine like terms on both sides of the equation. This gives us:

-x - (-4x - 6) = 6

We can then distribute the negative sign on the left side of the equation to get:

-x + 4x + 6 = 6

We can then combine like terms on the left side of the equation to get:

3x + 6 = 6

We can then subtract 6 from both sides of the equation to get:

3x = 0

We can then divide both sides of the equation by 3 to get the final result:

x = 0

Therefore, the simplified form of the given equation is x = 0.

Step-by-step explanation:

The solution is

A) The vertical asymptote of the function f ( x ) is = -3

B) The holes in the graph of f ( x ) = ( 0 , 6 )

C) The horizontal asymptote of the function f ( x ) is = 6

What are Asymptotes?

An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required

There are 3 types of asymptotes

Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero

Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero

Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b

Given data ,

Let the function be f ( x ) = ( 6x² + 6x - 36 ) / ( x² + 3x )

A)

Now , to find the vertical asymptote

To find the vertical asymptote of a rational function, we simplify it first to lowest terms, set its denominator equal to zero, and then solve for x values

So , when x² + 3x = 0

x ( x + 3 ) = 0

So , x + 3 = 0

x = 0 is a hole in the graph

x = -3 is the vertical asymptote

B) The hole in the graph is ( 0 , 6 )

C)

Now , to find the horizontal asymptote

If both the polynomials have the same degree, divide the coefficients of the leading terms

So , 6x² and x² are the polynomials having the same degree

So , the coefficients are 6 and 1

y = (leading coefficient of numerator) / (leading coefficient of denominator)

y = 6 is the horizontal asymptote

Hence ,

A) The vertical asymptote of the function f ( x ) is = -3

B) The holes in the graph of f ( x ) = ( 0 , 6 )

C) The horizontal asymptote of the function f ( x ) is = 6

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Answer:

B. H0 : p = 5.8% H1 : p > 5.8%

The null hypothesis, denoted H0, is a statement that asserts that there is no significant difference between a sample statistic and a population parameter. In this case, the null hypothesis would be that the true percentage of the population that suffers from long-term COVID symptoms is equal to 5.8 percent. This is represented symbolically as H0 : p = 5.8%.

The alternative hypothesis, denoted H1, is a statement that contradicts or negates the null hypothesis. In this case, the alternative hypothesis would be that the true percentage of the population that suffers from long-term COVID symptoms is greater than 5.8 percent. This is represented symbolically as H1 : p > 5.8%.

The equations for parallel lines:

y = -1/2 x - 2  ----- y = -1/2 x + 6

y = 1/2 x + 4   ----- y = 1/2 x - 4

y = 2x -4       -----  y =2/1x + 2

y = 5x + 2     -----  y = 5x - 1

y = 1/5 x + 10 ----   y = 1/5 x + 3

What is slope of line?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

If an equation in the form y = mx + c then m is the slope of the line.

Equation of line               slope          Slope parallel line

y = -1/2 x - 2                        -1/2                        -1/2

y = 1/2 x + 4                          1/2                           1/2

y = 2x -4                                2                            2

y = 5x + 2                               5                           5

y = 1/5 x + 10                          1/5                         1/5

Now identify the lines from the option whose slope are  -1/2,  1/2, 2, 5,  1/5.

The slope of the line y = -1/2 x + 6 is  -1/2.

The slope of the line y = 1/2 x - 4 is  1/2.

The slope of the line y = 2x -4 is 2.

The slope of the line y = 5x + 2  is 5.

The slope of the line y = 1/5 x + 10 is 1/5.

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1) Adam's monthly cash flows are:

2) I would save $300 monthly from the ending cash flow balance for retirement savings.

3) If Adam retires in 35 years and finds an IRA for 4.8%, the future value of their retirement account will be $326,070.43 when they retire.

4) In 35 years, Adam will deposit $126,000 in total to their IRA.

5) The accrued interest from the IRA will be $200,070.43.

The future value represents the balance in Adam's retirement savings account after 35 years of depositing $300 monthly at 4.8% interest.

The future value is computed by compounding the periodic deposits (present values).

Adam's total monthly earnings = $2,080 ($15 x 32 x 52 x 1/12)

Monthly Expenses:

Rent $650

Groceries $325 ($75 x 52 x 1/12)

Utilities $120

Car Insurance $118

Gasoline $130 ($30 x 52 x 1/12)

Miscellaneous $400

Total monthly expenses = $1,743

Ending cash flows = $337 ($2,080 - $1,743)

Retirement period = 35 years

IRA interest rate = 4.8%

Monthly savings = $300

N (# of periods) = 420 months (35 years x 12)

I/Y (Interest per year) = 4.8%

PV (Present Value) = $0

PMT (Periodic Payment) = $300

Results:

Future Value (FV) = $326,070.43

Sum of all periodic deposits = $126,000 ($300 x 420)

Total Interest = $200,070.43

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We know that Martin will need 16.5 gallons of gasoline using mathematical operations.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).

So, each day Martin travels:

12 * 2 / 24 miles from home to work and back home.

As she works for 22 days: 24*22 = 528 miles

So, the equation can be:

32x = 528

x = 528/32

x = 16.5

Therefore, we know that Martin will need 16.5 gallons of gasoline using mathematical operations.

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The starting salary of $31,000 and the annual raise of $3,100 indicates that the series is an arithmetic series and the total salary over a ten-year period is $467,500

An arithmetic series consists of the addition of the terms of an arithmetic progression.

The starting salary offered by the company = $31,000

The amount by which the company raises the salary every year = $3,500

The total salary over a ten year period can be found by expressing the situation using an arithmetic progression formula as follows;

The sum of n terms of an arithmetic progression can be found using the formula;

Sₙ = (n/2)·(2·a + (n - 1)·d)

Where;

Sₙ = The sum of n terms of the series

n = The number of terms in terms in the series

a = The first term of the series

d = The common difference between the terms of the series

The details from the question indicates;

n = 10

a = $31,000

d = $3,500

Therefore; S₁₀ = (10/2) × (2 × 31,000 + (10 - 1) × 3,500) = 467,500

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The length of the arc is = [tex]\frac{2}{27}22^{\frac{3}{2} }[/tex]m

In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.

According to the given information

We can find the length of the arc by

L = [tex]\int\limits^a_b {\sqrt{\frac{dx}{dt} ^{2}+\frac{dy}{dt} ^{2} } } \, dt[/tex]

Find the derivative of x w.r.t to t

dx/dt = [tex]3t^{\frac{1}{2} }[/tex]

Find the derivative of y w.r.t to t

dy/dt = 2

Putting the values in above equation

We get

L = [tex]\int\limits^a_b {\sqrt{\frac{dx}{dt} ^{2}+\frac{dy}{dt} ^{2} } } \, dt[/tex]

L= [tex]\int\limits^2_0 {\sqrt{9t+4} } \, dt[/tex]

L = [tex]\frac{2}{27}(9t+4)^{\frac{3}{2} }[/tex]

limit approaches from 0 → 2

Hence

The length of the arc is = [tex]\frac{2}{27}22^{\frac{3}{2} }[/tex]m

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Answer:

 [tex]\frac{24x+9}{4x}[/tex] or 6 + [tex]\frac{9}{4x}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4x}[/tex] × 8x +3

= [tex]\frac{3}{4x}[/tex] × [tex]\frac{8x +3}{1}[/tex]

= [tex]\frac{3(8x+3)}{4x}[/tex]

= [tex]\frac{24x+9}{4x}[/tex]

or 6x + [tex]\frac{9}{4x}[/tex]

Answer:4

Step-by-step explanation:

The correct option is angles are complementary if their sum is 90º.

When the sum of two angles is 90°, then they are complements of each other and hence called complementary angles.

Given is a statement, If the sum of two angles is 90º, then the angles are complementary.

Rewriting the sentence to check the hypothesis, in it.

It should be this:

The two angles are complementary if the sum of the two angles are 90 degrees.

A.) There are two angles.

While this is a true statement, it's a little too vague to understand. We can eliminate this answer choice.

B.) The sum of two angles is 90 degrees.

This is also a true statement, but it doesn't describe what type of angles sum to 90 degrees, so we can eliminate this as well.

C.) The angles are complementary.

This is similar to answer choice A. It's a little too vague for specific understanding. We can eliminate this answer choice.

D.) Angles are complementary if their sum is 90 degrees.

This is an accurate statement, and provides details to support its claim, also rewriting the original sentences into one properly.

Hence, the correct option is option D.

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The equation (i), (ii), and (v) are the equivalent.

What is the equivalent expression?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

We have,

2 + x = 5

x + 1 = 4

9 + x = 6

x + (-4) = 7

-5 + x = -2

If we take x =3,

the sums would be true.

for the equation (i) take x = 3,

2 + x = 5

2 + 3 = 5

LHS = RHS = 5

for equation (ii) take x = 3,

x + 1 = 4

3 + 1 = 4

LHS = RHS = 4

for equation (iii) take x = 3,

9 + x = 6

9 + 3 = 6

12 ≠ 6

LHS ≠ RHS

for the equation (iv) take x = 3,

x + (-4) = 7

3 + (-4) = 7

-1 ≠ 7

LHS ≠ RHS

for the equation (v) take x = 3,

-5 + x = -2

-5 + 3 = -2

-2 = -2

LHS = RHS = -2

Hence, if If we take x =3, the sums would be true. the equation (i), (ii), and (v) are the equivalent.

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The prove can be shown on the picture attached. And here the describe that support the picture:

Then we can know the 2 triangles are identical or congruent.

The median drawn from the vertex bisects the angle whose two adjacent sides are equal in isosceles and equilateral triangles. In the case of equilateral and isosceles triangles, the median not only bisects the side opposite the vertex, but it also bisects the angle of the vertex.

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Answer:

the answer is 163.375 lbs

Step-by-step explanation:

Rational numbers are numbers that can be expressed in the form of a ratio of two integers, where the denominator is not equal to zero. Examples of rational numbers include fractions such as 1/2, -3/4, 0.5 and -2.5.  The mathematical formula for a rational number is a/b, where a and b are both integers and b ≠ 0.

Solution:

85.4-28.4-215 +972-30.25

=85.4-28.4-21.625+97.75-30.25

=163.375

The quantity of food left at the end of the month is equal to the amount provided by the management at the beginning of the month plus the amount given in the middle of the month less the amount taken in previous weeks.

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The total price for the car is $26000.

The monthly payment is $500.

From the information illustrated, Bank AAA is charging 4% in total fees to borrow money for a car loan and the person want to buy a car that costs $25,000.

The total amount that will be paid will be:

= Amount of car + Interest

= $25000 + ($25000 × 4%)

= $26000

The amount on a 5 year loan will be:

Interest = PRT

= ($25000 × 4% × 5)

= $5000

Total amount to be paid = $25000 + $5000

= $30000

Monthly payment = Total amount / Number of months

= $30000 / 60

= $500

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The required quotient is given as [tex]3x^2-7x+10[/tex] and the remainder term is [tex]-\frac{1}{x+4}[/tex]

In the question, it is asked to determine the quotient of the expression, [tex]\frac{\left[3x^3+5x^2-18x+39\right]}{x+4}[/tex].

It is a method for performing the division of polynomials, with little writing and lesser calculations than complex division.

Here,

As performing synthetic division of polynomials, the terms in the product remaining as fractions will be the remainder of the division while the polynomial is said to be the quotient of the division.
[tex]= \frac{\left[3x^3+5x^2-18x+39\right]}{x+4}\\=3x^2-7x+10-\frac{1}{x+4}[/tex]

Thus, the required quotient is given as [tex]3x^2-7x+10[/tex] and the remainder term is [tex]-\frac{1}{x+4}[/tex]

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Answer:

The inequality which represents the graph shown is -6-y >= x^2 - 7x.

Answer:

[tex]7x+10[/tex]

Step-by-step explanation:

[tex]\frac{1}{3}(9x+12)+4x+6 \\ \\ =3x+4+4x+6 \\ \\ =7x+10[/tex]

Y Intercept is the point where a line or curve crosses the y-axis of a graph or in other words where x=0.

Knowledge of the y-intercept can be used when graphing lines or when writing an equation in slope-intercept form.

Formula to calculate y-intercept.

We get the y-intercept by using the equation of a straight line which is;

y = mx + b

Where;

m is the gradient of the slope

b is the y-intercept.

We can use the following formula to calculate the y-intercept.

y – a = m ( x – b )

a and b being a point on a line.

Example:

Suppose you have a straight line whose gradient is 3 and a point 2,1, calculate its y-intercept.

Since the y-intercept is when x=0, therefore;

y – 2 = 3 ( x – 1 )

y – 2 = 3x – 1

y = 3x – 1

Therefore, the number that has replaced b is -1, which means that -1 is the y-intercept.

There are 100 students and 400 adults.

The 480 tickets sold had a $10 fall in ticket sales.

What is system of equations?

A set of one or more equations involving numerous variables is referred to as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations, or the points where the components of these equations intersect.

Let d be the number of adults and y be the number of students.

⇒ d + s = 500                   ..(1)

The number of adult tickets sold at $6.50 and the number of student tickets sold at $3.50 each.

⇒ 6.5d + 3.5s = 2050         ..(2)

From equation (1) d = 500 - s

Plug the value of d in equation (2)

6.5(500 - s) + 3.5s = 2050

3250 - 6.5s + 3.5s = 2050

3250 - 3s = 2050

3s = 3250 - 2050

3s = 1200

s = 400

Plug s = 400 in d = 500 - s

⇒  d = 500 - 400 = 100

Hence, there are 100 students and 400 adults.

Now,  at one performance there were three times as many student tickets sold as adult tickets.

⇒ s = 3d

3d - s = 0          ..(3)

d + s = 480       ..(4)

⇒ 4d = 480

     d = 120  Adults

Plug d = 120 in equation (4)

120 + s = 480

         s = 480 - 120

         s = 360 Students

The money earned from these 480 people is

120 * 6.5 + 360 * 3.5 = 780 + 1260 = $2040.

$2040 - $2040 = $10

Hence, the 480 tickets sold had a $10 fall in ticket sales.

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The value of θ is 60°.

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin, cos , tan , cosec , sec and cot

Let the angle be θ , that is;

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

Thus, tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data that the angle be represented as θ

Now , we are given that the angle θ is acute

Since Acute angles measure less than 90 degrees

So , the value of θ < 90°

when the value of sec θ = 2

cos θ = 1/sec θ

, cos θ = 1/2

The value of θ when cos θ is 1/2.

when the angle θ is 60°

Therefore ,

the value of θ is 60°

sec 60° = 2

Hence , The value of θ is 60°

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Answer:

Step-by-step explanation:

73 = x + 85

x + 85 = 73

x = -12

(-12) is the value of x.

The equations of the perpendicular lines are matched as follows:

y = 1/3x + 4 → y = -3x - 4.

y = 2/5x - 7 → y = -5/2x + 7.

y = -5/2x + 8 → y = 2/5x - 6.

y = -2x + 6 → y = 1/2x + 3.

y = 7/5x - 9 → y = -5/7x - 11.

If the equations of lines are written in slope-intercept form as y = mx + b, where the slope is the value of m, then the slope of lines that are perpendicular to each other will be negative reciprocal of each other.

For example, if the equation of a line is y = 1/2x + 5, the equation of a line that is perpendicular to it would have a slope of -2.

y = 1/3x + 4 has a slope of 1/3. The negative reciprocal of 1/3 is -3. Therefore, the line that is perpendicular to it would be, y = -3x - 4.

y = 2/5x - 7 has a slope of 2/5. The negative reciprocal of 2/5 is -5/2. Therefore, the line that is perpendicular to it would be, y = -5/2x + 7.

y = -5/2x + 8 has a slope of -5/2. The negative reciprocal of -5/2 is 2/5. Therefore, the line that is perpendicular to it would be, y = 2/5x - 6.

y = -2x + 6 has a slope of -2. The negative reciprocal of -2 is 1/2. Therefore, the line that is perpendicular to it would be, y = 1/2x + 3.

y = 7/5x - 9 has a slope of 7/5. The negative reciprocal of 7/5 is -5/7. Therefore, the line that is perpendicular to it would be, y = -5/7x - 11.

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