18. What is the equation of the line
that passes through the point (-2, 7)
and has a slope of zero?
F X= 7
Gy=-2
H x = -2
) y = 7

The average track laid by the Union Pacific Company per month is 15.1 miles track per month.

"Your question is not complete, it seems to be missing the following information";

the two companies met at Utah, approximately 6 years after the construction began.

The given parameters;

let the average track laid by the Union Pacific Company per month = y

The average track laid by the Union Pacific Company per month is calculated as follows;

(12 x 6 )9.6 + (12 x 6)y = 1775

691.2 + 72y = 1775

72y = 1775 - 691.2

72y = 1083.8

\(y = \frac{1083.8}{72} \\\\y = 15.1 \ miles\ track\ per \ month\)

Thus, the  average track laid by the Union Pacific Company per month is 15.1 miles track per month.

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Answer:

n=1

Step-by-step explanation:

2n+1-1=3-1

2n=2 divide both sides by two

n=1

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The total price of the vehicle would be $18,192.88.

The total deferred price of the car would be $11,191.60.

The length of the financing agreement is 68 months .

The total deferred price after the payments was $19,601.84.

The monthly payments would be $516.92.

Subtotal = Base price + Options + Destination charges

Subtotal = $14,500 + $982 + $592 = $16,074

Dealer preparation = 5% of subtotal

Dealer preparation = 0.05 x $16,074 = $803.70

Sales tax = 7% of subtotal

Sales tax = 0.07 x $16,074 = $1,125.18

Total price = Subtotal + Dealer preparation + Sales tax + Tag fee + Title fee

Total price = $16,074 + $803.70 + $1,125.18 + $145 + $45 = $18,192.88

Tax = 8% of selling price = 0.08 x $8,850 = $708

Tag fee = $130

Title fee = $35

Total amount financed = Amount financed + Tax + Tag fee + Title fee = $7,350 + $708 + $130 + $35 = $8,223

Annual interest rate = 9.5%

Number of years financed = 3

Total finance charges = $8,223 x 0.095 x 3 = $2,341.595

Total financed amount = $8,223 + $2,341.595 = $10,564.595

Monthly payments = Total financed amount / (Number of years financed x 12 months) = $10,564.595 / (3 x 12) = $293.4615

Total deferred price = Selling price + Total finance charges = $8,850 + $2,341.595 = $11,191.595

Total deferred price = $28,000

Down payment = $2,100

Total amount financed = Total deferred price - Down payment = $28,000 - $2,100 = $25,900

Monthly payments = $380

Number of months = Total amount financed / Monthly payments = $25,900 / $380 = 68.16

The financing agreement is approximately 68 months long.

Sticker price = $19,200

Discount = 6% of sticker price = 0.06 x $19,200 = $1,152

Selling price = Sticker price - Discount = $19,200 - $1,152 = $18,048

Sales tax = 8% of selling price = 0.08 x $18,048 = $1,443.84

Total price = Selling price + Sales tax + Tag fee + Title fee = $18,048 + $1,443.84 + $65 + $45 = $19,601.84

Using the formula for monthly payments on a loan:

P = (PV x r x (1 + r)^ n) / ((1 + r) ^ n - 1)

= ($26,515.80 x 0.005265 x (1 + 0.005265) ^ 60 ) / ((1 + 0.005265) ^ 60 - 1) = $516.92

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Answer:

you will want to have a good understanding of these properties to make the problems in ... Here, the same problem is worked by grouping 5 and 6 first, 5 + 6 = 11. ... “three times the variable x” can be written in a number of ways: 3x, 3(x), or 3 · x. ... Use the distributive property to evaluate the expression 5(2x – 3) when x = 2.

y

The distributive property tells us that if were given an expression such as 3(x + 2), we can multiply the 3 by both the x and the 2 to get 3x + 6.

Answer:

x+100

Step-by-step explanation:

x^2-10,000/x-100

x^2-10000 is a difference in squares and can be factored.

x^2-10000 = (x+100)(×-100).

(x+100)(x-100)/(x-100)

(x-100) cancel each other.

x+100 remains.

Answer:An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.

Step-by-step explanation:

Answer: b

Step-by-step explanation:

take 12a common from both sides

Option(b)

Step-by-step explanation:

\({ \purple{ \tt{12a + 24b}}}\)

In this above problem, take 12a as common. Then, the answer will be

\({ \purple{ \tt{12a(1 + 2b)}}}\)

Note that if you take 12a as common, you might think there is no value i.e. zero but if we take any number as common even though there is no number, you should know there is one.

The dimensions of the enclosure that can be erected at minimum cost are 21.25 feet by 42.50 feet

From the question, the given parameters are

Area = 903 square feet

Shape = rectangle

From the question, we understand that:

One side of the area would be enclosed by the external wall of the store

If the dimensions of the area are Length (L) and Width (W), then we have

Area = LW

Perimeter = 2L + W

Rewrite as

A = LW

P = 2L + W

Substitute 903 for A in A = LW

LW = 903

Make W the subject

W = 903/L

Substitute W = 903/L in P = 2L + W

P = 2L + 903/L

Differentiate the equation

So, we have

P' = 2 - 903/L²

Set to 0

2 - 903/L² = 0

So, we have

903/L² = 2

This gives

L² = 903/2

Divide

L² = 451.5

Take the square roots

L = 21.25

Substitute L = 21.25 in W = 903/L

W = 903/21.25

Evaluate

W = 42.50

Hence, the dimensions of the enclosure are 21.25 feet by 42.50 feet

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Answer:

168 yd²

Step-by-step explanation:

1) Dark Grey:

\(A_1 = 2(2 * 9) = 2* 18 = 36\ yd^2\)

2) Light Grey:

\(A_2 = 2(2*6) = 2*12 = 24\ yd^2\)

3) Whitish-Grey:

\(A_3 = 2(6*9) = 2 * 54 = 108\ yd^2\)

4) Total Area:

\(A = A_1 + A_2 + A_3 = 36 + 24 + 108 = 168\ yd^2\)

The inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  

w + l ≥ 17.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Given:

Mackenzie is working two summer jobs, washing cars and landscaping. She must work at least 17 hours altogether between both jobs in a given week.

Total number of hours is w + l and it should be at least 17 hours, (equal to 17 or greater).

We can set inequality as:

w + l ≥ 17

Hence, the inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  w + l ≥ 17.

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Answer:

1 = y^2 - 2

y^2 = 3, so y = -√3

The tangents of the acute angles in the right triangle gives:

tan(G) = 2

tan(H) = 1/2

It should be noted that tangent is the ratio of opposite over adjacent. Thus:

tan(angle) = opposite/adjacent

So for reference angle G, we say,

tan(G) = JH/GJ = 2/1 = 2

We'll treat tan(H) in a similar fashion, but the opposite and adjacent sides swap roles. That means we'll apply the reciprocal to the result above to get 1/2 for tan(H)

So we have this interesting property where

tan(G)*tan(H) = 2*(1/2) = 1

In general,

tan(A)*tan(B) = 1 if and only if A + B = 90 degrees

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The total cost of materials can be found from a list of materials based on the market unit rate.

The correct responses are;

Reasons:

Part A: The given expression representing the purchase is presented as follows;

Purchases = 180·s + 9·p + 36·l

Where;

s = Screws

P = Posts

l = Lumber

The factored expression is found as follows;

Purchases = 180·s + 9·p + 36·l = 9 × 20·s + 9·p + 9 × 4·l, which gives;

180·s + 9·p + 36·l = 9 × (20·s + p + 4·l)

The factored expression is; 9 × (20·s + p + 4·l)

Part B: The costs are;

100 screws  = $6.99

1 posts = $16.40

10 pieces of lumber = $88.20

The materials Roberto need to buy are;

180 screws, which can be obtained by buying 2 cartons of screws.

9 posts, which is obtained by buying 9 pieces of posts.

36 lumber which can be obtained by buying 4 × 10 pieces = 40 pieces of lumber.

Therefore, the, material Roberto needs to buy are;

2 cartons of screws

9 pieces of posts

40 pieces of lumber

Part C: The total cost of the materials are therefore;

2 cartons of screws × $6.99 per carton = $13.98

9 pieces of posts × $16.40 per piece = $147.6

4 Sets of 10 pieces of lumber × $88.20 per set = $352.8

The total cost = $13.98 + $147.6 + $352.8 = $514.38

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Answer:

5(4 + 1)

Step-by-step explanation:

5 times 4 = 20. 5 times 1 =5. Add the 20 and 5 you'll get 25

Answer: 5(4+1)

Step-by-step explanation:

Yes

Answer:

8 10

Step-by-step explanation:

maybe this will help you

Answer: A. x <= -3

Step-by-step explanation:

First, let's begin by simplifying the inequality:

-4x >= 12    ← To isolate the x, we need to divide both sides of the inequality by -4 (we must make this change to both sides so that the inequality is still valid). Remember that when dividing an inequality by a negative number, the orientation of the sign switches (greater than → less than, less than → greater then, etc.). So...

-4x / -4 <= 12 / -4    ← Simplify...

x <= -3

Now, we need to find the right number line representing this inequality.

The number line that fits these criteria would be A.

. Suppose you received $ from your grandmother for your birthday. You spent $ on snacks. Using

addition, how would you write an equation to represent this situation?

+ (−) =

b. How would you model your equation on a number line to show your answer?

Real-world situations can be modeled with equations and represented on a real number line. In this exercise, positive

ten represents the $10 given as a birthday gift because it is a gain. Negative four represents the $4 spent on snacks

because it is a loss. Gaining $10 and then taking away $4 leaves you with $6.

The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.

The expression "F = {(x, y) :  φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function  φ, which takes the variables x, y, and p as inputs.

To fully understand the meaning of F, we need to delve into the function  φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.

For instance, let's consider a specific example where vraphi(x, y, p) is defined  φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.

It is important to note that the specific meaning and implications of F heavily rely on the nature of the function  φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.

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Answer:

B. Positive linear

Step-by-step explanation:

First, this graph is a linear graph because a linear graph is a straight line. The graph in the diagram is also a straight line, so it is linear.
Also, notice how as x increases, y increases. This means that the graph is positive

Answer:

The relationship between the areas of the three squares is that square A plus square B equals the area of square C.

The sum of the square of a and b is equal to the area of square of c

Data;

This theorem is used to calculated a missing side from a right angle triangle when we have the value of at least two sides.

Given that

\(c^2 = a^2 + b^2\)

This indicates a relationship such that the sum of square of two sides is equal to the area of the square of one side. I.e the area of the square of c is equal to the sum of the square of both a and b.

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The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.

The number of terms in a polynomial helps when performing operations like simplification, factoring, or evaluating expressions.

The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.

In order to determine the number of terms in a polynomial, we count the number of distinct algebraic expressions separated by addition or subtraction operations.

In this polynomial, we have:

Term 1: 18x³ (This is the term with the highest degree, which is 3 in this case, and it includes the coefficient 18.)

Term 2: -2x² (This term has a degree of 2 and a coefficient of -2.)

Term 3: 4x (This term has a degree of 1 and a coefficient of 4.)

Term 4: -1 (This is a constant term with a degree of 0.)

We can see that there are four distinct terms separated by addition and subtraction operations:

18x³, -2x², 4x, and -1.

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The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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An isosceles triangle have two equal sides. In this case, it can be either 2 or 12. One of them is correct, and we can use the existence theorem of a triangle. That is:

|L1 - L2| < L3 < L1 + L2

Here, we can choose: L1 = 2 and L2 = 12 (the order doesn't matter)

|2 - 12| < L3 < 2 + 12

10 < L3 < 14

So the remaining side must be greater than 10 and smaller than 14.

The correct lenght of L3 is 12

Option C is the correct answer

The sum total by the given data is equals to $658,880.

We are given that;

Percent=15%

Amount= $98,880

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

To divide by a percentage, we can convert it to a decimal by moving the decimal point two places to the left. This gives us:

15% = 0.15

To divide by 0.15, we can multiply by its reciprocal, which is 1/0.15. This gives us:

$98,880 / 0.15 = $98,880 x 1/0.15

To multiply by 100, we can move the decimal point two places to the right. This gives us:

$98,880 x 1/0.15 x 100 = $658,880

Therefore, by the percentage the answer will be $658,880.

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Answer:

Step-by-step explanation:

A range

Answer:

y = 1.75

x = 1.25

Step-by-step explanation:

Since the triangles have equal angles, you can use ratios to solve for x and y.

For y:

\(\frac{8}{10} =\frac{7}{a} \\8a=70\\a=8.75\)

Subtract 7 from a to find y.

y = 8.75 - 7

y = 1.75

For x:

\(\frac{8}{10} =\frac{5}{b} \\8b=50\\b=6.25\)

Subtract 5 from b to find x.

x = 6.25 - 5

x = 1.25

The car sell for​ in 2012 if a comparable model sold for ​$13,000 in​ 1999 at $19023.58

The Consumer Price Index (CPI) is a measure of the average change overtime in the prices paid by urban consumers for a market basket of consumer goods and services.

Given:

model sold for ​$13,000 in​ 1999

So,

(13000*229.6)/156.9

=2984800/156.9

= 19023.58

Hence, the car would sell at $19023.58.

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Answer:

70

Step-by-step explanation:

70 because as the number of trials increase, the actual ratio of outcomes will converge on the expected ratio.

Answer:

b

Step-by-step explanation:

-3x is the rate of change, so minus 3X= -17/3