The city is issuing bonds to raise money for a building project. You obtain a $6700 bond that pays 2% interest annually that matures in 5 years. How much interest will you earn?

Answer:

see explanation

Step-by-step explanation:

ratio required is houses : turbines

let x be the number of turbines required for 26 houses , then

[tex]\frac{6houses}{18turbines}[/tex] = [tex]\frac{26houses}{x}[/tex] ( cross- multiply )

6x = 26 × 18 = 468 ( divide both sides by 6 )

x = 78

78 turbines are required for 26 houses

In order to graph this equation, we first need to find two ordered pairs that are solution to this equation.

To do this, we can choose a value for x and calculate the corresponding value of y.

Choosing x = 0 and x = -1, we have:

Now, graphing the points (0, -8) and (-1, 0) and the line that passes through them, we have:

So the blue line represents the graph of the equation given.

A rectangle is graphed on a coordinate plane. For two of the vertices of the rectangle are (-5,8) and (-5,-6) what is the distance between the two vertices

A 2units

B 4 units

C 10 units or

D 14 units

Find out the distance between the given vertices

we have that

the two coordinates have the same x-coordinate

that means

the distance between the points is the difference of the y-coordinates

8-(-6)=8+6=14 units

Problem N 2

we have that

between -1 and -2 there are 5 spaces

the value of each space is 1/5=0.20

therefore

point A is -1.60

option C

Answer: Point: a zero dimentional object

Ray: a half line

One dimentional figure: a line

Line segment: a finite section of line
Plane: a 2 dimentional figure

Step-by-step explanation:

The time that the tank began leaking water is 12:40am

The time the tank will be empty is  11 : 23 pm.

The function that would determine the amount of water in the tank is a linear function. A linear function is a function that has a single power that is raised to the power of one. When drawn on a graph, a linear function is a straight line.

The first step is to determine the rate of leakage of the tank.

Rate = (water in the tank at 11am - water in the tank at 8:30am) / change in time

(137 - 115) / (11 - 8:30)

22 / 2:30

22 ÷ 2 1/2 hours = 8.8 gallons per hour

Linear function would have this form:

Water in the tank = water in the tank when full - (rate of leakage x number of hours)

137 = 200 - (8.8xh)

137 = 200 - 8.8h

200 - 137 = 8.8h

63 = 8.8h

h = 63 / 8.8

h = 7.16 hours = 7 4/15 hours

8 -  7 4/15 hours = 12 10/15 hours = 12.40am

When the tank is empty:

0 = 200 - 8.8h

200 - 0 = 8.8h

200 / 8.8 = 22.72 = 22 hours 43 minutes

22 hours 43 minutes + 12 : 40M = 11 : 23 pm

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The equation of the line parallel to the first line is y = 3 · x - 9.

(Correct option: B)

Given,

A design engineer is mapping out a new neighborhood with parallel streets. If one street passes through (4, 5) and (3, 2)

To find the equation for a passes through (2, -3).

How to determine an equation of the line parallel to another line

In this question we must derive the equation of the line for a given street and look for another equation of the line parallel to the previous one. Lines are first order polynomials of the form y = m · x + b, where m and b are the slope and the y-intercept, respectively.

Now, According to the question:

Now we present the procedure in detail. First, find the equation of the first line:

5 = 4 · m₁ + b₁           (1)

2 = 3 · m₁ + b₁          (2)

(m₁, b₁) = (3, - 7)

Second, determine the equation of the line parallel to the line found in the previous step: (Please notice that two lines are parallel to each other when they share the same slope but have different y-intercepts)

-3 = 3 · 2 + b₂

b₂ = -3 - 6

b₂ = - 9

Hence, The equation of the line parallel to the first line is y = 3 · x - 9.

(Correct option: B)

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Answer:

$41.50

Step-by-step explanation:

$3.29 per gallon of gas

12.6 gallons of gas

12.6 * 3.29 = 41.45400 ≈ 41.50

he will be charged $41.50

The graph is shifted right to 3 units, then the graph has a horizontal stretch by a factor of 2 and the graph is shifted up 4 units.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The function is:

f(x) = x²

First transformation:

x → (x- 3)

The graph is shifted right to 3 units.

F(x) = (x- 3)²

Second transformation:

F(x) → 2F(x)

The graph has a horizontal stretch by a factor of 2.

h(x) = 2(x- 3)²

Third transformation:

h(x) → h(x) + 4

The graph is shifted up 4 units.

g(x) = 2(x- 3)² + 4

Thus, the graph is shifted right to 3 units, then the graph has a horizontal stretch by a factor of 2 and the graph is shifted up 4 units.

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Answer:

The second one

Step-by-step explanation:

For the given values of x and y, the value of y/x (that represents the slope of the equation) = 3/1, 3/1, 3

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).

The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.

Given are the values of the x and y

y/x represents the slope of the equation,

for x = -1 and y = -3,

y/x = 3/1

for x = 1 and y = 3

y/x = 3/1

for x = 2 and y = 6

y/x = 6/2 = 3

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Answer:

x= 3

Step-by-step explanation:

Add

8

to both sides

3x-8=1

2

Simplify

Add the numbers

3x=9

3

Divide both sides by the same factor

3x=9

4

Simplify

Cancel terms that are in both the numerator and denominator

Divide the numbers

Answer:

x = 3

You first add 8 to both sides:

3x - 8 + 8 = 1 + 8

Simplify:

3x = 9

The divide both side by the same factor:

3x/3 = 9/3

9 divided by 3 is 3 so the solution is:

x = 3

Step-by-step explanation:

Hope it helps! =D

Given: Brian cut

of fishing line from a new reel.

Required: To find how much Brian cut in inches.

Explanation: Since 1 yard is equivalent to 36 inches. Hence we need to multiply by 36 to convert yards to inches.

Hence Brian cut-

Final Answer: Brian cut 147 inches of fishing line from a new reel.

The length of the tape is 3 and it is divided into equal parts or groups. The length of each group is 1/4. This means that the number of groups in 3(the tape) would be

3÷1/4

We can hold 3 and flip the fraction, 1/4. If we flip 1/4, it becomes 4/1 and the division sign becomes multiplication. The expression would be

3 x 4/1 = 12

The correct option is A

ANSWER

EXPLANATION

To find the number of square feet the window requires, we have to find the area of the shape.

The shape given is a kite, and the area of a kite is:

where p and q are the diagonal lengths.

From the question given:

Therefore, the area of the kite is:

That is the number of square feet of glass that the window requires.

Answer:

-44/5   (in decimal -8.8)

By using the secant line formula, the average rate of change of function f(x) on the interval [3, 11] is equal to 4.

In accordance with the statement, we must determine the average rate of change for a given closed interval of the function f(x). Graphically speaking, the average rate of change for this interval is represented by the slope of the secant line passing through the two limits of the interval [a, b], which is found by secant line formula:

m = [f(b) - f(a)] / (b - a)

If we know that a = 3, f(a) = 19, b = 11 and f(b) = 51, then the average rate of change is:

m = (51 - 19) / (11 - 3)

m = 32 / 8

m = 4

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Answer:

HIH

Step-by-step explanation:

HOW ARE

Answer:

unless you are looking for L, then it's

L = 189/d-7

⇒g(f(x)) means that in the place of x in the function g you will plug in the function f.

⇒This means that [tex]2x^{2} -5[/tex] will be plugged in the place of x in 5x+7 and the simplify.

⇒[tex]=5(2x^{2} -5)+7\\\\=10x^{2} -25+7\\=10x^{2} -18[/tex]

⇒Now you have the unknowns The coefficient of the variable [tex]x^{2}[/tex] is 10 and the constant number is -18.

Given the following question:

The family spends 90 dollars at a grocery store each week

The family spends 40 dollars each time they go out to eat.

Part one:

If the family goes out to eat four times they would have spent 250 dollars.

Part two:

The final point on the graph is (6, 330)

Which means if the family goes out six times, the budget is 330 dollars.

So, your answer is 6.

Benji's total score is -2.

If two numbers are negative, their sum will also be negative. When two negative numbers are added together, their value is further diminished, hence the sum of the two negative numbers is always negative.

Given:

Benji has four -0.5 cards.

According to the question, we have to determine his total score which will be equal to adding scores on all four cards.

As we are adding negative scores, upon adding them place a negative sign in front of the sum.

The total score of Benji = (-0.5) + (-0.5) + (-0.5) + (-0.5)

                                        = -2

Therefore, his total score is -2.

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Answer: 67.15

Step-by-step explanation:

A rational number is a number that can be expressed as a ratio of two integers. Integers can be positive or negative. Rational numbers are simply fractions. For example;

-5/2, -1/5, 3/1, 4/5 etc are all rational numbers because we can write them as a ratio of two integers.

Since some of this fractions can lead to both negativa and positive integers, hence rational number is a positive or negative whole number including 0.

Hence all the options are correct since rational numbers are are also repeating decimals

Answer:

x=9

Step-by-step explanation:

is the mean of 4, x, 5, 6, and 1 is 5, then 4+x+5+6+1=5*5=25, so 16+x=25,x=9

The simplification of the number (9-2/square root of 9)⁻² +(1-6)² is found as 25.18.

Simplify simply signifies to make something easier to understand. Simply or simplification in mathematics refers to reducing an expression /fraction /problem to a simpler form. It simplifies the problem by calculating and solving it.

We can —

For the given question;

The expression is given as;

(9-2/square root of 9)⁻² +(1-6)²

This can be written as;

= [(9-2)/√9]⁻² + (1-6)²

Do the prime factorization of √9 = √3×3

= [(9-2)/√3×3]⁻² + (1-6)²

On solving;

= [7/3]⁻² + (-5)²

Taking the reciprocal of first term

= (3/7)² + (-5)²

= (0.42)² + (-5)²

Squaring the values;

= 0.18 + 25

= 25.18

Thus, the result after the simplification becomes 25.18.

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Answer: the train is 230 and the car is 350

Step-by-step explanation: I think so im like 75% sure but that is still a risk so be carful