Oak and Maple streets are parallel to each other. Main Street has a traffic
light at (5, 1) and is perpendicular to Oak and Maple. What is the equation
of the line representing Main Street?
Oak St.: y =
A. Y
1
22
+3 Maple St.: y = 22
C. y = -2x + 11
B.y=2x-9
D. y = -2x + 15
+6

Answers

Answer 1

The equation of the line representing Main Street is option C. y = -2x + 11

How did we arrive at this equation?

The slope of the parallel lines is ½. The Main Street is perpendicular to Oak and Maple. So, the slope of Main Street is -2.

[The product of slopes of perpendicular Lines is -1.)

y - 1 = -2 (x -5)

y - 1 = -2x +10

y = -2x + 10 + 1

y = -2x + 11

Therefore, the best choice is option C. y = -2x + 11

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Since Main Street is perpendicular to Oak and Maple, its slope will be the negative reciprocal of the slope of Oak and Maple. Let's first find the equation of Oak Street.

We don't have enough information to determine the equation of Oak Street, so we need to make an assumption about its equation. Let's assume that Oak Street passes through the point (0,3) and has a slope of 2 (since the options suggest that Oak Street has a positive slope).

Using the point-slope form of a line, we have:

y - 3 = 2(x - 0)

y - 3 = 2x

y = 2x + 3

Now we can find the slope of Maple Street by noticing that it is parallel to Oak Street. Since parallel lines have the same slope, Maple Street also has a slope of 2.

To find the equation of Main Street, we need to use the fact that it passes through the point (5,1). Using the point-slope form of a line, we have:

y - 1 = -1/2(x - 5)

y - 1 = -1/2x + 5/2

y = -1/2x + 7/2

Therefore, the equation of the line representing Main Street is y = -1/2x + 7/2. The answer is (D).

Related Questions

Graphing Geometry. Show work

Answers

A graph of the reflection of line segment AB is shown on the coordinate plane below.

What is a reflection across the x-axis?

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative.

Furthermore, a reflection across the line y = x would interchange (switch) the x-coordinate and y-coordinate and this is represented by the following transformation rule:

(x, y) → (y, x)

Ordered pair A = (4, -1) → Ordered pair A' = (-1, 4).

Ordered pair B = (4, 5) → Ordered pair B' = (5, 4).

In this exercise, we would use an online graphing calculator to plot the image of line segment AB after a reflection about the line y = x.

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At the time of her grandson's birth, a grandmother deposits $14,000 in an account that pays 4.5% compounded
monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits
or withdrawals are made during this period?
i Click the icon to view some finance formulas.
The value of the account will be $
(Round to the nearest dollar as needed.)
4

Answers

Answer:

The value of the account will be $5,628

Step-by-step explanation:

Step-by-step explanation:

we know that

The compound interest formula is equal to

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

substitute in the formula above

therefore

The value of the account will be $5,628

The formula v= √√2gh gives the velocity v, in feet per second, of an object after it falls h feet accelerated by gravity g, in feet
per second squared. If g is approximately 32 feet per second squared, find how far an object has fallen if its velocity is 96 feet
per second.

Answers

We can rearrange the formula to solve for h:

v = √√2gh

Squaring both sides: v^2 = 2gh

Dividing both sides by 2g: h = v^2 / 2g

Substituting v = 96 ft/s and g = 32 ft/s^2, we get:

h = (96 ft/s)^2 / (2 × 32 ft/s^2)

h = 288 ft

Therefore, the object has fallen 288 feet.

Please help me who knows how to do this

Answers

X^2 - x - 12

Step 1: X^2+3x-4x-12

Step 2: (X^2+3x)+(-4x-12)

Step 3: X(x+3)-4(x+3)

Answer: (x-4)(x+3)

Rebecca invests 600 into an account with a 2.7% interest rate that is compounded quarterly. How much money will she have in this account if she keeps it for 10 years

Answers

The accrued value of the account in 10 years is $641.75

Determining the accrued value of the account in 10 years

From the question, we have the following parameters that can be used in our computation:

Rebecca invests 600 in an account2.7% interest compounded quarterly

Using the above as a guide, we have the following:

Amount = P * (1 + 0.25r)ᵗ

Where

P = Principal = 600

r = Rate = 2.7% = 0.27

t = time = 10

Substitute the known values in the above equation, so, we have the following representation

Amount = 600 * (1 + 0.25 * 0.27)¹⁰

Evaluate

Amount = 641.75

Hence, the amount is 641.75

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Find f(−3), f(0) and f(1) for the following function.
f(x)=2x

Answers

Answer:

-6, 0, 2

Step-by-step explanation:

f(x)=2x

note: putting anything in the f(x) parentheses replaces x in the function with that value

so,

f(-3) = 2(-3) = -6

f(0) = 2*0 = 0

f(2) = 2(2) = 4

A store has 300 televisions on order, and 90% are high definition. How many televisions on order are high
definition? You may find the bar model useful in completing this problem.
20% 30% 40%
70%
0%
0
10%
30
The store has
50% 60%
high-definition televisions on order.
80%
90%
100%
300

Answers

Answer:

90% of 300 = .90 × 300 = 270 high- definition televisions on order.

Solve the equation for the indicated variable

X= (simplify your answer)

Answers

B = (715x) / (h^2)

Step 1: Get rid of the denominator by multiplying both sides by h^2

(B)(h^2) = 715x

Step 2: Isolate x by dividing both sides by 715

(Bh^2) / 715 = x

Answer: x = Bh^2 / 715

Hope this helps!

1. Which of the following is a set or not?

(a) A=Set of tall man
(b) B=Set of beautiful women
(c) C=Set of tall students of class 10
(d) D=Set of counting number
(e) E=Set of good students
(f) F=Set of yellow roses

Answers

Answer:

Step-by-step explanation:
Set of tall students of class 10 is a set. Thus, option C is the correct answer.

A set is defined as objects or things that can be justified as similar things combined together and grouped together.

The other sets are not specified. When we look at option A it is said that all the men are tall so they have a common factor i.e. they are tall but could have been more specified. Also in option B it is said that all the women are beautiful, here the common factor is beautiful but it could have been more specified. Similarly option d, option e and option f are also not specified.

When we look at option c, here it specified that the tal students are of class 10 and so I consider option "c" is the correct answer.

To learn more about sets,

9. (a) The scale model of the rocket stood 54 inches high. What was the height of the actual rocket?
(b) Find the height of the actual rocket in feet.
10. The volume of the rocket in problem 9 is how many times the volume of the model?

Answers

The actual rocket height is 1080 inches and the height of the actual rocket is 90 feet.

How to calculate the value

If the 1/20 scale model of the rocket stands 54 inches high, we can find the height of the actual rocket by multiplying the height of the model by 20:

Actual rocket height = 54 inches x 20 = 1080 inches

In order to convert inches to feet, we divide by 12:

Actual rocket height = 1080 inches / 12 = 90 feet

Therefore, the height of the actual rocket is 90 feet.

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The 1/20 scale model of the rocket stood 54 inches high What was the height of the actual rocket?

(b) Find the height of the actual rocket in feet.

Anna baked 4 batches of cookies with c cookies in each batch she then ate 8 cookies there were 72 cookies left after Anna ate her cookies

Answers

The expression for the number of cookies Anna has left is [tex]3c - 8[/tex].

What does an expression means?

An expression refers to statement that have minimum of two numbers or variables or both and an operator connecting them.

The total number of cookies Anna baked is:

= 3 batches * c cookies/batch

= 3c cookies

After eating 8 cookies, Anna has left:

= 3c cookies - 8 cookies

So, the expression for the number of cookies Anna has left is [tex]3c - 8[/tex].

Full question "Anna baked 3 batches of cookies with c cookies in each batch she then ate 8 cookies. How many cookies does anna have left write your answer as an expression.

Answers

Answer:

S = 2π(14^2) + 2π(14)(154)

= 2π(196) + 2π(2,156)

= 4,704π = 14,778.1 ft^2

Using 3.14 for π:

S = 4,704(3.14) = 14,770.6 ft^2

The table represents the quadratic functions f(x) and g(x).

x f(x) g(x)
−8 16 4
−4 4 1
0 0 0
4 4 1
8 16 4

What transformation of f(x) will produce g(x)?
g of x equals one fourth times f of x
g of x equals f of the quantity of one fourth times x end quantity
g(x) = 4f(x)
g(x) = f(4x)

Answers

The transformation of f(x) that will produce g(x) is given as follows:

g(x) = f(x)/4.

How to obtain the function g(x)?

If we observe at the table, we have that each value of g(x) is one fourth of the value of the function f(x).

Hence the transformation of f(x) that will produce g(x) is given as follows:

g(x) = f(x)/4.

The transformation means that the function g(x) is a vertical compression by a factor of 4 of the function f(x).

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3d *5d*2=?
Please what is 3d times 5d times 2

Answers

Answer:

[tex]30d^2[/tex]

Step-by-step explanation:

It’s due tomorrow I really need help

Answers

Answer:

Step-by-step explanation:

As the steps imply,

Step 1 is to first convert the 3.5% (0.035) and then multiply it by 16 to find out by how many grams the amount should decrease (0.035 * 16 = 0.56). Step 2 is to subtract this amount from 16 to find the amount remaining after one hour (16 - 0.56 = 15.44). Step 3 is to convert 4.25% to a decimal (0.0425) and multiply it by the amount remaining at the end of one hour to find out by how many grams this amount should decrease after two hours (0.0425 * 15.44 = 0.6562)Step 4 finally is to subtract this amount from 15.44 to find the amount remaining after two hours (15.44 - 0.6562 = 14.7838)

Seven days a year, Tiger Stadium becomes the fifth largest city in the state of Louisiana. Over 92,000 fans pack the stadium to watch the Tigers play. After the game, if the fans leave at a rate of 10% per minute, how long will it take before the stadium is half empty?

1. Find the data using at least 10 numbers in the x column.
2. Create a scatter plot. Label the graph and show increments.
3. Write an exponential equation.
4. Interpret the meaning of the "a" and "b" in your function y=ab^x including the units.
5. Find out how long it will take before the stadium is half empty and all the way empty.

Answers

1. To find the data, we can use the formula:

y = 92000(0.9)^x

where y is the number of fans remaining in the stadium after x minutes.

Using this formula, we can plug in x values from 0 to 30 (or more) to generate a table of values:

| x | y |
|------|---------|
| 0 | 92000 |
| 1 | 82800 |
| 2 | 74520 |
| 3 | 67068 |
| 4 | 60361 |
| 5 | 54325 |
| 6 | 48892 |
| 7 | 43903 |
| 8 | 39313 |
| 9 | 35082 |
| 10 | 31174 |

2. Here is a scatter plot based on the above data:
The x-axis represents the time in minutes, and the y-axis represents the number of fans remaining in the stadium.

3. The exponential equation that best fits the data is:

y = 92000(0.9)^x

where y is the number of fans remaining in the stadium after x minutes.

4. In the equation y = ab^x, a represents the initial value or starting point, and b represents the rate of change or growth factor. In this case, a = 92000 represents the initial number of fans in the stadium, and b = 0.9 represents the rate at which the number of fans decreases per minute. The units of a are fans, and the units of b are fans per minute.

5. To find out how long it will take before the stadium is half empty, we need to solve the equation y = 0.5a for x:

0.5a = 92000(0.9)^x

0.5(92000) = 92000(0.9)^x

0.5 = 0.9^x

Taking the logarithm of both sides, we get:

log(0.5) = x log(0.9)

x = log(0.5) / log(0.9)

x ≈ 7.72 minutes

Therefore, it will take approximately 7.72 minutes for the stadium to be half empty.

To find out how long it will take for the stadium to be completely empty, we need to solve the equation y = 0 for x:

0 = 92000(0.9)^x

Taking the logarithm of both sides, we get:

log(0) = x log(0.9)

This equation has no real solution, which means that the stadium will never be completely empty (in theory). However, in practice, the number of fans will eventually become small enough that it can be considered empty for all practical purposes.

Help please!!!!
Whoever answers right gets brainliest!

Answers

Answer:

Step-by-step explanation:

To solve this problem you have to use this formula [tex](\frac{b}{2})^{2}[/tex] it. So in this case b is the term next to the x term. This number is 10. So all we have to do is insert it into the formula. This would give us:

[tex]=(\frac{10}{2})^{2}\\\\=(5)^{2}\\\\= 25[/tex]

The constant term is 25.

Could I get Brainilest, please? I'm trying to get to the expert level

What is the equation through the points: (-7, -3), (1, 2)
ASAP please

Answers

The equation of the line passing through the points (-7, -3) and (1, 2) is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].

What is the equation of the line?

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

First, we determine the slope of the line.

Given the two points are (-7, -3) and (1, 2)

We can find the slope of the line by using the slope formula:

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values, we get:

m = (2 - (-3)) / (1 - (-7))

m = 5/8

Using the point-slope form, plug in one of the given points and slope m = 5/8 to find the equation of the line.

Let's use the point (-7, -3:

y - y₁ = m(x - x₁)

[tex]y - (-3) = \frac{5}{8}( x - (-7) ) \\\\y + 3 = \frac{5}{8}(x + 7 )\\\\y + 3 = \frac{5}{8}x + \frac{35}{8} \\ \\y = \frac{5}{8}x + \frac{35}{8} - 3\\\\y = \frac{5}{8}x + \frac{11}{8}[/tex]

Therefore, the equation of the line is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].

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WILL AWARD BRAINLIEST!!
The base of a right prism ABC is an isosceles triangle with AB = BC and m∠ACB 35°. The diagonal of lateral face ABA is 18 cm and m∠BAB = 50°. Find the volume of the prism. Round your answer to the nearest cm

Answers

Answer:

351 cm^3

Step-by-step explanation:

The base of a right prism ABC is an isosceles triangle with AB = BC and m∠ACB 35°. The diagonal of lateral face ABA is 18 cm and m∠BAB = 50°. Find the volume of the prism. Round your answer to the nearest cm

ChatGPT

Let AB = BC = x be the base of the isosceles triangle ABC. Then, the third side AC is:

AC = 2x * sin(35°)

Using the sine rule in triangle ABA, we have:

AB / sin(50°) = 18 / sin(80°)

Solving for AB, we get:

AB = 18 * sin(50°) / sin(80°)

The height of the prism is AB * cos(35°). Therefore, the volume of the prism is:

V = (1/2) * x^2 * 2x * sin(35°) * AB * cos(35°)

Substituting the values we have calculated, we get:

V = (1/2) * x^2 * 2x * sin(35°) * [18 * sin(50°) / sin(80°)] * cos(35°)

V ≈ 351 cm^3

Therefore, the volume of the prism is approximately 351 cubic centimeters.

what is the probability that either event will occur

Answers

The probability that either event will occur is 7/25

What is probability?

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100% in percentage.

Probability = sample space /Total outcome

P(A or B) = P(A) +P(B) -P(A and B)

The total element = 25+5+15+5 = 50

therefore total outcome = 50

P(A) = 25/50

P(B) = 15/50

P(A and B) = 5/40

Therefore P(A and B) = 25/50+15/50 - 5/50

= 35/50 = 7/25

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Which number is irrational?

0.020202
0.8
0.333...

Answers

All the numbers are rational numbers.

We have,

Rational numbers are those numbers that are terminating and recurring non-terminating.

Irrational numbers are those numbers that are non-terminating and non-recurring.

The numbers are:

0.020202

This is non terminating recurring number.

It is a rational number.

0.8

This is a terminating number.

It is a rational number.

0.020202

This is non terminating recurring number.

It is a rational number.

Thus,

All the numbers are rational numbers.

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The height y(in feet) of a ball thrown by a child isy=−114x2+2x+3

where x is the horizontal distance in feet from the point at which the ball is thrown.

(a) How high is the ball when it leaves the child's hand? (Hint: Find y
when x=0)
Your answer is y=____

(b) What is the maximum height of the ball? _____

(c) How far from the child does the ball strike the ground?_____

Answers

(a) When the ball is thrown, x = 0. Therefore, we can find the height of the ball when it leaves the child's hand by substituting x = 0 into the equation:

y = -114(0)^2 + 2(0) + 3
y = 3

So the ball is 3 feet high when it leaves the child's hand.

(b) The maximum height of the ball occurs at the vertex of the parabola. We can find the x-coordinate of the vertex using the formula:

x = -b/2a

where a = -114 and b = 2. Substituting these values, we get:

x = -2/(2*(-114)) = 0.0088

We can find the maximum height by substituting this value of x into the equation:

y = -114(0.0088)^2 + 2(0.0088) + 3
y ≈ 3.036

So the maximum height of the ball is approximately 3.036 feet.

(c) To find how far from the child the ball strikes the ground, we need to find the value of x when y = 0. We can solve the equation for x:

-114x^2 + 2x + 3 = 0

Using the quadratic formula, we get:

x = (-2 ± sqrt(2^2 - 4*(-114)*3))/(2*(-114))
x = (-2 ± sqrt(9252))/(-228)

We can ignore the negative root since the ball is moving in the positive x-direction. Simplifying the expression for the positive root, we get:

x = (-2 + sqrt(9252))/(-228) ≈ 0.232

So the ball strikes the ground approximately 0.232 feet away from the child.

50 Points! Solve the equation or inequality. Please show as much work as possible. Photo attached. Thank you!

Answers

The equation 5ʷ ⁺ ³ = 17 when solved for w is approximately w = 0.41

Solving the equations or inequalities for w

From the question, we have the following parameters that can be used in our computation:

5ʷ ⁺ ³ = 17

Take the logarithm of both sides of the equation

So, we have

w + 3 = ln(17)/ln(3)

Evaluate the quotient on the left side of the equation

This gives

w + 3 = 2.59

So, we have

-3 + w + 3 = 2.59 - 3

Evaluate

w = 0.41

Hence, the equation when solved for w is approximately w = 0.41

Answers

The area of a shape is calculated by calculating the amount of space on the shape

How do you find area?

By definitinon, the area of a shape is the amount of space on the shape

using the above as a guide, we have the following:

Area of rectangle = Length * WidthArea of square = Length²Area of triangle = 1/2 * base * heightArea of circle = π * radius²Area of parallelogram = base * height

There are several formulas to calculate area

The formula to use is dependent on the shape whose area is being calculated

This means that the area of trapezoid cannot be calculated using the area of parallelogram

Answers

The value of the variable w is 56

What are algebraic expressions?

Algebraic expressions are described as expressions that are composed of terms, variables, factors, coefficients and constants.

Also, algebraic expressions are made up of mathematical or arithmetic operations, such as;

AdditionBracketSubtractionParenthesesMultiplicationDivision

From the information given, we have the algebraic equation as;

w - 54 = 2

To determine the value of the variable, we take the steps;

collect the like terms

w = 2 + 54

Now, add the values

w = 56

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solve for x, neg x over 4 = 12 A 48 or B -3 or C 3 or D -48?

Answers

The solution for x is -48, the answer is D) -48.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It represents a value that can change based on the values assigned to the variables.

Starting with:

x:4 = 12

Multiplying both sides by -1 gives:

(-x÷4) = -12

Simplifying the left side:

x÷4 = -12

Multiplying both sides by 4 gives:

x = -48

Therefore, the solution for x is -48, the answer is D) -48.

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The earrings that Mrs.Moore wants to buy are $55.00. She won’t buy them until they are at least 45% off. What is the most that Mrs.Moore is willing to spend?

Answers

Answer:

$30.25

Step-by-step explanation:

55% of 55$ is $30.25. she wants 45 % off of 55$. which is $24.75. 55-24.75 is 30.25

$30.25

since it's 45% off, you need to subtract 45% from 100%

100%-45%=55%

then turn the % into a decimal

55%/100=0.55

now multiply the original price by 0.55

0.55*55=30.25

A radioactive substance decays at a continuous rate of 14.4 % per day. After 15 days, what amount of the substance will be left if you started with 140 mg? (a) First write the rate of decay in decimal form. r = (b) Now calculate the remaining amount of the substance. Round your answer to two decimal places.

Answers

Answer:(a) The rate of decay is 14.4% per day, which can be written as a decimal by dividing by 100: r = 0.144.

(b) The formula for continuous decay is given by:

A = A₀ * e^(-rt)

where A is the remaining amount of the substance after time t, A₀ is the initial amount, r is the rate of decay, and e is the mathematical constant approximately equal to 2.71828.

Plugging in the given values, we get:

A = 140 * e^(-0.144*15)

A = 140 * e^(-2.16)

A ≈ 47.23

Therefore, after 15 days, approximately 47.23 mg of the radioactive substance will be left, rounded to two decimal places.

Step-by-step explanation:

Solve the following quadratic equation by completing the square. Simplify the solutions and rationalize denominators, if necessary.

3x^2−30x=−2

Answers

The solutions to this quadratic equation are x = √(73/3) + 5 or x = -√(73/3) + 5.

What is a quadratic equation?

In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

3x² - 30x = -2

By dividing all through by 3, we have:

x² - 10x = -2/3

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 10x + (-10/2)² = -2/3 + (-10/2)²

x² - 10x + 25 = -2/3 + 25

x² - 10x + 25 = 73/3

By simplifying, we have;

(x - 5)² = 73/3

x = √(73/3) + 5 or x = -√(73/3) + 5

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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42

Answers

The solution for x in the equation (x – 7)^2 = 36 are x = 13 and x = 1

Solving for x in the equation

We can solve for x by taking the square root of both sides of the equation:

(x – 7)^2 = 36

Taking the square root of both sides:

x - 7 = ±6

Adding 7 to both sides:

x = 7 ± 6

Therefore, the values of x are:

x = 7 + 6 = 13

x = 7 - 6 = 1

So the correct answers are x = 13 and x = 1. The values x = -29 and x = 42 are not solutions to the equation.

Oak and Maple streets are parallel to each other. Main Street has a traffic light at (5, 1) and is perpendicular to Oak and Maple. What is the equation of the line representing Main Street? Oak St.: y = A. Y 1 22 +3 Maple St.: y = 22 C. y = -2x + 11 B.y=2x-9 D. y = -2x + 15 +6

Answers

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Oak and Maple streets are parallel to each other. Main Street has a traffic
light at (5, 1) and is perpendicular to Oak and Maple. What is the equation
of the line representing Main Street?
Oak St.: y =
A. Y
1
22
+3 Maple St.: y = 22
C. y = -2x + 11
B.y=2x-9
D. y = -2x + 15
+6