Mathematics College

The equation for line A is shown below: Y= -2/3x-4 Line A and Line B are perpendicular, and the point (-2 , 1) lies on Line B. Which equation Below represents line B?

Answers

Answer 1

Answer:

$y = \frac{2}{3}x + \frac{7}{3}$

Step-by-step explanation:

Given

Line A:

$y = -\frac{2}{3}x - 4$

Line B:

$(-2,1)$

Required

Determine the equation of Line B

First, we need to determine the slope of A using

$y =mx + b$

Where:

$m = slope$

By comparison:

$y = -\frac{2}{3}x - 4$

$m = -\frac{2}{3}$

Since A and B are perpendicular:

The slope of B (m2) is:

$m_2 = \frac{-1}{m}$

$m_2 = -1/\frac{-2}{3}$

$m_2 = -1 * \frac{-3}{2}$

$m_2 = \frac{3}{2}$

The equation of B is calculated as thus:

$y - y_1 = m(x - x_1)$

Where

$(x_1,y_1) = (-2,1)$

$m = \frac{2}{3}$

So, the equation becomes

$y - 1 = \frac{2}{3}(x - (-2))$

$y - 1 = \frac{2}{3}(x + 2)$

Open bracket

$y - 1 = \frac{2}{3}x + \frac{4}{3}$

Make y the subject

$y = \frac{2}{3}x + \frac{4}{3} + 1$

$y = \frac{2}{3}x + \frac{4 + 3}{3}$

$y = \frac{2}{3}x + \frac{7}{3}$

Related Questions

How many diagonals will a decatriagon have?

Answers

Answer: 35 diagonals

Step-by-step explanation:

A decagon has (10 2) – 10 = 35 diagonals.

Answer:

35 diagonals.

I Hope it will help you ((:

Would really appreciate help on this statistics problem, 20 points :)

Answers

Answer:

Step-by-step explanation:jed

When solving: 1,175 ÷ 5, using partial quotients, how would you decide which power of 10, when multiplied by 5, should be subtracted first?
I need a step by step example please

Answers

Using partial quotient, the place value while subtracting is determined by the dividend.

The place value should never be more than the dividend not up to a tens place value less than the dividend's place value

How to perform division using partial quotients

divisor dividend quotient multiplication subtraction new dividend

5 1175 200 200 * 5 = 1000 1175 - 1000 = 175

5 175 30 30 * 5 = 150 175 - 150 = 25

5 25 5 5 * 5 = 25 25 - 25 = 0

The quotient is then added as

= 200 + 30 + 5

= 235

Assuming the quotient was written 2. While subtracting, the dividend for the first value (1175) is in thousands. placing the the 2 in thousands makes it more than the dividend hence the 2 should be in hundreds

1175 - 2000 incorrect

1175 - 200 correct

for the second stage

175 - 150 correct (since 150 < 175)

last stage

25 - 25

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100 Points! Geometry question. Find x and y. Photo attached. Please show as much work as possible. Thank you!

Answers

The calculated values of x and y in the figure are x = 2 and y = 4

How to calculate x and y in the figure

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

The figure

Where, we have

equal side lengths

This means that

2y - 1 = 3y - 5

Evaluate

y = 4

Next, we have

x + 3 = 3/2x + 2

So, we have

1/2x = 1

This gives

x = 2

Hence, the values of x and y in the figure are x = 2 and y = 4

Answers

Answer:

D) 48

Step-by-step explanation:

area = length x width x height

8 x 2 x 3

16 x 3 = 48

In the figure below D is the midpoint of segment AB, E is the midpoint of segment BC, and F is the midpoint of segment AC. Find the perimeter of triangle ABC.

Answers

Solution

For this case we can do the following

Perimeter= AB + BC+ AC

We have the following:

BC= 6+6 = 12

AB= 6+6 = 12

And solving for AC we have:

AC= 7.5+ 7.5 = 15

And replacing we got:

Perimeter = 12+12+ 15= 39

Work out the volume of the prism height of 12 4 and five

Answers

The calculated volume of the prism is 702 cubic cm

Finding the volume of the prism

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

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

Answers

Let the cost of 7 pencils be 'x' & the cost of 10 pencils be (7x + 15)/10

According to the Question,

⇒(7x + 15)/10 = x

⇒7x + 15 = x × 10

⇒7x + 15 = 10x

⇒7x - 10x = 15

⇒3x = 15

⇒x = 15/3

⇒x = 5

∴ The cost of a pencil is ₹5

principal: $300 annual interest rate: 5% time: 4 yr

Answers

Answer:

$364.65

Step-by-step explanation:

5% = 0.05 per year

300(1+0.05/1)(1) (4)

= 364.65

A patient is not allowed to have more than 300 milligrams of cholesterol per day from a diet of eggs and meat. Each egg provides 150 milligrams of cholesterol. Each once of meat contains 100 milligrams of cholesterol. Write an inequality that describes the patients dietary restrictions for x eggs and y ounces of meat.

Answers

On solving the provided question, we can say that the equation of inequality will be as follows 150x + 100y $\leq$ 300

What is inequality?

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

A patient is not allowed to have more than 300 milligrams of cholesterol per day from a diet of eggs and meat.

Each egg provides 150 milligrams of cholesterol.

Each once of meat contains 100 milligrams of cholesterol

so, the equation of inequality will be as follows

150x + 100y $\leq$ 300

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A rectangle has a length of 15 centimeters and a width of 7 centimeters. What is the area of the rectangle?

Answers

given:

length= 15cm

width= 7cm

to find:

area of the rectangle.

solution:

area of rectangle= length × width

a= l × w

a= 15 × 7

= 105 cm^2

Answer:

105 cm²

Step-by-step explanation:

The formula to find the area of a rectangle is :

Area = length × width

Given that,

length ⇒ 15 cm

width ⇒ 7 cm

Let us solve it now.

Area = length × width

Area = 15 × 7

Area = 105 cm²

Which of the four Venn diagrams represents this?

Answers

Answer:

I would day option B does

Answer:

A is the correct answer

Step-by-step explanation:

What is the value of x? A pair of intersecting lines is shown. The angle above the point of intersection is labeled left parenthesis 7 x minus 8 right parenthesis degrees. The angle directly opposite below the point of intersection is labeled left parenthesis 6 x plus 11 right parenthesis degrees. (1 point)
A –19
B 125
C 19
D 55

Answers

The value of x in the angles is 19.

How to find angles in intersecting lines?

When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles etc.

Therefore, let's find the value of x in the intersecting lines.

Hence,

7x - 8 = 6x + 11 (vertically opposite angles)

Vertically opposite angles are congruent and they share the same vertex point.

Hence,

7x - 8 = 6x + 11

subtract 6x from both sides of the equation

7x - 8 = 6x + 11

7x - 6x - 8 = 6x - 6x + 11

x - 8 = 11

add 8 to both sides of the equation

x - 8 + 8 = 11 + 8

x = 19

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x-2y what is the coefficient of x

Answers

Answer:

the coefficient of x is an implied 1

any variable that's by itself without a coefficient has an implied 1

Step-by-step explanation:

I hope this helps :)

Which function has a greater maximum?
�
(
�
)
=
−
2
(
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+
4
)
2
+
1
f(x)=−2(x+4)
2
+1f, left parenthesis, x, right parenthesis, equals, minus, 2, left parenthesis, x, plus, 4, right parenthesis, squared, plus, 1
A coordinate plane. The x- and y-axes both scale by one. The graph is the function y equals g of x which is a parabola that opens down. The function increases through negative four, negative five and negative three, negative two. It has a maximum at negative two, one, then the function decreases through negative one, negative two and zero, negative five.

Answers

The function f(x) = $-2(x+4)^2$ + 1 has a greater maximum.

1. The given function is f(x) = $-2(x+4)^2$ + 1.

2. To find the maximum of the function, we need to determine the vertex of the parabola.

3. The vertex form of a quadratic function is given by f(x) = $a(x-h)^2$ + k, where (h, k) represents the vertex.

4. Comparing the given function to the vertex form, we see that a = -2, h = -4, and k = 1.

5. The x-coordinate of the vertex is given by h = -4.

6. To find the y-coordinate of the vertex, substitute the x-coordinate into the function: f(-4) = $-2(-4+4)^2$ + 1 = $-2(0)^2$ + 1 = 1.

7. Therefore, the vertex of the function is (-4, 1), which represents the maximum point.

8. Comparing this maximum point to the information provided about the other function g(x) on the coordinate plane, we can conclude that the maximum of f(x) = $-2(x+4)^2$ + 1 is greater than the maximum of g(x).

9. The given information about g(x) is not sufficient to determine its maximum value or specific equation, so a direct comparison is not possible.

10. Hence, the function f(x) =$-2(x+4)^2$ + 1 has a greater maximum.

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(2a -36)
$(2a - {36)}^{2} $

Answers

Distribute the 5 into the parenthesis:
2
a
−
5
a
−
5

Simplify:

HELP ME PLSSSSSSSSSSSS

Answers

Answer:

Option A

Step-by-step explanation:

Required expression:

8/x + 1

Options:

A. 8/x + 1, correctB. 8x + 1, incorrectC. 8 - x + 1, incorrectD. 8 / (x - 1), incorrect

find the value of x and the measure of angle axc

Answers

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

Bridget Riley was just one of many artists associated with the 1960's 'Op Art' Movement. True or false

Answers

Answer:

True

Explanation:

Bridget Riley was one of the most prominent artists associated with the 1960s 'Op Art' movement, which was an art movement that explored optical illusions and effects to create abstract art that played with the viewer's perception. However, there were many other artists associated with this movement, including Victor Vasarely, Richard Anuszkiewicz, and Yaacov Agam, among others.

please answer the question I give you 50 point

Answers

First, you find the volume of each box
Volume = Length * Width * Height

Box A
V = 13 * 40 * 5
V = 2600 cm^3

Box B
V = 8 * 10 * 25
V = 2000 cm ^3

Box C
V = 11 * 20 * 30
V = 6600 cm ^3

Since 7400, the cubes trying to be packed, is bigger than any of the volumes of the boxes, 2 boxes must be used

The boxes with volumes that add up to a number greater than 7400 are Box C with Box A or B (either works, as long as C is one of them)

The total volume of the boxes together can be found with simple addition

2600 + 2000 + 6600 = 11200 cm ^3

Answer:

First, you find the volume of each box

Volume = Length * Width * Height

Box A

V = 13 * 40 * 5

V = 2600 cm^3

Box B

V = 8 * 10 * 25

V = 2000 cm ^3

Box C

V = 11 * 20 * 30

V = 6600 cm ^3

Since 7400, the cubes trying to be packed, is bigger than any of the volumes of the boxes, 2 boxes must be used

The boxes with volumes that add up to a number greater than 7400 are Box C with Box A or B (either works, as long as C is one of them)

The total volume of the boxes together can be found with simple addition

2600 + 2000 + 6600 = 11200 cm ^3

Mat hits a home run once every ten times at bat, and gets exactly two times at bat in every game. He wants to know the probability that he will hit at least one home run in a single game. Mat can use one of the following simulations to complete this probability. Model A - Use a random number generator to generate 500 two-digit numbers from 00 to 99. Assign "success" to the number value of 1, and count up all the random two-digit numbers that contain a 1. Model B - Use a spinner with ten different colors of equal area. Assign "success" to one of the colors. For one trial, spin the spinner twice. If the spinner lands on the color considered "success", start over. Count the trial if the spinner lands on the color considered "success" or not at all. Repeat this process for 20 trials. Model C - Use a standard six-sided die. Assign "success" to the number 1. For one trial, roll the die twice. If the die lands on 1, start over. Count the trial if the die either lands on 1 or not at all. Repeat this process for 50 trials. is the best simulation for this situation. Using this simulation, the probability that Mat will hit at least one home run in a single game is about .

Answers

Answer:Model A and 19%

Step-by-step explanation:

I saw the explanation on study island

The correct model for the probability is given as follows:

Model B.

The probability that Mat will hit at least one home run in a single game is about 0.19 = 19%.

How to obtain a probability?

A probability is calculated by the division of the number of desired outcomes by the number of total outcomes.

Mat hits a home run once every ten times at bat, and gets exactly two times at bat in every game, hence the total number of outcomes is of:

10² = 100.

This is why Model B is the correct model, as it has two trials of 10 outcomes, and each trial has a 0.1 probability of success.

The probability that he hits no home runs is of:

0.9² = 0.81.

Hence the probability of hitting at least one home run is of:

1 - 0.81 = 0.19 = 19%.

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two mechanics worked on a car . the first mechanic worked 20 hrs and the second worked 15 hrs. together they charged a Total of $1650. what was the rate charged per hour for each menchanic if the sum of the two rates was $95per hour

Answers

answer

20h = 942.857

15h= 707.14

Step-by-step explanation:

Which is the correct trigonometric substitution for evaluating

Answers

The correct trigonometric substitution for evaluating integral ∫√(x² + 64) dx is option B. x = 8 tan θ.

How did we get the correct trigonometric substitution?

To evaluate the integral ∫√(x² + 64) dx using trigonometric substitution, use the substitution x = 8 tan θ.

Let's go through the steps to see how this substitution leads us to the solution:

1. Substitute x = 8 tan θ.

This implies dx = 8 sec² θ dθ.

2. Substitute the expression for x and dx in the integral:

∫√(x² + 64) dx becomes ∫√((8 tan θ)² + 64) * 8 sec² θ dθ.

3. Simplify the expression:

∫√(64 tan² θ + 64) * 8 sec² θ dθ = ∫√(64(sec² θ - 1)) * 8 sec² θ dθ.

4. Further simplify:

∫√(64sec² θ - 64) * 8 sec² θ dθ = ∫√(64sec² θ) * 8 sec² θ dθ.

5. Simplify the expression inside the square root:

∫8sec θ * 8 sec² θ dθ = ∫64sec³ θ dθ.

6. Integrate with respect to θ:

∫64sec³ θ dθ = 64∫sec³ θ dθ.

Now, this integral can be evaluated using standard trigonometric integral identities or integration techniques. However, it's worth noting that the original integral did not involve the variable θ, so we would eventually need to convert the result back to x by substituting x = 8 tan θ.

The correct answer is B. x = 8 tan θ.

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Unitary method A car can cover a distance of 522km on 36litres of disesel. How far can it travel with 14litres,

Answers

Answer:

It can cover 203 km with 14 litres.

Step-by-step explanation:

Given that,

A car can cover a distance of 522km on 36litres of diesel.

522 km = 36 litres

1 l = (522/36) km

We need to find how far can it travel with 14 litres.

We can use the unitary method to solve it.

$14\ L=\dfrac{522}{36}\times 14\\\\=203\ km$

So, it can cover 203 km with 14 litres.

The equation C=24n+2 represents the cost

Answers

Jim did not buy any tickets (n_Jim = 0).

Larry bought 7 more tickets than Jim.

To determine the number of tickets Larry bought more than Jim, we need to find the values of n for Larry and Jim's ticket purchases.

For Larry:

Let's substitute C = $170 into the equation C = 24n + 2 and solve for n:

$170 = 24n + 2

Subtracting 2 from both sides:

$168 = 24n

Dividing both sides by 24:

n = 7

For Jim:

We can calculate the number of tickets Jim bought by subtracting 12 from Larry's number of tickets:

n_Jim = n_Larry - 12

n_Jim = 7 - 12

n_Jim = -5

Since we cannot have a negative number of tickets, we can conclude that Jim did not buy any tickets (n_Jim = 0).

To find the difference in the number of tickets bought, we subtract the number of tickets Jim bought from the number of tickets Larry bought:

n_difference = n_Larry - n_Jim

n_difference = 7 - 0

n_difference = 7

Therefore, Larry bought 7 more tickets than Jim.

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Question

The equation C=24n+2 represents the cost, C, in dollars, of buying n tickets to a play. J $170. How many more tickets did Larry buy than Jim? 12

Emily wants to find out if the carpool line around her school causes too much traffic on neighborhood roads. Which is a valid sample for her survey?

Answers

Answer:

25 families living near the school

Step-by-step explanation:

Answer:

25 families living near the school :D

Step-by-step explanation:

f(x) = x2 + 6x + 4
What is the increasing and decreasing

Answers

9514 1404 393

Answer:

decreasing: (-∞, -3)increasing: (-3, ∞)

Step-by-step explanation:

The leading coefficient is positive, so you know the parabola opens upward.

The ratio -b/(2a) is -6/(2·1) = -3, so you know the axis of symmetry is x = -3. The function will be decreasing from negative infinity to the vertex at x = -3, and will be increasing from there to positive infinity. At the vertex (x=-3), the function is neither increasing nor decreasing.

decreasing: (-∞, -3)increasing: (-3, ∞)

_____

Additional comment

For ax^2 +bx +c, the axis of symmetry is x=-b/(2a). The vertex (turning point) is on the axis of symmetry.

f(x) = x2 + 6x + 4What is the increasing and decreasing

f(x) = 3 x² + 5 x - 7 &
g(x) = x² + 8 x + 10

Asked=
a. f(x) + g(x) =
b. f(x) - g(x) =

Answers

Answer:

4x² + 13x + 3 and 2x² - 3x - 17

Step-by-step explanation:

(a)

f(x) + g(x)

= 3x² + 5x - 7 + x² + 8x + 10 ← collect like terms

= 4x² + 13x + 3

(b)

f(x) - g(x)

= 3x² + 5x - 7 - (x² + 8x + 10)

= 3x² + 5x - 7 - x² - 8x - 10 ← collect like terms

= 2x² - 3x - 17

Need answers for 1 and 2. Please

Answers

Answer:soultion

Step-by-step explanation: solution

What is the Domain and range of (3,4)(5,7)(-3,8)(2,0)(1,3)

Answers

The domain is all x-values.

The range is all y-values.

Domain: 3, 5, -3, 2, 1

Range: 4, 7, 8, 0, 3

Best of Luck!

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