What is the equation of a quadratic equation with a vertex of (3,5) and a y intercept of (0,12)? Show your work. 

The graph of the linear equality y ≥ 7x - 4 will be a solid line with a y-intercept of negative four and a slope of seven.

Mathematical expressions known as linear inequalities compare two expressions using the inequality symbol. The expression may be either a numerical or an algebraic expression, or it may be both.

Lets see the question

The inequality is expressed as y = 7x - 4.

Taking only the equality sign into account, y = 7x - 4, y = 7x + (-4) —- (1)

Any linear equation in slope-intercept form has the universal form y = mx + c. (2)

From (1) and (2) that mx = 7x, m = 7

Next, take into account the equation y = 7x - 4.

We know that generally for the signs ‘equal to and greater /smaller than', we use a solid line and for the signs ‘greater/smaller than’, we use a dashed line.

So, to graph this we use a solid line.

Now, find the y-intercept.

Put x = 0

y = 7(0) - 4

y = -4

Therefore, the graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.

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Answer:

Step-by-step explanation:

y=kx

(5,1)

1=k*5

1/5=k*5/5

1/5=k

The constant of proportionality between y and x in this graph is  

1/5

Answer:

U={2,3,4,5,7}

C={2,4}

D={2,7}

Now,

a.) CUD

= {2,4}U{2,7}

= {2,4,7}.

again,

b.) CnD

= {2,4}n{2,7}

= {2}.ans

Step-by-step explanation:

U(union) means all of the numbers but not similar one…

n(intersection) means common factors.

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Answer:

800 books

problem solving steps：

adults:60%

young people:5%

children=100%-60%-5%

=35%

35%=280 books

1%=280÷35

=8

100%=800

so,there are 800 books

Answer:

The answer is a^6 b^18

Step-by-step explanation:

The result to the equation is x = 7.

To find the results of the equation √( 2x- 5) 4 = 1, we can break it step by step

Abate 4 from both sides of the equation

√( 2x- 5) = 1- 4

√( 2x- 5) = -3

Square both sides of the equation to exclude the square root

√( 2x- 5))² = (- 3)²

2x- 5 = 9

Add 5 to both sides of the equation

2x = 9 + 5

2x = 14

Divide both sides of the equation by 2

x = 14/2

x = 7

Thus, the result to the equation is x = 7.

Checking the extraneous result

Substituting x = 7 back into the original equation

√(2(7)-5)+4=1

√(14-5)+4=1

√9+4=1

3+4=1

7 = 1

This equation isn't true, which means that x = 7 is an extraneous result.

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Answer:

166 years older.

Step-by-step explanation: Subtract 1751 from 1917

Project's cost at time 0 is $46,272.84

What is profitability index?

Profitability index is the present value of future cash flows divided by the project cost at time 0.

The present value of each future cash flow can be determined using the present value formula of a single cash flow as  below;

PV=FV/(1+r)^N

FV=future cash inflows in years 1-4

r=discount rate=8.5%

N=the year of cash flows, 1 for year 1 , 2 for year 2, 3 for year 3 and 4 for year 4.

PV of future cash flows=$12,150/(1+8.5%)^1+$12,600/(1+8.5%)^2+$15,700/(1+8.5%)^3+$10,200/(1+8.5%)^4

PV of future cash flow=$41,553.01

Profitability index=PV of future cash flows/Project cost

Profitability index= .898

Project cost=unknown(assume it is X)

.898=$41,553.01 /X

X=$41,553.01/ .898

X=project's cost=$46,272.84

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Answer:

21, 24, 27, 30, 33, 36, 39.

Step-by-step explanation:

Answer:

multiples of 3 : 21, 24, 27, 30, 33, 36, 39.

multiples of 2 : 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40

Step-by-step explanation:

An equation for the total cars and trucks for dealership A is: x + y = 164.

An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.

The number of cars that dealership A sold is: 98 cars.

The number of trucks that dealership B sold is: 66 trucks.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:

Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;

x + y = 164.

Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;

2x + 0.5y = 229.

By solving the systems of linear equations simultaneously, we have:

2x + 0.5(164 - x) = 229

1.5x + 82 = 229

x = 98 cars.

For the y-value, we have;

2(98) + 0.5y = 229

0.5y = 229 - 196

y = 33/0.5

y = 66 trucks.

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Answer:

Confidence Interval = (1.41, 1.59)

Step-by-step explanation:

To construct a confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (margin of error * standard error)

where the standard error is equal to the standard deviation divided by the square root of the sample size.

Given the information provided, we can calculate the standard error as:

standard error = 2.16 / sqrt(1370) = 0.058

Then, we can calculate the margin of error as 0.12.

Substituting these values into the formula, we get:

Confidence Interval = 1.5 ± (0.12 * 0.058)

Confidence Interval = (1.41, 1.59)

Therefore, we can interpret the 95% confidence interval as follows: we are 95% confident that the true population mean of the number of days that people feel lonely in the past 7 days is between 1.41 and 1.59. This means that if we were to take many samples of 1370 subjects and compute the confidence intervals for each sample using the same method, we would expect about 95% of the intervals to contain the true population mean.

Answer: 0.03

Step-by-step explanation:

Answer: 15

Step-by-step explanation: 15 ÷ 5 = 3

Answer:

Step-by-step explanation:

In (b) you may be more used to the formula for arc length: \(P=\frac{\theta }{180} \times \pi r\).

The result is the same.

What they asks us to do is to find the midpoint of the line that passes throught the points A and B, this between two point of the line, let's solve it graphically:

Answer:

25.15cm² which means option B 25.13

Because I used 22/7 for pi instead of 3.14

Step-by-step explanation:

radius of the small circle = 2 cm

diameter = 2 x 2 cm = 4cm

this is the radius for the big circle.

Area of big circle = pi × r²

= 22/7 x 4²

= 22/7 x 16

= 50.29cm²

Now area of small circle = pi x small radius²

= 22/7 x 2²

= 22/7 x 4

= 12.57

Now,

The area of shaded region = area of big circle - 2 x small circles

= 50.29 - 2 x 12.57

= 50.29 - 25.14

= 25.15cm²

The probability that a randomly selected point within the square falls in the red shaded square is 1/16

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

Probability = sample space /total outcome

sample space is the area of the red shaded square and the total outcome is the big square.

Area of red shaded square = 1 × 1 = 1unit²

area of the big square = 4 × 4 = 16 units²

Therefore the probability that a point selected falls on the red shaded square

= 1/16

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Answer:

1 and 2 are 8 and 3

Step-by-step explanation:

To make a regular polygon with 96 sides we can take a circle as a starting point and divide it into 96 equal sides.

To create a regular polygon with 96 sides, we must take into account that all its sides must be equal, so we can take a circumference as a starting point. In this case, the circumference has 360°, so we must divide this into 96 parts and the result would be the distance between the edges of the polygon.

In this case, we must make a circle with a protractor and mark every 3.75°, when we have completed this procedure in the entire circumference we will have a regular polygon with 96 sides.

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Answer:168 inches

Step-by-step explanation:

the answer is 168 inches because 28 times 6 is equivalent to 168 and then u have to put the inches on the end.

Answer:

the answer is  87!

Answer: 6561

Step-by-step explanation: 6+3=9

9^4 = 9*9*9*9 = 81 * 81 = 6561

Answer:

if they all have the same angle they r congruent

Step-by-step explanation:

Answer: 1/3

Step-by-step explanation: :)

Answer:

8 x 6 = 48, 48 divided by 2 (x 1/2) = 24 , 24 x 2(there are two triangles) = 48

12 x 10 = 120

8 x 12 = 96

12 x 6 = 72

Now let's add all the given areas:

48 + 120 + 96 + 72 = 336 ft^2 is your answer.

The total time for the trip is:

T =  3mi*( 3/2x).

Where x is the rate at which she comes home.

Remember the relation:

distance = rate*time.

We know that the distance is 3 miles (done twice).

First, the rate is 2x and then the rate is x, then the time it took the first half is:

t = 3mi/2x

And for the coming back:

t = 3mi/x

Then the total time for the trip is:

T =  3mi/2x +  3mi/x = 3mi( 1/2x + 1/x) = 3mi*( 3/2x).

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The equation that shows the point-slope form of the line passing through (3, 2) with a slope of (1/2) is:

y - 2 = (1/2)(x - 3)

In the point-slope form of a linear equation, the formula is y - y1 = m(x - x1), where (x1, y1) represents a point on the line, and m represents the slope of the line. By substituting the given values into the formula, we can determine the correct equation.

In this case, the given point is (3, 2) and the slope is (1/2). Plugging these values into the formula, we get:

y - 2 = (1/2)(x - 3)

This equation represents the line passing through the point (3, 2) with a slope of (1/2). It is in the point-slope form, which allows us to easily determine the equation of a line based on a given point and slope.

Therefore, the correct equation is y - 2 = (1/2)(x - 3).

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Answer: B

Step-by-step explanation: