find the equation of a parabola with a focus of (0, -4) and a directrix y=4

Answer:

your answer is -5/9

Step-by-step explanation:

Answer:

given that -7/3×5/21

=-7×5/3×21

=-35/63( divided by 7)

=-5/9

i hope this will help you

First, we can notice that all the optins have the same x values: 0, 1, 2 and 3.

These are at equal differences of 1.

A quadratic relationship has the property that the difference of the differences of subsequent points is constant.

So, to check wheter it is a quadratic relationship, we can calculate the differences between f(1) and f(0), f(2) and f(1) and f(3) and f(2):

And then we make the difference between the first and second differences and between the third and second. if they are equal and difference than 0, it is a quadratic relationship.

For the first, we have:

Now, the difference of differences:

They are equal, so the first one is a quadratic relationship.

The second, we have:

Now, the difference of differences:

They are the same but they are equal to zero, so the second is not a quadratic relationship. This will happen when the first differences are constant, becaise this is a linear relationship. Notice that the fifth also have constant differences, so the fifth is not a quadratic relationship.

For the third, we have:

e have:

Now, the difference of differences:

They are equal so, the third is also a quadratic relationship.

Answer:

39<3t+3

-3 -3

36<3t

÷3 ÷3

12<t

According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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\(\text{ Hello there! :)}\)

\(\large\boxed{w(h(x)) = 4x+ 7}\)

\(w(h(x) = \\\text{Substitute in the equation of h(x) into "x" of the equation w(x):}\\\\w(h(x)) = 4(x + 1) + 3\\\\\text{Simplify:}\\\\w(h(x)) = 4x + 4 + 3\\\\w(h(x)) = 4x + 7\)

The set of points that lies on the graph of the function is A, {(0, 0), (-1, -1), and (1, 1)}.

This can be verified by plugging the points into the equation y = x. When x = 0, y = 0. When x = -1, y = -1. Finally, when x = 1, y = 1. Therefore, all three points lie on the graph.

To verify this further, we can calculate the slope of the line using two points. The slope of the line is calculated by taking the difference in the y-values and dividing by the difference in the x-values. For example, to calculate the slope between the points (0, 0) and (-1, -1), we take the difference in the y-values (-1 - 0) and divide it by the difference in the x-values (-1 - 0). This results in the slope being -1. Since the slope is -1, this means that the points are lying on the graph of the function  y = x.

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Answer:

The set of points that lies on the graph of the function is A, {(0, 0), (-1, -1), and (1, 1)}.

This can be verified by plugging the points into the equation y = x. When x = 0, y = 0. When x = -1, y = -1. Finally, when x = 1, y = 1. Therefore, all three points lie on the graph.

To verify this further, we can calculate the slope of the line using two points. The slope of the line is calculated by taking the difference in the y-values and dividing by the difference in the x-values. For example, to calculate the slope between the points (0, 0) and (-1, -1), we take the difference in the y-values (-1 - 0) and divide it by the difference in the x-values (-1 - 0). This results in the slope being -1. Since the slope is -1, this means that the points are lying on the graph of the function  y = x.

Step-by-step explanation:

Complete Question

In 2015 as part of the General Social Survey, 1127 randomly selected American adults responded to this question: “Some countries are doing more to protect the environment than other countries. In general, do you think that America is doing more than enough, about the right amount, or too little?” Of the respondents, 514 replied that America is doing about the right amount. What is the 95 % confidence interval for the proportion of all American adults who feel that America is doing about the right amount to protect the environment.

Answer:

The 95% confidence interval is   \( 0.427  <  p <  0.4852 \)  

Step-by-step explanation:

From the question we are told that

   The sample size is  n = 1127

    The number that America is doing the about the right amount is k =  514

 Generally the sample proportion of the number that say america is doing about the right amount is mathematically represented as

              \(\^ p = \frac{k}{n}\)

=>          \(\^ p = \frac{514 }{ 1127}\)

=>          \(\^ p = 0.4561\)

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as

     \(E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } \)

=>   \(E =  1.96 * \sqrt{\frac{ 0.4561  (1- 0.4561)}{1127} } \)

=>   \(E =  0.0291  \)

Generally 95% confidence interval is mathematically represented as  

      \(\^ p -E <  p <  \^ p +E\)

=>   \( 0.4561 -0.0291  <  p <  0.4561 +0.0291 \)

=>   \( 0.427  <  p <  0.4852 \)  

This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

Ratio refers to the quantitative relationship between two or more quantities, expressing the proportion of one quantity to the other(s). It is typically expressed as a fraction, where the numerator represents one quantity, and the denominator represents the other quantity.

For example, the ratio of the number of boys to the number of girls in a class of 30 students might be expressed as 2:3, which means there are 20 girls and 10 boys in the class. Similarly, the ratio of the length to the width of a rectangle might be expressed as 4:3, indicating that the length is four times greater than the width.

The ratio of sheep to horses is 4:1, which means that for every 4 sheep on the farm, there is 1 horse. We can also say that the total ratio of sheep and horses on the farm is 4+1=5.

To express the relationship between the chickens and the sheep, we need to use the fact that there are 32 chickens and 12 sheep on the farm. We can write this as a ratio:

\(chickens : sheep = 32 : 12\)

We can simplify this ratio by dividing both sides by 4:

\(chickens: sheep = 8: 3\)

This means that for every 8 chickens on the farm, there are 3 sheep.

To determine the number of horses on the farm, we can use the fact that the total ratio of sheep and horses is 5. We know that the ratio of sheep to horses is 4:1, so we can write:

\(sheep : horses = 4 : 1\)

We can simplify this ratio by dividing both sides by 4:

\(sheep : horses = 1 : 0.25\)

This means that for every 1 sheep on the farm, there are 0.25 horses. To find the total number of horses, we can multiply the number of sheep by 0.25:

\(12 * 0.25 = 3\)

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Answer:

Step-by-step explanation:

We will write a proportion to solve this.

\(\frac{0.347}{1} = \frac{18,400}{y}\)

0.347y = 18,400 (which makes sense, since 18,400 is 34.7% of the total number of employees)

Divide by 0.347 to get y (the total number of employees) as 53025.9365994. Since you cannot have parts of a person, we round this to 53,026.

Sara should expect a paycheck of $91.80 from her first full of work.

In the question, we are given that Sara just started her first job as an assistant at an after-school child care center. She works 12 hours a week and makes $9 per hour. She has been told that 15% of her paycheck will be deducted for federal, state, and local taxes.

We are asked for the amount that Sara should expect her paycheck of, from her first full week of work.

The time for which Sara works weekly = 12 hours.

The per hour earning of Sara = $9.

Thus, the total earnings after working for 12 hours at the rate of $9 per hour is 12*$9 = $108.

Now, the deduction is given to be 15%.

Thus, the total deduction = 15% of $108 = $16.20.

The amount on the paycheck = The total earnings less the deduction,

or, the amount on the paycheck = $108 - $16.20 = $91.80.

Thus, Sara should expect a paycheck of $91.80 from her first full of work.

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Answer:

y =  0.7(x^2 - 64x - 576)

Average rate of change = -49.

Step-by-step explanation:

As the x intercepts are -8 and 72 we can write the equation

y = a(x + 8)(x - 72)     where a is some constant to be found.

As it passes through point  (62, -490) we have, substituting:

-490 = a(62+8)(62-72)

-490 =  - 700a

a = 0.7

So the equation of the parabola

y = 0.7(x + 8)(x - 72) or

y =  0.7(x^2 - 64x - 576).

Average rate of change between x = -8 and x = 2

=  [0.7(2+ 8)(2 - 72) -  0.7(-8+8)(-8-72)] / (2 - -8)

= -490 - 0 /10

= -49

Area of rectangular prism: Base x Height.

so 3x1/3x2/5=0.4 0r 2/5

If a parallelogram is (x + 5) cm long and (x-8) cm wide. The perimeter is: 4x - 6 cm.

The length of all four sides of a square constitutes its perimeter whereas the circumference of a circle which is also known as the perimeter is the distance around it.

One pair of opposite sides lengths are determined by (x + 5) cm and the other pair's length is determined by (x - 8) cm.

Let x represent the  perimeter P of the parallelogram:

P = 2(x + 5) + 2(x - 8)

Simplify

P = 2x + 10 + 2x - 16

P = 4x - 6

Therefore  we can conclude  that the perimeter  of x is 4x - 6 cm.

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The complete question is:

A parallelogram is (x+5)cm long and (x-8)cm wide. Find the perimeter of the parallelogram.

Answer:

He needs to deposit N76800 now.

Step-by-step explanation:

The amount of money is compound interest after t years is given by:

\(P(t) = P(0)(1+r)^t\)

In which P(0) is the initial amount of money invested and r is the interest rate, as a decimal.

25% compound interest so that after 3 years to buy a car for N150000.

This means that:

\(t = 3, P(t) = 150000, r = 0.25\). So

\(P(t) = P(0)(1+r)^t\)

\(P(t) = P(0)(1+0.25)^t\)

\(P(t) = P(0)(1.25)^t\)

\(150000 = P(0)(1.25)^3\)

\(P(0) = \frac{150000}{(1.25)^3}\)

\(P(0) = 76800\)

He needs to deposit N76800 now.

The probability of picking the title that is letter j is 4/25 in fraction and in percent is 16%. we are more likely to pick a tile that is the letter from the first bag.

The probability of picking a letter tile that is the letter from the first bag is given as and from the second bag, it is 4/25.

To write the probability of picking a tile that is the letter j as a fraction and a percent, we can use the formula:

Probability = Number of desired outcomes / Total number of possible outcomes

For the second bag, the number of desired outcomes (the number of letter j tiles) is 4 and the total number of possible outcomes (the total number of tiles) is 25. Therefore, the probability of picking a tile that is the letter j from the second bag is:

Probability = 4 / 25

To write this as a percent, we can multiply by 100:

Probability = 4 / 25 * 100%

Probability = 16%

Comparing the probabilities, we can see that the probability of picking a letter tile that is the letter from the first bag is higher (since it is given as ) compared to the probability of picking a tile that is the letter j from the second bag, which is 16%.

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Answer: no one cares

Step-by-step explanation:

Dy/dx = (dy/dt)/(dx/dt) denotes the slope of the tangent line of a parametric curve whose parametric equations are x = /(t) and y = g(t). Wherever dy/dt is zero and dx/dt is zero, a parametric curve has a horizontal tangent.

The x and y coordinates are defined as functions of t when parametric form is used to represent angles: Plot the entire circle by using the equations x = r cos t and y = r sin t. Polar equations are the name given to these parametric equations.

The given x=1+12+ dx=dt 0+12(1) =12

Parametric y Curve is as follows: ts-t dy 5t-1 dt z = ts+t dz dt 5t +1 (dz, dy, dz) = (12, 5t-1, St+1) dt 7 dt dt x = 13 =) When, 1+12 t = 13 12

(x(t), y(t), and z(t)) = (13,0,2) + + (12, 4, 6) x(t), y(t), and 2(t)) = (13+12t, ut, 2+ 6+) x(t) = 13+12t, y(t) = ut, 2(t).

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Full Question = Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

x = 1 + 12 t , y = t5 − t, z = t5 + t; (13, 0, 2)

x(t), y(t), z(t) =

Answer:

The answer is D.

Step-by-step explanation:

Just took the test. Got 100%.

The provided statement states that the equation's slope intercept form is y = -2x + 1.

A line's slope is the measure to the amount y increases when x increases by a specific amount. The a line's slope describes its steepness or the rate at which y climbs as x rises. The slope is consistent wherever along the line (the same).

The following is a representation of the slope intersect form equation:

y = mx + b

where

m = slope

b = y-intercept

Consequently, using the known locations,

(3, -5)(-2, 5)

m = 5 - (-5) / -2 - 3 = 10 / - 5 = -2

Consequently, let's use b to find (3, -5)

y  = -2x + b

-5 = -2(3) + b

-5 = -6 + b

b = -5 + 6

b = 1

y = -2x + 1

The following is how we can employ the equation to work out whether x = 1 and x = 2:

x = 1

y = -2(1) + 1 = -1

x = 2

y = -2(2) + 1 = -3

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The complete question is-

Complete the slope-intercept form of the linear equation that represents the relationship in the table.

ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

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

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

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

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

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

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

Answer:

25

Step-by-step explanation:

a2+b2=c2

3^2+4^2=c^2

9+16=25

25^2=625

Sqrt of 625 = 25

Answer:

x = 5

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 4² + 3² = 16 + 9 = 25 ( take the square root of both sides )

x = \(\sqrt{25}\) = 5

In the simple random sample, the probability that at least half of the students have brown eyes is 0.400

Probability is defined as the chance of occurrence of an event.

Probability is defined as follows:

P(E)=\(\frac{no of required outcome}{total of possible outcomes}\)

The given parameters are:

The sample size= 30 students

Number with brown eye=40%

40% x 30 = \(\frac{40}{100} * 30\)

=12

This means that there 12 students out of 30 that have brown eyes.

Applying the probability formula

\(\frac{12}{30}\)= 2/5

In conclusion 0.400 of the students have brown eyes.

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Answer:

why in kilometers? 87.3 km/h

answer:

c on edg

explanation:

sjdcnwdjcn

Given the equations a × b = 5742 × 6368, a × c = 5748 × 6362, and c × b = 5738 × 6372, we need to determine the relationship between the three variables a, b, and c.

By comparing the given equations, we notice that the numbers on the right-hand side of each equation are very close to each other, differing only by small amounts. This suggests that a, b, and c are approximately equal.Since a × b, a × c, and c × b involve the same numbers with slight variations, we can conclude that a, b, and c are all very close in value.

Therefore, the inequality we can infer from this information is a ≈ b ≈ c, indicating that a, b, and c are approximately equal.

In simple terms, based on the given equations, it suggests that the values of a, b, and c are very similar or approximately equal to each other.

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a.) The independent variable is the different types of music

b.) The dependent variable is the impact of listening felt by the rats

c.)An extraneous variable is the length of the maze.

d.) The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

An independent variable is defined as the type of variable that cannot be manipulated by a researcher and isn't affected by what is being measured.

A dependent variable is the variable that can be manipulated by a researcher and is affected by what is being measured.

For question a.)

The independent variable is the different types of music

For question b.)

The dependent variable is the impact of listening felt by the rats

For question c.)

An extraneous variable is the length of the maze.

For question d.)

The control group is the rat in the quite room while the experimental groups are the ones in the maze listening to classical music, and listening to heavy metal music.

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