Use the Distance Formula to write an equation of the parabola with directrix y=7 and focus (0,−7).

Answer:

y=-3x-2

Step-by-step explanation:

y=mx+b

y=-3x+b

y=3x-2

m is the slope, b is the y intercept

Answer:

y = -3x - 2

Step-by-step explanation:

At first glance, it is clear the slope is negative as the y value decreases as the x value increases.

The rise/run looks to be -3/1, so the slope is -3

The y value at x = 0, or y-intercept, is -2

The correct equation would be y = -3x - 2

The surface area of the net is 45 square inches.

A rectangular prism is a three-dimensional geometric shape that is composed of six rectangular faces, eight vertices, and 12 edges. It is also known as a rectangular parallelepiped or simply a rectangular box. A rectangular prism is different from a cube because its faces are rectangles of different dimensions.

A rectangular prism has several properties that make it useful in mathematics and engineering. Its faces are all rectangles, which means that it has uniform symmetry along two of its axes. It is also a prism, which means that its faces are parallel and congruent, and its lateral faces are all parallelograms.

The volume of a rectangular prism can be calculated by multiplying the length, width, and height of the prism. For example, if a rectangular prism has a length of 4 units, a width of 3 units, and a height of 2 units, its volume would be 4 x 3 x 2 = 24 cubic units. The surface area of a rectangular prism can be calculated by adding up the areas of all of its faces.

Rectangular prisms are used in many real-world applications, such as in architecture, engineering, and manufacturing. They can be used as building blocks for structures and machines, as well as in the design of containers and packaging. Rectangular prisms also have applications in mathematics and computer science, where they are used to model and analyze a variety of problems, such as optimization, data compression, and algorithms.

To find the surface area of the net, we need to find the area of each of the six faces and add them together.

Face 1: 2 in x 2 in = \(4 in^2\)

Face 2: 2 in x 5 in =\(10 in^2\)

Face 3: 3 in x 5 in = \(15 in^2\)

Face 4: 3 in x 2 in =\(6 in^2\)

Face 5: 2 in x 2 in = \(4 in^2\)

Face 6: 2 in x 3 in = \(6 in^2\)

Adding these up, we get:

4 + 10 + 15 + 6 + 4 + 6 = 45

Therefore, the surface area of the net is 45 square inches.

To know more about the area visit:

brainly.com/question/12187609

#SPJ1

Answer:

I am a 4th grader I don't know

Step-by-step explanation:

Answer:

1) y = -1.5x - 1     ||   2) y = -1.5x + 1    ||  3. D ( 2 , -8 )

Step-by-step explanation:

1)

two coordinates: ( 0 , -1 ) , ( 2 , -4 )

slope = ( y2-y1 )÷(x2-x1) = (-4--1)÷(2-0) = -1.5

then find equation using: y - y1 = m ( x - x1 )

                                        : y - - 1 = -1.5 ( x - 0 )

                                        : y = -1.5x - 1

2)

two coordinates: ( 0 , 1 ) , ( -2 , 4 )

slope = ( 4 - 1) ÷ (-2-0) = -1.5

Find equation using y = mx +b ........where m is slope and b is y-intercept

y = -1.5x + 1

3)

y + 8 = 3(x -2 )

y = 3x -14  ..........main equation in slope intercept form.

A)

y = 3(-2)-14

y = -20 .therefore option A is incorrect

B)

y = 3(8)-14

y = 10 .therefore option B is incorrect

C)

y = 3(-8)-14

y = -38.therefore option C is incorrect

D)

y = 3(2)-14

y = 6 -14

y = -8 . therefore it matches and is correct answer.

the line crosses D( 2 , -8 )

As per your questions,

IMAGE 1 :-

The equation is

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

(Explanation attached as 1st image. Check it!)

IMAGE 2 :-

The equation is

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

(Explanation attached as 2nd image. Check it!)

IMAGE 3 :-

When the point is (2,-8)

\(y + 8 = 3(x - 2)\)

\( = > - 8 + (- 8) = 3 \times (2 - 2)\)

\( = > 0 = 0\)

Therefore, (2,-8) is true.

So, the answer is the option (2,-8)

~ Benjemin360

Answer:

the answer is -77 I just looked it up

Answer:

90 minutes

Step-by-step explanation:

it will take twice as long therefore 90 minutes

Answer:

c) 4750

Step-by-step explanation:

Take a calculator and divide it or long division. You get 950.

Answer:

c) 4750

Step-by-step explanation:

c) 4750 is the answer of your question .

hope it is helpful to you

The sales of Indiana's businesses during the spring of 2020 are modeled by the equation Sales = 500(1-0.10)^t, where t is the number of days and sales are in millions of dollars. If sales reach $23.5 million, it will be considered a statewide economic crisis.

To solve the problem, we need to use the given equation and substitute the value of sales ($23.5 million) into it. Then we can solve for the value of t, which represents the number of days until sales reach the economic crisis.

500(1-0.10)^t = 23.5

(1-0.10)^t = 0.047

Taking the natural logarithm of both sides,

ln[(1-0.10)^t] = ln(0.047)

t ln(0.90) = -3.057

t = -3.057 / ln(0.90)

Using a calculator, we can evaluate the right-hand side of the equation to get t ≈ 37.28 days.

Therefore, it will take approximately 37.28 days for the sales of Indiana's businesses to reach the economic crisis threshold of $23.5 million.

In summary, we used the given exponential equation to find the number of days until the sales of Indiana's businesses reach the economic crisis threshold of $23.5 million. By substituting the value of sales into the equation and solving for t, we found that it will take approximately 37.28 days for this critical point to be reached. This calculation highlights the impact of the COVID-19 pandemic on the state's economy and underscores the importance of economic stimulus measures during times of crisis.

Learn more about Equation:

brainly.com/question/29657983

#SPJ11

To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

so the correct answer is A.

A 4(3+6)=12+24

B (4+3)+6=6+(4+3)

C (12+4)+0=12+4

D​ (12+4)+6=12+(4+6)

The exponential function is \(y = 1505.88(0.85)^x\).

The monthly number of defective parts will be less than 500 about 7 months after Jane was hired.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

To model the monthly number of defective parts, we can use an exponential equation of the form:

\(y=a(b)^x\)

Where y is the number of defective parts, x is the number of months after Jane was hired, a is the initial number of defective parts, and b is the common ratio between consecutive months.

To find the values of a and b, use the two data points given -

In the first month, there were 1,280 defective parts, which means that y = 1280 when x = 1.

In the second month, there were 1,088 defective parts, which means that y = 1088 when x = 2.

Substituting these values into the exponential equation -

1280 = a(b)

1088 = a(b)²

Dividing the second equation by the first equation -

1088/1280 = (a(b)²)/(a(b))

0.85 = b

Substituting b = 0.85 into the first equation -

1280 = a(0.85)

1280 = 0.85a

a = 1505.88 (rounded to two decimal places)

So the exponential equation that models the monthly number of defective parts is -

\(y = 1505.88(0.85)^x\)

To find when the monthly number of defective parts will be less than 500, we can set y = 500 and solve for x -

\(500 = 1505.88(0.85)^x\)

Dividing both sides by 1505.88 -

\(0.332 = (0.85)^x\)

Taking the logarithm of both sides (with any base) -

log(0.332) = x log(0.85)

Dividing both sides by log(0.85) -

x = log(0.332) / log(0.85)

x ≈ 6.87

Therefore,  the monthly number of defective parts will be less than 500 about 7 months after Jane was hired.

To learn more about exponential function from the given link

brainly.com/question/12626186

#SPJ1

The solution to the given initial-value problem is:y(t) = (7/4)e^(2t) + (1/4)e^(-2t). The given differential equation is d²y/dt² - 4 = 0.

Given that the differential equation is a second-order linear homogeneous differential equation, its general solution is obtained by solving the characteristic equation m² - 4 = 0. The roots of the characteristic equation are m = ±2.

Thus, the general solution of the given differential equation is y(t) = c₁e^(2t) + c₂e^(-2t), where c₁ and c₂ are constants of integration. To determine the values of c₁ and c₂, initial conditions must be given.

The initial value problem is said to be y(0) = 2 and y'(0) = 3.

Then we have:y(0) = c₁ + c₂ = 2  .............. (1)y'(0) = 2c₁ - 2c₂ = 3  .......... (

2)From (1), we have c₂ = 2 - c₁.

Substituting this in (2), we get:2c₁ - 2(2 - c₁) = 32c₁ - 4 + 2c₁ = 32c₁ = 7c₁ = 7/2

Thus, c₁ = 7/4 and c₂ = 1/4

Therefore, the solution to the given initial-value problem is:y(t) = (7/4)e^(2t) + (1/4)e^(-2t)

To know more about Equation  visit :

https://brainly.com/question/29657983

#SPJ11

The approximate probability of drawing one orange marble and one green marble from a bag containing five red marbles, four orange marbles, one yellow marble, and three green marbles is approximately 0.154.

To find the approximate probability of drawing marbles, we can use the following formula

probability = (number of favorable outcomes) / (total number of outcomes)

We need to find the number of favorable outcomes where one marble is orange and the other is green. We can choose one orange marble from four orange marbles in the bag in 4 ways, and one green marble from three green marbles in 3 ways. So, the number of favorable outcomes is 4 x 3 = 12.

The total number of ways of choosing two marbles from the bag is 13C2, which is the number of combinations of 2 marbles that can be drawn from the 13 marbles in the bag. Therefore, the total number of outcomes is

13C2 = (13 x 12) / (2 x 1) = 78

Thus, the approximate probability of drawing one orange marble and one green marble is

probability = number of favorable outcomes / total number of outcomes = 12/78 ≈ 0.154

Therefore, the approximate probability of drawing one orange marble and one green marble from the bag is approximately 0.154.

To know more about Probability:

https://brainly.com/question/11234923

#SPJ1

Answer:

So the odds of rolling an even number are 3:(6−3)=1:1

Step-by-step explanation:

Answer:

√60 is your right answer

Answer:

the answer is  21600000

Step-by-step explanation:

The expected number of balls in the first bin would be (1/n)^n

It is given that,

The number of balls and bins is same

If so, then there should always be one ball in each container. The likelihood that every ball will land in the first bin is (1/n)^n.

For example -

Let there be three balls and three bins. Put an A, B, and C next to each ball. The bins are marked 1, 2, and 3. Ball A is likely to land in bin 1 with a 1/3 chance. However, there is a 1/3 chance that ball B will land in bin 1, and there is a 1/3 chance that ball C will land in bin 1. As a result, bin 1 should have a value of 1/3 + 1/3 + 1/3 = 1. The expected values of bins 2 and 3 follow a similar rationale.

By the same reasoning, bins 2 and 3 should likewise have anticipated values of 1.

How likely is it that all three balls will fall into bin one?

1/3 x 1/3 x 1/3 = 1/27, or in the general situation, (1/n)^n, which equals (1/3)^3.

Hence, the expected number of balls in the first bin would be (1/n)^n

To learn more about, expected number of balls here

https://brainly.com/question/20262586

#SPJ4

The value of 3! (3 factorial) is 6. Factorial is a mathematical operation denoted by the exclamation mark (!).

It represents the product of all positive integers less than or equal to a given number. For example, 3! (read as "3 factorial") is calculated as 3 × 2 × 1.

To evaluate 3!, we can multiply the positive integers from 1 to 3:

3! = 3 × 2 × 1 = 6

In this case, 3! is equal to 6.

Factorial is commonly used in combinatorics and probability calculations to determine the number of permutations or combinations of a set of objects. It is also used in mathematical calculations involving series expansions, such as Taylor series.

In general, n! (n factorial) represents the product of all positive integers from 1 to n. The value of 0! is defined as 1.

To learn more about factorial, click here: brainly.com/question/31385028

#SPJ11

Answer:

x2 or x square

Step-by-step explanation:

hope it helps

Answer:

5.75 ft

Step-by-step explanation:

12 in = 1 ft

⇒ 9 in = 9/12 = 0.75 ft

⇒ 5 ft 9 in = 5 + 0.75 = 5.75 ft

The alternative hypothesis(h1) says that the treatment causes a change in the scores.

What is a hypothesis test?

In statistics, hypothesis testing involves putting an analyst's presumption about a population parameter to the test. The data type used and the study's purpose will determine the methodology the analyst uses.

Using sample data, hypothesis testing determines whether a claim is plausible. These data could originate from a broader population or a process that creates data.

Hence, the alternative hypothesis(h1) says that the treatment causes a change in the scores

To learn more about hypothesis tests from the given link

https://brainly.com/question/28273511

#SPJ4

Changes in income and the availability of substitutes can influence the demand for books.

The given paragraph discusses the demand function for books and its implications.

a. The demand curve is derived from the demand function QB = 30-3PB, where QB represents the quantity of books purchased and PB represents the price of books. By plotting PB on the vertical axis and QB on the horizontal axis, the demand curve can be visualized.

b. The demand for books is more elastic between PB = 2 and PB = 3 compared to PB = 8 and PB = 9. Elasticity of demand measures the responsiveness of quantity demanded to changes in price. A greater change in quantity demanded for a given price change indicates higher elasticity.

c. An increase in income for the individual, assuming books are a normal good, will shift the demand curve for books to the right. This means that at each price level, the individual will demand a greater quantity of books, reflecting their increased purchasing power.

d. If on-demand movies are considered substitutes for books and the price of on-demand movies declines, it will affect the demand for books. The demand curve for books may shift to the left, indicating a decrease in quantity demanded at each price level, as some consumers may switch to the cheaper alternative of on-demand movies.

Overall, changes in income and the availability of substitutes can influence the demand for books, resulting in shifts or movements along the demand curve.

Learn more about books

brainly.com/question/17061364

#SPJ11

The value of integral ∫ c ( x 2 y 2 z ) d s ∫c(x2 y2 z)ds is 156.864.

To evaluate the line integral ∫c(x^2 y^2 z)ds, we need to parameterise the curve C and then compute the integral along that curve.

The parameterization of C is given by → r ( t ) = ⟨ 2 cos ( 2 t ) , 2 sin ( 2 t ) , 5 t ⟩ r→(t)=〈2cos(2t),2sin(2t),5t〉 for 0 ≤ t ≤ 4 0≤t≤4.

To compute the line integral, we first need to get the unit tangent vector →T(t) of the curve C. The unit tangent vector is :

→T(t) = →r'(t)/|→r'(t)|

Taking the derivative of →r(t) gives:

→r'(t) = ⟨ -4 sin(2t), 4 cos(2t), 5 ⟩So, the magnitude of →r'(t) is:

|→r'(t)| = √( (-4 sin(2t))^2 + (4 cos(2t))^2 + 5^2 ) = √( 16 + 25 ) = √41

Therefore, the unit tangent vector is:

→T(t) = (1/√41) ⟨ -4 sin(2t), 4 cos(2t), 5 ⟩

Now, we can compute the line integral as follows:

∫c(x^2 y^2 z)ds = ∫0^4 (x^2 y^2 z) |→T(t)| dt

Substituting the parameterization and the unit tangent vector, we get:

∫c(x^2 y^2 z)ds = ∫0^4 (4 cos^2(2t) 4 sin^2(2t) 5t) (1/√41) dt

= (20/√41) ∫0^4 (16 cos^2(2t) sin^2(2t) t) dt

Using the identity sin(2θ) = 2sin(θ)cos(θ), we can simplify the integrand as follows:

16 cos^2(2t) sin^2(2t) = 4 sin^2(4t) = 2 (1 - cos(8t))

Substituting this back into the integral, we get:

∫c(x^2 y^2 z)ds = (20/√41) ∫0^4 [ 2 (1 - cos(8t)) t ] dt

Integrating by parts with u = t and dv = 1 - cos(8t), we get:

∫c(x^2 y^2 z)ds = (20/√41) [ t^2/2 - (1/8) sin(8t) ] |_0^4

= (20/√41) [ 8 - (1/8) sin(32) ]

≈ 156.864

Learn more about line integral here, https://brainly.com/question/28381095

#SPJ11

Based on the information provided, the correct statement is:

A. Years of completed schooling increase by 0.073 years for every 10-mile increase in distance from the nearest 4-year college.

The coefficient on distance (β₁) in the regression model represents the change in the dependent variable (years of completed schooling) for each unit increase in the independent variable (distance from the nearest 4-year college), holding other variables constant.

In this case, the coefficient on distance (β₁) is reported as 0.073. This means that for every 1 unit increase in distance (which is 10 miles in this case), the years of completed schooling increase by 0.073 years. Therefore, for every 10-mile increase in distance from the nearest 4-year college, the years of completed schooling increase by 0.073 years.

So, the correct statement is that years of completed schooling increase by 0.073 years for every 10-mile increase in distance from the nearest 4-year college (Option A).

To know more about Coefficient visit-

brainly.com/question/13431100

#SPJ11

Answer:

Step-by-step explanation:

ER=(5) [A single,1-tuple]. You start with 30 eggs. After selling 5 eggs, cooking 10, and frying 10 eggs 5 eggs remain.

PREMISES

ER=(E-S)-(C+F)

ASSUMPTIONS

Let E=the number of eggs at the start (30)

Let S=the number of eggs that were sold (5)

Let C=the number of eggs that were “cooked” i.e., hard-boiled, poached, and so forth (10)

Let F=the number of eggs that were fried (10)

Let ER=the number of eggs that remain having not been sold, cooked, or fried

CALCULATIONS

ER=(E-S)-(10+10)

ER=(30–5)-(20)

ER=25–20

ER=

5 eggs

PROOF

If ER=5, then the mathematic sentence ER=(E-S)-(C+F) returns

ER=(30–5)-(C+F)

5=25-(10+10)

5=25–20 and

5=5 verifies the result ER=5 of the sentence

The account balance in the bank after 5 years is $1,216.65.

An amount of $1,000 is deposited into a bank account that pays 4% annual interest. The amount in the bank account after 5 years can be calculated as follows:

Therefore,

\(A = p(1 + \frac{r}{n} )^{nt}\)

where

Therefore,

p = 1000 dollars

4 = 4 % = 4 / 100 = 0.04

t = 5 years

n = 1

Therefore,

A = 1000(1 + 0.04/1)¹ˣ⁵

A = 1,000(1 + 0.04)⁵

Therefore,

A = $1,216.65

learn more on compound interest here: https://brainly.com/question/16949620

#SPJ1