Write the equation of the parabola that has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f(x)=a(x-h)²+k.

f(x)=

Answer:

........

Step-by-step explanation:

...

....

.....

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We can rewrite the equation of the circle as:

(x + 4)^2 + (y + 4)^2 = 12^2

So the center is (-4, -4) and the radius is 12 units.

For a circle of radius R and center (a, b) the equation is:

(x - a)^2 + (y - b)^2 = R^2

Here we have the equation:

x^2 + 8x + y^2 + 8y - 112 = 0

We can complete squares to get:

(x^2 + 8x) + (y^2 + 8y) - 112 = 0

(x^2 + 2*4*x + 4^2) +  (y^2 + 8y + 4^2) - 4^2 - 4^2 - 112 = 0

(x + 4)^2 + (y + 4)^2 = 112 + 16 +  16 = 144

(x + 4)^2 + (y + 4)^2 = 12^2

So we have a circle of radius of 12 units, with a center at (-4 , -4)

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Answer:

The Horizontal Asymptote is the point (0, a).

The Horizontal Asymptote is the line =

= 0.

Step-by-step explanation:

The following statements are true regarding f(x) = aᵇ:

The Domain of the exponential functions is All Real Numbers.

The Horizontal Asymptote is the line y = 0.

The Range of the exponential functions is f(x) > 0.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

The horizontal asymptote is the horizontal line that the graph of the function approaches as x approaches infinity or negative infinity. In this case, the horizontal asymptote is the line y = 0, which means that as x gets very large, the value of f(x) approaches 0.

The domain of the function is the set of all values of x that can be plugged into the function. For exponential functions, the domain is all real numbers because any real number can be raised to any power.

The range of the function is the set of all possible output values that the function can produce. For exponential functions, the range is f(x) > 0, which means that the function can produce any positive real number as output.

The following conclusions about  f(x) = aᵇ are correct:

All Real Numbers are the domain of exponential functions.

The line y = 0 is the Horizontal Asymptote.

The exponential functions have a range of f(x) > 0.

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in this equation ox is your answer.

According to the plotted graph, the x intercepts are (1,0),(2,0) and (4,0) and the y intercept is (0, -8)

Intercepts:

In the graph theory, the x-intercept is the point where a line crosses the x-axis, similarly the y-intercept is the point where a line crosses the y-axis.

Given,

One factor of the function f(x) = x³ − 7x² + 14x − 8 is (x − 4).

Here we need to identify the x and y intercept of the function through the graph of the function.

Here we have to do the following steps on the graphing calculator, to plot the function,

1) Set the x and y axis values on the graphing calculator.

2) Enter the required function on the input box.

3) Which ever the point that placed on the x axis are the points that refers the x intercept

4) Similarly, which ever the point that placed on the y axis are the points that refers the y intercept.

Now, the graph of the function is plotted and attached below.

Therefore, the x intercept are (1,0), (2,0) and (4,0) and the y intercept is (0,-8)

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The range of the data divided by four gives the standard deviation, which is approximately.

The range of the data divided by four gives the standard deviation, which is approximately. Simply put, that's it. To determine the range, find the highest value—the maximum—and deduct the lowest—the minimum. The range should then be divided by 4.

The range rule states that a sample's standard deviation is roughly equal to one-fourth of the data range.

In order to calculate the standard deviation, we must first determine the mean, take this mean away from each data point, square the differences, add them, divide by one less than the number of data points, and (at the very end) take the square root. The range rule, however, only needs one division and one subtraction.

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Answer:

The F value is used in analysis of variance (ANOVA). It is calculated by dividing two mean squares. This calculation determines the ratio of explained variance to unexplained variance. The F distribution is a theoretical distribution.

Step-by-step explanation:

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The F ratio in ANOVA is the difference between two mean square values. If

Analysis of variance is a collection of statistical models and the estimation procedures that go with them that are used to analyze the differences between means. Ronald Fisher, a statistician, invented ANOVA. The ANOVA test compares more than two groups at the same time to see if there is a relationship between them.

If the null hypothesis is correct, you should expect F to be close to 1.0 most of the time. A high F ratio indicates that the variation among group means is greater than would be expected by chance.

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The time taken for the rocket to reach its maximum height as required in the task content is; 2.25 seconds.

The maximum height reached by the toy rocket is; 88 feet.

It follows from the task content that the maximum height reached by the rocket is to be determined.

The given function is; h (t) = -16 t² + 72t + 7.

Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.

Therefore; at maximum height;

h'(t) = 0

h'(t) = -32t + 72 = 0

-32t = -72

t = -72/-32

t = 2.25 seconds.

Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.

Also, the maximum height reached by the rocket is at; h (2.25);

h(2.25) = -16(2.25)² + 72 (2.25) + 7

= -81 + 162 + 7

= 88.

The maximum height reached is; 88 feet.

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Answer: 11z+2

Step-by-step explanation:

Answer:

88%

Step-by-step explanation:

The solution to inequalities are as follows.

What is inequality equation?

Inequalities are the mathematical expressions during which either side don't seem to be equal. In difference, in contrast to in equations, we tend to compare 2 values. The equal sign up between is replaced by but (or but or equal to), larger than (or larger than or equal to), or not capable sign.

Main body:

A) m-1 <-3

   to solve this we need to take link terms to one side

  = m< -3+1

  = m < -2

B) -4y <-20

  cancelling -ve sign on both sides,

= 4y <20

= y <5

C) 5+b>1

take link terms to one side

b > -4

Hence the graph is as given

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Step-by-step explanation:

Statements                                                Reasons

1. AK - angle bisector                                 1. Given

2. FP perpendicular AK                             2. Given

3. <FAK congr <PAK                                  3. Definition angle bisector

4. Seg AK congr seg AK                           4. Congr of seg's is reflexive

5. <AKF & <AKP are rt. angles                  5. Def perpendicular lines

6. <AKF is congr <AKP                              6. Thrm: Right angles are congr.

7. Triangle KAF congr triangle KAP         7. ASA

8. A_F = A_P                                                    8. Corresp parts of congr tr are

                                                                           congr

Answer:

[tex]\frac{x+4}{8x+8}[/tex]

Answer: 1/(x+2)

Step-by-step explanation:

[tex]\frac{x+4}{x^2+6x+8}\\[/tex]

[tex]\frac{x+4}{(x+2)(x+4)}[/tex]

the x+4 cancel each other so we are left with 1/(x+2)

if the main question was how to foil the denominator x2 + 6x + 8, i can quickly explain that.

x2 + 6x + 8

a2 + bx + c

first step is to multiply the first variable with that last or a * c which in this case would give 1 * 8 = 8

the next step would be to look at the middle number which is b, in our case 6.

so then you look for two number that can multiply to to give 8 as well as add up to 6. With easy guessing one will come up with 4 and 2.

with this values you can impute them directly into the equation as

x^2 +4x +2x+ 8

split the equation then factor

(x^2 +4x) (2x+ 8)

x(x+4) 2(x+4) note that the factored equation must always be the same in the bracket. If they are not the same then you have made a mistake somewhere across the line.

with the results giving (x+2)(x+4)

The procedure to calculate the p-value from z-score depends on one of two choices: one-tailed (which may be Left-tailed or Right-tailed) or two-tailed tests.

A z-table, otherwise termed the standard normal table, provides the area under the curve to the left of a z-score.

The technique for using z-tables to find p-values depends on the test being carried out; which may be; one- or two-tailed test.

For one-tailed tests, the directionality is also a factor.

It therefore follows that;

For a Left-tailed z-test: the p-value = Φ(Zscore)

For a Right-tailed z-test: the p-value = 1 - Φ(z-score).

For a Two-tailed z-test: the p-value = 2 * Φ(−|z-score|).

The procedure described above represents how to calculate p-value from z-score.

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The following formulas can be used to determine the p-value from its corresponding z-score

From the question, the parameters are given as

Also, from the question, we understand that:

The p value depends on the z-score for its own value

There are three types of test for z-score; these test are:

The p-value would assume different value for a z-score when the type of test is different

This means that the p value for z = 0.2 at right tail test is different at a left tailed test.

This means that there are three formulas for calculating the p-value from the z-score, and these formulas are

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The differentiated form of the function with respect to x will be e³ˣ³.9x².

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range. The exponential function is that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x where a is a constant and a>1.

It is given that the function is,

y=e³ˣ³

Differentiate the function with respect to x.

[tex]=\frac{dy}{dx} \\\\ =\frac{d}{dx}\left(\left(e^3\right)^{x^3}\right) \\\\ =e^{3x^3}\frac{d}{dx}\left(3x^3\right) \\\\ =e^{3x^3}\cdot \:9x^2[/tex]

Thus, the differentiated form of the function with respect to x will be e³ˣ³.9x².

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By using the concept of mathematical expression, it is obtained that

(62−42)×3 is represented by  3 times the difference between 62 and 42

First option is correct

What is mathematical expression?

A mathematical expression consist of numbers connected with addition, subtraction, multiplication and division.

Here the given  mathematical expression is (62−42)×3

Here, the signs shown are subtraction and multiplication. So the concept of difference and times will be used here

(62−42)×3  means whole of (62 - 42) is multiplied with 3

So, this is 3 times the difference between 62 and 42

First option is correct

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Correct Question

Which phrase represents this expression?

(62−42)×3

a) 3 times the difference of 62 and 42

b) 3 times the difference of 42 and 62

c) The difference of 62 and the product of 3 times 42

d) The difference of the product of 3 times 42 and 62

The person needs to sell a minimum amount of $550000 to earn $22000.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the income of the person is 4% of the total selling value.

Let the person sells $x to earn $22000, therefore,

4% of x is $22000

Or, 4x/100 = 22000

     4x = 2200000

       x = 550000

Hence, the person needs to sell a minimum amount of $550000 to earn $22000.

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Answer:

y=4x

Step-by-step explanation:

y2-y1/x2-x1

8-4/2-1

4/1

4 is the slope

We can find the intercept by finding when x is equal to zero by continuing the order pairs

(8,2),(4,1),(0,0)

The intercept is 0

Y=mx+b

M-slope

b- y intercept

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Answer:

8(x^2)+172x+920

Step-by-step explanation:

2(2x+20)+6

=4x+46

(4x+46)×(2x+20)

=4x(2x+20)+46(2x+20)

=8(x^2)+80x+92x+920

=8(x^2)+172x+920

The solution to the algebraic problem is [tex]x^{2}[/tex]

What is an Algebraic Equation?

An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.

Solution:

([tex]x^{3}[/tex] – 1) = (x+2)

On dividing ([tex]x^{3} - 1[/tex]) by (x+2)

The first term of the quotient will be x^2 by following the Long Division Method of Algebraic Division.

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Answer:

-8/9

Step-by-step explanation:

(-7/9) /( (-1 1/6) * (-3/4) )   make all fractions improper fractions

(-7/9) / (-7/6 * -3/4)       solve brackets

(-7/9) / (7/8)

(-7/9) * (8/7)

-8/9

Answer:

$5,227.41

Step-by-step explanation:

The compound interest formula is

[tex]A=P(1+\frac{r}{n}) ^{nt}[/tex]

A is the final amount

P is the initial amount

r is the interest rate as a decimal

n is the # of times the interest is applied per time period

t is the # of time periods.

We are given

Note: semi annually is twice per year.

[tex]P=4550[/tex]

[tex]r=0.035[/tex]

[tex]n=2[/tex]

[tex]t=4[/tex]

Lets solve for A.

[tex]A=4550(1+\frac{0.035}{2} )^{2*4}[/tex]

[tex]A=4550(1.0175)^{8}[/tex]

[tex]A=4550(1.14888178)[/tex]

[tex]A=5227.41211244[/tex]

Round to two decimals.

$5,227.41

The settle price at which you will get a demand for additional funds to be posted is $1.4840 per €.

What is contract?

An agreement between parties that results in legal duties for both parties is known as a contract. Mutual consent, demonstrated by a valid offer and acceptance, sufficient consideration, capability, and legality are the fundamental components needed for the agreement to be a legally enforceable contract.

Provided data from the question;

Futures contract to buy in euros = €62,500

Future contract to buy in dollar = $93,750 ( €62,500 × $1.50)

Initial performance of bond = $1,500

Maintenance level = $500

To determine the settle price at which you get a demand for additional funds to be posted =

Future contract to buy in dollar - (initial bond performance - maintenance level) ÷ future contract to in euros

$93,750 - ($1,500 - $500)

= $93,750 - $1,000

$92,750 ÷ €62,500

= $1.484

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The initial population size is 2800

The function represents growth

The percentage through which the population size changes is given as 7%.

The formula is given as

[tex]Po = 2800 (1.07)^t[/tex]

From the formula that we have above, the initial population size is given as 2800.

We have p = P₀(1 + r)^t

where 1 + r = 1.07

We are to find the value of r

r = 1.07 - 1

r = 0.07

Given that the value of r is positive, this is the representation of a growth.

The percentage through which the change would occur = 0.07 x 100

= 7%

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The conversion of .51 kg to milligrams using unit fractions is given by 510,000 mg

Units can be converted from one form to another.

Convert kilogram to milligram:

1000g = 1 kg

1 kg = 1,000,000 mg

That is,

A kilogram is equivalent to one million milligrams.

.51 kg to milligrams

= .51 × 1,000,000

= 510,000 mg

Hence, the conversion of .51 kg to milligrams is 510,000 mg.

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Answer: A and C

d + q = 5 is one correct answer, not 500

0.1d + 0.25q = 5 as this is literally just the equation you are doing.

The distance of the line segment from ( -5,5 ) to ( 3,-1 ) is 10 units

What is the distance of a line between 2 points?

The distance of a line between 2 points is always positive and given by the formula

[tex]D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

Given data ,

Let the two points be A and B

A ( x₁ , y₁ ) = A ( -5 , 5 )

B ( x₂ , y₂ ) = B ( 3 , -1 )

So , the distance between 2 points is given by the formula

[tex]D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

Substituting the values of x₁ , y₁ , x₂ , y₂ in the formula , we get

[tex]D = \sqrt{(-5-3)^{2} + (5-(-1))^{2} }[/tex]

[tex]D = \sqrt{(8)^{2} + (6)^{2} }[/tex]

[tex]D=\sqrt{(64+36)}[/tex]

[tex]D = \sqrt{100}[/tex]

[tex]D= 10 units[/tex]

Hence , the distance of the line is 10 units

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