A parabola has x-intercepts at (3,0) and (9,0) and a maximum at 4. Write the equation of the
parabola in vertex form.
Then, convert the equation of the parabola to standard form.

Answer:

Where is the graph, once you upload it, I will change the answer

Step-by-step explanation:

Answer:

The equation of the line is:

Step-by-step explanation:

Given the points

Finding the slope between the points

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-5,\:8\right),\:\left(x_2,\:y_2\right)=\left(-1,\:9\right)[/tex]

[tex]m=\frac{9-8}{-1-\left(-5\right)}[/tex]

[tex]m=\frac{1}{4}[/tex]

Using the point-slope form of the line equation

[tex]y-y_1=m\left(x-x_1\right)[/tex]

substituting the values m = 1/4 and the point (-5, 8)

[tex]y-8=\frac{1}{4}\left(x-\left(-5\right)\right)[/tex]

[tex]y-8=\frac{1}{4}\left(x+5\right)[/tex]

Add 8 to both sides

[tex]y-8+8=\frac{1}{4}\left(x+5\right)+8[/tex]

[tex]y=\frac{1}{4}x+\frac{37}{4}[/tex]

Thus, the equation of the line is:

Answer:

0 = 20 is false, therefore the system of equations has no solution.

NO SOLUTION

Step-by-step explanation:

Given the system of equations

[tex]\begin{bmatrix}4x+6y=-12\\ 2x+3y=4\end{bmatrix}[/tex]

solving the system by the elimination method

[tex]\begin{bmatrix}4x+6y=-12\\ 2x+3y=4\end{bmatrix}[/tex]

[tex]\mathrm{Multiply\:}2x+3y=4\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:4x+6y=8[/tex]

[tex]\begin{bmatrix}4x+6y=-12\\ 4x+6y=8\end{bmatrix}[/tex]

subtracting the equations

[tex]4x+6y=8[/tex]

[tex]-[/tex]

[tex]\underline{4x+6y=-12}[/tex]

[tex]0=20[/tex]

0 = 20 is false, therefore the system of equations has no solution.

NO SOLUTION

Answer:

65/140

as a percentage is 46.43

hundredth rounding

46.4

Step-by-step explanation:

Answer:

The rate of change is -4.5 and the relation of the table is a linear function

Step-by-step explanation:

Linear function.

A linear function can be identified because the rate of change is constant at every point of its domain.

The graph of a linear function is a straight line with a constant slope.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

We'll show the relation shown in the table is a linear function. We'll calculate the slope for any random pair of points. For example, using (2,83) and (3,78.5):

[tex]\displaystyle m=\frac{78.5-83}{3-2}=-4.5[/tex]

Now for (7,60.5) and (14,29):

[tex]\displaystyle m=\frac{29-60.5}{14-7}=\frac{-31.5}{7}=-4.5[/tex]

Proceeding in a similar way with any pair of points, the slope will always result in the same value, thus the rate of change is -4.5 and the relation of the table is a linear function.

Answer:

with what?

Step-by-step explanation:

Answer:

D= H(w) gets very large

Step-by-step explanation:

Answer:

x1=3     x2=-4

Step-by-step explanation

The value of the x₁ = 3.2, and x₂ = -3.8 if the linear equation in two variables is 3x₁ + 2x₂ = 2, and 5x₁ + 5x₂ = -3.1

It is defined as the group of numerical data, functions, and complex numbers in a specific way such that the representation array looks like a square, rectangle shape.

The determinant in arithmetic is a real number that is a variable of the rows and columns of a square matrix. It lets specifying a few aspects of the matrix and the linear map that the matrix provides.

It is given that:

[tex]\left[\begin{array}{ccc}3&2\\5&5\\\end{array}\right] \left[\begin{array}{ccc}x_1\\x_2\\\end{array} \right] = \left[\begin{array}{ccc}2\\-3\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}3x_1+2x_2\\5x_1+5x_2\\\end{array}\right] = \left[\begin{array}{ccc}2\\-3\\\end{array}\right][/tex]

On comparing:

3x₁ + 2x₂ = 2

5x₁ + 5x₂ = -3

The above two equations represent linear equations in two variables:

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

After solving with substituion method:

x₁ = 3.2

x₂ = -3.8

Thus, the value of the x₁ = 3.2, and x₂ = -3.8 if the linear equation in two variables is 3x₁ + 2x₂ = 2, and 5x₁ + 5x₂ = -3.

Learn more about the matrix here:

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Answer:

there can be 12 identical packages at most. each package will contain:

- 2 coloring books

- 5 crayons

- 7 markers

Step-by-step explanation:

Answer:

[tex]\boxed{x_1 = 5~~or~~x_2 = -5}[/tex]

.

Step-by-step explanation:

[tex]\to y = 0[/tex]

[tex]y = x^2 - 25[/tex]

[tex]x^2 - 25 = 0[/tex]

[tex]x^2 = 25[/tex]

[tex]x = \pm \sqrt{25}[/tex]

[tex]x = \pm 5[/tex]

.

[tex]x = 5[/tex]

[tex]x = -5[/tex]

The point where the reflector meets the lens is ± 5.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, A reflector on the inside of a certain flashlight is a parabola given by the equation y = x² - 25.

Now the points where the reflector meets the lens are,

0 = x² - 25.

x² = 25.

x = ± 5.

learn more about quadratic equations here :

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Answer:

2 and 1 over 12

Step-by-step explanation:

[tex]1 \frac{2}{3} \div \frac{4}{5} \\ \\ = \frac{1 \times 3 + 2}{3} \div \frac{4}{5} \\ \\ = \frac{5}{3} \times \frac{5}{4} \\ \\ = \frac{25}{12} \\ \\ = 2 \frac{1}{12} \\ [/tex]

Answer:

1 penny 3 nickels 2 dimes = 36 cents

quarter

Step-by-step explanation:

Answer:

Answer:

C

is your answer. Glad I could help!

Step-by-step explanation:

3 + 2 = 5 + 14 = 19

A. 18

B. 15

C. 19

D. 11

Answer:

7 red weights and 2 purple

Step-by-step explanation:

Answer:

5 purple weights and 5 red weights

Step-by-step explanation:

Answer:

$1300

Step-by-step explanation:

λ = average = 2 per day, Y denotes the number of breakdowns per day,

But E(Y) = λ, E[Y(Y - 1)] = λ²

E(Y²) = E[Y(Y - 1)] + E(Y), hence:

E(Y²) = λ² + λ

The daily revenue is R=1600−50Y². The expected daily revenue for the extruder E(R) is:

E(R) = E(1600−50Y²) = 1600 - 50E(Y²)

E(R) = 1600 - 50(λ² + λ)

Substituting:

E(R) = 1600 - 50(2² + 2)

E(R) = 1600 - 300 = 1300

E(R) = $1300

Answer:

Yes

Step-by-step explanation:

yes

They both have interior angles of 90-51-39, which automatically makes them similar.  You could also see the dilation factor of .75 based on the 2 sides of a right angle to prove it.

 ΔABC and ΔDEF are similar by AA Similarity Theorem.

   Given in the question,

In ΔABC,

In ΔDEF,

To prove these right triangles similar, we can use AA-Similarity Theorem,

By applying triangle sum theorem in ΔDEF,

m∠D + m∠E + m∠F = 180°

m∠D + 90° + 39° = 180°

m∠D = 51°

Hence, ∠D ≅ ∠A and ∠E ≅ ∠B

       Therefore, ΔABC ~ ΔDEF [By AA Similarity Theorem]

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Answer:

i think B

Step-by-step explanation:

It's the sum of the three masses:

[tex]7.3\cdot10^{22} + 590\cdot10^{22} + 1.3\cdot10^{22} = (7.3 + 590 + 1.3)10^{22} = 598.6\cdot10^{22}[/tex]

Answer:

145°

Step-by-step explanation:

As per the given information: quadrilateral ABCD is a parallelogram.

[tex] m\angle B + m\angle DCB =180\degree \\[/tex]

(adjacent angles of a parallelogram)

[tex] 110\degree + m\angle DCB =180\degree \\

m\angle DCB =180\degree - 110\degree \\

m\angle DCB =70\degree\\

m\angle DCG=\frac{1}{2} m\angle DCB \\(\because GC \: bisects \: \angle DCB) \\

m\angle DCF=\frac{1}{2}\times 70\degree... (\because C-G-F) \\

m\angle DCF=35\degree\\

m\angle BFC = m\angle DCF = 35\degree\\ (Alternate \: \angle s) \\\\

m\angle BFC + m\angle CFA = 180\degree\\ (straight \: line \: \angle s) \\\\

35\degree + m\angle CFA= 180\degree\\

m\angle CFA = 180\degree-35\degree \\\\

m\angle CFA= 145\degree \\\\

\huge\purple {\therefore m\angle GFA = 145\degree} \\(\because C-G-F) \\[/tex]

Answer:

Following are the solution to this question:

Step-by-step explanation:

please find the graph image in the attached file.

Given value:

[tex]AB= c= 1744 \ miles\\\\BC= a= 2451 \ miles\\\\AB= s= 714 \ miles[/tex]

using the law of cosines:  

[tex]\cos A = \frac{s^2+c^2-a^2}{2bc}\\\\[/tex]

        [tex]=\frac{714^2+1744^2-2451^2}{2 \times 714 \times 1744}\\\\= -0.9862[/tex]

[tex]A=cos^{-1} (-0.9862)\\\\A= 170.47^{\circ}[/tex]

[tex]\cos B = \frac{a^2+c^2-b^2}{2ac}\\\\=\frac{2451^2+1744^2-714^2}{2 \times 2451 \times 1744}\\\\= 0.9988\\\\B=cos^{-1} (0.9988)\\\\B= 2.7641^{\circ}\\\\[/tex]

[tex]\cos C = \frac{a^2+c^2-b^2}{2ac}\\\\=\frac{2451^2+1744^2-714^2}{2 \times 2451 \times 1744}\\\\= 0.9988\\\\C=cos^{-1} (0.9988)\\\\C= 2.7641^{\circ}[/tex]

Answer:

(2, -6)

Step-by-step explanation:

First you want to set both equations equal to each other so you can find one of the variables.

y = x^2 + 3x -4

for second equation lets rearrange so we start with y=

x=y-4

add 4 to both sides

4+x = y or y= x+4

since both equations equal y, lets set them equal to each other

x+4 = x^2 + 3x -4

set it equal to 0 by subtracting x and 4 from both sides

x^2 + 2x -8 = 0

factor

(x+4) (x-2) = 0

so x has to be either -4 or 2. We can shortcut and say only B makes sense since x=2.

to double check, plug in x=2 in both equations

y= 2^2 + 3(2) -4 = 4+6 -4 = 6

2 = y -4; y=6

so B is correct.

please give thanks by clicking the heart button, i spent a while :)

Answer:

3.

7d=7x7=49

2g=2x10=20

49-20 = 29

Step-by-step explanation:

4.

bc=8x2 = 16

c^3= 2x2x2 =8

bc - c^3 = 16-8 =8

Answer:

111.2

Step-by-step explanation:

It would just remain 111.2

The square root and the squared cancel out on eachother

For, square roots of number will be what times what gives you that number while squared numbers will give you a number multiplied by utsekf,  

Answer:

The value is  [tex]P( X > 0.50) = 0.089264[/tex]

Step-by-step explanation:

From the question we are told that

   The sample size is  n =  500

   The  population proportion is  p =  0.47  

Generally given that the sample size is sufficiently large , the mean of this sampling distribution is mathematically represented as

        [tex]\mu_x = p = 0.47[/tex]

Generally the standard deviation of the sampling distribution is mathematically represented as

       [tex]\sigma = \sqrt{\frac{p(1- p )}{ n} }[/tex]

=>     [tex]\sigma = \sqrt{\frac{ 0.47 (1-0.47 )}{ 500 } }[/tex]

=>     [tex]\sigma = 0.0223[/tex]

Gnerally the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is mathematically represented as

          [tex]P( X > 0.50) = P( \frac{ X - \mu }{ \sigma } > \frac{ 0.50 - 0.47 }{ 0.0223 } )[/tex]

[tex]\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )[/tex]

=>        [tex]P( X > 0.50) = P( Z> 1.3453 )[/tex]

From the z table  the area under the normal curve to the left corresponding to  1.3453   is

          [tex]P( Z> 1.3453 ) = 0.089264[/tex]

So  

          [tex]P( X > 0.50) = 0.089264[/tex]

Using the normal distribution and the central limit theorem, it is found that there is a 0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean.  

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample proportions of size n of a proportion p has [tex]\mu = p, s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this problem:

The mean and the standard deviation are:

[tex]\mu = p = 0.47[/tex]

[tex]\sigma = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.47(0.53)}{500}} = 0.0223[/tex]

The probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is 1 subtracted by the p-value of Z when X = 0.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.5 - 0.47}{0.0223}[/tex]

[tex]Z = 1.34[/tex]

[tex]Z = 1.34[/tex] has a p-value of 0.9099.

1 - 0.9099 = 0.0901

0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.

A similar problem is given at https://brainly.com/question/24663213

Answer:

It's 3 square units.

Count the "squares" and you get 3 and it's not real units so It's called "Square units".

:)

Answer:

no figures

Step-by-step explanation:

to work with and the answer is can't be determined

Answer:

[tex]f(10) = 173[/tex]

Step-by-step explanation:

Given

Exponential Function

[tex](x_1,y_1) = (3,10.125)[/tex]

[tex](x_2,y_2) = (6,34.2)[/tex]

Required

Determine f(10)

We have that

[tex]y = ab^x[/tex]

First, we need to solve for the values of a and b

For [tex](x_1,y_1) = (3,10.125)[/tex]

[tex]10.125 = ab^3[/tex] --- (1)

For [tex](x_2,y_2) = (6,34.2)[/tex]

[tex]34.2 = ab^6[/tex] ---- (2)

Divide (2) by (1)

[tex]\frac{34.2}{10.125} = \frac{ab^6}{ab^3}[/tex]

[tex]\frac{34.2}{10.125} = \frac{b^6}{b^3}[/tex]

[tex]3.38= b^{6-3}[/tex]

[tex]3.38= b^{3}[/tex]

Take cube root of both sides

[tex]b = \sqrt[3]{3.38}[/tex]

[tex]b = 1.5[/tex]

Substitute 1.5 for b in [tex]10.125 = ab^3[/tex]

[tex]10.125 = a * 1.5^3[/tex]

[tex]10.125 = a * 3.375[/tex]

Solve for a

[tex]a = \frac{10.125}{3.375}[/tex]

[tex]a = 3[/tex]

To solve for f(10).

This implies that x = 10

So, we have:

[tex]y = ab^x[/tex] which becomes

[tex]y = 3 * 1.5^{10[/tex]

[tex]y = 3 * 57.6650390625[/tex]

[tex]y = 172.995117188[/tex]

[tex]y = 173[/tex] -- approximated

Hence:

[tex]f(10) = 173[/tex]

Answer:

90

Step-by-step explanation:

You need to simply add all the given numbers together and enter the missing number that'll make the total 0. So:

-75 + (-25) = -100

-100 + 10 = -90

-90 + 90 = 0

Thus, adding a 90 in the empty box will make it 0.

Answer:

90

Step-by-step explanation:

This is the answer because:

1) -75 + (-25) = -100

2) -100 + 10 = -90

3) -90 + 90 = 0

Therefore, the answer is 90 because whenever a negative number is added with the same poitive number, it beomes a 0.

Hope this helps! :D