What is the value of x?
Pythagorean theorem

3. Graph the given quadratic function in the factored form as shown below.

4. The quadratic equation in vertex form, given the vertex (-1,3) and passes through (1, -5), is y = -2(x + 1)² + 3.

The given quadratic function in factored form is y = (x - 3)(x + 1).

Graph of the given quadratic function in the factored form as shown below.

Zeros: The zeros of the function occur when y = 0.

So the zeros of the function are x = 3 and x = -1.

Axis of Symmetry:  

The axis of symmetry is x = (3 + (-1)) / 2 = 1.

Vertex:

The vertex is (1, -4).

Y-intercept:

The y-intercept is (0, -3).

Domain: The domain of a quadratic function is all real numbers, so the domain is (-∞, ∞).

Range: Since the coefficient of the x² term is positive, the parabola opens upward. Therefore, the range is y ≥ -4.

Write the quadratic equation of the following in vertex form: vertex (-1,3) and passes through (1, -5)

Using the given information, the vertex form equation can be written as:

[tex]y = a(x - (-1))^2 + 3[/tex]

To find the value of 'a,' we can substitute the coordinates (1, -5) into the equation:

-5 = a(1 - (-1))² + 3

-5 = a(2)² + 3

-5 = 4a + 3

-8 = 4a

a = -2

Plugging the value of 'a' back into the equation, we get the quadratic equation in vertex form:

y = -2(x + 1)² + 3

Therefore, the quadratic equation in vertex form, given the vertex (-1,3) and passes through (1, -5), is y = -2(x + 1)² + 3.

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Answer:

The sequence converges

Step-by-step explanation:

Given the sequence Un = 10n-6/2n-3

To determine whether the sequence converges or diverges, we will have to take the limit of the sequence as n goes large.

[tex]\lim_{n \to \infty} \left\{\frac{10n-6}{2n-3}\right}\\[/tex]

Divide through by n

[tex]= \lim_{n \to \infty} \left\{\frac{10n/n-6/n}{2n/n-3/n}\right}\\= \lim_{n \to \infty} \left\{\frac{10-6/n}{2-3/n}\right}\\= \left\{\frac{10-6/\infty}{2-3/\infty}\right}\\= \frac{10-0}{2-0}\\= 10/2\\= 5[/tex]

Since the limit of the sequence gives a finite value, hence the sequence converges

Answer:

2564

Step-by-step explanation:

Andre draws this tape diagram for 3 divided by 23:

Andre says that 3 divided by 23 = 413 because there are 4 groups of 23 and 13 left. Do you agree with

Answer:

step 2

Step-by-step explanation:

he was not supposed to multiply by x

he was supposed to combine like terms

add -2x and 4x and add 6 and 5

Using trigonometric functions, it is found that the correct option regarding the appropriate function is:

B) the sine function unreflected

The most famous are the sine and cosine, which give information about the angles.

In this problem, the rider is at the bottom of the Ferris wheel at t = 0, hence f(0) = 0, which is true for the sine function, which means that option B is correct.

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Answer:

Answer is C, the cosine function reflected about its midline

Step-by-step explanation:

Answer:

The simplified form is [tex]x^{\frac{2}{3} }[/tex]

Step-by-step explanation:

So before solving this question we need to know that.....

[tex]\sqrt[6]{x}[/tex] = [tex]x^{\frac{1}{6} }[/tex]

(proof)

[tex]\sqrt[6]{x}[/tex] = [tex]x^{\frac{1}{6} }[/tex]

[tex](\sqrt[6]{x}) ^{6}[/tex] = [tex](x^{\frac{1}{6} })^{6}[/tex]

x = x

So now we can rewrite the question as.........

[tex](\sqrt[6]{x} )(\sqrt[6]{x} )(\sqrt[6]{x} )(\sqrt[6]{x} ) = (x^{\frac{1}{6} }) (x^{\frac{1}{6} }) (x^{\frac{1}{6} }) (x^{\frac{1}{6} }) = x^{\frac{4}{6} } = x^{\frac{2}{3} }[/tex]

Answer:

A

Step-by-step explanation:

x^2/3

Answer: they started at 360 feet

The y-intercept means the height above the canyon floor is 360 feet at

t = 0.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The y-intercept in a graph is the point on the y-axis.

This point is when x = 0.

So,

From the given context it means,

The height above the canyon floor is 360 feet at t = 0.

Thus,

The y-intercept means the height above the canyon floor is 360 feet at

t = 0.

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Answer:

its a i did it on egn

Step-by-step explanation:

Answer:

[tex]\displaystyle x=\frac{a+b}{c}[/tex]

Step-by-step explanation:

Equations

Solve the equation:

[tex]\displaystyle \frac{b-cx}{a}+\frac{a-cx}{b}+2=0[/tex]

Subtracting 2:

[tex]\displaystyle \frac{b-cx}{a}+\frac{a-cx}{b}=-2[/tex]

Multiply by ab to eliminate denominators:

[tex]\displaystyle ab\frac{b-cx}{a}+ab\frac{a-cx}{b}=-2ab[/tex]

Simplifying:

[tex]b(b-cx)+a(a-cx)=-2ab[/tex]

Operating:

[tex]b^2-bcx+a^2-acx=-2ab[/tex]

Subtracting [tex]b^2+a^2[/tex]

[tex]-bcx-acx=-2ab-b^2-a^2[/tex]

Multiplying by -1:

[tex]bcx+acx=2ab+b^2+a^2[/tex]

Factoring:

[tex]c(b+a)x=2ab-b^2+a^2[/tex]

The right side of the equation is the square of a+b:

[tex]c(b+a)x=(a+b)^2[/tex]

Simplifying (for a ≠ -b):

[tex]cx=(a+b)[/tex]

Dividing by c:

[tex]\boxed{\displaystyle x=\frac{a+b}{c}}[/tex]

Answer:

y = 3/4x -2

Step-by-step explanation:

Rise 3, run 4. Slope 3/4. Y intercept at -2.

Answer:

Sheldon has to sell at least 143 cups of coffee to purchase the kayak.

Step-by-step explanation:

First write an expression:

15 + 0.25x ≥ 50.75

Next use inverse operations:

15 + 0.25x - 15 ≥ 50.75 - 15

0.25x ≥ 35.75

0.25x ÷ 0.25 ≥ 35.75 ÷ 0.25

x ≥ 143

Sheldon has to sell at least 143 cups of coffee to purchase the kayak.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Answer:

143 cups

Step-by-step explanation:

Sheldon gets a flat $15, as well as 25 cents for each cup of coffee made.

He needs $50.75 to buy a Kayak.

Set the equation. Let the amount of cups of coffee = c.

0.25c + 15 = 50.75

Isolate the variable, c. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and equals:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, subtract 15 from both sides of the equation:

0.25c + 15 = 50.75

0.25c + 15 (-15) = 50.75 (-15)

0.25c = 50.75 - 15

0.25c = 35.75

Next, divide 0.25 from both sides of the equation:

(0.25c)/0.25 = (35.75)/0.25

c = 35.75/0.25

c = 143

Sheldon will need to sell 143 cups of coffee.

~

Answer:

Graph A

Step-by-step explanation:

The line starts at 1 since that is what he began with. Then it grows by two because every year he gets too more.

Answer:

I am pretty sure the answer would be Option B.

Step-by-step explanation:

If you look on the graph, Option B is the one that makes the most sense because it goes up by a ratio of 1:2 just like in the problem, 1 gift train + 2 trains per year.

Option A would not make sense because it goes up by the ratio of 1:3 and doesn't match up with the problem.

Note:

I hope this helps! :) Please correct me if I am wrong.

Answer:

[tex]f^{-1}[/tex](x) = x - 3

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = x + 3 (subtract 3 from both sides )

y - 3 = x

Change y back into terms of x with x = [tex]f^{-1}[/tex](x) , thus

[tex]f^{-1}[/tex](x) = x - 3

Answer:

Biased

Step-by-step explanation:

I thing this question is a little bias because it could imply that the more cars your family owns, the richer you are. There could be some other instances where this is not the case, but overall this could be taken as bias.

Answer:

[tex]slope = \frac{ {y}^{1} - {y}^{o} }{ {x}^{1} - {x}^{o} } \\ for \: points \: given \\ = \frac{11 - 7}{5 - 4} \\ = \frac{4}{1} \\ slope = 4[/tex]

Answer:

m = 4

Step-by-step explanation:

equation of point slope formulae

[tex]y = mx + c[/tex]

m = slope , c = y-intercept

1) find the slope

* use the two coordinates given to find the slope

slope formulae:

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

i) (4,7)

x1 = 4

y1 = 7

ii) (5,11)

x2 = 5

y2 = 11

substitute the values into the formulae

[tex]m = \frac{11 - 7}{5 - 4} [/tex]

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

[tex]m = 4[/tex]

the slope = 4

Answer:

Step-by-step explanation:

16.) B. y = 3x + 2

17.) y = -2

(show in graph below) - -

                                        |

                                       V

Answer:

1) The expected value of the "winnings" is $(-0.97[tex]\overline 2[/tex])

2) The variance for the "winnings" is $0.57966

3) The standard deviation for the "winnings" is$0.761354

4) The game is not a fair game because one is expected to lose $0.97[tex]\overline 2[/tex]

Step-by-step explanation:

1) The probability of having a sum of 2 = 1/6×1/6 = 1/36

The probability of having a sum of 3 = 1/6×1/6 = 1/36

The probability of having a sum of 4 = 1/6×1/6 + 1/6×1/6  = 1/18

The probability of having a sum of 5 = 1/6×1/6 + 1/6×1/6 = 1/18

The probability of having a sum of 6 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12

The probability of having a sum of 7 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12

The probability of having a sum of 8 = 1/6×1/6 + 1/6×1/6 + 1/6×1/6 = 1/12

The probability of having a sum of 9 = 1/6×1/6 + 1/6×1/6  = 1/18

The probability of having a sum of 10 = 1/6×1/6 + 1/6×1/6 = 1/18

The probability of having a sum of 11 = 1/6×1/6  = 1/36

The probability of having a sum of 12 = 1/6×1/6  = 1/36

The values are;

For 2, we have 1/36 × (20 - 5) = 0.41[tex]\overline 6[/tex]

For 3, we have 1/36 × (20 - 5) = 0.41[tex]\overline 6[/tex]

For 4, we have 1/18 × (20 - 5) = 0.8[tex]\overline 3[/tex]

For 5, we have 1/18 ×  (10 - 5) = 0.2[tex]\overline 7[/tex]

For 6, we have 1/12 × (10 - 5) = 0.41[tex]\overline 6[/tex]

For 7, we have 1/12 × (10 - 5) = 0.41[tex]\overline 6[/tex]

For 8, we have 1/12 × (10 - 5) = 0.41[tex]\overline 6[/tex]

For 9, we have 1/18 × (-20 - 5) = -1.3[tex]\overline 8[/tex]

For 10, we have 1/18 × (-20 - 5) = -1.3[tex]\overline 8[/tex]

For 11, we have 1/36 × (-20 - 5) = -0.69[tex]\overline 4[/tex]

For 12, we have 1/36 × (-25 - 5) = -0.69[tex]\overline 4[/tex]

The expected value of the winnings is given as follows;

0.41[tex]\overline 6[/tex] + 0.41[tex]\overline 6[/tex] + 0.8[tex]\overline 3[/tex] + 0.8[tex]\overline 3[/tex] + 0.8[tex]\overline 3[/tex] + 0.41[tex]\overline 6[/tex] + 0.41[tex]\overline 6[/tex] + -1.3[tex]\overline 8[/tex] -1.3 - 0.69[tex]\overline 4[/tex] - 0.69[tex]\overline 4[/tex] = -0.97[tex]\overline 2[/tex]

Therefore, the expected value = $-0.97[tex]\overline 2[/tex], which is one is expected to lose $0.97[tex]\overline 2[/tex]

2) Using Microsoft Excel, we have;

The variance for the "winnings", σ² = $0.57966

3) The standard deviation for the "winnings" = √σ² = √(0.57966) ≈ $0.761354

4) The game is not a fair game because one is expected to lose $0.97[tex]\overline 2[/tex]

Answer:

The answer is -0.5 or -1/2

Step-by-step explanation:

You can flip the second fraction over and multiply the two fractions by each other. It would be like this: 2/3 x -3/4, and multiply and you get -6/12 which can be further reduced to -1/2.

Hope this helped! Remember to use the formula Skip, Flip, Multiply in which you skip the first fraction, flip the division sign to multiply and flip the second fraction over!

Answer:

B.) 12

Step-by-step explanation:

h(x) = 3^x + 3

h(2) = 3^2 + 3

h(2) = 9 + 3

h(2) = 12

Answer:

i think [after solving] that it is option B and C

Step-by-step explanation:

Answer:

[tex]5(x - 2) = \frac{15x + 6}{3} - 12 \\ 5(x - 2) = \frac{15x + 6 - 36}{3} \\ 5(x - 2) = \frac{15x - 30}{3} \\ 5(x - 2) = \frac{15(x - 2)}{3} \\ 15(x - 2) = 15(x - 2)[/tex]

Answer:

All real numbers

Step-by-step explanation:

Given

5(x - 2) = [tex]\frac{15x+6}{3}[/tex] - 12

Multiply through by 3 to clear the fraction

15(x - 2) = 15x + 6 - 36 ← distribute left side and simplify

15x - 30 = 15x - 30

Since both sides are equal then any real value of x will be a solution.

Thus the solution is All real numbers

Multiply 14 by 0.3

14 x 0.3 = 4.2

The answer is 4.2

Answer:

4.2 is the answer

Step-by-step explanation:

Remember, in math, 'of ' always mean multiplication!!!

Answer:

yeet

Step-by-step explanation:

yeet yeet yeet yeet yeet yeet yeet yeet yeet eet yett yeet yeet yeet yeet yeet yeet yeet yeet yeety