Let a and b be real numbers where a . Which of the following functions could represent the graph below?


f(x) = x(x – a)3(x – b)3
f(x) = (x – a)2(x – b)4
f(x) = x(x – a)6(x – b)2
f(x) = (x – a)5(x – b)

Answer:

-6

30

22

8x² + 18x + 4

8x² - 2x - 6

Step-by-step explanation:

f(x) = 8x² + 2x - 6

f(0) = 8(0²) + 2(0) - 6 = -6

f(2) = 8(2²) + 2(2) - 6 = 32 + 4 - 6 = 30

f(-2) = 8 × (-2)² + 2(-2) - 6 = 32 - 4 - 6 = 22

f(x + 1) = 8(x + 1)² + 2(x + 1) - 6 = 8(x² + 2x + 1) + 2x + 2 - 6 = 8x² + 18x + 4

f(-x) = 8(-x)² + 2(-x) - 6 = 8x² - 2x - 6

Answer:

$123.21 (nearest cent)

Step-by-step explanation:

Annual Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=100\left(1+0.11\right)^{2}[/tex]

[tex]\implies \sf A=100\left(1.11\right)^{2}[/tex]

[tex]\implies \sf A=123.21[/tex]

Therefore, the value of the account in 2 years will be $123.21 (nearest cent).

The measure of angle ∠ACB is 70°. Then the correct option is C.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

∠ABC + ∠BCA + ∠CAB = 180°

        60° + ∠BCA + 50° = 180°

                           ∠BCA = 180° – 110°

                           ∠BCA = 70°

Then the correct option is C.

The complete question is given below.

Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.

The measure of ABC is 60

The measure of BAC is 50

The measure of ACB will be

a. 50

b. 60

c. 70

d. 120

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Answer:

Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.

The measure of angle ABC is

✔ 60

°.

The measure of angle BAC is

✔ 50

°.

The measure of angle ACB is

✔ 70

°.

Step-by-step explanation:

So

[tex]\\ \rm\Rrightarrow r=\sqrt{a^2+b^2}[/tex]

[tex]\\ \rm\Rrightarrow r=\sqrt{(-3)^2+(\sqrt{3})^2}[/tex]

[tex]\\ \rm\Rrightarrow r=\sqrt{9+3}[/tex]

[tex]\\ \rm\Rrightarrow r=\sqrt{12}[/tex]

[tex]\\ \rm\Rrightarrow r=2\sqrt{3}[/tex]

Find theta

[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{y}{x})[/tex]

[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{\sqrt{3}}{3})[/tex]

[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{-1}{\sqrt{3}})[/tex]

[tex]\\ \rm\Rrightarrow \theta=\dfrac{5\pi}{6}[/tex]

Polar form

[tex]\\ \rm\Rrightarrow r(cos\theta+isin\theta)[/tex]

[tex]\\ \rm\Rrightarrow 2\sqrt{3}(cos\dfrac{5\pi}{6}+isin\dfrac{5\pi}{6})[/tex]

The expression that represents the product of negative three-fourths x and –8x is 6x^2

The statement is given as:

the product of negative three-fourths x and –8x

Rewrite properly as:

-3x/4 * -8x

Divide 4 and 8 by 4

-3x * -2x

Multiply -3 and -2

6x * x

Multiply x and x

6x^2

Hence, the expression that represents the product of negative three-fourths x and –8x is 6x^2

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Answer:

answer is 6x2 or D

Step-by-step explanation:

The statements that would complete the proof where ∠2 ≅ ∠7 by the transitive property are:

∠2 ≅ ∠3

∠3 ≅ ∠7

The transitive property states that if x = y, and y = z, then x = z.

From the image given below, we have:

∠2 ≅ ∠3 because they are vertical angles which must be congruent.

∠3 ≅ ∠7 because corresponding angles are congruent.

Applying the transitive property, we can state that: ∠2 ≅ ∠7.

Therefore, the statements that would complete the proof are:

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The correct answer is option A which is segment D which is closer to home.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

From the given graph we can see that in segment D the distance between the home and the person is lesser than all the segments given in the graph.

Therefore the correct answer is option A which is segment D which is closer to home.

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Semiperimeter is used to find the area of various shapes including the equilateral triangle (False).

Semiperimeter is a term used in geometry to refer to half the perimeter of a polygon. It is generally used in formulas for triangles.

However, it is also part of calculations related to other geometric shapes. According to the above, it can be inferred that the semiperimeter can be used to find the area of various geometric figures.

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Answer:

Step-by-step explanation:

3x + 2(x − 1) − 4 =

3x + 2x - 2 - 4 =

5x - 6

Answer:

Step-by-step explanation:

[tex]\bf 3x + 2(x - 1) - 4?[/tex]

Distribute.

Subtract the numbers.

Combine like terms.

The exponent is negative , The exponent represents the number of places the decimal moves. , Option A and D is the correct answer.

The complete question is

Which statements describe writing 0.00000000003 in scientific notation? Check all that apply.

A.The exponent is negative.

B. The exponent is positive.

C.The coefficient is 0.3.

D.The exponent represents the number of places the decimal moves.

E.The decimal moves to the right.

Scientific Notation means writing a decimal number in the form of 10ˣ .

It is given that

A nitrogen molecule is 0.00000000003 meters larger than an oxygen molecule.

= 3 × 10⁻¹¹

(scientific notation)

The exponent is negative , The exponent represents the number of places the decimal moves. , Option A and D is the correct answer.

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Donte did a mistake that 'he did not apply the distributive property correctly for 4(1 3i)' option (A) is correct.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have an expression:

= 4(1 + 3i) – (8 – 5i)

= 4 + 12i - 8 + 5i  

He did not distribute the subtraction sign correctly for 8 – 5i.

= -4 + 17i

Thus, Donte did a mistake in that 'he did not apply the distributive property correctly for 4(1 3i)' option (A) is correct.

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Answer:

(A) is correct.

Step-by-step explanation:

The equation of line is y = 92x – 182631. The slope is 92 and the y-intercept is the negative 182631. And the health expenditure in 2010 will be 2289.

Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by

[tex]\rm (y - y_1) = \left [ \dfrac{y_2 - y_1}{x_2 - x_1} \right ] (x -x_1)[/tex]

In MODE, (second line), fix the number of decimal places to be 2.

Then the slope and the y-intercept values of the Lin Reg line will round to the nearest hundredth.

(x₁, y₁) → (1997, 1093)

(x₂, y₂) → (2002, 1553)

Then we have

y – 1093 = [(1553 – 1093) / (2002 – 1997)] (x – 1997)

y – 1093 = [460  / 5] (x – 1997)

y – 1093 = 92 (x – 1997)

           y = 92x – 182631

If x = 2010, then the value of y will be

y = 92 × 2010 – 182631

y = 184920 – 192631

y = 2289

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Answer:

big bodie built

Step-by-step explanation:

i used to be dusty

Based on the calculations, the value of the given prefix expression is equal to 2205.

The preorder traversal of a tree (T) are typically used in discrete mathematics to determine the value of a prefix expression on a specific expression tree.

For the preorder traversal of this tree (T), we would start from the right most expression:

Prefix expression = * + 3 + 3 ↑ 3 + 3 3 3

Prefix expression = * + 3 + 3 ↑ 3 6 3

Prefix expression = * + 3 + 3  3⁶  3

Prefix expression = * + 3 3 729 3

Prefix expression = * + 3 732 3

Prefix expression = * 735 3   ⇒ 735 × 3

Value = 2205.

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Complete Question:

Given the following prefix expression:

* + 3 + 3 ↑ 3 + 3 3 3

What is the value of the prefix expression?

Answer:

19.25(miles?)

Step-by-step explanation:

Assuming 3.5 is the x value or input of the function

3.5 x 5.5 = 19.25

cranberry juice = 350 ml

blueberry juice = 2 liters = 2000 ml

Ratio of cranberry juice : blueberry juice = 350 : 2000 = 7 : 40

The simplest ratio is 7 : 40    or    7/40

Answer:

38 is the correct solution

The point F lies on 4.5 in the number line.

Number line is a One dimensional representation of point referring by a number only.

We know that if a point divides a line joining the points at x,y in the number line respectively in m:n ratio then that point lies on = (my+nx)/(m+n) in the number line.

Here in the give problem that,

Point D lies on -6 in number line

Point E lies on 8 in number line

And F lies between D and E points and DE:EF = 3:1

So the point F clearly divides the staright line DE joining the point D at -6 and E at 8 in 3:1 ratio.

So the point F lies on = (1*(-6)+3*8)/(3+1) = (-6+24)/4 = 18/4 = 4.5

Hence the point F lies on 4.5 in the number line.

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Answer: 4.5

Step-by-step explanation:

Answer:

[tex]2y - 8x = 3[/tex]

Step-by-step explanation:

[tex]y - 4x = 9[/tex]

[tex]2y - 8x = 18[/tex]

So 2y - 8x = 3 is parallel to y - 4x = 9.

Answer:

24

Step-by-step explanation:

The question is saying, how many three digit numbers can be made from the digits 3, 4, 6, and 7 but there can't be two of the same digit in them. For example 346 fits the requirements, but 776 doesn't, because it has two 7s.

Okay, on to the problem:

We can do one digit at a time.

First digit:

There are 4 digits that we can choose from. (3, 4, 6, and 7)

Second digit:

No matter which digit we chose for the first digit, there is only going to be 3 of them left, because we already chose one, and you can't repeat that same digit. So there are 3 options.

Third digit:

Using the same logic, there are only 2 options left.

We have 4 choices for the first digit, 3 choices for the second, and 2 for the third.

Hence, this is 4 * 3 * 2 = 24 three-digit numbers that can be made.

2sin(x) - 1 =0

first, simplify and isolate sin(x)

2sin(x) - 1 = 0

2sin(x) = 1

sin(x) = 1/2

Then, do sin inverse of 1/2 which is 30 degrees

150 degrees also works because when you set 30 degrees as the reference angle in quadrant 2, you get 150 degrees. 180-30 = 150

C is the answer

Answer:b

Step-by-step explanation:

A ratio shows us the number of times a number contains another number. The maximum amount of purple that Susan can make is 25 ml.

A ratio shows us the number of times a number contains another number.

Susan makes purple paint by mixing red and blue paint in a ratio of 2:3. Now, if Susan wants to use the complete red paint then,

Purple paint she can make = 2/3 × 6/6 = 12 ml of red paint / 18 ml of blue paint

If Susan wants to use the complete blue paint then,

Purple paint she can make = 2/3 × 5/5 = 10 ml of red paint / 15 ml of blue paint

As per the first condition 18ml of blue paint is needed which is not possible, therefore, the second case is possible.

Thus, Susan needs to mix 10 ml of red paint and 15 ml of blue paint. Therefore, the amount of paint that Susan will make is,

Total Paint = 10ml + 15ml = 25ml

Hence, the maximum amount of purple that Susan can make is 25 ml.

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The equation of volume will be V = [(1/2)t + 4]³. The surface area as a function of time will be A(s) = 3/2 t² + 24t + 96. The number of hours when the surface area equal 294 square inches will be 3 1/2 hours.

Functions are found all across mathematics and are required for the creation of complex relationships.

Part A: The equation that gives the volume at t hours after freezing begins will be

V = s³

V = [(1/2)t + 4]³

Part B: The surface area as a function of time, using composition, and determine its range will be

A(s) = 6(1/2 t + 4)²

A(s) = 6 (t²/4 + 4t + 16)

A(s) = 3/2 t² + 24t + 96

Part C: The number of hours when the surface area equal 294 square inches will be

294 = 6(1/2 t + 4)²

49 = (1/2 t + 4)²

7 = 1/2 t + 4

1/2 t = 3

t = 3 1/2 hours

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Answer:

3

Step-by-step explanation:

Answer:

[tex]\mathrm{Slope=== > 0}[/tex]

Step-by-step explanation:

Hi student, let me help you out!

.............................................................................................................

First, let's recall the slope formula: [tex]\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}}[/tex], where y2 and y1 are y-coordinates; x2 and x1 are x-coordinates.

Plugin the values: [tex]\mathrm{\cfrac{0-0}{-17-(-9)}}[/tex].

Upon simplifying, we obtain [tex]\mathrm{\cfrac{0}{-17+9}}[/tex].

Upon simplifying this further, we obtain [tex]\mathrm{\cfrac{0}{-9}}[/tex].

0 divided by anything results in 0.

✨ ∴, the slope of this particular line is 0, and this line looks something like this: [tex]\rule{200}{1}[/tex].

See, it's a horizontal line, with a rise of 0, meaning that it goes up 0 units.

Hope this helped you out! Ask in comments if even the slightest queries arise.

Best Wishes!

[tex]\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]

[tex]\underline{\rule{300}{5}}[/tex]

Using it's concept, it is found that there is a 0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Considering the situation described, the ways that alternate colored balls can be taken with the probabilities given as follows:

Hence the probability that the first three balls are drawn out of the box alternated in colour is given by:

[tex]p = \frac{5}{8} \times \frac{3}{9} \times \frac{5}{11} + \frac{3}{8} \times \frac{5}{10} \times \frac{5}{11} = 0.0689 + 0.0852 = 0.1541[/tex].

0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.

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The t-test for the two means is appropriate in this situation because women and men are independent samples.

Independent samples are chosen randomly, ensuring that their results are independent of other observations' values.

The premise that samples are independent underlies many statistical analyses. Others are made to evaluate non-independent sample sets.

The samples of men and women are independent since their results are independent of other observations' values.

The Independent Samples t-Test analyzes the means of two separate groups to see if there is statistical support that the population means values are statistically substantially different.

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Answer:

Should be C

Step-by-step explanation:

Only the same power number can be use to add or subtract :)

But why is A, B and C same kinda stuff?

Answer:

The angles are 72° and 108°

Step-by-step explanation:

Supplementary angles add up to 180°

Ratio of supplementary angles = 2 : 3

The angles are 2x , 3x

2x + 3x = 180

        5x = 180

          x = 180 ÷ 5

         x = 36°

2x = 2*36 = 72°

3x = 3*36 = 108°

-------------------------------------------------------------------------------------------------------------

Answer:  [tex]\textsf{x = 1000}[/tex]

-------------------------------------------------------------------------------------------------------------

Given: [tex]\textsf{log(x) = 3}[/tex]

Find: [tex]\textsf{The value of x}[/tex]

Solution:  In order to solve for x we need to get rid of the log which means that we need to put it to the power of the same number as the base.  When a base isn't displayed it defaults to 10 so we raise everything to the base of 10.

Get rid of log

Therefore, the final answer would be that x is equal to 1000.