Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).

Answer:

x(3√6)

Step-by-step explanation:

Radicals:

  Take out a variable or number for every pair of the variable or number  inside the radicals

        [tex]\sf 3\sqrt{6x^2}=3*\sqrt{6*x*x}\\\\[/tex]

                   [tex]\sf = 3x \sqrt{6}[/tex]

This is a geometric sequence with first term 3 and a common ratio of -5/3.

Using the sum of a geometric series formula,

[tex]\frac{3(1-(-5/3)^{7}}{1-(-5/3)} \approx \boxed{41.31}[/tex]

Answer: 4 : 2

Step-by-step explanation:

I am going to assume you want a ratio between number of tires to headlights which is

4 : 2

The statement that is true about the linear inequality of y > 3/4x - 2 is that the graph intercepts the y-axis at (0, -2).

Linear inequality is defined as the comparison of two values using greater than, less than, greater than or equal to, and less than or equal to.

Using the general formula for linear inequality,

y >mx+ b

y > 3/4x - 2

Where m = slope of the graph

b = interception at y axis

Therefore, the statement that is true about the linear inequality of y > 3/4x - 2 is that the graph intercepts the y-axis at (0, -2).

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Answer:

130 degrees

Step-by-step explanation:

Let's assume that the angle is X. If angle is x, then:

x+260 = 3x

subtract x from both sides:

260 = 2x

130 = x because 260/2 is 130

so the answer is 130 degreees

Answer:

I feel like the answer is 70 degrees

Step-by-step explanation:

3(180-x)-260=x

540-3x-260=x

-3x+280=x

280=4x

x=70

The sum of the number of crew members (c) on the tour boat and the 5 passengers is 5 + c. Then the correct option is C.

The equivalent is the expressions that are in different forms but are equal to the same value.

The sum of the number of crew members (c) on the tour boat and the 5 passengers.

This can be written as in the form of the mathematical form.

⇒ 5 + c

Then the correct option is C.

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Answer: x+5 with a remainder of 3 (can also be said as 3/x-4)

Step-by-step explanation: See attachment

For this question, I will be writing 'csc' instead of 'cosec'

[tex]\sin 30^{\circ}=\frac{1}{2} \implies \csc 30^{\circ}=2\\\\\sin 45^{\circ}=\frac{1}{\sqrt{2}}\\\\\cos 60^{\circ}=\frac{1}{2} \implies \sec 60^{\circ}=2\\\\\\\therefore \csc^{2} 30^{\circ}-\sin^{2} 45^{\circ}-\sec^{2} 60^{\circ}=2^{2}-\left(\frac{1}{\sqrt{2}} \right)^{2}-2^{2}=\boxed{-\frac{1}{2}}[/tex]

Answer:

x = 3/2 ± [tex]\sqrt{5}[/tex] /2

Step-by-step explanation:

4x²-12x+9 = 5

Rearrange:

4x²-12x+4 = 0

Solve using the quadratic equation:

x = 3/2 ± [tex]\sqrt{5}[/tex] /2  

Answer:

second branch..................

Answer:

Step-by-step explanation:

The height of each story in a hotel is  feet. The height is measured from the ceiling to the floor. The hotel has 2 underground levels that are used as banquet halls. Stephen is a waiter who works two levels below ground. At what elevation are Stephen’s feet? Assume the ground level of the hotel is at 0 feet.

A.

feet

B.

feet

C.

D.

feet

The formula which used to describe the sequence is f(x)=1.2(2.5)ˣ⁻¹.

The given sequence is 1.2,3,7.5,18.75.

In geometric series, the ratio of two consecutive terms remains the same and this ratio is known as common ratio. a₁ is the first term of a geometric sequence and r is the common ratio, then the general term of the geometric sequence is of the form:

f(x)=a₁⋅rˣ⁻¹.

In the given sequence, a₁=1.2, a₂=3, a₃=7.5 and a₄=18.75.

Find the common ratio by

r=(aₙ₊₁)÷aₙ

r=a₂÷a₁

r=3÷1.2

r=2.5

Substitute the values in the general formula of geometric sequence.

f(x)=(1.2)(2.5)ˣ⁻¹

Hence, the formula which used to describe the sequence 1.2,3,7.5,18.75 is f(x)=(1.2)(2.5)ˣ⁻¹.

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Answer:

x = 72

y = 15

Step-by-step explanation:

m and n are parallel lines so we can write the following equation:

108 + x = 180 because these angles are supplementary

if we subtract 108 from both sides

x = 72 we can also write the following equation:

5y - 3 = x because these are alternate angles

5y - 3 = 72 add 3 to both sides

5y = 75 divide both sides by 5

y = 15

Answer:

x is 48 and y is 100

Step-by-step explanation:

Angle y = 100 degree

Angle x = 48 degree

Problem 10

The two functions are inverses of each other. Why? Because we can think of f(x) = (x-7)/(-2) as y = (x-7)/(-2).

Swap x and y to get x = (y-7)/(-2). Solving for y leads to y = -2x+7 showing that g(x) = -2x+7 is the inverse of f(x) = (x-7)/(-2). This process can be done in reverse to get the same result.

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Problem 11

y = a(6)^(t/2)

y = a( 6^(1/2) )^t

y = a(2.4494897)^t

y = a( b )^t

where b = 6^(1/2) = 2.4494897 approximately

Set b equal to 1+r and solve for r

1+r = 2.4494897

r = 2.4494897-1

r = 1.4494897

This rounds to about r = 1.45

The r value is the decimal form of the percentage, which means we move the decimal point over two spots to the right to get 145% approximately

Answers:

The equation is roughly y = a(1 + 1.4494897)^t

The growth rate is approximately 145%

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Problem 12

You have the correct answer. Nice work.

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Problem 13

You are very close to the correct answer. However, you're missing the base of the log.

The answer should be [tex]\log_{49}(343) = \frac{3}{2}[/tex]. So you'll need to write in a small "49" under the log.

The general rule is that exponential equations in the form [tex]b^x = y[/tex] are equivalent to the log version of [tex]\log_{b}(y) = x[/tex]. For each equation, b is the base. The idea of logs is to isolate the exponent.

[tex]A=\left(1+\dfrac{1}{2}\right)\cdot \left(1+\dfrac{1}{3}\right)\cdot\ldots\cdot \left(1+\dfrac{1}{2020}\right)=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\ldots\cdot \dfrac{2021}{2020}=\dfrac{\dfrac{2021!}{2}}{2020!}=\\\\=\dfrac{2021}{2}=1010.5[/tex]

Step-by-step explanation:

s.i= P×T×R/100

=2000×0.25×2/100

= 1000/100

= 10

Answer:

$10

Step-by-step explanation:

[tex]2000 \times .02 \times \frac{1}{4} = 10[/tex]

Answer:

If you attach the answers i can help you better

Step-by-step explanation:

Answer:

An Arc is a part of a circle that represents an angle.

From the given information, we have

[tex]13\sin(\theta) = 12\cos(\theta) \implies \dfrac{\sin(\theta)}{\cos(\theta)} = \dfrac{12}{13}[/tex]

In the expression of interest, divide through everything by [tex]\cos^2(\theta)[/tex] to get

[tex]\dfrac{2\sin(\theta)\cos(\theta)}{\cos^2(\theta) - \sin^2(\theta)} = \dfrac{2\frac{\sin(\theta)}{\cos(\theta)}}{1 - \frac{\sin^2(\theta)}{\cos^2(\theta)}}[/tex]

Then plugging in the given info, we get

[tex]\dfrac{2\sin(\theta)\cos(\theta)}{\cos^2(\theta) - \sin^2(\theta)} = \dfrac{2\times \frac{12}{13}}{1 - \left(\frac{12}{13}\right)^2} = \boxed{\dfrac{312}{25}}[/tex]

The value of x is 77 cm which will make the triangles similar by SSS similarity theorem

Given length of the three sides of one triangle are  35 , 20 and 20

and length of the three sides of another triangle are  x, 44,44

We need to find the values of x by using SSS Similarity theorem

We know that triangles are are similar by side - side - side similarity creation and hence the sides are in the same ratio

As both the triangles are isosceles triangles

Therefore ,

x/35 = 44/20=44/20 (Using ratio)

Solving the equation we get

x=44*35/20

x= 77

Hence the value of x is 77cm

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Answer:

3/5x + 3 = 6

3/5x = 6 - 5

3/5x = 1

3/5x (5x) = 1* 5x

3 = 5x

3/5 = X

The function that has an x-intercept of - 4 and a y-intercept of 3 when graphed is f(x) = 3/4x + 3

The x-intercept of a line is the point where the line crosses the x-axis while the y-intercept of a line is the point where the line crosses the y-axis.

For the x-intercept, y = 0

For the function f(x) = 3/4x + 3

0 = 3/4x + 3

0 = 3x + 12

-3x = 12

x = -4

This shows that the function has an x-intercept of -4

For the y-intercept, x = 0

For the function f(x) = 3/4x + 3

y = 3/4(0) + 3

y = 3

This shows that the function has an y-intercept of 3

Hence the function that has an x-intercept of - 4 and a y-intercept of 3 when graphed is f(x) = 3/4x + 3

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The absolute value equation that can be used to find the minimum and maximum radius accepted is:

A. |r - 1.25| = 0.1.

The absolute value function is defined as follows:

[tex]|x| = x, x \geq 0[/tex]

[tex]|x| = -x, x < 0[/tex]

It measures the distance of a point x to the origin.

In this problem, the absolute value of the difference between the radius and 1.25 cm must be of 0.1 to find the thresholds, hence the equation is:

A. |r - 1.25| = 0.1.

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Answer:

4

Step-by-step explanation:

the second column and the second row so, the answer is 4

( 1, ∞)  is the domain of (b o a)(x)

A function is defined as a relation between a set of inputs having one output each.

According to the question,

[tex]a(x) = 3x + 1 \\\\b (x) =\sqrt{x+4}[/tex]

To find the domain of the composite function,

[tex](b o x) (x) = b(a(x))\\\\(b o x) (x) = b(a(3x-1))\\\\(b o x) (x) = \sqrt{3x+ 1 -4} \\\\(b o x) (x) = \sqrt{3x -3}\\\\[/tex]

Therefore,

[tex]3x - 3 \geq 0\\3x \geq 3\\x \geq 1\\\\[/tex]

Hence , [ 1, ∞ ] is is the domain of (b o a)(x).

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Answer:

7

Explanation:

Use the distance formula to find the answer

Answer:

7 units

Step-by-step explanation:

since the x- coordinates of L and M are equal , both - 1 then the length of LM is the absolute value of the difference of the y- coordinates.

LM = | 4 - (- 3) | = | 4 + 3 | = | 7 | = 7

or

LM = | - 3 - 4 | = | - 7 | = 7