1. 8x^2 + 10x - 9
2. 3x^4 - 14x^2 - 9
3. 4x^2 + 5x - 9
4. 8x^2 + 10x - 18

Answer:

it's 10.00 because I used a calculator

let's bear in mind that on the III Quadrant, sine and cosine are both negative, whilst on the IV Quadrant, sine is negative and cosine is positive, that said

\(\cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{3}\\ o=opposite \end{cases} \\\\\\ o=\pm \sqrt{ 5^2 - 3^2} \implies o=\pm \sqrt{ 16 }\implies o=\pm 4\implies \stackrel{IV~Quadrant }{o=-4} \\\\[-0.35em] ~\dotfill\)

\(\tan(\beta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\implies \tan(\beta )=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{-3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \\\\\\ \tan(\alpha + \beta)\implies \cfrac{ ~~\frac{-4}{3}~~ + ~~\frac{-4}{-3} ~~ }{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \cfrac{0}{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \text{\LARGE 0}\)

Answer:

The transformations used were rotations, reflections, and  R(–3, –3). After a dilation, the image of P is. P'(4, 12). What is the scale factor of the dilation? 5.The triangle formed by a 4-foot-tall mail box and its 6-foot shadow is similar to the triangle formed by a utility pole and its 15-foot shadow at the same time of day.

Step-by-step explanation:

The equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

We have to given that,

A number line is shown in image.

Since,

A number lines are the horizontal straight lines in which the integers are placed in equal intervals.

And, All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

Now, By given number line,

Point C is two point left from point 8.

Hence, The point C is denoted as,

⇒ C = 8.2

⇒ C = 82/10

⇒ C = 8 2/10

Therefore, the equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

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Answer and Step-by-step explanation: the doc is below for how i did the problem

Answer: x = 10

Step-by-step explanation:

     To solve, we will isolate the variable x.

Given:

     2x + 7 = 5x - 23

Add 23 to both sides of the equation:

     2x + 30 = 5x

Subtract 2x from both sides of the equation:

     30 = 3x

Divide both sides of the equation by 3:

     10 = x

Reflexive property:

     x = 10

The solution of the equation -x² + 4 = x + 2 is at x = -2 and x = 1

An equation is an expression that shows how numbers and variables are related to each other.

Given the quadratic equation:

-x² + 4 = x + 2

Collecting like terms:

x² + x - 2 = 0

Plotting using a graph; the solution of the equation can be gotten by getting the point the graph crosses the x axis.

The solution is at x = -2 and x = 1

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Answer:

Step-by-step explanation:

If you remove the brackets you get

4x^2*x^2 + 4x*4x + 3*4x

4x^4 + 16x^2 + 12x

That definitely is a polynomial

In its factored form, one of the factors is a polynomial so the answer is true.

Answer:

56/25

Step-by-step explanation:

sksksjskskksdidid

Answer:

$712.80

Step-by-step explanation:

648×0.10=64.8

648+64.8=712.8

The total amount paid for the refrigerator is $712.8.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Sale price = $648

Sales tax = 0.10 times the price

The total amount paid.

= 648 + 0.10 x 648

= 648 + 64.8

= 712.8

Thus,

The total amount paid is $712.8.

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The ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) do not correspond to the intervals where the graph of f(x) is decreasing. The pairs (1, -2) and (-3, -18) are the correct ones.

To determine where the graph of f(x) is decreasing, we need to examine the intervals where the function's derivative is negative. The derivative of f(x) is given by f'(x) = -3x^2 - 8x + 3.

Now, let's evaluate f'(x) for each of the given x-values:

f'(-1) = -3(-1)^2 - 8(-1) + 3 = -3 + 8 + 3 = 8

f'(2) = -3(2)^2 - 8(2) + 3 = -12 - 16 + 3 = -25

f'(0) = -3(0)^2 - 8(0) + 3 = 3

f'(1) = -3(1)^2 - 8(1) + 3 = -3 - 8 + 3 = -8

f'(-3) = -3(-3)^2 - 8(-3) + 3 = -27 + 24 + 3 = 0

f'(-4) = -3(-4)^2 - 8(-4) + 3 = -48 + 32 + 3 = -13

From the values above, we can determine the intervals where f(x) is decreasing:

f(x) is decreasing for x in the interval (-∞, -3).

f(x) is decreasing for x in the interval (1, 2).

Now let's check the ordered pairs in the table:

(-1, -6): Not in a decreasing interval.

(2, -18): Not in a decreasing interval.

(0, 0): Not in a decreasing interval.

(1, -2): In a decreasing interval.

(-3, -18): In a decreasing interval.

(-4, -12): Not in a decreasing interval.

Therefore, the ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) are not located in the intervals where the graph of f(x) is decreasing. The correct answer is: (1, -2), (-3, -18).

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Note the complete and the correct question is

Q- Consider the function below, which has a relative minimum located at (-3, -18) and a relative maximum located at 1/3, 14/27).

\(f(x) = -x^3 - 4x^2 + 3x\).

Select all ordered pairs in the table which are located where the graph of f(x) is decreasing: Ordered pairs: (-1, -6), (2, -18), (0, 0),(1 , -2), (-3 , -18), (-4. , -12)

Answer:

B, (x-5) square =21

Step-by-step explanation:

B, (x-5)square =21

The 19th term of a geometric sequence is 1048576.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

We have,

a = 4 and r = 2

The nth term of a geometric sequence.

= a\(r^{n-1}\)

Now,

The 19th term of a geometric sequence.

= a\(r^{n-1}\)

Substituting a and r values.

= 4 x \(2^{19 - 1}\)

= 4  x \(2^{18}\)

= 4 x 262144

= 1048576

Thus,

The 19th term of a geometric sequence is 1048576.

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The domain, range, x-intercept, or y-intercept of g(x) = f(x + 4) + 8. The features of g depend on the corresponding features of f.

Given the function g(x) = f(x + 4) + 8, let's examine its features:

Domain:

The domain of the function g will be the same as the domain of the function f, which depends on the restrictions or constraints of f.  However, it is important to note that shifting the input by 4 units (x + 4) does not inherently change the domain unless there are specific restrictions imposed by f.

Range:

Similar to the domain, the range of the function g will depend on the range of the function f.

x-intercept:

The x-intercept of a function is the point where the graph intersects the x-axis, meaning the y-coordinate is zero (y = 0). To find the x-intercept of g(x), we set g(x) = 0 and solve for x.

0 = f(x + 4) + 8

By subtracting 8 from both sides:

-8 = f(x + 4)

Since the exact value of x that makes f(x + 4) equal to -8. The x-intercept will depend on the behavior of f.

y-intercept:

The y-intercept of a function is the point where the graph intersects the y-axis, meaning the x-coordinate is zero (x = 0). To find the y-intercept of g(x), we substitute x = 0 into the function:

g(0) = f(0 + 4) + 8

g(0) = f(4) + 8

Again, the specific value of f(4) will depend on the behavior of the function f.

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Answer:what

Step-by-step explanation:

Answer:

Sorry, This is not a question

Step-by-step explanation:

N/A

Answer:

D (13,5)

Step-by-step explanation:

X 2 3 4 5

Y 2 5 9 13

So the ordered pairs are (2,2),(3,5), (4,9), (5,13)

and the ordered pairs for the inverse are

(2,2),(5,3), (9,4), (13,5)

from which D (13,5) is found among the options.

Answer:

b

Step-by-step explanation:

Answer:

-5 1/3 - 3 1/3

Step-by-step explanation

both expressions equal -8 2/3

This is the expression for the orthogonal projection of v onto the plane P characterized by θ and θ_0 is, proj_P(v) = [v₁ - (v₁ cos(θ) + v₂ sin(θ)) cos(θ), v₂ - (v₁ cos(θ) + v₂ sin(θ)) sin(θ)]

Let's assume that the plane P is given by the normal vector n = [cos(θ), sin(θ)], and a point on the plane is given by r = [cos(θ_0), sin(θ_0)].

To find the orthogonal projection of a point v onto P, we need to find the component of v that lies in the direction of the normal vector n, and then subtract that component from v. This can be done using the dot product of v and n:

proj_n(v) = (v · n) / ||n||^2 × n

where · denotes the dot product, ||n|| is the length of n, and proj_n(v) is the projection of v onto n.

To find the projection of v onto P, we need to subtract the projection of v onto n from v:

proj_P(v) = v - proj_n(v)

= v - (v · n) / ||n||^2 × n

Substituting the expressions for n and θ, we get:

proj_P(v) = v - (v · [cos(θ), sin(θ)]) / (cos^2(θ) + sin^2(θ)) × [cos(θ), sin(θ)]

= v - (v₁ cos(θ) + v₂ sin(θ)) / (cos^2(θ) + sin^2(θ)) × [cos(θ), sin(θ)]

= v - (v₁ cos(θ) + v₂ sin(θ)) / 1 × [cos(θ), sin(θ)]

= [v₁ - (v₁ cos(θ) + v₂ sin(θ)) cos(θ), v₂ - (v₁ cos(θ) + v₂ sin(θ)) sin(θ)]

where v₁ and v₂ are the components of v in the x and y directions, respectively. This is the expression for the orthogonal projection of v onto the plane P characterized by θ and θ_0.

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The given question is incomplete, the complete question is:

Find an expression for the orthogonal projection of a point v onto a plane P that is characterized by θ and θ_0. Write your answer in terms of v, θ and θ_0

To find the value of x, we can set the two angle measures equal to each other and solve for x.

Given:

mZA = (4x - 2)°

mZB = (6x - 20)°

Setting them equal to each other:

4x - 2 = 6x - 20

Now, we can solve for x:

4x - 6x = -20 + 2

-2x = -18

Dividing both sides by -2:

x = -18 / -2

x = 9

Therefore, the value of x is 9.

Answer:

The answer is 9.

Step-by-step explanation:

We need to use the fact that the sum of the angles in a triangle is 180 degrees. Let A, B, and C be the three angles in the triangle. Then we have:

mZA + mZB + mZC = 180°

Substituting the given values, we get:

(4x - 2)° + (6x - 20)° + mZC = 180°

Simplifying the left side, we get:

10x - 22 + mZC = 180°

Next, we use the fact that angles opposite congruent sides of a triangle are congruent. Since we know that segment AC and segment BC are congruent, we have:

mZA = mZB

Substituting the given values and simplifying, we get

4x - 2 = 6x - 20

Solving for x, we get:

x = 9

Therefore, the value of x is 9.

Answer: 2.5

Step-by-step explanation: If you do 5/8 divided by 1/4 in the calculator it is 2.5.

Answer: 10

Step-by-step explanation: it is a 5+ 5 =

La encuesta indica que de entre todos los estudiantes de una carrera, 4500 les gusta leer.

The percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the example: \(\frac{30}{100} =\frac{3}{10}=0.3*100=30 \%\).

The question gives:

Then, you will have:

\(6000\cdot \frac{75}{100}\\ \\ 6000\cdot \frac{3}{4}\\ \\ \frac{18000}{4} =4500\)

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Answer: slope = 10/15

Step-by-step explanation: Identify two points in the graph

Make one of them (x1, y1) and the other (x2, y2)

Then use the slope equation:m= y2- y1/ x2 - x1

Sara and Ashton both have the same number of comic books after 10 months

From the question, we have the following parameters that can be used in our computation:

Sara

Initial = 12 comic books

Books at the fourth month = 20

Ashton

Initial = 2 comic books

Books each month = 3

The equations can be represented as

Total number of books = Initial + Books each month * Number of months

Rewrite as

y = Initial + Books each month * x

For Ashton, the equation is

y = 2 + 3x

For Sara, we have

y = 12 + Books each month * Number of months

So, we have

20 = 12 + Books each month * 4

This gives

Books each month = 2

So, the equation is

y = 12 + 2x

Substitute y = 2 + 3x in y = 12 + 2x

2 + 3x = 12 + 2x

Evaluate the like terms

x = 10

This means that

Number of months = 10

Hence, the number of months is 10

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Complete question

Sara started with 12 comic books in her collection. She collected the same number of comic books each month until she had 20 comic books in the 4th month. Ashton started with 2 comic books in his collection and continues to collect 3 comic books each month.

Calculate when they both have the same number of books

Answer:

3/8 or 3:8

Step-by-step explanation:

pink : not pink

6 : 16

Think of it as a fraction. Simplify it in the same way.

6/16 simplifies to 3/8

So the pink:notpink ratio is 3/8 or 3:8

Answer:

10

Step-by-step explanation:

x/2 =5

2 x x/2 = 2 x 5

2x5 = 10

Answer: 36

Step-by-step explanation:

78/13=6

6(6)=36

Answer: $30.90

Step-by-step explanation:

Multiply 25.75 by .20 which gets you $5.15 which you add to $25.75 to get $30.90

Answer: $30.90

Step-by-step explanation:

1st way:

20% of $25.75 = $5.15

Add $25.75 and $5.15 together = $30.90

2nd way:

100% + 20% = 120%

120% of $25.75 = $30.90

Answer:

The quadrilateral is a rhombus

Step-by-step explanation:

Given

\(A = (2, 8)\)

\(B = (3, 11)\)

\(C = (4, 8)\)

\(D=(3, 5)\)

Required

The true statement

Calculate slope (m) using

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Calculate distance using:

\(d= \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}\)

Calculate slope and distance AB

\(m_{AB} = \frac{11 - 8}{3 - 2}\)

\(m_{AB} = \frac{3}{1}\)

\(m_{AB} = 3\) -- slope

\(d_{AB}= \sqrt{(3 - 2)^2 + (11 -8)^2}\)

\(d_{AB}= \sqrt{10}\) -- distance

Calculate slope and distance BC

\(m_{BC} = \frac{8 - 11}{4 - 3}\)

\(m_{BC} = \frac{- 3}{1}\)

\(m_{BC} = -3\) -- slope

\(d_{BC} = \sqrt{(4-3)^2+(8-11)^2\)

\(d_{BC} = \sqrt{10}\) --- distance

Calculate slope CD

\(m_{CD} = \frac{5 - 8}{3 - 4}\)

\(m_{CD} = \frac{- 3}{- 1}\)

\(m_{CD} = 3\) -- slope

\(d_{CD} = \sqrt{(3-4)^2+(5-8)^2}\)

\(d_{CD} = \sqrt{10}\) -- distance

Calculate slope DA

\(m_{DA} = \frac{8 - 5}{2 - 3}\)

\(m_{DA} = \frac{3}{- 1}\)

\(m_{DA} = -3\) -- slope

\(d_{DA} = \sqrt{(2-3)^2 + (8-5)^2}\)

\(d_{DA} = \sqrt{10}\)

From the computations above, we can see that all 4 sides are equal, i.e. \(\sqrt{10}\)

And the slope of adjacent sides are negative reciprocal, i.e.

\(m_{AB} = 3\)  and \(m_{CD} = -3\)

\(m_{CD} = 3\) and \(m_{DA} = -3\)

The quadrilateral is a rhombus