True or false? The graph represents a function.
5
O A. True
O B. False

Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

Considering the table, the roots are given as follows:

[tex]x_1 = -4, x_2 = 5, x_3 = 12[/tex]

Hence the function is:

f(x) = a(x + 4)(x - 5)(x - 12).

f(x) = a(x² - x - 20)(x - 12)

f(x) = a(x³ - 13x² - 32x + 240).

When x = 0, y = 1, hence the leading coefficient is found as follows:

240a = 1

a = 0.004167

Then:

f(x) = 0.004167(x³ - 13x² - 32x + 240).

The end behavior is given by the limits of f(x) as x goes to infinity, hence:

Hence the end behavior is that the function decreases to the left and increases to the right.

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The value of x is 22

Based on the description in the question,

The angles 5x -40 and 5x are angles on a straight line

So, we have:

5x - 40 + 5x = 180

Evaluate the like terms

10x = 220

Divide by 10

x = 22

Hence, the value of x is 22

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Answer:

D = 50t

Step-by-step explanation:

we see, with every additional hour the distance increases by 50.

that means in general that the number of hours are multiplied by 50 to get the distance.

in other words, this just calculates for a vehicle going constantly 50 miles per hour the distance it is traveling.

The parametrization for the tangent line at time [tex]t_{0}[/tex] is (41 + 3t, -4/3 + 4t/3, 4/3 + 4t/3)

The point of intersection is (40, -4, 0)

The given curve is defined parametrically by the equations

x = 3t + 2

y = 4 cos t

z = 4 sin t

To find the parametrization for the tangent line at time t0 = 13, we need to find the point of tangency and the direction vector of the tangent line.

The point of tangency is the position of the curve at time t0, which is

(3 * 13 + 2, 4 cos 13, 4 sin 13) = (41, -4/3, 4/3)

The direction vector of the tangent line is the derivative of the curve at time t0, which is

(3, -4 sin 13, 4 cos 13) = (3, -4/3, 4/3)

Therefore, the parametrization for the tangent line is

(41 + 3t, -4/3 + 4t/3, 4/3 + 4t/3)

b. To find the point where this line intersects the -plane, we set z = 0 and solve for t. This gives us

4/3 + 4t/3 = 0

t = -1/2

Therefore, the point of intersection is

(41 - 3/2, -2, 0) = (40, -4, 0).

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Answer:

10

Step-by-step explanation:

[tex]\boxed{\textsf{If }y=x^n,\: \textsf{then }\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}}[/tex]

Given equation:

[tex]2y=x^3+2x^2[/tex]

Isolate y by dividing both sides by 2:

[tex]\implies y=\dfrac{1}{2}x^3+x^2[/tex]

Differentiate with respect to x:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=3 \cdot \dfrac{1}{2}x^{3-1}+2 \cdot x^{2-1}[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{3}{2}x^2+2x[/tex]

Finally, substitute x = 2 into the differentiated equation:

[tex]\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{3}{2}(2)^2+2(2)\\\\ & = \dfrac{3}{2}(4)+4\\\\ & = \dfrac{12}{2}+4\\\\ & = 6+4\\\\ & = 10\end{aligned}[/tex]

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The linear equation graphed is given by:

y - 5 = 3(x - 1).

A linear function is modeled by:

y = mx + b

In which:

In point-slope form, considering a point [tex](x_0, y_0)[/tex], the equation is:

[tex]y - y_0 = m(x - x_0)[/tex]

The line goes through points (0,2) and (1,5), hence the slope is:

m = (5 - 2)/(1 - 0) = 3.

Since the line goes through point (1,5), the equation is:

y - 5 = 3(x - 1).

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Answer:

X=-14

Step-by-step explanation:

16+22+x=24

38+x=24

x=24-38

x=-14

Based on the information, it can be inferred that payment option A means a payment of $450, while option B means a payment of $300.

The payment options contemplated by the employer are distributed as follows:

Option A

Option B

Note: This question is incomplete because there is some information missing. Here is the missing information:

Complete the tables to show how much money would be received for both payment options, each week, for 6 weeks.

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I don’t have an answer but by any chance did you complete the assignment?

The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.

According to the question

Using the key: 2|4 = 24, the following are the set of data represented by the stem-and-leaf plot showing:

Row one, 1| 5 6 6 7 9 :

This means there are 5 data set for the first row which are:

15, 16, 16, 17, 19

Row two, 2|0 1 3 :

There are 3 data here, which are:

20, 21, 23

Row 3, 3|2: = 32

Row 4, 4|2: = 42

So, The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.

Correct option is C.

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Answer:

C

Step-by-step explanation:

For lines AC and EF, line FC is a transversal.

Angles ACF and EFC are same side interior angles.

Since their measures add to 180°, then the lines are parallel.

Answer: Choice C

Given that, y varies indirectly as the square of x, the value of y when x equal 8 is 2.

Indirect variation is expressed as;

y ∝ 1/x

Given that;

y ∝ 1/x²

y = k/x²

Where k is the proportionality constant.

Given that;

First, we determine the proportionality constant.

y = k/x²

8 = k/4²

8 = k/16

k = 128

Now, we find y when x = 8

y = k/x²

y = 128 / 8²

y = 128 / 64

y = 2

Given that, y varies indirectly as the square of x, the value of y when x equal 8 is 2.

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Answer:

7 : 20

Step-by-step explanation:

2km = 2000m

Then the ratio of 700m to 2 km​ is :

700 / 2000

Then the ratio in simplest form is :

7 / 20

Answer:

[tex]0.75[/tex]

Step-by-step explanation:

750metres÷1000

Answer:

x² + 1 = 0

a = 1

b = 0

c = 1

[tex]x1.2 = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

[tex]x1.2 = \frac{ - 0 ±\sqrt{ {0}^{2} - (4.1.1) } }{2.1} [/tex]

[tex]x1.2 = \frac{0± \sqrt{0 - 4} }{2} [/tex]

[tex]x1.2 = \frac{± \sqrt{ - 4} }{2} [/tex]

There is no real solution because the discriminant is negative

Note.

Formula diskriminan

√b² - 4ac.

if the diskrimanan is negatif, so the quadratic equatoin dont have solution

The amount of time between interest payments is know as period.

Period is the time between when interests are paid. Period can vary depending on the terms of the investment. Periods can be yearly, quarterly, semi-annually, biweekly or weekly.

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By evaluating the quadratic function, we will see that the differential quotient is:

[tex]\frac{f(2 + h) - f(2)}{h} = 8 + h[/tex]

Here we have the quadratic function:

[tex]f(x) = x^2 + 4x + 5[/tex]

Evaluating the quadratic equation we get:

[tex]\frac{f(2 + h) - f(2)}{h}[/tex]

So we need to replace the x-variable by "2 + h" and "2" respectively.

Replacing the function in the differential quotient:

[tex]\frac{(2 + h)^2 + 4*(2 + h) + 5 - (2)^2 - 4*2 - 5}{h} \\\\\frac{4 + 2*2h + h^2 + 8 + 4h - 4 - 8 }{h} \\\\\frac{ 2*2h + h^2 + 4h }{h} = \frac{8h + h^2}{h}[/tex]

If we simplify that last fraction, we get:

[tex]\frac{8h + h^2}{h} = 8 + h[/tex]

The third option is the correct one, the differential quotient is equal to 8 + 4.

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Answer:

x = 5

Step-by-step explanation:

Since the line is vertical,

the equation of the line then is x = (some value).

Since this particular line passes throught (5,-4), where the x coordinate is 5, we can deduce the equation of this line to be x = 5.

Using trigonometric identities, the simplified expression, without quotients, is given as follows:

A. [tex]\cos{\beta}\cot{\beta}[/tex]

The cosecant of an angle is given by one divided by the sine of the angle, hence:

[tex]\csc{\beta} = \frac{1}{\sin{\beta}}[/tex]

The sine and the cosine of an angle are related as follows:

[tex]\sin^2{\beta} + \cos^2{\beta} = 1[/tex]

[tex]\cos^2{\beta} = 1 - \sin^2{\beta}[/tex]

The cotangent of an angle is:

[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}}[/tex]

The expression given is:

[tex]\csc{\beta} - \sin{\beta}[/tex]

Simplifying the cosecant:

[tex]\csc{\beta} - \sin{\beta} = \frac{1}{\sin{\beta}} - \sin{\beta} = \frac{1 - \sin^{2}\beta}{\sin{beta}}[/tex]

Then, applying the last two identities in the subsection above to remove the quotient, the simplified expression will be found as follows:

[tex]\frac{1 - \sin^{2}\beta}{\sin{beta}} = \frac{\cos^2{\beta}}{\sin{\beta}} = \frac{\cos{\beta}}{\sin{\beta}} \times \cos{\beta} = \cos{\beta}\cot{\beta}[/tex]

Hence option A is correct.

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The area of QOR from the given diagram is 2π square centimeters

A sector is said to be a part of a circle made of the arc of the circle along with its two radii.

The formula for calculating the area of a sector is expressed as;

A = r²β/2

where

r is the radius of the circle

β is the angle subtended

Given the following parameters

<QOR = 180 - <POQ

<QOR = 180 - 135

<QOR = 45 degrees

Determine the radius

L = rβ

π = r(π/4)

1 = r/4

r =  4

Determine the area of QOR

Area = 4²(π)/8

Area = 2π

Hence the area of QOR from the given diagram is 2π square centimeters

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Answer:

mother age 37

sons age 12

Answer:

Well a sovial reason is that no one would no what order yo do it in, which would cause arguments

Answer:

without the order of operations, maths literally doesn't work.

Step-by-step explanation:

like whilst some equations don't rely on a particular order for solving, if you for example, don't solve brackets first, then try to multiply them by something else basically the equation breaks and you get the wrong answer. So... kids remember your BODMAS :)

The ordered pairs of the equation y = 3^x are (0,1), (1,3) and (2,9)

The equation is given as:

y = 3^x

Let x = 0, 1 and 2

y = 3^0 = 1

y = 3^1 = 3

y = 3^2 = 9

So, we have the following ordered pairs (0,1), (1,3) and (2,9)

Hence, the ordered pairs of the equation y = 3^x are (0,1), (1,3) and (2,9)

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The brief report about what the attached data in the box plot shows that: "Women appear to marry around three years younger than males, although the shape and dispersion of the two distributions are extremely comparable."

A boxplot is a type of graph that shows how the values in the data are distributed.

A boxplot is a standardized technique of representing data distribution based on a five-number summary ("minimum", first quartile (Q1), median, third quartile (Q3), and "maximum").

It can provide information about your outliers and their values.

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Full Question:

In​ 1975, did men and women marry at the same​ age? Here are boxplots of the age at first marriage for a sample of U.S. citizens then. Write a brief report discussing what these data show.

The correct trigonometry formula to solve for x in the right angled triangle is sin(62°) = 18 / x

An equation is an expression that shows the relationship between two or more variables and numbers.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Hence:

sin(62°) = 18 / x

The correct trigonometry formula to solve for x in the right angled triangle is sin(62°) = 18 / x

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Answer:

Step-by-step explanation:

Hello : let A(0,-6) B(8,-8)

the slope is : (YB - YA)/(XB -XA)

(-8+6)/(8-0) = -2/8=-1/4

an equation is : y=ax+b a is a slope

y = (-1/4)x +b

the line through point A (0;-6) : -6 = (-1/4)(0)+b

b = -6            the equation is : y =(-1/)4x-6

The decimal equivalent of 45⁰ 32’ 55” is 45.55⁰

The given degree is:

45⁰ 32' 55''

This can be converted to decimal as shown below

[tex]45+\frac{32}{60} +\frac{55}{3600}[/tex]

This can be simplified further as:

[tex]45^o32'55'' = 45+0.53+0.0153\\\\45^o32'55'' = 45.55^0[/tex]

Therefore, the decimal equivalent of 45⁰ 32’ 55” is 45.55⁰

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Hi

the trick is to define price by referring only to one item.  

Here the bootle of water is you reference.  

there is 3 gallons  of milk

             6 bottles of water

              6 bags of chips

let's call bottle of water  " X"  

water cost  = X

milk = X+1.7

chips =  X/2

So we have  :  

3 (X+1.7 ) + 6X + 6 ( X/2) = 29.1

3X+ 5.1 + 6X + 6X/2 = 29.1

3X +6X + 3X + 5.1 = 29.1

 12X +5.1 = 29.1

  12X = 29.1 - 5.1

   12 X =  24

        X = 24/12

        X = 2

price of bottle is  2 dollars  

then milk is  2 + 1.7 = 3.7

        chips =  2/2 = 1

let's check =  3*3.7 + 6*2 + 6*1 =   11.1+12+ 6 = 29.1

A geometric shapes that can be used to create a logo that will fit in a measuring 15 cm by 15 cm is to use a square.

It should be noted that geometric shapes are the figure of area that is closed by a boundary.

In this case, a geometric shapes that. an be used to create a logo that will fit in a measuring 15 cm by 15 cm is to use a square.

This is because all the sides in a square are equal.

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The average price paid by him for the shares after 3 months is ksh. 163.33

Average price paid for the shares after 3 months

= (120 + 160 + 210) / 3

= 490 / 3

= 163.333333333333

Approximately,

ksh. 163.33

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