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3 years ago

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The table shows the outputs, y, for different inputs, x: Input (x) 3 7 11 15 Output (y) 4 6 8 10 Part A: Do the data in this tab

le represent a function? Justify your answer. (3 points) Part B: Compare the data in the table with the relation f(x) = 5x − 21. Which relation has a greater value when x = 11? (2 points) Part C: Using the relation in Part B, what is the value of x if f(x) = 99? (5 points) (10 points) Show/hide advanced buttons

1 answer:

stiv31 [10]3 years ago

3 0

Answer:

Step-by-step explanation:

x (3,7,11,15)

y (4,6,8,10)

A. This IS a function because u have no repeating x values

B. Data in table :

when x = 11, y = 8

relation : f(x) = 5x - 21....when x = 11

f(11) = 5(11) - 21

f(11) = 55 - 21

f(11) = 34.....so when x = 11, y = 34

therefore, the relation f(x) = 5x - 21 has a greater value then the table

C. f(x) = 5x - 21......f(x) = 99

99 = 5x - 21

99 + 21 = 5x

120 = 5x

120/5 = x

24 = x <====

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Which of the following equations have complex roots?

mestny [16]

Answer:

A

Step-by-step explanation:

Complex roots of quadratic functions occur when the <u>discriminant is negative</u>.

<u>Discriminant</u>

$b^2-4ac\quad\textsf{when}\:\:ax^2+bx+c=0$

Evaluate the discriminant of each of the given equations.

$\textsf{A.} \quad 3x^2+2=0$

$\implies a=3, \quad b=0, \quad c=2$

$\implies b^2-4ac=0^2-4(3)(2)=-24$

As -24 < 0 the equation will have complex roots.

$\textsf{B.} \quad 2x^2+1=7x$

$\implies 2x^2-7x+1=0$

$\implies a=2, \quad b=-7, \quad c=1$

$\implies b^2-4ac= (-7)^2-4(2)(1)=41$

As 41 > 0 the equation does not have complex roots.

$\textsf{C.} \quad 3x^2-1=6x$

$\implies 3x^2-6x-1=0$

$\implies a=3, \quad b=-6, \quad c=-1$

$\implies b^2-4ac=(-6)^2-4(3)(-1)=48$

As 48 > 0 the equation does not have complex roots.

$\textsf{D.} \quad 2x^2-1=5x$

$\implies 2x^2-5x-1=0$

$\implies a=2, \quad b=-5, \quad c=-1$

$\implies b^2-4ac=(-5)^2-4(2)(-1)=33$

As 33 > 0 the equation does not have complex roots.

Learn more about discriminants here:

brainly.com/question/27444516

brainly.com/question/27869538

Learn more about complex roots here:

brainly.com/question/26344541

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2 years ago

Given an arithmetic sequence with a3=5 and a5=19, find the 24th term.

krok68 [10]

The 24th term is 152

Step-by-step explanation:

The formula of the nth term of an arithmetic sequence is:

$a_n=a+(n-1)d$ , where

a is the first term
d is the common difference between consecutive terms

The third term means n = 3

∵ $a_3=a+(3-1)d$

∴ $a_3=a+2d$

∵ $a_3$ = 5

- Equate the right hand sides of the third term

∴ a + 2d = 5 ⇒ (1)

The fifth term means n = 5

∵ $a_5=a+(5-1)d$

∴ $a_5=a+4d$

∵ $a_5$ = 19

- Equate the right hand sides of the fifth term

∴ a + 4d = 19 ⇒ (2)

Now we have a system of equations to solve it

Subtract equation (1) from equation (2) to eliminate a

∴ 2d = 14

- Divide both sides by 2

∴ d = 7

- Substitute the value of d in equation (1) to find a

∵ a + 2(7) = 5

∴ a + 14 = 5

- Subtract 14 from both sides

∴ a = -9

The twenty fourth term means n = 24

∵ a = -9 and d = 7

- Substitute the values of a and d in the formula of the nth term

∴ $a_24=-9+(24-1)(7)$

∴ $a_24=-9+(23)(7)$

∴ $a_24=-9+161$

∴ $a_24=152$

The 24th term is 152

Learn more:

You can learn more about the arithmetic sequence in brainly.com/question/7221312

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3 years ago

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emmainna [20.7K]

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3 years ago

Four friends share 3 fruit bars equally. what fraction of a fruit bar does each person get?

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Answer:

3/4

Step-by-step explanation:

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3 years ago

Howard is designing a chair swing ride. The swing ropes are 4 44 meters long, and in full swing they tilt in an angle of 2 3 ∘ 2

qaws [65]

Question:

Howard is designing a chair swing ride. The swing ropes are 4 meters long, and in full swing they tilt in an angle of 23°. Howard wants the chairs to be 3.5 meters above the ground in full swing. How tall should the pole of the swing ride be? Round your final answer to the nearest hundredth.

Answer:

7.18 meters

Step-by-step explanation:

Given:

Length of rope, L = 4 m

Angle = 23°

Height of chair, H= 3.5 m

In this question, we are to asked to find the height of the pole of the swing ride.

Let X represent the height of the pole of the swing ride.

Let's first find the length of pole from the top of the swing ride. Thus, we have:

$cos \theta = \frac{h}{L}$

Substituting figures, we have:

$cos(23) = \frac{h}{4}$

Let's make h subject of the formula.

$h = 4cos(23) = 3.68$

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To find the height of the pole of the swing ride, we have:

X = h + H

X = 3.68 + 3.5

X = 7.18

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3 0

3 years ago