Identify the equation of the line graphed below. Prove by converting!

A. 2x + y = 4
B. 2x - y = 4
C. x + 2y = 8
D. x - 2y = 8

Answer:

The zeros of

y = x(x + 2)(x + 5)y=x(x+2)(x+5)

are

x=0,x=-2,x=-5x=0,x=−2,x=−5

EXPLANATION

The given function is

y = x(x + 2)(x + 5)y=x(x+2)(x+5)

To find the zeros of the above function, we just have to equate the function to zero and solve for x.

x(x + 2)(x + 5) = 0x(x+2)(x+5)=0

This implies that,

x = 0 \: \: or \: x + 2 = 0 \:or \: x + 5 = 0x=0orx+2=0orx+5=0

x = 0 \: \: or \: x = - 2\:or \: x = - 5x=0orx=−2orx=−5

To graph the above function, we need to consider the multiplicity.

We can see that the multiplicity of the roots are odd. This means that, the graph crosses the x-axis at each x-intercept.

We also need to consider the position of the graph on the following intervals,

x < - 5x<−5

When

x = - 10x=−10

y = - 10( - 8)( - 5) \: < \: 0y=−10(−8)(−5)<0

The graph is below the x-axis.

- 5 \: < \: x \: < \: - 2−5<x<−2

When

x = - 3x=−3

y = - 3(2)( - 1) \: > 0y=−3(2)(−1)>0

The graph is above the x-axis.

- 2 \: < \: x < \: 0−2<x<0

when

x = - 1x=−1

y = -1(1)(4) \: < \: 0y=−1(1)(4)<0

The graph is below the x-axis.

Finally the interval,

x \: > \: 0x>0

when

x = 1x=1

y = 1(3)(6) \: > \: 0y=1(3)(6)>0

The graph is above the x-axis.

We can now use the above information to sketch graph as shown in the diagram above

Answer:

Each movie costs 3.99

Step-by-step explanation:

If every month he is paying $7.99 initially for the service, you take $19.96 and subtract the initial cost ($7.99) then your left with $11.97 and since he bought 3 movies then you divide $11.97 by 3 and your left with $3.99 which is your final answer!

Hope this makes sense!

Answer:

N(h) = 17.5h + 15

Step-by-step explanation:

N(h) = 8.75h + 15              | write original equation

N(h) = 8.75(2) + 15            | multiply the original hourly fee by 2

N(h) = 17.5 + 15                 | solve

Stay healthy and happy <3.

Hope this helped.

The required function represents the new fees is given as N(h) = 17.5h + 15.

Given that,
An administrative assistant works from home and originally charged her clients $8.75 per hour for any clerical work plus a set fee of $15, or C(h) = 8.75h + 15. She decided to double her hourly fee but keeps her set fee the same.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given function,
C(h) = 8.75h + 15.
Now,
According to the question,
N(h) = 2× 8.75h + 15.
N(h) = 17.5h + 15.

Thus, the required function represents the new fees is given as N(h) = 17.5h + 15.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ2

Answer:

False.

General Formulas and Concepts:

Algebra I

Terms/Coefficients

Calculus

Differentiation

Derivative Rule [Basic Power Rule]:

Derivative Rule [Product Rule]:                                                                             [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle \frac{d}{dx}[x^3e^x][/tex]

Step 2: Differentiate

∴ [tex]\displaystyle \frac{d}{dx}[x^3e^x] \neq x^3e^x(3x + 2)[/tex]  but  [tex]\displaystyle \frac{d}{dx}[x^3e^x] = (x^3 + 3x^2)e^x[/tex].

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

Step-by-step explanation:

Sum of interior angles is 180

Sum of interior angles is 180

Vertical angles are same, the sum of remaining angles is same for both triangles:

Exterior angle is same as the sum of non-adjacent interior angles:

identicalAnswer:

1) 64, 2) 6, 3) 26, 4) 33

Step-by-step explanation:

#1

Sum of interior angles is 180

70 + 46 + x = 180

116 + x = 180

x = 64

#2

Sum of interior angles is 180

84 + 7x + 1 + 9x - 1 = 84

16x + 84 = 180

16x = 96

x = 6

#3

Vertical angles are identical, the sum of remaining angles is the same for both triangles:

35 + 25 = 34 + x

60 = 34 + x

x = 60 - 34

x = 26

#4

The exterior angle is the same as the sum of non-adjacent interior angles:

5x - 7 + 6x + 3 = 84

11x - 4 = 84

11x = 88

x = 8

m∠G = 5x - 7 = 5*8 - 7 = 40 - 7 = 33

Answer:

answer 215 nickels

Step-by-step explanation:

Answer:

11:18

Step-by-step explanation:

Hope this helped!

Proof:-

In ∆XYZ and ∆VWZ

[tex]\because\sf\begin{cases}\sf XZ\cong VZ(Given)\\ \sf YZ\cong WZ(Given)\\ \sf <XZY\cong <WZV(Opposite angles)\end{cases}[/tex]

Hence

∆XYZ[tex]\cong[/tex](Side-Angle-Side)

Answer:

x=1+sqr57,1-sqr57

Step-by-step explanation:

Answer:

  x = -6.5, x = 8.5

Step-by-step explanation:

The given equation ...

  x^2 -4x -31 = -2x +25

can be rewritten to a form that facilitates completing the square:

  x^2 -2x = 56 . . . . . add 2x+31

  x^2 -2x +1 = 57 . . . add 1 to complete the square

  (x -1)^2 = 57 . . . . . write the left side as a square

  x -1 = ±√57 . . . . . take the square root

  x = 1 ±√57 ≈ {-6.5, 8.5} . . . . . add 1, evaluate

Solutions are near x = -6.5 and x = 8.5.

Answer:6 . 625 or 6 5/8

Step-by-step explanation

10 + (-3 3/8)         (adding a negative is like subtracting a positive)

10 - 3 3/8

6 5/8

Given that √2 = 1.414

The value of (1/2)√(16200)

16200 can be written as

16200 = 2×8100

16200 = 2×2×4050

16200 = 2×2×2×2025

16200 = 2×2×2×5×405

16200 = 2×2×2×5×5×81

16200 = 2×2×2×5×5×3×27

16200 = 2×2×2×5×5×3×3×9

16200 = 2×2×2×5×5×3×3×3×3

√16200 = √(2×2×2×5×5×3×3×3×3)

√16200 = √2×(2×2)×(5×5)×(3×3)×(3×3)

√16200 = 2×5×3×3√2

√16200 = 90√2

Now,

(1/2)√16200

⇛(1/2)×90√2

⇛90√2/2

⇛45√2

⇛45×1.414

⇛63.63

Answer: Hence, value of (1/2)√(16200) is 63.63

also read similar questions: if √2=1.414 and√3=1.732,find the value of 1/√2+√3..

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If √2 = 1.414 then the value of 5+√2 / 5-√2 is..

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The value of 1/2√16200 given the value of √2 = 1.414 is 63.63

Prime factorization of √16200

= 3 × 3 × 5 × √2

= 90√2

Given:

1/2√16200

= 1/2 × 90√2

= 90√2 / 2

= 45√2

= 45 × √2

= 45 × 1.414

= 63.63

Therefore, the value of 1/2√16200 is 63.63

Learn more about prime factorization:

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Answer: yes they are perpendicular

Answer:

Step-by-step explanation:

Determine which climbed at a constant rate

A constant rate would produce a straight line.  The slope is the same for all the data for that climber.  We can either calculate the slope between the first and last intervals and see if the slope changes.  Or we can graph the points, which I chose to do.  See the attachment.

Note that Joe's rate is not constant.  It appears as though he's wearing down.  Both Zas and Stephon have constant slopes, so their climbing rates are constant over the period measured.

The slope is the climbing rate:

Joe:           Not Constant

Zas:            2.5 feet/sec

Stephon:     4.0 feet/sec

Time to Reach 30 feet

Joe:           Unknown - he's slowing down at an unpredictable rate.

For Zas and Stephen, use their slopes in the expression:

Use m for slope (ft/sec):  y = m(t) where t is time in seconds

Zas:            2.5 feet/sec:  y = 2.5(t)  Time to reach 30 is 30/2.5 or 12 sec.

Stephon:     4.0 feet/sec:  y = 4.0(t)  Time to reach 30 is 30/4.0 or 7.5 sec.

Answer:

1,015

Step-by-step explanation:

7 pounds of honey equals 1 pound of wax

So if we have 145 pounds of was, we multiply 145 by 7

145x7= 1,015

Answer:

when the coefficient of x^2 is negative

Step-by-step explanation:

Answer:

A pencil is about 19 centimeters long

Answer:

if 100 inches=254 centimeters

then 10 inches=x

100x=2540

x=2540/100

x=25.4 centimeters

Answer:

40 i think

Step-by-step explanation:

======================================================

Explanation:

Solve the inequality for x.

5x + 4 < 29

5x < 29-4

5x < 25

x < 25/5

x < 5

I subtracted 4 from both sides (step 2). Then I divided both sides by 5 to fully isolate x (step 4). The inequality sign stays the same the entire time.

Since x < 5, this means the original set {3,4,5,6} becomes {3,4} since these values make x < 5 a true statement. In other words, we erase 5 and 6 because something like 6 < 5 is false.

That's why {3, 4} is the final answer.

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

An alternative method is to go through the set {3,4,5,6} and plug those items one by one into the original inequality. If you get a true result, then it's part of the answer.

Let's try x = 3

5x + 4 < 29

5(3) + 4 < 29

15+4 < 29

19 < 29

We get a true statement at the end, so x = 3 is part of the solution set. A similar story happens for x = 4 as well.

If we tried x = 5, then,

5x + 4 < 29

5(5) + 4 < 29

25 + 4 < 29

29 < 29

which is false. No number is bigger than itself (or smaller than itself). Therefore, x = 5 is crossed out of the original set. You should get a false statement for x = 6, which means we'll kick this value out as well.

Answer:

\mathrm{X\:Intercepts}:\:\left(-\frac{431}{26},\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:43.1\right)

Step-by-step explanation:

Answer:

  (b)  {-8, 2}

Step-by-step explanation:

The given equation

  x³ +6x -16 = 0

cannot be factored in integers. It has one irrational real root near x=1.759, and two complex roots.

__

Perhaps you want to factor ...

  x² +6x -16 = 0

  (x +8)(x -2) = 0

This has solutions x = -8 and x = 2 that make the factors be zero.

_____

Additional comment

"Cubed" refers to an exponent of 3.

Answer:

Option b] (2,-8)

Step-by-step explanation:

⇒ x³ + 6x - 16 = 0

♦ the value of one root is irrational and other two are complex roots.

⇒ x² + 6x - 16 = 0

⇒ (x + 8)(x - 2) = 0

⇒ x = 2 , -8

Using the histogram, the mean of the data-set is estimated to be of 31.

In this problem, the intervals and relative frequencies are:

Hence, the mean is:

[tex]E(X) = 23\frac{4}{30} + 28\frac{8}{30} + 33\frac{14}{30} + 38\frac{4}{30} = \frac{23(4) + 28(8) + 33(14) + 38(4)}{30} = 31[/tex]

For more on mean of histograms, you can check https://brainly.com/question/24651197

Answer:

a. (10,10)

Step-by-step explanation:

This was by accident the first answer is right

Answer: y = 115 and x = 78

Step-by-step explanation:

y = 115 because it is parallel with the angle 115 and parallel are congruent, for x find the angle beside the angle 102 and that angle is parallel with the angle x and that will be 180 - 102 = 78 which is x  

Answer:

Step-by-step explanation:

Dilation does not affect angles or the direction of lines. The lines of a dilated figure will be parallel to the original, unless they go through the center of dilation.

Line CD does not go through P, so C'D' is distinct and parallel to it (True).

Angles B and B' are congruent. (True)