If f(x) = x^2-1 which of the following ordered pairs would be on the graph of f(x)

Answer:

  0, 1, or 2 real solutions

Step-by-step explanation:

Including complex and repeated solutions, a polynomial with real coefficients, and of degree n, always has n solutions.

If you're only concerned about real solutions, a 2nd degree equation in one variable may have 0, 1, or 2 real solutions. Here are some examples.

-5,3,-2,1 on a number line

<-|----|----|----|----|----|----|----|----|->

-5 -2 0 1 3

Answer:

[tex]5(4)^x=320\\\frac{5(4)^x}{5}=\frac{320}{5}\\ 4^x=64\\x*(log(4) )=log(64)\\x=\frac{log(64)}{log(4)}\\ x=3[/tex]

Step-by-step explanation:

Answer:

B = (3.3)

Step-by-step explanation:

The statements that can be used to describe the reasoning used to determine if Kelsey’s inequality is correct include:

It should be noted that the inequality symbol is incorrect because she can spend up to and including $65.

Based on the information given, the correct expression that can be used to solve the question should be:

65 - (5.50b + 7.5)

In conclusion, the correct options are B and C.

Read related link on:

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Answer:

B and C

Step-by-step explanation:

Answer:

12y-14

Step-by-step explanation:

we expand first and doing that we get

5y+15+7y-35+6

12y-14

2(6y-7)

Step-by-step explanation:

5(y+3) + 7(y-5) +6

5y+15+7y-35+6

5y+7y+15-35+6

12y-14

y= -14-12

y= +26

Answer:

(- 4, 17 ) and (2, - 1 )

Step-by-step explanation:

Given the 2 equations

y = x² - x - 3 → (1)

y = - 3x + 5 → (2)

Substitute y = x² - x - 3 into (2)

x² - x - 3 = - 3x + 5 ( subtract - 3x + 5 from both sides )

x² + 2x - 8 = 0 ← in standard form

(x + 4)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 2 = 0 ⇒ x = 2

Substitute these values into (2) for corresponding values of y

x = - 4 : y = - 3(- 4) + 5 = 12 + 5 = 17 ⇒ (- 4, 17 )

x = 2 : y = - 3(2) + 5 = (- 6 + 5 = - 1 ⇒ (2, - 1 )

Answer:

$1100

Step-by-step explanation:

First find the area of the trapezoid

A = 1/2 (b1+b2)*h

A = 1/2 ( 90+110) *44

A = 1/2(200)*44

A = 4400ft^2

The cost is .25 per square foot

4400* .25 =1100

Answer:

$1100

Step-by-step explanation:

((90 + 110)/2 * 44)) * .25 = 1100

Answer:

2.25 km to go

Step-by-step explanation:

In order to get this answer, you have to figure out how many km 10% is, 0.1125. Then multiply that by the remaining 20% because he already finished 80% of the trail. So, 0.1125 x 20 = 2.25.

Hope this helps! :)

Answer:

B

Step-by-step explanation:

So we have a table of values of a used car over time. At year 0, the car is worth $20,000. By the end of year 8, the car is only worth $3400.

We can see that this is exponential decay since each subsequent year the car depreciates by a different value.

To find the rate of change the car depreciates, we simply need to find the value of the exponential decay. To do this (and for the most accurate results) we can use the last term (8, 3400).

First, we already determined that the original value (year 0 value) of the car is 20,000. Therefore, we can say:

[tex]f(t)=20000(r)^t[/tex]

Where t is the time in years and r is the rate (what we're trying to figure out).

Now, to solve for r, use to point (8, 3400). Plug in 8 for t and 3400 for f(t):

[tex]3400=20000(r)^8\\3400/20000=17/100=r^8\\r=\sqrt[8]{17/100}\approx0.8[/tex]

In other words, the rate of change modeled by the function is 0.8.

As expected, this is exponential decay. The 0.8 tells us that the car depreciates by 20% per year.

The data from a dot plot can be analyzed to find the five number summary, from which a box plot can be constructed

The correct option for the details of the box plot that represents the dot plot data is;

Box plot titled ACT Score with a minimum of 18, quartile 1 of 21, median of 22, quartile 3 of 23, and maximum of 25

The process of deriving the five number summary of the box plot above is as follows;

Known:

The data from the dot plot can be expressed in increasing order for analysis of a box plot as follows;

18, 19, 19, 19, 21, 21, 21, 21, 22, 22, 22,22, 23, 23, 23, 24, 24, 25

The number of data points in the statistics, n = 18

Unknown:

The five number summary

Method:

Finding the five number summary as follows;

The minimum value = 18

The maximum value = 25

∴ Quartile 1 = Q₁ = 5th term = 21

Quartile 2 = 22

Quartile 3 = 23

Combining the above 5 number summary, the correct option for the box plot representing the dot plot data, is therefore;

Box plot titled ACT Score with a minimum of 18, quartile 1 of 21, median of 22, quartile 3 of 23, and maximum of 25

Learn more about box and whiskers, and dot plots here;

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Answer:

-3

Step-by-step explanation:

Answer:

Step-by-step explanation:

The expression 4 raised to 4 can be written in mathematical term as [tex]4^4[/tex] and this means the value of 4 in four places as shown;

[tex]4^4\\\\= 4 * 4* 4* 4\\\\= (4 * 4)* (4* 4)\\\\= 16*16\\\\= 256\\\\[/tex]

Hence the expression 4 raised to 4 is equivalent to 256

Answer:

4 pieces

Step-by-step explanation:

Total length of lumber = 9 feet

How many 2 1/4 foot pieces can you cut from this piece of lumber

To find the number of 2 1/4 foot pieces of lumber in a 9 feet of lumber, we will divide the total length of lumber by the length of each piece of lumber

9 ÷ 2 1/4

= 9 ÷ 9/4

= 9 × 4/9

= 36/9

= 4 pieces of lumber

Therefore, 4 pieces of 2 1/4 foot of lumber can be gotten from 9 feet of lumber

Answer:

8

Step-by-step explanation:

khan

Answer:

8

Step-by-step explanation:

Answer:

Option B, random sample

That should be the answer

We know

[tex]\boxed{\sf Area=Length\times Width}[/tex]

[tex]\\ \sf\longmapsto 336=x(x+5)[/tex]

[tex]\\ \sf\longmapsto x^2+5x=336[/tex]

[tex]\\ \sf\longmapsto x^2+5x-336=0[/tex]

[tex]\\ \sf\longmapsto x^2-16x+21x-336=0[/tex]

[tex]\\ \sf\longmapsto x(x-16)+21(x-16)=0[/tex]

[tex]\\ \sf\longmapsto (x-16)(x+21)=0[/tex]

[tex]\\ \sf\longmapsto (x-16)=0\:or\:(x+21)=0[/tex]

[tex]\\ \sf\longmapsto x=16\:or\:x=-21[/tex]

[tex]\\ \sf\longmapsto Length=x=16yd[/tex]

[tex]\\ \sf\longmapsto Width=x+5=16+5=21yd[/tex]

Answer:

XY = 17

Step-by-step explanation:

Intersect secant theorem, EX * EY = EZ*EW

34 * EY = 25.5 * 68

      [tex]EY = \frac{25.5*68}{34}\\\\ = 25.5* 2\\\\ = 51.0 = 51[/tex]

EY  = 51

EX + XY = 51

 34 + XY = 51

        XY = 51 - 34 = 17

Answer:

$420

.8 x = 336

x = 336/.8

X=$420

Step-by-step explanation:

Answer:

[tex]\frac{x^{3} }{4y^{5} }[/tex]

Step-by-step explanation:

Simplifica la expresión

Answer:

[tex]\boxed{ \{7, 6, 5, 3 \} }[/tex]

Step-by-step explanation:

The domain is all possible values for x.

The range is all possible values for f(x) or y.

The domain given is {-3, -2, -1, 1}.

Plug x as {-3, -2, -1, 1} and find the f(x) or y values.

[tex]f(-3)=-(-3)+4=7\\f(-2)=-(-2)+4=6\\f(-1)=-(-1)+4=5\\f(1)=-(1)+4=3[/tex]

The range is {7, 6, 5, 3}, when the domain is {-3, -2, -1, 1}.

Answer: 54.29%

Step-by-step explanation:

Given: The probability that they  will win both games is 38%.

i.e. P( both games will win) =0.38

The probability that they will win just the first game is  70%.

P(first game will win) = 0.70

To find : P(second game will win| first game will win)

Using formula: [tex]P(B|A)=\dfrac{P(\text{both A and B})}{P(A)}[/tex]

So, P(second game will win| first game will win) = [tex]\dfrac{\text{ P( both games will win)}}{\text{P(first game will win)}}[/tex]

[tex]=\frac{0.38}{0.70}\approx0.5429=54.29\%[/tex]

Hence, the required probability = 54.29%

Answer:

Length of diagonal = 6

Step-by-step explanation:

Given that

Diagonal of a rectangle makes an angle of [tex]30^\circ[/tex] with the longer side.

Kindly refer to the attached diagram of the rectangle ABCD such that diagonal BD makes angles of [tex]30^\circ[/tex] with the longer side CD and BA.

[tex]\angle CDB =\angle DBA =30^\circ[/tex]

Side AD = BC = 3 units

To find:

Length of diagonal BD = ?

Solution:

We can use the trigonometric ratio to find the diagonal in the [tex]\triangle BCD[/tex] because [tex]\angle C =90^\circ[/tex]

Using the sine :

[tex]sin\theta = \dfrac{Perpendicular }{Hypotenuse }[/tex]

[tex]sin\angle CDB = \dfrac{BC}{BD}\\\Rightarrow sin30^\circ = \dfrac{3}{BD}\\\Rightarrow \dfrac{1}2 = \dfrac{3}{BD}\\\Rightarrow BD =2 \times 3 \\\Rightarrow BD = \bold{6 }[/tex]

So, the answer is:

Length of diagonal = 6

The correct solution graph to the inequalities are

[tex]4(9x-18)>3(8x+12)[/tex]  →  C

[tex]-\frac{1}{3}(12x+6) \geq -2x +14[/tex]  → A

[tex]1.6(x+8)\geq 38.4[/tex]  →  B

(NOTE: The graphs are labelled A, B and C from left to right)

For the first inequality,

[tex]4(9x-18)>3(8x+12)[/tex]

First, clear the brackets,

[tex]36x-72>24x+36[/tex]

Then, collect like terms

[tex]36x-24x>36+72\\12x >108[/tex]

Now divide both sides by 12

[tex]\frac{12x}{12} > \frac{108}{12}[/tex]

∴ [tex]x > 9[/tex]

For the second inequality

[tex]-\frac{1}{3}(12x+6) \geq -2x +14[/tex]

First, clear the fraction by multiplying both sides by 3

[tex]3 \times[-\frac{1}{3}(12x+6)] \geq3 \times( -2x +14)[/tex]

[tex]-1(12x+6) \geq -6x +42[/tex]

Now, open the bracket

[tex]-12x-6 \geq -6x +42[/tex]

Collect like terms

[tex]-6 -42\geq -6x +12x[/tex]

[tex]-48\geq 6x[/tex]

Divide both sides by 6

[tex]\frac{-48}{6} \geq \frac{6x}{6}[/tex]

[tex]-8\geq x[/tex]

∴ [tex]x\leq -8[/tex]

For the third inequality,

[tex]1.6(x+8)\geq 38.4[/tex]

First, clear the brackets

[tex]1.6x + 12.8\geq 38.4[/tex]

Collect likes terms

[tex]1.6x \geq 38.4-12.8[/tex]

[tex]1.6x \geq 25.6[/tex]

Divide both sides by 1.6

[tex]\frac{1.6x}{1.6}\geq \frac{25.6}{1.6}[/tex]

∴ [tex]x \geq 16[/tex]

Let the graphs be A, B and C from left to right

The first graph (A) shows [tex]x\leq -8[/tex] and this matches the 2nd inequality

The second graph (B) shows [tex]x \geq 16[/tex] and this matches the 3rd inequality

The third graph (C) shows [tex]x > 9[/tex] and this matches the 1st inequality

Hence, the correct solution graph to the inequalities are

[tex]4(9x-18)>3(8x+12)[/tex]  →  C

[tex]-\frac{1}{3}(12x+6) \geq -2x +14[/tex]  → A

[tex]1.6(x+8)\geq 38.4[/tex]  →  B

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Answer:

4(9x − 18) > 3(8x + 12) = x > 9

(12x + 6) ≥ -2x + 14 = x ≤ -8

1.6(x + 8) ≥ 38.4 = x ≥ 16

Just follow the numbers with the dotted thing and see the numbers I underlined.

Step-by-step explanation:

Use the properties of inequality and real numbers to solve each inequality.

4(9x − 18) > 3(8x + 12)

36x − 72 > 24x + 36

12x − 72 > 36

12x > 108

x > 9

The graph has an open circle at 9, and moves toward the right on the number line.

(12x + 6) ≥ -2x + 14

12x + 6 ≤ 6x − 42

6x + 6 ≤ -42

6x ≤ -48

x ≤ -8

The graph has a closed circle at -8, and moves toward the left on the number line.

1.6(x + 8) ≥ 38.4

x + 8 ≥ 24

x ≥ 16

The graph has a closed circle at 16, and moves toward the right on the number line.

Answer:

$8

Step-by-step explanation:

Firstly, Let us identify the variables in the functions.

The function states that for every n ball, the price is $0.80. Plus the $5.50.

Now that we know what the function stands for, we can substitute 10 into n, and remove the entrance fee of $5.50.

P=0.80n

This gives us $8, which means the price for 10 balls not including the entrance fee is $8.

Answer:

Amdjss

Step-by-step explanation:

Answer:

Step-by-step explanation: Given that a civil servant own a car is 1/6.

A) The Pr. that each own a car = Pr of each multiplied by the other.

Pr = 1/6 ×1/6

P = 1/36

B) Pr that only one owns a car

= 1/6 × (1-1/6) + 1/6 × (1-1/6)

= 1/6 × 5/6 + 5/6 × 1/6

= 5/36 + 5/36

= 10/36

= 5/18

Answer:

7x + 2

Step-by-step explanation:

Answer:

All real numbers

Step-by-step explanation:

Adding f(x) and g(x) together gets you, (4x-5) + (3x-7) = 7x - 12

If you graph this function you get a slanted line, which extends forever so the domain will be all real numbers.

Answer:

Hello,

Answer B

Step-by-step explanation:

[tex]C(x)=300*x^2+200*x\\\\R(x)=-0.5*x^3+900*x^2-500*x+400\\\\\\P(x)=R(x)-C(x)\\\\=-0.5*x^3+900*x^2-500*x+400-(300*x^2+200*x)\\\\=-0.5x^3+900x^2-300x^2-500x-200x+400\\\\=-0.5x^3+600x^2-700x+400\\[/tex]