For the function f(x)= x^2+4x-1, what is the range of f (x) for the domain {-2,0,1}?

Answer:

  x = 3⁴

Step-by-step explanation:

You want the exponential form of log₃(x) = 4.

It can be helpful to remember that a logarithm is an exponent of the base of the logarithm.

  log₃(x) = 4   ⇔   x = 3⁴

The exponential form is x = 3⁴.

A computer is rendering two scenes then after 14 minutes of the scenes have the same amounts rendered.

As given in the question,

As per condition:

Computer rendered 540 thousands pixels of a kitchen scene and renders another 90kpx each minute:

The expression for the kitchen is illustrated as 540 + 90t

Computer rendered 960kpx of a garden scene and renders 60kpx more pixels each minute

The expression for the garden is illustrated as 960 + 60t

For the scenes have the same amounts rendered is given by :

540 + 90t = 960 + 60t

Collect like terms

90t - 60t = 960 - 540

⇒30t = 420

⇒t = 420/30

⇒t = 14

Therefore, a computer is rendering two scenes then after 14 minutes of the scenes have the same amounts rendered.

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⇒For perpendicular lines when their gradients are multiplied they have to give -1, in this case we are given a line with gradient [tex]\frac{1}{2}[/tex] meaning the gradient of the line perpendicular to it will be -2 since

[tex]-2*\frac{1}{2} =-1[/tex]  this means that the gradient of the new line will be -2

⇒Now we have a point and  gradient.

⇒And we know that the general equation for a straight line is y=mx+c

[tex]3=-2(0)+c\\3=c\\c=3[/tex]

The equation of the line perpendicular to the given one is

y=-2x+3

GOODLUCK!!

Answer:

First, find x.

(12x + 20) + (6x + 70) = 180 (sum of angles on straight line = 180°)

18x + 90 = 180

18x = 90

x = 5

Next, find z.

z = 12x + 20 (vertically opposite angles)

Substitute x = 5 into equation.

z = 12(5) + 20

= 80

580 miles.

On the first day of the tour, she went = east

On the second day she went = north

On the third day = west

On the fourth day she went = south

On the fifth day she went = east

Miles was she from her starting point at the end of the 40th day =?

She was 580 miles from her starting point at the end of the 40th day.

Solution is given in the attached picture.

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Answer:  [-4, 0] which is choice A

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

Reason:

lowest point is when y = -4

highest point is when y = 0

The range is any value of y between these values, including the endpoints themselves. We say the range is [tex]-4 \le y \le 0[/tex] which condenses to the interval notation [-4, 0]

Use square brackets to include the endpoints.

If there were open holes at the highest and lowest points, then we would use curved parenthesis instead.

Trenton’s scouting group make 15 purple T-shirts.

Suppose a number is 'a'. Suppose another number is 'b'. We want to know how much percent of 'b' is 'a'. Then, it is calculated as:

[tex]\dfrac{a}{b} \times 100[/tex]

We have been given that Trenton’s scouting group made 100 T-shirts for a charity fundraiser.

Also the angle measure of the section for purple is 54°, then;

54 / 360 = percent /100

percent = 15

Therefore, 15 percent of 100 T shirt would be;

15/100 x 100

15

Hence, Trenton’s scouting group make 15 purple T-shirts.

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Answer:

6.50 × 65 tickets.

Answer = $422.5

The theater sells 43 adult tickets and 22 child tickets.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let us assume,

The number of adult tickets sold is x

The number of tickets sold for children is y

Since the total number of tickets sold is 65,

x + y = 65 .....(i)

Charge per adult ticket=$10.50,

So the amount collected by selling adult tickets is 10.50×x

Charge per child ticket=$6.50,

So the amount collected by selling tickets for children is 6.50×y

We know that the total amount earned by the theater is $594.50

So, 10.5x +6.5y = 594.50  ......(ii)

After solving equations (i) and (ii), we get the values of x and y as

x = 43 and y = 22

Therefore, the theater sells 43 adult tickets and 22 child tickets.

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After solving the equation x^2-2x-7=0, values of x are -1 + 2√2 and

-1 - 2√2.

A quadratic equation has a leading coefficient of the second degree.

What is a quadratic equation?

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.

It is written in the form of ax²+bx+c.  

After applying the quadratic formula to it we get,

[tex]x = \frac{-b +\sqrt{b^{2} - 4ac } }{2a} \\ x = \frac{-b -\sqrt{b^{2} - 4ac } }{2a}[/tex]

where a = 1

b = 2

c = -7

After putting the values of a,b, and c, we get

x = -1 + 2√2 and,

x = -1 - 2√2 .

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Based on the given shopping list, when put in BIMDAS format and then solved, the total amount would be $26.90

In BIMDAS format, we have to solve the problem in the brackets first and then use the order of operations to find the total shopping cost.

The BIMDAS format would be:

= (Number of orange dozens x Cost per dozen) + (Number of bacon packets x Cost per packet) + (Number of strawberry packets x Price per packet)

= (3 x 4.50) + (2 x 2.50) + (2 x 4.20)

The solve those in the brackets:

= 13.5 + 5 + 8.40

Then add the costs to find the total cost on the shopping list:
= 13.5 + 5 + 8.40

= $26.90

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Based on the shopping list given in the problem, in BIMDAS format and then solved, the total amount will be; $26.90

In BIMDAS format, we need to solve the problem in the brackets first and then use the order of operations to determine the total shopping cost.

The BIMDAS format is:

= (Number of orange dozens x the Cost per dozen) + (Number of bacon packets x the Cost per packet) + (Number of strawberry packets x the Price per packet)

= (3 x 4.50) + (2 x 2.50) + (2 x 4.20)

The solutions in the brackets:

= 13.5 + 5 + 8.40

Then add the costs for the total cost on the shopping list which is;

= 13.5 + 5 + 8.40

= $26.90

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The length will then be L = 18(41/19) = 738/19 cm.

As a check, the area should be A = LW = (738/19)(41/19) = 30258 cm2

sorry if this isn't much help but i had a similar problem once and i used the same steps for your question

Answer:

i d k 20???????????

Step-by-step explanation:

Answer:

The visitor attended no special exhibits and so paid a total of $10 just to get in.

An equation to represent the cost of admission could look like this:

f(x) is the total cost.

x is the number of special exhibits attended.

f(x) = 2x + 10

If I see no special exhibits on my visit,

x = 0, then

f(0) = 2•0 + 10

f(0) = 10

I only pay $10.

This is given point in the fourth quadrant.

In this point, the adjacent is

The opposite is y.

Find hypotenuse h using the pythagorean theorem:

is equal to hypotenuse by adjacent.

is equal to adjacent by opposite.

In the fourth quadrant,

is positive , and

is negative.

So,

it's 27/8 .........................

The equation of the line is y = -2.5x - 1

The table represents the given parameter

On the table, we have the following points

Point, (x, y) = (0, -1) and (2, -6)

So, we start by calculating the slope of the line using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where x and y are defined above

So, we have

Slope = (-6 + 1)/(2 - 0)

Evaluate

Slope = -2.5

The equation of the line is then calculated as

y = m(x - x₁) +y₁

Where

Slope, m = -2.5

(x₁, y₁) = (0, -1)

So, we have

y = -2.5(x + 0) - 1

Open the brackets and evaluate

y = -2.5x - 1

Hence, the line has an equation of y = -2.5x - 1

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The final elevation of the AUV is [tex]-31 \frac{5}{12}[/tex] feet.

Given that, AUV is at an elevation of -8.25 ft. It dives down [tex]6\frac{2}{3}[/tex] ft to collect a specimen. Then the AUV dives another [tex]15\frac{3}{4}[/tex] ft.

The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".

Here, the mixed fraction can be written in improper fraction

[tex]6\frac{2}{3} = \frac{20}{3}[/tex] and [tex]15\frac{3}{4}=\frac{63}{4}[/tex]

Now, 8.25 = 825/100 = 33/4

The final elevation = -33/4-20/3-63/4

= -99/4 - 20/3

= -297/12 -80/12

= - 377/12

= [tex]-31 \frac{5}{12}[/tex]

Therefore, the final elevation of the AUV is [tex]-31 \frac{5}{12}[/tex] feet.

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Answer:

In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.

You're very welcome my sir or ma'am

Answer:

option a is the right answer .

Step-by-step explanation:

Cos theta = B/h = 8/21

theta = 67.6 °

Step-by-step explanation:

imagine the triangle being flipped upwards around DE, so that F is on top instead of on the bottom.

then you see clearly that

DF (21) is the radius of the trigonometric circle,

DE is cos(angle D)×radius,

EF (8) is sin(angle D)×radius.

so,

8 = sin(angle D)×21

sin(angle D) = 8/21 = 0.380952381...

angle D = 22.39268781...° ≈ 22.4°

and so, something is wrong with your problem definition.

the answer options seem to aim for angle F, for which EF (8) is the cosine × radius.

but for angle D EF is clearly the sine × radius.

and for answer option b (20.9°) EF would have to be about 7.5 units long (with the radius DF still being 21). that is all too much off.

your teacher made a mistake. send him/ her my regards.

The value of expression 4 1/5 + 3 2/3 + 1 1/6  is 9 1/30

Given that,

to  simplify: 4 1/5 + 3 2/3 + 1 1/6

Mixed fraction definition?

It is a type of fraction, and those that have both a fraction and a whole number are considered to be it.

How to convert Improper fraction to a mixed fraction?

Divide the fraction's numerator by its denominator, or 15/7, in step one.

Second Step: Since 2 is an integer, the answer's integer component will be a mixed fraction.

Step 3: The original denominator of seven will be used as the denominator.

Step 4: The incorrect fraction 15/7 is now a mixed fraction with the value 2 (1/7)

To simplify ,

4 1/5 + 3 2/3 = 7 13/15

7 13/15 + 1 1/6 = 9 1/30

Therefore the correct answer is 9 1/30

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Answer:

The selling price is:  [tex]\$77,520[/tex]

Step-by-step explanation:

Step 1: Identify the profit made

A profit of 14% is made on the article.

This means that the article was sold at a price that had 14% of its original price added to it.

The 14% of the original price is:

[tex]14\% \times 68000\\=\frac{14}{100}\times 68000\\\\\text{Calculate the value}\\\frac{14}{100}\times 68000\\=9520[/tex]

So, a profit of $9520 was made

Step 2: Calculate the selling price

The selling price will be the sum of the original price and the profit.

The selling price is:

[tex]68000+9520\\=77520[/tex]

The people of the Plymouth Colony fail to achieve the ideals of the Mayflower Compact as A. They did not come together to create a government.

The Mayflower Compact was the Plymouth colony's first government instrument. The Pilgrim Fathers, the emigrants who crossed the Atlantic on the Mayflower in search of religious freedom, wrote the manifesto. On November 11, 1620, it was signed on the sands of what is now Provincetown, near Cape Cod. The pilgrims knew they were in a land unfamiliar to the London Company when the Mayflower docked in Plymouth.

The strangers claimed that the Virginia Company contract was null and void. They believed that because the Mayflower landed outside of Virginia Company territory, they were no longer bound by the charter of the company. Because there was no official government over them, the stubborn strangers refused to acknowledge any regulations.

Many of the pilgrims were already weak from disease and a lack of food when they arrived in Plymouth. The journey had been lengthy, and they were running low on supplies. During the winter, the colony lost about half of its population owing to disease and famine.

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Answer:its A i did it on edge

Step-by-step explanation:

The given  polynomial function f(x)=x^3 - 2x^2 - 5x + 6 as a product of linear factors as (x+2).(x-3).(x-1)

In the above question, a polynomial function is given

f(x)=x^3 - 2x^2 - 5x + 6

However, we know that, zero of a polynomial means all the x-values that bring a polynomial, p(x), to zero are referred to as its zeros, which means putting any value of x in the function we should get value of f(x) as zero

And, in the question, it is given as

f(0)=6, f(2) = -4, f(-2) = 0, f(3) = 0 , f(-1) = 8 , f(1) =0

We can clearly see that,  f(-2) = 0, f(3) = 0, f(1) =0

=> (x+2), (x-3), (x-1) are the linear factors of the given polynomial

Hence, we can write the given  polynomial function f(x)=x^3 - 2x^2 - 5x + 6 as a product of linear factors as (x+2).(x-3).(x-1)

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Answer:

Rhombus:  All sides congruent, two pairs of parallel sides

Parallelogram: Two pairs of parallel lines

Rectangle: 4 right angles, Two pairs of parallel sides

Step-by-step explanation:

Multiplication is not possible with so similar variables in the denominator, in the given fractions and hence the answer is incorrect.

So, -4y × 1/5y:

Theefore, multiplication is not possible with so similar variables in the denominator, in the given fractions and hence the answer is incorrect.

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The solutions to the rational equation x / (x + 4) = 20 / (x² + 3 · x - 4) + 2 / (x - 1) are 7 and - 4, respectively.

In this problem we find a rational equation that must be solved for x by means of algebraic properties. The complete procedure is shown below:

Step 1 - We have the following expression:

x / (x + 4) = 20 / (x² + 3 · x - 4) + 2 / (x - 1)

Step 2 - Factor x² + 3 · x - 4:

x / (x + 4) = 20 / [(x + 4) · (x - 1)] + 2 / (x - 1)                

Step 3 - By existence of multiplicative inverse, modulative, associative and commutative properties:

[x · (x - 1)] / [(x + 4) · (x - 1)] = 20 / [(x + 4) · (x - 1)] + [2 · (x + 4)] / [(x + 4) · (x - 1)]

Step 4 - By compatibility with multiplication, existence of multiplicative inverse, modulative, associative and commutative properties:

x · (x - 1) = 20 + 2 · (x + 4)                                            

Step 5 - By distributive property:

x² - x = 20 + 2 · x + 8                                                  

Step 6 - By compatibility with addition, distributive, modulative and associative properties:

x² - 3 · x - 28 = 0  

Step 7 - Factor x² - 3 · x - 28:

(x - 7) · (x + 4) = 0                                                        

Step 8 - By understanding the factors found in the previous, we get the folowing result:

x = 7 or x = - 4                                                               Result

The solution to the equation are 7 and - 4.

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Answer:

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

Segment EF with:

Use midpoint equation:

Find unknown coordinates of the point F:

So the point is F = ( - 22, 4)

Answer:

F = (-22, 4)

Step-by-step explanation:

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\\\\ \textsf{where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.}[/tex]

Given information:

Define the endpoints of the line segment EF:

Substitute the given information into the formula:

[tex]\implies (x_M,y_M)=\left(\dfrac{x_F+x_E}{2},\dfrac{y_F+y_E}{2}\right)[/tex]

[tex]\implies (-6,-2)=\left(\dfrac{x_F+10}{2},\dfrac{y_F-8}{2}\right)[/tex]

Find the x-coordinate of M:

[tex]\implies \dfrac{x_F+10}{2}=-6[/tex]

[tex]\implies x_F+10=-12[/tex]

[tex]\implies x_F=-22[/tex]

Find the y-coordinate of M:

[tex]\implies \dfrac{y_F-8}{2}=-2[/tex]

[tex]\implies y_F-8=-4[/tex]

[tex]\implies y_F=4[/tex]

Therefore, the coordinates of endpoint F are (-22, 4).

We have to find how the interval (1-α) affects the width of the confidence interval.

The interval (1-α) represents the confidence required for the interval.

The greater the confidence required, the wider will be the interval.

This means also that when we decrease the confidence required, the interval width decrease too, as we are less strict with the number of sample means that have to fall within that interval.

Then, when (1-α) decreases, the width of the confidence interval also decreases.

Answer: A. Decreased,

The cosine ratio is given by the following formula:

The adjacent leg of angle Z is side ZY=12 and the hypotenuse of the triangle is the side XZ=20, thus the cosine ratio of Z is: