What is the range of g(x) = - 2x + 3, if the domain is {-2, - 1,0, 1, 2}?

Answer:

It is D. (x + 1)^2 + (y - 3)^2 = 16.

Step-by-step explanation:

The general equation of a circle is

(x - h)^2 + (y - k)^2 = r^2  where  the center is (h, k) and the radius is r.

So substituting the given values the required equation is:

(x + 1)^2 + (y - 3)^2 = 4^2.

Answer:

D. [tex](x+1)^2+(y-3)^2=16[/tex]

Step-by-step explanation:

We are asked to write equation of a circle whose center is at point [tex](-1,3)[/tex] and whose radius is 4 units.

We know that equation of a circle is standard form is in format [tex](x-h)^2+(y-k)^2=r^2[/tex], where [tex](h,k)[/tex] is the center of circle.

Upon substituting [tex]h=-1[/tex], [tex]k=3[/tex] and [tex]r=4[/tex] in the standard form of circle, we will get:

[tex](x-(-1))^2+(y-3)^2=4^2[/tex]

[tex](x+1)^2+(y-3)^2=16[/tex]

Therefore, our required equation would be [tex](x+1)^2+(y-3)^2=16[/tex] and option D is the correct choice.

Answer:

this was last last year sorry u never got an answer

Answer:

-x^3-3x^2+2x+4

Step-by-step explanation:

Just calculate each coefficient of the polynomial separately.

x^3-2x+6-(2x^3+3x^2-4x+2) = (1-2)x^3+(0-3)x^2+(-2-(-4))x+(6-2) = -x^3-3x^2+2x+4.

Answer:

- x³ - 3x² + 2x + 4

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x)

= x³ - 2x + 6 - (2x³ + 3x² - 4x + 2) ← distribute by - 1

= x³ - 2x + 6 - 2x³ - 3x² + 4x - 2 ← collect like terms

= - x³ - 3x² + 2x + 4 ← in standard form

Answer:

(gof) (1) = 0

Step-by-step explanation:

f(x) = -4x + 7

g(x) = 2x - 6

(gof) (1)

First find f(1)

f(1) = -4(1) + 7

f(1) = -4+7=3

Then put 3 in for x in g(x)

g(f(1) = 2(f(1))-6

        = 2 (3) -6

        = 6 -6

        = 0

[tex](g\circ f)(x)=2(-4x+7)-6=-8x+14-6=-8x+8\\\\(g\circ f)(1)=-8\cdot1+8=0[/tex]

Divide the number of bands by the total acts:

3 /16 = 0.1875

Multiply by 100:

0.1875 x 100 = 18.75% were bands.  ( Round answer as needed.)

Answer:

Explicit form:    [tex]a_n=8+4n[/tex]

Seventh term:  [tex]a_7=36[/tex]

You gave the recursive form:

[tex]a_n=a_{n-1}+4 \text{ with } a_1=12[/tex]

Step-by-step explanation:

You already have the recursive formula which is:

[tex]a_n=a_{n-1}+4[/tex] where [tex]a_1=12[/tex].

Maybe you looking for the explicit form and also the 7th term?

You were just looking for the 7th term.  Sometimes you can read the recursive formula pretty easily and understand the pattern that is happening.

[tex]a_{n-1}[/tex] is the term right before [tex]a(n)[/tex].  Just like [tex]a_5[/tex] would be the term right before [tex]a_6[/tex].

Anyways becak to our recursive for a sequence that was given:

[tex]a_{n}=a_{n-1}+4[/tex] says term=previous term+4.

So you adding 4 over and over to generate the terms of a sequence.  This is arithmetic sequence because it is going up by same number (or could go down by same number).  The common difference is 4.

[tex]a_1=12[/tex]

[tex]a_2=12+4=16[/tex]

[tex]a_3=16+4=20[/tex]

[tex]a_4=20+4=24[/tex]

[tex]a_5=24+4=28[/tex]

[tex]a_6=28+4=32[/tex]

[tex]a_7=32+4=36[/tex]

Now if you don't like that. You could just blindly without trying to understand the meaning of it just plug numbers in:

[tex]a_1=12[/tex]

For if we wanted to know the 2nd term; we would plug in 2 for n:

[tex]a_2=a_{2-1}+4[/tex]

[tex]a_2=a_1+4[/tex]

[tex]a_2=12+4[/tex]

[tex]a_2=16[/tex]

Plug in 3 for the 3rd term:

[tex]a_3=a_{3-1}+4[/tex]

[tex]a_3=a_2+4[/tex]

[tex]a_3=16+4[/tex]

[tex]a_3=20[/tex]

Plug in 4 for the 4th term:

[tex]a_4=a_{4-1}+4[/tex]

[tex]a_4=a_3+4[/tex]

[tex]a_4=20+4[/tex]

[tex]a_4=24[/tex]

Plug in 5 for the 5th term:

[tex]a_5=a_{5-1}+4[/tex]

[tex]a_5=a_4+4[/tex]

[tex]a_5=24+4[/tex]

[tex]a_5=28[/tex]

Plug in 6 for the 6th term:

[tex]a_6=a_{6-1}+4[/tex]

[tex]a_6=a_5+4[/tex]

[tex]a_6=28+4[/tex]

[tex]a_6=32[/tex]

Plug in 7 for the 7th term:

[tex]a_7=a_{6-1}+4[/tex]

[tex]a_7=a_5+4[/tex]

[tex]a_7=32+4[/tex]

[tex]a_7=36[/tex]

Now if you look at the points we just got (I will just go up to 4 terms):

n  (treat as x)  |  1           2                3                 4

a(n) (treat as y|  12        16               20                24

The explicit form in not in terms of other terms of the sequence.  You are looking here for an equation that relates n (x) to a(n) (y).

I'm just going to use x and y until the end where I will replace them back in terms of n and a(n).

This is a line because the's rise/run (the slope) is the same per choosing of points.

That is the following is true:

[tex]\frac{16-12}{2-1}=\frac{20-16}{3-2}=\frac{24-20}{4-3}[/tex] son on....

These all the the value 4, the same number that the arithmetic sequence is going up by.  

So in an arithmetic sequence, the common difference is the slope of the line.

I'm going to use point-slope formula which is [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point on the line and [tex]m[/tex] is the slope.

So we have m=4 and [tex](x_1,y_1)[/tex] could be any of the 7 we found, but I will choose (1,12) for it:

[tex]y-12=4(x-1)[/tex]

Add 12 on both sides:

[tex]y=12+4(x-1)[/tex]

[tex]a_n=12+4(n-1)[/tex].

This is actually in the form of most books formulas for an explicit form which is [tex]a_n=a_1+d(n-1)[/tex] where [tex]a_1[/tex] is the first term and d is the common difference.

So another way to do the problem:

You would have to know the following are equivalent:

[tex]a_n=a_{n-1}+d[/tex] with [tex]a_1 \text{ is given}[/tex]

and

[tex]a_n=a_1+d(n-1)[/tex].

If you know these are equivalent then you could compare [tex]a_n=a_{n-1}+d[/tex] to [tex]a_n=a_{n-1}+4[/tex] and determine d is 4.

You could also see that [tex]a_1[/tex] is give as 12.

Then you just plug into:

[tex]a_n=a_1+d(n-1)[/tex]

[tex]a_n=12+4(n-1)[/tex].

You could also simplify this equation just a bit.

You could distribute and then combine a pair of like terms.

Like so,

[tex]a_n=12+4(n-1)[/tex]

[tex]a_n=12+4n-4[/tex]

[tex]a_n=8+4n[/tex]

Answer:

The polygon has 9 sides

Step-by-step explanation:

We need to equate the given expression to the given value and solve for n.

The sum of the interior angles, s, in an n-sided polygon is given by the expression:

[tex]s = 180(n - 2)[/tex]

We want to use this formula, to calculate how many sides has a polygon if the sum of the interior angles is 1,260°.

We solve the following equation for n.

[tex]180(n - 2) = 1260[/tex]

Divide through by 180 to get:

[tex] \frac{180(n - 2)}{180} = \frac{1260}{180} [/tex]

[tex]n - 2 = 7[/tex]

Add 2 to both sides to get:

[tex]n = 7 + 2[/tex]

[tex] \therefore \: n = 9[/tex]

Hence the polygon has 9 sides

Answer: d

Step-by-step explanation:

Answer:

The beetle does

Answer:

The Ant travels farther per second

Step-by-step explanation:

To Find how far the ant and beetle travels we have to find out how many feet per second the Ant and Beetle travel.

To find that out for the Ant I divided 30 by 2 and got 15 which means the ant travels 1 foot in 15 second.

To find that out for the beetle I divided 90 by 5 and got 18 which means the beetle travels 1 foot in 18 seconds.

Therefore the Ant travels faster.

Answer:

3x+8 I think

Step-by-step explanation:

add 5, -1 and 4

Answer:

The CORRECT answer is C,  7x+4

Step-by-step explanation:

Answer:

The correct option is D.

Step-by-step explanation:

a = 9c²+4

b= 7+3c

Firstly solve 2nd equation for c in terms of b:

b=7+3c

b-7=3c

b-7/3 = c

Now substitute the value of c in equation 1:

a= 9c²+4

a=9(b-7/3)² +4

a=9(b-7)²/9+4

9 will be cancelled by 9, so the equation we get is:

a=(b-7)²+4

Apply whole square formula for (b-7)²

a=b²-14b+49+4

Solve like terms:

a=b²-14b+53

Therefore the correct option is D....

Answer:

[tex]\^v=-\frac{3}{5}i+\frac{4}{5}j[/tex]

Step-by-step explanation:

We have the following vector

[tex]v=3\sqrt{2}i-4\sqrt{2}j[/tex]

First we calculate its magnitude

The magnitude of the vector v will be

[tex]|v|=\sqrt{(3\sqrt{2})^2 + (4\sqrt{2})^2}\\\\|v|=\sqrt{9*2+16*2}\\\\|v|=\sqrt{18+32}\\\\|v|=5\sqrt{2}[/tex]

Now to create a unitary vector in the opposite direction to v, we divide the vector v between the negative of its magnitude

we call this new vector "[tex]\^v[/tex]"

[tex]\^v=\frac{3\sqrt{2}}{-5\sqrt{2}}i-\frac{4\sqrt{2}}{-5\sqrt{2}}j[/tex]

[tex]\^v=-\frac{3}{5}i+\frac{4}{5}j[/tex]

Check the picture below.

so a full circle is 360°, then if we just go 140° more, we'll be landing at 500°.

If we go from the 140° location and add say 360°, well end up 500, if we add another 360°, we'll be at 860° or the same location of 140° and 500°, and if we add again 360° we'll be landing on the same spot again and again.

(140 + 360n)°.   where "n" is an integer.

The expression that represents the measures of all angles that are co-terminal with a 500° angle is 140 + 360n

Co-terminal angles are angles in a standard position

The angle is given as:

Angle = 500

Add 0 to 500

Angle = 500 + 0

Express 0 as -360 + 360

Angle = 500 - 360 + 360

Evaluate the difference

Angle = 140 + 360

Express as a function

f(1) = 140 + 360 * 1

Substitute 1 for n

f(n) = 140 + 360 * n

This gives

f(n) = 140 + 360n

Hence, the expression that represents the measures of all angles that are co-terminal with a 500° angle is 140 + 360n

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Answer:

[tex](6g)(11g)=\bigg((6)(11)\bigg)(gg)=66g^2[/tex]

Answer:

r ≤ 29, r-5

The sale price can be compared with the regular price, r-5 ≤ 24

Step-by-step explanation:

Amount to spend = $24

Regular price = r

Sale = $5

Sale Price = r-5

The regular price will be $5, at the max, more than the amount Roopesh has to spend.

The sale price will be $24 or less than that for Roopesh to afford.

Inequality for regular price:

r-5 ≤ 24

r ≤ 29

So, the product Roopesh can afford is $29 or less than that.

What is the unknown? r ≤ 29

Following expression can represent the sale price:

Sale price = r-5  

The sale price can be compared with the regular price with the following:

Inequality representing the situation: r-5 ≤ 24

Answer:

Step-by-step explanation:

What is unknown?

We are missing the regular price of an item

Which expression can represent the sale price?

$24 - x = the sales price

and the x equals the original price since we don't know the actual price.

Which comparison could  be used?

$24 spend on a birthday gift to a the shopping sale offering $5 off the regular price.

And the rest I don't know son or girl

The given three functions all have the same y-intercept at (0,-3).

We have given that,

f(x) = −6x − 3

g(x) is the graph

h(x) = h(x) = 2 cos(x + π) − 1

A coordinate plane is a two-dimensional plane formed by the intersection of a vertical line called y-axis and a horizontal line called x-axis.

all you have to do is substitute 0 for x and you can also sub y for the function notation

So the first is y=-6x-3

When x=0 then all you have left is y=-3 so the point is (0,-3)

The second function is shown on the graph and the y-intercept (where x=0) is at -3, so the point for that is (0,-3)

And the third function has x=0, So you get[tex]y=2cos(\pi )-1.[/tex]The [tex]cos(\pi )=-1,[/tex]

So that gives

[tex]y=2(-1)-1\\y=-2-1\\ y=-3[/tex]

then and the point is (0,-3)

Therefore they all have the same y-intercept at (0,-3).

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Answer:

The answer should be 1.4<h<1.6

Step-by-step explanation:

Multiply 7 and 8 by 0.2 to find out what 20% is. 7*0.2=1.4 and 8*0.2=1.6. So it should be at or between those two numbers making the inequality 1.4<h<1.6

When an adult sleeps between 7 to 8 hours, they spend between 1.4 and 1.6 hours in REM (Rapid Eye Movement) sleep, which is associated with dreaming.

Given that an adult sleeps 7 to 8 hours, roughly 20% of this time is spent in REM or Rapid Eye Movement sleep, typically associated with dreaming. To find out how much time is spent in REM sleep, we calculate 20% of the total sleep time. If 20% of 7 hours is 1.4 hours and 20% of 8 hours is 1.6 hours, then the correct inequality showing how much time, in hours, is spent in REM sleep is 1.4 < h < 1.6 where 'h' represents number of hours in REM sleep.

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Answer:

x = 5, x=-2

Step-by-step explanation:

The factors are x-5 and x+2:

Set each factor equal to zero and then solve each of them for x to find out what values of x make the polynomial equal to zero.

x-5 = 0 , x+2 = 0

x=0+5 , x=0-2

x=5  , x= -2....

The values of x that make the polynomial 0, given its factors are x⁵ and x + 2, are x = 0 and x = -2.

If the factors of a polynomial are x⁵ and x + 2, to find the values of x that make the polynomial equal to zero, we set each factor equal to zero and solve for x.

For the factor x⁵ = 0, the only solution is x = 0.

For the factor x + 2 = 0, solving for x gives us x = -2.

Therefore, the values of x that make the polynomial 0 are x = 0 and x = -2.

Answer:

7.4

Step-by-step explanation:

The information given is in from SAS.

This is a job for law of cosines.

This is the law of cosines [tex]a^2=b^2+c^2-2bc cos(A)[/tex]

The angle A is opposite side a and b,c are the other sides.

So 13 degrees is opposite the y there.

[tex]y^2=16^2+22^2-2(16)(22)\cos(13)[/tex]

Now I'm going to put 16^2+22^2-2*16*22*cos(13) in my calculator:

[tex]y^2=54.04347439[/tex]

Now one more step. To get rid of the square, you need to square root both sides:

[tex]y=\sqrt{54.04347439}=7.351426691[/tex]

Sp the answer is approximately 7.4

Answer:

7.351

I don't know how they have rounded; the closest answer is A

Step-by-step explanation:

The only way I know to do this is with the cos law

y^2 = x^2 + z^2 - 2*x*z cos(Y)

x = 22

z = 16

y = ?

I have serious doubts that this will make a triangle. I ran it though a calculator and it does work -- surprise for me. Substitute the givens.

y^2 = 256 + 484 - 2*10*22*cos(13)

y^2 = 740 - 704*cos(13)

y^2 = 740 - 704*0.9744

y^2 = 740 - 685.95

y^2 = 54.05                                       Take the square root of both sides

y = √54.05

y = 7.351

Answer:

Range : {11,13,17,25}

Step-by-step explanation:

Given

f(x) = 2x+7

and

Domain = {2,3,5,9}

To find the range, the values in domain will be put in the function one by one

So,

f(2) = 2(2)+7 = 4+7 = 11

f(3) = 2(3)+7 = 6+7 = 13

f(5) = 2(5)+7 = 10+7 = 17

f(9) = 2(9)+7 = 18+7 = 25

Therefore the range is {11,13,17,25} ..

(6x+5)-(x+3).

6x+5-x-3.

Add the like terms.

6x-x+5-3.

We get.

5x+2.

Answer:

6x+5-x-3

=5x+2

The volume of the cube with edges of eight feet is approximately 18.96 cubic yards.

To find the volume of a cube, you need to know the length of one of its edges. In this case, the edge length is given as eight feet.

Volume of a cube = (Edge length)³

Volume = 8³ = 512 cubic feet.

Now, we need to convert cubic feet to cubic yards. Since 1 cubic yard is equal to 27 cubic feet:

Volume in cubic yards = 512 cubic feet / 27 cubic feet per cubic yard ≈ 18.96 cubic yards.

So, the volume of the cube is approximately 18.96 cubic yards.

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Answer:

A. Draw a line from the segment to any point on the fold line.

Step-by-step explanation:

When using the paper folding method to find the midpoint of a line segment we take the following steps:

These steps include statements B, C, and D. Drawing a line from the segment to any point on the fold line, which is statement A,  is not included in these steps because it is not needed.

Thus, choice A is not a step in using paper folding to find the midpoint of a line segment.

Answer:

21.26 inches to the nearest hundredth.

Step-by-step explanation:

By the Pythagoras theorem

d^2 = 14^2 + 16^2   (where d = the length of the diagonal).

d^2 = 452

d = 21.26 inches.

Answer:

21.26 inches.

Step-by-step explanation:

It can be inferred that the shape of the monitor is a rectangle, in which the length of the monitor is 16 inches and the height of the monitor is 14 inches. The diagonals of the rectangle cut it into two congruent right-angled triangles. Therefore, to find the length of the diagonal of the monitor, use the Pythagoras Theorem. Since the base (b) is 16 inches and the perpendicular (p) is 14 inches, the distance of the hypotenuse (i.e. the diagonal, denoted by h) can be found by the following formula:

[tex]h^2 = b^2 + p^2 [/tex]

Plugging in the values:

[tex]h^2 = 16^2 + 14^2[/tex]

Simplifying gives:

[tex]h^2 = 452[/tex]

Taking square root on both sides gives:

h = 21.26 inches (to the nearest 2 decimal places)

Therefore, the measure of the diagonal is 21.26 inches!!!

Answer:

n ≤  88.2

Step-by-step explanation:

Answer:

"n divided by four-point-two is greater-than or equal to twenty-one".

~

Answer:

1:1

Step-by-step explanation:

Since both equal up to 100% and both are 50%, it's 1:1.

1 stands for 50% and the other 1 stands for 50% too.

Answer:

C

Step-by-step explanation:

Its C because the graph is not up to scale in order to fit the other options B looks like it could but I cant see the whole graph so Id go with C

Its C because the graph is not up to scale in order to fit the other options B looks like it could but I cant see the whole graph so Id go with C.

Grid Reference a page number, column, and line combination used to identify a container's location in a bay layout. Each area must have a unique Grid Number for quick identification.

Without limiting the generality of the aforementioned, each credit party agrees that the administrative agent shall have the right to sell or otherwise dispose of all or any portion of the collateral at a public or private sale, at any broker's board.

It on any securities exchange, for cash, upon credit, or for future delivery as the administrative age approaches, subject to the mandatory requirements of applicable law.

Therefore, Its C because the graph is not up to scale in order to fit the other options B looks like it could but I cant see the whole graph so Id go with C.

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[tex]\frac{1}{30}[/tex]

Multiply the numerators together. [tex]-1*-1=1[/tex]

Multiply the denominators together. [tex]6*5=30[/tex]

Put the two products together in a new fraction. [tex]\frac{-1}{6}*\frac{-1}{5}=\frac{1}{30}[/tex]

Answer:

1/30

Multiply the numerators together.  

Multiply the denominators together.  

Put the two products together in a new fraction.

Step-by-step explanation:

Answer:

29/120

Step-by-step explanation:

-8/-15 · 29/64

Lets rewrite the problem

-8/64 *29/-15

We can simplify the first fraction

-1/8 * 29/-15

Multiply the numerators

-1*28 = -29

Multiply the denominators

8*-15 =-120

Put the numerator over the denominator

-29/-120

A negative over a negative is a positive

29/120

Are you sure you have the factions correct

[tex]\text{Hey there!}[/tex]

[tex]\dfrac{-8}{-15}\times\dfrac{29}{64}[/tex]

[tex]\dfrac{8\times29}{15\times64}[/tex]

[tex]{8 \times 29 = 232}\\\\\ 15\times 64 = 960[/tex]

[tex]\text{Both numbers goes into 8 (or the GCF is 8.)}\text{ So divide both numbers by 8.}[/tex]

[tex]231\div8 = 29\leftarrow \text{numerator (top number)}\\\\ 960\div8=120\leftarrow\text{denominator (bottom number)}[/tex]

[tex]\boxed{\boxed{\text{Answer: }\bf{\dfrac{29}{120}}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Step-by-step explanation:

for a³b²c-1d

given

a=2

b=4

c=10

d=15

a³b²c-¹d

=(2³4²10^-1*15

=2³4²15/10

=8*16*15/10

=8*8*3

=64*3

=192

now

a³b²c¹d

=(2³4²10 15)

=(8*16*10*15)

=120*16*10

=1200*16

=19200

Answer:

3/4 if meant [tex]a=2,b=4,c=10,d=15[/tex]

is [tex]a^3b^{-2}c^{-1}d[/tex]

Step-by-step explanation:

So the expression we want to evaluate for [tex]a=2,b=4,c=10,d=15[/tex]

is [tex]a^3b^{-2}c^{-1}d[/tex]

Please make sure I typed the expression and the values for the letters right.

[tex]a^3b^{-2}c^{-1}d[/tex]

Plug in the given values:

[tex](2)^3(4)^{-2}(10)^{-1}(15)[/tex]

In the following step I said 2^3 equals 8 because 2^3 means 2*2*2.  I also got rid of the negative exponents by taking reciprocal.

[tex]8 \cdot \frac{1}{4^2} \cdot \frac{1}{10^1} (15)[/tex]

In the following step I said 4^2=16 because 4^2 means 4*4.  I also wrote 10^1 as 10.

[tex]8 \cdot \frac{1}{16} \cdot \frac{1}{10} (15)[/tex]

In the following step, I'm going to rewrite everything as a fraction if it isn't already a fraction.  8=8/1 and 15=15/1.

[tex]\frac{8}{1} \cdot \frac{1}{16} \cdot \frac{1}{10} \cdot \frac{15}{1}[/tex]

To multiply fractions, you just multiply straight across on top and straight across on bottom.

[tex]\frac{8(1)(1)(15)}{1(16)(10)(1)}[/tex]

Actually performing the multiplication:

[tex]\frac{120}{160}[/tex]

Time to reduce:

[tex]\frac{12}{16}[/tex] I divided top and bottom by 10 to get this.

One more time for reducing:

[tex]\frac{3}{4}[/tex] I divided top and bottom by 4 to get this.