Suppose f(x) = x^2. What is the graph of g(x) =f(4x)?

Answer:

[tex]a_n=7 \cdot (-3)^{n-1}[/tex]

Step-by-step explanation:

The explicit form for a geometric sequence is [tex]a_n=a_1 \cdot r^{n-1}[/tex] where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio.

We have the following given:

[tex]a_2=-21[/tex]

[tex]a_5=567[/tex].

We also know that [tex]a_2=a_1 \cdot r[/tex] while [tex]a_5=a_1 \cdot r_4[/tex].

So if we do 5th term divided by second term we get:

[tex]\frac{a_1 \cdot r_4}{a_1 \cdot r}=\frac{567}{-21}[/tex]

Simplifying both sides:

[tex]r^3=-27[/tex]

Cube root both sides:

[tex]r=-3[/tex]

The common ratio, r, is -3.

Now we need to find the first term.

That shouldn't be too hard here since we know the second term which is -21.

We know that first term times the common ratio will give us the second term.

So we are solving the equation:

[tex]a_1 \cdot r=a_2[/tex].

[tex]a_1 \cdot (-3)=-21[/tex]

Dividing both sides by -3 gives us [tex]a_1=7[/tex].

So the equation is in it's explicit form is:

[tex]a_n=7 \cdot (-3)^{n-1}[/tex]

Check it!

Plugging in 2 should gives us a result of -21.

[tex]a_2=7 \cdot (-3)^{2-1}[/tex]

[tex]a_2=7 \cdot (-3)^1[/tex]

[tex]a_2=7 \cdot (-3)[/tex]

[tex]a_2=-21[/tex]

That checks out!

Plugging in 5 should give us a result of 567.

[tex]a_5=7 \cdot (-3)^{5-1}[/tex]

[tex]a_5=7 \cdot (-3)^4[/tex]

[tex]a_5=7 \cdot 81[/tex]

[tex]a_5=567[/tex]

The checks out!

Our equation works!

Final answer:

To find the nth term formula of a geometric sequence with given terms, divide one term by the other to find the common ratio, and then solve for the first term. For this sequence, the nth term is [tex]a_{n}= 7 (-3)^{n-1}[/tex].

Explanation:

To find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively, we must determine the common ratio (r) and the first term (a1) of the sequence. For a geometric sequence, the nth term is given by the formula [tex]a_{n}= a_{1} (r)^{n-1}[/tex].

Since the second term a2 is -21 and the fifth term a5 is 567, we can set up the following equations using the geometric sequence formula:

[tex]a_{2}[/tex] =  [tex]a_{1}[/tex] x r = -21

[tex]a_{5}[/tex] =  [tex]a_{1}[/tex] x [tex]r_{4}[/tex] = 567

Dividing the second equation by the first gives us:

[tex]r_{3}[/tex] = 567 / -21 = -27

Thus, the common ratio r is -3. Now using [tex]a_{2} =a_{1} r[/tex] , we find that [tex]a_{1}[/tex] = -21 / (-3) = 7. Therefore, the nth term of the sequence is:

[tex]a_{n}= 7 (-3)^{n-1}[/tex]

Answer:

B

Step-by-step explanation:

The x- intercepts are the points on the x- axis where the graph crosses.

That is (- 3, 0), (1, 0) and (2, 0) → set B

Answer:

D. (1,0), (2,0), (-3,0), and (0,6)

Step-by-step explanation:

G. 7,500 cubic feet

Answer:

if she would sell it for what it is worth now she would make $36.50

Step-by-step explanation:

0.75 x 83 = 62.5

62.5 + 8.75 = 71

71 is how much it is worth now

71 - 34.5 = 36.5

36.50 is how much she would make

Answer:

$36,50

Step-by-step explanation:

That is correct to me. You do those exact steps to arrive at that answer.

Answer: Step 3

Step-by-step explanation:

He should have divided 8 by 2 and then added it to 49.

In the third step, Rahul made his first mistake. Simplification is to be done using the BODMAS rule.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

Rahul simplified an expression. His work is shown below.

The expression is given below.

7 (8.5 - 1.5) + 8 / 2

Step 1. 7 (7) + 8 / 2

Step 2. 49 + 8 / 2

Step 3. 49 + 4

Step 4. 53

In the third step, Rahul made his first mistake.

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Answer:

[tex]l=\frac{P}{2}-w[/tex].

Step-by-step explanation:

The perimeter of a rectangle is the sum of it's side lengths.

A rectangle has 4 sides where it's opposite sides are congruent.

So if one side has measurement w, then there is another side that has measurement w.

If there is one side that has measurement l, then there is another side that has measurement l.

So if you add w+w+l+l you get 2w+2l.

They are giving us that the perimeter is P, so P=2w+2l.

we are being asking to solve for l.

P=2w+2l

First step: Isolate term that contains the l, so get 2l by itself first.

We are going to subtract 2w on both sides giving us:

P-2w=2l

2l=P-2w

Now that we have 2l by itself it is time to perform the last step in getting l by itself.

Second step: Divide both sides by 2.

This gives us:

l=(P-2w)/2

You may separate the fraction like so:

[tex]l=\frac{P-2w}{2}=\frac{P}{2}-\frac{2w}{2}=\frac{P}{2}-w[/tex].

I don't know your options but I have solve for l in terms of P and w

and got [tex]l=\frac{P}{2}-w[/tex].

Please let me know if you have further questions with this problem.

Answer:

Part A) Annual [tex]\$66,480.95[/tex]  

Part B) Semiannual [tex]\$66,862.38[/tex]  

Part C) Monthly [tex]\$67,195.44[/tex]  

Part D) Daily [tex]\$67,261.54[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

Part A)

Annual

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=1[/tex]

 substitute in the formula above  

 [tex]A=47,400(1+\frac{0.07}{1})^{1*5} \\A=47,400(1.07)^{5}\\A=\$66,480.95[/tex]

Part B)

Semiannual

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=2[/tex]

 substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{2})^{2*5} \\A=47,400(1.035)^{10}\\A=\$66,862.38[/tex]

 Part C)

Monthly

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=12[/tex]  

substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{12})^{12*5}\\A=47,400(1.0058)^{60}\\A=\$67,195.44[/tex]

 Part D)

Daily

in this problem we have  

[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=365[/tex] 

substitute in the formula above  

[tex]A=47,400(1+\frac{0.07}{365})^{365*5}\\A=47,400(1.0002)^{1,825}\\A=\$67,261.54[/tex]

Answer:

= 1/59049 ....

Step-by-step explanation:

9 to the 2 = 9^2 = 9*9 = 81

9 to the 7 = 9^7= 9*9*9*9*9*9*9 = 4782969

Now simplify the values by table of 9

=81/ 4782969

=9/531441

=1/59049 ....

Step-by-step explanation:

9 to the 2ND power is 81

9 to the 7th power is 4,782,969

81 divided by 81 is 1

4,782,969 divided by 81 is 59,049

so the final answer is 1

59,049

Answer:

C

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 5 =  - 3(x + 2) ← is in point- slope form

with slope m = - 3

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]

and (a, b) = (6, - 1), hence

y - (- 1) = [tex]\frac{1}{3}[/tex](x - 6), that is

y + 1 = [tex]\frac{1}{3}[/tex](x - 6) → C

Answer: D

Step-by-step explanation:

They are rectangles when the sides are 90 degrees. :)

A rhombus is a rectangle when all its angles are right angles.

A rectangle is a plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.

Given is a rhombus.

A rhombus is a rectangle when all its angles are right angles. Due to this, the tilt of the vertical sides of rhombus will become 0 degrees.

Therefore, a rhombus is a rectangle when all its angles are right angles.

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Answer:

See below.

Step-by-step explanation:

It decreases in the interval where x  > -2.

In interval notation this is (-2, ∞).

The quadratic function decreasing at x>-2.

A quadratic polynomial is a polynomial of degree two in one or more variables.

Given is a graph,

It decreases in the interval where x  > -2.

In interval notation, this is (-2, ∞).

Hence, the quadratic function decreasing at x>-2.

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Answer:

Murray can swim 3/4 km downstream

Step-by-step explanation:

Since the current adds to his speed and

then subtracts the same amount, you can

disregard the current

d=r*t

Convert 15 min to hrs ( time to swim downstream )

15(1/60)=1/4 hours

d=3(1/4)

d=3/4 km downstream.

Hence Murray can swim 3/4 km downstream....

Final answer:

Murray swam 0.417 km downstream before turning around and swimming back upstream. The calculation involves solving a simple algebraic equation using Murray's swimming speed and the river's flow rate, within the total time frame of 30 minutes.

Explanation:

The student is asking about a problem involving rates and time, which is a common topic in algebra and physics. In this scenario, Murray is able to swim at a speed of 3 km/h in still water, and the river flow adds an extra 2 km/h when swimming downstream, making his effective downstream speed 5 km/h. When swimming upstream, Murray has to work against the river flow, reducing his effective speed to 1 km/h (3 km/h - 2 km/h). Given that the total time spent swimming is 30 minutes (0.5 hours), we need to determine the distance Murray swam downstream before turning back.

Let the distance Murray swam downstream be d kilometers. The time to swim downstream at 5 km/h is d/5 hours, and the time to swim back upstream at 1 km/h is d hours. The sum of these times equals the total time Murray was swimming:

d/5 + d = 0.5

By solving the equation, we find that d = 0.417 km. Therefore, Murray swam 0.417 kilometers downstream before turning around and swimming back upstream.

The full length of one line times the length of the line outside the circle is equal the the other line.

(7+x)*7 = (13 +8) * 8

Simplify:

7x +49 = 21 * 8

7x +49 = 168

Subtract 49 from each side:

7x = 119

Divide both sides by 7:

x = 17

The answer is B. 17

The value of x for the given circle will be 17 so option (B) will be correct.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circle objects for example our bike wheel.

The longest line which can be drawn inside the circle will be the diameter.

Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.

By theorem in circle

( 13 + 8) × 8 = ( x + 7) × 7

21 × 8 =  ( x + 7) × 7

x + 7 = 3 × 8

x = 24 - 7

x = 17

Hence, The value of x for the given circle will be 17.

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Answer:

D. 31.42

Step-by-step explanation:

you can look up a calculator and it gives you the answer!

The circumference of a circle with a radius of 5 units is,

⇒ Circumference = 31.4 units

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The radius of circle = 5 units

Now,

Circumference = 2πr

Here, r = 5

⇒ Circumference = 2 × 3.14 × 5

⇒ Circumference = 31.4 units

Thus, The circumference of a circle with a radius of 5 units is,

⇒ Circumference = 31.4 units

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[tex]x^3-3x^2+81x-243=\\x^2(x-3)+81(x-3)=\\(x^2+81)(x-3)=\\(x-3)(x-9i)(x+9i)[/tex]

Answer:

Step-by-step explanation:

[tex]f(x)=x^2-x-2\\\\\text{The zeros are for}\ f(x)=0:\\\\x^2-x-2=0\\\\x^2-2x+x-2=0\\\\x(x-2)+1(x-2)=0\\\\(x-2)(x+1)=0\iff x-2=0\ \vee\ x+1=0\\\\x-2=0\qquad\text{add 2 to both sides}\\x=2\\\\x+1=0\qquad\text{subtract 1 from both sides}\\x=-1[/tex]

Answer:

19 t-shirts

Step-by-step explanation:

x= number of t-shirts

6x+54=168; now subtract 54 from both sides of the equation

6x=114; now divide both sides by 6 to isolate the "x"

x=19

Answer:

64 : 1

Step-by-step explanation:

Given 2 similar cylinders with linear ratio = a : b then

volume ratio = a³ : b³

Here the height ratio = 4 : 1, hence

volume ratio = 4³ : 1³ = 64 : 1

Answer:

The correct option is B) [tex]f(x)=-5x+250[/tex].

Step-by-step explanation:

Consider the provided information.

let x represents the number of weeks and y represents the fixed cars.

During week 10 of the recall, the manufacturer fixed 200 cars.

Thus, the ordered pair can be made with the help of the above data is: (10,200).

In week 15, the manufacturer fixed 175 cars.

Thus, the ordered pair can be made with the help of above data is: (15,175)

Now use two point slope formula: [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Substitute the [tex](x_1,y_1)=(10,200)\ \text{and}\ (x_2,y_2)=(15,175)[/tex] in the above formula.

[tex]y-200=\frac{175-200}{15-10}(x-10)[/tex]

[tex]y-200=\frac{-25}{5}(x-10)[/tex]

[tex]y-200=-5(x-10)[/tex]

[tex]y-200=-5x+50[/tex]

[tex]y=-5x+250[/tex]

Which also can be written as:

[tex]f(x)=-5x+250[/tex]

Hence, the correct option is B) [tex]f(x)=-5x+250[/tex].

There are 5 20% in 100% ( 20 x 5 = 100)

So 10% of a number would be 12 x 5 = 60

Then there are 10 10% in 100% ( 10 x 10 = 100).

So if 10% = 60, then 100% = 60 x 10 = 600.

The starting value is 600

600 x 10% = 600 x 0.1 = 60

60 x 20% = 60 x 0.2 = 12

Now you have the starting value you can calculate the other answer:

600 x 20% = 600 x 0.20 = 120

120 x 10% = 120 x 0.10 = 12

The answer would be 12

Answer:

12

Step-by-step explanation:

Long Answer:

"20% of 10% of a number is 12" translates to:

.2 (times) .1 (times) x         =   12

of translated to times.

20%=.20 or .2

10%=.10   or .1

number translated to variable.

is translated to equals.

We have the following equation to solve:

[tex].2 \cdot .1 \cdot x=12[/tex]

Simplifying the .2 times .1 part:

[tex].02 \cdot x=12[/tex]

Divide both sides by .02:

[tex]x=\frac{12}{.02}[/tex]

[tex]x=600[/tex]

Now it ask for "what is 10% of 20% of the same number?"

Multiplication is communicative and I wouldn't have done all of this work if I had seen them just switch the 10% and 20% around.  The answer is 12.

But for fun since we already done all of this work!

"10% of 20% of 600" translates to:

.1 (times) .2 (times) 600

[tex].1 \cdot .2 \cdot 600[/tex]

[tex].02 \cdot 600[/tex]

[tex]12[/tex].

Short Answer:

.2(.1)x=12 so .1(.2)x=12

Multiplication is commutative is the reason the answer is 12.

b) -4

- 8x +4 =36

First, we subtract 4 from 36 to get 32

36-4=32

-8x=32

Since a negative times a negative equals a positive, then the answer has to be negative because 36 is positive.

32 divided by 8 = 4

B) -4

Answer:

The answer is B, x=-4

Step-by-step explanation:

-8x + 4 = 36

-8x - 4 = 36 - 4

-8x = 32

-8x/-8 = 32/-8

x = -4

To solve this problem, we need to find the values of w and I. We can set up a system of equations based on the given information and solve for w and I.

The subject of this question is Mathematics and the grade level is Middle School. To solve this problem, we are given the cost of a wallet-sized portrait (w) and the cost of an 8" x 10" portrait (I). We are also given the prices for two different packages.

The Basic Package includes 30 wallet-sized photos and 1 8" x 10" portrait. The cost of the package is $17.65.

The Deluxe Package includes 20 wallet-sized photos and 3 8" x 10" portraits. The cost of the package is $25.65.

To find the value of w and I, we can set up a system of equations based on the given information:

1. 30w + I = 17.65

2. 20w + 3I = 25.65

By solving this system of equations, we can find the values of w and I.

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The variables w and I represent the cost of wallet-sized and 8 x 10 portraits. The basic and deluxe packages are defined, including the quantities and costs of photos.

The subject of this question is Mathematics. It involves the cost of different portrait packages offered by a photo studio.

The question asks for the definitions of variables w and I, which represent the cost of wallet-sized and 8 x 10 portraits, respectively.

Mathematically, the basic package includes 30 wallet-sized photos and 1 8 x 10 portrait for a cost of $17.65.

The deluxe package includes 20 wallet-sized photos and 3 8 x 10 portraits for a cost of $25.65.

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Answer:

y = - x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x + 2 ← is in slope- intercept form

with slope m = 1

Given a line with slope m then the slope of a perpendicular line is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{1}[/tex] = - 1, hence

y = - x + c ← is the partial equation of the perpendicular line

To find c substitute (4, - 1) into the partial equation

- 1 = - 4 + c ⇒ c = - 1 + 4 = 3

y = - x + 3 ← equation of perpendicular line

Answer:

see explanation

Step-by-step explanation:

We require to rationalise the denominator by multiplying the numerator and denominator by the complex conjugate of the denominator.

The conjugate of 5 + 3i is 5 - 3i

noting that i² = - 1, hence

[tex]\frac{(9-6i)(5-3i)}{(5+3i)(5-3i)}[/tex] ← expand factors

= [tex]\frac{45-57i+18i^2}{25-9i^2}[/tex]

= [tex]\frac{45-57i-18}{25+9}[/tex]

= [tex]\frac{27-57i}{34}[/tex]

= [tex]\frac{27}{34}[/tex] - [tex]\frac{57}{34}[/tex] i ← quotient

Final answer:

To find the quotient of 9-6i and 5+3i, multiply both the numerator and the denominator by the conjugate of the denominator 5-3i. Simplify by using the distributive property and knowing that i^2 equals -1. The final quotient is 27/34 - 57i/34.

Explanation:

To find the quotient of the complex numbers 9-6i divided by 5+3i, we must multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of 5+3i is 5-3i. So, the process is as follows:

Thus, the quotient is 27/34 - 57i/34 or approximately 0.7941 - 1.6765i.

Answer:

1) y=6

Step-by-step explanation:

The equation y=mx+b is called slope-intercept because it tells us the slope,m, and y-intercept ,b.

The equation y=a is a horizontal line and goes through a on the y-axis.  Horizontal lines have a slope of zero.

The equation x=b is a vertical line and goes through b on the x-axis.

Vertical lines have an undefined slope.

1) y=6 is horizontal so it's slope is 0

2) x=6 is vertical so it's slope is undefined

3) y=2x has slope 2

4) x+y=1 can be put into the form y=mx+b to determine the slope.

Subtract x on both sides:

       y=-x+1

The slope is -1.

Answer:

x = 2.68, x = -0.186

Step-by-step explanation:

We are given the following equation that we are to solve:

[tex] 2 x ^ 2 - 1 = 5 x [/tex]

Rearranging this quadratic equation to get:

[tex] 2 x ^ 2 -5 x - 1 = 0 [/tex]

Solving it by using the quadratic formula as we cannot find any factors for it.

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

[tex]x=\frac{-(-5) \pm (-5)^2-4(2)(-1)}{2(2)}[/tex]

[tex]x=\frac{5 \pm\sqrt{25+8} }{4}[/tex]

[tex]x=\frac{5+\sqrt{33} }{4}[/tex], [tex]x=\frac{5-\sqrt{33} }{4}[/tex]

x = 2.68, x = -0.186

Answer:

x = 2.68, x = -0.186 is the answer , i got a 100% on my test

Step-by-step explanation:

Answer:

Rounding to nearest hundredths gives us r=0.06.

So r is about 6%.

Step-by-step explanation:

So we are given:

[tex]A=P(1+r)^t[/tex]

where

[tex]A=2300[/tex]

[tex]P=1600[/tex]

[tex]t=6[/tex].

[tex]A=P(1+r)^t[/tex]

[tex]2300=1600(1+r)^6[/tex]

Divide both sides by 1600:

[tex]\frac{2300}{1600}=(1+r)^6[/tex]

Simplify:

[tex]\frac{23}{16}=(1+r)^6[/tex]

Take the 6th root of both sides:

[tex]\sqrt[6]{\frac{23}{16}}=1+r[/tex]

Subtract 1 on both sides:

[tex]\sqrt[6]{\frac{23}{16}}-1=r[/tex]

So the exact solution is [tex]r=\sqrt[6]{\frac{23}{16}}-1[/tex]

Most likely we are asked to round to a certain place value.

I'm going to put my value for r into my calculator.

r=0.062350864

Rounding to nearest hundredths gives us r=0.06.

Answer:

3 tyres

Step-by-step explanation:

56/4=14

14*3=42

Answer:

3 tyres he will fill.....

Answer:

x=8

Step-by-step explanation:

(x+4) = (x+8)

------     -------

3            4

Multiply each side by 12 to get rid of the fraction

      (x+4) = (x+8)

12 *------     ------- *12

       3            4

4*(x+4) = (x+8)*3

Distribute

​4x+16 = 3x+24

Subtract 3x from each side

4x-3x+16 = 3x-3x+24

x+16 = 24

Subtract 16 from each side

x+16-16 = 24-16

x = 8

Answer:

Angle of elevation of the highest point of the mountain is 77°

Step-by-step explanation:

Lynne is hiking. When she stands at the base of the mountain, the horizontal distance between Lynne and the highest point of the mountain is 588 feet.

Elevation of the mountain is 2610 feet.

We have to calculate the angle of elevation ∠C.

tanC = [tex]\frac{2610}{588}[/tex]

tanC = 4.439

C = [tex]tan^{-1}(4.439)[/tex]

C = 77.30 ≈ 77°

Therefore, angle of elevation of the mountain is 77°