If we change the -3 to a 3 in the equation what would happen to the graph

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Answer:

$392

Step-by-step explanation:

I may have solved it differently

500-18(6)=a

500-108=392

Juan will need $392 after 6 weeks of saving.

Answer:

Step-by-step explanation:

For (a), you will use that 2 points that are closest to lying on the line which are the points located at (1, 14) and (7, 7).

For (b), you will use those 2 points to find the slope of the line using the slope formula:

\(m=\frac{7-14}{7-1}=\frac{-7}{6}=-1.167\)

For (c), you will use point-slope form to write the equation. Point-slope form is

\(y-y_1=m(x-x_1)\) where x and y stay x and y in the equation and x1 and y1 are replaced with one of the coordinates. Let's use (7, 7). Keep in mind that IT DOESN'T MATTER WHICH POINT YOU PICK...YOU WILL GET THE SAME EQUATION WITH EITHER ONE! And this is because both those points lie on the same line...the line for which we will write the equation.

We have m = -1.167, y = 7 and x = 7:

y - 7 = -1.167(x - 7)

That's the point-slope form of the line, but rarely is it ever left in that form. I've only seen it left in point-slope form in calculus. Most of the time, from point-slope form, you are asked to put it into slope-intercept form, and here is no exception. Putting the equation into slope-intercept form is the same thing as solving it for y. So let's get y all by itself on one side of the equals sign and everything else over on the other side. We also of course need to distribute into the parenthesis:

y - 7 = -1.167x + 8.169 and

y = -1.167 + 8.169 + 7 so

y = -1.167 + 15.169

That's your equation in slope-intercept form, so you're done!

Answer:

5

Step-by-step explanation:

117/24 = 4.875

round up to 5 to get the total number of bags

Answer:

\(\boxed{\sf \ \ \ 11,464 \ \ \ }\)

Step-by-step explanation:

hello

we need to compute the following

\(\sum\limits^9_{i=0} {1000(1.03)^i}=1000\dfrac{1.03^{10}-1}{1.03-1}=11463.879...\)

hope this helps

Answer:

for every 1 book chloe reads payton reads 5

Answer:

ITS D GOOD LUCK WITH YOUR HMK

Answer:

half

Step-by-step explanation:

I got this answer by doing (22/7-2/3) and (22/7-2/3)/2 and comparing the results.

(22/7-2/3) = 52/21, which is about 2.47.

(22/7 - 2/3)/2 = 26/21, which is about 1.23.

With this, you can conclude that it would be half the value.

Answer:

2/21

Step-by-step explanation:

Answer:

the rise is 6 and the run is 7.  the rate of leaking per minunte is about .8  gallons per minute

Step-by-step explanation:

i think its right this time

Answer:

Step-by-step explanation:

Answer:

Below!

Explanation:

Looking at the system of equations, we can tell that they are forming a parallel line, which means that the system of equations have no solution because the system of equations have the same slopes, but different y-intercepts. Please check out the graph below to understand better.

Answer:

26

Step-by-step explanation:

7(4)+-2

28-2=26

Step-by-step explanation:

y = 4 and z = -2

\( = 7y + z\)

\( = 7 \times 4 + ( - 2)\)

\( = 28 - 2\)

\( = 26...\)

Answer:

2.559 × 10 to the 1st power

Step-by-step explanation:

using a SNC

Answer:

2.559 * 10^1

Step-by-step explanation:

Rules of scientific notation (that I always remember)

    - the number must be between 1 and 9

    - if number gets smaller, exponent gets bigger; if number gets bigger, exponents gets smaller

25.59 is bigger than 9 so we move the decimal one place value to the left

and the number gets smaller meaning the exponent increases

The required proof has been below that ΔJKL ≅ ΔLMN due to the SAS postulate.

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

The triangles are given in the question, as shown.

As per the given figure, we have

JK = LM

∠LJK ≅ ∠NLM (same side inner angles)

Since L is the midpoint of JN. (Definition of midpoint)

Then JL ≅ LN

Now, for triangles ΔJKL and ΔLMN

JK ≅ LM (sides)

∠LJK ≅ ∠NLM (angle)

JL ≅ LN (sides)

By SAS postulate, ΔJKL ≅ ΔLMN.

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Answer:

15

Step-by-step explanation:

30/2= 15 feet per second

Answer:

Well its basically 3 x 4 = 12, so for every lamb add four legs until you get to three

Step-by-step explanation:

Interest is a fee charged by a lender to a borrower for the use of money or credit, usually expressed as a percentage of the amount borrowed or invested over a period of time. Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.  The total interest earned after one year is $229

How much was in each account?

Let x be the amount invested in the first account that pays 3% interest, and let y be the amount invested in the second account that pays 8% interest. Since the total amount invested is $5800, we have:

\(x + y = 5800\)

The amount of interest earned on the first account is 0.03x, and the amount of interest earned on the second account is 0.08y. Since the total interest earned after one year is $229, we have:

\(0.03x + 0.08y = 229\)

We now have two equations with two unknowns:

\(x + y = 5800\)

\(0.03x + 0.08y = 229\)

We can solve for x and y by using elimination or substitution method. Here, we will use the substitution method.

Solve the first equation for x:

\(x = 5800 - y\)

Substitute this expression for x into the second equation and solve for y:

\(0.03(5800 - y) + 0.08y = 229\)

\(174 - 0.03y + 0.08y = 229\)

\(0.05y = 55\)

\(y = 1100\)

Now substitute this value of y into either equation to solve for x:

\(x + 1100 = 5800\)

\(x = 4700\)

Therefore, Brandon invested $\(4700\) at 3% interest and $\(1100\) at \(8\)% interest.

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

Work Shown:

s = sum of the heights of buildings A,B,C

s/3 = mean of the heights of buildings A,B,C

s/3 = 14.2

s = 3*14.2

s = 42.6

The buildings A,B,C have their heights add up to 42.6

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

r = sum of the heights of buildings A,B,C,D,E

r/5 = mean of the heights of buildings A,B,C,D,E

r/5 = 14.8

r = 5*14.8

r = 74

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

r-s = (sum of heights of A,B,C,D,E)-(sum of heights of A,B,C)

r-s = sum of the heights of buildings D and E

r-s = 74-42.6

r-s = 31.4

(r-s)/2 = mean height of buildings D and E

(r-s)/2 = 31.4/2

(r-s)/2 = 15.7 meters is the average height of buildings D and E.

Answer:

E) 45

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Answer:

Step-by-step explanation:

1st 10 days - 8 GB

2nd 10 days - 8 GB

3rd 10 days - 8 GB

________________

30 days    -  24 GB

Solution,

radius=21 cm

Circumference of circle=2 pi r

=2*3.142*21

=131.964 cm

hope it helps

Good luck on your assignment

Answer:

w= -9/8

Step-by-step explanation:

-1/3w -3/5 = 1/5w

+1/3w            +1/3 w

-3/5=1/5w+1/3w

Make common denominators to combine like terms of the right

-3/5=1/5w+1/3w

         *3       *5

-3/5=3/15w+5/15w

-3/5=8/15w

multiply both sides by the reciprocal of 8/15 which is 15/8

-3/5*15/8=8/15w*15/8

\(\frac{-3}{5}\)*\(\frac{15}{8}\) ----> cross reduce 5 in the denominator becomes 1 and 15 in the numerator becomes 3

\(\frac{-3}{1}\)*\(\frac{3}{8}\) -----> now multiply across

w= -9/8

Answer: -6/7

Step-by-step explanation:

-1/2w-3/5=1/5w

-w/2 - 3/5=w/5

Collect like terms

w/5 + w/2=-3/5

(2w + 5w)/10=-3/5

7w/10=-3/5

Cross multiply

7w x 5=-3 x 10

35w=-30

Divide both sides by 35

35w/35=-30/35

w=-6/7

Answer:r=2 cos^4(theta)

Step-by-step explanation:To find the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta), we need to find where the derivative of r with respect to theta is equal to zero, since the maximum r-values occur at these points.

First, we can simplify the equation by using the identity cos(2theta) = 2cos^2(theta) - 1 and substituting cos^2(theta) = (1 + cos(2theta))/2. This gives:

r = 2 cos^4(theta) = 2(1/2 + 1/2 cos(2theta))^2 = 1 + cos(2theta) + cos^2(2theta)/2.

Next, we can take the derivative of r with respect to theta, using the chain rule:

dr/dtheta = -sin(2theta) - 2cos(2theta)sin(2theta).

Setting this equal to zero and factoring out sin(2theta), we get:

sin(2theta)(-1 - 2cos(2theta)) = 0.

This equation is satisfied when sin(2theta) = 0 or cos(2theta) = -1/2.

When sin(2theta) = 0, we have 2theta = k*pi for some integer k. Therefore, theta = k*pi/2.

When cos(2theta) = -1/2, we have 2theta = 2*pi/3 + 2*k*pi or 2theta = 4*pi/3 + 2*k*pi for some integer k. Therefore, theta = pi/3 + k*pi or theta = 2*pi/3 + k*pi.

These are the values of theta where the maximum r-values occur on the graph of the polar equation r = 2 cos^4(theta).

Answer:

x = 121

Step-by-step explanation:

In order to solve for "x" you need to get it on one side by itself. To do that you need to add 93 to the other side. 93 + 28 is 121.

Answer:

121

Step-by-step explanation:

x-93=28

x=28+93

x=121

Answer:

Total amount = $4,902

Step-by-step explanation:

GIven:

Equation.

A(n) = 4,300 + (n - 1)(0.02 × 4,300)

Number of years (n) = 8

Amount deposit = $4,300

Rate of interset = 2%

Computation;

A(n) = 4,300 + (n - 1)(0.02 × 4,300)

By putting, n = 8

A(n) = 4,300 + (8 - 1)(0.02 × 4,300)

A(n) = 4,300 + (7)(86)

A(n) = 4,300 + 602

A(n) = 4,902

Total amount = $4,902

Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn

A rectangle is a type οf quadrilateral that has its parallel sides equal tο each οther and all the fοur vertices are equal tο 90 degrees. Hence, it is alsο called an equiangular quadrilateral. Since, the οppοsite sides are equal and parallel, in rectangle, therefοre, it can alsο be termed as a parallelοgram.

Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn

check the attachment given belοw tο understand.

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The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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