John and Sarah are each saving money for a car. The total amount of money John will save is given by the function j(x)= x^2 +2x, where x represents the number of weeks. The total amount of money Sarah will save is given by the function s(x)= -3x+6, where x represents the numbers of weeks.

Explain the point of intersection in context to the problem. Show all work

Answer:

(1,80)

Step-by-step explanation:

hope i am being a good help

Answer:

3,467,700 excluding years studying

Step-by-step explanation:

Every year the Surgeon makes $115,590 more than the Pharmacist (230,540-114,950)

$115,590 * 30 = $3,467,700

The surgeon makes $9,900,000 more in lifetime income than the pharmacist over a working period of 30 years.

To answer the question about how much more money a surgeon makes in lifetime income compared to a pharmacist, we first need to understand the potential earnings of both professions over a 30-year working period.

Step 1: Define Earnings for Each Profession

Let's assume:

Step 2: Calculate Lifetime Income

For the Surgeon:

For the Pharmacist:

Step 3: Calculate the Difference in Lifetime Income

To find out how much more the surgeon makes compared to the pharmacist, we subtract the pharmacist's total income from the surgeon's total income:

Conclusion

In conclusion, the surgeon makes $9,900,000 more in lifetime income than the pharmacist over a working period of 30 years.

Answer:

look it up on google if you havent tried already. also it doesn't hurt to ask for help from someone you know.

Step-by-step explanation:

Answer: Option C

We will factor 16 so that the sum of the factors is 8.

Such factors are 4 and 4.

So the factorization of the given expression is:

[tex]y^2+8y+16\\=y^2+4y+4y+16\\=y(y+4)+4(y+4)\\=(y+4)(y+4)\\=(y+4)^2[/tex]

So the given trinomial is a perfect square trinomial.

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Answer:

18h

Step-by-step explanation:

Answer:

Step-by-step explanation:

so you take the eight and round it so then it makes a zero and the 4 becomes a 5

Answer:

320

Step-by-step explanation:

320

As your rounding to the ten place if your number is above five you round up if its below you round down.

Answer:

The answer is B.

Step-by-step explanation:

All other answers are irrational

Answer:

Standard Form: 4x-1x^3-5x^2.

Answer:

[tex]4x + {x}^{3} - 5 {x}^{2} [/tex]

Step-by-step explanation:

[tex]4x - 3 {x}^{3} + 2 {x}^{3} - 5 {x}^{2} \\ = 4x + {x}^{3} - 5 {x}^{2} [/tex]

Answer:

3)a. (80 km/hour)(6 hours) = 480 km

b. 480 km/5 hours = 96 km/hour

Answer: 16y- 2xy

Step-by-step explanation:

Answer:

The answer is C) 14in.

Step-by-step explanation:

this is very easy, you just gotta do this, then that, then this, blablablabla you will get 100%

The radius of the hexagon with an apothem of 12 in is 14 inches.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

The angles of a hexagon measure 60 degrees each, since it is bisected, the angle becomes 30 degrees.

Let c represent the radius of the hexagon, hence:

cos(30) = 12/c

c = 14 in

The radius of the hexagon with an apothem of 12 in is 14 inches.

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Answer:

C) translate horizontally 5 units left

Step-by-step explanation:

f(x + 5)

Is a change in domain

The graph of f(x) is shifted 5 units towards the left to obtain the graph of f(x+5)

Answer:

C

Step-by-step explanation:

When we only change the x part of the function (that is, we add, subtract, multiply, or divide something in relation to the x part of f(x)), that is called a horizontal transformation. When we change the entire function, that's a vertical transformation.

In this case, because we are only changing the x (we turn f(x) into f(x + 5)), this is a horizontal transformation. One thing to note about horizontal transformations is that they are "backwards", which means that if we add to the x, we actually move the graph in the negative direction (which is to the left), whereas if we subtract from x, we move the graph in the positive direction (which is to the right).

Here, we're adding 5 to x, which we know means that we are translating the graph of f(x) horizontally to the left 5 units.

Thus, the answer is C.

Hope this helps!

Answer:

50+60h = 470

Step-by-step explanation:

50 is the constant as she charges a base fee.

"For each" => price varies => "varies" => variable => x

50+60h = 470.

Answer:

THE ANSWER IS A. I HAD THE SAME QUESTION

Step-by-step explanation:

Answer:

I think its A

Step-by-step explanation:

Step-by-step explanation:

Slope of this equation is 3

Answer:

Slope = 3

Step-by-step explanation:

[tex]y = - 1 + 3x \\ y = 3x - 1 \\ equating \: it \: with \\ y = mx + b \\ \huge \red{ \boxed{slope \: (m) = 3 }}\\ [/tex]

The average rate of change of the function g(x) = x^2 + 10x + 23 over the interval -8 < x < -4 is -0.5.

To determine the average rate of change for the function g(x) = x^2 + 10x + 23 over the interval -8 < x < -4, we first plug these x-values into the function to find the corresponding y-values:

G(-8) = (-8)^2+ 10*(-8) + 23 = 9

G(-4) = (-4)^2+ 10*(-4) + 23 = 7.

The average rate of change will then be the change in y-values divided by the change in x-values, so:

Average Rate of Change = [G(-4) - G(-8)]/[-4 - (-8)] = (7 - 9)/(-4 - (-8)) = -2/4 = -0.5.

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Answer:

c

Step-by-step explanation:

The deviation from the mean for the data point 27 in a data set with mean 30 is -3.

In mathematics, the deviation from the mean of a data set is a measure of the distance between each data point and the mean. It is obtained by subtracting the mean from the data point. In this case, the mean of the data set is given as 30. To find the deviation from the mean for the data point 27, you simply subtract 30 (the mean) from 27 (the data point).

So 27 - 30 = -3

This means the deviation from the mean for the data point 27 is -3 which corresponds to option b.

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In a coordinate plane, the x-intercept of the line x + 2y + 4 = 0 will be (–4, 0).

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

A line has a slope of Negative one-half and a y-intercept of –2.

m = – 1/2

c = – 2

The equation of line will be

                y = –(1/2)x – 2

1/2x + y + 2 = 0

  x + 2y + 4 = 0

For the x-intercept, the value of y will be zero.

x + 2y + 4 = 0

Put x = 0, then the value of y will be

x + 2(0) + 4 = 0

         x + 4 = 0

               x = –4

Then the x-intercept of the line x + 2y + 4 = 0 will be (–4, 0).

The equation of the line is drawn in the graph.

It can be clearly observed the line intersect at (-4, 0) and (0, -2).

More about the equation of line link is given below.

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Answer:

-4 is the answer

Step-by-step explanation:

Answer:

75π [tex]m^{2}[/tex]  ≈  235.62 [tex]m^{2}[/tex]

Step-by-step explanation:

R represents the radius of the lawn

r represents the area of the circular bed

So,

Area of the remaining lawn, A = area of the lawn - area of the circular flower bed

A = πR^2 - π^2

A = π(R^2 - r^2)

A = π(10^2 - 5^2)

A = π( 100 - 25)

A = 75π  [tex]m^{2}[/tex]  ≈   235.62[tex]m^{2}[/tex]

Answer:

84

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The inscribed angle ABD is on half the central angle ACD, that is

∠ ABD = 0. × 50° = 25°

The measure of arc AD is equal to the central angle it subtends, thus

arc AD = 50°

1. The measure of inscribed angle [tex]\( \angle ABD \)[/tex] is 25 degrees. 2. The measure of arc [tex]\( AD \)[/tex] is 50 degrees.

To solve this problem, we need to understand the relationship between central angles, arcs, and inscribed angles in a circle.

1. Measure of Arc AD:

The measure of an arc created by a central angle in a circle is equal to the measure of the central angle itself. Given that the central angle [tex]\( \angle ACD \)[/tex] is 50 degrees, the measure of arc [tex]\( AD \)[/tex] is also 50 degrees.

[tex]\[ \text{Measure of arc } AD = 50^\circ \][/tex]

2. Measure of Inscribed Angle ABD:

An inscribed angle that intercepts the same arc as a central angle will have a measure that is half the measure of the central angle. In this case, the inscribed angle [tex]\( \angle ABD \)[/tex] intercepts arc [tex]\( AD \)[/tex], which has a measure of 50 degrees.

[tex]\[ \text{Measure of } \angle ABD = \frac{1}{2} \times \text{Measure of arc } AD = \frac{1}{2} \times 50^\circ = 25^\circ \][/tex]

The complete question is:

Central angle ACD of circle C has a measure of 50 degrees. What is the measure of arc AD? What is the measure of inscribed angle ABD?

1. [tex]\( \angle ABD \)[/tex] = ______.

2. arc [tex]\( AD \)[/tex] = ______.

Answer:

= -18/2.25

Step-by-step explanation:

We can find the slope by using the following

m = (y2-y1)/(x2-x1)

   = (-12-6)/(3.75 - 1.5)

   = -18/2.25

Answer:

The answer to your question is the letter D.

Step-by-step explanation:

Data

Point A = (1.5, 6)

Point B = (3.75, -12)

Slope measures the steepnees of a line.

Formula

slope = m = (y2 - y1) / (x2 - x1)

-Asign values to x1, y1, x2 and y2

    x1 = 1.5  y1  = 6  x2 = 3.75  y2 = -12

-Substitution

          m = (-12 - 6) / (3.75 - 1.5)

-Simplification

          m = -18 / 2.25

-Result

         m = 8

It is possible to simplify more the result so slope = 8.

a) 17.5a + 15.5p = t

b) Total mass of the shipment is 1195.5kg

Step-by-step explanation:

Mass of 1 box of apple= 17.5kg

Mass of 1 box of pears = 15.5kg

a) expression for getting total mass:

Let the no. of boxes of apple be 'a'

Let the no. of boxes of pears be 'p'

Let the total mass be 't'

17.5a + 15.5p = t

b) a = 32

p = 41

17.5a + 15.5p = t

17.5(32) + 15.5(41)  = t

560 + 635.5 =t

1195.5 = t

Total mass of the shipment is 1195.5kg

Answer:

C(3,3)

Step-by-step explanation:

Final Answer:

After 5 years, the account balance would be approximately $11,541.20.

Explanation:

To calculate the account balance for a certificate of deposit that has an initial amount of $10,000.00, with an annual interest rate of 2.89% compounded monthly over 5 years, we must use the compound interest formula:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

where:
- A is the amount of money accumulated after t years, including interest.
- P is the principal amount, which is the initial amount of money ($10,000.00 in this case).
- r is the annual interest rate in decimal form (2.89% or 0.0289 in this case).
- n is the number of times that interest is compounded per year (12 times per year for monthly compounding).
- t is the time the money is invested for, in years (5 years in this case).

Firstly, we convert the annual interest rate from a percentage to a decimal by dividing by 100:

r = 2.89% = 0.0289

Now we substitute the given values into the formula:

[tex]\[ A = \$10,000.00 \left(1 + \frac{0.0289}{12}\right)^{12 \cdot 5} \][/tex]

We calculate the rate per period by dividing the annual interest rate by the number of compounding periods per year:

[tex]\[ \frac{0.0289}{12} = 0.00240833 \][/tex] (rounded to 8 decimal places for precision)

Now calculate the growth factor:

[tex]\[ \left(1 + \frac{0.0289}{12}\right) = 1 + 0.00240833 = 1.00240833 \][/tex]

This growth factor is raised to the power of 60 (since there are 12 months in a year and we are compounding for 5 years):

[tex]\[ (1.00240833)^{60} \][/tex]

Using a calculator, raise 1.00240833 to the power of 60 to get approximately:

[tex]\[ 1.00240833^{60} \approx 1.15412 \][/tex](rounded to 5 decimal places for simplicity)

Finally, multiply this result by the principal amount to find the accumulated amount:

[tex]\[ A = \$10,000.00 \times 1.15412 \approx \$11,541.20 \][/tex]

Therefore, after 5 years, the account balance would be approximately $11,541.20.

Answer:

c)   (-∞, -4] or [7,∞)

Step-by-step explanation:

x² - 3x - 28 ≥ 0

x² - 7x + 4x -28 ≥ 0

x (x - 7) + 4(x - 7) ≥ 0

(x-7) (x + 4) ≥ 0

When x value lies in (-∞, -4],  (x-7)  value will be negative and (x+ 4) will be negative. So, result will be positive

When x value lies in [7,∞),  both (x-7)  and (x+ 4) will be positive. So, result will be positive

Answer:

B

Step-by-step explanation:

Count from the y-intercept to the next natural point. 2 up and then 3 across