PLEASE HELP
Suppose that the functions fand g are defined for all real numbers x as follows.
f(x) = 5x
g(x)=4x-4
Write the expressions for (g.f)(x) and (g-f)(x) and evaluate (g+f)(2).
(g•f)(x) =
(g-f)(x) =
(g+r) (2)=

Answers

Answer 1
(g•f)(x) = (4x - 4) • (5x)
= 20x^2 - 16

(g - f)(x) = (4x - 4) - (5x)
= (-1x) - 4
= -x -4

(g + f)(2) = (4(2) - 4) + (5(2))
= 4 + 10
= 14

Related Questions

Please calculate the volume of a solid oblique pyramid with a triangular base, given that the base has a length of 8 inches and a height of 6 inches, and the height of the pyramid is 10 inches. Round your answer to the nearest cubic inch.

Answers

Answer: 74

Step-by-step explanation:

The volume of the pyramid can be found using the formula:

Volume = (1/3) x Base Area x Height

To find the base area, we need to find the area of the triangular base. The area of a triangle can be found using the formula:

Area = (1/2) x Base x Height

Substituting the given values, we have:

Area = (1/2) x 8 x 6 = 24 square inches

To find the height of the pyramid, we can use the Pythagorean theorem. The slant height and one-half of the base form a right triangle, so we have:

Height^2 = (Slant Height)^2 - (1/2 x Base)^2

Height^2 = 10^2 - 4^2

Height^2 = 84

Height = √84 ≈ 9.165 inches

Now we can substitute the values into the formula for the volume:

Volume = (1/3) x Base Area x Height

Volume = (1/3) x 24 x 9.165

Volume ≈ 73.96 cubic inches

Therefore, the volume of the pyramid is approximately 73.96 cubic inches.Step-by-step explanation:

(Sumita plans to deposit Rs. 21000 in any bank for 3 years. (a) Define compound interest. (b) How much amount will she get at 10% simple interest when she deposits it in a bank N ? Calculate it. (c) How much amount will she get at 9% interest being compounded annually when she deposits it in another bank M?Calculate it. (d) Which bank is better to deposit the sum and how much more amount will she get (e) from the better bank?

Answers

Answer:

(Sumita plans to deposit Rs. 21000 in any bank for 3 years. (a) Define compound interest. (b) How much amount will she get at 10% simple interest when she deposits it in a bank N ? Calculate it. (c) How much amount will she get at 9% interest being compounded annually when she deposits it in another bank M?Calculate it. (d) Which bank is better to deposit the sum and how much more amount will she get (e) from the bet

(a) Compound interest is the interest earned on both the initial principal amount and any accumulated interest from previous periods. Unlike simple interest, which is calculated only on the principal amount, compound interest takes into account the interest that has been added to the principal over time.

(b) To calculate the amount Sumita will get at 10% simple interest when she deposits Rs. 21,000 in bank N for 3 years, we can use the formula for simple interest:

Simple Interest = (Principal * Rate * Time) / 100

In this case:

Principal (P) = Rs. 21,000

Rate of interest (R) = 10%

Time (T) = 3 years

Simple Interest = (21,000 * 10 * 3) / 100

Simple Interest = 6,300

Amount = Principal + Simple Interest

Amount = 21,000 + 6,300

Amount = Rs. 27,300

Therefore, Sumita will get Rs. 27,300 at 10% simple interest when she deposits it in bank N.

(c) To calculate the amount Sumita will get at 9% interest compounded annually when she deposits Rs. 21,000 in bank M for 3 years, we can use the formula for compound interest:

Compound Interest = Principal * [(1 + Rate/100) ^ Time] - Principal

In this case:

Principal (P) = Rs. 21,000

Rate of interest (R) = 9%

Time (T) = 3 years

Compound Interest = 21,000 * [(1 + 9/100) ^ 3] - 21,000

Calculating the compound interest:

Compound Interest = 21,000 * (1.09^3) - 21,000

Compound Interest ≈ 21,000 * 1.29503 - 21,000

Compound Interest ≈ 27,139.63 - 21,000

Compound Interest ≈ Rs. 6,139.63

Amount = Principal + Compound Interest

Amount = 21,000 + 6,139.63

Amount ≈ Rs. 27,139.63

Therefore, Sumita will get approximately Rs. 27,139.63 at 9% interest compounded annually when she deposits it in bank M.

(d) To determine which bank is better to deposit the sum, we compare the amounts received in bank N (simple interest) and bank M (compound interest).

In bank N, Sumita will receive Rs. 27,300, while in bank M, she will receive approximately Rs. 27,139.63.

Comparing the amounts, we can see that Sumita will get a slightly higher amount in bank N.

(e) The amount she will get from the better bank (bank N) is Rs. 27,300 - Rs. 27,139.63 = Rs. 160.37 more than bank M.

Step-by-step explanation:

hope it help


The slope of line BD is
y
2b
2a-c
E(a, b)
A(0, 0)
G
B(2a, 2b)
D(c, 0)
F
LL
C(2c, 0)
What is the equation of BD, simplified?
y - y₁ = m(x − x₁)
(x-c)
= √2²²= c)
2b
2a -
y -0 =
0 y = | D x - (₂22bcc)
b
C
1
2a -
0 y =
0 y = | 2²0 |x-12 2²0-c
2a
2a C
0 y = ( 2b )x - ( 2bc)
(2a-c) (2a - 2c)

Answers

Answer:

  (c)  y = 2b/(2a -c)x -2bc/(2a -c)

Step-by-step explanation:

Given the equation of line BD in point-slope form you want the simplified equation.

  y -0 = (2b/(2a -c))(x -c)

Simplified

The equation is simplified by using the distributive property to eliminate parentheses.

  [tex]y-0=\dfrac{2b}{2a-c}(x -c)\\\\\\y=\dfrac{2b}{2a-c}x-\dfrac{2b}{2a-c}c\\\\\\\boxed{y=\dfrac{2b}{2a-c}x-\dfrac{2bc}{2a-c}}\qquad\text{matches choice C}[/tex]

<95141404393>

What is the slope of the Line y=-3x+2

Answers

Answer:

m = -3

Step-by-step explanation:

The slope-intercept form is y = mx + b

m = the slope

b = y-intercept

The equation is  y = -3x + 2

m = -3

So, the slope of the line is -3

Answer:

The slope is -3

Step-by-step explanation:

You were given the easiest form of linear equation, the slope-intercept form, because these are the ones that directly tell you the slope and       the y-intercept.

y=mx+b, Where m is the slope and b is the y-intercept.

PLEASE HELP

4920+56+pi

Answers

To perform the calculation, we need to know the value of π (pi). Pi is a mathematical constant approximately equal to 3.14159. However, since my training data only goes up until September 2021, I am unable to provide the current value of π.

Assuming we use the approximate value of π as 3.14159, the calculation would be as follows:

4920 + 56 + 3.14159 = 4980.14159

Therefore, the result of the expression 4920 + 56 + π (assuming π is approximately 3.14159) is approximately 4980.14159.

The values in the table represent a function.
x
-6
7
4
3
-5
f(x)
8
3
-5
-2
12
Use the drop-down menus to complete the
statements.
The ordered pair given in the first row of the table can
be written using function notation as
(3) is
f(x)=-5 when x is
Done

Answers

The ordered pair given in the first row of the table can be written using function notation as (x, f(x)) = (-6, 8).

f(x) = -5 when x is 4.

In function notation, we represent the input value as 'x' and the corresponding output value as 'f(x)'.

Looking at the first row of the table, we see that when x is -6, the corresponding value of f(x) is 8.

Therefore, we can write this ordered pair as (-6, 8) in function notation.

Similarly, we can determine that f(x) = -5 when x is 4 by examining the second row of the table.

The value of f(x) is -5 when x is 4, so we can express it as f(4) = -5.

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Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below

Answers

Part 1- The lower class boundary for the first class is 100.

Part 2- Approximately 75% of students take exactly two courses.

Part 1:

To find the lower class boundary for the first class, we need to consider the given class intervals. The lower class boundary is the smallest value within each class interval.

Given the class intervals:

100 - 104

105 - 109

110 - 114

115 - 119

120 - 124

125 - 129

130 - 134

The lower class boundary for the first class interval (100 - 104) would be 100.

So, the lower class boundary for the first class is 100.

Part 2:

To determine the percentage of students who take exactly two courses, we need to calculate the relative frequency for that particular category.

Given the data:

of Courses Frequency Relative Frequency Cumulative Frequency

1 23 0.4423 23

2 - 39

3 13 0.25 -

We can see that the cumulative frequency for the second class (2 courses) is 39. To find the relative frequency for this class, we need to divide the frequency by the total number of students surveyed, which is 52.

Relative Frequency = Frequency / Total Number of Students

Relative Frequency for 2 courses = 39 / 52 ≈ 0.75 (rounded to 4 decimal places)

To convert this to a percentage, we multiply the relative frequency by 100.

Percentage of students taking exactly two courses = 0.75 * 100 ≈ 75%

Therefore, approximately 75% of students take exactly two courses.

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Question

Part 1.

Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below.

Lengths (mm) Frequency

100 - 104 1

105 - 109 16

110 - 114 71

115 - 119 108

120 - 124 83

125 - 129 18

130 - 134 3

What is the lower class boundary for the first class?

class boundary =

Part 2

In a student survey, fifty-two part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

Please round your answer to 4 decimal places for the Relative Frequency if possible.

# of Courses Frequency Relative Frequency Cumulative Frequency

1 23 0.4423 23

2   39

3 13 0.25

What percent of students take exactly two courses? %

A farmer earns $___ for each orange she sells. She had to pay $___ for fertilizer. Part A: Rewrite the description by filling in the blanks with values of your choice to show the amount of money the farmer could earn selling any number of oranges, n. Make sure the values you choose make sense for this situation. (6 points) Part B: Write an algebraic expression from your written description used in Part A. Let n stand for the number of oranges. (6 points)

Answers

Part A: A farmer earns $0.20 for each orange she sells. She had to pay $25 for fertilizer. If she sells any number of oranges, n, the amount of money she could earn is 0.20n - 25 dollars.

Part B: The algebraic expression for the amount of money the farmer could earn selling any number of oranges, n, is 0.20n - 25.

What is the solution for t in the equation?
2/3t-1/5t=2

Answers

Answer:

Step-by-step explanation:

To solve the equation (2/3)t - (1/5)t = 2 for t, we need to combine like terms and isolate the variable t. Here are the steps:

(2/3)t - (1/5)t = 2

To combine the fractions, we need to find a common denominator for 3 and 5, which is 15.

[(2/3)(5/5)]t - [(1/5)(3/3)]t = 2

(10/15)t - (3/15)t = 2

[(10 - 3)/15]t = 2

(7/15)t = 2

To isolate t, we can multiply both sides of the equation by the reciprocal of (7/15), which is (15/7).

[(7/15)t][(15/7)] = 2[(15/7)]

t = (2 * 15) / 7

t = 30/7

Therefore, the solution for t in the equation (2/3)t - (1/5)t = 2 is t = 30/7 or t ≈ 4.286.

Which order pair? Explain.

Answers

A function can't have more than one value for an argument. Therefore, it's either (1,1) or (1,3), but since there's not (1,3) among the possible answers, it must be (1,1).

which of the following are like radicals? Check all
of the boxes that apply.
3x√√xy
-12x√√xy
-2x√√xj
x-√4x2²
-x√x²y
2√xy

Answers

Answer:

the first 2

Step-by-step explanation:

let me know if it is wrong

Dewan’s bank account balance is -$16.75. He deposits checks totaling $23.59. What is his new balance? -$1.08

Answers

Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

Original balance: -$16.75Deposit: $23.59New balance: -$16.75 + $23.59 = $6.84

Q.14 In the figure given below, let the lines 1, and 1, be parallel and t is transversal. Find
the value of x.
J

Answers

Answer:

I wish you good luck in finding your answer

Answer: 115

Step-by-step explanation:

God please this one too I keep getting different answers

Answers

Answer:

The domain of this function is all real numbers.

On January 1, 2022, ABC Company was established (trading firm engaged in buying and selling of laptop computers ), with an initial owner’s equity of P1,000,000. The company has an inventory 10 laptops each costing P50,000. In addition, it purchased a delivery equipment amounting to P250,000 (five years depreciation, straight line). The rest of the assets were in the form of cash.

At the end of 2022, operations showed that 5 laptops were sold at P50,000 each, 50% cash, 50% to be received in March of P2022. Aside from depreciation, a total of P50,000 (paid in cash) was incurred as operating expenses. Taxes are 50% of operating income to be paid in the same year of operations, if there are any. (Tax will not be deducted if there is an operating loss).


Construct the following :
a.) Balance sheet as of January 1, 2022 and December 31, 2022.
b.) Income Statement for the year ended Dec. 31, 2022 .
c.) Statement of Cash Flows for the year ended Dec. 31, 2022.

Answers

a) Balance Sheet as of January 1, 2022: Total Assets: P1,750,000

b) Income Statement for the year ended December 31, 2022: Net Income: Operating Income - Tax Expense

c) Statement of Cash Flows for the year ended December 31, 2022: None (Assuming no financing activities are mentioned in the information)

a) Balance Sheet as of January 1, 2022:

Assets:

Cash: P1,000,000

Inventory (10 laptops * P50,000): P500,000

Delivery Equipment (less depreciation): P250,000

Total Assets: P1,750,000

Liabilities:

None (Assuming no liabilities are mentioned in the given information)

Owner's Equity: P1,750,000

Balance Sheet as of December 31, 2022:

Assets:

Cash: (Assuming no cash transactions are mentioned in the information)

Accounts Receivable (50% of P50,000): P25,000

Inventory (5 laptops * P50,000): P250,000

Delivery Equipment (less depreciation): P200,000

Total Assets: P475,000

Liabilities:

Accounts Payable (50% of P50,000): P25,000

Income Tax Payable: (50% of Operating Income)

Total Liabilities: P25,000 + Income Tax Payable

Owner's Equity: (Initial Owner's Equity + Net Income)

b) Income Statement for the year ended December 31, 2022:

Sales Revenue: 5 laptops * P50,000 = P250,000

Operating Expenses: P50,000

Operating Income: Sales Revenue - Operating Expenses

Tax Expense: (50% of Operating Income)

Net Income: Operating Income - Tax Expense

c) Statement of Cash Flows for the year ended December 31, 2022:

Cash Flows from Operating Activities:

Cash received from sales: (50% of P250,000)

Cash paid for operating expenses: P50,000

Tax payments: (50% of Tax Expense)

Cash Flows from Investing Activities:

Purchase of delivery equipment: P250,000

Cash Flows from Financing Activities:

None (Assuming no financing activities are mentioned in the information)

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Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the following exercise.
Find the following sums without using a calculator or a formula. Hint: Apply the procedure used by Gauss. (See the Math Matters on page 31.)
+393 +394 + 395
(a) 1+2+3+4+...+392
(b) 1+2+3+4
x
546 + 547 +548 + 549
(c) 2+4+6+8+...+76 + 78 + 80 +82

Answers

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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point slope form (0,12), (-6,0)

Answers

This is the equation of the line in point-slope form, where the slope is 2 and the given point is (0, 12).

To find the equation of a line in point-slope form, we need a point on the line and the slope of the line.

Given the points (0, 12) and (-6, 0), we can calculate the slope using the formula:

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

Using the coordinates (0, 12) as (x1, y1) and (-6, 0) as (x2, y2):

slope = (0 - 12) / (-6 - 0)

slope = -12 / -6

slope = 2

Now that we have the slope, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Using the point (0, 12) as (x1, y1) and the slope (m) as 2:

y - 12 = 2(x - 0)

Simplifying the equation:

y - 12 = 2x

This is the equation of the line in point-slope form, where the slope is 2 and the given point is (0, 12).

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Find the measure of the numbered angles
Look at picture for reference
Show work when possible

Answers

The measure of the numbered angles in the rhombus is determined as angle 1 = 90⁰, angle 2 = 57⁰, angle 3 = 45⁰, and angle 4 = 45⁰.

What is the measure of the numbered angles?

The measure of the numbered angles is calculated by applying the following formula as follows;

Rhombus has equal sides and equal angles.

angle 2 = angle 57⁰ (alternate angles are equal)

angle 1 = 90⁰ (diagonals of rhombus intersects each other at 90⁰)

angle 3 = angle 4 (base angles of Isosceles triangle )

angle 3 = angle 4 = ¹/₂ x 90⁰

angle 3 = angle 4 = 45⁰

Thus, the measure of the numbered angles in the rhombus is determined as angle 1 = 90⁰, angle 2 = 57⁰, angle 3 = 45⁰, and angle 4 = 45⁰.

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

Answer:

B. Lenghts of the diagonals

Step-by-step explanation:

The overnight temperature drops from 11°C to -2°C. B how many degrees has the temperature dropped?

Answers

Answer: I'm pretty sure it's 13.

Step-by-step explanation: Hope this helped!!

Find the measure of KV
LEO
K
L
V
N
128°
M
202°

Answers

The measure of the arc angle KV is 54 degrees.

How to find angle measure in a circle?

If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore, let's find the arc angle KV in the circle as follows:

Hence,

let

arc angle KV = x

128 = 1 / 2 (202 + x)

128 = 101 + 0.5x

128 - 101 = 0.5x

27 = 0.5x

divide both sides by 0.5

x = 27 / 0.5

x = 54 degrees.

Therefore,

arc angle KV = 54 degrees.

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One more question thank you

Answers

Answer:

Step-by-step explanation:

n=30

r=12

Plug into formula

you get:

1.7 in²

52 divided by 7 = 6r3
A. Incorrect
OB. Correct

Answers

Answer:

incorrect

Step-by-step explanation:

as 7 * 6 = 42 and r is 10

so 6r3 is incorrect

and 7 * 7 = 49 and r is 3

so 7r3 is correct

The hip width x of adult females is normally distributed with a mean of 37.6 cm and a standard deviation of 4.36 cm. The maximum width of an aircraft seat that will accommodate 98% of all adult women is about: (Give your answer to one decimal places if necessary.​)

Answers

Answer:

Step-by-step explanation:

To find the maximum width of an aircraft seat that will accommodate 98% of all adult women, we need to determine the corresponding z-score for the 98th percentile of the normal distribution.

First, we find the z-score corresponding to the 98th percentile using a standard normal distribution table or calculator. The z-score for the 98th percentile is approximately 2.05.

Next, we use the z-score formula to find the corresponding value in the original distribution:

z = (x - μ) / σ

Solving for x (the maximum width of the aircraft seat):

x = z * σ + μ

Substituting the values given:

x = 2.05 * 4.36 + 37.6

x ≈ 45.98

Therefore, the maximum width of an aircraft seat that will accommodate 98% of all adult women is approximately 46 cm (rounded to one decimal place).

The cost of 2.5 litres of petrol in the United Kingdom is £1.70. The cost of 1 US gallon of petrol in the United States is $3.30. £1 = $1.42 1 litre = 0.26 US gallons Is petrol cheaper in the United Kingdom or United States? ​

Answers

The cost of 2.5 liters of petrol in the United Kingdom is £1.70. The cost of 1 US gallon of petrol in the United States is $3.30. £1 = $1.42 and 1 liter = 0.26 US gallons. So, is petrol cheaper in the United Kingdom or the United States.

Let's find out the cost of 2.5 liters of petrol in the United States dollars;Cost of 1 litre of petrol in the United Kingdom = £1.70/2.5 = £0.68Cost of 1 liter of petrol in the United States = $3.30/3.78 (as 1 US gallon = 3.78 liters) = $0.87We know that £1 = $1.42£0.68 = $0.68 x 1.42 = $0.96So, the cost of 1 liter of petrol in the United Kingdom is $0.96 (approximately)The cost of 1 liter of petrol in the United States is $0.87 (approximately)

Therefore, petrol is cheaper in the United States than the United Kingdom.

So, the answer is that petrol is cheaper in the United States than in the United Kingdom.

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Question 5 of 8
Which choice is the solution set of the inequality below?

OA. x< 4.1
OB. X<-4.1
OC. X> 4.1
O D. x≤ 4.1
OE. -4.1 OF. x<-4.1 or x> 4.1

Answers

x < 4.1, as it represents the solution set for the given inequality. A.

The solution set of the inequality x < 4.1 can be determined by examining the given answer choices:

OA. x < 4.1:

This choice represents all values of x that are strictly less than 4.1.

It is a valid solution set for the given inequality.

OB. x < -4.1:

This choice represents all values of x that are strictly less than -4.1.

It is not a valid solution set for the given inequality.

OC. x > 4.1:

This choice represents all values of x that are strictly greater than 4.1.

It is not a valid solution set for the given inequality.

OD. x ≤ 4.1:

This choice represents all values of x that are less than or equal to 4.1.

It is not a valid solution set for the given inequality because the inequality is strict (x < 4.1), not inclusive.

OE. -4.1 < x < 4.1:

This choice represents all values of x that are strictly between -4.1 and 4.1.

It is not a valid solution set for the given inequality because it does not include the possibility of x being less than -4.1 or greater than 4.1.

OF. x < -4.1 or x > 4.1:

This choice represents two separate solution sets: one for x < -4.1 and another for x > 4.1.

It is not a valid solution set for the given inequality because it combines two separate possibilities.

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if 2540cm is increase by 15%, the result is

Answers

Answer:

2921

Step-by-step explanation:

[tex]2540 + 2540 * \frac{15}{100} \\\\= 2540 + 381\\\\= 2921[/tex]

71)
Mia buys 4 calculators and 2 pens for $20.60
Heidi buys 5 calculators and 3 pens for $26.90.
Write down a pair of simultaneous equations and solve
cost of a pen.

Answers

Answer:

Therefore, the cost of a pen is $2.30.

Step-by-step explanation:

Let's assign variables to represent the cost of a calculator and the cost of a pen.

Let c represent the cost of a calculator.

Let p represent the cost of a pen.

Based on the given information, we can form the following pair of simultaneous equations:

Equation 1: 4c + 2p = 20.60   (Mia buys 4 calculators and 2 pens for $20.60)

Equation 2: 5c + 3p = 26.90   (Heidi buys 5 calculators and 3 pens for $26.90)

To solve for the cost of a pen, we'll eliminate the variable c by multiplying Equation 1 by 5 and Equation 2 by 4. Then we'll subtract Equation 1 from Equation 2:

5 * (4c + 2p) = 5 * 20.60

4 * (5c + 3p) = 4 * 26.90

20c + 10p = 103.00

20c + 12p = 107.60

Subtracting Equation 1 from Equation 2:

(20c + 12p) - (20c + 10p) = 107.60 - 103.00

20c - 20c + 12p - 10p = 4.60

2p = 4.60

p = 4.60 / 2

p = 2.30

Therefore, the cost of a pen is $2.30.

Answer:

Let's assume that the cost of a calculator is x and the cost of a pen is y. Then we can write the following pair of equations:

4x + 2y = 20.60    (equation 1)

5x + 3y = 26.90    (equation 2)

To solve for the cost of a pen, we need to eliminate x from the equations. We can do this by multiplying equation 1 by 5 and equation 2 by -4, and then adding them:

(5)(4x + 2y = 20.60)  becomes  20x + 10y = 103    (equation 3)

(-4)(5x + 3y = 26.90) becomes -20x - 12y = -107.60    (equation 4)

                                 

Adding Equation 3 and Equation 4 gives:

-2y = -4.60

Divide both sides by -2:

y = 2.30

Therefore, the cost of a pen is $2.30.

Step-by-step explanation:

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in this chart, × is the length of a persons forearm in centimeters and y is the persons height in centimeters. the question is if someones forearm (x) is 24.5 cm, how tall would they be? how do i find this? and how would i make a linear regression graph? thanks

Answers

The height of a person whose length of forearm is 24.5 cm is equal to 163.38 centimeters.

How to construct and plot the data in a scatter plot?

In this exercise, we would plot the length of forearm on the x-axis of a scatter plot while height would be plotted on the y-axis of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit on the scatter plot;

y = 3.01x + 89.63

Based on the equation of the line of best fit above, the height of a person whose length of forearm is 24.5 cm can be determined as follows;

y = 3.01x + 89.63

y = 3.01(24.5) + 89.63

y = 163.375 ≈ 163.38 centimeters.

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help please i need help

Answers

The number line inequality that represents x > -7 is: Option D

How to identify the  Inequality number line?

In number line inequalities we know that:

A closed circle indicates "greater than or equal to" or "less than or equal to" .

Meanwhile an open circle indicates "greater than" or "less than".

A closed circle pointing to the right indicates  "greater than or equal to" while a closed circle pointing to the left indicates "less than or equal to,"

Similarly:

An open circle pointing to the right indicates "greater than" while An open circle pointing to the left indicates  "less than".

Thus , the correct number line that shows x > -7 is: Option D

Read more about Inequality number line at: https://brainly.com/question/24372553

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