a) The factored expression for h(t) is -16t(t - 10), obtained by factoring out a common factor of -16 and a common factor of t from the original expression -16t^2 + 160t.
b) Both the original expression -16t^2 + 160t and the factored expression -16t(t - 10) yield the same result of 144 when evaluated at t = 1, confirming the correctness of the factoring.
a) To factor out a common factor with a negative coefficient from the expression h(t) = [tex]-16t^2 + 160t[/tex], we can rewrite it as:
h(t) = [tex]-16(t^2 - 10t)[/tex]
Now, let's focus on factoring the quadratic expression inside the parentheses. We can factor out a common factor of t:
h(t) = -16t(t - 10)
Therefore, the factored expression for h(t) is -16t(t - 10).
b) To check the factoring by evaluating both expressions for h(t) at t = 1, we substitute t = 1 into the original expression and the factored expression and compare the results.
Using the original expression:
h(1) = [tex]-16(1)^2 + 160(1)[/tex]
h(1) = -16 + 160
h(1) = 144
Using the factored expression:
h(1) = -16(1)(1 - 10)
h(1) = -16(1)(-9)
h(1) = 144
Both expressions yield the same result of 144 when evaluated at t = 1. Therefore, the factoring is correct.
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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.
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:
God please this one too I keep getting different answers
Answer:
The domain of this function is all real numbers.
Dewan’s bank account balance is -$16.75. He deposits checks totaling $23.59. What is his new balance? -$1.08
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 = $6.84What is the solution for t in the equation?
2/3t-1/5t=2
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.
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
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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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?
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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point slope form (0,12), (-6,0)
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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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
Answer:
I wish you good luck in finding your answer
Answer: 115
Step-by-step explanation:
One more question thank you
Answer:
Step-by-step explanation:
n=30
r=12
Plug into formula
you get:
1.7 in²
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.)
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).
What is the slope of the Line y=-3x+2
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.
(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?
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
Which order pair? Explain.
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).
PLEASE HELP
4920+56+pi
52 divided by 7 = 6r3
A. Incorrect
OB. Correct
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
Find the measure of KV
LEO
K
L
V
N
128°
M
202°
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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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
(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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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
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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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
B. Lenghts of the diagonals
Step-by-step explanation:
Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below
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? %
help please i need help
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
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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)
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
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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if 2540cm is increase by 15%, the result is
Answer:
2921
Step-by-step explanation:
[tex]2540 + 2540 * \frac{15}{100} \\\\= 2540 + 381\\\\= 2921[/tex]
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.
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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Find the measure of the numbered angles
Look at picture for reference
Show work when possible
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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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)
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)
SimplifiedThe 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>
The overnight temperature drops from 11°C to -2°C. B how many degrees has the temperature dropped?
Answer: I'm pretty sure it's 13.
Step-by-step explanation: Hope this helped!!
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
Answer:
the first 2
Step-by-step explanation:
let me know if it is wrong
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.
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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