Answer:
44 feet in 10 seconds = 44 x 6 (since there are 60 seconds in a minute) = 264 feet per minute
264 feet per minute x 60 minutes (since there are 60 minutes in one hour) = 15,840 feet per hour
15,840 feet per hour / 5,280 feet (since there are 5,280 feet in 1 mile) = 3 miles per hour
Plot the numbers -1 1/6 and 17/6 on the number line below.
The number line where we plotted -1 1/6 and 17/6 is added as an attachment
Plotting -1 1/6 and 17/6 on a number lineFrom the question, we have the following parameters that can be used in our computation:
-1 1/6 and 17/6
To start with, we convert both numbers to the same form
i.e. decimal or fraction
When converted to fractions, we have
-7/6 and 17/6
This means that we can plot -7/6 at -7 and 17/6 at point 17 where the difference in each interval is 1/6
Using the above as a guide, we have the following:
The number line is attached
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An annual salary of K31 600 had an increase of 8%. What is the new salary amount? Working out:
To calculate the new salary amount, we need to add the increase to the original salary.
The increase in salary is 8% of the original salary, which is:
8/100 x K31 600 = K2 528
So, the new salary amount is:
K31 600 + K2 528 = K34 128
Therefore, the new salary amount is K34 128.
To find the new salary after an 8% increment, first find what 8% of the original salary is by multiplying it by 0.08. Add this amount to the original salary to calculate the new salary, which is K34 128.
Explanation:In order to calculate the new salary after an 8% increment, you first need to figure out how much 8% of the original salary is and then add this to the original salary. So first, remember that 'percent' means 'per hundred', so to calculate 8% of K31 600, you would multiply 31 600 by 0.08 (which is the decimal equivalent of 8%). This gives you K2 528. Then you add this amount to the original salary to get the new salary. Therefore, K31 600 + K2 528 equals to a new salary of K34 128.
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what is the value of y?
Answer:
y ≈ 34
Step-by-step explanation:
using the tangent ratio in the right triangle
tan y = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{32}{48}[/tex] = [tex]\frac{2}{3}[/tex] , then
y = [tex]tan^{-1}[/tex] ( [tex]\frac{2}{3}[/tex] ) ≈ 34 ( to the nearest whole number )
answer
y = 33.69°
tan= opposite /adjacent
tan y° = 32 / 48
tan y° = 2/3
tan y° = 0.67
y° = tan^-1 (0.67)
y° = 33.69°
She wants to put a total of 5 shapes on the card congruent to the one shown on the grid above. If one unit on the grid represents 1 cm, what area of the card will be covered under all the shapes? A. 18 square cm B. 72 square cm C. 30 square cm D. 90 square cm
Based on the above, the total Card area is C: 30 square cm.
What is the area?Note that the shape is congruent to the one shown on the grid, and thus all shape has the same area. So, to find the total area that is covered by 5 shapes, we need to find the area of one shape as well as then multiply it by 5.
To find total area covered by 5 congruent shapes, we need to multiply one shape's area by 5. To find the area, count 6 unit squares covered by shape on the grid.
Therefore, the total Card area covered by 5 shapes is:
5 × 6 cm² = 30 cm²
Therefore, the total area is C: 30 square cm.
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HELP ASAP! ( I MEAN 10 MINUTES ) ( 15 POINTS )
Jeremiah needed dog food for his new puppy. He compared the prices and sizes of three types of dog food.
Canine Cakes Bark Bits Woofy Waffles
Size (pounds) 30 40 28
Cost $54 $70 $42
Part A: Calculate the corresponding unit rate for each package. (9 points)
Part B: Determine the best buy using the unit rates found in Part A. Explain your answer. (3 points)
Part A
Canine Cakes: $1.8 per pound
Bark Bits: $1.75 per pound
Woofy Waffles: $1.5 per pound
Part B:
Woofy Waffles has the best buy. The unit rate is the least of three.
What is known by the term rate?The term "rate" generally refers to the measure of change in one quantity with respect to another quantity. It describes how one quantity changes in relation to another quantity, often expressed as a ratio or a fraction.
What is the buying price?The buying price, also known as the purchase price or the cost price, is the amount of money that is required to purchase an item, product, or service. It is the price at which a buyer acquires a product or service from a seller or a vendor.
Canine cakes= 30pounds
cost =$54
Unit rate= $54/30 = $1.8 per pound
Bark Bits= 40 pounds
cost =$70
Unit rate= $70/40= $1.75 per pound
Woofy Waffles = 28pounds
cost =$42
Unit rate=$42/28= $1.5 per pound
The best buy is 28 pounds of Woofy Waffles for $42. The rate is least of the three.
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Showing results for a rectangular glass dish has a measurements of 2.5 inches high, 6.75 inches wide and 8.5 inches long. the density of the glass in the dish is 2.23 grams per cubic centimeter and the mass of the dish is about 0.9 kilograms, what is the thickness of the glass?
How likely is it that
at least > or them are vowe tiles?
) Which simulation could be used to fairly represent the situation?
There is a probability of 0.117 for at least 2 of the tiles to be vowel tiles.
Given that,
Probability that the tiles getting is a vowel tile is 30%.
P(V) = 30% = 0.3
That is there will be only 3 tiles out of 10 tiles which are vowels.
Out of 8, there will be 8 × 0.3 = 2.4 tiles which are vowels.
There would be either 2 or 3 vowels.
Probability that at least 2 of them is vowel tiles is,
Probability = (0.3)² + (0.3)³
= 0.117
Here,
The simulation which can be used to fairly represent the situation is,
Use a computer to randomly generate 8 numbers from 1 to 10. Each time 1, 2 or 3 appears, it represents a vowel tile.
Hence the required probability is 0.117.
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If you invest $3900 at a 7.84 simple annual interest rate, approximately how long will it take for you to have a total of $10,000
It would take approximately 19.94 years to accumulate a total of $10,000 from an initial investment of $3,900 at a simple annual interest rate of 7.84%.
To determine how long it will take to accumulate $10,000 from an initial investment of $3,900 at a simple annual interest rate of 7.84%, we can use the formula for simple interest:
I = Prt
where I is the interest earned, P is the principal or initial investment, r is the annual interest rate as a decimal, and t is the time in years.
To find the time required to reach a final amount of $10,000, we can rearrange the formula:
t = (I/P) / r
First, we need to calculate the interest earned on the initial investment:
I = Prt
I = (3900)(0.0784)t
I = 305.76t
To reach $10,000, we need to earn an additional $10,000 - $3,900 = $6,100 in interest. So we can set up the equation:
6100 = 305.76t
Solving for t, we get:
t = 6100 / 305.76
t ≈ 19.94 years
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Given this equation what is the value of x at the indicated point
Answer:
[tex]x = -\sqrt{5}[/tex]
Step-by-step explanation:
[tex]4 = x^2-1\\5 = x^2\\x = \frac{+}{-} \sqrt{5}[/tex]
We would then chose negative square root 5 since it is in quadrant two
Surface Area of a Cylinder
3 cm
3 cm
7 cm
1. What is the surface Area of a Cylinder in terms of π
A. 70π cm ²
B. 50π cm²
C. 40π cm²
D. 60π cm²
2. What is the surface area of the cylinder, in terms of π, if the height of the cylinder is increased by 1 cm?
A. 72π cm²
B. 62π cm²
C. 66π cm²
D. 68π cm²
Answer:
1) D
2) C
Step-by-step explanation:
1. The formula for the surface area of a cylinder is 2πr² + 2πrh, where r is the radius of the base and h is the height of the cylinder.
Given that the radius of the cylinder is 3 cm and the height is 7 cm, we can substitute these values into the formula to get:
SA = 2π(3)² + 2π(3)(7) = 2π(9) + 2π(21) = 18π + 42π = 60π cm²
Therefore, the answer is (D) 60π cm².
2. If the height of the cylinder is increased by 1 cm, the new height would be 8 cm.
We can use the same formula to find the new surface area:
SA = 2π(3)² + 2π(3)(8) = 2π(9) + 2π(24) = 18π + 48π = 66π cm²
Therefore, the answer is (C) 66π cm².
Find the inverse of the function below and sketch by hand a graph of both the function and its inverse on the same coordinate plane.
Share all steps as described in the lesson to earn full credit. Images of your hand written work can be uploaded.
f(x)=x^2+2 with the domain x \geq0
The inverse function is:
f⁻¹(y) = √(y - 2), where y ≥ 2.
What is an inverse function?An inverse function is a function that "undoes" the action of another function. In other words, if we start with a value, apply a function to it, and then apply the inverse function to the result, we should get back to the original value. For example, if we have a function f(x) that doubles a number, the inverse function would be one that halves a number. The notation for an inverse function is f⁻¹(x), and it is defined as follows:
If f is a function with domain A and range B, then its inverse function f⁻¹ is a function with domain B and range A, where f⁻¹(y) = x if and only if f(x) = y.
According to the given informationTo find the inverse of the function f(x) = x² + 2, we need to solve for x in terms of y.
Step 1: Replace f(x) with y.
y = x² + 2
Step 2: Solve for x in terms of y.
y - 2 = x²
±√(y - 2) = x
Note that we use ± because when we take the square root of a number, we get both a positive and a negative solution. However, since the domain of the function is x ≥ 0, we only consider the positive solution.
So the inverse function is:
f⁻¹(y) = √(y - 2), where y ≥ 2.
To sketch the graphs of f(x) and f¹(x) on the same coordinate plane:
Step 1: Plot a few points on the graph of f(x).
We can choose some x-values, plug them into f(x) to find the corresponding y-values, and then plot the points (x, y) on the coordinate plane. For example:
f(0) = 2, so (0, 2) is a point on the graph.
f(1) = 3, so (1, 3) is a point on the graph.
f(2) = 6, so (2, 6) is a point on the graph.
We can also notice that the graph is a parabola that opens upward and has its vertex at (0, 2).
Step 2: Reflect the points across the line y = x to get the graph of the inverse function.
To do this, we swap the x and y coordinates of each point on the graph of f(x) to get the corresponding point on the graph of f⁻¹(x). For example:
(0, 2) becomes (2, 0)
(1, 3) becomes (3, 1)
(2, 6) becomes (6, 2)
We can also notice that the graph of f⁻¹(x) is a curve that starts at (2, 0) and moves upward as x increases.
Step 3: Plot the graphs of both functions on the same coordinate plane.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer: Adam's base pay
Step-by-step explanation:
The equation, y = 0.28x + 38000, is the equation Adam is using to find his annual salary which is said to include base pay and commission pay.
His total commission pay is going to be dependent on his number of sales, which we're told is x.
So, his commission pay is 0.28x.
Therefore, his base pay has to be 38,000; his annual salary if he makes no sales.
If f(x)=2x^2+3 and g(x)=x^2-7, find (f-g)(x).
Answer:
To find (f-g)(x), we need to subtract g(x) from f(x):
(f-g)(x) = f(x) - g(x)
Given f(x) = 2x^2 + 3 and g(x) = x^2 - 7, we can substitute these expressions into the formula above:
(f-g)(x) = f(x) - g(x)
= (2x^2 + 3) - (x^2 - 7)
Now we simplify by combining like terms:
(f-g)(x) = 2x^2 + 3 - x^2 + 7
= x^2 + 10
Therefore, (f-g)(x) = x^2 + 10.
Answer: To find (f-g) (x)
(f-g)(x)= f(x) -g(x)
Given f(x) = 2x^2 + 3 and g(x) = x^2 - 7, we can substitute these expressions into the formula above:
(f-g)(x) = f(x) -g(x)
=(2x^2+3) - (x^2-7)
Now we can simplify the equation:
(f-g)(x)= 2x^2+3 - x^2+7
= x^2 + 10
Hence, (f-g)(x) = x^2+10
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A ladder leans against the side of a house. The angle of elevation of the ladder is 61 degrees , and the top of the ladder is 5 m above the ground. Find the distance from the bottom of the ladder to the side of the house. Round your answer to the nearest tenth.
Answer:
50.8
Step-by-step explanation:
answer pls!! quick asp
Answer:
ZR = 145°
Step-by-step explanation:
the secant- secant angle ZAR is half the difference of the measures of the intercepted arcs , that is
∠ ZAR = [tex]\frac{1}{2}[/tex] ( ZR - KV )
30 = [tex]\frac{1}{2}[/tex] (5x + 10 - (3x + 4) ) ← multiply both sides by 2 to clear the fraction
60 = 5x + 10 - 3x - 4
60 = 2x + 6 ( subtract 6 from both sides )
54 = 2x ( divide both sides by 2 )
27 = x
Then
ZR = 5x + 10 = 5(27) + 10 = 135 + 10 = 145°
A dodecahedral die (one with 12 sides numbered from 1 to 12) is tossed once.
A dodecahedral die. Only the front half, which is composed of 6 sides, is visible. In the center, a pentagonal side labeled 12 connects along its 5 edges to 5 other pentagonal sides, labeled 3, 8, 7, 9, and 11, respectively. Find the following probability. (Enter your probability as a fraction.)
The number on the upward face is not 1.
Probability of the number on the upward face is not 1
P(not 1) = 11/12
Find the following probability of the number on the upward face is not 1?There are 12 possible outcomes when a dodecahedral die is tossed, each with probability 1/12. If the number on the upward face is not 1, then there are 11 favorable outcomes out of 12 possible outcomes. Therefore, the probability that the number on the upward face is not 1 is:
P(not 1) = 11/12
Since this probability is already in simplified form, there is no need to further reduce it. Thus, the answer is:
P(not 1) = 11/12
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Múltiplos de 17 hasta el 1000
Answer:
Translation? what does that mean? sorry can't understand in this language
Solve for the length of the missing side in the triangle. Show your work and explain how you got your answer.
15
√559
n
2. The point (-1,5) is the solution
to a set of linear equations. One
of the following CANNOT be the
other equation?
A. y = -2x
B. y = -5x
C. y = -x +4
1
Dy=-x+²/
2
9
2
Therefore, the equation that cannot be the other equation is A. y = -2x.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. It usually consists of two sides separated by an equal sign (=). The expressions on both sides of the equal sign can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
Here,
To check which equation cannot be the other equation, we can substitute the coordinates of (-1,5) into each of the equations and see if they hold true.
A. y = -2x
When x = -1, then y = -2(-1) = 2, so (-1,5) does not satisfy this equation. Therefore, this cannot be the other equation.
B. y = -5x
When x = -1, then y = -5(-1) = 5, so (-1,5) does satisfy this equation.
C. y = -x + 4
When x = -1, then y = -(-1) + 4 = 5, so (-1,5) does satisfy this equation.
D. y = -x²/2 + 9/2
When x = -1, then y = -(-1)²/2 + 9/2 = 5, so (-1,5) does satisfy this equation.
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Goran used 2 1/2 gallons of gas on Sunday and 1/4 gallons of gas on Monday. How many gallons did he use on the two days combined? Write your answer as a mixed number in simplest form.
Okay, here are the steps to solve this problem:
* Goran used 2 1/2 gallons on Sunday
* Goran used 1/4 gallons on Monday
* So on Sunday he used 2 1/2 gallons and on Monday he used 1/4 gallons
* To find the total gallons used on both days:
** 2 1/2 gallons (used on Sunday)
+ 1/4 gallons (used on Monday)
= 2 3/4 gallons (total used on both days)
So in simplest form as a mixed number, the total gallons Goran used on both days combined is:
2 3/4
[tex]\sf 2\dfrac{3}{4}.[/tex]
Step-by-step explanation:To find this answer, all we need to do is add up both of the fractions, that will give us the total amount of gas used on both days. Let's calculate:
1. Convert the first fraction into an improper fraction.[tex]\sf 2\dfrac{1}{2} =\\ \\\dfrac{2}{2}+\dfrac{2}{2}+\dfrac{1}{2}=\dfrac{5}{2}[/tex]
2. Write the sum of the two fractions that express the daily gas consumption.[tex]\sf \dfrac{5}{2}+ \dfrac{1}{4}[/tex]
3. Using the formula from the attached image, rewrtite the fraction addition.[tex]\sf \dfrac{5}{2}+ \dfrac{1}{4}= \dfrac{(5*4)+(2*1)}{2*4}= \dfrac{(20)+(2)}{8}=\dfrac{22}{8}=\dfrac{11}{4}[/tex]
4. Convert the resulting improper fraction into a mixed fraction.[tex]\sf \dfrac{11}{4}=2.75[/tex]
Take the entire part of the decimal number (2) and write it as the whole number on the mixed number. Also, since the fraction has a denominator of 4, a unit of this fraction would be 4/4, then, the 2 units that we're going to express as a whole number would be 8/4. So, subtract 8/4 from 11/4 and express in the following fashion:
[tex]\sf 2(\dfrac{11}{4}-\dfrac{8}{4} )\\ \\\\ \sf 2(\dfrac{3}{4}) \\ \\ \\\ 2\dfrac{3}{4}[/tex]
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A business has 40,000 to spend on advertising in an upcoming sale. The money is to be divided between television (x), radio (y) and newspapers (z). The business manager has decided to spend three times as much money on television as on radio. The manager has also decided to spend 8000 less on radio advertising than on newspapers. Find out, using matrix inversion method, the total amount divided between television, radio and newspapers.
Okay, let's break this down step-by-step:
* The business has $40,000 total to spend on advertising
* Some will go to TV (x), some to radio (y), and some to newspapers (z)
* 3 times as much will go to TV as radio, so x = 3y
* They will spend $8,000 less on radio than newspapers, so y = z - 8,000
* We have:
x = 3y (1)
y = z - 8,000 (2)
x + y + z = 40,000 (3)
To solve this using matrix inversion:
1) Turn the equations into a matrix:
3 1 0 y
1 -1 1 z
1 1 1 x
2 0 40,000
2) Invert the matrix:
0.3333 0.3333 0.3333
-0.25 0.75 0
0.125 0.125 0.750
3) Plug in the values from (2) and (3):
y = 0.3333(z - 8,000)
x = 0.125z + 0.125(40,000 - z)
4) Solve for z, the amount for newspapers. We get:
z = 40,000 * (0.75) = 30,000
5) Plug z = 30,000 back into the other equations:
x = 0.125 * 30,000 + 0.125 * 10,000 = 12,000
y = 0.3333 * (30,000 - 8,000) = 8,000
z = 30,000
So in total:
TV (x) = $12,000
Radio (y) = $8,000
Newspapers (z) = $30,000
Does this make sense? Let me know if you have any other questions!
which expression is equivalent to
Answer:
B. w - 1
Step-by-step explanation:
Using PEMDAS, we start see there are no expressions inside parenthesis or exponents we move to multiplication/division. The expression 1/4(4) can be rewritten as 1/4 * 4 or as 4/4, both of which equal 1.
So w - 1 is an equivalent expression.
What is the soultion to the system of equations? {-3x-y+z=8 -3x-y+3z=0x -3z= 3
The solution to the system of equations is x = -9; y = 15 and z = -4
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
Given the system of equations:
-3x - y + z = 8 (1)
-3x - y + 3z = 0 (2)
and:
x - 3z = 3 (3)
Solving the three equations simultaneously gives:
x = -9; y = 15 and z = -4
The solution is x = -9; y = 15 and z = -4
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David runs a printing and typing service business. The rate for services is K32 per hour plus a K31.50
one-time charge. The total cost to a customer depends on the number of hours it takes to complete the
job. Find the equation that expresses the total cost in terms of the number of hours required to complete
the job
The equation expressing the total cost in terms of the number of hours required to accomplish the task is C = 32h + 31.50
How to find the equation that expresses the total cost in terms of the number of hours required to complete the jobLet C be the entire cost of the job, and h represent the number of hours needed to accomplish the job.
The hourly charge for services is K32, hence the total cost for services is 32h.
There is a one-time fee of K31.50, making the total cost:
C = 32h + 31.50
Hence, the equation expressing the total cost in terms of the number of hours required to accomplish the task is C = 32h + 31.50
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O is the center of the regular decagon below. Find its area. Round to the nearest tenth if necessary. 2
The area of Regular Decagon is 325 square units.
How to find the area of a regular decagon?The formula for the area of a regular polygon is :
Area (A) = [number of sides (n) × length of side (l) × apothem (a)] /2
Apothem Formula is given by:
For the decagon, n = 10 (10 sides) and a = 10
Now, we calculate the length of the decagon:
a = l / 2tan(180/n)°
10 = l / 2tan(180/10)°
10 = l / 2 tan18°
l = 10 × 2 × tan18°
l = 6.50 units
We have to find the area of decagon:
A = [number of sides (n) × length of side (l) × apothem (a)] /2
A = (10 × 6.50 × 10)/2
A = 325 square units
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Foe complete question, to see the attachment.
Math: please answer this, very important for me, I’ll give brainliest!
Q3. A Ferris wheel reaches a maximum height of 60 m above the ground and takes twelve minutes to complete one revolution. Riders have to climb a 4 m staircase to board the ride at its lowest point.
(a) [4 marks] Write a sine function for the height of Emma, who is at the very top of the
ride when t = 0.
(b) [2 marks] Write a cosine function for Eva, who is just boarding the ride.
(c) [2 marks] Write a sine function for Matthew, who is on his way up, and is at the same height as the central axle of the wheel.
A Ferris wheel reaches a maximum height:
(a) sine function for the height of Emma y = 60 sin (2π/720 t)
(b) cosine function for Eva y = 4 + 60 cos (2π/720 t - π/2)
(c) sine function for Matthew y = 32 + 30 sin (2π/720 t - π/2)
How to create sine and cosine function?(a) Let's start by determining the amplitude and period of the sine function for Emma's height on the Ferris wheel.
The maximum height of the ride is 60 m, which will be the amplitude of the function.
The period is the time it takes for one complete revolution, which is 12 minutes or 720 seconds.
The general form of the sine function is y = A sin (ωt + φ),
where A = amplitude, ω = angular frequency (2π divided by the period), t = time, and φ = phase shift.
So, the sine function for Emma's height can be written as:
y = 60 sin (2π/720 t)
(b) The cosine function for Eva's height will be similar to the sine function for Emma's height, but with a phase shift of 90 degrees, since Eva is starting at the lowest point of the ride (when the sine function is equal to 0).
The general form of the cosine function is y = A cos (ωt + φ), so the cosine function for Eva's height can be written as:
y = 4 + 60 cos (2π/720 t - π/2)
4 meters to account for the height of the staircase.
(c) Matthew is at the same height as the central axle of the wheel, which means his height will vary sinusoidally with the same period as Emma's height, but with a different amplitude and phase shift.
Since his maximum height is halfway between the minimum and maximum heights of the Ferris wheel (i.e. at a height of 32 meters), his amplitude will be half of Emma's amplitude (i.e. 30 meters).
The phase shift will depend on where he is in relation to the starting point of Emma's height function, but assume that he is starting at the lowest point of the ride (like Eva), so his phase shift will also be 90 degrees.
Therefore, the sine function for Matthew's height can be written as:
y = 32 + 30 sin (2π/720 t - π/2)
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The time spent waiting in the line is approximately normally distributed. The mean waiting time is 5 minutes and the standard deviation of the waiting time is 3 minutes. Find the probability that a person will wait for more than 3 minutes.
Answer: 71.4%
Step-by-step explanation:
Mean = ~5 mins
Deviation = 3 mins
This means that you have a range of 2 mins - 8 mins.
2, 3 || 4, 5, 6, 7, 8
The double lines represent 3 minutes or less, and more than 3 minutes.
There are 7 number, 5 are greater than 3, that is 71.4%.
How tall is the building?
The perimeter of the rectangle below is 132 units. Find the length of side RS.
Write your answer without variables.
S
P
5x
R
4x + 3
Q
Check the picture below.
[tex](5x)+(5x)+(4x+3)(4x+3)=132\implies 18x+6=132\implies 18x=126 \\\\\\ x=\cfrac{126}{18}\implies x=7\hspace{9em}\underset{RS }{\stackrel{ 5(7) }{\text{\LARGE 35}}}[/tex]
please help me i suck at math hurry
Part 1:
To see why, notice that when x increases by 1, y increases by 2. This corresponds to the coefficient of x in the equation being 2. Also, when x is 0, y is 2, which corresponds to the y-intercept of 2 in the equation. Therefore, the equation that fits the given table is y = 2x + 2.
Part 2:
(a) 2.35 x 10⁻³ can be written in standard form as 0.00235
(b) 2.35 x 10³ can be written in standard form as 2350
Part 3:
A linear equation is an equation where the highest power of the variable is 1. In other words, the graph of a linear equation is always a straight line.
Part 4:
(b) (2,4):
For y=x+3, when x=2, y=5.
For -2x+y=1, when x=2, y=5.
Since (2,4) satisfies both equations, it is a solution.
(c) (2,5):
For y=x+3, when x=2, y=5.
For -2x+y=1, when x=2, y=5.
Since (2,5) satisfies both equations, it is a solution.
Part 5:
Using the Pythagorean Theorem:
a² + b² = c²
8² + b² = 10²
64 + b² = 100
b² = 100 - 64
b² = 36
b = 6
Use the formula for the area of a triangle:
A = (1/2)bh
A = (1/2)(8)(6)
A = 24 cm²
Therefore, the area of triangle ABC is 24 cm². Answer: (b) 24 cm²
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