Answer:
Sure, here's the solution to the word problem:
Jack has $10 in his lunch account and plans to spend $2 a week on snacks. To find out how long it will take his lunch account to reach zero, we can divide the total amount of money in his account by the amount he spends each week.
```
$10 / $2 = 5 weeks
```
Therefore, it will take Jack 5 weeks to spend all of the money in his lunch account.
Here's another way to solve the problem:
We can also set up an equation to represent the situation. Let x be the number of weeks it takes Jack's lunch account to reach zero. We know that Jack starts with $10 and spends $2 each week, so we can write the equation:
```
$10 - $2x = 0
```
Solving for x, we get:
```
x = 5
```
Therefore, it will take Jack 5 weeks to spend all of the money in his lunch account.
Answer:
in 5 weeks he will have 0$ in his account
Step-by-step explanation:
Help with this please
Answer:
sin(θ) = (2/9)√14; csc(θ) = (9√14)/28cos(θ) = 5/9; sec(θ) = 9/5tan(θ) = (2/5)√14; cot(θ) = (5√14)/28Step-by-step explanation:
Given cos(θ) = 5/9, you want the six trig functions of θ.
IdentitiesThe relevant identities are ...
sin(θ) = ±√(1 -cos(θ)²)tan(θ) = sin(θ)/cos(θ)csc(θ) = 1/sin(θ)sec(θ) = 1/cos(θ)cot(θ) = 1/tan(θ)SineThe sine of θ is ...
sin(θ) = √(1 -(5/9)²) = √(81 -25)/9 = (√56)/9
sin(θ) = (2/9)√14
Then the cosecant is ...
csc(θ) = 1/sin(θ) = (9/2)/√14
csc(θ) = (9√14)/28
TangentThe tangent of θ is ...
tan(θ) = sin(θ)/cos(θ) = ((2/9)√14)/(5/9)
tan(θ) = (2/5)√14
Then the cotangent is ...
cot(θ) = 1/tan(θ) = (5/2)/√14
cot(θ) = (5√14)/28
SecantThe secant of θ is ...
sec(θ) = 1/cos(θ) = 1/(5/9)
sec(θ) = 9/5
The cosine is given in the problem statement.
What is the volume of this shape? help me please i really need help
The volume of the given shape is 125 unit³ if the length is 5 unit, breadth is 5 unit, and height is 5 unit.
A cube is a three-dimensional geometric shape that has six identical square faces, where each face meets at a right angle with the adjacent faces. It is a regular polyhedron, meaning that all of its faces are congruent (identical) and its edges are of equal length.
Volume of cube = length × breadth × height
length = 5 unit
breadth = 5 unit
height = 5 unit
Volume = 5 × 5 × 5
= 125 unit³
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what is the product of -5 and -10 sign and result
Answer:
50, positive
Step-by-step explanation:
(-5) * (-10) = 50
When a negative multiplies by another negative, the answer is positive
So, the answer is 50 and the sign is positive
pls some help with this question!
5) Write the rule for the reflection shown below.
Answer: 2,2
Step-by-step explanation: if you have the 2,-2 then that would be your answer because the reflection is the same as the 2,-2 but on a different thing
Consider triangle ABC with vertices A(0,0), B (0,6), and C (4,0). The image of triangle ABC after a dilation has vertices A'(0,0), B' (0,21), and C' (14,0).
What is the scale factor of the dilation?
k = ?
Answer:
k=0.3
Step-by-step explanation:
Let's call the length of each of the other two sides x. Since the triangle is isosceles, it has two sides of equal length. Therefore, the perimeter of the triangle can be expressed as 6 + x + x Simplifying this equation, we get 2x + 6 We know that the perimeter is 22 cm so we can set up an equation and solve for x. 22 = 2x + 6 Subtracting 6 from both sides, we get 16 = 2x Dividing both sides by 2, we get x=8
The function f (x) = 15(0.85)^x
models the height, in feet, of a bouncing ball after x seconds.
What is the initial height of the bouncing ball?
What is the percent rate of change?
What is the height of the bouncing ball after 5 seconds? Express your answers as a decimal rounded to the nearest hundredth.
a. The initial height of the bouncing ball is 15 feet.
b. The percent rate of change is 85%.
c. The height of the bouncing ball after 5 seconds is approximately 6.79 feet (rounded to the nearest hundredth).
What is Function ?In mathematics, a function is a rule that assigns each element in a set (the domain) to a unique element in another set (the range). The domain and range can be any sets, but they are typically sets of real numbers.
The function f(x) = 15 (0.85)ˣ models the height, in feet, of a bouncing ball after x seconds.
a. The initial height of the bouncing ball is given by f(0). Plugging in x = 0, we get:
f(0) = 15*1
f(0) = 15(1)
f(0) = 15
Therefore, the initial height of the bouncing ball is 15 feet.
b. The percent rate of change is given by the coefficient of the base, which is 0.85 in this case. To convert this decimal to a percentage, we can multiply by 100:
0.85 × 100 = 85
Therefore, the percent rate of change is 85%.
c. The height of the bouncing ball after 5 seconds is given by f(5). Plugging in x = 5, we get:
f(5) = 15
f(5) ≈ 6.79
Therefore, the height of the bouncing ball after 5 seconds is approximately 6.79 feet (rounded to the nearest hundredth).
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A coin (H: heads; T: tails) is flipped and a number cube (1, 2, 3, 4, 5, 6) is rolled. What is the sample space for this experiment?
The sample space for this experiment contains a total of 12 possible outcomes.
How to find the probability and determine the sample space?The sample space for this experiment is the set of all possible outcomes. In this case, we have two independent events: flipping a coin and rolling a number cube.
The possible outcomes for flipping a coin are H (heads) and T (tails).
The possible outcomes for rolling a number cube are 1, 2, 3, 4, 5, and 6.
To determine the sample space for the experiment, we need to consider all possible combinations of these outcomes. Therefore, the sample space consists of all possible pairs of outcomes:
Sample space = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
So the sample space for this experiment contains a total of 12 possible outcomes.
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G
Given: ABCD is a trapezoid.
BA CD
CA
Prove: BD
Proving Trapezoid Theorems
C
Pretests
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Angles Segments Triangles Statements Reasons
ZBAD
Statements
ZCDA
Reasons
BD = CA is proved using the Pythagorean theorem.
What is a trapezium?It is a quadrilateral that has one pair of parallel sides and a height.
The area is calculated as 1/2 x the sum of the parallel sides x height.
Examples:
Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.
Area = 1/2 x (3 + 4) x 5
Area = 1/2 x 7 x 5
Area = 35/2 = 17.5 cm^2
We have,
From the trapezium ABCD,
BA = CD ______(A)
Now,
We can have two triangles:
ΔABD and ΔACD
Using the Pythagorean theorem.
BD² = AB² + AD² _____(1)
And,
CA² = CD² + AD² ______(2)
From (1), (2), and (A).
BD² = BA² + AD²
CA² = BA² + AD²
This means,
BD² = CA²
BD = CA
Proved
Thus,
BD = CA can be Proven as above.
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Answer:
Step-by-step explanation:
How much interest has accrued after one month at a rate of 15. 5%? Use the formula I=Prt. *
A $19. 24
B $18. 71
C $18. 81
The interest accrued after one month at a rate of 15.5% on a principal amount of $1,000 is $12.92.
To use the formula I=Prt to calculate the interest accrued after one month at a rate of 15.5%, we need to know the principal amount (P) and the time period (t) in years.
Assuming that the principal amount is $1,000, and the time period is one month, which is equivalent to 1/12 of a year, we can calculate the interest as follows:
[tex]I = Prt[/tex]
[tex]I[/tex] [tex]= 1000 x 0.155 x (1/12)[/tex]
[tex]I = $12.92[/tex]
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From the following facts, complete a depreciation schedule by using
the straight-line method:
Cost of Honda Account Hybrid - $40000
Residual Value - $10000
Estimated Life - 6 years
Using the straight-line method, we can find the depreciation expense per year by dividing the depreciable value (cost - residual value) by the estimated life:
Depreciable Value = Cost - Residual Value
Depreciable Value = $40000 - $10000
Depreciable Value = $30000
Annual Depreciation Expense = Depreciable Value / Estimated Life
Annual Depreciation Expense = $30000 / 6
Annual Depreciation Expense = $5000
To create a depreciation schedule, we can subtract the annual depreciation expense from the cost each year until we reach the residual value:
| Year | Cost | Depreciation | Accumulated Depreciation | Book Value |
|------|---------------|----------------- |----------------------------------------|------------|
| 1 | $40000 | $5000 | $5000 | $35000 |
| 2 | $35000 | $5000 | $10000 | $30000 |
| 3 | $30000 | $5000 | $15000 | $25000 |
| 4 | $25000 | $5000 | $20000 | $20000 |
| 5 | $20000 | $5000 | $25000 | $15000 |
| 6 | $15000 | $5000 | $30000 | $10000 |
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CDE is a tangent to the circle below.
Calculate the size of angle θ.
Fully Justify your answer.
Applying the inscribed angle theorem, the measure of the size of angle ∅ = 85 degrees.
How to Apply the Inscribed Angle Theorem?If an inscribed angle in a circle is subtended by an arc, the inscribed angle theorem states that the measure of the intercepted arc would be twice the measure of the inscribed angle.
Therefore, we have:
measure of arc DF = 2(31) = 62 degrees [inscribed angle theorem]
measure of arc BD = 2(54) = 108 degrees.[inscribed angle theorem]
∅ = 1/2(measure of arc BDF) [inscribed angle theorem]
∅ = 1/2(m(DF) + m(BD))
Substitute:
∅ = 1/2(62 + 108)
∅ = 1/2(170)
∅ = 85 degrees.
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A store has 25 VCRs in stock, but 2 of these are defective. What is the probability
that the second person to buy a VCR gets a defective one and the first
customer's VCR was not defective? Round your answer to the nearest
thousandth. *
. 083
. 0736
. 077
. 08
A store has 25 VCRs in stock, but 2 of these are defective he answer is the probability that the second person to buy a VCR gets a defective one and the first customer's VCR was not defective is .077.
The probability that the first customer's VCR is not defective is 23/25, as there are 23 working VCRs out of the total 25.
Since one VCR has already been sold, there are 24 VCRs left and 1 defective VCR. Thus, the probability that the second customer gets a defective VCR is 1/24.
To find the probability that both events occur, we multiply the individual probabilities:
P = (23/25) x (1/24)
P = 0.077 or 0.0778 when rounded to the nearest thousandth.
Therefore, A store has 25 VCRs in stock, but 2 of these are defective he answer is the probability that the second person to buy a VCR gets a defective one and the first customer's VCR was not defective is .077.
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Which of these variables is your dependent variable?
How many jumps I can do
Which one is the independent variable?
How long I am jumping (2 minutes)
Write a sentence that describes the relationship between the dependent variable and the independent variable. (Hint: Ratio language can help. )
In this scenario, the dependent variable is "how many jumps I can do," while the independent variable is "how long I am jumping (2 minutes)."
The relationship between these variables can be described as follows: The number of jumps completed depends on the duration of time spent jumping, with a specific focus on a 2-minute interval.
When we say the dependent variable is "how many jumps I can do," it means that the number of jumps completed is determined by or depends on the independent variable, which is the duration of time spent jumping.
This suggests that as the duration of time increases or decreases, it will likely have an impact on the number of jumps performed.
In this particular case, you have specified a 2-minute interval as the focus. It suggests that you are examining the relationship between the number of jumps completed and the specific duration of 2 minutes.
This implies that you are interested in understanding how the number of jumps varies within this fixed time frame.
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3 For y=f(x) = 9x, x= 3, and Ax = 0.03 find a) y for the given x and Ax values, b) dy = f'(x)dx, to) dy for the given x and Ax values.
a) To find y for the given x and Δx values, first calculate x + Δx:
x + Δx = 3 + 0.03 = 3.03
Now, use the function y = f(x) = 9x to find the y values:
y = 9(3) = 27 (for x = 3)
y = 9(3.03) = 27.27 (for x = 3.03)
b) To find dy, we first need to find the derivative of the function (f'(x)). The function is y = f(x) = 9x, and its derivative (using differentiation) is:
f'(x) = 9
c) To find dy for the given x and Δx values, we can now use the formula dy = f'(x)dx:
dy = f'(x)dx = 9(0.03) = 0.27
So, for the given x and Δx values, a) y is 27 and 27.27, b) dy is equal to 9, and c) dy for the given x and Δx values is 0.27.
7. kayla uses her credit card to purchase a new television for $487.89. she can pay off up to $175 per month. the card has an annual rate of 23.5% compounded monthly. how
much will she pay in interest? (2 points)
o $22.78
$156.76
o $8.95
$18.87
save & exit
submit all answers
o
7:42
hp
o
الا : 2
96
5
4
8
backspace
If Kayla can pay off up to $175 monthly for the purchase of a new television for $487.89, the interest she will pay at 23.5% compounded monthly is D. $18.87.
How the compound interest is computed?The compound interest payable on the credit card for the purchase of a new television can be computed using an online finance calculator as follows:
N (# of periods) = 3 months
I/Y (Interest per year) = 23.5%
PV (Present Value) = $487.89
PMT (Periodic Payment) = $-175
Results:
FV = $18.23
Sum of all periodic payments = $525.00
Total Interest = $18.87
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What 2 number multiple to make -14 and add to make -3?
By using factoring and the zero product property the two numbers that multiply to make -14 and add to make -3 are -7 and 4.
What is zero product property?The zero product property is a fundamental property of algebra that states that if the product of two or more factors is zero, then at least one of the factors must be zero. In other words, if a × b = 0, then either a = 0 or b = 0 or both a and b are zero. This property is often used to solve equations and factor polynomials. For example, if we have the equation (x - 3)(x + 5) = 0, we know that the only way the product can be zero is if one of the factors is zero, so we set each factor equal to zero and solve for x:
(x - 3)(x + 5) = 0
x - 3 = 0 or x + 5 = 0
x = 3 or x = -5
Thus, the solutions to the equation are x = 3 and x = -5.
According to the given informationWe can solve this problem by using factoring and the zero product property.
First, we need to find two numbers that multiply to make -14. The factors of -14 are (-1, 14) and (1, -14), so the two numbers could be -1 and 14, or 1 and -14.
Next, we need to find which pair of numbers adds up to -3. The only pair of numbers that works is -7 and 4 because (-7) + 4 = -3.
Therefore, the two numbers that multiply to make -14 and add to make -3 are -7 and 4.
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11. April shoots an arrow upward at a speed
of 80 feet per second from a platform 25
feet high. The pathway of the arrow can
be represented by the equation h =-
16t2 + 80t + 25, where h is the height
and t is the time in seconds. What is the
maximum height of the arrow? [3]
The maximum height of the arrow is 105 feet. To find the maximum height of the arrow, we need to determine the vertex of the quadratic function h = -16[tex]t^{2}[/tex] + 80t + 25.
The vertex is the highest point on the graph of the function, which represents the maximum height of the arrow.
To find the t-value at the vertex, we use the formula t = -b/2a, where a = -16 and b = 80. Plugging these values into the formula gives us t = -80/(2(-16)) = 2.5 seconds.
To find the maximum height, we plug t = 2.5 into the equation to get h = -16[tex](2.5)^{2}[/tex] + 80(2.5) + 25 = 105 feet. Therefore, the maximum height of the arrow is 105 feet.
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what is 5 less than the square of a number in an algebraic expression
Answer:
let x be the no.
So, 5 less than the square of a number in an algebraic expression is:
x^2 - 5
Write an exponential function to model the following situation.
a population of 140,000 grows 5% per year for 15 years.
how much will the popluation be after 15 years?
write an exponential function in terms of x.
An exponential function in terms of x is [tex]P(x) = 140,000(1.05)^x[/tex]
The population would be 291049.95 after 15 years.
How to determine the population after a number of year?In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:
[tex]P(x) = I(1 + r)^x[/tex]
Where:
P(t ) represent the population.x represent the time or number of years.I represent the initial number of persons.r represent the exponential growth rate.By substituting given parameters, we have the following:
[tex]P(x) = 140,000(1 + 0.05)^x\\\\P(x) = 140,000(1.05)^x[/tex]
After 15 years, we have:
[tex]P(15) = 140,000(1.05)^{15}[/tex]
P(15) = 291049.95 units.
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HELP ASAP!!!!!!!!!!!
Answer:
25%
Step-by-step explanation:
The total number of 7th grade students = 9 + 11 + 11 + 13 = 44
Out of the 44 students 11 play bass
Probability that a seventh grader chosen at random will play the base is:
11/44 = 1/4 = 0.25
As a percentage, this would be 0.25 x 100 = 25%
Mrs. Ramirez worked on her personal trainer to help develop a nutrition plan. The circle graph shows the recommended percentages for her daily intake. If she will be eating 1800 cal, then how many calories should be from proteins?
630 calories of total calory intake of Mrs. Ramirez should be from proteins.
From the circle graph we can see that,
percentage of calories from fruits is = 15%
percentage of calories from grains is = 15%
percentage of calories from vegetables is = 25%
percentage of calories from proteins is = 35%
percentage of calories from Dairy is = 10%
Here it is also given that Mrs. Ramirez need to eat 1800 calories.
So the calories should be from proteins
= 35% of 1800 calories
= (35/100)*1800 calories
= 35*18 calories
= 630 calories.
Hence, 630 calories should be from proteins.
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The question is incomplete. The complete question will be -
1pt A clothing company needs to determine how much fabric to use for a sleeve on a shirt. It uses the following model arm as a way to test the fit. The sleeve needs to cover
the 20 centimeters from the shoulder to the elbow.
Upper Arm
What solid best represents the model for the sleeve? What is the minimum surface area of fabric needed for the sleeve?
The minimum surface area of fabric needed for the sleeve is approximately 628.32 cm².
How much fabric for sleeve?Based on the given model arm, a right circular cylinder would best represent the model for the sleeve.
To calculate the minimum surface area of fabric needed for the sleeve, we need to find the lateral surface area of the right circular cylinder.
The lateral surface area of a right circular cylinder is given by the formula:
Lateral surface area = 2πrh
where r is the radius of the cylinder, h is the height of the cylinder.
In this case, the height of the cylinder needs to be 20 cm (to cover the distance from the shoulder to the elbow), and the radius can vary depending on the desired fit. Let's assume a radius of 5 cm for the purposes of this calculation.
Plugging in the values, we get:
Lateral surface area = 2π(5 cm)(20 cm)
= 628.32 cm²
Therefore, the minimum surface area of fabric needed for the sleeve is approximately 628.32 cm².
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Question 3 of 10
What property does the equation show?
32 19
14
56
1 3
+
=
A. The associative property
B. The commutative property
OC. The distributive property
32 19
14 56
D. The identity property of multiplication
5 8
1 3
+
32
14
19
56
4
7
Answer:
C. The distributive property
Sam needs 2/5 pound of turkey to make one sandwich he is going to make 7 sandwiches how many pounds of turkey does he need
If Sam needs 2/5 pound turkey to make one sandwich, then to make 7 sandwiches, he will need:
(2/5) x 7 = (2 x 7)/5 = 14/5 = 2.8 pounds of turkey
Therefore, Sam needs 2.8 pounds of turkey to make 7 sandwiches.
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Rachel and nicole are training to run a half marathon. rachel begins by running 30 minutes on the
tirst day of training. each day she increases the time she runs by 3 minutes. nicole's training follows the
function f(x) = 5x + 30, where x is the number of days since the training began, and f(x) is the time in
minutes she runs each day. what is the rate of change in minutes per day for the training program that
has the least rate of change?
rachel:
starting minutes:
increase in rate:
equation:
nicole:
starting minutes:
increase in rate:
equation:
The training program with the least rate of change is Rachel's, with an increase of 3 minutes per day.
Rachel:
Starting minutes: 30
Increase in rate: 3 minutes per day
Equation: f(x) = 3x + 30
Nicole:
Starting minutes: 30 (since f(0) = 5(0) + 30 = 30)
Increase in rate: 5 minutes per day
Equation: f(x) = 5x + 30
To find the training program with the least rate of change, we need to find the derivative of each equation and set it equal to zero:
f'(x) = 3 for Rachel's equation
f'(x) = 5 for Nicole's equation
Since 3 is less than 5, Rachel's training program has the least rate of change. Therefore, the rate of change in minutes per day for Rachel's training program that has the least rate of change is 3 minutes per day.
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Jessica's cookie recipe calls for 1 1/2
cups of flour. She only has enough
flour to make 1/3 of a batch. How much
flour does she have?
A 1/3 cup
B 1/2 cup
C 1 cup
D 2 cups
Answer:
B
Step-by-step explanation:
1 1/2 x 1/3
=1/2
So therefore the answer is B (1/2 cup)
Answer:
The answer is B ( 1/2 cup)
1) Amy deposits $2,300 in an account that pays 8.5% interest. How much money will Amy have after 4 years?
2)Andres deposits $10,000 in an account that pays 8% interest. How much money will Andres have after 4 years?
a
$ 13,604.89
b
$ 604.90
c
$ 20,004.98
3) Kara deposits $500 in an account that pays 5% interest. How much money will Kara have after 2 years?
a
$ 1,009.34
b
$ 13.97
c
$ 551.25
1) If Amy deposits $2,300 in an account that pays 8.5% interest, after 4 years, the future value will be $3,187.48.
2) If Andres deposits $10,000 in an account that pays 8% interest, after 4 years, the future value will be A. $13,604.89.
3) If Kara deposits $500 in an account that pays 5% interest, after 2 years, the future value will be C. $551.25.
How the future values are determined:The future values represent the present investment compounded at an interest rate.
The future values can be determined using an online finance calculator as follows:
1) N (# of periods) = 4 years
I/Y (Interest per year) = =8.5%
PV (Present Value) = $2,300
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $3,187.48
Total Interest = $887.48
2) N (# of periods) = 4 years
I/Y (Interest per year) = =8%
PV (Present Value) = $10,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $13,604.89
Total Interest = $3,604.89
3) N (# of periods) = 2 years
I/Y (Interest per year) = 5%
PV (Present Value) = $500
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $551.25
Total Interest = $51.25
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the life of light bulbs is distributed normally. the standard deviation of the lifetime is 20 hours and the mean lifetime of a bulb is 580 hours. find the probability of a bulb lasting for at most 624 hours. round your answer to four decimal places.
The probability of a bulb lasting for at most 624 hours is 0.9861, rounded to four decimal places.
The standard deviation of the lifetime is a measure of how spread out the lifetimes are. In other words, it tells us how much the lifetimes of bulbs vary from the mean. In this case, the standard deviation of the lifetime is 20 hours.
Now, let's get to the question at hand. We want to find the probability of a bulb lasting for at most 624 hours. To do this, we need to use the properties of the normal distribution.
First, we need to calculate the z-score, which tells us how many standard deviations a value is from the mean. We can use the formula z = (x - mu) / sigma, where x is the value we are interested in, mu is the mean, and sigma is the standard deviation. In this case, x = 624, mu = 580, and sigma = 20.
Plugging these values into the formula, we get z = (624 - 580) / 20 = 2.2.
Next, we need to find the probability of a bulb lasting for at most 624 hours, which is the same as finding the area under the normal curve to the left of z = 2.2. We can use a standard normal distribution table or a calculator to find this probability.
Using a calculator, we can use the normal cdf function with the values -9999 (a very large negative number) and 2.2 to find the probability. This gives us a probability of 0.9861.
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circles P and Q are tangent to eachother and to the axis shown. PQ = 26 and AB = 24. Find the coordinates of P and the coordinates of Q.
The coordinates of P and Q are P(5, 5) and Q(7, 7) respectively.
Understanding TangentLet the centres of the circles be:
P (a, r) and
Q (b, s)
where r and s are the radii of the circles.
Since the circles are tangent to the x-axis, we know that r = a and s = b.
Also, since the circles are tangent to each other, we have
a + b = PQ = 26
Let the point of contact of circle P with the x-axis be (p, 0)
Let the point of contact of circle Q with the x-axis be (q, 0).
Then, we know that
p + q = AB = 24
Using Pythagorean theorem, we can write:
(r² - p²) + (r² - (24 - p)²) = (s²- q²) + (s² - (24 - q)²)
Expanding and simplifying, we get:
2r² - 24r + 576 = 2s² - 24s + 576
Substituting r = a and s = b, and using the fact that a + b = 26, we get:
2a² - 24a + 576 = 2b² - 24b + 576
Simplifying further, we get:
a² - 12a + 288 = b² - 12b + 288
(a - b)(a + b - 12) = 0
Since a + b = 26, we have a - b = 0 or a + b - 12 = 0. The first case gives us a = b, which is not possible since the circles are tangent to each other. Therefore, we have a + b = 12.
Using substitution method to solve the simultaneous equations:
a + b = 12
a + b = 26
We get a = 7 and b = 5.
Therefore, the centres of the circles P and Q are (7, 7) and (5, 5) respectively.
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