A savings account is started with an initial deposit of $500. The account earns 1.5% interest compounded
annually.
swer:
(a) Write an equation to represent the amount of money in the account as a function of time in years.
(b) Find the amount of time it takes for the account balance to reach $800. Show your work.

According to the image, we can infer that the shapes which have at least 1 pair of perpendicular sides are the top leftmost trapezium and the bottom-center rectangle.

Perpendicular sides is a term to refer to a shape with a special characteristic. These shapes have two sides connected through an angle or vertex of 90°. So, to select the correct shapes we have to take into account this feature. According to the above, the correct shapes would be:

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[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Lwh}{3} ~~ \begin{cases} L=\stackrel{base's}{length}\\ w=\stackrel{base's}{width}\\ h=height\\[-0.5em] \hrulefill\\ L=6L\\ w=6w \end{cases}\implies V=\cfrac{(6L)(6w)h}{3}\implies \stackrel{ \textit{36 times the volume} }{V=\cfrac{Lwh}{3}(36)}[/tex]

Florian has to pay $2,013.3, then he own on his car for 3 months

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value. For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

According to our question-

6040 is the total amount

he has to repay in 3 months

dividing the total amount/3

6040/3

$2,013.3

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By answering the question the answer is Therefore, landscapers should equation use 35 gallons of an 80% pesticide solution.

In mathematics, an equation is a statement that two expressions are equal. The equation consists of her two sides divided by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The goal of solving an equation is to find the values ​​of the variables to make the equation true. Simple or complex equations, regular or nonlinear, and equations involving one or more factors are all possible. For example, the expression "[tex]x2 + 2x - 3 = 0\\[/tex]" squares the variable x. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.  

Let's say a landscaper needs to use x gallons of an 80% pesticide solution.

The amount of pesticide for an 80% solution is 0.8 x gallons and the amount of pesticide for a 30% solution is 0.3 (35) = 10.5 gallons.

After mixing the two solutions, the total amount of pesticides in the mixture is 0.8 x + 10.5 gallons and the total volume of the mixture is x + 35 gallons.

Since we need a 55% pesticide solution, we can set the following formula:

[tex]0.8x10.5 0.55(x+35)0.8x10.5 0.55x+19.250.25x = 8.75x = 35[/tex]

Therefore, landscapers should use 35 gallons of an 80% pesticide solution.

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Answer:

can you give me the answer to this question sin y minus cos (y + 20), sin theta minus cos theta equals to 0 cos theta equals to sin theta - 10​

Step-by-step explanation:

To solve sin y - cos (y + 20) = 0, we can rearrange it as sin y = cos (y + 20).

Then, we can use the identity sin (90 - x) = cos x to rewrite the right side as cos (y + 20) = sin (70 - y).

Substituting this into the equation, we get sin y = sin (70 - y).

Now, there are two possibilities:

y = 70 - y, which gives y = 35 degrees.

y = 180 - (70 - y), which gives y = 105 degrees.

To solve cos theta = sin theta - 10, we can rearrange it as cos theta - sin theta = -10 and then use the identity cos (x - 90) = sin x to rewrite it as -sin (theta - 90) = -10.

Taking the inverse sine of both

Among the given factors, global competition does not contribute to the quest for quality. The correct answer is Option A.

In today's business environment, quality has become an important factor that can make or break a company's success. A successful firm must focus on the quality of the products and services they offer, as this can help them maintain their competitive advantage and ensure customer loyalty.

Quality is important for a variety of reasons, including customer satisfaction, reduced costs, increased productivity, and increased revenue. When firms focus on quality, they can provide better products and services to their customers, which can lead to increased customer loyalty and repeat business. This can help firms build a strong reputation in the market and maintain a competitive advantage.

Global competition has made it necessary for firms to focus on quality to maintain their competitive advantage. When firms face global competition, they need to ensure that their products and services are of high quality to compete effectively in the global market. High-quality products and services can help firms differentiate themselves from their competitors and gain a competitive advantage. This can help firms increase their market share and revenue.

Several factors contribute to the quest for quality. These include:

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3BE² + 3DF²- (2AC²- AB) is the answer of the following question

The calculation is as follows

Let E and F be the feet of the perpendiculars from B and D, respectively, to AC. We can use the fact that the area of a quadrilateral is equal to half the product of the diagonals multiplied by the sine of the angle between them to find the length of the diagonal BD.

Since ABCS is a quadrilateral, we have:

Area of ABCS = (1/2) * AC * BD * sin(angle between AC and BD)

Substituting the given values, we get:

924 = (1/2) * 33 * BD * sin(angle between AC and BD)

sin(angle between AC and BD) = 924 / (16.5 * BD)

Now, consider triangles ABC and ACD. Using the Pythagorean theorem, we can write:

AB² + BC² = AC² (1)

CD²+ BC² = AC² (2)

Adding equations (1) and (2), we get:

AB² + 2BC²+ CD²= 2AC²

Substituting AC = 33 and rearranging, we get:

BC² = (2AC²- AB² - CD²) / 2

We can also write:

BE²= AB²- AE² (3)

DF² = CD²- CF²(4)

Adding equations (3) and (4), we get:

BE² + DF²= AB²+ CD² - AE²- CF²

Substituting BC²from earlier, we get:

BE²+ DF² = 2AC² - BC²- AE²- CF²

We want to find BE + DF. Squaring both sides of equation (3), we get:

BE²= AB² - AE²

AE²= AB²- BE²

Similarly, squaring both sides of equation (4), we get:

DF²= CD²- CF²

CF²= CD² - DF²

Substituting these expressions into the equation for BE²+ DF², we get:

BE²+ DF² = 2AC² - BC² - (AB² - BE²) - (CD²- DF²)

Simplifying, we get:

BE² + DF²= 2AC² - BC²- AB²- CD² + 2BE² + 2DF²

Collecting like terms, we get:

BE²+ DF²- 2BE² - 2DF²= 2AC²- BC² - AB² - CD²

Simplifying, we get:

BE²- DF² = 2AC²- BC²- AB²- CD²- 2BE² - 2DF²

Substituting the values we know, we get:

BE²- DF²= 2(33)²- BC²- AB² - CD²- 2BE²- 2DF²

Rearranging, we get:

3BE²+ 3DF² - BC²- AB²- CD²= 2(33)² - 924

Substituting BC^2 from earlier, we get:

3BE²+ 3DF² - (2AC²- AB)

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Answer:

(1,3)

Step-by-step explanation:

Given system of equations is :-

We can solve this by using substitution method by substituting the value of y from equation (1) into equation (2) as ,

2x + 1 = x + 2

Subtract x on both sides,

2x - x + 1 = 2

Simplify,

x = 2 - 1

x = 1

Substitute this value of x into equation (2) as ,

y = 1 + 2

y = 1 + 2

y = 3

Hence the required answer is (1,3) .

and we are done!

Let f be a continuous function in c[a, b] such that f(a) = 200. Then for all real numbers c, the scalar multiple cf is also a continuous function in c[a, b]. Specifically, cf(a) = c(200) = 200c.

To demonstrate that c[a, b] is a subspace, the following facts must be proved:
1. If f and g are both continuous functions in c[a, b], then the sum f + g is also a continuous function in c[a, b].
2. If f is a continuous function in c[a, b], then the scalar multiple cf is also a continuous function in c[a, b], where c is a real number.
3. The zero vector of c[a, b] is the constant zero function.

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Answer:

24.4 degrees

Step-by-step explanation:

This is a right triangle so you can use trig to solve. If you take the arctan of 5/11 you get 24.4(rounded to the nearest tenth)

Answer:

285°

Step-by-step explanation:

x + x + 2x + 2x + 40 + 2x + 10 = (5 - 2)180

8x + 50 = 540

8x = 490

x = 61.25

2x + 40 = 2(61.25) + 40 = 285

Answer:

Step-by-step explanation:

Interior angles in a pentagon equal 540°.

Simplify

x°,x°,2x°, (2x+40) and (2x+10) = 8x+50

Calculate x

8x + 50 = 540

8x = 540 - 50 = 490

x = 490/8

x = 61.25°

Calculate largest angle

2x + 40, where x = 61.25°

=162.5°

The data we get from the question is a random experiment can result in one of the outcomes {a,b,c,d} with probabilities from that information, P(A U B U C) = 0.8.
         

The given probabilities of events and outcomes are:

       P({a}) = 0.4,P({b}) = 0.1,P({c}) = 0.3,P({d}) 0.2

 So the given events are:

        A = {a,b},B = {b,c,d},C = {d}

   We have to find P(A U B U C) Using the formula of the probability of the union of two events,

    we get:

          P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)

Now we will find the values of all probabilities:

                  P(A) = P({a}) + P({b})

                         = 0.4 + 0.1

                         = 0.5

                   P(B) = P({b}) + P({c}) + P({d})

                          = 0.1 + 0.3 + 0.2

                           = 0.6

                   P(C) = P({d})

                            = 0.2

                      P(A ∩ B) = P({b})

                                     = 0.1

                      P(A ∩ C) = P({d})

                                     = 0.2

                      P(B ∩ C) = P({d})

                                     = 0.2

               P(A ∩ B ∩ C) = 0

 (No common event) Put all the above values in the formula:

           P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) +

                                     P(A ∩ B ∩ C)

                                 = 0.5 + 0.6 + 0.2 - 0.1 - 0.2 - 0.2 + 0

                                 = 0.8

         Therefore, P(A U B U C) = 0.8 is the required probability.

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22 gallons of the first brand (35% pure antifreeze) and 88 gallons of the second brand (60% pure antifreeze) to make 110 gallons of a mixture that contains 55% pure antifreeze.

Let x be the number of gallons of the first brand (35% pure antifreeze) needed, and y be the number of gallons of the second brand (60% pure antifreeze) needed to make the desired mixture.

We know that the total volume of the mixture is 110 gallons and the desired concentration of antifreeze is 55%.

We can set up two equations based on the amount of antifreeze and the total volume of the mixture:

0.35x + 0.6y = 0.55(110) (amount of antifreeze)

x + y = 110 (total volume)

Simplifying the first equation, we get:

0.35x + 0.6y = 60.5

Now we can use substitution or elimination to solve for x and y. Here's one way to use substitution method

x + y = 110 (equation 1)

x = 110 - y (solve for x)

0.35x + 0.6y = 60.5 (equation 2, substitute x)

0.35(110 - y) + 0.6y = 60.5 (substitute x into equation 2)

38.5 - 0.35y + 0.6y = 60.5 (distribute 0.35)

0.25y = 22 (combine like terms)

y = 88 (divide both sides by 0.25)

So we need 88 gallons of the second brand (60% pure antifreeze). To find the amount of the first brand (35% pure antifreeze), we can substitute y back into equation 1:

x + y = 110

x + 88 = 110

x = 22 gallons

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The exponential distribution is a probability distribution that models the time between events in a Poisson process, where events occur randomly and independently at a constant average rate.

It is commonly used in reliability theory, queuing theory, and other fields to model the failure or waiting times of systems.

(a) The mean time to decay for Cobalt-60 is 5.27 years.

(b) The standard deviation of the decay time is 2.6355 years.

(c) The 99th percentile is 13.6825 years.

(d) The mean time of the experiment is 15.8175 years and the standard deviation is 4.86788 years.

Note: The answers are calculated based on the exponential distribution of radioactive decay with a half-life of 5.27 years for Cobalt-60.

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Answer: 1.1. The donation per learner cannot be determined from the given table.

1.2. TABLE 1: INCOME IN RANDS OF FUNDRAISING

Number of learners that paid Income (R)

1 200

1.3. To calculate the missing value A, we need to add up all the given incomes and subtract it from the total income for 45 learners, which is 45 x A. Then we can solve for A:

Total income = 200 + 150 + 10(2,000) + 20(45) + A + 4,000 + 9,000

Total income = 45A

45A = 25,150

A = 558.89

Therefore, the missing value A is R558.89.

1.4. The dependent variable in the table is the income received from fundraising.

To find the ratio of income received from 10 learners to income received from 45 learners, we need to divide the income received from 10 learners by the income received from 45 learners and simplify the fraction:

Income from 10 learners = R1,100 (since each learner donates R110)

Income from 45 learners = R215

Ratio = Income from 10 learners : Income from 45 learners

= 1,100 : 215

= 20 : 3 (in its simplest form)

The total number of learners enrolled at the school is 1,100. If 80% of the learners paid, then the number of learners who paid is:

80% of 1,100 = 0.8 x 1,100 = 880 learners

The minimum income that the school can raise if 80% of the learners paid is when each of the 880 learners paid the minimum donation, which is R150:

Minimum income = 880 x 150 = R132,000

Since R132,000 is less than R170,000, the SGB chairperson's statement is not valid.

Step-by-step explanation:

16h^(10/2) *remove the root sign

16h^5 *simplify the exponent

Answer: 16h^5

Step-by-step explanation: im correct

Step-by-step explanation:

No,

if the sprinkler covers a distance of 12 m meaning the 12 m is the diameter...then to find the area that it covers we use the formula for the circle since it's circular

A=πr2

A=3.142*36

A=113.112 cm3

Thus, the ratio for the number of blueberries to banana is 4:1.

A ratio in mathematics is a correlation of at least two numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or integer that is dividing is referred to as the consequent.

A ratio compares two numbers by division. Comparing one quantity to the total, for example the dogs that belong to all the animals in the clinic, is known as a part-to-whole analysis. These kinds of ratios occur considerably more frequently than you might imagine.

The given data for preparing fruit smoothie:

Then,

ratio of  blueberries to banana:

blueberries/banana = 4/1

Thus, the ratio for the number of blueberries to banana is 4:1.

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An inverse of a modulo m for a = 55, m = 89 using the Euclidean algorithm is 34.

In order to find an inverse of a modulo for each of the following pairs of relatively prime integers using the Euclidean algorithm can be found by:

Using the Euclidean algorithm to find the greatest common divisor (gcd) of a and m. In this case, we have:

89 = 1 x 55 + 34

The gcd of 55 and 89 is 1.

Using the extended Euclidean algorithm, work backwards up the chain of remainders to express 1 as a linear combination of a and m. In this case, we have: 34 x 55 - 21 x 89

   The coefficient of a in the expression from step 3 is the inverse of a modulo m. In this case, the inverse of 55 modulo 89 is 34.

To verify that the inverse is correct, multiply a and its inverse modulo m. The product should be congruent to 1 modulo m. In this case, we have:

   55 x 34 = 1870

   11 = 1 x 11 + 0

Since the remainder is 0, we know that 55 x 34 is a multiple of 89, so it is congruent to 0 modulo 89. Therefore, we have:

55 x 34 ≡ 0 |89|

Adding 89 to the left-hand side repeatedly until we get a number that is congruent to 1 modulo 89, we find:

55 x 34 ≡ 0 + 89 x 7 ≡ 1 |89|

Therefore, the inverse of 55 modulo 89 is indeed 34.

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Answer:

The simplified expression is sec^2a

Step-by-step explanation:

We can start by using the trigonometric identities:

cot^2 a + 1 = csc^2 a

tan^2 a + 1 = sec^2 a

Using these identities, we can rewrite the expression as:

(cos^2 a - cot^2 a)/(sin^2 a - tan^2 a)

= (cos^2 a - (csc^2 a - 1))/(sin^2 a - (sec^2 a - 1))

= (cos^2 a - csc^2 a + 1)/(sin^2 a - sec^2 a + 1)

Now we can use the identity:

sin^2 a + cos^2 a = 1

to rewrite the expression further:

= (1/sin^2 a - 1/sin^2 a cos^2 a)/(1/cos^2 a - 1/cos^2 a sin^2 a)

= (1 - cos^2 a)/(sin^2 a - sin^2 a cos^2 a)

= sin^2 a / sin^2 a (1 - cos^2 a)

= 1 / (1 - cos^2 a)

= sec^2 a

Therefore, the simplified expression is sec^2 a.

Answer:

ames have 18 litres of water. He poured unequally into 3 tank

I. Poured three quarter of water from tank one into tank 2

II. Poured half of the water that is now in tank 2 into tank 3

III. Poured one third of water that is now in tank 3 into tank 1

Find how much water is in each tanks

Step-by-step explanation:

Let's start with the amount of water in tank 1 as x liters.

I. Poured three quarter of water from tank one into tank 2, so tank 1 now has 1/4 of x liters and tank 2 has 3/4 of x liters.

II. Poured half of the water that is now in tank 2 into tank 3, so tank 2 now has 3/8 of x liters and tank 3 has 3/8 of x liters.

III. Poured one third of water that is now in tank 3 into tank 1, so tank 3 now has 1/3 * 3/8 * x = 1/8 * x liters and tank 1 has 1/4 * x + 1/8 * x = 3/8 * x liters.

We know that James poured 18 liters of water into the three tanks, so the sum of the water in the three tanks must be 18 liters.

3/8 * x + 3/8 * x + 1/8 * x = 18

Simplifying the equation, we get:

7/8 * x = 18

x = 18 * 8 / 7 = 20.57 (rounded to two decimal places)

Therefore, the amount of water in each tank is:

Tank 1: 3/8 * x = 7.71 liters

Tank 2: 3/8 * x = 7.71 liters

Tank 3: 1/8 * x = 2.57 liters

Answer:

To find the equation of the line passing through the points (5,-12) and (0,-2), we first need to find the slope of the line:

slope = (change in y) / (change in x)

slope = (-2 - (-12)) / (0 - 5)

slope = 10 / (-5)

slope = -2

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

y - y1 = m(x - x1)

where m is the slope, and (x1, y1) is one of the given points on the line.

Let's use the point (5,-12):

y - (-12) = -2(x - 5)

y + 12 = -2x + 10

y = -2x - 2

Therefore, the equation of the line passing through the points (5,-12) and (0,-2) is y = -2x - 2.

All of the reasons that the range is an appropriate measure of variability to describe the variation in the hours slept by eighth graders include the following:

A. The data are evenly distributed between 7 hours and 9 hours.

D. There is no outlier in the data.

In Mathematics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.

Mathematically, the range of a data set can be calculated by using the following mathematical equation;

Range = Highest number - Lowest number

By critically observing the double box-and-whisker plots or box plot for the variation in the hours slept by eighth graders, we can logically deduce that there is no outlier in the data because they are evenly distributed and centered about the mean.

In conclusion, the box-and-whisker plot or box plot is symmetrical.

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Answer:

Step-by-step explanation:

Yeah what the other guy said

The approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis is 67.59 square units.

To solve the question, we can use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. Polar curve is a type of curve that is made up of points that represent polar coordinates (r, θ) instead of Cartesian coordinates.

A polar curve can be represented in parametric form, but it is often more convenient to use the polar equation for a curve. According to the question, r = 7 cos(20), [0, Phi/4] is the polar equation and we need to find the approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis.

To solve the problem, follow these steps: Convert the polar equation to a rectangular equation. The polar equation r = 7 cos(20) is converted to a rectangular equation using the following formulas: x = r cos θ, y = r sin θx = 7 cos (20°) cos θ, y = 7 cos (20°) sin θx = 7 cos (θ - 20°) cos 20°, y = 7 cos (θ - 20°) sin 20°

Sketch the curve in the plane. We can sketch the curve of r = 7 cos(20) by plotting the points (r, θ) and then drawing the curve through these points. Use the polar equation to set up the integral for the volume of the solid of revolution.

The volume of the solid of revolution is given by the formula: V = ∫a b πf2(x) dx where f(x) = r, a = 0, and b = Φ/4.We can find the volume of the solid of revolution using the polar equation: r = 7 cos(20) => r2 = 49 cos2(20) => x2 + y2 = 49 cos2(20)Thus, f(x) = √(49 cos2(20) - x2) = 7 cos(20°) sin(θ - 20°)

So, V = ∫a b πf2(x) dx = ∫0 Φ/4 π(7 cos(20°) sin(θ - 20°))2 dθStep 4: Use a graphing utility to evaluate the integral to two decimal places. Using a graphing utility to evaluate the integral, we get V ≈ 67.59.

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The equation has two distinct real roots if 64 - 4c > 0, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.

The discriminant of a quadratic equation of the form [tex]ax^2 + bx + c = 0[/tex] is given by [tex]b^2 - 4ac[/tex]. In the given quadratic equation, a = 1, b = 8, and c = c. Therefore, the discriminant is:

[tex]b^2 - 4ac[/tex]

[tex]= 8^2 - 4(1)(c)[/tex]

[tex]= 64 - 4c[/tex]

Now, we can use the discriminant to determine the nature of the solutions of the quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If the discriminant is zero, the equation has one real root (a double root). If the discriminant is negative, the equation has no real roots (two complex conjugate roots).

In this case, we do not have enough information about the value of c to determine the nature of the roots of the equation. All we know is that the discriminant is 64 - 4c.

Hence, if 64 - 4c > 0, we can state that the equation has two separate real roots, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.

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Answer:

equal

Step-by-step explanation:

The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98

Given that a credit risk study found that an individual with good credit score has an average debt of $15,000 and the debt of an individual with good credit score is normally distributed with standard deviation $3,000.

Then the 95% confidence interval can be calculated as follows:

Upper limit: µ + Zσ

Lower limit: µ - Zσ

Where

The z-score corresponding to a 95% confidence interval can be found using the standard normal distribution table.

The area to the left of the z-score is 0.4750 and the area to the right is also 0.4750.

The z-score corresponding to 0.4750 can be found using the standard normal distribution table as follows:z = 1.96Therefore

Upper limit: µ + Zσ= $15,000 + 1.96($3,000) = $20,880

Lower limit: µ - Zσ= $15,000 - 1.96($3,000) = $9,120.02

The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98.

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Answer:

169 - 144p²

Step-by-step explanation:

(13 - 12p) × (13 + 12p)

each term in the second factor is multiplied by each term in the first factor

13(13 + 12p) - 12p(13 + 12p) ← distribute parenthesis

= 169 + 156p - 156p - 144p² ← collect like terms

= 169 - 144p²