Find the length in each isosceles right triangle.


a. Find the leg if the hypotenuse is 102√



Leg =


b. Find the hypotenuse if the leg is 92√


Hypotenuse =

(33 points)

Answer:

p ≈ 11.3 , q ≈ 4.1

Step-by-step explanation:

using the cosine ratio in the right triangle

cos20° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{p}{12}[/tex] ( multiply both sides by 12 )

12 × cos20° = p , then

p ≈ 11.3 ( to 1 decimal place )

using the sine ratio in the right triangle

sin20° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{q}{12}[/tex] ( multiply both sides by 12 )

12 × sin20° = q , then

q ≈ 4.1 ( to 1 decimal place )

You therefore paid $21.26 to travel to the beach.

One mile is 5,280 feet long. To determine how many steps this should require walking a mile, simply split 5,280 feet by the length of your typical stride. For instance, if your typical stride is 2 feet, walking a mile will need 2,640 steps.

a) We must divide the total amount of miles travelled by the quantity of gas consumed in order to compute mpg (miles per gallon). If 141 miles are covered by 3/8 of a tank, we may calculate the tank's total capacity as follows:

18 gallons = 8/8 tank (full tank)

So, 3/8 tank = (3/8) x 18 = 6.75 gallons

Therefore, the mpg is:

mpg = distance traveled ÷ gas used

mpg = 141 miles ÷ 6.75 gallons

mpg = 20.89 miles per gallon (rounded to two decimal places)

b) The entire amount of gas consumed must be multiplied by the gallon price in order to get the cost of gas. Gas is expensive at:

Cost of gas = gas used x price per gallon

Cost of gas = 6.75 gallons x $3.15/gallon

Cost of gas = $21.26

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Answer:

300

Step-by-step explanation:

because you do it for 1 hundred years you multiply it by 100 and it would be 3x100=300

$7,008 is the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7%.

percentage, a relative value indicating hundredth parts of any quantity.

The formula to calculate the future value of an investment with simple interest is:

FV = P(1 + rt)

where FV is the future value, P is the principal amount, r is the annual interest rate expressed as a decimal, and t is the time period in years.

P = $6,525

r = 0.037

t = 2 years

Plugging these values into the formula, we get:

FV = $6,525(1 + 0.037×2)

FV = $6,525(1.074)

FV = $7,008.

Therefore, the future value of a 2-year investment of $6,525 into a simple interest rate account with an annual interest rate of 3.7% is $7,008.

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The equation of the conic section shown below is x² + y² + 10x + 2y - 20 = 0

A circle is a two-dimensional geometric shape that consists of a set of points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius.

A circle can be defined by its center point and radius or by its circumference, which is the distance around the perimeter of the circle. The circumference of a circle can be calculated using the formula:

C = 2πr

where C is the circumference, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14.

The center of the circle is (-5,-1) and its radius is the distance from the center to any point on the circle. Using the distance formula, we can find the radius:

r = √((0 - (-1))² + (-10 - (-5))²) = √(1 + 25) = √(26)

So, the equation of the circle in standard form is:

(x + 5)² + (y + 1)² = 26

Alternatively, in general form, it can be written as:

x² + y² + 10x + 2y - 20 = 0

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The cost of 6 sets of cards is $105.95

Each set has 100 cards, then in 6 sets there are 6*100 = 600 cards.

We know that the first 200 cards costs $49.95, and from then, the cost per set is $14.

So we have a piecewise function which can be written as:

y = $49.95   if x ≤ 200

y = $49.95 + $14*(x - 200) if x > 200.

Then we have 200 cards and 4 sets, then the total cost will be:

$49.95 + 4*$14 = $105.95

That is the cost of the 6 sets.

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Answer: 37.21 dollars

Step-by-step explanation: 25% of 45 is 11.25 so after the sale it is 33.75 then you multiply by .1025 which gives you 3.46 rounded then add it
33.75+3.46= 37.21

The coordinates of the image of the points following the reflection transformation can be presented as follows;

Preimage   [tex]{}[/tex] Reflect x-axis    Reflect y-axis    Reflect y = x

(1, 5)  [tex]{}[/tex]           (1, -5)                   (-1, 5)                 (5, 1)

(-4, 7) [tex]{}[/tex]          (-4, -7)                 (4, -7)                  (7, -4)

(6, -2)[tex]{}[/tex]           (6, 2)                   (-6, 2)                 (-2, 6)

(-3, -8) [tex]{}[/tex]         (-3, 8)                  (3, -8)                 (-8, -3)

A reflection transformation is a transformation in which a preimage point is flipped across a line of reflection.

The coordinates of the image of the point (x, y), following a reflection across the x-axis is the point (x, -y)

The coordinates of the image of the point (x, y) following a reflection across the y-axis is the point (-x, y)

The coordinates of the image of the point (x, y) following a reflection across the line, y = x is the point (y, x)

The coordinates of the images of the specified points after the specified reflections are therefore;

The values in the table of the coordinates of the Preimages and images can therefore, be obtained as follows;

Preimage point (1, 5);

The image after a reflection across the x-axis is therefore;

The image after a reflection across the y-axis, therefore;

The image after a reflection across the line y = x is therefore;

Preimage point (-4, 7);

The image after a reflection across the x-axis is therefore;

The image after a reflection across the y-axis, therefore;

The image after a reflection across the line y = x is therefore;

Preimage point (6, -2);

The image after a reflection across the x-axis is therefore;

The image after a reflection across the y-axis, therefore;

The image after a reflection across the line y = x is therefore;

Preimage point (-3, -8);

The image after a reflection across the x-axis is therefore;

The image after a reflection across the y-axis, therefore;

The image after a reflection across the line y = x is therefore;

Please find above the completed table including the coordinates of the images following the reflection across the x, y-axis and the line y = x

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Answer:

onomatopoeia

Step-by-step explanation:

onomatopoeia are words that are sounds

Answer:

Onomatopoeia

Step-by-step explanation:

Answer:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Step-by-step explanation:

A part of basic arithmetic, long division is a method of solving and finding the answer and remainder for division problems that involve numbers with at least two digits. Learning the basic steps of long division will allow you to divide numbers of any length, including both integers (positive,negative and zero) and decimals. This process is an easy one to learn, and the ability to do long division will help you sharpen and have more understanding of mathematics in ways that will be beneficial both in school and in other parts of your life.[1]

Answer: 13:26

Step-by-step explanation:

8 + 5 = 13. Philip will be twice as old as Lori will be.

13 x 2 = 26

So, the ratio will be 13:26

Hope this helps!

From the percentage of the coffee bags with 10.9 ounces, we can see that it is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.

What is meant by percentage?

A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the per cent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred. Per 100 is what the word per cent means. As there is no unit of measurement for percentages, they are dimensionless numbers. This is because we divide numbers with the same units in percentage calculation.

Given,

Amount of coffee in A bag of ground coffee = 11 ounces

Number of bags = 250 bags

Number of bags which contain 10.9 ounces of coffee = 50

The percentage of bags which contain 10.9 ounces of coffee

= (50/250) × 100 = 20%

This percentage shows that the company's claim is not true because they claim every bag contains 11 ounces of coffee.

Therefore from the percentage of the coffee bags with 10.9 ounces, we can see that it is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.

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Answer: x = 60 degrees

Step-by-step explanation:

As we see, there is a 90 degree angle formed the top left corner. You divided it by 2 and it is formed by both triangles and u get 45 degrees.

Now, according to angle sum property:

angle A + Angle B + Angle C = 180 degrees

therefore, 75 + 45 + angle c = 180

and by linear equation , angle c = 180 - [75 + 45]

                                                       =  180 -120

                                                       = 60

therefore, x = 60

Answer:

60 degrees

Step-by-step explanation:

A right triangle is 180 degrees. 60+75+a= 180degrees. It shows a right angle, with a line right at the middle. half of 90 is 45, so put that in the equation and you get 60+75+45=180 degrees. to solve for ? you want to take 45 + 75 + ? = 180 degrees 45 plus 74 is 135 so take 180-135 is 60. the ? will be 60 degrees.

I hope this helps : )

Therefore , the solution of the given problem of ratio comes out to be 1:3 is the decreased loss-to-games-played ratio.

A collection of integers "a" as well as "b" that seem to be equal can be defined using the straightforward fraction calculation "a / b," at which "b" may be larger than zero. A ratio is created by combining two ratios. The ration would be 1:1 if there were just one male and three women. There are 1/4 guys and 3/4 women in the group. Portions can be a divide between different things, a number, or a specific portion of the volume of a component.

Here,

In events played, win:

Out of the 12 games contested, 8 were victories. We can split the numerator and denominator by 4 to decrease the ratio:

=> 8/12 = 2/3

The decreased win-to-games-played ratio is 2:3.

win to loss ratio

If a squad has 8 victories, they have 4 defeats (since they have played 12 games in total). As a result, the winning/losing split is as follows:

8:4, which is further diminished by multiplying the number and denominator by 4:

=> 2:1

The decreased win-to-loss ratio is 2:1.

Played events lost:

If a squad has 4 losses and has played a total of 12 games, the ratio of losses to games played is as follows:

=> 4/12 = 1/3

=> 1:3 is the decreased loss-to-games-played ratio.

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Answer:

To find the efficiency of the ramp, we need to compare the work output to the work input. Work input is the force applied to the ramp multiplied by the distance over which the force is applied, and work output is the weight of the box multiplied by the distance it is lifted.

The force applied to the ramp is 600 N, and the distance over which it is applied is the length of the ramp, which is 2.5 m. So the work input is:

work input = force x distance = 600 N x 2.5 m = 1500 J

The weight of the box is 1200 N, and the distance it is lifted is 1.0 m (the height of the truck). So the work output is:

work output = weight x distance = 1200 N x 1.0 m = 1200 J

The efficiency of the ramp is the ratio of work output to work input:

efficiency = work output / work input = 1200 J / 1500 J = 0.8 = 80%

So the efficiency of the ramp is 80%.

To find the mechanical advantage of the ramp, we need to compare the output force to the input force. The output force is the weight of the box, which is 1200 N. The input force is the force applied to the ramp, which is 600 N.

So the mechanical advantage of the ramp is:

mechanical advantage = output force / input force = 1200 N / 600 N = 2

So the mechanical advantage of the ramp is 2.

The true statement is A, for x < 0 the function is negative.

On the image we can see the graph of the parent cube root function.

y = ∛x

And we want to see which statements are true. Remember that the function is negative if the graph is below the x-axis and positive if it is above, using that we can analyze the graph.

First, notice that for x < 0 the graph is below the x-axis, then the first statement is true.

When x < 0, the function is negative.

So the only correct option is A.

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The value of the ratio g(24)/g(21) is 729, and other solutions are shown below

The domain and the range of h(n)

Given that

h(n) is the number of houses

The possible values of n and h(n) are whole numbers

So, we have

The values of h(5) and h(11)

Based on the patterns in the sequence, we have

h(n) = n

So, we have

h(5) = 5

h(11) = 11

The explicit function of h(n)

In (b), we have

h(n) = n

The values of s(4) and s(7)

Given that

s(n) is the number of segments

Based on the patterns in the sequence, we have

s(n) = 2n

So, we have

s(4) = 8

s(7) = 14

The growth pattern of s(n)

Above, we have

s(n) = 2n

The above equation is a proportional equation

This means that

The growth pattern of s(n) is linear, with a constant rate of change

The explicit function of s(n)

Above, we have

s(n) = 2n

Complete the table for f(5) and f(7)

From the table, we can see that

As n increases, the value of f(n) is divided by 2 to get the next term

So, we have

f(5) = 2/2 = 1

f(7) = 1/2/2 = 1/4

The domain of f(n)

The possible values of n are real numbers

So, we have

Domain: All set of real numbers

The observation of the function

Above, we have

As n increases, the value of f(n) is divided by 2 to get the next term

This means that

As n gets larger and larger, the value of f(n) get halved

The value of g(4)

From the question, we have

First term, a = 9

Common ratio, r = 2

This means that

g(n) = 2(9)^n-1

So, we have

g(4) = 2(9)^3

g(4) = 1458

Completing the statements

Based on the function definitions, the statements when completed are

Recall that

g(n) = 2(9)^n-1

So, we have

g(24) = 2(9)^23

g(21) = 2(9)^20

Divide the equations

g(24) = 2(9)^23

-------     ----------

g(21) = 2(9)^20

Evaluate

g(24)/g(21) = 729

Hence, the value of the ratio is 729

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The little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

The term "operation" in mathematics refers to the process of computing a value utilising operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Rote tells the little monsters to do an overhead press every 12 seconds and a squat every 30 seconds.

The prime factorization of 12 is 2² x 3, and the prime factorization of 30 is 2 x 3 x 5.

To find the smallest common multiple, we need to take the highest power of each prime factor that appears in either factorization. Thus, the smallest common multiple of 12 and 30 are:

2² x 3 x 5 = 60

This means that the little monsters will do an overhead press and a squat at the same instant every 60 seconds.

To find out how many times this will happen during the 200-second drill, we can divide 200 by 60:

200 ÷ 60 = 3 remainder 20

This means that there will be 3 complete cycles of both exercises during the 200-second drill, with an additional 20 seconds left over.

Therefore, the little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

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In accordance with the provided assertion, (A) the shorter leg is 3√3 inches and the hypotenuse is 6√3 inches (B) the longer leg is 4√3 cm and the hypotenuse is 8 cm.

The measurement or size of a thing end to end is referred to as its length. To put it another way, it is the bigger of the higher two or three dimensions of a geometric form or object.

For a 30°−60°−90° triangle, the ratios of the side lengths are:

Using these ratios, we can solve the problems:

Longer leg = x√3 = 9

x = 9/√3 = 3√3

Shorter leg = x = 3√3

Hypotenuse = 2x = 2(3√3) = 6√3

Therefore, the shorter leg is 3√3 inches and the hypotenuse is 6√3 inches.

    2. If the shorter leg is 4 cm, we have:

Shorter leg = x = 4

Longer leg = x√3 = 4√3

Hypotenuse = 2x = 2(4) = 8

Therefore, the longer leg is 4√3 cm and the hypotenuse is 8 cm.

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The monthly decay factor is 0.0733 of the four-wheeler, and the equation is x = P(D)ˣ.

Depreciation is an important subject in finance and economics since it is used to determine an asset's worth over time. For accounting and financial reporting needs, it enables people and businesses to monitor the fall in the value of their assets. Depreciation may be utilised to lower taxable income, which in turn lowers tax liabilities, hence it also plays a part in tax legislation.

The yearly decay factor is given as:

yearly decay factor = 1 - depreciation rate

yearly decay factor = 1 - 0.12

yearly decay factor = 0.88

Divide the yearly decay factor by 12:

monthly decay factor = yearly decay factor / 12

monthly decay factor = 0.88 / 12

monthly decay factor = 0.0733

n equivalent equation using the monthly decay factor as follows:

value after x months = initial value x (monthly decay factor)ˣ

x = P(D)ˣ

Hence, the monthly decay factor is 0.0733 of the four-wheeler, and the equation is x = P(D)ˣ

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the solutions are x = -13 and x = -5. So, the correct answer is (A) x = -5, x = -13.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given an algebraic expression:

5 - 3|x + 8| = 20

First, we can begin by adding 3|x+8| to both sides of the equation, giving us:

5-20 = 3|x+8|

Simplifying the left-hand side, we get:

-15 = 3|x+8|

Next, we can divide both sides by 3, giving us:

-5 = |x+8|

Now we have an absolute value equation, which has two possible solutions depending on whether x+8 is positive or negative.

If x+8 is positive, then we have:

-5 = x+8

Solving for x, we get:

x = -13

If x+8 is negative, then we have:

-5 = -(x+8)

Solving for x, we get:

x = -5

Therefore, the solutions are x = -13 and x = -5. So, the correct answer is (A) x = -5, x = -13.

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Answer:

300.20

Step-by-step explanation:

because it was a nice guesss

A reasonable prediction for the number of times a dime will be drawn is approximately 90.

Probability is the measure of how likely it is that an event will happen. The event is expressed as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty. Probability is used in many areas, such as mathematics, science, engineering, and finance. For example, in mathematics, probability is used to determine the likelihood of an event occurring or a certain outcome occurring.

When 2 dimes, 2 nickels, and 1 penny are placed into a bag, there are 5 total coins. Therefore, the probability of drawing a dime is 2/5. When a coin is drawn and replaced 175 times, the probability of drawing a dime will remain the same (2/5) and the expected value of drawing a dime is 175*2/5 = 90. Since this is a reasonable prediction, it is a valid solution.

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Probability that a randomly selected students scored of then 65 on the  faunal exam is 65.54%.

mean μ = 63

standard deviation  σ = 5

x = 65

Find z-score:

z = (x - μ)/σ

z = (65 - 63)/5

z = 2/5

z = 0.4

Using z score table:

Probability that a randomly selected students scored of then 65 on the  faunal exam is :

P(x = 65) = P(z = 0.4)

P(x = 65) = 0.6554

Thus, Probability that a randomly selected students scored of then 65 on the  faunal exam is 65.54%.

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a) The altitude οf the plane is apprοximately 10,780 meters.

b) The pilοt will have apprοximately 14.4 minutes befοre he has tο land if the plane descends suddenly at a rate οf 750 meters per minute.

Trigοnοmetric functiοns are mathematical fοrmulas that cοnnect a triangle's angles and side ratiοs. Sine, cοsine, and tangent are the three fundamental trigοnοmetric functiοns; they are alsο knοwn as sin, cοs, and tan, respectively. These functiοns are emplοyed in the study οf physics, engineering, and οther branches οf science as well as in the study οf geοmetry, trigοnοmetry, and οther branches οf mathematics. They can be used tο sοlve issues invοlving angles and distances, such as determining a building's height, the separatiοn between twο οbjects, οr the speed οf a mοving οbject.

a) The Pythagοrean theοrem, which relates the three sides οf a right triangle, can be used tο determine the plane's altitude. In this instance, the slant range serves as the hypοtenuse οf a right triangle, with the grοund range serving as οne οf the legs and the height serving as the οther leg. As a result, we have:

altitude² + grοund range² = slant range²

Substituting the given values, we get:

altitude² + (10.15 km)² = (14.5 km)²

Simplifying and sοlving fοr altitude, we get:

altitude² = (14.5 km)² - (10.15 km)²

altitude² = 116.205 km²

altitude = √116.205 km² ≈ 10.78 km ≈ 10,780 m

Therefοre, the altitude οf the plane is apprοximately 10,780 meters.

b) If the plane descends suddenly at a rate οf 750 meters per minute, its altitude will decrease by 750 meters every minute. Tο find hοw much time the pilοt has befοre he has tο land, we can divide the initial altitude by the rate οf descent. Therefοre, we have:

time = initial altitude/rate οf descent

Substituting the initial altitude and rate οf descent, we get:

time = 10,780 m / 750 m/min

Simplifying, we get:

time = 14.3733 min ≈ 14.4 min

Therefοre, the pilοt will have apprοximately 14.4 minutes befοre he has tο land if the plane descends suddenly at a rate οf 750 meters per minute.

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Answer: :)

Step-by-step explanation:

To find the angle that the ramp makes with a horizontal line, we need to use trigonometry. The angle we are looking for is the angle between the ramp and the ground, which is the same as the angle between the hypotenuse of a right triangle (the ramp) and its adjacent side (the ground).

We can use the tangent function to find this angle:

tan(theta) = opposite/adjacent

In this case, the opposite side is the height of the ramp (4.1 feet) and the adjacent side is the length of the ramp along the ground (6 feet). So we have:

tan(theta) = 4.1/6

Using a calculator, we can solve for theta:

theta = tan^-1(4.1/6)

theta ≈ 34.3°

Therefore, to the nearest tenth of a degree, the measure of the angle that the ramp makes with a horizontal line is 34.3°.

The possible value of angle M is 30.6°.

Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.

That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,

a / sin A = b / sin B = c / sin C

Given is a triangle LMN.

Given,  m = 4.1 inches, I = 3.9 inches

∠L = 151°. We have to find ∠M.

Using law of sines,

l / sin L = m / sin M

3.9 / sin (151°) = 4.1 / sin (M)

sin (M) = [4.1 × sin (151°)] / 3.9

           = 0.5097

M = sin⁻¹ (0.5097) = 30.64° ≈ 30.6°

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The question is incomplete. The complete question is,

In triangle LMN, m = 4.1 inches, I = 3.9 inches and ∠L = 151°. Find all possible values of ∠M to the nearest 10th of a degree.

Answer:

Step-by-step explanation:

Using the remainder theorem we get:

[tex]f(-2)=-5[/tex],  [tex]f(1)=4[/tex], and [tex]f(-1)=0[/tex]

So we get

[tex]f(-2)=(-8)(p-1)+4p-2q+r=-5[/tex]

                 [tex]-8p+8+4p-2q+r=-5[/tex]

                              [tex]-4p-2q+r=-13[/tex]  [tex](a)[/tex]

[tex]f(1)=(p-1)+p+q+r=4[/tex]

                       [tex]2p+q+r=5[/tex]               [tex](b)[/tex]

[tex]f(-1)=-(p-1)+p-q+r=0[/tex]

                                 [tex]-q+r=-1[/tex]    [tex](c)[/tex]

We need to solve (a), (b) and (c) simultaneously to find p,q, and r.

from [tex](c)[/tex]  [tex]r=q-1[/tex]. Sub this into (a) and (b):

[tex]-4p-2q+(q-1)=-13 \rightarrow -4p-q=-12[/tex]    [tex](d)[/tex]

      [tex]2p+q+(q-1)=5 \rightarrow q=3-p[/tex]              [tex](e)[/tex]

Sub (e) into (d) we get

[tex]-4p-(3-p)=-12 \rightarrow p=3[/tex]

Sub [tex]p=3[/tex] into [tex](e) \rightarrow q=0[/tex]

Sub  [tex]p=3,q=0[/tex] into [tex](c) \rightarrow r=-1[/tex]

SOLUTION: [tex]p=3,q=0,r=-1[/tex]    

So [tex]f(x)=2x^3+3x^2-1[/tex]

by dividing (x+1) into f(x) we get  (I am not showing working for this division)

[tex]f(x)=(x+1)(2x^2+x-1)[/tex]

[tex]\rightarrow f(x)=(x+1)(2x-1)(x+1)[/tex]

Sergio's new balance is $87

Sergio's savings showed a previous balance of $234.95 and interest of $1.06

The statement also showed deposits of $123.42 and $50.66 and withdrawals of $323.09

The new balance can be calculated by adding the previous balance, interest, deposits in the statement and then subtract the sum total from the withdrawal amount

234.95 + 1.06 + 123.42 + 50.66 - 323.09

= 410.09 - 323.09

= 87

Hence Sergio's new balance after adding the deposits, previous balance then subtracting from the withdrawal is $87

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