What is the maximum number of solutions an
equation of the form ||ax − b| + c| = d can have?
Justify your reasoning with an example

What Is The Maximum Number Of Solutions Anequation Of The Form ||ax B| + C| = D Can Have?Justify Your

Answers

Answer 1

Answer:

4 for c < 02 for c > 0

Step-by-step explanation:

You want the maximum possible number of solutions to the equation

  ||ax -b| +c| = d

Analysis

The values of 'a' and 'b' represent a vertical scale factor and a horizontal shift, so don't really contribute to the number of possible solutions. That means we can consider only the equation ...

  ||x| +c| = d

Positive c

We know |x| is always positive, and may have the same value for two different values of x. For positive 'c', the outside absolute value function does nothing, so the equation is effectively ...

  |x| = d-c

For d < c, there can be no solutions. For d = c, there will be one solution, and for d > c, there will be two solutions.

Negative c

When 'c' is negative, then sum |x| +c may have either sign. This gives rise to another pair of possible solutions, for a total of four solutions.

Graph

The attached graph shows the two cases. The red graph shows the left side expression with c > 0; the purple graph shows the left side expression with c < 0. The orange horizontal line represents a value of 'd'. The number of intersection points with that horizontal line is the number of possible solutions to the given equation.

For c > 0, there are two possible solutions.

For c < 0, there are four possible solutions.

What Is The Maximum Number Of Solutions Anequation Of The Form ||ax B| + C| = D Can Have?Justify Your

Related Questions

What is the greatest common factor (GCF) of 3x^3+5x^5

Answers

Answer:

1

Step-by-step explanation:

What is the constant of proportionality for the relationship shown in the table? x 2 4 6 8 y 1 2 3 4
1/2
2
or not proportional

Answers

Lol need sum point in

103,688- 89,176 equal to what? ​

Answers

Answer:

The answer is 14512

Step-by-step explanation:

106,688

- 89,176

“According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. [Round your answer to three decimal places, for example: 0.123]”

According to Masterfoods, the company that manufactures M&amp;Ms, 12% of peanut M&amp;Ms are brown, 15%

Answers

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

How to find the probabilities?

12% of peanut M&M’s = brown

15% = yellow

12% = red

23% = blue

23% = orange

15% = green

Here, Probability of an event is represented as P

a) P(not green) = 100% - 15%

                        = 85%

                        = 0.85

b) P(yellow or red) = 15% + 12%

                               = 27%

                               = 0.27

c) P(three blue) = 0.23*0.23 *0.23

                         = 0.012 (rounded to 3 decimal places)

d) P(not green if you choose 6 )= \((0.85)^{6}\)

                                                    = 0. 377

e) P(at least 1 green if you choose 6 ) = 1 - 0.377

                                                              = 0.623

What is probability?Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. To forecast how likely occurrences are to occur, probability has been introduced in mathematics. The degree to which something is likely to happen is essentially the definition of probability. This is the fundamental theory of probability, which is also applied to the probability distribution, and from which you will discover the likelihood of results for a random experiment. We must first determine the total number of outcomes in order to calculate the probability that a single event will occur.

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Gia opened two savings accounts at two different banks. One account earns an annual 3.4% simple interest, and the other earns half as much.

If she deposited $500 in each account, how much total interest will she have earned in 4 years?

Answers

Answer:

$127.50

Hope this helps:)

Gina has 32 items to ship and 11 shipping boxes. The large shipping boxes can hold 4 items each. The small shipping boxes can hold 2 items each. Gina has exactly enough boxes for her items. How many of each type of box does she have?

Answers

Answer:

Gina has 5 large shipping boxes and 6 small shipping boxes.

Step-by-step explanation:

32 items to ship and 11 shipping boxes.

Large=4 items

4 X 5 = 20

Small=2 items

2 X 6 = 12

20 + 12 = 32

If x = 2, solve for y. y = 6.3x y=[?]​

Answers

Answer: y = 12.6

Step-by-step explanation:

Since x = 2 and y = 6.3 * x, y = 6.3 * 2.

6.3 * 2 is equal to 12.6, so y is 12.6.

Answer:

y = 12.6

Step-by-step explanation:

y = 6.3x                     x = 2

Solve for y.

y = 6.3(2)

y = 12.6

So, the answer is 12.6

what is 3+7, i got 346 but i dont know if its right

Answers

Answer:

10

Step-by-step explanation: The sum of 3+7 is 10

Answer:

10

Step-by-step explanation:

3+7 is 10

if you add 1 on to 7 three times, we get

8,9,10

(i know this is a troll question lol)

hope this helps!

give brainliest :)

help! asap! algebra 2

help! asap! algebra 2

Answers

We can subtract the function that represents the cost in 2000 from the function that represents the cost in 1990.

Doing this gives us \((-20t^{2}+1000)-(-10t^{2}+1500)=\boxed{-10t^{2}-500}\)

50 Points! Multiple choice geometry question. Photo attached. Thank you!

50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

The distance between the side AB are 314.2 ft.

In a triangle ABC AC = 200 ft, m ∠A = 72°, and m ∠B = 37°. we need to find the measure of the side AB,

So,

Using sine law.

Sin A / CB = Sin B / AC = Sin C / AB

Using the angle sum property of a triangle we find the value of angle C,

∠C = 180° - (∠A + ∠B)

∠C = 180° - (72° + 37°)

∠C = 180° - 109°

∠C = 71°

So,

Sin 37° / 200 = Sin 71° / AB

AB = 200 / Sin 37° × Sin 71°

AB = 314.2 ft

Hence the distance between the side AB are 314.2 ft.

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+
P
8
2. Find the interest earned on a $25,000 deposit for 2 years at 4.7%
2
interest, compounded continuously?
(25000) (4.7
25,000
P
P(25,000) (47)
+-117500
= 117
com
or

Answers

Interest earned on $25,000 when it is compounded annually for 2 years at the rate of 4.7% is $2,405.23.

What is compounding interest?

Compound interest is the term for interest that is earned on interest.

This may be shown using simple math: if you start with $100 and it earns 5% interest every year, you will have $105 at the end of the first year.

At the end of the second year, you will have $110.25.

So, we know that:
Principal amount = $25000

Interest rate = 4.7%

Time = 2 years

Compounded annually

Then, using the compounding calculator:

(Refer to the graph attached below)

The amount after 2 years will be $27,405.23.

Interest in this is:
$27,405.23 - $25,000

$2,405.23

Therefore, interest earned on $25,000 when it is compounded annually for 2 years at the rate of 4.7% is $2,405.23.

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Correct question:

Find the interest earned on a $25,000 deposit for 2 years at 4.7% interest, compounded annually.

+P82. Find the interest earned on a $25,000 deposit for 2 years at 4.7%2interest, compounded continuously?(25000)

Which choice is equivalent to the product below? Square root of 8 Times Square root 5?

Answers

Answer:

Step-by-step explanation:

Which choice is equivalent to the product below? Square root of 8 Times Square root 5?

Pomóżcie potrzebne jak najszybciej się da proszę

Pomcie potrzebne jak najszybciej si da prosz

Answers

Answer:

can you please write it in english

Learning Task 3 Answer the questions that follow. Put a check mark (/) on the space provided. Copy and answer in your math notebook. 1. The units for Volume are always ______squared _____cubed 2. Volume is the amount of space an object takes up. ___True ___False Calculate for the volume of solid. 3. Chona is selling Pringle Chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches. 4. A 3-tier cake with the same height of 10 in and radius of 12 in, 8 in, 5 in respectively is to be delivered to a birthday party. How much space does this cake take up? Use 3.14 for π. 5. A Styrofoam model of a volcano is in the shape of a cone. The model has a circular base with a diameter of 48 centimeters and a height of 12 centimeters. Find the volume of foam in the model to the nearest tenth. Use 3.14 for π.

Answers

3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.

4. The cake takes up approximately 7317 cubic inches of space.

5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.

1. The units for Volume are always cubed.

2. Volume is the amount of space an object takes up. True.

3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:

V = 3.14 * (4.5)^2 * 32

V = 3.14 * 20.25 * 32

V ≈ 2034.72 cubic inches

4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.

Tier 1:

V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches

Tier 2:

V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches

Tier 3:

V3 = 3.14 * (5)^2 * 10 = 785 cubic inches

Total volume:

Total V = V1 + V2 + V3

Total V = 4521.6 + 2010.4 + 785

Total V ≈ 7317 cubic inches

5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:

V = (1/3) * 3.14 * (24)^2 * 12

V = (1/3) * 3.14 * 576 * 12

V ≈ 7234.08 cubic centimeters

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I don't know how to do.

I don't know how to do.

Answers

view the attached image to see the answer. in decimals the answer is 7.74596669 i
I don't know how to do.

PLEASE HELP ASAP I WILL MARK YOU BRAINLIEST!!!
Find the volume of the following
square pyramid.
26 om
20 cm
20 cm
V = [?] cm3

PLEASE HELP ASAP I WILL MARK YOU BRAINLIEST!!!Find the volume of the followingsquare pyramid.26 om20

Answers

Answer:

Step-by-step explanation:

10400

Answer:

3200 cm^3

Step-by-step explanation:

1. Calculate the sides of the right triangle to get the height

We know that side c = 26 and the shortest leg is 10 cm (20cm/2) because this right triangle splits the 20cm in two)

\(10^{2} + b^{2} = 26^{2} \\100 + b^{2} = 676\\b^{2} = 576 \\b = \sqrt{576} \\b = 24\)

a = 10, b = 24, c = 26

2. Use the formula for the volume of a square pyramid now that you have the height (which is b)

\(V = a^{2} \frac{h}{3} \\\\V = 20^{2} * \frac{24}{3} \\V = (400)(8)\\V = 3200 cm^{3}\)

V = 3200

I hope this helped! :)

Find an expression for the n-th term (t_(n)) in each sequence.

A). 1,(1)/(2),(1)/(3),(1)/(4),(1)/(5),(1)/(6),...

B). 3,9,15,21,27,....

Answers

Answer:

A) (1)/(7)

B) 33

Step-by-step explanation:

For (A), the sequence follows in 1 divided by numbers in a consecutive order, therefore after (1)/(6), the next term is (1)/(7)

For(B), the sequence follows in multiples of three but skips one in between

Example: Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36...

In the sequence, 6, 12, 18 and 24 are skipped, meaning that the next number to be skipped is 30, hence 33 is the next number in the sequence.

Because all the numbers in the sequence are odd numbers we can say that the sequence follows in odd consecutive numbers which are multiples of 3.

Original price: $22 Discount percent: 25%

Answers

Answer: 16.5

Step-by-step explanation:

Original price is 22 remove 25% by multiplying 22 by 0.75

If trying to find the original price when the discount is 25% and the discounted price is 22 take 22 and divide it by 3 and then multiply it by 4

Solve the inequality. Graph the solution on the number line and then give the answer in interval notation.

Solve the inequality. Graph the solution on the number line and then give the answer in interval notation.

Answers

Answer:

[-infinity, 4]

Step-by-step explanation:

-9x + 3 >= -33
-9x >= -36

x<=4 (sign switched because of dividing both sides by a negative integer in an inequality)
Therefore, x is less than or equal to 4

[ - infinity, 4]

Kirsten is making lanyards for a convention. She needs to make 1,000 lanyards and knows that one lanyard uses 1.75 feet of cord. How much cord will Kirsten need?

Answers

Answer:

1000*1.75ft=1,750ft

She needs 1,750 feet of cord.

Step-by-step explanation:

The sum of a number and six is eleven. Find the number.​

Answers

Answer:

17

Step-by-step explanation:

6 + 11 = 17

Sum (addition of 2 numbers)

Since the sum of a number and six is eleven, the number is equal to 5.

Let the unknown number be n.

To find the unknown number:

In this exercise, you're required to determine an unknown number by translating the word sentence into an algebraic equation.

Translating the word sentence into an algebraic expression, we have;

The sum of a number and six is eleven:

\(n + 6 =11\)

Next, we would rearrange the equation by collecting like terms:

\(n = 11-6\)

n = 5

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Stefan sells Jin a bicycle for ​$104 and a helmet for ​$17. The total cost for Jin is 110​% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend​ originally? How much money did he make by selling the bicycle and helmet to​ Jin?

Answers

The amount Stefan spent originally to buy the bike is; $100.91.

The amount Stefan made in profit by selling the bicycle and helmet to Jin is; $10.09.

How much did the bicycle cost originally?

According to the task content;

Stefan sold the bicycle and helmet for a total of;

104 + 17 = $111.

Also, since the total cost ($111) for Jin is 110% of what Stefan spent to buy the bicycle and helmet, x originally; we have

110% × x = 111

x = (111 × 100) / 110

x = $100.91.

Therefore, Stefan spent $100.91 originally to buy the bike and helmet.

Consequently, the money Stefan made by selling the bicycle and helmet to Jin is; 111 - 100.91 = $10.09.

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need help 15.3+7.2 it is adding

Answers

it is adding the answer is 22.5

Answer: below

Step-by-step explanation: 22.5

If a bike travels 15m in 2 sec, what is its speed in km/h?

Answers

Answer:

27km/h

Step-by-step explanation:

Juan and his father went on a driving trip.
Juan drove 32 miles more than his father.
Together, they drove 260 miles. How many
miles did Juan drive?

Answers

Answer:

162

Step-by-step explanation:

260/2=130

130+32=162

answer would be 6 thousand because operating

What percent of 2 is 32? If necessary, round your answer to the nearest tenth.

Answers

Answer:

Below

Step-by-step explanation:

32/2 x 100% = 1600 %

What is the distance between the points (7,5) (4,9)

Answers

The Distance will be  5.

The distance between two points is the length of the line segment connecting the two points on the plane. The formula for finding the distance between two points is usually d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on the coordinate or x-y plane.

Let point (7,5) be A and point (4,9) be B

Distance formula =

Ab  = √(x1- x2) ² + (y1 -y2) ²

Then Distance AB will be

Ab  = √(7-4) ² + (5 -9) ²

= √ 3² + 4²

= √ 9 + 16

= 5

Hence the distance  will be 5.

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The points \((7,5)\)  \((4,9)\) are separated by a distance of \(5\) units.

The distance between the two points is given by the length of the segment between them.

The Distance Formula is a helpful tool for figuring out how far apart two points are when they are arbitrarily represented on a coordinate plane as points A\((x_{1},y_{1})\) and B\((x_{2},y_{2})\).

The Pythagorean Theorem is essentially the source of the Distance Formula. Calculating the right triangle's hypotenuse's length is the fundamental purpose of the distance formula.

Use the distance formula to get the distance between two places.

\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)

In the posted query,

\((x_{1},y_{1})=(7,5)\\\\(x_{2},y_{2})=(4,9)\)

Distance formula,

\(d = \sqrt{ (x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} }\)

\(d = \sqrt{ (4-7)^{2} +(9-5)^{2} }\)

\(d = \sqrt{ (-3)^{2} +(4)^{2} }\)

\(d = \sqrt{ 9+16 }\)

\(d = \sqrt{ 25 }\)

\(d = 5\)

Therefore, the points \((7,5)\)  \((4,9)\) are at a distance of \(5\) units.

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sin¹(x)-cos¹ (x)/sin²(x)-cos² (x) =1

sin(x)-cos (x)/sin(x)-cos (x) =1

Answers

The answer is CCCCCCCCC


Given 2.2 <√5 <2.3, find the corresponding range for the value of each expression.
√5 +2

Answers

The range of the expression is: 4.2  < √5 + 2 < 4.3.

Explain the term range of the function?When a function is applied to its entire set of outputs, its range seems to be the set of outputs it produces. The range in the metaphor of the function machine refers to the collection of objects that really exit the machine after being fed all of its inputs.

For the stated question;

2.2 < √5  <2.3  .....eq 1

To find the range of √5 +2.

2.2 + 2 < √5 + 2 <2.3 +2

4.2  < √5 + 2 < 4.3

Thus, the range of the expression is: 4.2  < √5 + 2 < 4.3.

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Suppose Deandre places $5000 in an account that pays 8% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
(b) Find the amount in the account at the end of 2 years.

Answers

The amount in the account at the end of 1 year is $5400.

The amount in the account at the end of 2 year is $5832.

What do you mean by interest rate?

The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number.

According to data in the given question,

We have:

Deandre places $5000 in an account that pays 8% interest compounded each year.

And no withdrawals are made from the account.

Now, we need to determine the amount of 8% interest on the $5000,

\(=\frac{5000}{100}*8\\ =400\)

Then, the amount in the account at the end of 1 year =$5000+$400

=$5400.

Now, we need to determine the amount of 8% interest on the $5400,

\(=\frac{5400}{100}*8\\ =432\)

So, the amount in the account at the end of 2 year =$5400+$432

=$5832.

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