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

Answer:

( x , y , z) = ( 1 , 3 , - 2)

the solution

Answer:

1/6(x) = 16

Step-by-step explanation:

You can just solve for x which goes as follows:

6 * 1/6 = 6 * 16 - Multiply both sides by 6.

x = 96

Answer:

x=96

Step-by-step explanation:

To figure out the weight of the person on the moon we would need to take their weight and divide by 6. we don't know the weight so it's x. We know the final weight so the x divided by 6 should be 16.

this translates to:

x/6=16

x=16*6

x=96

Answer:

The unknow number is 5.

Explanation and Check part below

Hope this helps :)

Step-by-step explanation:

1. To solve, first wrote it into an equation. Also, the letter x will stand for the unknown number.

4 + 7 = 11

11 + x = 16

2. Isolate the varable by subtracting 11 from both sides of the equation.

11 + x = 16

- 11 - 11

x = 5

The unknow number is 5.

Check:

11 + 5 = 16

16 = 16

True statement.

The exponential form is a way of writing numbers using bases and powers. (-10)^2*3^5 is the expression in exponent form for expression (-10) . (-10) . 3 . 3 .3 .3 .3 .

The exponential form is a way of writing numbers using bases and powers.

Given expression is  (-10) . (-10) . 3 . 3 .3 .3 .3, we need to write in exponent form.

An exponential function is defined by the formula f(x) = a^x, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

(-10) is 2 times and 3 is five times,

we can write in the form (-10)^2.(3)^5

Therefore the required answer is (-10)^2.(3)^5 for expression  (-10) . (-10) . 3 . 3 .3 .3 .3 .

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The solution to this equation is x = -3

The equation is given as

5x + 3 = 2x - 6

Collect the like terms

5x - 2x = -3 - 6

Evaluate the like terms

3x = -9

Divide both sides by 3

x = -3

Hence, the solution to this equation is x = -3

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Answer:

no

Step-by-step explanation:

Functions are wavy lines

Answer:

yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

In the given picture with 4 lines l, m and r, s. The l and m, r and s line are parallel lines.

Given that,

There is a picture with 4 lines l, m and r, s.

We have to check that those lines are parallel or not

To check that the line are parallel we have a condition.

If two lines are cut by the transversal and corresponding angles are congruent then we can say that those 2 lines are parallel.

In the figure we can see that ∠2 and∠6 are congruent.

So, we can say that lines r and s are parallel lines.

Similarly,

In the figure we can see that ∠1 and∠7 are congruent.

So, we can say that lines l and m are parallel lines.

Therefore, the l and m, r and s line are parallel lines.

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Answer:

5/11

Step-by-step explanation:

make sure next time to say how much books do you have I have answered a similar question with this wording so I hope this helps :))

The slope of line: 1. m= 6 , 2. m= -6 , 3. m= 2.5,  4. m= .5

The slope of the line :

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.

The net change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx.

Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,

m = change in y/change in x = Δy/Δx

Where “m” is the slope of a line.

Tan θ = Δy/Δx can also represent the slope of the line

So, tan θ to be the slope of a line.

Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The letter ‘ m’ usually represents the slope.

If P(x1,y1) and Q(x2,y2) are the two points on a straight line, then the slope formula is given by:

Slope,

m = Change in y-coordinates/Change in x-coordinates

m = (y2 – y1)/(x2 – x1)

Therefore, based on the above formula, we can easily calculate the slope of a line between two points.

In other terms, the slope of a line between two points is also said to be the rise of the line from one point to another (along the y-axis) over the run (along the x-axis). Therefore,

Slope, m = Rise/Run

1.

(-1,-1) & (0,5)

m = (y2 – y1)/(x2 – x1)

m = (5 – (-1)) /(0– (-1))

m = (5 +1)/(0 +1)

m = (6)/(1)

m = 6

2.

(3,5) & (4,-1)

m = (-1 – 5)/(4 – 3)

m = (-6)/(1)

m = -6

3.

(2,1)  & (4,6)

m = (6 – 1)/(4 – 2)

m = (5)/(2)

m = 2.5

4.

(-5,-2) & (3,2)

m = (2 – (-2))/(3 – (-5))

m = (2 +2/(3 +5)

m = (4)/(8)

m = (2/(4)

m = (1)/(2)

m = 0.5

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The weight represents the 42nd percentile.

=6.712

This is further explained below.

Generally, the given data is

8.3,6.5,6,6,5,4,6.7,6.5,8: 1,9.2,6.4,8 0,6.8,9.0,8.7,9.3,8.0

The ascending order of the data is

5.4,6.0,6.4,6.5,6.5,6.7,6.8,8.0,8.0,8.1,8.3,8.7,9.0

n=15.

42ndPercentile

=P_{42}

[tex]=42\left(\frac{n+1}{100}\right)^{\text {th }} \text { term } \\[/tex]

[tex]&=42\left(\frac{16}{100}\right) \text { th term } \\[/tex]

=6.72th term

=6th+0.72(72nd -6th) term

=6.7+0.72(6.8-6.7)

=6.712

In conclusion, the weight represents the 42nd percentile.

=6.712

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The rate of change of the linear equation that has the given points on its graph is; -2.

The rate of change of a linear function can be determined by using the following formula:

Rate of change = change in y / change in x = y2 - y1 / x2 - x1.

Given the following points on a graph of a linear function:

​(−5​,4​) = (x1, y1)

​(−2​,−2​) = (x2, y2)

Plug in the values

Rate of change = change in y / change in x = (-2 - 4) / (-2 -(-5))

Rate of change = -6 / 3

Rate of change = -2 / 1

Rate of change = -2

Thus, the rate of change of the linear equation that has the given points on its graph is; -2.

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Answer:

hope this explanation helps you

Answer:

[tex]\textsf{b)} \quad -\dfrac{3\sqrt{13}}{13}[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

[tex]\textsf{If}\; \tan(\theta)=-\dfrac{2}{3} \implies \sf O=2 \; \textsf{and} \; A=3.[/tex]

Use Pythagoras Theorem to calculate the length of the hypotenuse:

[tex]\sf \implies O^2+A^2=H^2[/tex]

[tex]\implies \sf H=\sqrt{O^2+A^2}[/tex]

[tex]\implies \textsf{H}=\sqrt{2^2+3^2}[/tex]

[tex]\implies \textsf{H}=\sqrt{13}[/tex]

Therefore, substituting the values of A and H into the cosine ratio:

[tex]\implies \cos \theta=\dfrac{3}{\sqrt{13}}[/tex]

[tex]\implies \cos \theta=\dfrac{3}{\sqrt{13}}\cdot \dfrac{\sqrt{13}}{\sqrt{13}}[/tex]

[tex]\implies \cos \theta=\dfrac{3\sqrt{13}}{13}[/tex]

As the terminal side of the angle is in Quadrant II, and cosine is negative in Quadrants II and III, the exact value of cos(θ) is:

[tex]\implies \cos \theta=-\dfrac{3\sqrt{13}}{13}[/tex]

Answer:

500,000 =

 5 × 100,000  

+ 0 × 10,000  

+ 0 × 1,000  

+ 0 × 100  

+ 0 × 10  

+ 0 × 1  

Step-by-step explanation:

there are more then one ways of writing this so here's another example

500,000 =

 500,000  

+ 0  

+ 0  

+ 0  

+ 0  

+ 0  

Answer:

[tex]18 {m}^{2} [/tex]

Step-by-step explanation:

The figure shown in the image is a parallelogram.

To find the area of a parallelogram we use the following formula:

A = b • h (b: base, h: height)

The height is 4.5m while the base is given as 4m

(4.5) • 4 = 18

Since the area is put in square units the answer is

[tex]18 {m}^{2} [/tex]

To graph an equation on the co-ordinate plane we plot points that satisfy the given equation .

The graph of a linear equation is two variables gives a straight line on the co-ordinate plane.

the given equation is y=3x-5

at x=0 ,y=3×0-5 or y=-5

at x=2 , y=(3×2)-5 or y=1

at x=-1,y=(3×-1)-5 or y=-8

Now we make the table to get the desired points.

x               y                    point

0              -5                  A (0,-5)

2               1                   C(2,1)

-1             -11               B (-1,-8)

The graph for the equation y=3x-5 is drawn.

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Step-by-step explanation:

The commonly used methods to find the LCM of 15 and 20 are:

1) Division Method

2) Prime Factorization Method

3)Listing Multiples

The greatest common factor for 4x³+16x² +8x is 4x(x2- 4x - 2).

This solution focuses on simplification:

4x(x2-4x-2)

(4(x3)-24x2)-8x

(22x3-24x2) -8x

Take similar factors aside:

4x3-16x2-8= 4x(x2-4x-2)

Factoring  x2 - 4x - 2

x2 is the initial term, and it has a coefficient of 1.

The coefficient of the intermediate term, which would be -4x, is 4.

"The constant," the final term, is -2.

Multiply the constant by the coefficient of the first term. 1  -2 = -2

The second step is to find two -2 factors whose sum is equal to the -4 coefficient of the middle word.

-2 + 1 = -1

-1 + 2 = 1

No two of these factors can be discovered!!

Trinomial cannot be factored.

Hence,  The greatest common factor is  4x(x2- 4x - 2).

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Using relations in a right triangle, it is found that the distance between the towns is of 15 km.

The relations in a right triangle are given as follows:

For the first town, we have that:

Hence:

tan(37º) = xA/10

xA = 10 x tan(37º).

xA = 7.5 km.

For the second town, we have that:

Hence:

tan(66º) = xB/10

xB = 10 x tan(66º).

xB = 22.5 km.

Hence the distance is:

22.5 km - 7.5 km = 15 km.

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There exists no even integer with the given parameters

Consecutive even integers are integers that have a difference of 2

i.e x and x + 2

Where x is the lesser number

Using the given mathematical statement, we have

4x < 2(x + 2)

Divide by 2

2x < x + 2

Subtract x from both sides

x < 2

There is no even number less than 2

Hence, there exists no even integer with the given parameters

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The expression written in another way is -9 + m

Expressions are mathematical statements that are represented by variables, coefficients and constants

The expression is given as:

m - 9

By the subtraction property of an equation, we have

a - b = -b + a

x - y = -y + x

Using the above equations as a guide, we have

m - 9 = -9 + m

Hence, the expression written in another way is -9 + m

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X²-X+6

X+6

Answer:

1 out of 6 part of time 15 and 3 mains time 15 and 3 has 6 parts and that you should take one out of this six paths

1/6 (15 x 3) = 1/6. x 45 = 15/2

then,multiple by 5

15/2 × 575/2 = 37 1/2

When Lydia buys 4 jewelry sets, the amount spent is $24.

From the information given, we are told that Michelle is preparing for her birthday and that each set is $5 and shipping is $4 flat. If Lydia buys 4 jewelry sets.

Therefore, the equation will be:

4 + (5 × x)

where x = number of set

4 + 5x

4 + (5 × 4)

= 4 + 20

= $24

The amount is $24.

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The magnitude of the repulsive force between a +500μC charge and a +100μC charge which are 5 m apart is 2N.

The repulsive force between two charges = (k q₁ q₂)/r²

q₁ q₂ are the charges

r is distance between the charges

k= 9×10⁹ Nm²C²

F= (500μC) (+100μC)9×10⁹/25

 = 2N

A movement between two charges that are same or comparable is referred to as repulsion. The tension between two electrons (negative charge). Two charges of a different sort are drawn toward one another by the force of attraction, which is defined as "a force between two charges that are distinct or different."

At a distance, magnetism is an attractive or repulsive force. The repulsive force gives rise to a metric that measures how a system's gravitational mass changes. According to the force-based approach, the forces that attract and repel other atoms come from their subatomic arrangement and control how they behave.

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Answer:

At least 20

Hope this helps :)

Step-by-step explanation:

85 ÷ 3.5 = 24.2857142857

24.2857142857 is approximately rounded to 20.

So she need at least 20 pieces of ribbon (which means greater than or equal to 20 pieces).

The error that the manager made was that B. The manager divided 5/4 by 16 instead of dividing 4/5 by 16.

The information illustrates that the project manager is calculating work forecasts and he manager's team completed 4/5 of a job in 16 days.

Therefore, the amount that was done each day will be:

= 4/5 ÷ 16

= 4/5 × 1/16

= 4/80

= 1/20

Therefore, the error that the manager made was that the manager divided 5/4 by 16 instead of dividing 4/5 by 16. This was the reason that he got 5/64.

Therefore, the correct option is B.

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Answer: 156

Step-by-step explanation:

13x2=26

26x6=156

The required volume of the box is given as 936 cubic centimeters.

Given that, A box of Tyler's favorite snack, Cheesy Snaps, is 13 centimeters tall and 6 centimeters wide. It has twice as long as it is wide.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
height  = 2 × width
height = 2 × 6 = 12
The volume of the box = length × width  × height
                             = 13 × 6 × 12 = 936
                       

Thus, the required volume of the box is given as 936 cubic centimeters.

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