Rewrite the equation without absolute value.
y=|x-3|+|x-2|-|x-5|
Answers
Answer:
y = {-x, x < 2; x-4, 2 ≤ x < 3; 3x -10, 3 ≤ x < 5; x, 5 ≤ x}
Step-by-step explanation:
The absolute value function is a piecewise linear function that changes its definition when its argument changes sign.
Here, the three different absolute value expressions will change their behavior at three different values of x. That is, this equation will be described by a piecewise linear function in four (4) pieces.
For x < 2:
y = (3 -x) +(2 -x) -(5 -x) = -x
For 2 ≤ x < 3:
y = (3 -x) +(x -2) -(5 -x) = x -4
For 3 ≤ x < 5:
y = (x -3) +(x -2) -(5 -x) = 3x -10
For 5 ≤ x:
y = (x -3) +(x -2) -(x -5) = x
In summary, the equation can be written ...
[tex]y=\begin{cases}-x,&\text{for }x < 2\\x-4,&\text{for }2\le x < 3\\3x-10,&\text{for }3\le x < 5\\x,&\text{for }5\le x\end{cases}[/tex]
_____
Additional comment
The absolute value function itself can be described by ...
[tex]y=|x-a|=\begin{cases}a-x,&\text{for }x < a\\x-a,&\text{for }a\le x\end{cases}[/tex]
Related Questions
a grocery store sells a 6-pack of bottled water for $3.79, a 9- pack for $4.50, and a 12-pack for $6.89. which package cost the least per bottle explain your reasoning ?
Answers
Answer:
Cost per bottle. Therefore cost/bottle. Set 1: 3.79/6=.63 Side note, don’t forget to round each time to the nearest cent. Set 2: 4.50/9=.50 Set 3: 6.89/12=.57 The second package (9-pack for $4.50) is the costs least per bottle.
Step-by-step explanation:
Miguel measured a house and its lot and made a scale drawing. The backyard, which is 40 feet wide in real life, is 20 inches wide in the drawing. What scale did Miguel use?
1 inch :
feet
Answers
Answer:
1 inch:2 feet
Step-by-step explanation:
Friday’s temperature was 40 degrees and the temperature increased by 130% by Sunday evening. What was the temperature on Sunday evening?
Answers
Answer:
By Sunday evening the temperature would be 92 degrees
Step-by-step explanation:
Find 130% of 40
40 × 1.3 = 52
Add the product to your original temperature (40)
40 + 52 = 92
To get an A, you need more than 200 points on a two-part test. You score 109 points on the
first part. How many more points do you need?
Answers
Answer:
91 more points are needed
Step-by-step explanation:
Answer:91
Step-by-step explanation:
need this asap so if you know it please let me know quickly
Answers
Answer:
Step-by-step explanation:
-20d + 12
4(d + 9) - 8(-3d - 3)
4d + 36 - 24d - 24
4d - 24d + 36 - 24
-20d + 12
Please help!
Find the area of the kite.
Answers
area of a triangle = 1/2 (L • W)
[1/2 (10mi • 5 mi)] • 2 = 50 mi^2
[1/2 (5mi • 5 mi)] • 2 = 25 mi^2
50 mi^2 + 25 mi^2 = 75 mi^2
Can some Please help me with this please please :(((( (The Image is In The Question)
When Hana goes to the mall, she always buys the same lunch and also buys some books. The table shows the number of books she buys, x, and the total amount of money she spends, y.
If this data were displayed in a scatter plot, select ALL statements that would be true about a good trend line summarizing the data.
SELECT GROUP OF ANSWER CHOICES
A. The y-intercept approximates the average cost of one book.
B. The y-intercept approximates the cost of Hana's lunch.
C. The slope approximates the cost of Hana's lunch.
D. The trend line goes through the origin.
E. The slope approximates the average cost of one book.
Answers
The total cost of the dinner is found by adding the two prices together. Then this sum is multiplied by 1.05, which is 100% + 5%, to get a cost of $11.72.
Answers
Answer:
2( 4 + 2X) = 3x + 4
8 + 4x = 3x + 4
8 + 4x - 3x - 4 = 0
x + 4 = 0
x = -4
Step-by-step explanation:
Alice was having a conversation with her friend Trina, who had a discovery to share:
Pick any two integers. Look at the sum of their squares, the difference of their squares,
and twice the product of the two integers you chose. Those three numbers are the
sides of a right triangle.
a. Write an equation that models this conjecture using the variables x and y.
b. Investigate this conjecture for at least three pairs of integers. Does her trick
appear to work in all cases, or only in some cases? Explain.
c. Use Trina’s trick to find an example of a right triangle in which all of the sides
have integer length, all three sides are longer than 100 units, and the three side
lengths do not have common factors.
BONUS: If Trina’s conjecture is true, use the equation found in part a to prove the
conjecture. If it is not true, modify it so it is a true statement, and prove the new
statement
Answers
Answer:
a. (x² + y²)² = (x² - y²)² + (2xy)²
b. The conjecture works in all cases.
c. Sides of 119, 120, and 169
Step-by-step explanation:
a. Equation that models this conjecture
x² + y² = sum of squares
x² - y² = difference of square
2xy = twice the product of the integers
If these are the sides of a right triangle then
(x² + y²)² = (x² - y²)² + (2xy)²
b. Test the conjecture
(i) Try x = 2, y = 1
(2² + 1²)² = (2² - 1²)² + (2×2×1)²
5² = 3² + 4²
25 = 9 + 16
(ii) Try x = 3, y = 1
(3² + 1²)² = (3² - 1²)² + (2×3×1)²
10² = 8² + 6²
100 = 64 + 36
(iii) Try x = 3, y = 2
(3² + 2²)² = (3² - 2²)² + (2×3×2)²
13² = 5² + 12²
169 = 25 + 144
The conjecture appears to work in all cases.
c. A possible triangle
We must have one side greater than 100. That means,
x² > 100 or x >1 0.
Let x = 12
One side = 12² + y²
The second side = 12² - y²
The third side must have 2xy > 100
24y > 100
y > 4.2
Try y = 5
(12² + 5²)² = (12² - 5²)² + (2 × 12 × 5)²
169² = 119² + 120²
So, one right triangle could have sides of 119, 120, and 169.
Furthermore, these sides have no common factors.
Check:
169² = 119² + 120²
28561 = 14161 + 14400
28561 = 28561
Helppp with this question plzz
Answers
Answer:
306
Step-by-step explanation:
There are 102 triangles, a triangle has 3 sides, each side is 1 cm. 102 x 3=306
1
Ruth needs 5
quarts of oil to change
4
1
the oil in her car. She has 2
quarts in
2
, 1
one bottle and 1
quarts in another. How
4
many more quarts of oil does Ruth need
to change the oil in her car?
Answers
Answer:
Ruth needs 5quarts of oil, she has 2quarts in one bottle and 1 quart in another.
therefore:
2+1=3
5-3=2
Ruth needs 2 more quarts.
The perimeter of a rectangular pool is 246 m.
If the width of the pool is 52 m, what is its length?
Answers
P=L+L+W+W
W= 52
So 52+52= 104
246-104= 142
Since that’s the two L added up divide by 2
142/2= 71
71+71+52+52= 246
Please assist!!!! No links
Answers
Answer:
The choice C.
Step-by-step explanation:
[tex] {( \frac{ {2}^{ - 10} }{ {4}^{2} } )}^{7} = \frac{ {(2}^{ - 10}) ^{7} }{ {( {4}^{2}) }^{7} } = \frac{ {2}^{ - 10 \times 7} }{ {4}^{2 \times 7} } = \frac{ {2}^{ - 70} }{ {4}^{14} } \\ \\ = \frac{1}{ {2}^{70} \times {4}^{14} } [/tex]
Tucker deposited $20,000 in a savings account with simple interest. Five years later, he had earned $14,000 in interest. What was the interest rate? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answers
Answer:
the interest rate should be 14%
zachary has six times as many nickels as dimes and four times as many quarters as dimes. zachary has a total of ninety-nine nickels, dimes, and quarters. The total value of the coins is $12.60. How many of each coin does he have?
Answers
Answer:
nickels: 54dimes: 9quarters: 36Step-by-step explanation:
The ratio of nickels to dimes to quarters is given as ...
N : D : Q = 6 : 1 : 4
The total number of ratio units is 6 +1 +4 = 11. The total number of coins is given as 99, so each "ratio unit" must represent 99/11 = 9 coins. That is, the actual coin count ratios are ...
N : D : Q = 54 : 9 : 36
Zachary has 54 nickels, 9 dimes, and 36 quarters.
__
Check
The value of the coins is ...
$0.05 × 54 +$0.10 × 9 +$0.25 ×36 = $2.70 +0.90 + 9.00 = $12.60
What value belongs next to the 1 in the table? What does it mean in this context?
Answers
Answer:
The number next to 1 is 2.5.
It means 2.5 dimes are in 1 quarter (1 quarter = 2.5 dimes)
Step-by-step explanation:
The value next to 1 in the table above = number of dimes we have in 1 quarter.
Let the value next to 1 be "x".
That is:
1 quarter = x dimes
If 4 quarters = 10 dimes, then,
Cross multiply to find, how many dimes, x is equal to.
Thus:
1*10 = 4*x (cross multiplication)
10/4 = 4x/4 (dividing both sides by 4)
2.5 = x
The number next to 1 is 2.5.
It means 2.5 dimes are in 1 quarter (1 quarter = 2.5 dimes)
The figures shows two parallel lines AB and DE cut by the transversals AE and BD::
AB and DE are parallel lines and AE and BD are transversals. The transversals intersect at C. Angle CAB is labeled 1, angle ABC is labeled 2, angle ACB is labeled 3, angle ACE is labeled 4, angle CDE is labeled 6, and angle CED is labeled 5.
Which statement best explains the relationship between Triangle ABC and Triangle EDC ?
Triangle, because m∠3 = m∠6 and m∠1 = m∠4
Triangle ABC is congruent to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5
Triangle ABC is congruent to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
Triangle ABC is similar to triangle EDC , because m∠6 = m∠2 and m∠3 = m∠4
Answers
Answer:
Triangle ABC is similar to triangle EDC because Measure of angle 3 equals measure of angle 4 and Measure of angle 1 equals measure of angle 5
Step-by-step explanation:
Answer:
D) Triangle ABC is similar to triangle EDC , because m∠6 = m∠2 and m∠3 = m∠4
Step-by-step explanation:
trust me on this one ;)
HELP ME:(
When a solid is enlarged by a scale factor greater than 1, the volume of the new solid will be ___________ the volume of the original solid. When a solid is reduced by a scale factor between 0 and 1, the volume of the new solid will be _________ the volume of the original solid.
Answers
Answer:
blank one: greater than blank two: less than
Step-by-step explanation:
Solve for T
V = x + at
Answers
Answer:
t=V‒x/a
Step-by-step explanation:
V=x+at (add ‒x in both side)
V‒x=x+at‒x
V‒x=at
V‒x/a=at/a
V‒x/a=t
so the formula is t=V‒x/a
Which of the following equations will form a system with the same solution as the above set of equations?
Select all that apply.
Answers
Answer:
x=-3 and 2x-3y=-12
Step-by-step explanation:
The solution to lines 1 and 2 is (-3, 2)
The only lines that intersect that point are x=-3 and 2x-3y=-12
Please Help!!!
simplify (x-4)(6x^2+2x-1)
Answers
Answer:The solution is in the attached file
Step-by-step explanation:
Mr. Campbell decides that too many students are getting a pass on homework. He adds 10 yellow marbles to the jar. Tell whether each part of the probability model does or does not change.
The sample space change.
Each event within the sample space change. The probability of each event
change.
Answers
Answer:
The new probability of drawing a red marble is ()=.
Step-by-step explanation:
The sample space change. Each event within the sample space change. The probability of each event changes.
can you help me understand this
Answers
Answer:
For the small boxes on the side, drag the one that you think is correct to the grey spaces. Your supposed to enter the fraction in the simpliest form
Step-by-step explanation:
(PLS HELP)The diameter of a cylindrical water tank is 12 ft, and its height is 17 ft. What is the volume of the tank?
Use the value 3.14 for л, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer.
Answers
Answer: The volume is equal to 1922.65.
Step-by-step explanation:
Diameter is 12 ft, height is 17 ft.
V = πr2h
V = πr2h = π·62·17≈ 1922.65
The volume of the tank is approximately 1814 cubic feet.
What is a cylinder?A cylinder is a 3-D figure that has a radius and a height.
The volume of a cylinder is given as πr²h.
Example:
The volume of a cup with a height of 5 cm and a radius of 2 cm is
Volume.
= 3.14 x 2 x 2 x 5
= 62.8 cm³
We have,
The formula for the volume of a cylinder is:
V = πr²h
where V is the volume, r is the radius, h is the height, and π is a constant equal to approximately 3.14.
We are given the diameter of the tank, which is 12 feet.
The radius is half the diameter, so:
r = 12/2 = 6 feet
We are also given the height of the tank, which is 17 feet.
Substituting these values into the formula, we get:
V = πr²h
V = 3.14 × 6² × 17
V ≈ 1814
Therefore,
The volume of the tank is approximately 1814 cubic feet.
Learn more about cylinder here:
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Are Figures A and B congruent? Explain your reasoning.
Answers
Answer:
no bc the two figures need to be exactly the same size
Step-by-step explanation:
What is the value of x in the equation -5/8x=-160
Answers
Answer:
x=256
Step-by-step explanation:
Answer:
x=256
Step-by-step explanation:
50 POINTS FOR CORRECT AWNSER!
Answers
Answer: y > x + 4
Step-by-step explanation:
First lets find a linear equation for the dividing line, in the form:
y = mx + b
We know that b is 4, since this is the y-intercept
lets use any point on the graph, I'll use (-4, 0):
y = mx + 4
0 = m(-4) + 4
-4 = -4m
m = 1
So the slope is 1. Our completed formula for the line is:
y = x + 4
Since the left side of this graph is shaded, we know it will either be > or ≥. Since the line is also dotted we know it is denoted by a simple ">" sign.
So our completed inequality equation is: y > x + 4
Hope this helped!
Answer:
[tex]\sf y > x+4[/tex]
Step-by-step explanation:
Choose 2 points on the line: (-4, 0) and (0, 4)
Let [tex]\sf (x_1,y_1)=(-4,0)[/tex]Let [tex]\sf (x_2,y_2)=(0,4)[/tex][tex]\sf slope=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-0}{0-(-4)}=1[/tex]
point-slope form of linear equation: [tex]\sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-0=1(x-(-4))[/tex]
[tex]\implies \sf y=x+4[/tex]
Solid line : ≤ or ≥
Dashed line: < or >
Therefore as the line is dashed, and the shading is above the line,
[tex]\implies \sf y > x+4[/tex]
A soccer coach plans to order more shirts for her team. Each shirt costs $9.85. She has $77 left in her uniform budget. What are the possible number of shirts she can buy?
Answers
Explanation: divide 77 by 9.85 you get 7.88888 repeating. You can’t have part of a shirt so she can buy 7 shirts.
A soccer coach plans to order more shirts for her team so Each shirt costs $9.85 and She has $77 left in her uniform budget. The possible number of shirts she can buy is 7 shirts.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that A soccer coach plans to order more shirts for her team. Each shirt costs $9.85 and She has $77 left in her uniform budget. WE need to find the possible number of shirts she can buy.
Therefore,
77/9.85 = 7.88888
We an’t have part of a shirt so, she can buy 7 shirts.
Hence, A soccer coach plans to order more shirts for her team so Each shirt costs $9.85 and She has $77 left in her uniform budget. The possible number of shirts she can buy is 7 shirts.
Learn more about the unitary method;
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Please Help Me In Math
Will mark U Brainliest
!!!
#soconfused
Answers
Answer:
[tex]\tt volume=\boxed{6}\: units^3[/tex]
Step-by-step explanation:
[tex]\tt volume=(\frac{9}{2})(\frac{4}{3} )[/tex]
[tex]\tt volume=\frac{36}{6}[/tex]
[tex]\tt volume=6[/tex]
~
Can some help me please
Answers
Answer:
Your answer is 140
Step-by-step explanation:
Rectangle:
16 x 8 = 128
Triangle:
1/2(6 x 4)
1/2(24)
24 / 2 = 12
Add areas:
128 + 12 = 140