Use the definition of absolute value to rewrite each equation or inequality.
[tex]|x| = \begin{cases} x & \text{if } x\ge0 \\ -x & \text{if }x < 0 \end{cases}[/tex]
1. (E) From the definition it follows that
[tex]x-4 \ge 0 \implies |x-4| = x-4 = 8 \implies x = 12[/tex]
[tex]x-4 < 0 \implies |x-4| = -(x-4) = 4-x = 8 \implies x = -4[/tex]
Then the solution set contains exactly 2 elements, and we write it as shown in choice (E), [tex]x\in\{-4,12\}[/tex].
2. (D) We solve the inequality in essentially the same way as in (1), we just need to keep track of the direction of the inequality.
[tex]x-4\ge0 \implies|x-4|=x-4\ge8 \implies x\ge12[/tex]
[tex]x-4<0 \implies|x-4|=4-x\ge8 \implies x\le-4[/tex]
Note the inclusion of [tex]x=12[/tex] and [tex]x=-4[/tex]. We write this as a union of two half-closed intervals, [tex]x\in(-\infty,-4]\cup[12,\infty)[/tex].
3. (C) This follows from the same steps as in (2). This time the inequality is strict, so we exclude the endpoints and with open intervals write [tex]x\in(-\infty,4)\cup(12,\infty)[/tex].
4. (A) Since [tex]|x|[/tex] always returns a non-negative number, any real number [tex]x[/tex] satisfies the inequalty [tex]|x-4|<\infty[/tex]. We write the solution set as the entire real line, [tex]x\in(-\infty,\infty)[/tex].
5. This leaves us with (B) for the last solution set. This inequality is complementary to the one in (3), which means the solution set to [tex]|x-4|\le8[/tex] is the complement of the set we found in (3). That interval removes everything between and including -4 and 12 from the real line. So the solution in this case is what we omit from the solution to (3), and we write [tex]x\in[-4,12][/tex].
larry has 4 pounds of dirt He gives Curly 1 1/3 pounds of dirt and Moe 2 3/5 of dirt. how much dirt does larry have left.
Larry is carrying 4 pounds of dirt. Moe receives 2 3/5 pounds of dirt, and Curly receives 1 1/3 pounds. Larry has 0.07 pounds of dirt.
Given that,
Larry is carrying 4 pounds of dirt. Moe receives 2 3/5 pounds of dirt, and Curly receives 1 1/3 pounds.
We have to find how much dirt does Larry have
Larry =4 pounds of dirt
Larry=4 pound of dirt-Moe receives 2 3/5 pounds of dirt- curly receives 1 1/3 pounds of dirt.
Larry=4-2 3/5-1 1/3
Larry=4-13/5-4/3
Larry=4-2.6-1.33
Larry=4-3.93
Larry=0.07
Therefore, Larry has 0.07 pounds of dirt.
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Lorie ordered a shed to hold her gardening supplies. The shed had a length of 10.25 ft, a width of 14 ft, and a height of seven and one fifth ft.
Determine the volume, V, using the formula V = lwh.
31.45 cubic ft
103.32 cubic ft
983.2 cubic ft
1,033.2 cubic ft
The volume of the shed is 1033.2 cubic feet.
What is volume?Space occupied by an object in three-dimensional space is called as volume of an object. In simple words, space is taken by object.
Given:
Lorie ordered a shed to hold her gardening supplies.
The shed had a length of 10.25 ft, a width of 14 ft, and a height of seven and one fifth ft.
l = 10.25 feet,
w = 14 feet
h = [tex]7\frac{1}{5}[/tex] = 7.2 feet
And we have the formula to calculate volume,
V = lwh
Substituting all the values,
V = 10.25 x 14 x 7.2
V = 1033.2 cubic feet.
Therefore, the volume is 1033.2 cubic feet.
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Stephen has logged 220 minutes of game play today. His dashboard says that today's game time represents 11% of his game
play for the week. How many minutes has he played this week? List your answer as a whole number.
According to the percentage, Stephen played this week is 24.2 minutes.
According to the statement
We have to find that the number of minutes has he played this week.
So, For this purpose, we know that the
A percentage is a number or ratio expressed as a fraction of 100.
From the given information:
Stephen has logged 220 minutes of game play today. His dashboard says that today's game time represents 11% of his game play for the week.
Then
Time of logged of game play = 220 minutes
Today's game time = 11% of his game play
Then
The minutes he played game in a week = 11% of 220 minutes
The minutes he played game in a week = 11/100*220
The minutes he played game in a week = 0.11*220
The minutes he played game in a week = 24.2 minutes.
So, According to the percentage, Stephen played this week is 24.2 minutes.
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The graph of the absolute value parent function, f(x) = |xl, is stretched
horizontally by a factor of 3 to create the graph of g(x). What function is g(x)
Answer:
[tex]y = l \frac{1}{3} xl \\ [/tex]
A chef plans the menu for a particular reception for 322 guests. The appetizer is a 6-ounce serving of tomato juice for each guest. How many 46-ounce cans of tomato juice are ordered for this reception?
The number of 46-ounce cans of tomato juice to be ordered for the reception is 42.
How to find the amount of tomatoes ordered in ounces?A chef plans the menu for a particular reception for 322 guests.
The appetizer is a 6-ounce serving of tomato juice for each guest.
He has 322 guest to cater for.
Each of his guest will get an appetizer of 6 -ounce serving of tomatoes juice.
Therefore,
1 guest = 6 ounce of tomato serving
322 guest = ?
cross multiply
amount of tomato serving required = 322 × 6
amount of tomato serving required = 1932 ounces
Therefore,
the number of 46-ounce cans tomatoes juice ordered = 1932 / 46
the number of 46-ounce cans tomatoes juice ordered = 42
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At the beginning of every soccer practice, Coach Alex has the players warm up and stretch. They do 3 minutes of warm-up exercises for every 2 minutes of stretching.
Answer:
See attached table and graph!
Step-by-step explanation:
Brainly says there was "inappropriate language" in my explanation ( I assure you, there isn't!) So I attached it as an an image below! Hope this helps!
A hawk was 2 feet above the surface of the water. The hawk then flew down 5 feet to catch a fish. How many feet
below the surface of the water was the hawk?
Answer:
3 feet below the surface
Step-by-step explanation:
2 - 5 = -3
a business company distributed bonus to its 24 employees from the net profit of rs 16,48000. if every employee received rs 8,240.what was the bonus percent?
it is called business company
Conner has 4 game card packets and each has 3 cards. If he gives 3 to
Kennedy, what fraction is left?
3/4 1/4 1/2 or 5/4
A rectangular field is 294 yards in length and 340 yards in width. Find the area of the field in ACRES (1 acre = 43,560 square feet). Round to the nearest tenth of an acre
Answer:
20.7 acres
Step-by-step explanation:
A=wl=340·294=99960
convert 99960 yards to acres
Formula
divide the area value by 4840
= 20.7 acres
Please I need to knowing
Answer:
46
Step-by-step explanation:
75 degrees is the entire angle and you need to find out what h is, you need to subtract 29 from 75 and you will get h.
H=46.
En cierta ciudad, el costo del servicio de agua potable es de $ 62.44, y por cada m³ de consumo se paga
$ 6.35, como se muestra en la tabla.
OC) T=7
OD) T= 6.35 +
¿Con cuál expresión algebraica se calcula correctamente el total a pagar (7) a partir del consumo (CJ?
OA) T=6.35 + 62.44C
OB) T-6.35C+ 62.44
C
6.35+62.44
C
Consumo en m³ (C)
C
62.44
0
1
3
5
Total a pagar
en pesos (7)
$62.44
$68.79
$81.49
$94.19
In a certain city, if the cost of availing drinking water service is $62.44, and we have to pay an additional $6.35 for every m³ of water consumed, then the algebraic expression that describes the total to be paid (T) on a consumption of (C) m³ of water will be [T = (6.35C + 62.44)].
As per the question statement, in a certain city, the cost of availing drinking water service is $62.44, and we have to pay an additional $6.35 for every m³ of water consumed.
We are required to determine an algebraic expression that can describe the total amount to be paid (T) for a consumption of (C) m³ of drinking water.
Here, if we suppose that 1 m³ of drinking water is consumed, then total amount to be paid = [tex][(6.35*1)+62.44][/tex]
Similarly, if we suppose that 2 m³ of drinking water is consumed, then total amount to be paid = [tex][(6.35*2)+62.44][/tex]
Thus, on consumption of "C" m³ of drinking water is consumed, total amount to be paid [tex][T=(6.35*C)+62.44][/tex]
[tex]or, [T=(6.35C+62.44)][/tex].
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A phone company offers a monthly data plan for $10 a month plan includes 2 MB of data in charge $.10 per megabyte above the 2 MB of data write a piecewise defined function for MX the cost for X megabytes of data used in a month
Function for MX the cost for X megabytes of data used in a month is -
m(x) = {0.149.8,ifr>2
{10,ifr≤2
What is a function?A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
• Data exceeding 2 MB is charged at a rate of $0.10 per MB; one-time fee is $10;
The cost per month for x MB of data is:
1. Up to 2 Mb of data utilized; $10
2. Data use of over 2 MB
• m(x) = 10+ 0.1(x-2)= 10+ 0.1x 0.2 0.1x + 9.8 m(x) = 0.1x + 9.8
Thus, the function is:
m(x) = = {0.1x+9.8, if r>2
{ 10,ifr≤2
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a cylinder is 9 in tall 5 in in diameter what is the area
The total surface are of the cylinder is approximately 180.64 square inches.
One of the most fundamental curvilinear geometric shapes, a cylinder is a three-dimensional solid. It has been regarded geometrically as a prism whose base is a circle.
The properties of a cylinder with radius r and height h are:
The total surface area is 2πr(r+h)The curved surface is 2πrhThe volume of a cylinder is given by πr²hGiven dimension of the cylinder are:
Diameter=5 inches and height=9inches
We know that radius=diameter/2
Therefore radius of the cylinder is 5/2=2.5 inches
Now the total surface are of the cylinder
=2πr(r+h)
=2π×2.5×(2.5+9)
=2π×28.75
=57.5π square inches
=180.6415...
≈180.64 square inches
The total surface area of the cylinder is approximately 180.64 square inches.
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9y - 2 < 13 and 3y - > -29
Hence , the shading of the linear inequalities 9y - 2 < 13 and 3y - > -29 is given below.
An difference compares 2 values, showing if one is a smaller amount than, larger than, or just not adequate another worth.a ≠ b says that a isn't adequate ba < b says that a is a smaller amount than ba > b says that a is larger than bIn math, a graph may be outlined as a picturing or a diagram that represents knowledge or values in AN organized manner.The graph of the equation 9y - 2 < 13 equation (1) is represented by green colour and graph of the equation 3y - > -29 equation (2) is represented by yellow colour .
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The complete question is given below :
Shade the graph of 9y - 2 < 13 and 3y - > -29 .
A wireless keyboard is 10/12 foot long. The area of the wireless keyboard is 5/24 square foot. What is the width of the wireless keyboard, in feet? Enter the answer as a fraction in lowest
Answer:
1/4 ft
Step-by-step explanation:
A = l x w
5/24 = 10/12 x w
Solve for w
5/24 divided by 10/12 = w
Take inverse of 10/12 and multiply
5/24 times 12/10
1/4
The sum of two numbers is 88. If one number is 4 more than half the other number, determine the two numbers by setting up a linear equation.
a: 44
b: 56
c: 61.3
d: 126
e: 138
f: 176
Answer:
b: 56
Step-by-step explanation:
x + y = 88
x is 4 more than half the other number.
half of y is 1/2y
4 more than that is 1/2y + 4
substitute
1/2y + 4 + y = 88
solve for y
3/2y = 84
y = 168 / 3 = 56
solve for x
x = 88 - 56 = 32
not sure where you would answer 32 from what's given :)
The total arm and blade of a windshield wiper is 15 in. long and rotates back and forth through an angle of 98°. The shaded region in the figure is the portion of the windshield cleaned by the 10-in. wiper blade. What is the area of the region cleaned?
The area of the portion of the windshield cleaned by the 10-in wiper blade is 106.85in² .
We have been provided that the Length of blade is 15 inches and the Angle of rotation = 98°
We are required to calculate the area of the portion of the windshield cleaned by the 10-in wiper blade.
We have to solve this by using area of a sector.
Area of a sector = ½r²θ
where θ is in radians.
So, angle of rotation (98°) must first be converted to radians
Converting 98º to radians, we get
98×π/180 = 49π/90
The area of the region swept out by the wiper blade
= (area of the sector where r = 15 and θ = 49π/90) - (area of the sector where r = (15-10) and θ = 49π/90).
So, Area = ½×15²×49π/0 - ½×5²×49π/90
= ½×49π/90(15²-10²)
= 49π/180× (225 - 100)
= 49π/180 × 125
= 1225π/36
Area = 106.8472in²
=106.85 in²
Hence, the area of the portion of the windshield cleaned by the 10-in wiper blade is 106.85in²
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please help
please hury
Answer:
(2,4)
Step-by-step explanation:
The range is the second number of each set. Take all of those and you get 2,4,2,4. You only need one of each number so you end up with (2,4).
HELP ILL MARK AS BRAINLIEST
Which division problem does the model below show?
Answer: should be C
Step-by-step explanation:
I need the answer for the bottom question please let me know what it is and how to do these type of questions
Answer:
Step-by-step explanation:
x -> +1 ->×2
Write 7 thousand, 80 tens, 9 ones in standard form.
Answer:
7089
Step-by-step explanation: Hope it helped have a good day!
Solce by quadratic formular 5x^2+3_2=0
Answer:
(5x-2)(x+1)
means that x = -1 or x =[tex] \frac{2 }{5} [/tex]
Step-by-step explanation:
the quadratic formula is
[tex] \frac{ -b ± \sqrt{(b)^{2} - 4ac } }{2a} [/tex]
where a = 5
b = 3
c = -2
substitute with the equation above this gives you the answer
hope this helps
Francis bought 5 holiday gifts that were between $42 and $87. What is a reasonable amount that he paid for the items?
Answer:
322.5$Step-by-step explanation:
Francis bought 5 holiday gifts that were between $42 and $87. What is a reasonable amount that he paid for the items?
we find the average between 42 and 87 and multiply by 5
[(42 + 87) : 2] * 5 =
(129 : 2 ) * 5 =
64.5 * 5 = 322.5$
3422 divided by 12. What would the decimal turned into a fraction?
When 3,422 is divided by 12, the decimal that remains when converted to fraction form is 1 / 6
What is the decimal remaining?First, divide 3,422 by 12 to find the result.
Dividing 3,422 by 12 gives:
= 3,422 / 12
= 285.16667
You need to convert 0.16667 to a fraction. When done, this is:
= 16,667 / 100,000
= 2 / 12
= 1 / 6
In conclusion, the decimal when turned to a fraction is 1/6.
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NEED HELP ASAP DUE TODAY 10 POINTSSSS
Answer the following question for the expression.
5x - 3y + 7z + 1.
A) How many terms does this expression have?
_____________________________________
B) What is the constant of this expression?
_____________________________________
C) What is the second term in the expression?
_____________________________________
D) Whats the coefficient of the third term?
_____________________________________
A. 4 terms
B. 1
C. -3y
D. 7
hope you get a good grade
.Tim weighs twice as much as Jim. Jim weighs 50 pounds less than
George. Rick weighs 10 pounds more than George. If Rick weighs 200 pounds, how
much does Tim weigh?
Answer: Tim weighs 280 pounds
Step-by-step explanation:
Rick weighs 200 pounds
George weighs (200-10)=190 pounds
Jim weighs (190-50)=140 pounds
Tim weighs 140*2=280 pounds
What is the area, in square meters, of the trapezoid below?
14.6 m
5.2 m
7m
The area, in square meters, of the trapezoid is 56.16 m²
A trapezoid with height 5.2m and parallel base is 14.6m and 7m.
We have to find the area of area of this trapezoid.
Area of trapezoid = 1/2(sum of parallel sides)(height)
= 1/2(14.6+7)(5.2)
= 1/2(21.6)(5.2)
= 1/2(112.32)
= 56.16 m²
A quadrilateral with as a minimum one pair of parallel aspects is known as, in American and Canadian English, a trapezoid (/ˈtræpəzɔɪd/). In British and other forms of English, a (North American) trapezoid is known as a trapezium (/trəˈpiːziəm/). The transposition of these two terms become a result of an blunders in Charles Hutton's mathematical dictionary.
A trapezoid is always a convex quadrilateral in Euclidean geometry. The parallel aspects are known as the bases of the trapezoid. the opposite facets are known as the legs (or the lateral aspects) if they're no longer parallel; otherwise, the trapezoid is a parallelogram, and there are pairs of bases)
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Write the equation of the horizontal line and the vertical line that passes through point (13,−13).
The equation of the horizontal line through point (13,−13) is
.
Question 2
The equation of the vertical line through point (13,−13) is
Equation of the horizontal line through the given point is: y = -13.
Equation of the vertical line through the given point is: x = 13.
What is the Equation of a Horizontal Line and a Vertical Line?The equation of a vertical line is expressed as, x = b, where b is the constant representing the point where the line intercepts the x-axis. The line is parallel to the y-axis.
On the other hand, the horizontal line intersects the y-axis at a point, b, and it is parallel to the x-axis. It is written as y = b.
Given the point, (13, -13), we have the following:
Equation of the horizontal line through the given point is: y = -13.
Equation of the vertical line through the given point is: x = 13.
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What is the area of the circle? (Pic below)
The area of the circle is 254. 502 square units
How to determine the area
The formula for area of a circle is expressed as;
Area = πr²
Where;
r is the radius of a circle
Note that the radius of a circle with an inscribed triangle is expressed as;
Radius = ABC/4A
Where;
A, B and C are the sides of the inscribed triangle
Radius = 6 × 6 × 6 / 4(6)
Radius = 216/ 24
Radius = 9 units
Now, substitute the value of the radius into the formula
Area = 3. 142 × (9)²
Area = 3. 142 × 81
Area = 254. 502 square units
Thus, the area of the circle is 254. 502 square units
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