Answers
Answer:
C
Step-by-step explanation:
The absolute value function always returns a positive value
However, the expression inside the bars can be positive or negative
| 3 | = 3 and | - 3 | = 3, hence the solution of
| x | = 3 is x = ± 3
Extending this to
| x² - 4 | = 3, then
| x² - 4 | = 3 and | - (x² - 4) | = 3
x² - 4 = 3 ; - (x² - 4) = 3 → C
Answer:
C
Step-by-step explanation:
[tex]|x^2-4|=3[/tex]
Before we say what this implies, we need to know that |-1|=1 and |1|=1.
So what I'm saying is:
[tex]|-(x^2-4)|=|-1 \cdot (x^2-4)|=|-1| \cdot |x^2-4|[/tex]
[tex]=|x^2-4|[/tex].
So [tex]|x^2-4|=3[/tex] implies:
[tex](x^2-4)=3[/tex] or [tex]-(x^2-4)=3[/tex].
Related Questions
which of the following is the quotient of the rational expressions shown below 2x/4x+3 divided x-1/2x
Answers
Answer:
4x^2/4x^2-x-3
Step-by-step explanation:
boomchakalaka
The quotient is 4x²/4x²-x-3.
What's known as a quotient?
In mathematics, a quotient is a quantity produced with the aid of the department of numbers.
How do you discover a quotient?The quotient is the solution acquired whilst we divide one range by using every other. for example, if we divide the quantity 4 by means of 2, we get the end result as 2, that's the quotient.
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5) A banker learned that $842.40 is withheld from his monthly check for taxes and insurance. If
this represents 18% of his total pay, find the total pay.
Answers
Since 18% is 18/100 you just have to multiply the $842.4 by the reciprocal of that to find your answer
Reciprocal of 18/100 is 100/18
842.4* 100/18 equals 84240/18
84240/18 equals 4680
What is the domain of the function y=^3 sqrt x-1
Answers
Answer:
Domain is all real numbers also known as [tex](-\infty,\infty)[/tex] in interval notation.
[tex]f(x)=\sqrt[3]{x-1}[/tex]?
Step-by-step explanation:
If your function is [tex]f(x)=\sqrt[3]{x-1}[/tex] then the domain is all real numbers because you can cube root any real number.
If x is a real number, then x-1 is a real number.
So if you cube root (x-1) for any x then you still get a real number back.
Now if it was a square root, that is when we can run into some problems.
Answer: -infinity and positive infinity
Step-by-step explanation: It's either a on your test or two zero's that look twisted :)
A triangle has two sides of lengths 7 and 9. What value could the length of the third side be?
Answers
Answer:
The length of the third side could be all real numbers greater than 2 units and less than 16 units
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
so
Applying the triangle inequality theorem
Let
x ------> the length of the third side
we have
First case
1) 7+9 > x
16 > x
Rewrite
x< 16 units
Second case
2) 7+x > 9
x > 9-7
x > 2 units
therefore
The solution for the third side is the interval
(2,16)
All real numbers greater than 2 units and less than 16 units
There are 10 pennies, 14 nickels, and 6 dimes in a bag, and you remove three at random without replacing any. What is the probability that you will remove a penny, a nickel, and a dime in that order?
1. 1/29
2. 1/10
3. 1/30
4. 1/812
Answers
Answer:
1/30
Step-by-step explanation:
Given the diagram below, which of the following ordered pairs represents the
vertex, A?
A. (b cos C,c sin C)
B. (a cos B, a sin B)
C. (a cos C, b sin C)
D. (b cos c, b sin c)
Answers
Andy was playing a memory game with his sister. He turned over a tile to reveal a picture of the sun at the coordinates (5, 4). He looked under a tile that was 3 units to the left and 2 units down but revealed a picture of a tree. His sister knew that the other sun was 1 unit to the left and 1 unit up from the tree. What are the coordinates of the second sun? (JUSTIFY)
Answers
Answer:
(1, 3).
Step-by-step explanation:
The tree tiles coordinates are x = 5-3 = 2 and the y coordinate = 4 - 2 = 2
- that is (2, 2).
So the coordinates of the second sun are (2-1, 2 + 1)
= (1. 3).
What is the order of rotational symmetry for the figure
Answers
Answer:
Order of symmetry = 1
Step-by-step explanation:
First of all we will define rotational symmetry.
Rotational symmetry is when a shape looks the same after some rotation or less than one rotation.
The order of rotational symmetry is how many times it matches the original shape during the rotation.
The given shape, when rotated will only have the shape like original shape after one complete rotation so the order of symmetry is one ..
What is the rule for the reflection?
Answers
This image is being reflected over the y-axis. When reflecting over the y-axis the y-coordinate will stay the same, but the x-coordinate will have the opposite sign. Here is the rule for this reflection:
(-x, y)
Hope this helped!
~Just a girl in love with Shawn Mendes
A boy is flying a kite. The length of the string is 61 meters and the
horizontal distance between the boy and the kite is 60 meters. Assuming
there is no slack in the string, find the height of the kite from the ground.
Answers
Answer:
11 meters
Step-by-step explanation:
Using the Pythagorean Theorem
a^2 + b^2 = c^2
a^2 + 60^2 = 61^2
a^2 + 3600 = 3721 (subtract 3600 from both sides)
a^2 = 121 (square root both sides so a^2 becomes a)
a = 11
Answer:
11 meters.Step-by-step explanation:
This problem models a right rectangle, where the hypothenuse is the length of the string, and the legs are the height and the horizontal distance. So, to find the answer, we just have to use the pythagorean theorem
[tex]a^{2}=b^{2}+c^{2}[/tex]
Where
[tex]a=61;b=60;c=x[/tex]
Replacing and solving for [tex]x[/tex], which is the height
[tex]a^{2}=b^{2}+c^{2}\\61^{2}=60^{2}+x^{2} \\x^{2}=61^{2}-60^{2}\\x=\sqrt{3721-3600}=\sqrt{121}=11[/tex]
Therefore, assuming there is no slack in the string, the height of the kite from the ground is 11 meters.
On Monday, Florencia's hair was h centimeters long. She got a haircut on Tuesday, so her hair was only 75%, percent of the length it was on Monday.
Which of the following expressions could represent how many centimeters long Florencia's hair was after the haircut?
Choose 2 answers
Answers
y=x-.25x
Don’t know what the answer choices are but these could be possible answers
Answer:
.75
Step-by-step explanation:
What is the absolute value of 9? -3?
Show your work
Answers
Answer:
|9| = 9|-3| = 3Step-by-step explanation:
The absolute value of number a:
|a| = a for a ≥ 0
|a| = -a for a < 0
|9| = 9
|-3| = -(-3) = 3
7. Select True or False for each statement.
A. The ordered pair (2, -5.2) is located in Quadrant IV.
B. Quadrant Il contains ordered pairs of the form
(positive number, negative number)
C. The point (-6, 0) is located on the y-axis
D. The origin is located in Quadrant |
E. To plot points in Quadrant III, move left and down
From the origin.
Answers
B. False
C. False
D. False
E. True
B. Quadrant II contains ordered pairs of the form (negative number, positive number)
C. (-6,0) is located on the x-axis
D. The origin is not located on any of the quadrant. It’s in the center
The answer addresses the true or false nature of five statements about the properties of coordinate pairs in a two-dimensional graph with respect to their quadrants, and the location of specific points on the coordinate plane.
The coordinates (x, y) indicate the position of a point on a two-dimensional graph in relation to the origin, which is at (0, 0). In a standard coordinate system, Quadrant I has both x and y as positive, Quadrant II has x as negative and y as positive, Quadrant III has both x and y as negative, and Quadrant IV has x as positive and y as negative.
A. False - The ordered pair (2, -5.2) is located in Quadrant IV, which is incorrect since Quadrant IV should have x as positive and y as negative, which is actually the case here, so the statement should be True.B. False - Quadrant II contains ordered pairs of the form (negative number, positive number), not positive x and negative y.C. True - The point (-6, 0) located on the x-axis, not the y-axis, since the y-coordinate is zero.D. False - The origin (0, 0) is not located in any quadrant as it is the point of intersection of all the quadrants.E. True - To plot points in Quadrant III, one indeed moves left (negative x direction) and down (negative y direction) from the origin.i need help please can someone help
Answers
Answer:
x = 8Step-by-step explanation:
[tex]\sqrt{\dfrac{896z^{15}}{225z^6}}=\dfrac{xz^4}{15}\sqrt{14z}\\\\\sqrt{\dfrac{896z^{15}}{225z^6}}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=\sqrt{\dfrac{(64)(14)z^{15-6}}{225}}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b},\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}\\\\=\dfrac{\sqrt{64}\cdot\sqrt{14}\cdot\sqrt{z^9}}{\sqrt{225}}=\dfrac{8\cdot\sqrt{14}\cdot\sqrt{z^{8+1}}}{15}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=\dfrac{8\sqrt{14}\cdot\sqrt{z^8z}}{15}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}[/tex]
[tex]=\dfrac{8\sqrt{14}\cdot\sqrt{z^8}\cdot\sqrt{z}}{15}=\dfrac{8\sqrt{14}\cdot\sqrt{z^{4\cdot2}}\cdot\sqrt{z}}{15}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\dfrac{8\sqrt{14}\cdot\sqrt{(z^4)^2}\cdot\sqrt{z}}{15}\qquad\text{use}\ (\sqrt{a})^2=a\\\\=\dfrac{8\sqrt{14}\cdot z^4\cdot\sqrt{z}}{15}=\dfrac{8z^4\sqrt{14}\cdot\sqrt{z}}{15}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{8z^4\sqrt{14z}}{15}[/tex]
[tex]\dfrac{8z^4\sqrt{14z}}{15}=\dfrac{xz^4\sqrt{14z}}{15}\iff x=8[/tex]
A number cube has 6 faces, numbered from 1 to 6. If the cube
is rolled six times, what is the probability that a face with a 6
comes up exactly once?
Answers
[tex]|\Omega|=6^6\\|A|=6\cdot 5^5\\\\P(A)=\dfrac{6\cdot5^5}{6^6}=\dfrac{5^5}{6^5}=\dfrac{3125}{7776}\approx40.2\%[/tex]
The probability that a face with a 6 comes up exactly once will be 0.40.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
A number cube has 6 faces, numbered from 1 to 6.
If the cube is rolled six times.
Then the probability that a face with a 6 comes up exactly once will be
The total number of the event will be
Total event = 6⁶
Total event = 46656
Favorable event = 6 x 5⁵
Favorable event = 18750
Then the probability will be
P = 18750 / 46656
P = 3125 / 7776
P = 0.40
More about the probability link is given below.
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A_____ is invested by Managers in a diversity of stocks bonds and other securities
Answers
Answer:
Step-by-step explanation:
A Mutual Fund is invested by Managers in a diversity of stocks bonds and other securities.
A mutual fund is a type of investment in which investors pool their money together to buy a portfolio of stocks, bonds or other securities in order to take advantage of diversification and professional portfolio management at a reasonable cost. It is operated by money managers, who invest the fund capital on the investors behalf. Investing in mutual funds enables those investing a modest amount of money to benefit from the same advantages enjoyed by large institutional investors....
Find the value of y for the following system of equations. -x - y = 7 x - y = 9
Answers
Answer:
y = -8
Step-by-step explanation:
It is given that,
-x - y = 7 ---(1)
x - y = 9 ---(2)
To find the solution
Add eq (1) and eq(2) we get
-x - y = 7 ---(1)
x - y = 9 ---(2)
0 - 2y = 16
y = 16/(-2) = -8
Substitute the value of y in eq(1)
-x - y = 7 ---(1)
-x - -8 = 7
-x + 8 = 7
x = 8 - 7 = 1
Therefore x = 1 and y = -8
Find the next two terms in the sequence.
0, 1, 4, 9, ...
oo o
16, 25
13, 17
o
13, 18
o
16, 23
Answers
0,1,4,9
0+1= 1
1+3= 4
4+5= 9
Add the numbers by using an odd number each time.
9+7= 16
16+9= 25
Answer is 16, 25 ( first choice):
0, 1, 4, 9, 16, 25
Which of the following is equivalent to the expression below?
√(-300)
A. -10i √(3)
B. -3i √(10)
C. 3i √(10)
D. 10i √(3)
Answers
The square root of 100 is 10
The square root of -1 is i
sqrt(300)
=sqrt(100)*sqrt(3)*sqrt(-1)
=10*sqrt(3)*i
Order of multiplication doesn't matter
Answer D
btw you accidentally uploaded a selfie xD
Answer:
D. 10i √(3)
Step-by-step explanation:
√(-300)
We know sqrt (ab) = sqrt(a) sqrt(b)
sqrt(-300) = sqrt(-3) sqrt(100)
= sqrt(-1) sqrt(3) sqrt(100)
The sqrt(-1) =the imaginary number 1 and sqrt(100) =10
= i * sqrt(3) * 10
=10i sqrt(3)
what is the sum of the polynomials (-x^2+9)+(3x^2-11x+4)
Answers
The answer is:
[tex](-x^{2}+9)+(3x^2-11x+4)=2x^{2}-11x+13[/tex]
Why?To solve the problem, we must remember how to add/subtract like terms. The like terms are the terms that share the same variable and the same exponent.
For example:
[tex]2x+3x+x^{2}=x^{2}+(2x+3x)=x^{2}+5x[/tex]
We were able to add only the linear terms (terms that contains the variable x") because they were like terms: they share the same variable and the same exponent.
We need to perform the following operation between polynomials:
[tex](-x^{2}+9)+(3x^2-11x+4)[/tex]
So, calculating we have:
[tex](-x^{2}+9)+(3x^2-11x+4)=2x^{2}-11x+13[/tex]
Have a nice day!
What is the distance between the points (2,-3) and (-6,4) on the coordinate plane?
Answers
d = sqrt (2-(-6))² + (-3-4)²)
d = sqrt ( 8² + 7² )
d = sqrt ( 64 + 49 )
d = sqrt (113)
Answer: The distance between the two points is roughly 10,63:
B)
The distance between the points (2,-3) and (-6,4) on the coordinate plane is 10.63 units. This can be obtained by using the distance formula.
What is the distance formula ?
The distance between two points (x₁,y₁) and (x₂,y₂) is
d = [tex]\sqrt{{(x_{2}-x_{1} )}^{2} + (y_{2}-y_{1} )^{2}[/tex]
In the given question, (x₁,y₁) is (2,-3) and (x₂,y₂) is (-6,4),
the distance d = [tex]\sqrt{{(x_{2}-x_{1} )}^{2} + (y_{2}-y_{1} )^{2}[/tex]
=[tex]\sqrt{{((-6)-2 )}^{2} + (4-(-3) )^{2}[/tex]
=[tex]\sqrt{{(-8)}^{2} + (7 )^{2}[/tex]
= [tex]\sqrt{{64 + 49[/tex]
=√113 =10.63 units
Hence the distance between the points (2,-3) and (-6,4) on the coordinate plane is 10.63 units. Thus option B is correct.
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what are natural number less than 5
Answers
Answer:
Natural numbers = {1,2,3,4,5…} Answer 1: A is the set of Natural numbers between 1 and 5 inclusive. Answer 2: A is the set of Natural numbers less than 6.
Step-by-step explanation:
Answer:
n = 1, 2, 3, 4
Step-by-step explanation:
Natural numbers are any integers (whole numbers) that are positive.
In this case, all natural number (n) is less than (<) 5
n < 5 is your equality, but in reality it looks like: 0 < n < 5
The numbers that can fit into your problem is n = 1 , 2, 3, 4
n = 1, 2, 3, 4 is your answer.
~
Look at the figure. Find TW
Answers
Answer: NUMBER 9 I'm on gradpoint too
Step-by-step explanation:
12. A fruit basket contains oranges and grapefruits. One-third of the orange
and one-fourth of the grapefruits were spoiled. You threw away 4 oranges
and 7 grapefruits. How many pieces of fruit were in the basket?
Answers
Answer:
There were 12 + 28 = 40 pieces of fruit in the basket.
Step-by-step explanation:
Suppose there were x oranges and y grapefruit.
Then we have
1 /3 x = 4
x = 4*3 = 12.
1/4 y = 7
y = 7*4 = 28.
Elise picks 6 pounds of apples.She uses 1/2 pounds to make 1 container of apple sauce. How many containers of applesauce can Elise make with all apples?
Answers
Answer:
12
Step-by-step explanation:
Mass of apples = number of containers × mass in each container
6 lb = No of containers × ½ lb
No of containers = 6/½
To divide a whole number by a fraction, invert the fraction and change divide to multiply.
6/½ = 6 × 2/1
Multiply the numerator by the whole number.
6 × 2/1 = 12/1
Simplify the fraction.
12/1 = 12
Elise can make 12 containers of applesauce.
Complete the solution of the equation. Find the value of y when x equals 1. 9x+7y=-12
Answers
Hey there! :)
Find the value of y when x=1 : 9x + 7y = -12
To find the value of y, simply plug in 1 for x in our given equation.
9(1) + 7y = -12
Simplify!
9 + 7y = -12
Subtract 9 from both sides so that we can isolate y.
7y = -12 - 9
Simplify.
7y = -21
Now, divide both sides by 7 to fully isolate y.
7y ÷ 7 = -21 ÷ 7
Simplify!
y = -3
~hope I helped!~
CraftWork rents a storage space that measures 200 ft x 300 ft x 30 ft.
CraftWork pays $1500 for the storage space each month. What is the cost
per cubic foot?
O
A. $0.008
O B. $0.0002
O C. $0.0015
O D. 50.00083
Answers
Answer:
0.00083
Step-by-step explanation:
200*300*30=1800000
1500/1800000=0.00083
The cost per cubic foot of the storage space is approximately $0.00083 per cubic foot. Hence the correct option is D.
To find the cost per cubic foot of the storage space, we need to calculate the total cubic footage of the space and then divide the monthly cost by that number. The storage space measures 200 ft x 300 ft x 30 ft, so the total volume is:
Total Volume = length times width times height
= 200 ft x 300 ft x 30 ft
= 1,800,000 cubic feet
Now, we calculate the cost per cubic foot:
Cost Per Cubic Foot = Total Monthly Cost / Total Volume
= $1500 / 1,800,000 cubic feet
= $0.00083 per cubic foot (rounded to five decimal places).
Here is the histogram of a data distribution.
Which best describes the shape of this distribution?
Answers
Answer:
B. Unimodal-Skewed
Step-by-step explanation:
A distribution is called unimodal if it has only one hump in the histogram.
A symmetric distribution is equally divided on both sides of the highest hump.
The given histogram has only one hump at 4 and as it is not symmetrically distributed, it is skewed.
So the correct answer is:
B. Unimodal-Skewed ..
Answer:
B. Unimodal Skewed
Step-by-step explanation:
The Histogram given in figure has one peak and it is skewed to the right So, it is Right Skewed Unimodal Histogram.
Moreover, Unimodal means the distribution has one peak, Skewed means this peak is present in either the left or right side of the center of the distribution.
Option A is incorrect because the given histogram is not symmetric, it is skewed distribution.
Option C can't be taken because uniform means the size of bars is approximately same for the given distribution.
Options D & E is not correct because the given distribution is not Bimodal it has only one peak.
Graph the linear equations in three points: -x-2y=-10
Answers
Answer:
Step-by-step explanation:
Rewrite -x-2y= -10 as -2y= x - 10 and then as y = (-1/2)x + 5.
Then choose any 3 x values and find the corresponding y values using this formula. For example:
x y = (-1/2)x + 5 (x, y)
----- -------------------- ---------
0 5 (0, 5)
-4 (-1/2)(-4) + 5 = 7 (-4, 7)
6 (-1/2)(6) + 5 = 2 (6, 2)
Plot these three points and then draw a line through them.
Answer:
0,5 2,6 4,7
Step-by-step explanation:
You have to solve the equation by keeping y on its own. The equation is
y=-1/2x-5
Coordinates are:
0,5 2,6 4,7
If a rectangle's length is y−2 and the width is 3y+2 write an expression for the perimeter and an expression for the area.
Answers
Answer:
Area = [tex]3y^2 - 4y - 4[/tex] units square.
Perimeter = 8y units.
Step-by-step explanation:
Area of a rectangle = length * width.
Perimeter of a rectangle = 2*(length + width).
It is given that length = y−2 units and width = 3y+2 units. To find the area and the area of the rectangle in terms of y, simply put the length and the width in the above area and perimeter equations.
Area = length * width = (y-2)*(3y+2).
Expanding the expression gives:
Area = 3y^2 + 2y - 6y - 4 = (3y^2 -4y - 4) units square.
Similarly,
Perimeter = 2*(length + width) = 2*(y-2 + 3y+2) = 2*4y = 8y units.
Therefore, the expression for the area and the perimeter of the given rectangle is ([tex]3y^2 - 4y - 4[/tex]) units square and (8y) units respectively!!!