|1/4 x +2| -3 =5 solve for x and graph on number line
Answers
The value of x on the number line is 24 and - 40
A number line in elementary mathematics is a representation of a graduated straight line that acts as an abstraction for real numbers, represented by the letter R. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
When seen as a geometric space, namely the one-dimensional Euclidean space, the number line, also known as a real line in advanced mathematics, is technically defined as the set R of all real numbers. It can be conceptualized as a linear continuum, metric space, topological space, vector space (or affine space), measure space, or topological space.
The given equation is
[tex]|\frac{1}{4}x+2 | -3=5[/tex]
Solving the equation:
[tex]or,|\frac{1}{4}x+2 | =5+3\\or,|\frac{1}{4}x+2 |=8\\or,\frac{1}{4}x+2=\pm8\\or,x+8=\pm32\\or,x=-8\pm32[/tex]
Now we take the two separate values of x:
either x=-8+32 or x=-8-32
or,x=24 or x=-40
The value of x is 24 and - 40.
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Related Questions
A store had apples on sale for $1.10 a pound. Mike spent $5.94 on apples. How many pounds did buy?
Answers
Answer:
5.4 lbs
Step-by-step explanation:
5.94 / 1.10 = 5.4
hope this helps! <3
Qin Corp. Issued 10-year bonds 2 years ago at a coupon rate of 9 percent. The bonds
make semiannual payments. If these bonds currently sell for 102 percent of par value,
what is the YTM? (Do not round Intermediate calculations and enter your answer as a
percent rounded to 2 decimal places, e.g., 32.16.)
Answers
In linear equation , 8.65% is the YTM .
What is a formula for linear equations?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.Assuming face value to be $1000
Coupon = (0.09 * 1000) / 2 = 45
Number of periods = 8 * 2 = 16
Price = 102% of 1000 = 1020
YTM = 8.65%
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reflection across the y-axis
Please I need help ASP
Answers
Answer:
See the picture below.
Step-by-step explanation:
HELP WITH MATH QUETSION PLEASE I WILL GIVE BRAINLYEST The first 5 terms arithmetic sequence are shown on the graph.
a. describe the sequence in words.
b. what is the value of the 6th term?
c. write an explicit formula to find the nth term of the sequence.
Answers
The sequence is an AP with a = 11 and d = - 4 , 6th term is - 9 and formula is a + ( n - 1 ) d .
First Term = 11
Second Term = 7
Third Te3rm = 3
Fourth Term = - 1
Fifth Term = - 5
a ) Sequence is 11 , 7 , 3 , - 1 , - 5
b ) a + ( n - 1 ) d
11 + ( 6 - 1 ) ( - 4 )
11 + 5 ( - 4 )
11 - 20 = - 9
c ) a + ( n - 1 ) d
where a is the first term , n is the tem no . and d is the common difference of an AP .
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What is the image of image of the point (-7,-3) after a rotation of 180 degrees counterclockwise
PLEASE
Answers
The image of image of the point [tex](-7,-3)[/tex] after a rotation of [tex]180[/tex] degrees counterclockwise is [tex](7,3)[/tex]
According to the question statement, point [tex](-7,-3)[/tex] is rotated by [tex]180[/tex] degrees counterclockwise, we are supposed to find out the image of the point after the rotation.
Point [tex](-7,-3)[/tex] lies in the Third quadrant of the Cartesian Plane.
When it will be rotated by [tex]180[/tex] degrees counterclockwise, it will shift to the first quadrant of the Cartesian Plane.
Therefore the coordinates will become as [tex](7,3)[/tex].
Cartesian Plane: The cartesian plane is defined as a two-dimensional coordinate plane that is made or formed by the intersection of the x-axis and y-axis or horizontal and vertical axes.To learn more about coordinates and plane, click on the link given below:
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=
Find the exact value of the expression. Do not use a calculator.
sin 26° - cos 64°
sin 26° - cos 64° =
=
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
Answers
The value of the expression is 0 without calculation.
We have to find the exact value of
sin 26° - cos 26°
From the trigonometric function we know that:
cos (90°-Ф) = sinФ and,
sin(90° -Ф) = cosФ
By this, we have an expression that,
=sin 26° - cos 64°
=sin 26° - cos (90° - 26)
=sin 26° - sin 26°
=0
Therefore the value of sin 26° - cos 64° =0.
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Rewrite (10 + 6) + 5+ 3 using the Associative Law of Addition,
O 10+6+5+3
O 10+(6+5) + 3
O 3+5+ (10+6)
O (10+6) + 3+5
Answers
Rewriting (10 + 6) + 5+ 3 using the Associative Law of Addition will be 3+5+ (10+6).
How to compute the value?It should be noted that the Associative Law of Addition explains that a + (b + c) is the same as (a + b) + c.
Therefore, Rewriting (10 + 6) + 5+ 3 using the Associative Law of Addition will be 3+5+ (10+6).
It should be noted that this will still give same value.
Therefore, the correct option is B.
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In a survey of 720 human resource professionals, each was asked about the importance of the education of a job applicant. The survey subjects were randomly selected by pollsters from a reputable market research firm.
Answers
It seems to be reasonable so because survey data is unbiased.
What is defined as the unbiased survey data?An unbiased sample is one in which every individual or element in the population does have an equal chance of being chosen.
A sample assessment of a population parameter for whom sampling distribution does have a mean equal to the parameter of been estimated is an unbiased statistic. Some traditional statistics provide unbiased estimates of their associated parameters, while others do not. The sample mean is the most basic example of an unbiased statistic. The sample mean is normally distributed with a mean equal to the population mean under the usual assumptions of population normality and simple random sampling with a mean equal to the population mean and a standard deviation equal to the population variance divided by the square root of the sample size.As, for the given question, the 720 human resource professionals survey is done considering each individual equal weight age for all.
A population proportion is also a unbiased estimate of a sample proportion.
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pedro wants to make 3 1/2 batches of granola bars. His dad tells him that he needs 5 1/4 cup of oatmeal. How much oatmeal does pedro need for a single batch
Answers
Answer:
If he needs 5 1/4 cups for 3 1/2 batches then he needs 1 1/2 cups for a single batch.
Write the equation of the line in fully simplified slope-intercept form
Answers
Answer:
y = 3x - 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (1, - 4) ← 2 points on the line
m = [tex]\frac{-4-2}{1-3}[/tex] = [tex]\frac{-6}{-2}[/tex] = 3
the line crosses the y- axis at (0, - 7 ) ⇒ c = - 7
y = 3x - 7 ← equation of line
What is the radius of a circle with a circumference of 64 feet?
Answers
10.19 feet is the radius of a circle with a circumference of 64 feet.
A line that is bent such that its ends meet and all of its points are equally spaced from the middle. We gathered in a circle around the hearth. Something shaped like or like a circle.
Dimensional terms include circumference, diameter, radius, chord, segment, tangent, point of contact, arc, angles on major and minor arcs, angle of center, and sectors. A circle's circumference is the distance that surrounds it.
A curving line makes up the shape of a circle. It is spherical, and every point along the curved line is equally spaced from the center. Due to its two-dimensional nature, this shape is flat.
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A toy ball in the shape of a sphere expands and contracts. When it is completely closed, it has a diameter of 20.5 inches. Find the volume of the sphere when it is completely closed. Use 3.14 for π.
Answers
The volume of the sphere when it is completely closed is 4508.58 cubic inches
Volume of a sphereThe formula for calculating the volume of a sphere is expressed as:
V = 4/3πr³
where
r is the radius = 20.5/2
radius = 10.25 in
Substitute
V = 4/3 (3.14)*10.25³
V = 4/3(3.14)
V =4508.58 cubic inches
Hence the volume of the sphere when it is completely closed is 4508.58 cubic inches
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The midpoint of \overline{\text{AB}}
AB
is M(5, 6)M(5,6). If the coordinates of AA are (3, 8)(3,8), what are the coordinates of BB?
Answers
=================================================
Explanation:
Point B is at the location (x, y)
The x coordinates of A and B are 3 and x respectively. Add them up, divide in half, and set the result equal to the x coordinate of M which is 5
(3+x)/2 = 5
3+x = 2*5
3+x = 10
x = 10-3
x = 7 which is the x coordinate of point B
Repeat this same idea for the y coordinates.
(8+y)/2 = 6
8+y = 2*6
8+y = 12
y = 12-8
y = 4
Therefore, point B is located at (x,y) = (7, 4)
Visual verification is shown below. You could also use the midpoint formula on segment AB to find that M = (5,6) is the midpoint.
Steven has a rope that is 6ft long. He cuts it into 9 pieces. How many are in each piece
Answers
Answer:2/3
Step-by-step explanation:
Got it wrong hehe :)
Answers
6/1 = 42/7
42/7 - 33/7 = 9/7 = 1 2/7
25) Which of these numbers cannot be a probability? (There is more than one answer.)
A -0.02
B0
C 1.002
D 1
Answers
Answer:
1.002, -0.02
Step-by-step explanation:
Probabilities range between 0 and 1.
What is 13 1 3 percent as a fraction in simplest form
Answers
Answer:
2/15
Step-by-step explanation:
A percent is a number given out of 100
13 1/3% basically is 13 1/3 | 100
You divide and you get 40/3 x 1/100
Simplify by 20 = 40/300 simplify again and you get 2/15.
F (x) =2x+3^2 (x-1)3 state of degree
Answers
kofi use 15min to type 500papers. How many minutes will he take 900papers
Answers
Answer:
27 minutes
Step-by-step explanation:
Hello!
500 and 900 are both multiples of 100, so let's first find the rate at which it takes Kofi to type 100 pages.
15m = 50015m / 5 = 500/53m = 100It takes 3 minutes to type 100 papers.
Since 900 is 9 times 100, we can also multiply the time by 9.
3m = 1003m*9 = 100*927m = 900It takes 27 minutes to type 900 papers.
Belinda buys a flat screen plasma television costing R20 000 on hire purchase. She traded in an old television for R3 000 and paid a deposit of R 2000. The balance was paid by means of monthly instalments of R900 over two years. Calculate the total simple interest paid and the rate of simple interest.
Answers
Based on the monthly installments and the amount that Belinda traded in the television for, the total simple interest paid was $6,600 and the rate of simple interest was 22%.
What was the simple interest paid?The balance after the trading in and deposit was:
= 20,000 - 3,000 - 2,000
= R15,000
The total simple interest paid was:
= (900 x 2 x 12months) - 15,000
= $6,600
The rate of simple interest was:
= (6,600 / 2 years) / 15,000
= 22%
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The perimeter of a rectangular window is 324 cm .
If the width of the window is 73 cm , what is its length?
Answers
Answer:
The length is 89 cm============================
Perimeter equationP = 2(l + w), where
P- perimeter, l- length, w- widthGivenP = 324 cm,w = 73 cmFind the value of l:
324 = 2( l + 73)l + 73 = 324/2l + 73 = 162l = 162 - 73l = 89Answer:
L = 89 cm
Step-by-step explanation:
Formula we use,
→ P = 2(L + W)
Then the value of its length is,
→ P = 2(L + W)
→ 324 = 2(L + 73)
→ 324 = 2L + 146
→ 2L = 324 - 146
→ L = 178/2
→ [ L = 89 cm ]
Hence, the length is 89 cm.
f(x) = x² + 2x - 3
Find f(2)
Answers
Answer:
5
Step-by-step explanation:
f(2) = (2)^2 +2(2) - 3
f(2) = 4 + 4 - 3
f(2) = 8 - 3
f(2) = 5
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If DM = 26 and point G lies on the perpendicular bisector of DM¯¯¯¯¯¯¯, what is the value of r? Segment D M with point G between the endpoints. Segment D G has length R plus 3, and segment G M has length 4R minus 28. A. 10 B. 13 C. 30 D. 52
Answers
The value of R in the line segment is R = 1
How to determine the value of r on the line segment?The given parameters on the line segment are:
Line segment DM = 26Point G is on the perpendicular bisector of DMSegment DG = R + 3Segment GM = 4R - 28Because the point G is on the perpendicular bisector of DM, then it means that
DM = DG + GM
This means that
26 = R + 3 + 4R - 28
Collect the like terms
So, we have
4R + R = 3 + 28 - 26
Evaluate the like terms
So, we have
5R = 5
Divide both sides by 5
So, we have
R = 1
Hence, the value of R in the line segment is R = 1
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Expand and simplify (5x - 2)^2
Answers
Answer:
The value of x = 2/5
Step-by-step explanation:
=>(5x - 2)²
=> (5x)² + 2² - 2(5x)(2)
=> 25x² -20x +4
=> 25x² -10x -10x +4
=> (5x-2) (5x-2)
=> x = 2/5 or 2/5
Show that the equation x³ - 3x² + 3 = 0 can be rearranged to give x = √√3x² -3
Answers
Joe's employer will reimburse him $0.07 per mile driven. If Joe drives 253.63 miles on a business trip, what
is his mileage reimbursement?
Answers
Answer:
17.75
Step-by-step explanation:
253.63 ×0.07=17.7541
I NEED HELP PLS SOMEONE
Answers
1. 15/4 written as a decimal is 3.75
2. 5/6 written as a decimal is 0.83(repeating 3)
3. 11/3 written as a decimal is 3.6(repeating 6)
Division operationFrom the question, we are to write each fraction as a decimal
1. 15/4
3.75
4)15.00
-12
3.0
-28
20
-20
0
15/4 written as a decimal is 3.75
2. 5/6
0.833
6)5.00
-48
20
-18
20
-18
2
5/6 written as a decimal is 0.83(repeating 3)
3. 11/3
3.66
3)11.00
- 9
20
-18
20
-18
2
11/3 written as a decimal is 3.6(repeating 6)
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. Given the relation = {(5,2), (7,4), (9,10), (, 5)}. Which of the following values for x will make relation a function?
Answers
Answer:
0
Step-by-step explanation:
since a function maps only one member in the co-domain
-4p + (-2) +2p + 3 combine like terms
Answers
Answer:
Step-by-step explanation:
-4p+-2= -6p
-6p+2= -4p
-4p+3= -1p
= -1p
The formula for the nth pentagonal number is
[tex]P_{n}[/tex] = n(3n-1)/2
Use the formula to find the 16th pentagonal number.
Answers
The 16th pentagonal number is 376
What is a function?A function can be defined as an expression that explains the relationship between a dependent and an independent variable.
Given the function for the nth pentagonal number as;
Pn = n( 3n -1 )/ 2
To determine the 16th pentagonal number, we need to substitute the value of n as 16
We have;
P16 = 16(3(16) - 1)/ 2
P16 = 16( 48 - 1)/ 2
P16 = 16(47)/ 2
expand the bracket
P16 = 376
Thus, the 16th pentagonal number is 376
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