In the above question the |x| represents the absolute value. |x - 1| < 5 is equivalent to -5 < x - 1 < 5.
What do you mean by absolute value?Algebra usually requires us to be careful about not just size of a value but also its sign. -10 is different than the 10. 3+7 yields a different result than the 3+(-7) . But there are circumstances in which sign doesn’t matter, in mathematics and in real life. Have you ever stumbled stepping on or off the moving walkway? It doesn’t really matter if you’re moving faster or slower than ground surface—it’s the magnitude of difference that makes you lose your balance. Or think of taking long hike—your feet will get just as the sore whether you go to north or south. Direction doesn’t matter, only the distance.
In mathematics, there’s a concept for dealing with the situations where size matters more than sign. It’s called the absolute value. Absolute value of a number is it's value regardless of its sign.
Given,
|x - 1| < 5
|x| this represents absolute value. It is the distance of x from 0, so value of x can be both positive and negative.
⇒ |x - 1| < 5 can be (x - 1) < 5 and -(x - 1) < 5
⇒ -(x - 1) < 5
⇒ (x - 1) < -5
So equivalent of |x - 1| < 5 is -5 < x - 1 < 5
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Answer:
Its C
which is –5 < x – 1 < 5
9y-5+9y-1=
Please help us
Step-by-step explanation:
9y - 5 + 9y - 1 = 9y + 9y - 5 - 1
= (9 + 9)y - 6
= 18y - 6
Evaluate 4xy for x=1, and y=2
3. m/U = 3x°, and m/V = 3(m/U). Find the value of x that makes ZU and
ZV supplementary angles.
The value of x that makes ∠U and ∠V to be supplementary angles are; x = 15°
What are supplementary angles?
When we are talking about angle theorem and congruency in mathematics, it is well know that supplementary angles are defined as angles whose sum is equal to 180 degrees.
Now, we are given;
∠U = 3x°
∠V = 3(∠U)
Thus;
∠V = 3(3x°) = 9x°
From definition of supplementary angles, we can say that;
3x° + 9x° = 180°
12x = 180°
x = 180/12
x = 15°
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Completely stumped. If anyone can help, that would be greatly appreciated! Picture below.
Using translation concepts, we have that the table of values for the function p(x) = x - 7 is given by:
x = -2, p(x) = -9.x = -1, p(x) = -8.x = 0, p(x) = -7.x = 1, p(x) = -6.x = 2, p(x) = -5.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the parent function is:
y = f(x).
A translation down 7 units is represented by a subtraction by 7 in the range, that is:
p(x) = f(x) - 7 = x - 7.
The numeric values to be inserted in the table are given by:
x = -2, p(x) = -9.x = -1, p(x) = -8.x = 0, p(x) = -7.x = 1, p(x) = -6.x = 2, p(x) = -5.In the graph at the end of the exercise, both functions are shown.
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HELP ME! AND PLSSSS EXPLAIN!
Ariel received so many flowers for her birthday that they wouldn't all fit on her desk. By
lunch, her office was decorated with 7 flower bouquets, 5 of which were rose bouquets.
If Ariel randomly selected 4 bouquets to take home, what is the probability that all of them
are rose bouquets?
Write your answer as a decimal rounded to four decimal places.
The probability that all of them are rose bouquets is 0.143.
How to calculate the probability?It should be noted that this question is about probability without replacement.
The probability of picking a rise bouquet is 5/7. It should be noted that each value decreases since Ariel is selecting 4 bouquets.
The probability that all of them are rose bouquets will be:
= 5/7 × 4/6 × 3/5 × 2/4
= 5/7 × 2/3 × 3/5 × 1/2
= 30/210
= 1/7
= 0.143
The probability is 0.143.
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The point (4, 1) is reflected over the line y=-x to create Point B. What are the coordinates of B?
(-1, -4)
(-1,4)
(1, -4)
(1,4)
Answer:
(-1, -4)
Step-by-step explanation:
y = -x is the 45° diagonal through the origin from top left to bottom right.
a reflection across that line brings anything that is in quadrant 1 (x and y are positive) to quadrant 3 (x and y are negative) like this point. and vice versa.
points in quadrant 2 stay in quadrant 2, points in quadrant 4 stay in quadrant 4.
but in every case x and y are exchanged and both signs are flipped like (-1, 2) turns into (-2, 1).
or for our point : (4, 1) turns into (-1, -4)
Tommy pays $550 dollars for a new cell phone plus $121-dollar monthly fee (f) for data. write an expression for the total expense of his phone?
Answer: C=550+121m
Step-by-step explanation:
What is the range of the function f(x) = 4x – 5 over the interval of 1 < x ≤ 5? Give your answer in interval notation.
Answer:
Hello,
Step-by-step explanation:
[tex]1 < x\leq 5 \ \\\Longrightarrow\ 4 < 4x \leq 20 \ \\\Longrightarrow\ -1 < 4x-5 \leq 15 \\\Longrightarrow\ -1 < f(x) \leq 15 \\\\range=]-1; 15][/tex]
The range of the function f(x) = 4x - 5 will range from -1 to 15.
What are the function and range?The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Given that the function f(x) = 4x – 5 and the interval is 1 < x ≤ 5. The range will be calculated as,
1 < x ≤ 5
4 < 4x ≤ 20
4-5<4x - 5< 20-5
-1 < 4x - 5 < 15
Therefore, the range of the function f(x) = 4x - 5 will range from -1 to 15.
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What is the circumference of a radius equals 6 inches
The circumference of a radius equals 6 inches is 37.68 inches
What is the circumference of a radius equals 6 inches?The radius is given as
r = 6 inches
The circumference of a circle is calculated as
C = 2pi r
So, we have
C = 2 * 3.14 * 6 inches
Evaluate the product
C = 37.68 inches
Hence, the circumference of a radius equals 6 inches is 37.68 inches
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Solve the inequality: c² < − 3c + 70
Answer:
Answer is (-10,7) and inequality form: -10<c<7
Step-by-step explanation:
First factor the equation.
(c+7)(c-10)
Then find out which intervals make (c+7)(c-10)<0.
Bob mows lawns for 5 weeks during summer break. He mows 2 lawns every day. By the end of 5 weeks, how many lawns has Bob mowed?
Answer: 70
Step-by-step explanation:
7 days a week x 2 lawns = 14
14 lawns x 5 weeks = 70 lawns
Answer:
70 lawns
Step-by-step explanation:
If Bob mows lawns every day for 5 weeks this is how the equation would work:
2 * 7 = 14
14 * 5 = 70
I got the 7 because there's seven days per week.
Find a linear function h, given h(7
)equalsnegative 10
and h(negative 2
)equals8.
Then find h(3
)
The linear function of h is h(x) = -2x -13 and the values of h(3) = -19.
Two point form is a method for finding the equation of a function if two of its points are known. If (x1, y1) and (x2, y2) are the two points then equation of the function is given as-
(y - y1) = {(y1 - y2)/ (x1 - x2)} (x - x1)
Here, we are given that h(7) = -10 and h(-2) = 8
This, means that (7, -10) and (-2, 8) will satisfy the given function
Since, we have two points, we will use the two point form to find the equation of function h.
Substituting, x1 = 7, y1 = -10, x2 = -2 and y2 = 8 in the two point form equation we get-
( y - 7) = {(-10 - 8) / (7 + 2)} (x + 10)
y - 7 = (-18/9) (x + 10)
y - 7 = -2(x + 10)
y - 7 = -2x -20
y = -2x -20 + 7
y = -2x -13
Thus, h(x) = -2x -13
Hence, h(3) = -2(3) -13
= -6 -13
= -19
Therefore, h(3) = -19
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Which figure below represents a rotation of 90° clockwise of the trapezoid shown?
Figure in option A is the figure that represents a rotation of 90° clockwise of the trapezoid
What is rotation?
The term rotation refers to the circular movement of an object or something about a point. The point mentioned is also called axis. The movement is circular because it involves turning round.
Rotation may be clockwise or anticlockwise. clockwise is the reverse of anticlockwise, and clockwise involves moving in same direction as the clock is turning,
As regards the trapezium, rotating it clockwise will result to the image depicted by option A
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How do I solve this problem?
On Friday, 4/7 of Parkden School chose pasta for lunch, 1/5 chose pizza and the rest chose salad. What fraction of the pupils chose salad?
Answer:
i think is 7/12
because if 4/7 chose pasta,1/5 chose pizza then we add 7+5=12 then we sudstract 12-4-1 = 7.
hope that helps
PLEASE HELP ALGEBRA 2
just do the first 2 or 3
4. Plans to vote
“yes” on issue Q
Plans to vote
“no” on issue Q Total
Plans to vote
“yes” on issue P 8 12 20
Plans to vote
“no” on issue P 14 16 30
Total 22 28 50
The table above shows a survey of 50 registered voters
in a city. Each voter was asked whether they planned to
vote “yes” or “no” on two different issues. If a voter who
plans to vote “yes” on issue P is randomly selected, what
is the probability that voter also plans to vote “yes” on
issue Q
The probability that voter also plans to vote “yes” on issue Q is found to be 0.4.
What is defined as the probability?The ratio of the total count of favorable outcomes to a total number of outcomes like an event is defined as probability. The number of favorable outcomes for an experiment with 'n' outcomes is denoted by x.The following equation is used to determine the probability of an event.
Probability(Event) = Favorable Outcomes/Total Outcomes
Probability(Event) = x/n
Eight voters intend to vote "yes" on both issues.
So, the favourable outcome becomes = 8.
Twenty voters intend to vote "yes" on issue P.
Thus, the total outcome = 20.
This is denoted by 8 /20 = 0.4.
Therefore, the likelihood that a voter will vote "yes" on issue Q is found to be 0.4.
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simplify:39÷(5+(4×5÷2) )
Answer:
this question is wrong .................
Answer:
39÷(5+(4×5÷2) )
39÷(5+(20÷2) )
39÷(5+10)
39÷15
2.6
An online store sells two types of speaker docks for smartphones. The higher-priced speaker dock sells for $170 and the lower-priced speaker dock sells for $90. Last week the store sold three times
as many lower-priced speaker docks as higher-priced speaker docks. Combined sales totaled $3,080. How many lower-priced speaker docks did it sell?
Answer:
21
Step-by-step explanation:
the price of the lower priced docs for that week would be 3x because the store sold 3 times as many low priced than the higher priced.
> so 90(3x) = 270x
170x + 270x = 440x
3080/440 = 7
7 high priced speakers were sold
to find out the cost of the lower ones you'd do
3x7 and get 21
What is answer to X/2 - X/5 = 3
Answer:
x = 10Step-by-step explanation:
What is answer to X/2 - X/5 = 3
x/2 - x/5 = 3
(3/10)x = 3
x = 3 : 3/10
x = 3 * 10/3
x = 10
-------------
check
10/2 - 10/5 = 3
3 = 3
the answer is good
Which equation matches the graph of the greatest integer function given below?
Answer:
A
Step-by-step explanation:
The last number represents where the line meets y-axis
Help me ASP SHOW UR WORK THANK YOU!!
The value of x is 4 , 12 , - 1 resp. in eq 1 , 2 and 3 .
Finding values of unknown variable x .
Following are linear equations in one variable .
On solving them we get ,
1 ) 2 ( 3 x - 5 ) = - 4 x + 30
6 x - 10 = - 4 x + 30
10 x =40
x = 4
2 ) 5 x - 6 - 3 x = 18
2 x = 18 + 6
2 x = 24
x = 12
3 ) - 11 - 5 x = 6 ( 5 x + 4 )
- 11 - 5 x = 30 x + 24
- 35 x = 35
x = - 1
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If the BMI of a person who is 1.9 meters tall is 20 when the person weighs 55 kilograms, what is the constant of variation?
The height is 5.225 meters and the constant of variation will be 10.5
How to calculate the constant?From the information, the BMI of a person who is 1.9 meters tall is 20.
Therefore, the constant of variation when the person has a weight of 55 kilograms will be:
= 20/1.9 = 10.5
The height will be:
= 1.9 × 55/20
= 1.9 × 2.75
= 5.225 meters.
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The table lists how poverty level income
cutoffs (in dollars) for a family of four have
changed over time. Use the midpoint
formula to approximate the poverty level
cutoff in 1987 to the nearest dollar.
The poverty level cutoff in 1987 was dollars.
(Round to the nearest dollar as needed.)
Year
1970
1980
1990
2000
Points: 0 of 1
Income (in dollars)
3703
8234
13575
17371
Midpoint formula : -
Midpoint calculation
The midpoint formula is a method used to locate the midway point between two coordinates on a graph. The midpoint of a line segment with endpoints A and B is the point that is precisely between A and B, that is, it is placed at the same distance from A and B, as shown in the illustration below.
The midpoint formula can be utilized when two points on a graph in the coordinate plane are known. The midpoint M of two points (x1, y1) and (x2, y2) is:
Notice that the midpoint formula includes calculating an average of the x- and y-values of two coordinates. The midway formula may be simpler to recall as a result. The sum of two number is equal to multiplying a number by 2. In a coordinate system, a line segment's midpoint is defined as the point midway between two points in the vertical and horizontal directions. This value is equivalent to the line segment's average x- and y-coordinates. It should be rather simple to recall the midway formula if you keep this in mind.
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a cuckoo clock has birds that pop out of their nests every 6 minutes and dancers that pop out every 15 minutes. the birds and dancers have just popped out at the same time. when will this happen again in the next 60 minutes?
We get that the birds and the dancers will clock out again in 30 minutes.
We are given that:
a cuckoo clock has birds that pop out of their nests every 6 minutes.
And the dancers that pop out every 15 minutes.
Now, they have popped out the same time. For this to happen again, we will find the LCM of 6 and 15.
6 = 2 × 3
15 = 3 × 5
LCM = 2 × 3 × 5
LCM = 3 × 10
LCM = 30
So, they will pop out again after 30 minutes.
Therefore, we get that the birds and the dancers will clock out again in 30 minutes.
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The perimeter of the triangle below is 73 units. Find the value of x.
Answer:
3x+4x-1+x+2=73
8x+1=73
8x=73-1
8x=72
8x/8=72/8
x=9
Perimeter (p) of a triangle:
[tex]p = a + b + c[/tex]
P = 73 units
To find the value of x
[tex]73 = 3x + 4x - 1 + x + 2[/tex]
→[tex]73 = 8x + 1 \\ 73 - 1 = 8x[/tex]
→[tex]8x = 72[/tex]
→[tex] \frac{8x}{8} = \frac{72}{8} [/tex]
[tex]x = 9[/tex]
Suppose that $3000 is placed in an account that pays 9% interest compounded each year. Assume that no withdrawals are made from the account. Follow the instructions below. Do not do any rounding. (a) Find the amount in the account at the end of 1 year. (b) Find the amount in the account at the end of 2 years.
Answer: (a) 3270 (b) 6270
Step-by-step explanation:
Formula for compound interest: P (1 + r/100 ) ^n,
where P = principal, r = interest rate, n = number of years
------------------------------------------------------------------------------------------------------------
In question (a),
P = $3000
r = 9%
n = 1
3000 ( 1 + 9/100) ^1 = $3270
------------------------------------------------------------------------------------------------------------
In question (b),
P = $3000
r = 9%
n = 2
3000 ( 1 + 9/100) ^2 = $6270
17 + 2 × 9 ÷ 3 + 4 × 6 ÷ 8
Answer: 26
Step-by-step explanation:
17 + 2 × 9 ÷ 3 + 4 × 6 ÷ 8=
17 + (2 × 9 ÷ 3) + (4 × 6 ÷ 8)= ==> multiplication and division come before addition
17 + (18 ÷ 3) + (24 ÷ 8)=
17 + 6 + 3=
23+3=26
could someone please help answer this.
Answer:
C.) Equally as distant.
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
Pedro requires [tex]1\frac{1}{2}[/tex] cups oatmeal for a single batch of granola bars as calculated by division of fractions.
A fraction is a piece of a whole or, to put it more broadly, any number of equal portions.
The Latin word fractus, which means "broken," is where the word fraction originates.A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of components of a particular size as it is represented in common English. There is a non-zero denominator and a common, or simple fraction below (or after) that line.Compound fractions, mixed numeral fractions, and difficult fractions are examples of uncommon fractions that use numerators and denominators.Total batches required [tex]= 3 \frac{1}{2} = \frac{7}{2} = \frac{14}{4}[/tex] cups
Total oatmeal required [tex]= 5 \frac{1}{4} =\frac{21}{4}[/tex] cups
Therefore now to calculate the amount of oatmeal needed for single
batch we divide the fraction [tex]\frac{21}{4}[/tex] by [tex]\frac{14}{4}[/tex] cups
1 batch requires = [tex]=\frac{21}{4}\div\frac{14}{4}=\frac{3}{2} = 1\frac{1}{2}[/tex] cups.
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1 Without graphing, determine the characteristics of the graph.
(a) y = |x-3) -1
What is the vertex?
Answer: (3, -1)
Step-by-step explanation:
y = |x-3|-1
When y=|x|, vertex is (0, 0).
Now, let's translate the graph so it becomes y = |x-3|-1.
|x| ==> |x-3| Translate the graph 3 units to the right
Vertex: (0+3, 0) ==> (3, 0)
|x-3| ==> |x-3|-1 Translate the graph 1 unit down
Vertex: (3, 0-1) ==> (3, -1)
Vertex: (3, -1)