The graphs of y = |x| and y = |x| - 4 are similar in their overall V-shape and slope behavior, but differ in their vertical position due to the constant term difference in the equations. The second graph is essentially a downward translation of the first by 4 units.
Similarities:
Both represent absolute value functions.
Both graphs pass through the origin (0, 0)
Both graphs have a slope of 1 for positive values of x and a slope of -1 for negative values of x.
Differences:
The graph of y = |x| - 4 is shifted downwards by 4 units
The y-intercept is different for both graphs.
Evaluate the function rule for the given value. Y=12×3^x for x=-2
Answer:
The value of function at x = -2 is [tex]\frac{4}{3}[/tex].
Step-by-step explanation:
Given : Function [tex]Y=12\times 3^x[/tex]
We have to evaluate the given function at x = - 2
Consider the given function [tex]Y=12\times 3^x[/tex]
Since, y is a function in terms of x.
So, put x = - 2 in given function.
We get,
[tex]Y=12\times 3^{-2}[/tex]
Since, [tex]3^{-2}=\frac{1}{3^2}=\frac{1}{9}[/tex]
[tex]Y=12\times \frac{1}{9}[/tex]
Simplify, we have,
[tex]Y=\frac{4}{3}[/tex]
Thus, The value of function at x = 2 is [tex]\frac{4}{3}[/tex].
the line of best fit drawn on a scatter plot ____
A. is a line that goes through each data plot.
B. always has a positive slope.
C. is a line drawn through the first and last points.
D. approximates the linear relationship of the data.
A line with a slope of 0 passes through the point (0, -5) . what is its equation i n slope -intercept form?
Find the zeros of the function. f(x) = 4x3 - 12x2 - 40x
Use allfour operations only once without parentheses to write an expression that has a value of 100 only using 3's
There are a lot of ways to write an expression using only 3 to get an answer of 100. Some examples are:
1st example:
3 / 3 + 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3
= 1 + 99
= 100
2nd example:
3 / 3 + 3 * 3 * 3 * 3 + 3 * 3 * 3 – 3 * 3
1 + 81 + 27 – 9 = 100
Suppose A and B are independent events if P(A) = 0.4 And P(B) = 0.1, what is P(A'uB)? APEX
Answer:0.6
Step-by-step explanation:
what is the solution to y=x+16 and y=-x+4??
Please show work and explanation in how its done...
so i can understand better cause I'm new to these problems...
so i can get all the help i can get (:
A runner is running 5 miles per hour. how many feet is the runner running per second.
How do you simplify the square root of 27?
The estimated measurements of the objects are shown below.
-length of a grain of salt: 0.0002 centimeters
-width of a key ring: 0.02 centimeters
Find the measurements written in standard notation to the estimated measurements in scientific notation.
The standard notation 0.0002 cm becomes 2 × 10^-4 and 0.02 cm becomes 2 × 10^-2, both in scientific notation.
Explanation:The standard notation for 0.0002 centimeters is 2 × 10^-4 in scientific notation. Meanwhile, the standard notation for 0.02 centimeters is 2 × 10^-2 in scientific notation.
You arrive at these translations by recognizing that the number 0.0002 means you've moved the decimal point four units to the right from 2 (thus raising 10, the base, to -4), and 0.02 represents moving the decimal point two units to the right from 2 (thus raising 10 to the -2).
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A golfer would like to test the hypothesis that the variance of his golf score equals 10.0. a random sample of 28 rounds of golf had a sample standard deviation of 3.5. what is the number of degrees of freedom for this hypothesisâ test?
What is the 32nd term of the arithmetic sequence where a1 = −32 and a9 = −120?
Answer:
-373
Step-by-step explanation:
A
n
=
A
1
+
d
(
n
−
1
)
A
1
=
−
32
A
9
=
−
120
⇒
A
9
=
−
32
+
d
(
9
−
1
)
⇒
−
120
=
−
32
+
d
(
8
)
⇒
−
88
=
8
d
⇒
d
=
−
11
A
32
=
−
32
+
(
−
11
)
(
32
−
1
)
⇒
A
32
=
−
32
+
(
−
11
)
(
31
)
⇒
A
32
=
−
32
+
−
341
⇒
A
32
=
−
373
PLZ HELP I NEED THIS TODAY!!!!Write an expression for the perimeter of the triangle shown below: A triangle is shown with side lengths labeled 2.3x plus 14, 2x, and negative 0.2x plus 15.
A file that is 256 megabytes is being downloaded. If the download is 18.6% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
Q and R are independent events. If P(Q)= 1/8 and P(R)=2/5 find P(Q and R).
The probability of independent events Q and R both occurring is calculated by multiplying the individual probabilities of each event. Thus in this case, P(Q and R) = (1/8) * (2/5) = 1/20.
Explanation:The question posed asks for the probability of events Q and R both occurring. Given that Q and R are independent events, the likelihood of both happening is calculated by multiplying the probabilities of each event.
That is, P(Q and R) = P(Q)P(R). From the question, we know that P(Q) is 1/8 and P(R) is 2/5.
Therefore, the probability of both Q and R occurring would be (1/8) * (2/5) = 1/20.
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A box has dimensions of 17 inches long.1.3 feet wide, and 8 inches high. What is the valine of the box? The formula for the volume is V = l• w •h.
convert the feet to inches so all 3 dimensions are in the same measurement
1.3 x 12 = 15.6 inches
now multiply them all
17 x 15.6 x 8 = 2121.6 cubic inches
round the answer if you need to
2. Richmond Appliance repairs washing machines. The revenue that the company earns is given by the function R(h) = 20 + 45h dollars for every h hours spent repairing washing machines. The company’s overhead cost is given by the function C(h) = 5h2 – 30 dollars. For what number of hours does the company break even? Show your work.
Answer:
The number of hours needed for the company to break even happens when
, rearranging to make the equation 'zero' on LHS
, divide each term by 5
, factorise
, equate each factor to zero
and
We choose the positive value of
Hence, the number of hours needed to break even is
Step-by-step explanation:
The mass of mercury is 330,200,000,000,000,000,000,000 kilograms. how can this number be written in scientific notation?
Final answer:
The mass of mercury, 330,200,000,000,000,000,000,000 kg, can be written in scientific notation as 3.302 × 10²⁰ kg. Scientific notation helps to express very large numbers in a more manageable form, using a coefficient between 1 and 10 multiplied by a power of ten.
Explanation:
To write the mass of mercury in scientific notation, we need to express it as a number between 1 and 10 multiplied by a power of ten. The mass given is 330,200,000,000,000,000,000,000 kilograms, which can be written as 3.302 × 10²⁰. Since there are 20 digits to the right of the first digit (3), the exponent in the scientific notation will be 20.
In scientific notation, the mass of mercury is thus written as 3.302 × 10²⁰ kg.
When converting to scientific notation, we use multiplication and division techniques to adjust the original number, so the resulting coefficient is a value from 1 up to, but not including, 10. This method is commonly used by scientists and astronomers when dealing with astronomical numbers, as in this case with the mass of a planet or in chemistry with the mass of an atom.
Use a translation rule to describe the translation of X that is 1 units to the left and 6 units up.
A.
T < -1, 6> (x)
B.
T < -1, -6> (x)
C.
T < 1, 6> (x)
D.
T < 1, -6> (x)
Answer:
C. < 1,6 > (x)
Step-by-step explanation:
We know that,
Translation is the transformation that shifts the image in any direction.
The general form of horizontal translation of f(x) to f(x±k) and vertical translation of f(x) to f(x)±k where k is any constant.
Now, as the given function 'X' is translated 1 unit to the left i.e. translated horizontally by 1 unit i.e. X+1.
Also, the function is translated 6 units up i.e. translated vertically by 6 units i.e. X+6.
Hence, the solution is < 1,6 >(x).
Samantha loves to download new music. She originally had 52 songs but plans to purchase 2 new songs each week. She wants to know how many songs she will have after 93 weeks. Which equation should she use?
a93 = 93 + 2(52 − 1)
a93 = 93 + 2(52 + 1)
a93 = 52 + 2(93 + 1)
a93 = 52 + 2(93 − 1)
Hint: It's either A, B, C, or D
If the area of a rectangle is 16 then the length is 4 and the width is 4 what is the counterexample
Lana Powell has cumulative earnings of $110,000 at the end of September. In the first week in October she earns $2,000. The amount deducted for Social Security and Medicare from her check is (assume Social Security rate of 6.2% on $110,100 and Medicare of 1.45%):
Answer:
Lana Powell has cumulative earnings of $110,000 at the end of September. In the first week in October she earns $2,000. The amount deducted for Social Security and Medicare from her check is (assume Social Security rate of 6.2% on $110,100 and Medicare of 1.45%):
Step-by-step explanation:
In the first week of October on the $ 2,000, we must deduct the two expenses, that of 6.2% and 1.45%, and then add them between them and subtract them from the $ 2000.
It would be the following: 2000 x 6.2% = $ 124; 2000 x 1.45% = 29; 124 + 29 = $ 153 is the amount to be deducted from the $ 2,000; $ 2000 - $ 153 = $ 1847.
Lana Powell's paycheck for the first week in October would have $124 deducted for Social Security and $29 for Medicare, resulting in a total deduction of $153. Her cumulative earnings are not considered here as she has exceeded the earnings threshold of $110,100 for Social Security tax.
Explanation:Lana Powell's earnings for the first week in October are subject to deductions for Social Security at a rate of 6.2% and Medicare at a rate of 1.45%. To calculate these deductions, you multiply her weekly earnings by the respective rates:
Social Security deduction = $[tex]2000*6.2/100 = $124[/tex]Medicare deduction = $[tex]2000*1.45/100 = $29[/tex]Therefore, the total amount deducted from Lana Powell's paycheck for Social Security and Medicare is $124 + $29 = $153.
Note that you do not consider her cumulative earnings in this case. The Social Security tax is applicable only up to a wage base limit of $110,100 and since her cumulative earnings have already exceeded this limit, she would not be paying any additional Social Security tax beyond this earnings threshold.
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Which of the following is a solution to the inequality y < –2x + 3?
A. (1,1)
B. (3,0)
C. (-3,10)
D. (0,0)
Please select the best answer from the choices provided
y < -2x +3
A. (1, 1) → x = 1, y = 1
substitute:
1 < -2(1) + 3
1 < 1 FALSE
B. (3, 0) → x = 3, y = 0
substitute
0 < -2(3) +3
0 < -3 FALSE
C. (-3, 10) → x = -3, y = 10
substitute
10 < -2(-3) +3
10 < 9 FALSE
D. (0, 0) → x = 0, y = 0
substitute
0 < -2(0) + 3
0 < 3 CORRECT
Answer: D. (0, 0)
(02.07)Solve for L: A = L ⋅ W ⋅ H
The scatter plot shows the test scores of a group of students who surfed the Internet for different amounts of time in a day.
What will most likely happen to the test scores of students if the number of hours they surf the Internet increases?
Test scores will decrease because the graph shows a negative association.
Test scores will increase because the graph shows a positive association.
Test scores will increase because the graph shows a negative association.
Test scores will decrease because the graph shows a positive association.
Answer: The correct answer is "Test scores will increase because the graph shows a negative association."
Step-by-step explanation: Negative association is decreasing and positive is increasing but in this case we flip it to get our answer.
The impact of time spent surfing the internet on students' test scores depends on whether the association represented on the scatter plot is positive or negative. In a positive association, scores increase with increased internet time, while in a negative association, scores decrease.
Explanation:Based on the question, it seems there is a relationship between the time spent surfing the Internet and students' test scores which is represented by a scatter plot. The association between these variables can be either positive, negative, or no association. A positive association means as the hours of surfing the internet increase, the test scores also increase. A negative association implies that as the hours of surfing the internet increase, the test scores decrease.
However, the question didn't provide the information about whether the scatter plot shows a positive or a negative association between these two variables, which is crucial to determine what happens to the test scores as internet surfing time increases.
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The point-slope form of the equation of the line that passes through (–9, –2) and (1, 3) is y – 3 = 1/2 (x – 1). What is the slope-intercept form of the equation for this line?
Answer:
[tex]y=\frac{x}{2}+\frac{5}{2}[/tex]
Step-by-step explanation:
Hello
thanks for asking this question, I think I can help you with this
if you have the point-slope form of the equation of a line, just isolate "y" to find the slope-intercept form
Step 1
[tex]y-3=\frac{1}{2} (x-1)\\\\y-3=\frac{x}{2}-\frac{1}{2} \\Add\ 3\ in\ both sides\\\\y-3+3=\frac{x}{2}-\frac{1}{2} +3\\y=\frac{x}{2}-\frac{1}{2}+3\\y=\frac{x}{2}+\frac{5}{2}[/tex]
so the answer is
[tex]y=\frac{x}{2}+\frac{5}{2}[/tex]
where 1/2 is the slope, and 5/2 is the intercept with y-axis
I really hope it helps , Have a great day.
What is the square root of 75 in simplified form?
Answer:The answer is
5 3
Step-by-step explanation:
(3x/4)>51 ( line underneath >)
In which one of the above figures is AB = AC?
A. Figure B
B. Figure C
C. Figure A
D. Figure D
Answer: The answer is (D). the image is attached.
Step-by-step explanation: We are given four figures from which we are to select the one with AB = AC.
In figure (A), AB and AC are two chords of the circle with common point A. Since the lengths of two chords of a circle may not be equal, so AB may not be equal to AC. This option is not correct.
In figure (B), AB is a tangent at point B and AC is the extension of a chord which meets the tangent AB at point A. Since the lengths of AB and AC may not be equal, so this option is also incorrect.
In figure (C), AB and AC are extensions of two chords which meets at point A outside the circle, so they may not be congruent. So, this option will also not work.
In figure (D), AB and AC are two tangents from a common point A to the circle at B and C respectively.
We have the Two-Tangent Theorem which states that if two tangent segments are drawn to one circle from the same external point, then they are congruent.
So, we have AB ≅ AC.
Thus, (D) is the correct option.
7x7-9exponent x 7 7exponent
Answer:
1/7
Step-by-step explanation: