The function f(x) = |x|, after shifting it down by 4 units and right by 3 units can be written as -
(y - 4) - |x - 3| = 0
What is Modulus function?The modulus function can be written as follows -
|x| = x [for x ≥ 0]
|x| = - x [for x < 0]
Given that a function f(x) = |x| which is shifted down by 4 units and right by 3 units. Therefore, we can write -
y = f(x) = |x|
Change in y - coordinate = y + 4.
Change in x - coordinate = x - 3.
We will plot the graph of h(x) after the doing the given changes in the coordinates.
Now, we have -
y = |x|
y - |x| = 0
Change in y - coordinate can be written as -
(y + 4) - |x| = 0
Change in x - coordinate can be written as -
(y - 4) - |x - 3| = 0
Now, the graph of both f(x) and and h(x) is attached at the end.
Therefore, the function f(x) = |x|, after shifting it down by 4 units and right by 3 units can be written as -
(y - 4) - |x - 3| = 0
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)) Ronnie has already run 21 miles on his own, and he expects to run 1 mile during each
track practice. How many track practices would it take for Ronnie to run 47 miles?
Answer:
It would take him 47 track practices
Step-by-step explanation:
I need help ASAP and I need to show my work
Answer:
Hey there!
Total students: 7+9+5+3+12=36
Students that like math: 7
7/36=19.4% of students like math.
Let me know if this helps :)
Answer:
19% (Math)
Step-by-step explanation:
7 divide by total number of students (36) X100% =19%
i have two bags of marbles. The first bag contains 4 red marbles, 2 blue marbles, and 3 green marbles. The second bag contains 6 red marbles, 3 blue marble, and 6 green marbles. I will randomly select one marble from each bag.
What is the probability that i will select a green
marble from each bag?
A.2/15
B.1/135
C.1/3
D.11/15
Answer:
1/3
Step-by-step explanation:
You add up the amount in each bag then you take the amount of green then that will be the answer but since there is 2 bags it is 1/3
Find the volume.please :>
Answer:
The volume of the cube is 77 inches.
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answer:
6.63 ft
Step-by-step explanation:
10² + h² = 12²
h² = 12² - 10²
h² = 144 - 100
h = √(44)
h = 2√11
6.63325 ft
BRAINLIEST please if this helped!How many 11-card hands are possible with a 20-card deck?
There is only 1 possible 11-card hand that can be formed from a 20-card deck.
To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.
The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.
The formula for combinations is:
nCk = n! / (k!(n-k)!)
Where "!" denotes the factorial of a number.
Substituting the values into the formula:
20C11 = 20! / (11!(20-11)!)
Simplifying further:
20C11 = 20! / (11! * 9!)
Now, let's calculate the factorial values:
20! = 20 * 19 * 18 * ... * 2 * 1
11! = 11 * 10 * 9 * ... * 2 * 1
9! = 9 * 8 * 7 * ... * 2 * 1
By canceling out common terms in the numerator and denominator, we get:
20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)
Performing the multiplication:
20C11 = 39,916,800 / 39,916,800
Finally, the result simplifies to:
20C11 = 1
Consequently, with a 20-card deck, there is only one potential 11-card hand.
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How wide is a rectangular strip of land with length 1 1/2 kilometers and area 3/4 square kilometers?
Answer: The wideness of the rectangular strip of land is 1/2 km
The length of the rectangular strip = 1 1/2 kilometers
The area of the rectangular strip = 3/4 square kilometers
Area of a rectangle = Length x width
Let the width of the rectangular strip = x
\(\begin{gathered} \text{Length = 1}\frac{1}{2}\text{ km} \\ \text{Convert the length to an improper fraction} \\ \frac{(1\text{ x 2) + 1}}{2} \\ \frac{2\text{ + 1}}{2} \\ \frac{3}{2}\text{ km} \\ \text{ Since, area = 3/4 } \\ \frac{3}{4}\text{ = }\frac{3}{2}\cdot\text{ x} \\ \frac{3}{4}\text{ =}\frac{3x}{2} \\ \text{Cross multiply} \\ 3\text{ x 2 = 3x }\cdot\text{ 4} \\ 6\text{ = 12x} \\ \text{Divide both sides by 12} \\ \frac{12x}{12}\text{ = }\frac{6}{2} \\ x\text{ = }\frac{1}{2}\text{ kilometer} \end{gathered}\)The widenes of the rectangular strip is 1/2 km
A DVD normally costs $22. This week it is on sale for 25% off the original price. What is the sale price of the DVD?
Answer:
$16.5
Step-by-step explanation:
25 % of 22 is 5.5
22 - 5.5 = 16.5
The sale price of the DVD in this week on sale for 25% off on the original price is $16.5.
Given that the original price of a DVD is $22, that means the cost of the DVD is $22.
This week the sale on the original price of a DVD. The sale is that 25% off on the original price of a DVD, that is 25% off on $22.
Here, calculate the discount on the original price of a DVD.
\(Discount=22\times25 \%\\Discount=22\times\frac{25}{100}\\Discount=\frac{22}{4} \\Discount=\$5.5\)
The discount is $5.5 on the original price of a DVD.
Therefore, the sale price of a DVD on this week after the discount:
\(Sale\ price= \$22-$5.5\\Sale\ price=\$16.5\)
Thus, the sale price of a DVD is $16.5.
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Claim: The mean pulse rate (in beats per minute) of adult males is equal to 69 bpm. For a random sample of 175 adult males, the mean pulse rate is 68.1 bpm and the standard deviation is 11.2 bpm. Find the value of the test statistic. Round to two decimal places as needed.
The value of the test statistic is approximately -1.063
We have,
To find the value of the test statistic, we need to calculate the z-score using the given information.
The formula for calculating the z-score is:
z = (x - μ) / (σ / √n)
Where:
x is the sample mean (68.1 bpm)
μ is the population mean (69 bpm)
σ is the standard deviation (11.2 bpm)
n is the sample size (175)
Plugging in the values into the formula, we have:
z = (68.1 - 69) / (11.2 / √175)
Calculating the numerator:
68.1 - 69 = -0.9
Calculating the denominator:
11.2 / √175 ≈ 0.846 (rounded to three decimal places)
Now, we can calculate the value of the test statistic:
z = -0.9 / 0.846 ≈ -1.063 (rounded to three decimal places)
Therefore,
The value of the test statistic is approximately -1.063
(rounded to two decimal places).
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Compare the values of the following numbers, using the symbols > (greater than), < (less than), and = (equal to).
0.5 _____0.500
Answer:
0.5 = 0.500
Step-by-step explanation:
Both numbers are five-tenths. The zeros to the right of the 5 are not place holders and do not change the value of the number.
0.5 = 0.500
6. Which is an equation of the line with a slope of 1/4 and a y-intercept of -2 ?
A. x - 4y = 8
B. x +4y = -8
C. 4x + y = -2
D. 4x - y = 2
Answer:
ANSWER ' A '
x - 4y = 8
Step-by-step explanation:
What is the product?
(3a^2b^7) (5a^3b^8)
Answer:
\(\boxed{\sf \ \ \ 15a^5b^{15} \ \ \ }\)
Step-by-step explanation:
hello,
\((3a^2b^7) (5a^3b^8)=15a^{2+3}b^{7+8}=15a^5b^{15}\)
hope this helps
HELPP!!!
The area of the figure is ____ square units.
Answer:
The answer is 132 square units
Step-by-step explanation:
Cutting the shape
we have two trapeziums
A=(area of small +Area of big)Trapezium
A=1/2(3+9)8 + 1/2(9+12)8
A=1/2×12×8 + 1/2×21×8
A=12×4 + 4×21
A=48+84
A=132 square units
100 points!!
f (x) = −√x + 2 + 3
Fully explain the three transformations required to produce this function from the
parent function.
Answer: the first thing is your answer :)
thx for the points
Step-by-step explanation:
g
(
x
)
=
x
2
−
3
The parent function is the simplest form of the type of function given.
f
(
x
)
=
x
2
The transformation being described is from
f
(
x
)
=
x
2
to
g
(
x
)
=
x
2
−
3
.
f
(
x
)
=
x
2
→
g
(
x
)
=
x
2
−
3
The horizontal shift depends on the value of
h
. The horizontal shift is described as:
g
(
x
)
=
f
(
x
+
h
)
- The graph is shifted to the left
h
units.
g
(
x
)
=
f
(
x
−
h
)
- The graph is shifted to the right
h
units.
In this case,
h
=
0
which means that the graph is not shifted to the left or right.
Horizontal Shift: None
The vertical shift depends on the value of
k
. The vertical shift is described as:
g
(
x
)
=
f
(
x
)
+
k
- The graph is shifted up
k
units.
g
(
x
)
=
f
(
x
)
−
k
- The graph is shifted down
k
units.
Vertical Shift: Down
3
Units
The graph is reflected about the x-axis when
g
(
x
)
=
−
f
(
x
)
.
Reflection about the x-axis: None
The graph is reflected about the y-axis when
g
(
x
)
=
f
(
−
x
)
.
Reflection about the y-axis: None
Compressing and stretching depends on the value of
a
.
When
a
is greater than
1
: Vertically stretched
When
a
is between
0
and
1
: Vertically compressed
Vertical Compression or Stretch: None
Compare and list the transformations.
Parent Function:
f
(
x
)
=
x
2
Horizontal Shift: None
Vertical Shift: Down
3
Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: None
image of graph
please help me I dont know how to do this!
The above figure is a square
All sides in a square are all equal
A square has an equal Length
Hence, The area of a square
\(A=a^2\)find the slope-intercept equation of the line that passes through (3,-1) and has a slope of -1
Answer:
y= -x+2Step-by-step explanation:
slope formula: (y2-y1)/(x2-x1)at the point (3,-1), it is known that x=3 and y= -1.[y-(-1)]/(x-3)= -1 (y+1)/(x-3)= -1 (y+1)= -1(x-3) y+1= -x+3 y= -x+2In Rebecca's neighborhood, 89% of the houses have garages and 48% have a
garage and a pool. What is the probability (in percent) that a house in her
neighborhood has a pool, given that it has a garage? Round your answer to 1
decimal place.
why are there two of these?
Answer:
53.9
Step-by-step explanation:
89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9
A contractor better job at $750 for materials plus $43 per hour for labor. The total cost for the job can be modeled by C= 43H+ 750$.
Find the number of hours that he has for the job if the owner would like the total cost to be under $2000, rounded to the nearest hour.
The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.
To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.
Since the owner wants the total cost to be under $2000, we can set up the inequality:
43H + 750 < 2000
Now, let's solve this inequality for H, the number of hours:
43H < 2000 - 750
43H < 1250
Dividing both sides of the inequality by 43:
H < 1250/43
To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.
Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:
H < 29
Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.
By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.
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Which is the slope of the line that passes through the points (4, 2) and
(6, 7)?
Answer:
2.5
Step-by-step explanation:
Use the formula y2-y1 divided by x2-x1
Plug in the values: (7-2)/(6-4)
5/2
=2.5
I need help plslslsls
Answer:
a) Positive
b) 146
Step-by-step explanation:
As the data os going up, it is a positive correlation. For part b, you need to draw a line through the general area of all the points and see how much revenue is made from raincoats.
Which method would determine the volume of the prism with dimensions 2 x 2 1/4 x 4?
Answer:
There are 8 one-quarter cubes and 16 unit cubes so (8 times one-fourth) + 16 will give the volume.
Step-by-step explanation:
4 × 2 × 2¼ = 18
A cereal box has dimensions of 12 inches, (7)3/4 inches, and 2 inches. A pastry box has a dimensions of (3)2/3 inches, (3)1/2 inches, and (2)1/3 inches. What is the difference in volume, cubic inches, between the two boxes. show your work
The difference in volume between the two boxes would be = 156in³
How to calculate the difference in volume between the boxes?To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;
Volume = length×width×height.
For box 1 = length = 12in, width = 7¾in, height= 2in
Vol = 12×7¾×2 = 186in³
For box 2; length = 3⅔in, width = 3½in, height= 2⅓in
Volume = 3⅔×3½×2⅓ = 30
The difference = 186-30 = 156in³
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Can someone help me pls
9514 1404 393
Answer:
Amir: 2/3
Whitney: 1/4
Step-by-step explanation:
We can let w represent the fraction Whitney eats. Then the fraction Amir eats is (w+5/12). The total amount they eat is found by ...
w + (w +5/12) + 1/12 = 1
2w = 1/2 . . . . . subtract 6/12
w = 1/4 . . . . fraction Whitney eats
w+5/12 = 3/12 +5/12 = 8/12 = 2/3 . . . . fraction Amir eats
Subtract. 4/5−1/4 Enter your answer as a fraction in simplest form by filling in the boxes.
|_|
|_|
Answer:
11/20
| 11 |
|20|
Step-by-step explanation:
for this we need to find the Least Common Denominator in each fraction
4/5 = 16/20
1/4 = 5/20
then we subtract the numerator in each fraction (in bold above)
16 - 5 = 11
meaning we now have...
11 / 20
this is the simplest form for this fraction, so lets figure out what to put in each box
see the way the ' / ' is angled? that means the FIRST number is ON TOP of the second number
Let s(t) = 4t³ – 6t² – 72t be the equation of motion for a particle. Find a function for the velocity.
v(t)=
Where does the velocity equal zero?
t= and t=
Find a function for the acceleration of the particle.
a(t)
The function for the velocity is v(t) = 12t² – 12t – 72.
The velocity is zero at t = 3 and t = -2.
The function for the acceleration is a(t) = 24t – 12.
To find the velocity function v(t), we need to take the derivative of the position function s(t) with respect to time.
Given that s(t) = 4t³ – 6t² – 72t, we can differentiate it to obtain the velocity function v(t):
v(t) = s'(t) = d/dt (4t³ – 6t² – 72t)
To differentiate each term, we can apply the power rule of differentiation:
v(t) = 12t² – 12t – 72
Therefore, the function for the velocity is v(t) = 12t² – 12t – 72.
To find when the velocity equals zero, we set v(t) = 0 and solve for t:
12t² – 12t – 72 = 0
We can factor out a common factor of 12:
12(t² – t – 6) = 0
Now, we can solve the quadratic equation t² – t – 6 = 0 by factoring or using the quadratic formula:
(t – 3)(t + 2) = 0
This gives us two possible values for t when the velocity equals zero: t = 3 and t = -2.
Therefore, the velocity is zero at t = 3 and t = -2.
To find the function for acceleration a(t), we need to take the derivative of the velocity function v(t):
a(t) = v'(t) = d/dt (12t² – 12t – 72)
Differentiating each term:
a(t) = 24t – 12
Therefore, the function for the acceleration is a(t) = 24t – 12.
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A bag contains 8 yellow marbles and 6 blue marbles. What number of
yellow marbles can you add to the bag so that the ratio of yellow to blue marbles is 2 : 1? help...
You can add 4 more yellow marbles to make the ratio of yellow to blue marbles 2 to 1.
A ratio of 2 to 1 means that one of the objects have twice the amount of the other. Since blue originally had 6 marbles, simply multiply that by 2 and you should get how many yellow marbles you need in total and since you already have 8 yellow marbles, all you need is to add four.
The final ration will be
yellow : blue
12 : 6
2 : 1
PLEASE HELP AND SHOW WORK GEOMETRY THX
For the statement "If a polygon lacks right angles, then it is a parallelogram.", the counter example is -
Option A : a right triangle
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
A counterexample for a conditional statement is an example that satisfies the hypothesis (the first part of the statement) but does not satisfy the conclusion (the second part of the statement).
In this case, the statement is "If a polygon lacks right angles, then it is a parallelogram."
A right triangle is a polygon that lacks right angles, but it is not a parallelogram.
Therefore, a right triangle is a counterexample for this statement.
A square, a regular hexagon, and a rectangle all have right angles, so they are not counterexamples for this statement.
Therefore, the triangle is the counterexample.
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Which of the following choices is correct about the information shown on the graph below?
Help much needed pls and thank you.
Answer:
Step-by-step explanation:
A full revolution on a circle/radians is 2\(\pi\), so keep adding or subtracting 2\(\pi\) til you get a base angle, that's when the sign changes. Then decide which quadrant your in.
For this one the equivalent of 2\(\pi\) is \(6\pi /3\)
-29\(\pi\)/3 + \(6\pi /3\)
= -23\(\pi\)/3 + \(6\pi /3\)
= -17\(\pi\)/3 + \(6\pi /3\)
= -11\(\pi\)/3 + \(6\pi /3\)
= -5\(\pi\)/3 + \(6\pi /3\)
= 1\(\pi\)/3 sign changed it's equavalent to \(\pi /3\) Which is in the first quadrant. See unit circle.
-5\(\pi\)/6 + \(12\pi /6\)
=\(7\pi /6\) third quadrant, i count quadrants by know \(\pi\)/6 is 30°, so every 30° line is 1/6 of the unit circle. when i count 7 of them that's in the 3rd quadrant. Don't forget to count the axis's
2\(\pi\)/3 is in the 2nd quadrant. Count my pi/3's which is 60°
45\(\pi\)/7 - 14\(\pi\)/7
= 31\(\pi\)/7 - 14\(\pi\)/7
=17\(\pi\)/7 - 14\(\pi\)/7
=3\(\pi\)/7 - 14\(\pi\)/7
= -11\(\pi\)/7 1/7th's is not your typical unit circle angle
This one i think of logically. this is -1 4pi/7
1 pi going backwards is 180
keep going backards 4/7 is bigger than 1/2 so it's in the 1st quadrant
One spring day, Camila noted the time of day and the temperature, in degrees Fahrenheit. Her findings are as follows: At 6 a.m., the temperature was 60° F. For the next 4 hours, the temperature rose 2° per hour. For the next 2 hours, it rose 3° per hour. The temperature then stayed steady until 6 p.m. For the next 3 hours, the temperature dropped 2° per hour. The temperature then dropped steadily until the temperature was 66° at midnight. On the set of axes below, graph Camila's data.
The graph of Camila's data representing temperature on the y-axis and time on the x-axis is as attached
How to Graph a Table of Values?
The question is a word problem that involves constructing a table of values and then graph the table values data as below;
Time Temperature
6:00 56
7:00 59
8:00 62
9:00 65
10:00 66
11:00 67
12:00 68
13:00 69
14:00 70
15:00 70
16:00 70
17:00 70
18:00 70
19:00 67
20:00 64
21:00 61
00:00 60
The graph of Camila's data representing temperature on the y-axis and time on the x-axis is as attached
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