The translation of the parent function f (x) = | x | depends upon whether x value has been changed of whether the y value has been changed.
We are given the parent function as:
f (x) = | x |
Now, we need to match the functions with their correct translations.
For the function f (x) = | x | - 4:
This can also be written as:
f (x) + 4 = | x |
So, the translation will be vertical translation up 4 units.
For the function f (x) = | x + 4 | :
The translation for this will be horizontal translation right 4 units as x will increase by 4 units.
For the function f (x) = | x | + 4:
This can also be written as:
f (x) - 4 = | x |
So, the translation will be vertical translation down 4 units.
For the function f (x) = | x - 4 | :
The translation for this will be The translation for this will be horizontal translation right 4 units as x will increase by 4 units as x will decrease by 4 units.
Therefore, we get that, the translation of the parent function depends upon whether x value has been changed of whether the y value has been changed.
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(1 point) The expression
where n, the leading coefficient, is:
and r, the exponent of a, is: 3
and S, the exponent of b, is: 10
and finally t, the exponent of c, is: 15
(5b¹c-5)-³(4b⁰a²)-5 equals na'bs ct
I
NOTE: The value for n may be given as a fraction or as a just number. All other values must be
Note: You can earn partial credit on this problem.
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Answer:
n = 1/128000r = -10s = -3t = 15Step-by-step explanation:
You want the simplified form of (5b^1c^-5)^-3(4b^0a^2)^-5.
Rules of exponentsThere are several useful rules of exponents here:
(ab)^c = (a^c)(b^c)
(a^b)^c = a^(bc)
a^-b = 1/(a^b)
ApplicationSimplifying the top-level exponents first, we have ...
[tex](5b^1c^{-5})^{-3}(4b^0a^2)^{-5}=(5^{-3}b^{1(-3)}c^{(-5)(-3)})(4^{-5}b^{0(-5)}a^{2(-5)})\\\\=(5^{-3}4^{-5})a^{-10}b^{-3+0}c^{15}=\dfrac{1}{5^34^5}a^{-10}b^{-3}c^{15}=\boxed{\dfrac{1}{128000}a^{-10}b^{-3}c^{15}}[/tex]
In terms of answer requirements:
n = 1/128000
r = -10
s = -3
t = 15
Challenge A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the
coins, 12% are pennies and 40% are dimes. There are 5 more nickels than pennies. How much
money does the bag contain?
The bag contains $
Answer:
$5.86
Step-by-step explanation:
12% of 50=6 pennies
40% of 50= 20 dimes
6+5= 11 nickels
11+20+6= 37 coins
50 total coins-37= 13 quarters
13 quarters = $3.25
20 dimes = $2.00
11 nickels = $0.55
6 pennies = $0.06
$3.25+$2.00+$0.55+$0.06=$5.86
Answer:
$5.86
Step-by-step explanation:
Please need help on this one
PLS HELP Solve 4 • (−6). (20 points)
a
−42
b
−24
c
10
d
24
Find the equation of the line that contains a slope of 3/4 and a 'y'-intercept of (0,3). Write the answer in slope-intercept form.
Answer:
Step-by-step explanation:
y=-3/4 x-3
this is a bit confusing for me, can someone explain, or just do it for me to show? Thank you!
Answers:
Row 1: 4 sig digits, 1.705*10^4
Row 2: 5 sig digits, 1.9080*10^-5
Row 3: 300, 1 sig digit
Row 4: 0.00246, 3 sig digits
AB formed by (-3, 8) and (3, 2) and CD formed by (7.1) and (5, -1). Are these
parallel, perpendicular, or neither?
Answer:
Unknown
Step-by-step explanation:
ajkdfhlkhalukdjglahgfjhgdljhdfjgajdfgaiufgyhj
Solve for y in terms of x. 9x + 3 2 y = 14
Answer:
x=
−32/9y +14/9
Step-by-step explanation:
One year Roger had the lowest ERA (earned-run average, mean number of runs yielded per nine
innings pitched) of any male pitcher at his school, with an ERA of 3.49. Also, Kate had the lowest ERA of any female pitcher at the school with an ERA of 3.44. For the males, the mean ERA was 3.805 and the standard deviation was 0.671. For the females, the mean ERA was 3.967 and the standard
deviation was 0.604. Find their respective z-scores. Which player had the better year relative to their
peers, Roger or Kate? (Note: In general, the lower the ERA, the better the pitcher.)
Answer:
id. k
Step-by-step explanation:
I. dk
Did ancient mathematicians use a ruler to determine the values of sine and cosine in a circle?
No answer needed! Just take points.
Answer and Explanation:
No, they did not use a ruler to compute the values of trig functions. They used geometry to prove theorems about trigonometry, then used those results and ordinary computations involving addition, subtraction, multiplication, division, and square roots to determine the entries in trigonometric tables.
Claudius Ptolemy (85 C.E.–165) created the first trig tables that we know of, and he included proofs of the theorems he used. One of the main theorems he used is what is now called Ptolemy’s theorem.
In order to prove his sum and difference forumlas, Ptolemy first proved what we now call Ptolemy’s theorem.
Ptolemy’s theorem. The product of the diagonals of a cyclic quadrilateral is equal to the sum of the products of the opposite sides.
A cyclic quadrilateral is a quadrilateral inscribed in a circle as ABCD. Ptolemy’s theorem says:
AC ⋅ BD = AB ⋅ CD + AD ⋅ BC
When one of the diagonals (like ) is a diameter of the circle, that gives you a way to determine the trig functions for sum and differences of angles.
Sometimes, the sum and difference formulas for sine and cosine are still called Ptolemy’s formulas.
sin(α + β) = sin α cos β + cos α sin β
cos(α + β) = cos α cos β − sin α sin β
sin(α − β) = sin α cos β − cos α sin β
cos(α − β) = cos α cos β + sin α sin β
Ptolemy started with angles he knew the trig functions for. These included angles in various isosceles triangles: 45°-45°-90°, 60°-60°-60°, and 36°-72°-72°, the last one described by Euclid in Proposition IV.10. That gave him the trig functions for 36°, 60°, and 90°. Using half-angle formulas (mentioned by Hipparchus (190–120 B.C.E.), he could compute trig functions for half of those angles and a quarter of those angles. Then using the sum and difference formulas he computed the rest of the numbers in his trig table.
Hope this helps! :)
Jocelyn has read 160 pages in a book. This is of the entire book. How many pages
does the book have?
you need more information to finish this question. You can't get an answer for a math question like this one with that little information.
Answer:
Step-by-step explanation:
lol it means 4/5,
your in rsm i aleready know
1/sin10°-√3/cos10°=4
Answer:
[tex]\frac{1}{\sin \left(10^{\circ \:\:}\right)}\:\:\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=4[/tex]
Step-by-step explanation:
Given the expression
[tex]\frac{1}{\sin \left(10^{\circ \:}\right)}-\frac{\sqrt{3}}{\cos \left(10^{\circ \:}\right)}=4[/tex]
Taking the left-hand side and solving it
[tex]\frac{1}{\sin \left(10^{\circ \:}\right)}-\frac{\sqrt{3}}{\cos \left(10^{\circ \:}\right)}[/tex]
as
[tex]\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=5.76[/tex]
and
[tex]\frac{\sqrt{3}}{\cos \left(10^{\circ \:\:}\right)}=1.76[/tex]
so the expression becomes
[tex]\frac{1}{\sin \left(10^{\circ \:\:}\right)}\:\:\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=5.76-1.76[/tex]
[tex]=4[/tex]
Thus, we conclude that
[tex]\frac{1}{\sin \left(10^{\circ \:\:}\right)}\:\:\frac{1}{\sin \:\left(10^{\circ \:\:}\right)}=4[/tex]
A dose of 4500mg of medication has ordered for a patient. The medication comes in 5g/0.3mL. What volume will you give the patient?
please show conversions
According to the given statement the volume of medicine will give to the patient = 0.27ml.
What specifically is density?A substance's density is defined as its mass per unit volume. The most common symbol for density is, but the Latin letter D is also an option.
What is the significance of density?Density is an important topic because it tells us which compounds will float and which will sink when placed in some kind of liquid. Substances float in general if their density is smaller than the density of the liquid in which they are immersed.
ρ = m/v
ρ = density
m = mass
V = volume
According to the given information:Medicine = 4500mg
The medication comes in 5g/0.3mL
We know that:
mL = mg / 1000
So,
ml = 4500/1000
= 4.5ml
Formula for finding volume = weight/density
= 4.5/(5/.3)
= (4.5 * 0.3)/5
= 0.27ml
According to the given statement the volume will give to the patient = 0.27ml.
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Use the Binomial Theorem to expand each binomial (2x-1)^6
Allen went out to dinner and hls total bill
came to $22.14. The tax on his meal was
8%, or $1.64. What was the subtotal of
his dinner?
Instructions: Find the missing side lengths. Leave your answers as radicals in simplest form.
Help quick.
Answer: y=8 and x=8 radical 3
The Martin family and the Kelly family each used their sprinklers last summer. The water output rate for the Martin family's sprinkler was 30L per hour. The water output rate for the Kelly family's sprinkler was 35L per hour. The families used their sprinklers for a combined total of 60 hours resulting in a total water output of 1925L. How long was each sprinkler used?
Answer:
The Martins used their sprinkler for 35 hours, while the Kellys used their sprinkler for 25 hours.
Step-by-step explanation:
As the Martins and the Kellys used their sprinklers for 60 hours combined last summer, and the water output rate of the Martins' sprinkler is 30 liters per hour, while the Kelly's is 35 liters per hour To determine how many hours each family used their sprinklers, knowing that in total 1925 liters of water were used, the following logical reasoning must be carried out:
There is a 5 liter difference between the Kelly sprinkler and the Martin sprinkler. If both used 30 liters of water per hour, for 60 hours 1800 liters (30 x 60) would have been used. Therefore, there is an excess of 125 liters that corresponds to an excess of consumption, attributable to the Kelly sprinkler, which consumes 5 liters more of water per hour than the Martin's. Thus, since 125/5 equals 25, in total the Kellys used their sprinkler for 25 hours, while the Martins did it for 35 hours.
This reasoning is proved with the following calculation:
25 x 35 = 875
35 x 30 = 1,050
875 + 1,050 = 1,925
PLEASE HELP!!!!!!!!!!!!!!!!!!!!
Tyler and his children went into a bakery and will buy cupcakes and donuts. He must buy a maximum of 11 cupcakes and donuts altogether. Write an inequality that would represent the possible values for the number of cupcakes purchased, cc, and the number of donuts purchased, d.d.
Answer:
0 < cc + dd ≤ 11
Step-by-step explanation:
≤ means equal to or less than.
It has to be more than zero, obviously.
Answer:
c+d≤11
Step-by-step explanation:
welcome
A tree measures 40.5 feet. Over the next 7 1/2 year, it grows to a height of 78 feet. During the 7 1/2 years, what was the average yearly growth rate of the height of the tree?
Will give brainlist.
Answer:
10.4 feet per year
Step-by-step explanation:
Divide the tree growth by the number of years.
78/7.5=10.4
300 feet above sea level??
Answer:
300
Step-by-step explanation:
if it is 300 feet ABOVE sea level, then it is a positive answer.
you would want to look for the words 'above' or 'below' if it is talking about sea level.
3 2/4(15×5/6 .........................................
A graph titled Fast Freddy has time (minutes) on the x-axis and Distance (miles) on the y-axis. A line goes through points (0, 0) and (4, 1). A 2-column table with 3 rows titled Speed Sam. Column 1 is labeled Time (minutes) x with entries 4, 20, 32. Column 2 is labeled Distance (miles) y with entries one-half, 2 and one-half, 4.
Find the slope from the graph and from the table to compare the speeds of two marathon runners.
What is the constant speed of Fast Freddy?
Answer:
yes this is right that you have have done
Answer:
What is the constant speed of Fast Freddy?: 1/4
What is the constant speed of Speedy Sam? : 1/8
Who ran faster?: Freddy
Step-by-step explanation:
2021 edge
Jack wants to model a situation where the perimeter of the rectangle to the right is 6 feet plus or minus 1.5 feet. Because he is modeling a length "plus or minus" another length, he decides to use an absolute value equation for his model. Do you agree with his decision? Explain your reasoning.
The absolute value of the equation will not work because the value of x would have to be negative for the perimeter to be 6 ft plus or minus 1.5 ft.
What is the perimeter of the rectangle?The perimeter of the rectangle is given as:
Perimeter = 2(Length + Breadth)
The perimeter of a rectangle is 6 feet plus or minus 1.5 feet.
So, we have:
Perimeter = 2(Length + Breadth) = 6 feet ± 1.5 feet.
Then Substitute values for length and width
2(Length + Breadth) = 6 feet ± 1.5 feet.
2(4 + x) = 6 feet ± 1.5 feet.
Now,
2(4 + x) = 6 feet + 1.5 feet.
8 + 2x = 6.5 ft
2x = 6.5 - 8
x = -0.25 ft
2(4 + x) = 6 feet - 1.5 feet.
8 + 2x = 4.5 ft
2x = 4.5 - 8
x = -1.75ft
Here Both values of x are negative.
This means that the absolute value model can't work, because a rectangle cannot have a negative dimension.
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Bentley wants to ride his bicycle 39.6 miles this week. He has already ridden 8 miles.
If he rides for 4 more days, write and solve an equation which can be used to
determine x, the average number of miles he would have to ride each day to meet his
goal.
Answer:
Step-by-step explanation:
Using a linear function, it is found that he would have to ride his bicycle 7.9 miles a day to meet his goal.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, we have that:
The 8 miles he has already ridden is the intercept.The daily average he needs is the slope.When x = 4, y = 39.6, hence:
39.6 = 4m + 8
4m = 31.6
m = 31.6/4
m = 7.9.
He would have to ride his bicycle 7.9 miles a day to meet his goal.
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Find the midpoint of GH
Answer:
2.3 is the mid point of gh
The radioactive isotope 14C has a half-life of approximately 5715 years. A piece of ancient charcoal contains only 81% as much of the radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal
Answer:
1758 years
Step-by-step explanation:
0.693/t1/2 = 2.303/t log No/N
t1/2 = half life of the C-14
t= time taken
No= amount of radioactive material originally present
N= amount of isotope after time t.
But N= 0.81 No
0.693/5715= 2.303/t log No/0.81No
0.00012 = 0.211/t
t =0.211 /0.00012
t= 1758 years
Evaluate the given expression. Subscript 10 Baseline C Subscript 4 Baseline times Subscript 4 Baseline C Subscript 2 a. 1,260 c. 1,275 b. 1,278 d. 1,270
Answer:
The answer is A: 1,260
Step-by-step explanation:
I took the test on Edge
Answer:
A-1,260
Step-by-step explanation:
What is the greatest common factor of 12a and 9a2
Answer:
For these types of problems, You must look at the coefficients and variables separately and find the GCF for each. Then, combine the two
First, take 12 and 9
Factors of both
9- 1, 3, 9
12- 1, 2, 3, 4, 6, 12
So the gcf of 12 and 9 is 3
Now do the variables a and a^2
a^2 is just a twice
The GCF is a
Now combine a and 3
Answer: GCF is 3a
Answer:
GCF is 3a
Step-by-step explanation:
I just know LOLLL
Sheila buys two concert tickets from her friend.
She pays $90 for the two tickets. She looks at the
tickets and sees that each ticket has a face value
of $52.50.
a. How much of a markdown did her friend give
Sheila? Explain how you know.
B. What was the perecent markdown, rounded to the nearst whole percent?
Answer:
15 because the 2 tickets were originally 105
Step-by-step explanation:
52.50 x 2 = 105 because 52 + 52 = 104 and .50 + .50 = 1 so 104 + 1 = 105