Using translation concepts, it is found that the correct option, which represents the transformation made to function [tex]g(x) = 8|x - 15| - 30[/tex], is given by:
D. p is translated 15 units right, then has a vertical stretch by a factor of 8, and then is translated 30 units down.
The parent function is:
[tex]p(x) = |x|[/tex]
The first transformation was [tex]x \rightarrow x - 15[/tex], which means that it was shifted 15 units to the right.
Then, the function was multiplied by 8, which means that it was stretched vertically by a factor of 8.
Finally, 30 was subtracted from the function, which means that it was shifted down 30 units.
Hence, the correct option is given by:
D. p is translated 15 units right, then has a vertical stretch by a factor of 8, and then is translated 30 units down.
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Please help me with parts b and c.
9514 1404 393
Answer:
b. A × B = GCF(A, B) × LCM(A, B)
c. 15 = GCF × LCM / 20
Step-by-step explanation:
b. The products of the numbers in the table are 80, 108, 216, 45.
The products of the corresponding GCF and LCM are 80, 108, 216, 45.
Conjecture: the product of the numbers is equal to the product of the GCF and LCM.
__
c. GCF×LCM = 5×60 = 300 = A×B = 20×B
B = 300/20 = 15
The other number is 15, found by using the conjecture of part b.
_____
Additional commentIf you think for a minute about what the GCF and LCM are, you realize the relationship discussed in this problem must be the case. Consider the factors of two numbers A and B:
A = (factors in common with B) × (factors unique to A)
B = (factors in common with A) × (factors unique to B)
The GCF, by definition, are (factors in common between A and B).
The LCM, by definition, is the product of unique factors:
(common factors) × (factors unique to A) × (factors unique to B)
__
Then the product of the LCM and the GCF is ...
GCF × LCM =
(factors in common) × ((factors in common) × (unique to A) × (unique to B))
Using the associative and commutative properties of multiplication, we can rearrange this product to be ...
((factors in common)×(unique to A)) × ((factors in common)×(unique to B))
= A × B
__
Personally, I use a kind of diagram to represent the factorization of A and B and their LCM and GCF:
[unique to A (common] unique to B)
Then A = factors in [ ], and B = factors in ( ). The stuff in (common] is the GCF, and the overall product is the LCM.
Using the example of part c, this would look like [4 (5] 3), so A = 4·5 = 20 and B = 5·3 = 15. The GCF is 5, and the LCM is 4·5·3 = 60.
The end parts [unique to A( and ]unique to B) can have no common factors. Any common factors must reside in the (common] part.
(a) The area of a rectangular parking lot is 5964 m².
If the length of the parking lot is 84 m, what is its width?
Answer:
71 m................
area =length *width
5864=84*width
width=5864/84
hence width is 71m
25×2- (42÷6) + 18 can someone help me?
Answer:
The answer is 61
Answer:
61
Step-by-step explanation:
solve pls brainliest
Step-by-step explanation:
-4+13=9
-16-(-29)=13F lower
Can anyone help me with the question in the picture?
Answer: x=26
set 4x+8=6x-44
then get the x to the left side and make it stand alone by subtracting the other numbers to get them over
Hope this helped a little XD
Who does edge still in 2021?
Everyone uses this sofware to develop there decent knowledge about different courses that are best taught by Artificial Intelligence (A.I.).
How are different types of linear equations similar and how are they different
Answer:
The graph of linear inequalities include a dashed line if they are greater than or less than but not equal to. Linear equations, on the other hand, include a solid line in every situation. Moreover, linear inequalities include shaded regions whereas linear equations do not.
Step-by-step explanation:
(Please help!) Which table shows a function that is decreasing only over the interval (–1, ∞)?
Answer:
Table DStep-by-step explanation:
Lets verify is the function is decreasing in the given interval.
Table A-5, -2, -1, 2 ⇒ this is increasing, noTable B-7, -6, -1, 1 ⇒ this is increasing, noTable C-1, 2, 1, -6 ⇒ this is neither increasing, nor decreasing, noTable D1, 0, -4, -8 ⇒ this is decreasing, yes1. Preeta watches an ant and a beetle crawl in a hole in the ground. The beetle is inch below ground level. The beetle climbs the distance the ant is below ground level. The beetle is now inches below ground level.
(a) Let x = the position of the ant relative to ground level. What equation can be written to solve for x?
(b) Solve the equation from Part (a). Show your work.
(c) What is the distance between where the ant is and where the beetle is? Answer the question in a complete sentence. Show your work.
Answer:
1a: [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]
1b: See below
1c: [tex]2\frac{3}{4}[/tex] inches between the beetle and ant
Step-by-step explanation:
1a. To build the equation, we need to see that the beetle started at 3/4th inches below ground level, then "climbed" (which is poor English, it should be descended) a certain distance, and then it ended up at 2 1/2 inches below ground. The distance "climbed" can be represented as 1/3X, where "X" is the ant's current distance. We would do 1/3rd times "X" to figure out how much the beetle climbed down.
So that means, if we added together the starting position of 3/4, plus the distance the beetle descended (1/3X), that would get us TO 2 1/2 inches below ground (the beetle's new current position). So therefore our equation is:
[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]
1b. Solve the equation written above from 1a.
[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]
-3/4 -3/4 [subtract 3/4 to start the process of getting x by itself]
[tex]\frac{1}{3}x[/tex] = 1[tex]\frac{3}{4}[/tex]
*3/1 *3/1 [Multiply Reciprocal to get X by itself]
x= [tex]5\frac{1}{4}[/tex]
1c. So we take the position of the ant figured out on 1b (5 1/4 inches), and the new current position of the beetle (2 1/2 inches), and subtract them
5 1/4 - 2 1/2 = [tex]2\frac{3}{4}[/tex]
These answers were found by using this info:
the beetle is 3/4 inch below the ground level. The beetle climbs 1/3 the distance. The beetle is now 2 1/2 inches below ground.
solve pls branliest!
Answer:
(a) -7+3
(b)-7+(-3)
Un conjunto de 10 000 observaciones tiene una distribución normal con media de
450. Si 1700 de ellas están comprendidas entre 450 y 460. ¿Cuál es la desviación
estándar?
Answer:
567898765
Step-by-step explanation:
need an answer, please need an answer, please.
Answer:
Step-by-step explanation:
1) c
x² = 1
x² - 1 = 0
Degree of quadratic equation should be 2.
2) 'a'- coefficient of x² cannot be 0
option a
3) option c
Standard form: ax² + bx +c = 0
4) c = 5
3x² + 8x = -5
3x² + 8x + 5 = 0
option c
5) b= 0
option a
What is the length of BC?
A.7
B.12
C.13
D.17
E V60
F. V119
Answer:
BC = 13
Step-by-step explanation:
Pitagoras:
H^2= 5^2 + 12^2
H^2=25 + 144
H^2= 169
H= V 169 ---- square root
H= 13 -------BC
Answer: C. 13
Step-by-step explanation:
Using pythagoras ;
[tex]BC = \sqrt{5^{2}+12^{2} }[/tex]
[tex]BC=\sqrt{25 + 144}[/tex]
[tex]BC =\sqrt{169}[/tex]
[tex]BC= 13[/tex]
Please give me a brianliest answer
Peter owns a store that sells men's clothing. His most significant monthly expenses to run the store are the cost of retail items and the power bill. This month, he purchased 50 suits for his store. He also
needed to buy 35 pairs of shoes, which cost $25 dollars more than each suit. The expression shows Peter's total expenses for this month:
50 (x) + 35 (x + 25) + 450
What does (x + 25) represent?
А-the cost of 25 suits
B-the cost of each pair of shoes
C-the total cost of the pairs of shoes
D-the price of one suit and one pair of shoes
Answer:
B-the cost of each pair of shoes
Step-by-step explanation:
This is because each pair of shoes cost $25 dollars more than each suit (which is represented by x)
x + 25, represents the cost of each pair of shoes. Option B is correct.
Given that,
This month Peter purchased 50 suits for his store. He also needed to buy 35 pairs of shoes, which cost $25 dollars more than each suit. The expression shows Peter's total expenses for this month
50 (x) + 35 (x + 25) + 450, What x + 25 represents the equation is to e determined.
A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.
Here,
Let x be the rate of each suit,
and the cost of the shoe is $25 dollars more than each suit. So,
50 (x) + 35 (x + 25) + 450
In the equation, x + 25 represent the cost of each pair of shoe.
Thus, x + 25, represents the cost of each pair of shoes. Option B is correct.
Learn more about polynomial function here:
https://brainly.com/question/12976257
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At the end of the night, a restaurant had 3/4 of a large birthday cake left over. The 5 employees each took home the same amount of leftover cake. How much cake did each employee take home?
Answer:
3/20
Step-by-step explanation:
This is a division question.
The equation is 3/4 ÷ 5 or, to simplify this, 3/4 ÷ 5/1.
When you divide fractions you have to flip the second number and multiply the two fractions.
So, you have to do 3/4 x 1/5 which is 3/20.
Thus, the answer is 3/20.
Good luck!
James lives 4 miles from the town library. He lives 256 miles from the post office.
How much closer is James to the post office than to the library?
Enter your answer in the box as a mixed number in the simplest form. (Please Help!)
Answer:
1 1/6 miles
Step-by-step explanation:
i failed the test sooo haha here you go hopefully you dont fail:)
Using the unitary method we can conclude that James is 64 times closer to the post office than to the library.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We have been given that James lives 4 miles from the town library.
James lives 256 miles from the post office.
Therefore, we will divide the 256 by 4 to get the answer;
256/4 = 64
Thus, we can conclude that James is 64 times closer to the post office than to the library.
To learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
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What is the result of the division?
2x^3-5x*4
—————-
x-3
Answer:
2x² + 6x + 13 remainder 43Step-by-step explanation:
Long division:
2x³ - 5x + 4 ÷ x - 3 = 2x² + 6x + 13 rem 43
2x³ - 6x²
6x² - 5x
6x² - 18x
13x + 4
13x - 39
43
Lira has flowers. 2/9 of them are roses, and 3/7 of the remainder are sunflowers and the rest are tulips. If she has 36 tulips, how many sunflowers and roses does she have all together?
The total sunflowers and roses Lira has is 18 and 27 respectively
Let
Total flowers = x
Roses = 2/9 of x
= 2/9x
Remaining = x - 2/9x
= (9x-2x) / 9
= 7/9x
Sunflowers = 3/7 of 7/9x
= (3 × 7)/(7 ×9)x
= 21/63x
Tulips = 36
Total = roses + sunflowers + tulips
x = 2/9x + 21/63x + 36
x - 2/9x - 21/63x = 36
(63x -14x-21x) / 63 = 36
28/63x = 36
cross product
28x = 36 × 63
28x = 2268
x = 2268/28
x = 81
Therefore,
Total flowers = x
= 81 flowers
Roses = 2/9x
= 2/9 × 81
= 18 flowers
Sunflowers = 21/63x
= 21 / 63 × 81
= 27 flowers
Read More:
https://brainly.com/question/2261275
what does this mean??
Answer:
"do you mock people's mental states?"
Bvtcctctctc CJ bububuv
Answer:
A) [tex]y+7=-3(x-4)[/tex]
Step-by-step explanation:
Hi there!
The given equations are written in point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where m is the slope of the line and [tex](x_1,y_1)[/tex] is a point that falls on the line
Notice how the line is travelling infinitely down as x increases. This means that the slope is negative.
Therefore, the equation of the line is either A or B.
Now, let's look at A:
[tex]y+7=-3(x-4)[/tex]
This equation suggests that the point (4,-7) falls on the line, which it does.
Therefore, the equation of the graph is [tex]y+7=-3(x-4)[/tex].
I hope this helps!
Answer: A.) y + 7 = - 3 ( x - 4 )
Step-by-step explanation:
i didnt know i was a graph lolz im just playin have a nice day kind person and sorry for answering late!!!!!!
Helpp need it now
9.) Find the N' .
1.) {j , u , d , g}
2.) {m , n , t , a , l}
3.) {j , u , d , g , e}
4.) {m , e , n , t , a , l}
10.) Find the N U I.
1.) {m , n , t , a , l}
2.) {j , u , d , g , e}
3.) {m , e , n , t , a , l}
4.) {j , u , d , g , m , e , n , t , a , l}
Answer:
8.) ans {e}
9.) ans {j, u, d, g}
10.) ans {j, u, d, g, m, e, n, t, a, l}
I need help please !!! Help noww
Answer:
Sorry link only if you have enough rupees
Step-by-step explanation:
78x
87x
09x
cc
bb
dom=cb
makes sense now c.r.y because this answer is too smart f/.or y.o.u not helping you? just pray and god will give you your answer or talk morshu he'll give you help BUT only if you have enough rupees.
solve pls brainliest
Answer:
(1,6)
Step-by-step explanation:
all u gotta do is look at the graph, the school is at x=1 and y=6 so therefore (1,6)
Answer:
(1,6)
Step-by-step explanation:
Are constants like terms
Step-by-step explanation:
yes , all constant are like terms.
How many songs can Chet download for $1.00 using Get Tunes? If she downloaded 27 for $13.50
Answer:
2
Step-by-step explanation:
Whats the two answers? ( Branliest )
Answer:
B and CStep-by-step explanation:
Factors:
(A) x + y, no product(B) 5(x + y), two factors(C) (x - y)(x + y), two factors(D) xyz, three factors#A
x+yNo
#B
5(x+y)5x+5yYes
#C
(x-y)(x+y)Yes
#D
xyzNo
Completely Factor the following equations.
a) 3x^3 + 15x^2 + 18x
Help please! I’m a bit young so it might be easy for you! Can you please tell me this and maybe I’ll understand? Giving brainliest!
Answer:
2.36 miles
Step-by-step explanation:
subtraxt them from each other
What is the value of x in the proportion below? -
2/3 over 5 = x over 15
•2
•3
•10
•75
Answer:
2/3 over 15 is 10
so 10/5=2
2 is the answer
Step-by-step explanation:
Brisa is 2 years older than Aja. Damaris is 1 year younger than half of Brisa's age. The sum of all their ages is 27.
brisa is 12.5 aja is 10.5 and damaris is 4