Answers
Answer:
9) a = ¾, vertex: (-4, 2), Equation: y = ¾|x + 4| + 2
10) a = ¼, vertex: (0, -3), Equation: y = ¼|x - 0| - 3
11) a = -4, vertex: (3, 1), Equation: y = -4|x - 3| + 1
12) a = 1, vertex: (-2, -2), Equation: y = |x + 2| - 2
Step-by-step explanation:
Note:I could only work on questions 9, 10, 11, 12 in accordance with Brainly's rules. Nevertheless, the techniques demonstrated in this post applies to all of the given problems in your worksheet.
Definitions:The given set of graphs are examples of absolute value functions. The general form of absolute value functions is: y = a|x – h| + k, where:
|a| = determines the vertical stretch or compression factor (wideness or narrowness of the graph).
(h, k) = vertex of the function
x = h represents the axis of symmetry.
Solutions:Question 9) ⇒ Vertex: (-4, 2)Solve for a:
In order to solve for the value of a, choose another point on the graph, (0, 5) and substitute into the general form (equation):
y = a|x – h| + k
5 = a| 0 - (-4)| + 2
5 = a| 0 + 4 | + 2
5 = a|4| + 2
5 = 4a + 2
Subtract 2 from both sides:
5 - 2 = 4a + 2 - 2
3 = 4a
Divide both sides by 4 to solve for a:
[tex]\LARGE\mathsf{\frac{3}{4}\:=\:\frac{4a}{4}}[/tex]
a = ¾
Therefore, given the value of a = ¾, and the vertex, (-4, 2), then the equation of the absolute value function is:
Equation: y = ¾|x + 4| + 2
Question 10) ⇒ Vertex: (0, -3)
Solve for a:
In order to solve for the value of a, choose another point on the graph, (4, -2) and substitute into the general form (equation):
y = a|x – h| + k
-2 = a|4 - 0| -3
-2 = a|4| - 3
-2 = 4a - 3
Add 3 to both sides:
-2 + 3 = 4a - 3 + 3
1 = 4a
Divide both sides by 4 to solve for a:
[tex]\LARGE\mathsf{\frac{1}{4}\:=\:\frac{4a}{4}}[/tex]
a = ¼
Therefore, given the value of a = ¼, and the vertex, (0, -3), then the equation of the absolute value function is:
Equation: y = ¼|x - 0| - 3
Question 11) ⇒ Vertex: (3, 1)
Solve for a:
In order to solve for the value of a, choose another point on the graph, (4, -3) and substitute into the general form (equation):
y = a|x – h| + k
-3 = a|4 - 3| + 1
-3 = a|1| + 1
-3 = a + 1
Subtract 1 from both sides to isolate a:
-3 - 1 = a + 1 - 1
a = -4
Therefore, given the value of a = -4, and the vertex, (3, 1), then the equation of the absolute value function is:
Equation: y = -4|x - 3| + 1
Question 12) ⇒ Vertex: (-2, -2)
Solve for a:
In order to solve for the value of a, choose another point on the graph, (-4, 0) and substitute into the general form (equation):
y = a|x – h| + k
0 = a|-4 - (-2)| - 2
0 = a|-4 + 2| - 2
0 = a|-2| - 2
0 = 2a - 2
Add 2 to both sides:
0 + 2 = 2a - 2 + 2
2 = 2a
Divide both sides by 2 to solve for a:
[tex]\LARGE\mathsf{\frac{2}{2}\:=\:\frac{2a}{2}}[/tex]
a = 1
Therefore, given the value of a = -1, and the vertex, (-2, -2), then the equation of the absolute value function is:
Equation: y = |x + 2| - 2
Related Questions
Mort and George are 18 miles apart on a path when they start moving toward each other. Mort runs at a constant speed of 7 miles per hour, and George walks at a constant speed of 5 miles per hour. How long does it take until Mort and George meet?
Answers
Answer:
1 1/2 hours
Step-by-step explanation:
In one hour, the distance between them is reduced by 7+5 = 12 miles. At that rate, the 18 mile distance between them will be reduced to zero in ...
time = distance/speed
time = (18 mi)/(12 mi/h) = 3/2 h
It will take 1 1/2 hours until Mort and George meet.
Are the ratios 6:1 and 19:3 equivalent?
Answers
Answer: no<3
Step-by-step explanation:
leave a thanks if helped plz
An object is launched directly in the air at a speed of 8 feet per second from a platform located 4 feet above the ground. The position of the object can be modeled using the function f(t)=−16t2+8t+4, where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach?
Answers
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
If a submarine dives 378 feet in 14 seconds, the average change in elevation is feet per second.
Answers
Answer:
27 feet per second.
Step-by-step explanation:
You already have your time unit in second and length measurement in feet so just divide the two 378/14=27 feet per second.
Answer:
-27 feet per second
Step-by-step explanation:
378 ÷ 14 = 27
because the submarine is going down, the sign has to be negative
In the EXPLORE online library, the ratio of the number of novels to that of dictionaries is 2:3 and the total number of novels is 624. If Joe buys more novels and the ratio becomes 7:3, then how many novels have been bought in total?
Answers
Using a system of equations, it is found that 1530 more novels have been bought in total.
For the system, we have that:
x is the number of novels.y is the number of dictionaries.The ratio of the number of novels to that of dictionaries is 2:3, hence:
[tex]\frac{x}{y} = \frac{2}{3}[/tex]
[tex]3x = 2y[/tex]
[tex]y = \frac{3x}{2}[/tex]
Total number of novels is 624, hence:
[tex]x = 624[/tex]
[tex]y = \frac{3}{2} \times 624 = 936[/tex]
Buys z more novels, and the ratio becomes [tex]\frac{7}{3}[/tex], hence:
[tex]\frac{624 + z}{923} = \frac{7}{3}[/tex]
[tex]1872 + 3z = 6461[/tex]
[tex]z = \frac{6461 - 1872}{3}[/tex]
[tex]z = 1530[/tex]
1530 more novels have been bought in total.
A similar problem is given at https://brainly.com/question/17096268
solve using quadratic formula
3n^2-2n-5=0
Answers
=5/3 =−1
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
Can someone please help me
Answers
Answer:
Answer for question 16 $24.64
Answer:
$3.36
17. 31%
18 $ 24.50
Step-by-step explanation:
28 x 0.12 = $3.36
17. 484 - 333.96 = 150.04
What percentage is 150.04 of 484
X/100 = 150.04/484 (% / 100 = is/of)
= 31%
8. 35 x 0.30 = 10.50
$35 - $10.50 = $24.50
If x = 5-2√6, find the value of:
(i) x + 1/x
(ii) x² + 1/x²
Please solve ASAP
Answers
Answer:
x+(1/x) = 10 and x²+ (1/x²) = 98Step-by-step explanation:
Given that :
x = 5-2√6
1/x = 1/(5-2√6)
The denominator = 5-2√6
The Rationalising factor of 5-2√6 = 5+2√6
On Rationalising the denominator then
⇛ 1/x = [1/(5-2√6)]×[(5+2√6)/5+2√6)]
⇛ 1/x = (5+2√6)/[5-2√6)(5+2√6)]
⇛ 1/x = (5+2√6)/[5²-(2√6)²]
Since (a+b)(a-b) = a²-b²
Where ,
a = 5 and b = 2√6⇛1/x = (5+2√6)/(25-24)
⇛ 1/x = (5+2√6)/1
⇛ 1/x = 5+2√6
Now,
x +(1/x)
⇛ 5-2√6+5+2√6
⇛ 5+5
⇛ 10
Therefore, x+(1/x) = 10.
On squaring both sides then
⇛ [x+(1/x)]² = 10²
⇛ x²+2(x)(1/x)+(1/x)² =100
⇛ x²+2+(1/x)² = 100
⇛ x²+(1/x²) = 100-2
⇛ x²+(1/x²) = 98
Therefore, x²+(1/x²) = 98.
Read more:
Similar questions;
Check all that apply. 2(x + 2) + 2 = 2(x + 3) + 1 2x + 3(x + 5) = 5(x – 3) 4(x + 3) = x + 12 4 – (2x + 5) = 1/2 (–4x – 2) 5(x + 4) – x = 4(x + 5) – 1.....
https://brainly.com/question/24697983?referrer
17) Which number is located the same distance on
a number line from -5 as 3 is?
Answers
Answer: -13
Step-by-step explanation:
I know that the distance between -5 and 3 is 8 so I subtracted 8 from the negative 5 so it would be the same distance and I got -13
Answer:
-13
Step-by-step explanation:
Pls help I need ASAP pls
Answers
Answer:
-1
Step-by-step explanation:
The line goes down 1 grid square for each grid square to the right. Each grid square represents 1 unit in both the x- and y-directions. That means the slope is ...
m = rise/run = -1/1 = -1
The slope of the line is -1.
Round any answers to the nearest tenth if necessary.
ad
Technology required. Find the
missing measurements.
nd
35
А.
21
B
BC is 40
I
units,
degrees, and
60
degrees.
Answers
help pls home work home qork
Answers
Answer:
the answer is this sign >. it means the answer on the left is greater than the one on the right
if f(x) = 7(x-1) + 8 , what is rhe value of f(11) ?
Answers
Answer:
f(11)=78
Step-by-step explanation:
f(11)=7(11-1)+8
f(11)=77-7+8
f(11)=78
Answer:
F(11) = 78
Step-by-step explanation:
f(11) means that you would just have to replace “x” on the equation with 11 and then solve;
=> f(11) = 7(11 - 1) + 8
=> f(11) = 7(10) + 8
=> f(11) = 70 + 8
=> f(11) = 78
therefore the answe is 78
Hope this helps!
Body surface area is calculated a) in m2 from weight and height. b) from height. c) from weight. d) in meters from weight and height.
Answers
Answer:
Body surface area is calculated a) in m2 from weight and height.
Step-by-step explanation:
Basically the surface has to be in m2, because you have two dimensions when you multiply: e.g. when you have a lawn 10m x 10m, then you multiply 10 times 10, and meters times meters, so
[tex]10m * 10m = 100m^2[/tex]
3. If Superman can fly .25 miles in 8 seconds, how far could he fly in...
(a) 40 seconds?
Answers
Answer:
1.25 miles
Step-by-step explanation:
0.25 miles = 8 seconds
x miles = 40 seconds
0.25/8 = x/40
0.25 * 40 = 8x
10 = 8x
x = 1.25
-Chetan K
1 2/15 + -3 1/2 in simplest form
Answers
17/15 - 7/2
17/15 Multiply by (2) = 34/30
7/2 Multiply by (15) = 105/30
Subtract
34/30 - 105/30
-74/30
- 2 14/30 divide by 2 ( 7/15)
- 2 7/15
when a company produces 5,000 units, variable costs are $35 per unit and total cost in $200,000. What is the total cost when the company produces 8,000 units? (both 8000 and 5000 units produced are within the relevant range.)
Answers
5. Use the point-slope formula to determine the equation of a line that passes through the points (1, 2) and (-2, 1).
Answers
Answer:
In point-slope form the equation is:
[tex]y - 2 = \binom{1}{3} \times (x - 1)[/tex]
Pls i need an answer now
Answers
Answer:
Step-by-step explanation:
1. 5, 3.5, [tex]\sqrt{9\\}[/tex], [tex]-\frac{12}{5}[/tex], -7
2. 10, π ,3.1415, 0, -10
3. 1[tex]\frac{1}{2}[/tex], 1.44, 1.4(3), 1.(43), [tex]\frac{7}{5}[/tex]
The recursive algorithm given below can be used to compute gcd(a, b) where a and b are non-negative integer, not both zero. procedure gcd(a, b) if a > b then gcd(a, b) := gcd(b, a) else if a = 0 then gcd(a, b) := b else if a = 1 then gcd(a, b) := 1 else if a and b are even then gcd(a, b) := 2gcd(a/2, b/2) else if a is odd and b is even then gcd(a, b) := gcd(a, b/2) else gcd(a, b) := gcd(a, b − a) Use this algorithm to compute (a) gcd(124, 244) (b) gcd(4424, 2111).
Answers
Coding the given algorithm in python 3, the greatest common divisor of the values (124 and 244) and (4424 and 2111) are 4 and 1 respectively.
The program implementation goes thus :
def gcd(a, b):
#initialize a function named gcd which takes in two parameters
if a>b:
#checks if a is greater than b
return gcd (b, a)
#if true interchange the Parameters and Recall the function
elif a == 0:
return b
elif a == 1:
return 1
elif((a%2 == 0)and(b%2==0)):
#even numbers leave no remainder when divided by 2, checks if a and b are even
return 2 * gcd(a/2, b/2)
elif((a%2 !=0) and (b%2==0)):
#checks if a is odd and B is even
return gcd(a, b/2)
else :
return gcd(a, b-a)
A sample run if the program on the values given :
print(gcd(124, 244))
print()
#leaves a space after the first output
print(gcd(4424, 2111))
Learn more :brainly.com/question/25506437
regal furniture company allocates its indirect salaries of $22,500 on the basis of sales. Determine the indirect salaries allocated to Departments 1 and 2 using the following information.
Answers
Answer:
$15750 and $6750Step-by-step explanation:
Revenue share of Dept. 1:
182000/260000*100% = 70%Revenue share of Dept. 2:
100% - 70% = 30%Allocate the indirect salary with same ratio.
Dept. 1:
22500*70/100 = 15750Dept. 2:
22500 - 15750 = 6750In February Lana got a puppy that weighed 13 kilograms. By October the puppy weighed 16.9 kilogram. What was the puppy’s weight increase?.
Answers
Answer:
3.9
Step-by-step explanation:
16.9 take away 13 and you get 3.9 kilograms
(9x+3)5 i really need help with this pleaseeee
Answers
Answer:
1/15
Step-by-step explanation:
Thats my guess I think its that though.
Answer: 3
Step-by-step explanation:
PEMDAS
Would you rather have 15/20 of a pizza or 3/4 of a pizza? Explain your answer and how you solved the problem. plz hurry!
Answers
if 9/24 equals 3/x , then x is ____
Answers
[tex]\\ \sf\longmapsto \dfrac{9}{24}=\dfrac{3}{x}[/tex]
[tex]\\ \sf\longmapsto \dfrac{3}{8}=\dfrac{3}{x}[/tex]
[tex]\\ \sf\longmapsto 3x=24[/tex]
[tex]\\ \sf\longmapsto x=24/3[/tex]
[tex]\\ \sf\longmapsto x=8[/tex]
John buys a computer on sale for $450.00. He
pays $50.00 less than have the original price. How
much was the original price of the computer?
Write and solve an equation
Answers
Answer:
$450+$50= X
X=$500
Step-by-step explanation:
The sale price is $450.00, so you take that amount and $50.00 which the amount he paid less and add them both. We do this because we want to see the original price of the computer. If it mentioned the original price already and the amount $50.00 and asked the sail price instead, we would have to subtract to get the answer.
Here we have to add.
450+50=500
(add the dollar sign)
$450+$50=X
X=$500
5/12+2/3=37 I need help
Answers
Answer:
13/12=37
Step-by-step explanation:
Does "greater than" sign and "not equal to" sign denote the same thing?
Answers
Hello!
The "greater than sign" means one number is greater than the other.
Example: 4>2 (4 is greater than 2)
The "not equal to sign" means one number is not equal to another one.
Example: 15[tex]\neq[/tex]17 (15 is not equal to 17)
Hope this helps!
~Just a determined gal
#CarryOnLearning
[tex]MysteriousNature[/tex]
no they dont
greater than sign denotes that the first digit is greater than the other digit
Some students have a goal of collecting 200 leaves for a science
project. What does 0% of the goal mean in this situation? What does 100% mean?
Answers
Answer:
0% is none of the leaves and 100% is collecting all of them
e/kaid_274404147475337871026587/assig!
Khan Academy
Percent word problems
Of the 50 U.S. states, 4 have names that start with the letter W.
What percentage of U.S. states have names that start with the letter W?
0
Stuck? Review related articles/videos or use a hint.
Answers
Answer:
Step-by-step explanation:
4/50 = 0.08
0.08(100) = 8%