Answers
9514 1404 393
Explanation:
General information
All of these questions have to do with various translations of the square root function. The first problem deals with the basic function. Other problems translate the graph in various ways.
The basic square root function has its vertex at (0, 0) and is defined for x-values (domain) that are 0 or positive. The resulting y-values (range) are also zero or positive.
The basic function intercepts the x- and y-axes only at the point (0, 0), so both intercepts are 0. Unless the function is reflected vertically or horizontally, its minimum will be at the left end of any interval, and its maximum will be at the right end.
The transformation of a function g(x) to f(x) = g(x -a) +b causes it to be translated 'a' units to the right and 'b' units up. For the functions here, that means the vertex is translated from (0, 0) to (a, b). For the functions here, the vertex values are the limits of the domain and range, so those will be altered accordingly.
Problems
1.
a) The graph is shown in the attachment as f1 (orange).
b) vertex: (0, 0); domain: [0, ∞); range: [0, ∞)
c) x-intercept: 0; y-intercept: 0
d) On the interval [1, 4], the minimum is √1 = 1, and the maximum is √4 = 2.
__
2.
a) The graph is shown in the attachment as f2 (green). The basic function is translated left 1 and down 2.
b) vertex: (-1, -2); domain: [-1, ∞); range: [-2, ∞)
c) x-intercept: 3; y-intercept: -1 (read from the graph)
d) On the interval, [0.5, 5], the minimum is √1.5 -2 ≈ -0.78; the maximum is √6 -2 ≈ 0.45. Min and max values are shown in the table in the second attachment.
__
3.
a) The graph is shown in the attachment as f3 (purple). The basic function is translated up 3.
b) vertex: (0, 3); domain: [0, ∞); range: [3, ∞)
c) x-intercept: (none); y-intercept: 3 (the vertex)
d) On the interval, [2, 4], the minimum is √2 +3 ≈ 4.41; the maximum is √4 +3 ≈ 5. Min and max values are shown in the table in the third attachment.
__
4.
a) The graph is shown in the attachment as f4 (red). The leading multiplier of -2 causes the graph to be reflected over the x-axis and vertically expanded by a factor of 2 before being translated right 2 and up 3.
b) vertex: (2, 3); domain: [2, ∞); range: (-∞, 3]. Note the range is all y-values less than or equal to 3 because of the vertical reflection.
c) x-intercept: 4.25; y-intercept: (none). The x-intercept is found by solving ...
0 = -2√(x -2) +3
(-3/-2)² = x-2
2 +2.25 = x = 4.25
d) On the interval, [4, 7], the minimum is -2√(7 -2)+3 = 3-2√5 ≈ -1.47; the maximum is -2√(4-2)+3 = 3-2√2 ≈ 0.17. Min and max values are shown in the table in the second attachment.
Related Questions
1. The area of a square tile is 36 square centimeters. What is the length of the tile?
a. 4 cm
b. 6 cm
c. 18 cm
d. 24 cm
Answers
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Mandy created a treasure hunt in the sand at the beach. To keep track of where she buried four items, she graphed their locations in the coordinate plane.
Write the correct ordered pair to show the location of each item.
1. What is the location of item 1? Explain how you found its coordinates. Be sure to tell how you identified the sign of each coordinate.
Write your answer in the space below.
2. What is the location of item 2?
Write your answer in the space below.
3. What is the location of item 3?
Write your answer in the space below.
4. What is the location of item 4?
Write your answer in the space below.
PLEASE I NEED HELP ASAP!!
Answers
Answer:
1. (-3,3 ½)
2. (2.9,1) or (2 9/10,1)
3. (-1,-2.5) or (-1,2 1/2)
4. (1.9,-1) or (1 9/10,-1)
Step-by-step explanation:
Since some points were not directly on a line, they must have not been a whole number, so I estimated and used logical reasoning to get the coordinates of the items. Hope this helps.
A paddock contains ducks and sheep. There are a total of 42 heads and 96 feet in the paddock. Determine how many ducks and how many sheep are in the paddock using simultaneous elimination.
Answers
Answer:
Number of ducks in paddock = 36
Number of sheep in paddock = 6
Step-by-step explanation:
Let d be the number of ducks and s be the number of sheep
Then according to given statements, the equations will be:
[tex]d+s = 42\ \ \ Eqn\ 1\\2d+4s = 96\ \ \ Eqn\ 2[/tex]
For elimination, multiplying equation 1 by 2 and then subtracting from equation 2:
[tex]2(d+s) = 2*42\\2d+2s = 84\\Subtraction:\\2d+4s-(2d+2s) = 96-84\\2d+4s-2d-2s = 12\\2s = 12\\\frac{2s}{2} = \frac{12}{2}\\s = 6[/tex]
Putting s = 6 in equation 1:
[tex]d+6 = 42\\d = 42-6\\d = 36[/tex]
Hence,
Number of ducks in paddock = 36
Number of sheep in paddock = 6
Number of sheep and Number of duck are 6 and 36
Elimination method:Given that;
Number of total heads = 42
Number of total feet = 96
Find:
Number of ducks and sheep
Computation:
Number of legs in 1 sheep = 4
Number of legs in 1 duck = 2
So,
Assume;
Number of sheep = a
Number of duck = b
So,
a + b = 42 ...... Eq1
4a + 2b = 96 ......... Eq2
Eq2 / 2
2a + b = 48..... Eq3
From Eq 3 and Eq1
a = 6
So,
b = 36
Number of sheep = 6
Number of duck = 36
Find out more information 'Elimination method'
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Two cars start from the same point and move in a straight line, one east at a speed of 60 km per hour and the other west at a speed of 80 km per hour. After what time will they live at a distance of 770 km?
Answers
Answer: At 5.5 hours they will be 770 km apart.
Step-by-step explanation: Divide the distance by the total speed at which they are moving apart.
60 km/h + 80km/ = 140 km/h
770 km ÷140 km/h = 5.5 hours
Find the slope given the 2 points, (-7, -3) and (-2,7).
Answers
Answer:
the answer is negative 7 over 2
Step-by-step explanation:
prove that under root 2 is a irrational number
Answers
Answer:
Let's suppose √2 is a rational number. Then we can write it √2 = a/b where a, b are whole numbers, b not zero.
We additionally assume that this a/b is simplified to lowest terms, since that can obviously be done with any fraction. Notice that in order for a/b to be in simplest terms, both of a and b cannot be even. One or both must be odd. Otherwise, we could simplify a/b further.
From the equality √2 = a/b it follows that 2 = a2/b2, or a2 = 2 · b2. So the square of a is an even number since it is two times something.
From this we know that a itself is also an even number. Why? Because it can't be odd; if a itself was odd, then a · a would be odd too. Odd number times odd number is always odd. Check it if you don't believe me!
Okay, if a itself is an even number, then a is 2 times some other whole number. In symbols, a = 2k where k is this other number. We don't need to know what k is; it won't matter. Soon comes the contradiction.
If we substitute a = 2k into the original equation 2 = a2/b2, this is what we get:
2=(2k)2/b22=4k2/b22*b2=4k2b2=2k2
This means that b2 is even, from which follows again that b itself is even. And that is a contradiction!!!
WHY is that a contradiction? Because we started the whole process assuming that a/b was simplified to lowest terms, and now it turns out that a and b both would be even. We ended at a contradiction; thus our original assumption (that √2 is rational) is not correct. Therefore √2 cannot be rational.
(I copied this from the internet, but hope it helps!)
Answer:
Let's suppose √2 is a rational number. Then we can write it √2 = a/b where a, b are whole numbers, b not zero.
We additionally assume that this a/b is simplified to lowest terms, since that can obviously be done with any fraction. Notice that in order for a/b to be in simplest terms, both of a and b cannot be even. One or both must be odd. Otherwise, we could simplify a/b further.
From the equality √2 = a/b it follows that 2 = a2/b2, or a2 = 2 · b2. So the square of a is an even number since it is two times something.
From this we know that a itself is also an even number. Why? Because it can't be odd; if a itself was odd, then a · a would be odd too. Odd number times odd number is always odd. Check it if you don't believe me!
Okay, if a itself is an even number, then a is 2 times some other whole number. In symbols, a = 2k where k is this other number. We don't need to know what k is; it won't matter. Soon comes the contradiction.
If we substitute a = 2k into the original equation 2 = a2/b2, this is what we get:
2 = (2k)2/b2
2 = 4k2/b2
2*b2 = 4k2
b2 = 2k2
This means that b2 is even, from which follows again that b itself is even. And that is a contradiction!!!
WHY is that a contradiction? Because we started the whole process assuming that a/b was simplified to lowest terms, and now it turns out that a and b both would be even. We ended at a contradiction; thus our original assumption (that √2 is rational) is not correct. Therefore √2 cannot be rational.
If y=−3x+5, what is y when x=2/3?
Answers
Answer:
y = 3
Step-by-step explanation:
-3(2/3) + 5= y
-3 * 2/3 = -2
-2 + 5 = 3
So the answer is y = 3
s = 6t² + 3t + 7, 0 ≤ t ≤ 2 Find the body's displacement and average velocity for the given time interval. *
A) 30 m, 30 m/sec
B) 44 m, 22 m/s
C) 18 m / sec , 27 m /sec
D) 30 m / sec , 15 m /sec
Answers
Answer:
no choice
use calculus to find vav
s'=v=12t+3
v(0)=3
v(2)=27
so vav=(27-3)/2
vav=12
-7x + 17 > 115 solution
Answers
Answer:
x<-14
Step-by-step explanation:
Isolate x
-7x>98
x<-14
(can I get brainliest please)
i need help please with all
Answers
Answer:
13. 230°
14. -3
14. 14
15. 9
Step-by-step explanation:
I'm srry if these are wrong
Marta’s fruit stand sold x oranges on Thursday and twice as many on Friday. All together, on both days, she sold 108. Which bar diagram represents the equation?
Answers
Step-by-step explanation:
Thursday = x
Friday = 2x (Since thursday is x and she landed up selling twice the amount she did on thursday, friday would be 2x)
Thursday + Friday = 108
For this problem you would need to find the value of x so you would need to substitute x into the equation that was created for the oranges sold on both the days
Thursday + Friday = x+2x = 108
x +2x = 108
3x = 108
x = 108/3
x= 36
Since x is thursday, Marta sold 36 oranges on thursday
To find the amount of oranges sold on friday you would need to multiply x, which is 36, by 2
2x = 2(36) = 72
72 oranges were sold on friday
Hope this helps!!!
Answer:
A on edge
Step-by-step explanation:
Given that the highest common factor (HCF) and the lowest common multiple (LCM) of 20 and p are 10 and 60 respectively.
Answers
Answer:
Value of p = 30
Step-by-step explanation:
Given:
Two number = 20 , p
Highest common factor (HCF) = 10
Lowest common multiple (LCM) = 60
Find:
Value of P
Computation:
Product of two number = HCF x LCM
20 x p = 10 x 60
20 p = 600
p = 600 / 20
Value of p = 30
If m ∠ 1 = 122, what is the value of x?
Answers
Answer:
122
Step-by-step explanation:
They are equal
How would you solve a linear equation with X and Y on the same side
Answers
Either the question is printed wrong..
Or the answer should simply be
3x + 4y = 10
Answer:
see explanation
Step-by-step explanation:
To solve, choose a value of x or y, substitute into the equation and evaluate for the other variable.
Choose x = 2, then
3(2) + 4y = 10
6 + 4y = 10 ( subtract 6 from both sides )
4y = 4 ( divide both sides by 4 )
y = 1
Thus (2, 1 ) is a solution to the equation
Helpppppppppppppppppppppppppppppppp[ppppppppp
Answers
Find the solution set of the inequality. \qquad16x - 7 \leq -7116x−7≤−71
Answers
Answer:
[tex]x \le -4[/tex]
Step-by-step explanation:
Given
[tex]\qquad16x - 7 \leq -71[/tex]
Required
Solve
Start by adding 7 to both sides
[tex]\qquad16x - 7 + 7 \leq -71 + 7[/tex]
[tex]\qquad16x - 7 + 7 \leq -64[/tex]
[tex]\qquad16x \leq -64[/tex]
Divide both sides by 16
[tex]\frac{16x}{16} \leq \frac{-64}{16}[/tex]
[tex]\frac{16x}{16} \leq -\frac{64}{16}[/tex]
[tex]x \leq -\frac{64}{16}[/tex]
[tex]x \le -4[/tex] --- The solution
Answer:
x < -4
I did this on khan academy
What is the difference between percent difference and percent change?
Answers
Answer:
Percent change is comparing one current number or value to another.
Percent difference is comparing a number or value to another number or value.
Step-by-step explanation:
The graph represents function 1 and the equation represents function 2:
A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3.
Function 2
y = 3x + 1
How much more is the rate of change of function 2 than the rate of change of function 1? (5 points)
1
2
3
4
Answers
Answer:
The rate of change of function 1 = 0The rate of change of the function 2 = 3Therefore, the rate of change of function 2 is 3 more than the rate of change of function 1.
Hence, option C is true.
Step-by-step explanation:
Function 1
A horizontal straight line is drawn joining the ordered pairs (0, 3) and (4, 3).
Given the points
(0, 3)(4, 3)It means
at x = 0, y = 3
at x = 4, y = 3
Since the y-values are same, it means the points lie on a horizontal.
The rate of change or slope of a horizontal line is zero because it does not rise vertically ( i.e. y₁ - y₂ = 0).
Therefore, the rate of change of function 1 = 0
Function 2
y = 3x+1
comparing with the slope-intercept form
y = mx+b
here m is the rate of change or slope and b is the y-intercept
so the rate of change of the function 2 = m = 3
Conclusion:
The rate of change of function 1 = 0The rate of change of the function 2 = 3Therefore, the rate of change of function 2 is 3 more than the rate of change of function 1.
Hence, option C is true.
Write in terms of i . Simplify your answer as much as possible. Square root -27
Answers
Answer:
3i[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] and [tex]\sqrt{-1}[/tex] = i
Given
[tex]\sqrt{-27}[/tex]
= [tex]\sqrt{9(3)(-1)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{3}[/tex] × [tex]\sqrt{-1}[/tex]
= 3i[tex]\sqrt{3}[/tex]
A carton contains 1.92 liters of milk. There are 8 servings in the carton. How many liters of milk are in each serving? A. 0.14 B. 0.19 C. 0.24 D. 0.29
Answers
Answer:
C. 0.24
Step-by-step explanation:
A carton contains 1.92 liters of milk. There are 8 servings in the carton. How many liters of milk are in each serving? A. 0.14 B. 0.19 C. 0.24 D. 0.29
From the above question:
8 servings = 1.92 liters of milk
1 serving = x liters
Cross Multiply
8 × x liters = 1 × 1.92 liters
x liters = 1.92 liters/8
x liters = 0.24 liters
There are 0.24 liters of milk, in 1 serving
Answer:
0.24
Step-by-step explanation:
Here is a polygon. A scaled copy of the polygon is created using a scale factor of 1/2. What are the new side lengths in the copy?
Answers
Answer:
3 by 4
Step-by-step explanation:
Given the dimension of the polygon as 6 by 8
If the scale factor is 1/2, the new side length is gotten by multiplying both dimensions by 1/2 as shown:
For the side length 6:
New length = 1/2 * 6 = 3
For the side length 8:
New length = 1/2 * 8
New length = 4
Hence the new side lengths in the copy is 3 by 4
Please help!
What does c equal
3c + 9 - 2c -6
Answers
Answer:
c= is what ur answer will go in front of so whatever ur answer is u do c= then ur answer
Step-by-step explanation:
3c-2c+9-6=0
c+3=0
c=3
Answer:
3c-2c+9-6=0
c+3=0
c=-3
Make x the subject of y = 3x - 2
You may use the flowchart to help you if you wish.
x 3
- 2 .
+
Answers
Answer:
x = (y + 2)/3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Equality PropertiesStep-by-step explanation:
Step 1: Define
y = 3x - 2
Step 2: Rewrite
Add 2 to both sides: y + 2 = 3xDivide 3 on both sides: (y + 2)/3 = xRewrite: x = (y + 2)/3Answer:
x = [tex]\frac{y+2}{3}[/tex]
Step-by-step explanation:
Given
y = 3x - 2 ( add 2 to both sides )
y + 2 = 3x ( isolate x by dividing both sides by 3 )
[tex]\frac{y+2}{3}[/tex] = x
TJ rented a truck to move to a apartment the regular price of a Truck Rental is $200 TJ has a 50% off coupon he wants to know the sale tax of the truck rental
Answers
Answer:
$100
Step-by-step explanation:
From the question, we are given the following
Rental price of the truck
percentage off coupon = 50%
Required
Sale tax of the truck rental
Sale tax of the truck rental = 50% of the truck price
Sale tax of the truck rental = 50% of $200
Sale tax of the truck rental = 50/100 * 200
Sale tax of the truck rental = 0.5 * 200
Sale tax of the truck rental = $100
Hence the sale tax of the truck rental is $100
What is the total cost of a $95.00 item with a sales tax of 6%?
Answers
Answer:
$100.7
Step-by-step explanation:
Total cost
= cost of item + amount of sales tax
= 95 + 6% of 95
= 95 + 0.06*95
= 95 + 5.7
= $100.7
Answer:
Since the sales tax is 6%, the object will cost 1.06 (100% + 6%) times the original value.
1.06 × $95.00 = $100.70
The object will cost $100.70.
Step-by-step explanation:
Credits to : Padoru
Check : https://brainly.com/question/14308615 to see their response
Plz help below!⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️⬇️
Answers
9514 1404 393
Answer:
3) 1,440
Step-by-step explanation:
The dimensions of the prism can be expressed in terms of the cube dimensions.
1 2/6 inches = 8/6 inches = 8×(1/6 inch)
5/6 inch = 5×(1/6 inch)
6 inches = 36/6 inches = 36×(1/6 inch)
So, the volume of the prism in terms of small cubes is ...
8×5×36 = 1,440 . . . small cubes
Which choice represents the fraction below as a single exponential
expression?
Answers
Answer:
d^5
Step-by-step explanation:
Given the indicinal expression
d^8/d^3
Based on the law of indices, if the base are the same, subtract the powers. This is as shown:
d^8/d^3 = d^{8-3}
d^{8-3} = d^5
Hence the solution is d^5
Select all of the fractions that are equivalent to –23 –2 3 .
Answers
Answer:
=−46
Step-by-step explanation:
What is the value of x in the equation 8+4 = 2(x-1)?
05
11/2
13/2
7
Answers
Answer:
7
Step-by-step explanation:
8+4=2(x-1)
12=2(x-1)
x-1 = 12/2
x-1 = 6
x = 6+1 = 7
Can someone help me