The graphs below have the same shape. What is the equation of the blue
graph?
G(x) =
A. G(x) = (x + 3)2-5
B. G(x) = (x+3)2 +5
C. G(x) = (x - 3)2 + 5
D. G(x) = (x - 3)2-5
Answers
The equation of the translated function is:
g(x) = (x + 3)^2 - 2
How to get the equation for the blue graph?We can see that the blue graph is a translation of the red one, where the equation for the red graph is:
f(x) = x^2
Remember that the translations are:
Horizontal translation:
For a general function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N).
If N is positive, the shift is to the left.
If N is negative, the shift is to the right.
Vertical translation:
For a general function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N.
If N is positive, the shift is upwards.
If N is negative, the shift is downwards.
By analyzing the vertices, we can see that the vertex of the blue graph is at (-3, -2) so we have a translation of 3 units to the left and 2 units down, meaning that we have:
g(x) = f(x + 3) - 2 = (x + 3)^2 - 2
So the correct option is A.
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Related Questions
Jack went to the store to buy orange juice. The one-liter container was $2.99. The one-quart container was the same price. Which is the better buy?
help plss
Answers
The one-quart container is the better than one-liter container
What is measurement?
Measurement refers to the comparison of an unknown quantity with a known quantity. The result of the measurement is a numeric value with certain units.
The One- Lite Container is better than the One Quart Container.
One Liter = 1000 ml
and, 1 quart= 946.353 ml
So, One-quart< One Liter
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how do you find the perfect square (x+1)^2=0
Answers
Answer:
By multiplying the term by itself (x+1)(x+1)
Some people like to use the box technique, which formats like this:
x + 1
x x^2 1x
+
1 1x 1
The terms multiply in columns, and then add all together
So
x^2 + 1x + 1x + 1 can be simplified to x^2+2x+1 = 0, which is the perfect square of (x+1)^2 = 0
Step-by-step explanation:
carrie is building a wooden birdhouse for her mom. She finds a plank in the garage to use for the base. When she realizes its too long, Carrie cuts 3 inches off the plank. Now its the correct length of 8.25 inches. what does she subtract the 3 with to get 8.25?
Answers
volume of the cylinder=?
Answers
Answer:
628.32
Step-by-step explanation:
Volume:
πr2h
=π×52×8
= 200π
= 628.31853071796
rate= 5 mi
height= 8 mi
to find:the volume of the cylinder.
solution:[tex]v =\pi {r}^{2} h[/tex]
[tex]v = \pi \times {5}^{2} \times 8[/tex]
[tex]v = 628.3185307 \: {mi}^{3} [/tex]
[tex]v = 628.3 \: {mi}^{3} [/tex]
therefore, the volume of the cylinder is 628.3 cubic miles.
The splasher pool holds what percent of the water the paddler pool holds?
Answers
Answer:
the splasher pool holds 133%.
Step-by-step explanation:
sponsored / paddler equals 144 pi over 108 pi equals 1.3 * 100 = 133%
10. Select the three lengths that could
form a right triangle.
A. 5
B. 6
C. 8
D. 12
E. 13
F. 15
Answers
Answer:
5, 8, 12
Step-by-step explanation:
l ]
l ] 8
l. ]
5 l
l________________]
12
Nolan is designing a new board game, and is trying to figure out all the possible outcomes . How many different possible outcomes are there is he flips a coin, spin a spinner with 5 equal -sized sections labeled Monday ,Tuesday, Wednesday, Thursday, Friday and spins a spinner with three equal sized sections labeled walk , run stop?
Answers
Answer:
The answer is 1/10
Step-by-step explanation:
3+2=5+5=10 outcomes so 1/10
help me please please asap help me
Answers
Answer:
36ft
Step-by-step explanation:
3ft + 3ft x 6 = 36ft
there are 90 sixth-graders and 75 seventh graders and 15 groups how many students are in each group of their grade level be in their group?
Answers
Answer: 11 students in each group
Step-by-step explanation: I answered the other one but u do 90 + 75 which is 165 and then divide by 15
165 divided by 15 is 11 students in each group
Needing a bit of help
Answers
Answer:
x=2, y=-4
Step-by-step explanation:
If you put a vertical or horizontal line straight through the shape and it looks the same, then it is symmetrical. You can put a symmetrical line both vertically AND horizontally. To do this, you just need a line going through the points at the tips and the points at the sides of the quadrilateral. A line that is vertical will be an x=, because it only covers one x-value. So, the line for x will be x=2, because it goes through both tips of the quadrilateral. A horizontal line will be y= because it only covers one y-value. So, the line for the horizontal line will by y=-4, because this goes through both sides of the quadrilateral.
Hope this helps!
A square has sides of 2x + 3. If a rectangle is made up of three of these squares, which expression would represent the perimeter of the rectangle?
A.
6x + 9
B.
8x + 12
C.
12x + 18
D.
16x + 24
Answers
Answer:16X + 24 D
Step-by-step explanation:
Length of rectangle = 3(2X + 3) = 6X +9
Width = 2X + 3
Perimeter = 2(Lengtb + Breadth)
= 2(6X +9) + 2(2X +3)
In a fish tank, 1/5 of the fish are guppies and 1/12 of the fish are goldfish. Which equation most closely estimates the fraction of fish that are guppies or goldfish in the fish tank?
Answers
Answer:
[tex] \frac{1}{4} + 0 = \frac{1}{4} [/tex]
Step-by-step explanation:
[tex] \frac{1}{5} + \frac{1}{12} = \frac{12}{60} + \frac{5}{60} = \frac{17}{60} [/tex]
1/5 is close to 1/4, 1/12 is close to 0, so
1/5 + 1/12 = 17/60, which is close to 1/4.
Hell pleaseeee!! :))
Answers
Answer:
see the attachment!
PLSSSS HELP IVE TRIED EVERYTHING AHHHHHHH
For each graphically defined functions below, state the domain, the range, and the intervals on which the function is increasing, decreasing, or constant.
Domain:
Range:
Increasing:
Decreasing:
Constant Intervals?
Answers
Answer:
Domain: input values (x-values)
Range: output values (y-values)
Increasing function: the average rate of change is positive
Decreasing function: the average rate of change is negative
Constant function: y-values do not vary, regardless of x-values
Graph 1From inspection of the graph, 2 squares = 1 unit.
Domain: [-2, 3]
Range: [-2, 2]
Increasing function: (-2, 0)
Decreasing function: (0, 3)
Graph 2From inspection of the graph, 2 squares = 1 unit.
Domain: [-2, 3]
Range: [-2.5, 2]
Increasing function: (-2, -1) ∪ (1.5, 3)
Decreasing function: (-1, 1.5)
Graph 3From inspection of the graph, 2 squares = 1 unit.
Domain: [-2, 3]
Range: [-1, 2]
Increasing function: (-2, -1)
Constant: (-1, 1)
Decreasing function: (1, 3)
Please help me on this!
Answers
Answer: Choice B
The initial amount in the account.
==================================================
Reason:
x is the number of years
x = 0 is the starting point. Let's plug that in to find...
[tex]y = 982(1.07)^x\\\\y = 982(1.07)^0\\\\y = 982(1)\\\\y = 982\\\\[/tex]
At the start, Sammy has $982 in the bank.
Side note: The 1.07 means the account is growing by 7% each year.
Which is the value of this expression when p = -2 and q = -1?
-4
-1/16
1/16
4
Answers
Answer:
Here is the ans...hope it helps:)
a rectangle has a height of 4x and a width of 3x + 1
express the area of the entire rectangle (expression should be expanded)
Answers
Answer: X should just equal 1 therefore the area of the triangle is 16
Step-by-step explanation:
4(1) * 4= 16
3(1)+1= 4 ^^^
The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. Function 1 graph of function f of x equals negative x squared plus 8 multiplied by x minus 15 Function 2 f(x) = −x2 + 2x − 15 Function 1 has the larger maximum at (4, 1). Function 1 has the larger maximum at (1, 4). Function 2 has the larger maximum at (−14, 1). Function 2 has the larger maximum at (1, −14). Question 10(Multiple Choice Worth 1 points) (08.03 MC) The steps to derive the quadratic formula are shown below: Step 1 ax2 + bx + c = 0 Step 2 ax2 + bx = − c Step 3 Provide the next step to derive the quadratic formula. a times the quantity x squared plus b over a times x end quantity equals negative c x(ax + b) = −c x squared over a plus b over a times x equals negative c over a x squared over a plus b over a equals negative c over a Question 11(Multiple Choice Worth 1 points) (08.01 MC) A food packet is dropped from a helicopter and is modeled by the function f(x) = −12x2 + 19200. The graph below shows the height f(x), in feet, of the food packet at different times x, in seconds: graph of function f of x equals 19200 minus 12 multiplied by x squared Use the graph to determine the domain of f(x) for all viable x values, based on the context. All real numbers x ≤ 19200 −40 ≤ x ≤ 40 0 ≤ x ≤ 40 Question 12(Multiple Choice Worth 1 points) (08.06 LC) The graphs of f(x) and g(x) are shown below: Graph of function f of x equals x squared minus x minus 12. Graph of function g of x equals negative 2.5 times x minus 2 What are the solutions to the equation f(x) = g(x)? x = −3, 4 x = −4, 2.5 x = −0.8, 2.5 x = 8, −8 Question 13(Multiple Choice Worth 1 points) (08.02 MC) The function f(x) = −x2 − 9x + 10 shows the relationship between the vertical distance of a diver from a pool's surface f(x), in feet, and the horizontal distance x, in feet, of a diver from the diving board. What is a zero of f(x), and what does
Answers
The function 2 represented by the equation f(x) = -(x - 2)² + 5 has the larger maximum.
How to complete the function?The functions are given as:
Function 1
f(x) = -(x - 4)² + 1
Function 2:
f(x) = -(x - 2)² + 5
A quadratic function is represented as a (x - h)² + k, when a is negative then, the vertex of the function is a maximum. In both functions, the value of a is -1. This means that both functions are at a maximum
The values of k in both functions are k = 1 and k = 5. By comparison, 5 is greater than 1. Therefore, function 2 has larger maximum.
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Leo is buying candies for his friends. Each pound of chocolate candies costs $5.28 and each pound of hard candies costs $2.09. How much will Leo spend if he buys nine pounds of each type of candy? $
Answers
Answer: $66.33
Step-by-step explanation: Since Leo buys 9 pounds of each candy, multiply $5.28 x 9 and $2.09 x 9.
$5.28 x 9 is $47.52.
$2.09 x 9 is $18.81.
Add $47.52 and $18.81.
Total is $66.33
Solve the equation.
24 - 3x = 2x – 1
-
=
OA) X= 4
OB) X = 5
OC) X= 6
OD X = 25
Answers
Answer:
x=5
Step-by-step explanation:
Subtract
2
x
from both sides of the equation.
24
−
3
x
−
2
x
=
−
1
Subtract
2
x
from
−
3
x
.
24
−
5
x
=
−
1
Move all terms not containing
x
to the right side of the equation.
Subtract
24
from both sides of the equation.
−
5
x
=
−
1
−
24
Subtract
24
from
−
1
.
−
5
x
=
−
25
Divide each term in
−
5
x
=
−
25
by
−
5
and simplify.
Divide each term in
−
5
x
=
−
25
by
−
5
.
−
5
x
−
5
=
−
25
−
5
Simplify the left side.
Cancel the common factor of
−
5
.
Cancel the common factor.
−
5
x
−
5
=
−
25
−
5
Divide
x
by
1
.
x
=
−
25
−
5
Simplify the right side.
Divide
−
25
by
−
5
.
x
=
5
Answer:
5
Step-by-step explanation:
1) 24 - 3x = 2x - 1 Normal equation
2) 24 - 5x = -1 Subtracted 2x from the side
3) -5x = -25 Subtracted 24 from side
4) x = 5 Divided
= 2. Given the quadratic equation 3x2 – 8x + k = 0 has no real roots. Find the range of values of k.
Diberi persamaan kuadratik 3x2 – 8x + k = 0 tidak mempunyai punca nyata. Cari julat nilai k.
Answers
[tex]\text{If there are no real roots, then}\\\\~~~~~\text{Discriminant} < 0\\\\\implies b^2 -4ac < 0\\\\\implies (-8)^2 -4 \cdot 3 k < 0\\\\\implies 64-12k < 0\\\\\ \implies 12k > 64\\\\\implies k > \dfrac{64}{12}\\\\\implies k > \dfrac{16}3\\\\\text{Interval,}~ \left( \dfrac{16}3, ~\infty\right)[/tex]
In rhombus ABCD, AB=12 and AC=22. Find the area of the rhombus to the nearest 10.
a) 195
b) 221.3
c) 105.5
d) 100.8
Answers
Answer:
c) 105.5 square units
Step-by-step explanation:
The area of a rhombus can be computed as half the product of the diagonal lengths.
__
Half the diagonal BD will be one leg of the right triangle formed by the diagonals and the sides of the rhombus. The length of that leg is found using the Pythagorean theorem:
a² +b² = c²
11² +b² = 12²
b² = 144 -121 = 23
b = √23 ≈ 4.796
This value is half the length of diagonal BD, so multiplying it by the length of diagonal AC will give the area of the rhombus.
Area = 1/2(AC)(BD) = (22)(4.796) ≈ 105.5 . . . . square units
Calculate the perimeter of quadrilateral ABCD. (Hint: use distance formula}
Answers
Check the picture below.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-5}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) ~\hfill AB=\sqrt{[ -1- (-5)]^2 + [ 6- 2]^2} \\\\\\ ~\hfill \boxed{\sqrt{32}} \\\\\\ B(\stackrel{x_1}{-1}~,~\stackrel{y_1}{6})\qquad C(\stackrel{x_2}{3}~,~\stackrel{y_2}{2}) ~\hfill BC=\sqrt{[ 3- (-1)]^2 + [ 2- 6]^2} \\\\\\ ~\hfill \boxed{\sqrt{32}}[/tex]
[tex]C(\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-2}) ~\hfill CD=\sqrt{[ -1- 3]^2 + [ -2- 2]^2} \\\\\\ ~\hfill \boxed{\sqrt{32}} \\\\\\ D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-2})\qquad A(\stackrel{x_2}{-5}~,~\stackrel{y_2}{2}) ~\hfill DA=\sqrt{[ -5- (-1)]^2 + [ 2- (-2)]^2} \\\\\\ ~\hfill \boxed{\sqrt{32}}[/tex]
[tex]~\dotfill\\\\ \sqrt{32}\implies \sqrt{16\cdot 2}\implies \sqrt{4^2\cdot 2}\implies 4\sqrt{2}\implies \stackrel{\textit{four times that much}}{4(4\sqrt{2})\implies \blacksquare~~ 16\sqrt{2} ~~\blacksquare}[/tex]
It's a rhoumbus as AC and BD both diagonals are perpendicular to each other .
Find one side
A(-5,2)D(-1,-2)AD
√(-1+5)²+(2+2)²√4²+4²4√2So
Perimeter
4a4(4√2)16√2unitsWhat is the value of 2.4×27.316
Answers
Answer:
65.5584
Step-by-step explanation:
if you forget about the decimal place so you end up with
24 x 27316 you can complete that as long multiplication which youll end up with 655584.
then you count how many numbers you have after the decimal point in your equation and add them together so 2.4 has 1 (the 4) and 27.316 has 3 (the 3,1 and 6) which add 1 + 3 = 4
so you find the decimal place on your answer and you count back 4 places so
1 place ) 65558.4
2 place ) 6555.84
3 place ) 655.584
4 place ) 65.584
they hey presto youve multiplied with decimal places !
PLEASE HELP DUE IN 10 MINS!!!
Use the space below to show your work check your work very carefully because you will need to use your answers to complete part 2 HELP ME WITH THE ONE ON THE BOTTOM BUT IF I HAVE A MISTAKE PLS TELL ME
Answers
Answer:
yes, all answers are correct
Step-by-step explanation:
You deposit $200 in a savings account that earns
5% annual interest compounded continuously.
How much money will you have after 5 years?
A. $255.26
B. $1518.75
C. $2436.50
D. $256.81
Answers
The answer is B which is 1518.75
Simplify: 6(x-2y) - 3(2x+y)
Answers
Answer: -15y
Step-by-step explanation:
6(x-2y) - 3(2x+y)
6x-12y -6x-3y
0x -15y
-15y
Answer:
-15y
Step-by-step explanation:
6(x-2y) - 3(2x+y)
6x-12y -6x-3y
0x -15y
-15y
What is the value of 45÷15+2⋅3?
9
8
15
2
Answers
Answer:
9
Step-by-step explanation:
By BODMAS rule,
45 ÷ 15 + 2 ⋅ 3
= ( 45 ÷ 15 ) + ( 2 ⋅ 3 )
= 3 + ( 2 ⋅ 3 )
= 3 + 6
= 9
Note : -
B - Bracket
O - Of
D - Division ( step 1 )
M - Multiplication ( step 2 )
A - Addition ( step 3 )
S - Subtraction ( step 4 )
Answer:
the answer is 9
Step-by-step explanation:
45/15 = 3
2*3=6
3+6=9
What is TU in circle D?
5.1
3.4
ا
O 3.4
O 3.8
O 7.6
O 5.1
Answers
Answer:
answer-3.4
Step-by-step explanation:
2022 edge
Hi, I'm often really slow at learning math and my condition makes it harder, can someone help me?
Find the zeroes of the function and state their multiplicities.
q(x) = 10x^3 - 58x^2 + 40x
Answers
Explanation: first, we factor out 2x and get: 2x(5x^2-29x+20)=0
In order for this equation to be equal to zero, either 2x must equal to zero or (5x^2-29x+20) must equal to zero
Having said that, if:
2x = 0
X=0
If:
(5x^2-29x+20) = 0
X=4/6, x=5
