Answer:
Horizontal translation of the parent graph
Step-by-step explanation:
Definitions:In the vertex form of a quadratic function, f(x) = a(x - h)² + k, where:
(h, k) = vertex of the grapha = determines the width and direction of the graph's opening.A horizonal translation to the parent graph is given by, y = f(x - h), where:
h > 0 ⇒ Horizontal translation of h units to the righth < 0 ⇒ Horizontal translation of |h | units to the leftIn the graph of g(x) = (x + 12)², the vertex occurs at point (-12, 0).
While the vertex of the parent graph, f(x) = x² occurs at point, (0, 0).
Answers:Since the vertex of g(x) occurs at point, (-12, 0), substituting the value of (h, k ) into the vertex form will result into:
g(x) = a(x - h)² + k
g(x) = [x - (-12)]² + 0
g(x) = (x + 12)² + 0
g(x) = (x + 12)²
Therefore, the graph of g(x) = (x + 12)² represents the horizontal translation of the parent graph, f(x) = x², where the graph of g(x) is horizontally translated 12 units to the left.
The aquarium in Mrs. Mnon's
class holds 10 gallons. How many
quarts does the tank hold? How
many pints? Please
The work of a student to solve the equation 4(2x − 4) = 8 + 2x + 8 is shown below:
Step 1: 4(2x − 4) = 8 + 2x + 8
Step 2: 6x − 8 = 16 + 2x
Step 3: 6x − 2x = 16 + 8
Step 4: 4x = 24
Step 5: x = 6
In which step did the student first make an error and what is the correct step?
A). Step 2; 8x − 4 = 2(6 + x + 6)
B). Step 2; 8x − 16 = 16 + 2x
C). Step 3; 6x − 2x = 16 − 8
D). Step 3; 6x + 2x = 16 + 8
Answer:
B
Step-by-step explanation:
He added 4 to 2 instead of multiplying.
Use intercepts to graph the equation -x+5y=5
Anyone know how to answer this
Answer:
21
Step-by-step explanation:
The average rate of change of function f(x) from x = a to x = b is
[tex] \dfrac{f(b) - f(a)}{b - a} [/tex]
Here we have
a = -1
b = 2
f(a) = f(-1) = 1
f(b) = f(2) = 64
[tex] \dfrac{f(b) - f(a)}{b - a} = [/tex]
[tex] = \dfrac{f(2) - f(-1)}{2 - (-1)} = [/tex]
[tex] = \dfrac{64 - 1}{2 + 1} [/tex]
[tex] = \dfrac{63}{3} [/tex]
[tex] = 21 [/tex]
If 5 gallons of gas cost $7.79, how much
will 7 gallons cost?
Answer:
$10.91
Step-by-step explanation:
7 gallons cost:
[tex](\frac{7.79}5}) (7)=\frac{(7.79)(7)}{5} =10.906[/tex]
rounded to cents: 10.91
I hope this help you
6.
Which of the following equations describes the graph?
A. y= -2x^2 - 4
B. y= 2x^2 + 4
C. y= -2x^2 + 4
D. y= 2x^2 - 4
Answer:
C. y= -2x^2 + 4
Step-by-step explanation:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
(
0
,
−
4
)
Focus:
(
0
,
−
33
8
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
−
31
8
x
y
−
2
−
12
−
1
−
6
0
−
4
1
−
6
2
−
12
________________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
0
,
4
)
Focus:
(
0
,
33
8
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
31
8
x
y
−
2
12
−
1
6
0
4
1
6
2
12
______________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
(
0
,
4
)
Focus:
(
0
,
31
8
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
33
8
x
y
−
2
−
4
−
1
2
0
4
1
2
2
−
4
_______________
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
0
,
−
4
)
Focus:
(
0
,
−
31
8
)
Axis of Symmetry:
x
=
0
Directrix:
y
=
−
33
8
x
y
−
2
4
−
1
−
2
0
−
4
1
−
2
2
4
find the domain below
Answer:
Interval Notation: [-2, 10]
Set Notation: {x|-2≤x≤10}
Step-by-step explanation:
C = 5/9 (F − 32)
The equation above gives the Celsius temperature, C, corresponding to the Fahrenheit temperature, F. Find the Celsius temperature equivalent to 77° F.
A. 25° C
B. 57° C
C. 45° C
D. 30° C
a point on the circumference of the circle with the equation (x+10)^(2)+(y+1)^(2)=25 is?
The point on the circumference of the circle with the equation (x+10)^(2)+(y+1)^(2) = 25 is (-6 , 2).
What is the equation of the circle with radius r units, centered at (x,y) ?If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane,
then, its equation is given as:
(x-h)^2 + (y-k)^2 = r^2
The given equation is
(x+10)^(2)+(y+1)^(2)=25
Where,
h = - 10
k = -1
r = 5
If x = -6 and y = 2
then the given equation of circle is stidfy the given points.
Hence, the point on the circumference of the circle with the equation (x+10)^(2)+(y+1)^(2) = 25 is (-6 , 2).
Learn more about equation of a circle here:
https://brainly.com/question/10165274
#SPJ2
Can someone help me with this. I tried to total all them up with 180 but none of the answers i got match the ones from the riddle
Answer:
9. x=102
10. x=56
11. x=104
12. x=138
Step-by-step explanation:
9. In this problem, they are alternate exterior angles, meaning they are the same value. x=102
10. x is a corresponding angle, meaning they are the same. x=56
11. There are consecutive interior angles. The sum of these two angles is 180. to find x, subtract 76 from 180. 180-76 = 104 x = 104
12. These two angles are verticle angles, meaning they are equivalent. x = 138
Is this answer right?
Answer:
Step-by-step explanation:
all angles are congruent:false
B.consecutive angles are congruent:false
corresponding angles are congruent:true.
c.diagonals bisect eachother:true.
d.diagonals bisect opposite angles:false.
Find your own values that prove that tan(u-v) does not equal tan u - tan v. Show your work and explain why you chose these values.
To prove that tan(u - v) does not equal tan u - tan v, we start by assuming values for u and v.
To do this, we assume the following values
[tex]\mathbf{u = 75}[/tex]
[tex]\mathbf{v = 45}[/tex]
So, we have:
[tex]\mathbf{tan(u - v) \ne tan(u) - tan(v)}[/tex]
Substitute the assumed values for u and v
[tex]\mathbf{tan(75 - 45) \ne tan(75) - tan(45)}[/tex]
Subtract 45 from 75
[tex]\mathbf{tan(30) \ne tan(75) - tan(45)}[/tex]
Using a calculator, calculate the values of tan(30), tan(45) and tan(75)
So, we have:
[tex]\mathbf{0.5774 \ne 3.7321 - 1}[/tex]
Subtract 1 from 3.7321
[tex]\mathbf{0.5774 \ne 2.7321}[/tex]
Notice that the expression on the left-hand side and the expression on the right-hand side are not equal.
Hence, [tex]\mathbf{tan(u - v) \ne tan(u) - tan(v)}[/tex] is true
Read more about proofs of trigonometry at:
https://brainly.com/question/22698523
A. Complete the table if y varies
directly as x or x2
B. Complete the table if y varies inversely as x.
Direct variation is represented by the equation y = k × x and inverse variation is represented by y = k/x
Table 1:
y = k × x
30 = k × 5
30 = 5k
k = 30/5
k = 6
So,
y = 30
y = 30 k = 6
y = 30 k = 6x = 5
y = 30 k = 6x = 5Equation: y = 6x
y = k × x
y = 10 × 8
y = 80
So,
y = 80
y = 80 k = 10
y = 80 k = 10x = 8
y = 80 k = 10x = 8Equation: y = 10x
y = 3x
18 = 3x
x = 18/3
x = 6
So,
y = 18
y = 18k = 3
y = 18k = 3x = 6
y = 18k = 3x = 6Equation: y = 3x
y = 2x²
72 = 2x²
x² = 72/2
x² = 36
x = √36
x = 6
So,
y = 72
y = 72k = 2
y = 72k = 2x = 6
y = 72k = 2x = 6Equation: y = 2x²
Table 2:
y = k/x
5 = k/6
5 × 6 = k
30 = k
So,
y = 5
y = 5k = 30
y = 5k = 30x = 6
y = 5k = 30x = 6Equation: y = 30/x
y = k/x
y = 36/4
y = 9
So,
y = 9
y = 9k = 36
y = 9k = 36x = 4
y = 9k = 36x = 4Equation: y = 36/x
y = 60/x
20 = 60/x
20x = 60
x = 60/20
x = 3
So,
y = 20
y = 20k = 60
y = 20k = 60x = 3
y = 20k = 60x = 3Equation: y = 60/x
y = 24/x
y = 24/12
y = 2
So,
y = 2
y = 2k = 24
y = 2k = 24x = 12
y = 2k = 24x = 12Equation: y = 24/x
Read more:
https://brainly.com/question/472621
please help me :) there is a picture
4-7 questions need help
Select the correct answer.
Ann is buying a house that costs $250,000. She is making a down payment of 15 percent, and her closing costs will amount to 3 percent. Over the life of her loan, she will pay $282,089.89 in monthly payments. What is the total cost of her house?
A.
$327,089.89
B.
$338,390.89
C.
$339,560.89
Answer:
c i think
Step-by-step explanation:
I'm sorry if not
I need help thanks a lot
Answer:
Below!
Step-by-step explanation:
First, let's simplify the roots for each.
√49 = √7 x 7 = 7√40 = √4 x 10 = 2√10 = 6.32√36 = √6 x 6 = 6Please check out the file so you can see the graphed points on the line. I apologize for the bad mouse-writing.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
$75 to $25 show your work
Answer:
decrease
Step-by-step explanation:
the percent change measures FROM the first value. A change from 50 to 75 is a change of 50% (25 is the difference between the two numbers, and 25 is 50% of 50). A change from 75 to 50 is a change of -33.3% (25 is still the difference between the two. 25 is 33.3% of 75
John earned $12 a day for babysitting his siblings after school each weekday (he did not babysit on weekends). He liked to have a small amount of money to spend on treats at the school canteen that his parents refuse to buy, but he also wanted to build up some savings. John decided to put a fraction of his earnings into a jar straight away. He spent all the rest on canteen treats.
How much money did John earn over a nine week term?
After 9 weeks, John had $378 in his jar. What percentage of his money did he save?
Answer:
He earns $540
70% of his money went to savings
Step-by-step explanation:
9 weeks x 5 days a week = 45 days
45 days x $12 a day = $540
378 * 100 / 540 = (378*100) / 540 = 37800/540 = %70
PLEASE HELP!!! URGENT!!!!!!!!!!!!
Answer:
C
Step-by-step explanation:
For a relation to be a function then every value of x must map to exactly one unique value of y.
Here every x- value corresponds to exactly one y- value
Then the ordered pairs represent a function
Please help find x it would helpful
Answer:
12
Step-by-step explanation:
Apply the second theorem of Euclides.
x^2= 16*9 follows that x = sqrt(9*16) = sqrt(144) = 12
sqrt means square root
Is this answer right?
Answer:
Blank 1: 64° (or 32°, depending on what the label applies to)
Blank 2: 42
Step-by-step explanation:
It is a common mistake to believe you have solved the problem when you have found the value of the variable(s) in the problem. You have correctly found the values of n (42) and m (9). However, that is not what the problem is asking for.
We cannot tell if the value (1/2n+11)° is referring to angle DAB, or to angle CAB. In any event, (1/2n+11)° = (1/2×42 +11)° = 32°.
If that is angle CAB, then angle DAB is twice that value, 64°.
If that is angle DAB, then angle DAB is 32°.
__
The side length CD is the same as any other side length in a rhombus, so ...
CD = 4m+6 = 4×9 +6
CD = 42 . . . . units
How do I factor this expression
2xy-x^2y-6+3x
write the equation of the line that passes through the given point and has the given slope write all final answers in slope intercept form (3,-8); slope = -3
Step-by-step explanation:
the general slope intercept form is
y = ax + b
a is the slope.
b is the y-intercept (the point, where the line crosses the y-axis, meaning the y value when x=0).
we get b by using the point coordinates in the equation and solve for b :
-8 = -3×3 + b = -9 + b
1 = b
so, the full line equation is
y = -3x + 1
Evaluate [tex]\frac{15}{k}[/tex] when k =3
8
-6
4
ल
-8-
What is the domain of function m?
co
-2
-8
6
- 4
x
HELPP
Answer:
( - ∞, ∞ )
Step-by-step explanation:
The domain of the function is all values of x , that is
- ∞ < x < ∞ , or in interval notation
(- ∞, ∞ )
Gavin deposited $200 into his savings account that is compounded semi-annually at an interest rate of 9%. Gavin hoped he would have enough money in 8 years to buy a $400 gaming console for college. Is Gavin correct? Write and solve an equation, showing your work to justify your answer
Answer:
His answer was correct:
(200*0.09)=18
18*16=288
200+288=488
which shows 2^-2 * 2^6 in exponential form
Answer:
16
Step-by-step explanation:
2^-2=0.25
2^6=64
times
=16
Find 56÷512 . Write in simplest form.
Answer:
0.109375
Step-by-step explanation:
Answer:
[tex]^7/_{64}[/tex]
Step-by-step explanation:
[tex]56\div512={^5^6}/_{512}[/tex]
Look for the [tex]GCF[/tex] of [tex]56[/tex] and [tex]512[/tex]
we find that it's [tex]8[/tex]
[tex]56\div8=7\\512\div8=64[/tex]
our fraction in simplest form is [tex]^7/_{64}[/tex]
If (x 2y)dy/dx=2x-y what is the value of.
The second differential of the function is 3/7
Given the differential function [tex](x +2y)=\frac{dy}{dx} (2x-y)[/tex]
Differentiate both sides with respect to x implicitly
[tex](x +2y)=\frac{dy}{dx} (2x-y)[/tex]
[tex]1+2y'=y"(2x-y)+y'(2-y') \\y''=\frac{1+2y'}{(2x-y)+y'(2-y') }[/tex]
Get the first derivative at the point (3, 0)
[tex]y'=\frac{2x-y}{x+2y} \\y'=\frac{2(3)-0}{0+2(3)}\\y'=\frac{6}{6} \\y'=1[/tex]
Substitute into the second derivative to have:
[tex]y''=\frac{1+2y'}{(2x-y)+y'(2-y') }\\y''=\frac{1+2(1)}{(2(3)-0)+(1)(2-(1)) }\\y''=\frac{3}{6+1} \\y''=\frac{3}{7}[/tex]
Hence the second differential of the function is 3/7
learn more on differential equation here; https://brainly.com/question/18760518
Complete question:
If (x 2y)dy/dx=2x-y what is the value of [tex]\frac{d^2y}{dx^2}[/tex] the point (3,0)