The quadratic function f(x) has a vertex at (5,-5) and opens downward.
If g(x) = (x + 5)2 + 5, which statement is true?
A. The axis of symmetry of f(x) is x = 5, and the axis of symmetry of g(x) is x = -5.
B. The axis of symmetry of f(x) is x = -5, and the axis of symmetry of g(x) is x = -5.
C. The axis of symmetry of f(x) is x = 5, and the axis of symmetry of g(x) is x = 5.
D. The axis of symmetry of f(x) is x = -5, and the axis of symmetry of g(x) is x = 5.
Answers
Answer:
The correct answer is A.
Step-by-step explanation:
We're told that f(x) has its vertex at 5, -5 and opens downward. This tells us that it's axis of symmetry is x = 5.
The format of the function g(x) shows us that its axis of symmetry is x = -5. We're shown this because of the (x + 5)² component.
So the correct answer is A.
Using the properties of the quadratic function we can review the different answers, the correct one is
D. The axis of symmetry of f(x) is x = -5,
the axis of symmetry of g(x) is g(x) = 5.
The quadratic function is a quadratic polynomial that has a parabolic form and a general equation
g (x) = a x² + bx + c
where a, b, c are the coefficients, x is the independent variable and g the dependent
If the function has real roots it can be written in vertex form
g (x) = a (x-h) ² + k
where (h, k) are the coordinates of the vertex
The quadratic function has several properties:
The graph of this function opens up if the coefficient "a" is positive and down if it is negative, The axis of symmetry is parallel to the y axis, passing through the vertex of the function The vertex of the parabola corresponds to the maximum or minimum of the curveThe function can be written as a vertex value that cancels the binomial is where the symmetry axis passes
in this case, for the parabola to open downwards, the curve must be:
g (x) = - (x + 5) ² + 5
this is the expression in vertex form, let's find the value that cancels the binomial,
x + 5 = 0
x = -5
at this point where the axis of symmetry passes
The value of the function for this point is
x = -5
g (x0 = - (-5 + 5) ² + 5
g (x) = 5
Using the properties of the quadratic function we can review the different answers, the correct one is
D. The axis of symmetry of f(x) is x = -5, and the axis of symmetry of g(x) is
g(x) = 5
Learn more about quadratic function here:
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Related Questions
What is the coefficient of 3y+7?
Answers
Answer:
3
Step-by-step explanation:
it's 3 because the number is infront of a variable
The sum of 6.7 and a number is negative. What is a possible value for that number? Explain.
Answers
Answer:
The number must be greater than 6.7. Thus, the sum will be negative.
For example, the number could be 7.
6.7 - 7 = -0.3
The number can be in the range - x ∈ (- ∞ , - 6.7)
We have - the sum of 6.7 and a number is negative.
We have to determine the possible value of that number.
For what range of values of x, the given function is equals to a negative value -y = f(x) = 2x + 10For f(x) to be negative -
f(x) < 0
2x + 10 < 0
2x < - 10
x < - 5
x ∈ (- ∞ , - 5)
According to the question, we have - the sum of 6.7 and a number is negative.
Now -
6.7 + x < 0
x < 6.7
x ∈ (- ∞ , - 6.7)
Hence, the number can be in the range - x ∈ (- ∞ , - 6.7).
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Simplify the expression by combining like terms: -3+7c+c+7+10
Answers
Answer:
21 + 2c
Step-by-step explanation:
-3 + 7 + 7 + 10 = 21
c + c = 2c
Which equation shows how to rewrite the sum of 30 and 45 using their greatest common factor? 30 + 45 = 5(6 + 9) 30 + 45 = 15(2 + 3) 30 + 45 = 5(6) + 15(3) 30 + 45 = 5(6)(3)
Answers
Answer: 30 + 45 = 15(2 + 3)
Step-by-step explanation:
The greatest common factor for 30 and 45 will be gotten as follows:
Factor of 30 = 2 × 3 × 5
Factor of 45 = 3 × 3 × 5.
GCF = 3× 5 = 15
Therefore, the equation that shows how to rewrite the sum of 30 and 45 using their greatest common factor will be:
30 + 45 = 15(2 + 3)
If x = 8, what is the value of 4x + 6?
I NEED HELP! I’m on a test!!
Answers
Answer:
=38
Step-by-step explanation:
Use substitution :3
4(8)+6=38
substitute x to 8 then calculate!
There you'll get your answer.
the required value of expression 4x + 6 is 38 when x = 8.
If x = 8, what is the value of 4x + 6 to be determine.
In mathematics, it deals with numbers of operations according to the statements.
The equation is the relationship between variables and is represented as y = 4x +8 is an example of a polynomial equation.
Here, the expression is given as,
y = 4x + 8
now we have x = 8, put this x in y
y = 4(8) + 6
Solving the equation using the PEMDAS rule of mathematics
1St open the parenthesis of 8 then multiply this 8 by 4.
y = 4*8 +6
y = 32 + 6
Now adding 32 and 6 will give 38
y = 38
Thus, the required value of expression 4x + 6 is 38 when x = 8.
Learn more about arithmetic here:
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how would the numbers 6870000 appear in scientific notation on a calculator screen
Answers
Answer: D
Step-by-step explanation:
Helppp meee pleaseee
Answers
Answer:
I'm not sure sorry if I'm wrong but I think the answers would be 3,4,5
How do I find x in this problem?
Answers
Answer:
(6-2)×180 = 720
101+154+72+123+145+x=720
595 + x = 720
x = 720-595
x= 125
Find the slope of the line that
passes through the following
points. (0,0), (-2,-4)
Answers
Answer:
m=2
Step-by-step explanation:
math is hard
Answer:
2
Step-by-step explanation:
The equation for finding slope is:
[tex]\frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex]
Plugging in our values of x and y gives us:
(-4 - 0)/(-2-0) =
-4/-2 =
4/2 =
2
What is -1 1/3 in a decimal
Answers
Answer:
1.333
Step-by-step explanation:
if rounded then it's 0.333
if wrong I apologize
15 POINTS-
Karen invented a new product that she makes for $2.45. She sells the
product to Walmart marked up 45%. How much does Walmart pay for the
product?
Answers
I think this because if u subtract 2.45- 45% = 1.10 sooo u will have to add $1.10 to 2.25 and that will add up the 45% that Walmart is paying with the original price.
y=2x^2-8x
find a b and c then find the vertex then graph it
Answers
Answer:
y=2x2−8x
y=2x2−8x
Step-by-step explanation:
Xmin:
-10
Xmax:
10
Ymin:
-10
Ymax:
10
Round 543,539 to the nearest hundred thousand
Answers
Answer:
500,000
Step-by-step explanation:
The nearest hundred thousand is the first 5
In rounding when something is 4 or lower it becomes a zero and if it is 5 or higher it is goes up to the next number for example if it is rounded to the nearest ten, and the number is 338, it would be 340
Cook´s bakery is making 15 cakes . Each contains 2 cups of flour . How many cups of flour {f} are needed to make all the cakes
Answers
Answer:
A
Step-by-step explanation:
i got from USATestprep
PLEASE I BEG OF YOU TO HELP ME PLEASE
Answers
Answer:
its B
Step-by-step explanation:
i did it earlier today
Answer:
A
Step-by-step explanation:
-1x-12≤-4
-x≤8
x≥-8
help me this is due this period please please ill mark brainiest with a bunch of points.
Answers
Answer:
(-4,1)
Step-by-step explanation:
The answer is just where the two lines intersect
I'm rather tired so double check me on this but I'm getting about (-4,1) and it's asking for an approximation so think (-4,1) is fine
Answer:
It's around (-4. 5, 1.5). It's somewhere in that range.
write 8,000,000 in scientific notation ?
Answers
Answer:
A: 8 x 10^6
Step-by-step explanation:
A card is in the shape of a rectangle. The length of the card is 7 cm
and the area of the card is 35 sq cm. What is the width of the card in
centimeters?
Answers
lol ok so
7*something or you can make it into a variable x=35
7*x=35
/7 /7
x=5.
Billy charges $15 to mow yard.He needs at least $200 for the new bycicle that he wants.
Answers
Answer:
billy has to mow at least 14 yards
Step-by-step explanation:
200 divided by 15 = about 14
how do you solve this
Answers
Evaluate each expression
P + 8 when P = 6
show ya work
Answers
Answer:umm so with my super jimmy neutron powers the answer is 14 because since P = 6 the equation turns into 6 + 8=14
please help! Giving points!
Answers
Answer:
Bee
Step-by-step explanation:
Ya like jazz?
PLZ HELP ME ASAP PLZ
Answers
Answer:
14
Step-by-step explanation:
5×2²-2-4
5×4-2-4
20-2-4
18-4
14
Answer:
Rewrite the absolute value equation as four equations without absolute value bars.
5z−2=z+65−2=−(z+6)−(5z-2)=z+6−(5z−2)=−(z+6)
After simplifying, there are only two unique equations to be solved.
5z−2=z+65z−2=−(z+6)
Solve
5z−2=z+6 for z.
Tap for more steps...
z=2
Solve
5z−2=−(z+6)for z.
Tap for more steps...
z=−23
List all of the solutions.
z=2,−23
The result can be shown in multiple forms.
Exact Form:
z=2,−23
Decimal Form:
z=2,−0.6
Step-by-step explanation:
it is 0.6
Carson wants to install wallpaper on the wall in his bedroom with the shape and dimensions shown below. 14 ft 11 ft 12 ft - To determine the area of the wall, he divides it into a triangle and a rectangle. What are the dimensions of the triangle?
Answers
Answer:
B
Step-by-step explanation:
Answer:
Its B
Step-by-step explanation:
I did the test.
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 55% salt and Solution B is 80%
salt. She wants to obtain 30 ounces of a mixture that is 65% salt. How many ounces of each solution should she use?
Answers
55 videos to 77 videos
Answers
Answer:
The ratio is 55:77
Step-by-step explanation:
Solve the inequality
x2-x-12 < 0
+
Answers
Step-by-step explanation:
x2-x-12<0
x2-x<12
x=12
what is 9/32 + 7/8 plz help
Answers
Answer:
1 5/32
Step-by-step explanation:
First, find common denominators. What you do to the denominator, you must do to the numerator.
First, multiply 4 to both the numerator and denominator of the second fraction:
(7/8)(4/4) = (7 * 4)/(8 * 4) = 28/32
Next, add across:
9/32 + 28/32 = 37/32
Simplify. Turn the improper fraction into a mixed fraction:
37/32 = (32 + 5)/32 = 1 5/32
1 5/32 is your answer.
~
Answer:
37 /32
Step-by-step explanation:
Find the least common denominator or LCM of the two denominators:
LCM of 8 and 32 is 32
For the 1st fraction, since 8 × 4 = 32,
7 /8 = 7 × 4
8 × 4 = 28 /32
Likewise, for the 2nd fraction, since 32 × 1 = 32,
9 /32 = 9 × 1
32 × 1 = 9 /32
Add the two fractions:
28 /32 + 9/32 = 28 + 9 /32 = 37 /32
So, 7/8 + 9/32 = 37/32
In mixed form: 1 5 /32
Please mark as brainliest!
find the simple interest on each amount 1500 at 11% for two years
Answers
Answer:
330.00
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 11%/100 = 0.11 per year,
then, solving our equation
I = 1500 × 0.11 × 2 = 330
I = $ 330.00
The simple interest accumulated
on a principal of $ 1,500.00
at a rate of 11% per year
for 2 years is $ 330.00.
Evaluate the following expressions given x=6 and y=-3
Answers
a.
[tex] \purple{5 \times 6 - 4 \times ( - 3)}[/tex]
[tex] = 30 + 12[/tex]
[tex] \blue{ = \boxed{42}}[/tex]
b.
[tex] \purple{ {6}^{2} + \frac{6}{ - 3} }[/tex]
[tex] = 36 - 2[/tex]
[tex] \blue{ = \boxed{34}}[/tex]
c.
[tex] \purple{(6 - 5 {)}^{3} + {( - 3)}^{2} }[/tex]
[tex] = {1}^{3} + 9[/tex]
[tex] = 1 + 9[/tex]
[tex] \blue{ = \boxed{10}}[/tex]
=============================Hope it helps
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