1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sergeu [11.5K]
2 years ago
13

Three functions are given below: f(x), g(x), and h(x). Explain how to find the axis of symmetry for each function, and rank the

functions based on their axis of symmetry (from smallest to largest).

Mathematics
1 answer:
vredina [299]2 years ago
5 0

9514 1404 393

Answer:

  f, h, g

Step-by-step explanation:

The axis of symmetry for a vertically-opening parabola is the line ...

  x = constant

where the constant is the x-coordinate of the vertex.

__

<u>h(x)</u>

The equation of f(x) is given in vertex form ...

  f(x) = a(x -h)² +k . . . . . vertex: (h, k)

where (h, k) = (-4, 1).

The axis of symmetry of f(x) is x = -4.

__

<u>g(x)</u>

The equation of g(x) is given in standard form ...

  g(x) = ax² +bx +c

The line of symmetry for this parabola is ...

  x = -b/(2a) = -(-16)/(2(2)) = 16/4 = 4

The axis of symmetry of g(x) is x = 4.

__

<u>h(x)</u>

The x-coordinate of the vertex can be read from the graph:

  x = 1

The axis of symmetry of h(x) is x = 1.

__

From smallest to largest, the rank is f(x), h(x), g(x).

You might be interested in
Let b = 64. What is the value of b ÷ 4?
FrozenT [24]
64/4 is 16 if that's what you meant.
3 0
3 years ago
Read 2 more answers
8/x = 32 <br> ..................
krok68 [10]

Answer:

Step-by-step explanation:

x= 1/4

6 0
2 years ago
A news report states that the 99% confidence interval for the mean number of daily calories consumed by participants in a medica
expeople1 [14]

Answer:

The sample mean is of 1925 calories.

The margin of error is of 75 calories.

The sample standard deviation is of 109.7992 calories.

Step-by-step explanation:

Sample mean:

The sample mean is the mean value of the two bounds of the confidence interval. So

M = \frac{1850 + 2000}{2} = 1925

The sample mean is of 1925 calories.

The margin of error

Difference between the bounds and the sample mean. So

2000 - 1925 = 1925 - 1850 = 75 calories.

The margin of error is of 75 calories.

Sample standard deviation:

Here, I am going to expand on the t-distribution.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 18 - 1 = 17

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.99}{2} = 0.995. So we have T = 2.898

The margin of error is:

M = T\frac{s}{\sqrt{n}}

In which s is the standard deviation of the sample and n is the size of the sample.

Since M = 75, T = 2.898, n = 18

M = T\frac{s}{\sqrt{n}}

75 = 2.898\frac{s}{\sqrt{18}}

s = \frac{75\sqrt{18}}{2.898}

s = 109.7992

The sample standard deviation is of 109.7992 calories.

6 0
2 years ago
Under what circumstances are two nonright triangles congruent?
soldier1979 [14.2K]
If these are the given choices of the above problem,

a. one side and one angle are equal. 
<span>b.three sides are equal </span>
<span>c.two angles are equal </span>
<span>d. three angles are equal

Two non-right triangles are congruent when B. THREE SIDES ARE EQUAL.

Two triangles are congruent if:
1) All corresponding sides are equal (SSS)
2) A pair of corresponding sides and the included angle are equal (SAS)
3) A pair of corresponding angles and the included side are equal (ASA)
4) A pair of corresponding angles and a non-included side are equal (AAS)</span>
3 0
3 years ago
Ashley has $62, part of which she wants to use to pay back the money she owes people. She owes $13 to her brother and she owes $
laila [671]

Answer:

Step-by-step explanation:

Amount at hand = $62

Amount owed = $13 + $39

= $52

$62 - $52

= $10

5 0
2 years ago
Other questions:
  • There are 27 pupils. There are twice as many boys than girls. how many boys and girls are there
    10·2 answers
  • Turning improper fractions into mixed numbers . Help?
    10·1 answer
  • 3 divided by 5 (step by step)<br><br>​
    13·1 answer
  • Help me find the slope of this imagine. it a quizizz question and i cant figure it out
    11·1 answer
  • What is the value of this expression 1/3-5
    10·2 answers
  • PLEASE GIVE LATERAL SURFACE AREA AND TOTAL SURFACE AREA ASAP. WILL GIVE BRAINLIEST.​
    9·2 answers
  • X^2 + 4x – 7 = 0 <br> Pls n thx
    5·1 answer
  • Help me plssssssssssa
    6·2 answers
  • (1+i)^2(x+yi)=4+5i<br> Solve for x and y
    8·1 answer
  • Does anyone know the correct equation?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!