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
Ket [755]
3 years ago
10

For question 3, is it right though? Thankss

Mathematics
1 answer:
pishuonlain [190]3 years ago
8 0

Yes it is correct, 7/12 is the equivalent to C. 7 divided by 12

You might be interested in
2y+3x² +5+y+2x+x²+2 what are the coefficients?
saw5 [17]

Answer: 200

The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

Any quadratic function can be rewritten in standard form by completing the square. (See the section on solving equations algebraically to review completing the square.) The steps that we use in this section for completing the square will look a little different, because our chief goal here is not solving an equation.

Note that when a quadratic function is in standard form it is also easy to find its zeros by the square root principle.

Example 3.

Write the function f(x) = x2 - 6x + 7 in standard form. Sketch the graph of f and find its zeros and vertex.

f(x) = x2 - 6x + 7.

= (x2 - 6x )+ 7.        Group the x2 and x terms and then complete the square on these terms.

= (x2 - 6x + 9 - 9) + 7.

We need to add 9 because it is the square of one half the coefficient of x, (-6/2)2 = 9. When we were solving an equation we simply added 9 to both sides of the equation. In this setting we add and subtract 9 so that we do not change the function.

= (x2 - 6x + 9) - 9 + 7. We see that x2 - 6x + 9 is a perfect square, namely (x - 3)2.

f(x) = (x - 3)2 - 2. This is standard form.

From this result, one easily finds the vertex of the graph of f is (3, -2).

To find the zeros of f, we set f equal to 0 and solve for x.

(x - 3)2 - 2 = 0.

(x - 3)2 = 2.

(x - 3) = ± sqrt(2).

x = 3 ± sqrt(2).

To sketch the graph of f we shift the graph of y = x2 three units to the right and two units down.

If the coefficient of x2 is not 1, then we must factor this coefficient from the x2 and x terms before proceeding.

Example 4.

Write f(x) = -2x2 + 2x + 3 in standard form and find the vertex of the graph of f.

f(x) = -2x2 + 2x + 3.

= (-2x2 + 2x) + 3.

= -2(x2 - x) + 3.

= -2(x2 - x + 1/4 - 1/4) + 3.

We add and subtract 1/4, because (-1/2)2 = 1/4, and -1 is the coefficient of x.

= -2(x2 - x + 1/4) -2(-1/4) + 3.

Note that everything in the parentheses is multiplied by -2, so when we remove -1/4 from the parentheses, we must multiply it by -2.

= -2(x - 1/2)2 + 1/2 + 3.

= -2(x - 1/2)2 + 7/2.

The vertex is the point (1/2, 7/2). Since the graph opens downward (-2 < 0), the vertex is the highest point on the graph.

Exercise 2:

Write f(x) = 3x2 + 12x + 8 in standard form. Sketch the graph of f ,find its vertex, and find the zeros of f. Answer

Alternate method of finding the vertex

In some cases completing the square is not the easiest way to find the vertex of a parabola. If the graph of a quadratic function has two x-intercepts, then the line of symmetry is the vertical line through the midpoint of the x-intercepts.

The x-intercepts of the graph above are at -5 and 3. The line of symmetry goes through -1, which is the average of -5 and 3. (-5 + 3)/2 = -2/2 = -1. Once we know that the line of symmetry is x = -1, then we know the first coordinate of the vertex is -1. The second coordinate of the vertex can be found by evaluating the function at x = -1.

Example 5.

Find the vertex of the graph of f(x) = (x + 9)(x - 5).

Since the formula for f is factored, it is easy to find the zeros: -9 and 5.

The average of the zeros is (-9 + 5)/2 = -4/2 = -2. So, the line of symmetry is x = -2 and the first coordinate of the vertex is -2.

The second coordinate of the vertex is f(-2) = (-2 + 9)(-2 - 5) = 7*(-7) = -49.

Therefore, the vertex of the graph of f is (-2, -49).

8 0
2 years ago
Which expression represents the lateral surface area of the cone?
Brrunno [24]

Answer:

Option "3" is the correct answer to the following question:

Step-by-step explanation:

Given:

Radius of cone (r) = 6 centimeter

height of cone (h) = 8 centimeter

slant height of cone (l) = 10 centimeter

Find:

Lateral surface area of the cone = ?

Computation:

⇒ Lateral surface area of the cone = \pirl

⇒ Lateral surface area of the cone = \pi(6 centimeters) (10 centimeters)

⇒ Therefore, option "3" is the correct answer.

3 0
3 years ago
Please answer the following questions correctly.
mamaluj [8]

Note that a translation along the horizontal is affected by the dependent variable. Hence the correct graphical representation will be Graph C

<h3>Translation and transformation</h3>

Translation is the transformation technique of changing the position of an object on the xy-plane.

Give the parent function f(x) = x^2, if the parent function is translated to the right by 4 units (along the horizontal), the resulting function h(x) will be (x+4)^2

Note that a translation along the horizontal is affected by the dependent variable. Hence the correct graphical representation will be Graph C

Learn more on translation here: brainly.com/question/12861087

#SPJ1

5 0
1 year ago
Jane has gone on a diet.She starts with weight of 61kg and loses 2kg every 3 weeks for 12 weeks.she abandoned her diet at the st
andrezito [222]

Answer:

55 kg

Step-by-step explanation:

lose 2kg per 3 week

for 12 weeks

3×4=12

4×2=8

61-8=53

1kg per week gained for 2 weeks = 2kg

53kg + 2 kg =55kg

Hope you understand...

7 0
1 year ago
|7m–56|, if m&lt;8 write without using absolute value
Ilia_Sergeevich [38]

Answer:

56-7m

Step-by-step explanation:

l7m–56l m<8

so lets replace m with something smalller then 8, how about 7

so then it would be...

l 7 * 7 - 56 l=

l 49-56 l = l -7 l

but the absulute value of -7 is 7, so how does this help us? well lets see

56-49= 7  this proves that all we have to do is  switch the order giving us the solution 56-7m

hope this helped :)

4 0
3 years ago
Other questions:
  • Please, help me on this question, guys! I know the answer for (a) so I'll write down, too. For (b) I tried "$89,000 because that
    6·1 answer
  • Whats 23 X 3 need to know now teacher is getting me to the answer help plzzzzzzz
    6·1 answer
  • PLS HELP WILL GIVE BRAINLIEST TO PERSON WHO ANSWERS WITHIN 4 AND AN HALF MINUTES
    6·1 answer
  • Verify the equation below with each of the values listed for z to find a solution . 3-2z=1/10
    12·2 answers
  • The four-member math team at Pecanridge Middle School is chosen from the math club, which has three girls and five boys. How man
    5·1 answer
  • Help appreciated, thanks so much!
    15·1 answer
  • Can you help me in this question
    12·1 answer
  • Hey can i please <br> get help!
    6·2 answers
  • Solve tan(x)(tanx+1)=0
    12·1 answer
  • Show how to add 2 1/2+ 4/5 using the number line below
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!