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
saul85 [17]
3 years ago
6

Please help me :) Thanks!

Mathematics
2 answers:
ohaa [14]3 years ago
7 0
The minimum value for y in the equation y = x² + 12x + 5 is (-6,-31). Here's how I figured it out:

Step 1: Figure out if the parabola is going up or down. If "a" is positive, the parabola will go up. If "a" is negative, the parabola will go down. In your case...

a = 1
Positive
Up
____________________________________________________________

Step 2: Find the Axis of Symmetry.

Formula:      -b             -12               -12
                 --------- =  ------------ =  ------------- = -6
                    2a            2(1)                 2

The axis of symmetry is x = -6.
____________________________________________________________

Step 3: Plug in the value you found for the axis of symmetry for x into your original equation.

f(-6) = -6² + 12(-6) + 5
f(-6) = 36 - 72 + 5
f(-6) = -36 + 5
f(-6) = -31

The minimum gets written as an ordered pair: (-6,-31).
⊕ The axis of symmetry is the first number in the coordinate pair.
⊕ The answer that you get to step 3 is the second number in the pair.
____________________________________________________________

I hope that my answer helps you! This is the method that I use to solve these types of problems, but there are also other methods.


 

Oksanka [162]3 years ago
3 0
X^2+12x+5 = (x+6)^2 -31,

So the minimum value is y = -31. Dunno if -31 or you have to type =-31, I guess just '-31'?

With derivatives:

y' = 2x+12=0, x = -6, then y(-6) = 36-72+5 = -36+5 =-31

Just to be sure!!!! lol
You might be interested in
3
zimovet [89]

Answer:

m less then 5

Step-by-step explanation:

its telling you itw no less than 5 so you want to use a less than symbol.

7 0
3 years ago
What rule would you allow to test weather (x,y) is on line l
n200080 [17]

Answer:

Step-by-step explanation:

If a point (x, y) lies on a straight line, coordinates of the point will satisfy the equation.

Slope of a line passing through two points C(4, 5) and D(8, 10),

m = \frac{y_2-y_1}{x_2-x_1}

m = \frac{10-5}{8-4}

m = \frac{5}{4}

Equation of the line passing through C(4, 5) and slope m = \frac{5}{4}

y - y' = m(x - x')

y - 5 = \frac{5}{4}(x-4)

y = \frac{5}{4}x-5+5

y = \frac{5}{4}x

If point B(4, 0) lies on the line CD,

0 = \frac{5}{4}(4)

0 = 5

Which is not true.

Therefore, point B doesn't lie on line CD.

8 0
2 years ago
Karl drove 619.5 miles. For each gallon of gas, the car can travel 41 miles. What is a reasonable estimate of the number of gall
dusya [7]

Answer:

15

Step-by-step explanation:

Calculation for What is a reasonable estimate of the number of gallons of gas Karl used

Estimated number of gallons used=619.5 miles/41 miles

Estimated number of gallons used=15

Therefore the reasonable estimate of the number of gallons of gas Karl used is 15

6 0
2 years ago
You have quarters and dimes that total $2.80. your friends says its possible that the number of quarters is 8 more than the numb
Sidana [21]

\text{Let the number of dimes be x, then as per the friend the number of }\\
\text{quarters should be 8 more than dimes, so number of quarters}=x+8\\
\\
\text{we know that the value of 1 dime is }\$ 0.10 \text{ value of one quarter is }\$0.25\\
\\
\text{And since the total value of quarters and dimes is }\$2.80, \text{ so we have}\\
\\
0.10(x)+0.25(x+8)=2.80\\
\\
\Rightarrow 0.10x+0.25x+2=2.80\\
\\
\Rightarrow 0.35x=2.80-2\\
\\
\Rightarrow 0.35x=0.80

\Rightarrow x=\frac{0.80}{0.35}=2.29\\
\\
\text{so if we take 2 dimes then we'll have to take 10 quarters according to friend.}\\
\\
\text{So the statement of friend is } WRONG

6 0
2 years ago
The cost of making a shirt is half of what the shirt normally sells for. Today, the shirt is in a 15 percent discount from its n
Vaselesa [24]

Answer:

.85 times the cost to make the shirt

Step-by-step explanation:

Let x represent cost to make the shirt.

Today, the shirt is in a 15 percent discount from its normal price.

Discount = 15/100 * x = 0.15x

Current cost = Original cost - discount

Current cost = x - 0.15x = 0.85x

The answer is;

.85 times the cost to make the shirt

4 0
2 years ago
Other questions:
  • How many inches are there in 32 feet?
    15·2 answers
  • Is anyone able to explain this step by step for next questions also thank you.
    14·1 answer
  • If a straight angel is bisected, what type of angels are the resulting angels
    11·2 answers
  • What is the answer mattes has 8 pencils. Three of them do not have erasers on the end. What fraction of the pencils do not have
    13·1 answer
  • Find the 39th term of the arithmetic sequence
    6·1 answer
  • A graph creates a triangle with the x-axis, the line 3x-2y=0, and the line x+2y=10. Find the area of the triangle formed in squa
    7·1 answer
  • Hello, can i please have help on this question.thank you
    6·2 answers
  • George borrowed $25,000 for a new car. If George pays simple interest at a rate of
    13·2 answers
  • How much are 6 of these $40’s
    12·1 answer
  • Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 11 feet by 11 feet by 2 inches for a patio if
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!