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
yarga [219]
3 years ago
7

How to find the vertex of y=2x^2+12x+16

Mathematics
1 answer:
kap26 [50]3 years ago
4 0
First you divide 2 on the whole thing to get x^2 by itself then -b/2a and results in (-3,-1)

You might be interested in
A spring has a natural length of 7 m. If a 4-N force is required to keep it stretched to a length of 11 m, how much work W is re
bezimeni [28]

Answer:

18 J is the work required to stretch a spring from 7 m to 13 m.

Step-by-step explanation:

The work done is defined to be the product of the force F and the distance d  that the object moves:

W=Fd

If F is measured in newtons and d<em> </em>in meters, then the unit for is a newton-meter, which is called a joule (J).

This definition work as long as the force is constant, but if the force is variable like in this case, we have that the work done is given by

W=\int\limits^b_a {f(x)} \, dx

Hooke’s Law states that the force required to maintain a spring stretched x    units beyond its natural length is proportional to

f(x)=kx

where k is a positive constant (called the spring constant).

To find how much work W is required to stretch it from 7 m to 13 m you must:

Step 1: Find the spring constant

We know that the spring has a natural length of 7 m and a 4 N force is required to keep it stretched to a length of 11 m. So, applying Hooke’s Law

4=k(11-7)\\\\\frac{k\left(11-7\right)}{4}=\frac{4}{4}\\\\k=1

Thus F=x

Step 2: Find the the work done in stretching the spring from 7 m to 13 m.

Recall that the natural length is 7 m, so when we stretch the spring from 7 m to 13 m, we are stretching it by 6 m beyond its natural length.

Work needed to stretch it by 6 m beyond its natural length

W=\int\limits^6_0 {x} \, dx \\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1\\\\\left[\frac{x^{1+1}}{1+1}\right]^6_0\\\\\left[\frac{x^2}{2}\right]^6_0=18

18 J is the work required to stretch a spring from 7 m to 13 m.

5 0
3 years ago
jade buys a blouse and a skirt for 3/4of thier original price jade pays a total of 31.50 for the two items if the original price
aleksandrvk [35]

Answer: the original price of the skirt is $24

Step-by-step explanation:

Let x represent the original price of the skirt. if the original price of the blouse is 18, then the original price of the skirt and blouse is (x + 18)

Jade buys a blouse and a skirt for 3/4of their original price. It means that the amount at which she bought the skirt and blouse is

0.75(x + 18)

Applying the distributive property, it becomes

0.75x + 13.5

Jade pays a total of 31.50 for the two items. It means that

0.75x + 13.5 = 31.5

0.75x = 31.5 - 13.5

0.75x = 18

x = 18/0.75

x = $24

3 0
3 years ago
Homework Help ASAP
Vlad [161]

Answer:

3/4 gallon of purple paint left

Step-by-step explanation:

3/8 + 5/8 =8/8

he uses 2/8 so

8/8 - 2/8 = 6/8

3/4 (simplified)

5 0
2 years ago
The difference of two numbers is more than 12,and one of the numbers is 3
klio [65]
X+y = 12
x-y = 3
x = 3+y

Substitute it in 1st equation,
3+y+y=12
2y = 9
y = 4.5

Substitute it in 1st eq.,
x = 12-4.5 = 7.5

So, the two numbers are 7.5 & 4.5

Hope this helps!
6 0
3 years ago
(x÷(y÷z))÷((x÷y)÷z)<br>also the variables are not specified.
Bumek [7]
The answer is:  z² .
__________________________
Given: <span>(x÷(y÷z))÷((x÷y)÷z) ;  without any specified values for the variables; 
_______________________
we shall simplify.
___________________
We have: 
__________
</span>(x÷(y÷z))  /  ((x÷y)÷z) .
_____________________________________
Start with the first term; or,  "numerator":  (x÷(y÷z)) ;
_____________________________________
x  ÷ (y / z) = (x / 1) * (z / y) = (x * z) / (1 *y) =  [(xz) / y ] 
_____________________________________
Then, take the second term; or "denominator":
_____________________________________
((x ÷ y) ÷z ) = (x / y) / z =  (x / y) * (1 / z) = (x *1) / (y *z) = [x / (zy)]
_________________________________________
So (x÷(y÷z))  /  ((x÷y)÷z)  = (x÷(y÷z)) ÷  ((x÷y)÷z) =

 [(xz) / y ] ÷ [x / (zy)]  = [(xz) / y ] /  [x / (zy)] =
                                                                    [(xz) / y ] * [(zy) / x] ;
_______________________________________
                               The 2 (two) z's "cancel out" to "1" ; and
                                  The 2 (two) y's = "cancel out" to "1" ; 
______________________________________________
And we are left with: z * z = z² .  The answer is:  z² .
______________________________________________


4 0
3 years ago
Other questions:
  • Question in image. Thanks!
    10·1 answer
  • How do you do this math problem?
    12·1 answer
  • Help meee.. its due today!!
    15·2 answers
  • What is the perimeter of a rectangle in which<br> A= 154 in² and h = 11 in?
    5·1 answer
  • I don't know this help me​
    8·1 answer
  • I have no clue for both of these please help
    12·1 answer
  • I don't get it at all like I just need help
    8·1 answer
  • The perimeter of a triangle is 34 feet. One side of the triangle is 2 times the second side. The third side is 6 feet longer tha
    9·1 answer
  • Select the most specific name for the quadrilateral shown​
    6·2 answers
  • What is the slope of a line perpendicular to
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!