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
pashok25 [27]
2 years ago
14

A dozen more than a number minus twice the number

Mathematics
2 answers:
scZoUnD [109]2 years ago
8 0
X•2+12 I’m not sure if that’s what you’re looking for though
igor_vitrenko [27]2 years ago
6 0
(x + 12) - 2x. i think that’s it lol
You might be interested in
What is the range of the function graphed below?<br> A. 1_ B. -3 C. -2_ D. -3_
kap26 [50]
It would be B because it does to -3
3 0
2 years ago
Read 2 more answers
The height y of a ball (in feet) is given by the function and x is the horizontal distance traveled by the ball.
bazaltina [42]
Given: <em>The height y of a ball (in feet) is given by the function </em><em>y=-1/12x^2+2x+4 </em><em>and x is the horizontal distance traveled by the ball.</em>

Part A:<em> </em><em>How high is the ball when it leaves the child's hand?</em>

Right after the ball leaves the child's hand, it has travelled 0 feet horizontally. Horizontal distance is represented by x, so we could say that x = 0.
Plug in 0 for our equation and solve for y, the height.

y=-\frac{1}{12}x^2+2x+4\\\\y=\frac{1}{12}\cdot0^2+2\cdot0+4\\\\y=0+0+4\\\\\boxed{y=4}

Part B & C: <em>How high is the ball at its maximum height?
</em>
What we basically want to do is find the vertex of the function.
There are multiple ways to do this. You could graph it or make a table, but this method is not efficient.
The method I am going to go over right now is putting the equation in vertex form.

y=-\frac{1}{12}x^2+2x+4

Move the constant to the left side.

y-4=-\frac{1}{12}x^2+2x

Factor out the x² coefficient.

y-4=-\frac{1}{12}(x^2-24x)

Find out which number to add to create a perfect square trinomial.
(Half of 24 is 12, 12 squared is 144. We have to add 144/-12 (which is -12) to each side so that we end up with 144 inside the parentheses on the right side)

y-4-12=-\frac{1}{12}(x^2-24x+144)

Factor the perfect square trinomial and simplify the right side.

y-16=-\frac{1}{12}(x-12)^2

Isolate y on the left side.

y=-\frac{1}{12}(x+12)^2+16

And now we are in vertex form.
Vertex form is defined as y = a(x-h)² + k with vertex (h, k).
In this case, our vertex is (12, 16).

You could've also taken the shortcut that for any quadratic f(x) = ax² + bx + c, the vertex (h, k) is (-b/2a, f(h)). That's basically a summation of this method which you can use if your teacher has taught it to you.

Part D & E: <em>What is the horizontal distance travelled by the ball when it hits the ground?</em>
When the ball hits the ground, y is going to be 0, since y is the ball's height.
There are many ways to solve a quadratic...split the middle, complete the square, and the quadratic formula.

-\frac{1}{12}x^2+2x+4=0
<u>
</u><u>Solving by splitting the midlde</u>
If your quadratic has fractions, this is not a good option.
<u>
</u><u>Solving by completing the square</u>
Move the constant over the right side.

y=-\frac{1}{12}x^2+2x=-4

Divide by the x² coefficient.
(Dividing by -1/12 is the same as multiplying by its reciprocal, -12.)

x^2-24x=-4\times-12

Simplify the right side.

x^2-24x=48

Halve the x coefficient, square it, and then add it to each side.
(Half of -24 is -12, and -12 squared is 144.)

x^2-24x+144=192

Factor the perfect square trinomial.

(x-12)^2=192

Take the square root of each side.

x-12=\pm\sqrt{192}

192 = 8 × 8 × 3, so we can simplify √192 to 8√3.
Add 12 to each side and we get our answer.

x=12\pm8\sqrt{3}

Our function does not apply when x or y is less than 0, of course.
12-8√3 is negative, so this cannot be our answer.
So, the ball had travelled 12+8√3 feet at the time when it hit the ground.

<u>Solving with the quadratic formula</u>
For any equation ax² + bx + c = 0, the solution for x is \frac{-b\pm\sqrt{b^2-4ac}}{2a}.

Our equation, y=-1/12x^2+2x+4, has a = -1/12,  b=2, and c=4.
Let's plug these values into the quadratic formula.

\frac{-2\pm\sqrt{2^2-4\cdot\frac{-1}{12}\cdot4}}{2\cdot\frac{-1}{12}}=\frac{-2\pm\sqrt{4-\frac{-4}3}}{\frac{-1}6}=\frac{-2\pm\sqrt{\frac{16}{3}}}{\frac{-1}6}=\frac{-2\pm\frac{4}{\sqrt{3}}}{\frac{-1}6}

Dividing by a fraction is the same as multiplying by its reciprocal...

-6(-2\pm\frac{4}{\sqrt{3}})=12\pm\frac{-24}{\sqrt{3}}=12\pm\frac{24}{\sqrt{3}}=12\pm\frac{24\sqrt{3}}3=\boxed{12\pm8\sqrt{3}}

Of course, we only want the positive value, 12+8√3.

Revisiting Part B & C:
Since parabolae are symmetrical, if you know two values of x for some value of y (like the x-intercepts we just found in part B) then you can find the average between them to find what the x value of the vertex is, then plug that in to find the y value of the vertex (the height we want)

The average between 12+8√3 and 12-8√3 is 12. Plug that in and we get 16!
5 0
3 years ago
Which expressions are equivalent to the one below? Check all that apply. log 2-log 6 A.log(2)+log(1/6) B.log 2 C.log 3 D.log(1/3
hjlf

Answer:option D is correct Log(1/3)

Step-by-step explanation:

Log2-Log6

Log(2/6)

Log(1/3)

3 0
2 years ago
Multiply the following and COMBINE LIKE TERMS if possible.
Pachacha [2.7K]

Answer:

B.) x2+4x+4

Step-by-step explanation:

(x+2)2

(x+2)(x+2)

x2+2x+2x+4

x2+4x+4

8 0
3 years ago
The line graphed below has a slope of ____.<br><br> 3<br> 1/3<br> -3
Scilla [17]
It is -3 because it had a negative slope
5 0
2 years ago
Read 2 more answers
Other questions:
  • Is cos 314 positive, negative or zero
    8·1 answer
  • Which is the graph of y = 3^ cube root x+1-2
    9·1 answer
  • 3. Given: Circle Q<br>&lt;A = 35<br>Find: m AB​
    10·1 answer
  • Evaluate BC for A = 5, B = -4, and C = 2.<br> -8<br> 6<br> -6
    5·1 answer
  • What Percentage is 7 out of 12
    6·1 answer
  • Kalvin and 4 of his friends want
    5·2 answers
  • afamily had dinner in a restaurant. If the cost of the cdinner was Rs. 2500, how much did the family pay with 10% service charge
    6·1 answer
  • Which property is
    9·2 answers
  • The figure shows two triangles on a coordinate grid:
    10·1 answer
  • If you multiply two prime numbers, will the result be prime or composite?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!