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
Anton [14]
2 years ago
9

The _____ of a line is y=mx+b. The variable m in the equation stands for the _____. The variable b in the equation stands for th

e _____.
Dictionary: Slope of a Line,
y-intercept, slope-intercept form, x-intercept.

(we have to chose from those words what fits, plz help!!)
Mathematics
1 answer:
baherus [9]2 years ago
6 0

Answer:

The answers in order are:

slope-intercept form

slope of a line

y-intercept

Step-by-step explanation:

These are the definitions of the terms.

y=mx+b is called slope-intercept form because it contains the slope (m) and y-intercept (b)

slope of a line is change in y over change in x (steepness) which is m

y-intercept is point line intercepts y-axis and is b

You might be interested in
HELP PLEASE I NEED A ANSWER ASAP
nata0808 [166]

Answer:

5x+6+48+81=180°

5x+135=180

5x=45

x=9

Step-by-step explanation:

I HOPE it will help you

8 0
2 years ago
Read 2 more answers
The width of a rectangle is y feet long. The rectangle is 4 feet longer than it is wide. What is the area of the rectangle? Whic
Korolek [52]

y(y + 4) sq ft  =   is the answer

   


8 0
3 years ago
Read 2 more answers
Mary has a recipe for banana bread. She uses 712 cups of flour to make 3 loaves of banana bread. Andrea will follow the same rec
Softa [21]
237.3f= 1b. Explanation: is 712/3(237.3) so 1b is 237.3f
6 0
2 years ago
Read 2 more answers
Which of the following is the graph of<br> x2 + 2x - 3?<br><br> x+2
geniusboy [140]
-1+ 5 i think I dont know
8 0
3 years ago
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
Other questions:
  • Solve the following equations
    14·2 answers
  • A number is divided by 2. If 16 is added to the quotient you get 20. What is the number? A.2 B.8 C.18 D.72
    8·2 answers
  • The graph of r = 1/ 1-5 sin theta is symmetric about the
    11·2 answers
  • Ernie bought 3 12-packs of regular cola, 4 12-packs of diet cola, and 2 6-packs of orange soda. how many cans did he buy?
    14·2 answers
  • A train travels 150 miles in 3 hours. At this same rate, how many miles will it travel in 8 hours?
    10·2 answers
  • Given f(x) = 3 and g(x) = cos(x). What is Limit of left-bracket f (x) minus g (x) right-bracket as x approaches negative pi?
    7·1 answer
  • can you please tell me what are all the answers to the unit test on Edg for equations 7th grade trimester 2 please
    8·1 answer
  • Help please! I'll mark brainliest!
    9·1 answer
  • PLEASE HELPME NO ONE IS HELPING
    14·1 answer
  • What is the value of a in the equation -1/4 a -5=5-2?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!