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
KIM [24]
3 years ago
6

I'm stuck, could someone help me?

Mathematics
1 answer:
disa [49]3 years ago
6 0
H = -0.5x² + 0.5x + 15 <em>where</em> x = distance from stump and h = height
We want to find the value of x when h = 10.92.
10.92 = -0.5x² + 0.5x + 15
There are many ways to solve a quadratic like this, let's start by subtracting 10.92.
0 = -0.5x² + 0.5x + 4.08
Now we have everything on one side. Let's solve for x.
Since these numbers aren't whole, I wouldn't try to factor/split the middle.
You could either complete the square or use the quadratic formula.
<u>
</u><u>Completing the square</u>
-0.5x² + 0.5x + 4.08 = 0
We need our x² coefficeint to be 1, so let's multiply by -2.
x² - x - 8.16 = 0
Move the constant to the other side.
x² - x = 8.16
Halve the x coefficient -1 to get -0.5, then square it to get 0.25.
Add this to each side.
x² - x + 0.25 = 8.41
Now we have a perfect square trinomial on the left we can factor...
(x-0.5)² = 8.41
Take the square root of each side...
x-0.5 = <span>±2.9
</span>Add that 0.5 to each side...
x = 0.5<span>±2.9
</span>Of course, the frog can't be a negative distance x from the stump, so we have to take the positive value x = 3.4.
<u>
</u><u>Using the quadratic formula
</u>-0.5x² + 0.5x + 4.08 = 0
I'm going to multiply everything by 100 just to get rid of any decimal points.
-50x² + 50x + 408 = 0
To use the quadratic formula:
The solution to any quadratic ax² + bx + c is x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.
In this case, a = -50, b = 50, and c = 408. Let's input these into our formula.

x=\frac{-50\pm\sqrt{50^2-4(-50)(408)}}{2(-50)}=\frac{-50\pm\sqrt{2500+81600}}{-100}=\frac{-50\pm{84100}}{-100}

=\frac{-50\pm290}{-100}=\frac{240}{-100}\ or\ \frac{-340}{-100}=-0.24\ or\ 0.34

Of course, the frog can't be a negative distance x from the stump, so we have to take the positive value x = 0.34.
You might be interested in
X + 23 = −4 need help
laila [671]

Answer:

-27

Step-by-step explanation:

x+23−23=−4−23

x=−27

6 0
2 years ago
Read 2 more answers
What is the multiplicative inverse of -1/9
Sedaia [141]
A multiplicative inverse is the same thing as a reciprocal, which is basically just flipping the fraction and changing the sign. Therefore the multiplicative inverse of -1/9 is 9
7 0
2 years ago
Read 2 more answers
35,520 divided by 96
Vlada [557]

The answer would be 370

3 0
2 years ago
What is the scale factor very urgent
alisha [4.7K]

Answer:

The scale factor of the triangle if of 3.

Step-by-step explanation:

All you have to do is use figure A and either multiply or divide by a number to get figure B. In this case, the straight vertical side of Figure A is 6 units, and the straight vertical side of Figure B is 2. So 6 divided by 2 is 3. That means that the scale factor of the triangle is of 3. The triangle contracted it's size by 3.  

4 0
2 years ago
Marshall divides his money into four categories. He saves 1/3 of his money. He gives 1/6 of his money to a charity. He uses 1/14
Len [333]
1/3 + 3/7
save + fun + extra

(7/21 + 9/21) = 16/21 on save and fun
7 0
3 years ago
Read 2 more answers
Other questions:
  • A textbook that Janelle needs for her psychology class costs $119 plus 7% sales tax. Which of the following equations correctly
    10·1 answer
  • Simplify the following c^2+4c-12
    11·1 answer
  • 2357111317 what is the next number
    14·1 answer
  • Need help plz I'm really stuck
    7·1 answer
  • I don’t know this please help..
    9·1 answer
  • Which statement describes the graph of function g?
    14·1 answer
  • An image point of a tranformation has coordinates Y'(2, -4). If the pre-image point had coordinates Y(6, -12) what was the trans
    5·1 answer
  • A die is rolled 25 times and 12 evens are observed. Calculate and interpret a 95% confidence interval to estimate the true propo
    15·1 answer
  • The eqution of the diagonal of a parallelogram is 3y=5x +k. The two opposite vertices of a parallelogram are the points (1,-2),
    9·1 answer
  • the greatest common divisor of positive integers $m$ and $n$ is $8$. the least common multiple of $m$ and $n$ is $112$. what is
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!