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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.
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Choose all that give the correct expression for the quantity described. The difference of nine times a number x and the quotient
ohaa [14]

Step-by-step explanation:

We are to get the expression for the following statements;

1) The difference of nine times a number x and the quotient of that number and 5.

The product of nine and a number x is expressed as;

=9 \times x\\= 9x

The quotient of that number and 5.

= \frac{x}{5}

The difference between both expression;

9x - \frac{x}{5}

Hence, the difference of nine times a number x and the quotient of that number and 5 is expressed as 9x - \frac{x}{5}

2) Eight more than the quotient of twelve and a number n

Quotient of twelve and a number n is expressed as:

\frac{n}{12}

Eight more than the resulting function is;

\frac{n}{12}+8

Hence eight more than the quotient of twelve and a number n is expressed as \frac{n}{12}+8

3) The product of a number and the quantity 'six minus the number' plus the quotient of eight and the number.

Let the number be x:

six minus the number is expressed as;

6-x

product of a number x and the quantity 'six minus the number is;

x(6-x)

quotient of eight and the number is;

\frac{8}{x}

Taking the resulting sum of the last two expression

x(6-x) + 8x

Hence the product of a number and the quantity 'six minus the number' plus the quotient of eight and the number is expressed as;

x(6-x) + 8x

4) Sum of three consecutive even integers. 2x + (2x + 2) + (2x + 4).

Let the first even number be 2x

The consecutive even numbers are gotten by adding 2 to the preceding number. The two consecutive even integers are 2x+2 and 2x+2+2

the sum of three consecutive even integers is expressed as;

= 2x +(2x+2)+(2x+2+2)\\=  2x+(2x+2)+(2x+4)

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3 years ago
The Wares want to buy a new computer. The regular price is $1,049. The store is offering a 20% discount and a sales tax of 4.25%
MariettaO [177]

Answer:

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Step-by-step explanation:


5 0
3 years ago
Read 2 more answers
Please help me it is due today
boyakko [2]

Answer:

B

Step-by-step explanation:

A give me 2'zero

b give me 9'zero

c give 8'zero

d gives 5 zero

e give me 4'zero

for example it give me two zero it 100

or if five 5 zero it 100000

hope this helps

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2 years ago
Use the figure to write and solve an equation for x.
Digiron [165]

Answer:

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Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask :)

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