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Reika [66]
3 years ago
12

The given lengths are two sides of a right triangle. All three side lengths of the triangle are integers, and together they form

Mathematics
1 answer:
mel-nik [20]3 years ago
8 0
The correct answer is “A” 40,leg
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The difference of two numbers is 15.Five times the smaller is the same as 9 less than twice the larger.Find the numbers
Lana71 [14]

Answer:

small number = -3

large number = 12

Step-by-step explanation:

Suppose two numbers are x and y

smaller number = x

larger number = y

Given that,

The difference of two numbers is 15

<h2>Equation 1</h2><h3>y - x  = 15</h3>

Five times the smaller is the same as 9 less than twice the larger.

<h2>Equation 2</h2><h3>5x = 9 - 2y</h3>

Solve them

-x = 15 - y

x = y -15

put value of x in equation 2

5(y - 15) = 9 - 2y

-75 + 5y = 9 - 2y

-75 - 9 = -2y - 5y

-84 =  -7y

y = 84/7

y = 12

x = 12 - 15

x = -3  

8 0
2 years ago
I have a question about polynomial division it is in the picture
Cloud [144]

To answer this question, we have to do the long division process for polynomials. We can do the operation as follows:

To do this division process, we have:

1. Divide the first term of the dividend by the first element of the divisor. They are:

\frac{-4x^3}{4x^2}=-x

2. Now, we have to multiply this result by the divisor, and the result will change its sign since we have to subtract that result from the dividend as follows:

-x\cdot(4x^2_{}-4x-4)=-4x^3+4x^2+4x

And since we to subtract this result from the dividend, we end up with:

-(-4x^3+4x^2+4x)=4x^3-4x^2-4x

3. Then we have the following algebraic addition:

\frac{\begin{cases}-4x^3+24x^2-15x-15 \\ 4x^3-4x^2-4x\end{cases}}{20x^2-19x-15}

4. Again, we need to divide the first term of the dividend by the first term of the divisor as follows:

\frac{20x^2}{4x^2}=5

5. And we have to multiply 5 by the divisor, and the result will be subtracted from the dividend:

5\cdot(4x^2-4x-4)=20x^2-20x-20

Since we have to subtract this from the dividend, we have:

-(20x^2-20x-20)=-20x^2+20x+20

6. And we have to add this algebraically to the dividend we got in the previous step:

\frac{\begin{cases}20x^2-19x-15 \\ -20x^2+20x+20\end{cases}}{x+5}

And this is the remainder of the division, x + 5.

As we can see from the division process, we got as:

1. The quotient: -x + 5

q=-x+5

2. The remainder: x + 5.

R=x+5

Since we have that the dividend = divisor * quotient + remainder.

Therefore, the result for this division is:

-4x^3+24x^2-15x-15=(4x^2-4x-4)\cdot(-x+5)+(x+5)

4 0
11 months ago
Solve. x – 6 = 14 – 8 0 12 20 –12
lana [24]
The answer is 12 because first we have to simplify 14-8 to 6 so it will be
x-6=6
Then add 6 to both sides lastly simplify 6+6 to 12
So x=12
7 0
3 years ago
What is the solution of the equation below?<br> x² - 4= - 5
madam [21]

Answer:

Not possible to work out

Step-by-step explanation:

NO Explanation can be explained as this question cannot be solved

8 0
2 years ago
Members of a college chemistry department agree to contribute equal amounts of money to make up a scholarship fund of $280. Then
Zarrin [17]

Answer:

7 members

Step-by-step explanation:

Lets say that the department has n members. If each member contributes with an equal amount x and make a total of $280, we know that:

n*x = 280

Where each one colaborated with:

n*x/n = 280/n

Or what is the same that: (as the n on the left eliminate themselves)

x = 280/n (*)

Now the department hires 3 more members, so we now have n+3 members. And we know that the pass from contributing x to contribute $30 less, it is, x-30 (I omit the $ symbol for simplicity). So, know we have:

x-30 = 280/(n+3)

We can replace x here by the formulation of x we did in the (*) equation:

( 280/n) - 30 = 280/(n+3)

using common denominator:

( 280/n) - 30 n/n = 280/(n+3)

( 280 - 30 n)/n = 280/(n+3)

Cross multiplying the denominators:

( 280 - 30 n)*(n+3) = 280*(n)

280n - 30n^2 + 840 - 90n = 280n

Subtracting 280 n in both sides:

30n^2 + 840 - 90n = 0

Dividing both sides by 30:

-n^2 - 3n + 28 = 0

Factorizing this term (you can notice the factor immediately or solving with baskara resolution, I omit the baskara for simplicity):

-(n + 7)(n - 4) =0

So, n is equal to 4 and -7. As we are dealing with people we can not have -7 people, so we keep only n=4.

So, previous the new hiring there were 4 members, now there are 7.

The used to collaborate with 280/4 = $70, now the collaborate with 280/7=$40, and we see the collaboration decreased in $30.

7 0
3 years ago
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