Kids 12 and under get a discount at Golden Corral. If x represents age, write an inequality for those who do NOT get a discount.

2. A right triangle has a hypotenuse of 15 cm. What are possible lengths for the two legs of the triangle? Explain your reasonin

dolphi86 [110]

Answer:

Two possible lengths for the legs A and B are:

B = 1cm

A = 14.97cm

Or:

B = 9cm

A = 12cm

Step-by-step explanation:

For a triangle rectangle, Pythagorean's theorem says that the sum of the squares of the cathetus is equal to the hypotenuse squared.

Then if the two legs of the triangle are A and B, and the hypotenuse is H, we have:

A^2 + B^2 = H^2

If we know that H = 15cm, then:

A^2 + B^2 = (15cm)^2

Now, let's isolate one of the legs:

A = √( (15cm)^2 - B^2)

Now we can just input different values of B there, and then solve the value for the other leg.

Then if we have:

B = 1cm

A = √( (15cm)^2 - (1cm)^2) = 14.97

Then we could have:

B = 1cm

A = 14.97cm

Now let's try with another value of B:

if B = 9cm, then:

A = √( (15cm)^2 - (9cm)^2) = 12 cm

Then we could have:

B = 9cm

A = 12cm

So we just found two possible lengths for the two legs of the triangle.

4 0

2 years ago

Productivity: My candy bar company made 100 million bars last year, sold for $1 each. I also paid [L] people last year, with an

Murljashka [212]

Answer:

5

Step-by-step explanation:

Productivity: My candy bar company made 100 million bars last year, sold for $1 each. I also paid [L] people last year, with an average salary of $100K last year. I have overhead cost of $10M. What was my TOTAL productivity (no units, rounded to 2 decimal places)?

Solution:

Total productivity is the average of labour and capital productivity weighted and adjusted to price fluctuations. It is the ratio of total output to the total input. The total productivity is given by the formula:

Total productivity = total output / total input

Total output = Revenue = number of bars sold * price per bar

Total output = 100 million * $1 = $100 million

Total input = Total salary + overhead cost

Total salary = number of people * average salary = 100 *$100000 = $10 million

overhead cost = $10 million

Total input = $10 million + $10 million = $20 million

Total productivity = total output / total input = $100 million / $20 million

Total productivity = 5

7 0

2 years ago

What 2 numbers add to get 2 and multiply to 4

rusak2 [61]

Factor 4
4=1 times 4
2 times 2
they don't add to 2
set up equation
x+y=2
xy=4

first equation, subtract x from both sides
y=2-x
subsitute for y
x(2-x)=4
distribute
2x-x^2=4
add x^2
2x=x^2+4
subtract 2x
0=x^2-2x+4
use quadratic formula which is
if you have ax^2+bx+c=0 then
x= $\frac{ -b+/-\sqrt{b^{2}-4ac} }{2a}$ so

1x^2-2x+4=0
a=1
b=-2
c=4
x= $\frac{ -(-2)+/-\sqrt{(-2)^{2}-4(1)(4)} }{2(1)}$
x= $\frac{ 2+/-\sqrt{4-16} }{2}$
x= $\frac{ 2+/-\sqrt{-12} }{2}$
we have $\sqrt{-12}$ and that doesn't give a real solution
therefor there are no real solutions
but if you want to solve fully
x= $\frac{ 2+/-2\sqrt{-3} }{2}$
i= $\sqrt{-1}$
x= $\frac{ 2+/-2i\sqrt{3} }{2}$
x= $1+/-i\sqrt{3}$
x= $1-i\sqrt{3}$ or x= $1+i\sqrt{3}$ (those are the 2 numbers)

6 0

3 years ago

A rectangular garden is 6 feet longer than its wide. The perimeter of it is 52 feet. What equation can be used to find the width

fenix001 [56]

Answer:

Hi there!

Your answer is;

the equation

(w+6)+(w+6)+(w)+(w) = 52

The width of this rectangle is 10. The length of this rectangle is 16.

Step-by-step explanation:

Rectangular perimeter:

l+l+w+w

l= w+6

w= w

(w+6)+(w+6)+(w)+(w)

4w+12= 52

4w = 40

/4

w= 10

Hope this helps!

8 0

3 years ago

please help!! Drag each pair of equations to show whether the system has no solution, one solution, or infinitely many solutions

Vanyuwa [196]

For the given system of equations, considering different systems are split by ;, we have that:

No solutions: 3y = x + 2, 9y = 3x + 7; y = 2x + 3, y = 2x + 5

One solution: 2y = 3x, -5y = -10x,; x = 6, y = 9.

Infinitely many solutions: y = 5x + 2, 3y = 15x + 6.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

It's equations can be written in the format:

Ax = b

Using the above format, we have that:

If A is different from zero, the system has one solution.

If A is zero and B is different of zero, the system has no solutions.

If both are zero, the system has infinite solutions.

At the first system, multiplying the first equation by -3 and adding with the second, we end up with:

0y = 0x + 2

0 = -2

Which is a false statement, hence it has no solutions.

At the second system, the equations are multiples, hence it has infinite solutions.

At the third system, the coefficients are not zero and are not multiples, and it has one solution.

In the fourth system, the one solution is already given.

At the fifth system, we have that:

2x + 3 = 2x + 5

0x = 2

Hence no solutions.

To learn more about system of equations, you can take a look at brainly.com/question/24342899

5 0

2 years ago