A human has 1 head and 2 legs.
A horse has 1 head and 4 legs.

Let's make two equations from what we know.

There were a total of 74 heads.
There were a total of 196 legs.

Let's call humans 'x' and horses 'y'

The total number of heads were 74.
Humans have 1 head, and so do horses.

Our first equation is:
x + y = 74

There were a total of 196 legs.
Humans have 2 legs, and horses have 4 legs.

Our second equation is:
2x + 4y = 196

Our two equations are:

x + y = 74
2x + 4y = 196

We need to solve this system of equations to find out how many humans and horses were at this racing event.

Multiply the first equation by 2.

2(x + y) = 2(74)
2x + 2y = 148

Our two equations are:

2x + 2y = 148
2x + 4y = 196

Subtract the first equation from the second equation.

2x - 2x + 2y - 4y = 148 - 196
2y - 4y = 148 - 196
-2y = - 48

Divide both sides by -2

y = 24

That means that there were 24 horses.

We can plug back in y = 24 into our first equation to find out how many humans there were.

x + y = 74
x + 24 = 74
x + 24 - 24 = 74 - 24
x = 50

There were 50 humans.

At the horse racing event, there were 24 horses and 50 humans.

Your final answer is B. 24 horses and 50 humans.

7 0

3 years ago

Read 2 more answers

Help plzzzz.................

insens350 [35]

Answer:

a = 6, b = - 12

Step-by-step explanation:

Expand the left side and compare the coefficients of like terms to those on the right side.

a(4x - 10) ← distribute parenthesis

= 4ax - 10a

Compare to 24x + 5b , then

4a = 24 ( divide both sides by 4 )

a = 6

Then

5b = - 10a = - 10(6) = - 60 ( divide both sides by 5 )

b = - 12

7 0

2 years ago

Problem page the longer leg of a right triangle is 1ft longer than the shorter leg. the hypotenuse is 9ft longer than the shorte

LenKa [72]

Hello,

To solve this problem we want to use the Pythagorean Theorem.
The pythagorean theorem states that for a 90° triangle,

$a^{2} + b^{2} = c^{2}$

where a and b represent the two legs of the triangle, and c represents the hypotenuse.

Let a = the longer leg and b = the shorter leg.
If the longer leg of the triangle is 1 foot longer than the shorter leg, then
a = b +1.

If the hypotenuse is 9 feet longer than the shorter leg, then c = b + 9.
Using the equations we created, we can plug them into the Pythagorean Theorem to solve for a, b, and c.

Doing this, we have:
$a^{2} + b^{2} = c^{2}$
$(b+1)^{2} + b = (b+9)^{2}$

Expanding this, we get $b^{2} + 2b + 1 + b^{2} = b^{2} + 18b + 81

 2b^{2} + 2b + 1 = b^{2} + 18b + 81

 b^{2} + 1 = 16b + 81

 b^{2} = 16b + 80
 
b^{2} - 16b - 80 = 0

$

Solving for b, we get b = 20, and b = -4.
The length of the side of a triangle cannot be negative, so we know that b = 20.

However, we should check this with the original question to make sure it checks out.

a = b + 1
a = 20 + 1 = 21

c = b + 9
c = 20 + 9 = 29

So, we have a = 21, b = 20, and c = 29. (Also, 20-21-29 is a well known Pythagorean triple)
Using the Pythagorean Theorem, we have:

$21^{2} + 20^{2} = 29^{2}$
441 + 400 = 841
841 = 841, checks out.

So, the shorter leg is 20 feet, the longer leg is 21 feet, and the hypotenuse is 29 feet.

Hope this helps!

7 0

3 years ago

Can sum1 help me cs this and then the opts don’t make sense to me and ik it says don’t use calc but the Calc also got what I got

rewona [7]

Answer:

Answer whatt the calculator said

Step-by-step explanation:

6 0

3 years ago