A race car travels 400 km in a time of 2 hours. Determine the speed of<br> the race car

Nicole sold 1 cherry pie and 9 pumpkin pies for $60. Lisa sold 11 cheery pies and 4 pumpkin pies for $90. what's the cost each o

zubka84 [21]

X= cost per cherry pie
y= cost per pumpkin pie

NICOLE
1x + 9y= $60

LISA
11x + 4y= $90

STEP 1
multiply Nicole's equation by -11

-11(1x + 9y)= -11($60)
multiply -11 by all terms

(-11 * x) + (-11 * 9y)= (-11 * 60)

-11x - 99y= -660

STEP 2
add Nicole's new equation from step 1 to Lisa's equation to solve for y (using the elimination method)

-11x - 99y= -660
11x + 4y= 90
the x terms "cancel out"

-95y= -570
divide both sides by -95

y= $6 per pumpkin pie

STEP 3
substitute y value into either original equation to solve for x

x + 9y= $60

x + 9(6)= 60

x + 54= 60
subtract 54 from both sides

x= $6 per cherry pie

CHECK
11x + 4y= $90
11(6) + 4(6)= 90
66 + 24= 90
90= 90

ANSWER: Each cherry pie costs $6 and each pumpkin pie costs $6.

Hope this helps! :)

3 0

2 years ago

How many times can 12 go into 307

FinnZ [79.3K]

12 can only go into 30 about 25 whole times.

5 0

2 years ago

If , find the value of 2 square root of 17-x = 2x-10, find the value of x/4.

ira [324]

$2 \sqrt{17-x} =2x-10\ \ \ \ \Rightarrow\ \ \ D:(17-x \geq 0\ \ \ and\ \ \ 2x-10 \geq 0)\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x \leq 17\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x \geq 5\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ D=\\\\2 \sqrt{17-x} =2(x-5)\ /:2\\\\ \sqrt{17-x} =x-5\ \ \ \Rightarrow\ \ \ (\sqrt{17-x})^2 =(x-5)^2\\\\17-x=x^2-10x+25\\\\$

$x^2-9x+18=0\\\\ x^2-3x-6x+18=0\\\\x(x-3)-6(x-3)=0\\\\(x-3)(x-6)=0\ \ \ \ \Leftrightarrow\ \ \ (x-3=0\ \ \ \ or\ \ \ \ x-6=0)\\\\x=3\ \notin\ D\ \ \ \ \ \ \ \ \ \ \ x=6\ \in\ D\ \ \ \Rightarrow\ \ \ \frac{x}{4} = \frac{6}{4} =1.5\\\\Ans.\ \frac{x}{4} =1.5$

7 0

3 years ago

PLEASE HELP ME!

marshall27 [118]

Answer is (4x³ - 6)(16x² + 36 + 24x³)

8 0

3 years ago

Let $f(x)$ be the real-valued function defined for all real $x$ except for $x = 0$ and $x = 1$ and satisfying the functional equ

Mademuasel [1]

We have to find the values of F.
In this case. F is unlikely to be a polynomial.
But the problem is, we can’t calculate the values of F directly.
There is no real value of x for which x = x−1 x because F isn’t defined at 0 or 1. so,
substituting x = 2.
F(2) + F(1/2) = 3.

Substitute, x = 1/2
F(1/2) + F(−1) = −1/2.
We still are not getting the required value,
therefore,
Substitute x = −1

As, F(2) +F(−1) = 0.
now we have three equations in three unknowns, which we can solve.
It turns out that:
F(2) = 3/4
F(3) = 17/12
F(4) = 47/24
and
F(5) = 99/40

Setting
g(x) = 1 − 1/x
and using
2 → 1/2
to denote
g(2) = 1/2
we see that :
x → 1 - 1/x → 1/(1-x) →x

so that:
g(g(g(x))) = x.

Therefore, whatever x 6= 0, 1 we start with, we will always get three equations in the three “unknowns” F(x), F(g(x)) and F(g(g(x))).
Now solve these equations to get a formula for F(x)

As,
h(x) = (1+x)/(1−x)
which satisfies h(h(h(h(x)))) = x

Now, mapping x to h(x) corresponds to rotating the circle by ninety degrees.

7 0

2 years ago

A race car travels 400 km in a time of 2 hours. Determine the speed of the race car