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2 years ago

Is this equation an infinite solution, no solution, or one solution?? 36-7x=-7(x-5) is

Mathematics

1 answer:

Rzqust [24]2 years ago

6 0

Answer:

no solution

Step-by-step explanation:

36-7x=-7(x-5)

first what we have to do is do the multiplications

36 - 7x = -7x + 35

we add 7x from both sides

36 - 7x + 7x = - 7x + 7x + 35

36 = 35

we subtract 36 from both sides

36 - 36 = 35 - 36

0 = -1

This means that the system has no solution

if we look at the equation at the beginning we can realize since we have the same term on both sides "-7x" and a term without x on each side, this means that we can never find a value of x that meets the conditions

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you can buy 5 cans of green beans at the village market for $3 you can buy 10 of the same cans of beans at Sams Club for $6.10 w

ioda

Each can of green beans costs ($3.00/5) = 60¢ at the
village market, and ($6.10/10) = 61¢ at Sam's Club.

If you're watching every penny, then that MIGHT be enough
of a difference to make you decide to buy your beans at the
village market, but not necessarily.

If, say, the village market is farther away from you, or if there are
other things you're going to get from Sam's anyway, then you
should buy your beans there too.

6 0

3 years ago

Help!! 50 points and brainliest!

Viktor [21]

Answer:

Second choice:

$x=2t$

$y=4t^2+4t-3$

Fifth choice:

$x=t+1$

$y=t^2+4t$

Step-by-step explanation:

Let's look at choice 1.

$x=t+1$

$y=t^2+2t$

I'm going to subtract 1 on both sides for the first equation giving me $x-1=t$ . I will replace the $t$ in the second equation with this substitution from equation 1.

$y=(x-1)^2+2(x-1)$

Expand using the distributive property and the identity $(u+v)^2=u^2+2uv+v^2$ :

$y=(x^2-2x+1)+(2x-2)$

$y=x^2+(-2x+2x)+(1-2)$

$y=x^2+0+-1$

$y=x^2$

So this not the desired result.

Let's look at choice 2.

$x=2t$

$y=4t^2+4t-3$

Solve the first equation for $t$ by dividing both sides by 2:

$t=\frac{x}{2}$ .

Let's plug this into equation 2:

$y=4(\frac{x}{2})^2+4(\frac{x}{2})-3$

$y=4(\frac{x^2}{4})+2x-3$

$y=x^2+2x-3$

This is the desired result.

Choice 3:

$x=t-3$

$y=t^2+2t$

Solve the first equation for $t$ by adding 3 on both sides:

$x+3=t$ .

Plug into second equation:

$y=(x+3)^2+2(x+3)$

Expanding using the distributive property and the earlier identity mentioned to expand the binomial square:

$y=(x^2+6x+9)+(2x+6)$

$y=(x^2)+(6x+2x)+(9+6)$

$y=x^2+8x+15$

Not the desired result.

Choice 4:

$x=t^2$

$y=2t-3$

I'm going to solve the bottom equation for $t$ since I don't want to deal with square roots.

Add 3 on both sides:

$y+3=2t$

Divide both sides by 2:

$\frac{y+3}{2}=t$

Plug into equation 1:

$x=(\frac{y+3}{2})^2$

This is not the desired result because the $y$ variable will be squared now instead of the $x$ variable.

Choice 5:

$x=t+1$

$y=t^2+4t$

Solve the first equation for $t$ by subtracting 1 on both sides:

$x-1=t$ .

Plug into equation 2:

$y=(x-1)^2+4(x-1)$

Distribute and use the binomial square identity used earlier:

$y=(x^2-2x+1)+(4x-4)$

$y=(x^2)+(-2x+4x)+(1-4)$

$y=x^2+2x+-3$

$y=x^2+2x-3$ .

This is the desired result.

3 0

3 years ago

Read 2 more answers

A rectangle has an area of 40 square units. The length is 6<br> units greater than the width.

stiks02 [169]

Answer:

Answer:

The width is 4 units, and the length is 10 units.

Step-by-step.

Step-by-step explanation:

area of rectangle = length * width

Let L = length; let W = width.

"The length is 6 units greater than the width.": L = W + 6

area = LW = 40

Since L = W + 6, we substitute L with W + 6.

(W + 6)W = 40

W^2 + 6W = 40

W^2 + 6W - 40 = 0

(W - 4)(W + 10) = 0

W - 4 = 0 or W + 10 = 0

W = 4 or W = -10

A width cannot be a negative number, so we discard the solution W = -10.

W = 4

L = W + 6 = 4 + 6 = 10

The width is 4 units, and the length is 10 units.

3 0

2 years ago

Read 2 more answers

Seven clowns hold 4 balloons each at the fair. Draw and label a tape diagram to show the total number of balloons the clowns hol

Inessa05 [86]

Answer:

7 times 4 which is 28 at each fair.

8 0

3 years ago

Solve this equation 4log√x - log 3x =log x^2

ruslelena [56]

Answer:

$x = \frac{1}{3}$

Step-by-step explanation:

*Move terms to the left and set equal to zero:

4㏒(√x) - ㏒(3x) - ㏒(x²) = 0

*simplify each term:

㏒(x²) - ㏒(3x) - ㏒(x²)

㏒(x²÷x²) -㏒(3x)

㏒(x²÷x² / 3x)

*cancel common factor x²:

㏒( $\frac{1}{3x}$ )

*rewrite to solve for x :

10⁰ = $\frac{1}{3x}$

1 = $\frac{1}{3x}$

1 · x = $\frac{1}{3x}$ · x

1x = $\frac{1}{3}$

*that would be our answer, however, the convention is to exclude the "1" in front of variables so we are left with:

x = $\frac{1}{3}$

5 0

2 years ago