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2 years ago

What is the solution to this system of equations?

Mathematics

1 answer:

dalvyx [7]2 years ago

8 0

There is no solution.

Step-by-step explanation:

Given:

y = 2x + 1

4x - 2y = 4

Substitute y = 2x + 1 into 4x - 2y = 4

4x - 2(2x + 1) = 4

4x - 4x - 2 = 4

0x = 4 + 2

0x = 6

Anything to the multiple of zero is zero. Hence 0x = 0, and 0 ≠ 6

So there is no solution to the equation.

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You have a 1-gallon paint can in the shape of a cylinder. One gallon is 231 cubic inches. The radius of the can is 3 inches. Wha

aleksandr82 [10.1K]

Answer:

The approximate height of the paint can is 8.2 in

Step-by-step explanation:

we know that

The volume of the cylinder ( can of paint) is equal to

$V=\pi r^{2} h$

we have

$V=231\ in^{3}$

$r=3\ in$

$\pi=3.14$

Substitute the values and solve for h

231=(3.14)(3)^{2} h

h=231/(3.14*9)=8.2 in

3 0

3 years ago

Read 2 more answers

The first, third and thirteenth terms of an arithmetic sequence are the first 3 terms of a geometric sequence. If the first term

Salsk061 [2.6K]

Answer:

The first three terms of the geometry sequence would be $1$ , $5$ , and $25$ .

The sum of the first seven terms of the geometric sequence would be $127$ .

Step-by-step explanation:

Let $d$ denote the common difference of the arithmetic sequence.

Let $a_1$ denote the first term of the arithmetic sequence. The expression for the $n$ th term of this sequence (where $n\!$ is a positive whole number) would be $(a_1 + (n - 1)\, d)$ .

The question states that the first term of this arithmetic sequence is $a_1 = 1$ . Hence:

The third term of this arithmetic sequence would be $a_1 + (3 - 1)\, d = 1 + 2\, d$ .
The thirteenth term of would be $a_1 + (13 - 1)\, d = 1 + 12\, d$ .

The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let $r$ denote the ratio of the geometric sequence in this question.

Ratio between the second term and the first term of the geometric sequence:

$\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d$ .

Ratio between the third term and the second term of the geometric sequence:

$\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}$ .

Both $(1 + 2\, d)$ and $\left(\displaystyle \frac{1 + 12\, d}{1 + 2\, d}\right)$ are expressions for $r$ , the common ratio of this geometric sequence. Hence, equate these two expressions and solve for $d$ , the common difference of this arithmetic sequence.

$\displaystyle 1 + 2\, d = \frac{1 + 12\, d}{1 + 2\, d}$ .

$(1 + 2\, d)^{2} = 1 + 12\, d$ .

$d = 2$ .

Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be $1$ , $(1 + (3 - 1) \times 2) = 5$ , and $(1 + (13 - 1) \times 2) = 25$ , respectively.

These three terms ( $1$ , $5$ , and $25$ , respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be $r = 25 /5 = 5$ .

Let $a_1$ and $r$ denote the first term and the common ratio of a geometric sequence. The sum of the first $n$ terms would be:

$\displaystyle \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}$ .

For the geometric sequence in this question, $a_1 = 1$ and $r = 25 / 5 = 5$ .

Hence, the sum of the first $n = 7$ terms of this geometric sequence would be:

$\begin{aligned} & \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}\\ &= \frac{1 \times \left(1 - 2^{7}\right)}{1 - 2} \\ &= \frac{(1 - 128)}{(-1)} = 127 \end{aligned}$ .

7 0

2 years ago

3y - 2 = y + 4

blagie [28]

Well.. There's 3y-2=y+4 right?
Add 2 and you get 3y=y+6
Minus y- you get 2y=6
Divide it at 2 and you get y=3.
Sorry for the explanation but I'm from another country and this is the best I can

6 0

3 years ago

A trader bought x mangoes at the rate of 4 mangoes for 10 naira, five of the mangoes were bad so he sold the remaining at the ra

Artemon [7]

Answer:

Step-by-step explanation:

The cost of the x mangoes was ...

c = 10(x/4)

The revenue from the sale of mangoes was ...

r = 20(x-5)/5

The profit is the difference between revenue and cost:

10 = r - c = 20(x -5)/5 -10(x/4) = 1.5x -20 . . . . substitute and simplify

30 = 1.5x . . . . . add 20

20 = x . . . . . . . .divide by 1.5

The trader bought 20 mangoes.

_____

<em>Check</em>

He paid 20(10/4) = 50 naira. He sold the 15 good mangoes for 20/5(15) = 60 naira, so made a 10 naira profit.

8 0

3 years ago

Find the value of x, please helppp

Ratling [72]

Answer:

x = 3

Step-by-step explanation:

The two triangles at the left have the same angles and share a side, so they are congruent. Therefore, the vertical side is also 6x−2.

Using the same logic, the two triangles on the right have the same angles and share a side, so they are congruent. Therefore, the vertical side is also 9x−11.

So:

6x − 2 = 9x − 11

9 = 3x

x = 3

5 0

3 years ago