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3 years ago

8

Solve the rational equation (3x^2+1)/(x-1) + x =4 + 4/(x-1)

1 answer:

natita [175]3 years ago

4 0

Answer:

The answer to your question is letter D

Step-by-step explanation:

Rational equation

$\frac{3x^{2} + 1}{x - 1} + x = 4 + \frac{4}{x - 1}$

Simplify

$\frac{3x^{2} + 1 + x(x - 1)}{x - 1} = \frac{4(x - 1) + 4}{x - 1}$

Cancel the denominators and expand

3x² + 1 + x² - x = 4x - 4 + 4

Simplify

4x² - x + 1 - 4x = 0

4x² - 5x + 1 = 0

Factor

4x² - 4x - 1x + 1 = 0

4x(x - 1) - 1(x - 1) = 0

(4x - 1)(x - 1) = 0

x₁ = 1/4 x₂ = 1

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How many cubic centimeters of water can this paper cone cup hold?

blagie [28]

48π cm^3

Step-by-step explanation:

The formula for the volume of a cone is...

$V=\frac{1}{3}\pi r^2h$

We can plug everything we know from the photo into the equation, but note that the picture gives us the diameter, which is 8, instead of the radius. The radius is half of the diameter, so the radius will be 4. Also we will be leaving pi as it is, instead of changing it to 3.14.

$V=\frac{1}{3}*(\pi *4*4*9)$

$V=\frac{1}{3}*(144\pi )$

V = 48π

The paper cone can hold <u><em>48π cubic centimeters</em></u> of water.

3 0

3 years ago

Read 2 more answers

For the arithmetic sequence 42, 32, 22, 12... find the 18th term.

Stella [2.4K]

Answer:

The18th term of the given sequence is -128

Explanation:

To find the 18th term of the sequence:

42, 32, 22, 12, ..., we need to find the nth term of the sequence first.

The nth term of a sequence is given be the formula:

$T_n=a+(n-1)d$

Where a is the first term, and d is the common difference.

Here, a = 42, d = 32 - 42 = -10

$\begin{gathered} T_n=42+(n-1)(-10) \\ =42-10n+10 \\ T_n=52-10n \end{gathered}$

To find the 18th terem, substitute n = 18 into the nth term

$\begin{gathered} T_{18}=52-10(18) \\ =52-180 \\ =-128 \end{gathered}$

7 0

1 year ago

5x6-1+3=28 brackets or braces should be added

Artyom0805 [142]

5 · (6 - 1) + 3
= 5·5 + 3
= 25 + 3
= 28

7 0

3 years ago

The teachers sold 32 tickets this is 80% of the tickets given to the teachers how many tickets were given to the teachers

UkoKoshka [18]

You would give the teacher 40 tickets

6 0

3 years ago

Read 2 more answers

Triangles P Q R and S T U are shown. Angles P R Q and T S U are right angles. The length of P Q is 20, the length of Q R is 16,

dimaraw [331]

Answer:

$\angle P$

Step-by-step explanation:

Given

$\triangle PRQ = \triangle TSU = 90^o$

$PQ = 20$ $QR = 16$ $PR = 12$

$ST = 30$ $TU = 34$ $SU = 16$

<em>See attachment</em>

Required

Which sine of angle is equivalent to $\frac{4}{5}$

Considering $\triangle PQR$

We have:

$\sin(P) = \frac{QR}{PQ}$ --- i.e. opposite/hypotenuse

So, we have:

$\sin(P) = \frac{16}{20}$

Divide by 4

$\sin(P) = \frac{4}{5}$

Hence:

$\angle P$ is correct

7 0

3 years ago