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2 years ago

(x-4)/(2x+1)-3 can you help me with this question

Mathematics

1 answer:

lilavasa [31]2 years ago

4 0

Answer:

$\frac{(x - 4)}{(2x + 1)} - 3$ $=$ $\frac{-7x- 7}{3x + 1}$

Step-by-step explanation:

Given

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

Required

Solve

Express 3 as a fraction

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

Take LCM

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

$\frac{x - 4 - 6x - 3}{3x + 1}$

Collect Like Terms

$\frac{x - 6x- 4 - 3}{3x + 1}$

Simplify like terms

$\frac{-7x- 7}{3x + 1}$

Hence:

$\frac{(x - 4)}{(2x + 1)} - 3$ $=$ $\frac{-7x- 7}{3x + 1}$

You might be interested in

Let A(t) be the area of a circle with radius r(t), at time t in min. Suppose the radius is changing at the rate of drdt=6 ft/min

mylen [45]

Answer:

The rate of change is $108\pi$ ft^(2)/min

Step-by-step explanation:

The area of a circle is given by the following equation:

$A(t) = \pi r^{2}$

To solve this question, we have to realize the implicit differentiation in function of t. We have two variables, A and r. So

$\frac{dA(t)}{dt} = 2\pi r \frac{dr}{dt}$

We have that:

$\frac{dr}{dt} = 6, r = 9$ .

We want to find $\frac{dA}{dt}$

$\frac{dA(t)}{dt} = 2\pi*9*6$

$\frac{dA}{dt} = 108\pi$

Since the area is in square feet, the rate of change is in ft^(2)/min.

So the rate of change is $108\pi$ ft^(2)/min

5 0

2 years ago

Divide: (-7x+x^2+15)÷(-3+x)

kakasveta [241]

Since the divisor is in the form (x + #) or (x - #), This can be done by synthetic division.
First put the polynomial ion descending order: x^2 - 7x + 15
Take the coefficients of the terms and follow these steps:

3 | 1 -7 15
   3 -12
___________ Bring down the 1, multiply the 3 by the 1 and place under the
   1 -4    3 -7, then add.
   Multiply 3 by -4, place under the 15, then add.
   The bottom row is our answer. Since the problem started with a second power, the answer will start with a first power.
The bottom row are the coefficients of the terms and the last number is the remainder.
x - 4 remainder 3 ALSO WRITTEN x - 4 + 3/(x -3)

3 0

2 years ago

I'm confused on how to do this. Please explain step by step. If you respond with just the answer I WILL report you. I would like

Tcecarenko [31]

Answer:

Exact Form:

√2−1

Decimal Form:

0.41421356

…

Step-by-step explanation:

Since 9π/8 is not an angle where the values of the six trigonometric functions are known, try using half-angle identities.

9π/8 is not an exact angle

First, rewrite the angle as the product of 1/2 and an angle where the values of the six trigonometric functions are known. In this case, 9π/8 can be rewritten as

(1/2)* 9π/8 tan ((1/2)* 9π/8)

Use the half-angle identity for tangent to simplify the expression. The formula states that

tan (0/2)=sin(0)/1+cos(0) sin(9π/4)/1+cos(9π/4)

Simplify

Remove full rotations of 2π until the angle is between 0 and 2π.

sin(π/4)/1+cos(9π/4)

The exact value of sin(π/4) is √2/2

√2/2/1+cos(9π/4)

Simplify the Denominator

Remove full rotations of 2π until the angle is between 0 and 2π.√2/2/1+cos(π4)

The exact value of cos(π/4) is √2/2.√2/2/1+√2/2

To write 1/1 as a fraction with a common denominator, multiply by 2/2 .√2/2/1/1⋅2/2+√2/2

Write each expression with a common denominator of 2, by multiplying each by an appropriate factor of 1.

Combine.

√2/2/1⋅2/1⋅2+√2/2

Multiply 2 by 1

√2/2/1⋅2/2+√2/2

Combine the numerators over the common denominator.

√2/2/1⋅2+√2/2

Multiply 2 by 1

√2/2/2+√2/2

Multiply the numerator by the reciprocal of the denominator

√2/2 ⋅ 2/2+√2

Cancel the common factor of 2 .

Factor out the greatest common factor 2

√2/2⋅1 ⋅ 2⋅1/2+√2

Cancel the common factor

√2/2⋅1 ⋅ 2⋅1/2+√2

Rewrite the expression.

√2/1 ⋅ 1/2+√2

Simplify

Multiply √2/1 and 1/2+√2

√2/2+√2

Multiply √2/2+√2 by 2−√2/2−√2

Combine

√2(2−√2)/(2+√2)(2−√2)

Expand the denominator using the FOIL method.

√2(2−√2)/4−2√2+√2⋅2−√2^2

Simplify

√2(2−√2)/2

Apply the distributive property

√2⋅2+√2(−√2)/2

Move 2 to the left of the expression √2⋅2.

2⋅√2+√2(−√2)/2

Simplify

√2(−√2) .

Raise √2 to the power of 1 .

2⋅√2−(√2^1√2)/2

Raise √2 to the power of 1 .

2⋅√2−(√2^1√2^1)/2

Use the power rule a^m a^n=a^m+n to combine exponents.

2⋅√2−√2^1+1/2

Add 1 and 1 .

2⋅√2−√2^2/2

Simplify each term.

Multiply 2 by √2 .

2√2−√2^2/2

Rewrite √2^2 as 2 .

2√2−1⋅2/2

Multiply −1 by 2.

2√2−2/2

Reduce the expression by cancelling the common factors.

Factor 2 out of 2√2.

2(√2)−2/2

Factor 2 out of −2.

2(√2)+2⋅−1/2

Factor 2 out of

2(√2)+2(−1)2(√2−1)/2

Cancel the common factors.

Factor 2 out of 2 .

2(√2−1)/2(1)

Cancel the common factor.

2(√2−1)/2⋅1

Rewrite the expression.

√2−1/1

Divide √2−1 by 1 .

√2−1

The result can be shown in multiple forms.

Exact Form:

√2−1

Decimal Form:

0.41421356…

Hope it help. Good luck.

4 0

3 years ago

You were paid $82.50 for seven 1/2 hours <br> of work what is your rate of pay

sertanlavr [38]

$11 per hour. Divide 82.5 by 7.5 and you get how much money she earns in an hour (11 dollars)

6 0

3 years ago

The following results come from two independent random samples taken of two populations.

photoshop1234 [79]

Answer:

$(a)\ \bar x_1 - \bar x_2 = 2.0$

$(b)\ CI =(1.0542,2.9458)$

$(c)\ CI = (0.8730,2.1270)$

Step-by-step explanation:

Given

$n_1 = 60$ $n_2 = 35$

$\bar x_1 = 13.6$ $\bar x_2 = 11.6$

$\sigma_1 = 2.1$ $\sigma_2 = 3$

Solving (a): Point estimate of difference of mean

This is calculated as: $\bar x_1 - \bar x_2$

$\bar x_1 - \bar x_2 = 13.6 - 11.6$

$\bar x_1 - \bar x_2 = 2.0$

Solving (b): 90% confidence interval

We have:

$c = 90\%$

$c = 0.90$

Confidence level is: $1 - \alpha$

$1 - \alpha = c$

$1 - \alpha = 0.90$

$\alpha = 0.10$

Calculate $z_{\alpha/2}$

$z_{\alpha/2} = z_{0.10/2}$

$z_{\alpha/2} = z_{0.05}$

The z score is:

$z_{\alpha/2} = z_{0.05} =1.645$

The endpoints of the confidence level is:

$(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$

$2.0 \± 1.645 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}$

$2.0 \± 1.645 * \sqrt{\frac{4.41}{60}+\frac{9}{35}}$

$2.0 \± 1.645 * \sqrt{0.0735+0.2571}$

$2.0 \± 1.645 * \sqrt{0.3306}$

$2.0 \± 0.9458$

Split

$(2.0 - 0.9458) \to (2.0 + 0.9458)$

$(1.0542) \to (2.9458)$

Hence, the 90% confidence interval is:

$CI =(1.0542,2.9458)$

Solving (c): 95% confidence interval

We have:

$c = 95\%$

$c = 0.95$

Confidence level is: $1 - \alpha$

$1 - \alpha = c$

$1 - \alpha = 0.95$

$\alpha = 0.05$

Calculate $z_{\alpha/2}$

$z_{\alpha/2} = z_{0.05/2}$

$z_{\alpha/2} = z_{0.025}$

The z score is:

$z_{\alpha/2} = z_{0.025} =1.96$

The endpoints of the confidence level is:

$(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}$

$2.0 \± 1.96 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}$

$2.0 \± 1.96* \sqrt{\frac{4.41}{60}+\frac{9}{35}}$

$2.0 \± 1.96 * \sqrt{0.0735+0.2571}$

$2.0 \± 1.96* \sqrt{0.3306}$

$2.0 \± 1.1270$

Split

$(2.0 - 1.1270) \to (2.0 + 1.1270)$

$(0.8730) \to (2.1270)$

Hence, the 95% confidence interval is:

$CI = (0.8730,2.1270)$

8 0

3 years ago