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3 years ago

3/8 - 1/4x =1/2 x - 3/4 please help solve for x and show work

Mathematics

1 answer:

cluponka [151]3 years ago

7 0

Answer:

x=3/2 (or 1.5)

Step-by-step explanation:

Subtract 3/8 from both sides

Simplify

Subtract 1/2x from both sides

Simplify

Multiply both sides by 4

Simplify

Divide both sides by -3

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Let a and b be roots of x² - 4x + 2 = 0. find the value of a/b² +b/a²

erastovalidia [21]

Answer:

$\dfrac{a}{b^2}+\dfrac{b}{a^2}=10$

Step-by-step explanation:

Given equation: $x^2-4x+2=0$

The roots of the given quadratic equation are the values of x when $y=0$ .

To find the roots, use the quadratic formula:

$x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0$

Therefore:

$a=1, \quad b=-4, \quad c=2$

$\begin{aligned}\implies x & =\dfrac{-(-4) \pm \sqrt{(-4)^2-4(1)(2)}}{2(1)}\\& =\dfrac{4 \pm \sqrt{8}}{2}\\& =\dfrac{4 \pm 2\sqrt{2}}{2}\\& =2 \pm \sqrt{2}\end{aligned}$

$\textsf{Let }a=2+\sqrt{2}$

$\textsf{Let }b=2-\sqrt{2}$

Therefore:

$\begin{aligned}\implies \dfrac{a}{b^2}+\dfrac{b}{a^2} & = \dfrac{2+\sqrt{2}}{(2-\sqrt{2})^2}+\dfrac{2-\sqrt{2}}{(2+\sqrt{2})^2}\\\\& = \dfrac{2+\sqrt{2}}{6-4\sqrt{2}}+\dfrac{2-\sqrt{2}}{6+4\sqrt{2}}\\\\& = \dfrac{(2+\sqrt{2})(6+4\sqrt{2})+(2-\sqrt{2})(6-4\sqrt{2})}{(6-4\sqrt{2})(6+4\sqrt{2})}\\\\& = \dfrac{12+8\sqrt{2}+6\sqrt{2}+8+12-8\sqrt{2}-6\sqrt{2}+8}{36+24\sqrt{2}-24\sqrt{2}-32}\\\\& = \dfrac{40}{4}\\\\& = 10\end{aligned}$

6 0

2 years ago

Read 2 more answers

A hotel charges a $10,000 annual fee plus an additional $200 for each night you stay there. What is the average cost per night i

Anton [14]

Answer:

$\$400$

Step-by-step explanation:

GIVEN: A hotel charges a $\$10000$ annual fee plus an additional $\$200$ for each night you stay there.

TO FIND: average cost per night if you stay at the hotel for $50$ nights.

SOLUTION:

Annual fee charged by hotel $=\$10000$

amount charged each night we stay there $=\$200$

Total number of nights we stay $=50$

Total amount paid for $50$ nights $=50\times\$200$

$=\$10000$

Total amount paid $=\text{annual fee}+\text{total amount paid for 50 nights}$

$=\$10000+\$10000$

$=\$20000$

average cost per night $=\frac{\text{total amount paid}}{\text{total number of nights of stay}}$

putting values,

average cost per night $=\frac{20000}{50}$

$=\$400$

Hence average cost per night if we stay at hotel for $50$ days is $\$400$

6 0

3 years ago

Am I correct on #13? ONLY REAL ANSWRS OR YOULL GET REPORTED

drek231 [11]

Answer:

Yeah

Step-by-step explanation:

8 0

3 years ago

How to solve this problem step by step. Make brainliest answer if its done. Please

sladkih [1.3K]

D is halfway between A and B

so the coordinates of D are (2,2)

E is halfway between A and C so the coordinates of E are (-1,1)

now you need to find the gradient/slope of DE and BC using the formula:

$\frac{y2 - y1}{x2 - x1}$

<h3>Gradient of DE: </h3>

SUB IN COORDINATES OF D AND E

$\frac{1 - 2}{ - 1 - 2}$

therefore the gradient of DE is 1/3.

<h3>Gradient of BC:</h3>

SUB IN COORDINATES OF B AND C

 $\frac{ - 2 - 0}{ - 3 - 3}$ 

therefore the gradient of BC is -2/-6 which simplifies to 1/3.

<h3>therefore, BC and DE are parallel as they both have a gradient/slope of 1/3 and parallel lines have the same gradient</h3>

6 0

3 years ago

(2x to the 5th power) 3x to the 3/5th power

saul85 [17]

The expression simplifies to 6x^(28/5)
hope this helps :)

6 0

3 years ago