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Algebraic Fractions grade 10
I am a a student and I am having difficulty with answering this question. I keep getting the answer wrong. Please may I have a step by step solution to this question so that I won't have difficulties with answering these type of questions in the future.
Solve
$\frac{3 x}{4} + \frac{2}{3} = x$
$x$ = ____

odcizit49o 2022-11-07

Find $\arctan (\frac{1}{3}) + \arctan (\frac{1}{9}) + \arctan (\frac{7}{19})$
Firstly used this formula
$\begin{aligned} \arctan (α) + \arctan (β) & = \arctan (\frac{1 - x y}{x + y}), x > 0, y > 0 \\ = \arctan (\frac{1 - \frac{1}{3} \frac{1}{9}}{\frac{1}{3} + \frac{1}{9}}) \\ = \arctan (2) \end{aligned}$
So it is $\arctan (2) + \arctan (\frac{7}{19}) .$

Laila Murphy 2022-11-07

Multiply.
$3 \times \frac{7}{2}$

Laila Murphy 2022-11-06

Prove the next cyclic inequality
Let $a, b, c > 0$ such that
$a + b + c = 1$
prove that
$c y c l i c \sum \frac{a b}{\sqrt{c + a b}} \leq \frac{1}{2}$
By symetrie, i proved it by assuming $a = b = c$ but i cannot justify this hypothesis.

Emma Hobbs 2022-11-06

Simplify the following expression. $13 x^{2} + 3 - 2 x - 6 x^{2} - 7 x$

Cortez Clarke 2022-11-06

The speed of light is 186, 282.3976 miles per second. Round this number to the nearest hundredth

assupecoitteem81 2022-11-06

How many quarters do you need for $$ 10$ ?

Alexia Avila 2022-11-06

Prove this inequality $\sum_{c y c} \frac{a}{a b + 1} \geq \frac{3}{2}$
For $a > 0$ $b > 0$ and $c > 0$ such tat $a + b + c = 3$ prove that:
$\frac{a}{a b + 1} + \frac{b}{b c + 1} + \frac{c}{c a + 1} \geq \frac{3}{2}$
By AM-GM
$\frac{a}{a b + 1} = a - \frac{a^{2} b}{a b + 1} \geq a - \frac{a^{2} b}{2 \sqrt{a b}} = a - \frac{a \sqrt{a b}}{2}$
$\Rightarrow L . H . S \geq a + b + c - \frac{a \sqrt{a b} + b \sqrt{b c} + c \sqrt{c a}}{2}$
$\geq 3 - \frac{a^{2} + b^{2} + c^{2} + a b + b c + c a}{4}$
Help me to continue

Elliana Molina 2022-11-06

Reducing combinations in fractions
$\frac{b * (\binom{b - 1}{k - 1}) (\binom{r}{n - k})}{n * (\binom{b}{k})} * \frac{(\binom{r + b}{n})}{(\binom{r}{n - k}) (\binom{b}{k})}$
How would I go about reducing this into $\frac{k}{n}$ ?
My attempt was $\frac{b!}{n * (k - 1)! (b - k - 2)!} * \frac{k!}{b!} = \frac{k!}{n * (k - 1)! (b - k - 2)!} = \frac{k}{n * (b - k - 2)!}$
Don't know where the errors are / where to go from here

Ty Gaines 2022-11-06

Inequality $\frac{1}{n + 1} + \frac{1}{n + 2} + . . . + \frac{1}{3 n + 1} > 1$
This is a 9th grade problem. I was trying to take the greatest numerator, which is the last numerator of the last fraction. But there are only $2 n + 1$ terms. Right? After that I have no idea. Thx!

Karley Castillo 2022-11-05

Simplifying a recursive fraction involving Lambert function
Is there a simplification for the following recursive fraction :
$\frac{\frac{\frac{n}{W (n)}}{W (\frac{n}{W (n)})}}{W (\frac{\frac{n}{W (n)}}{W (\frac{n}{W (n)})})}$
The above formula uses a recursion 3 times. I'm looking for a simplification when we have such a finite recursion, for instance when this one appears $i$ times. I would like to remove the recursion, i.e. obtain a single fraction.
Thank you.

figoveck38 2022-11-05

How would I simplify this fraction easily?
Original question :
$\frac{\tan (x)}{\log_{e} x}$
I used the quotient rule and got the following fraction.
Fraction :
$\frac{\frac{x \cdot \sec (x)^{2} \cdot (\log_{e} x) - \tan (x)}{x}}{\log_{e} x}$
apologies in advance for the fractions, i tried to put in $\log_{e} x$ underneath the denominator of the other fraction but for some reason it wasn't working.

dannigurl21ck2 2022-11-05

What is 5 feet 10 inches in inches?

Fahdvfm 2022-11-05

3.31 Game of dreidel. A dreidel is a four-sided spinning top with the Hebrew letters nun,1d shin, one on each side. Each side is equally likely to come up in a single spin ofthe dreidel. Suppose you spin a dreiler three times. Calculate the probability of getting
(a) at least one nun?
(b) exactly 2 nuns?
(c) exactly 1 hei?
(d) at most 2 gimels?

Brenda Jordan 2022-11-05

Evaluate the following algebraic expression at x=−3x=−3, y=4y=4 and simplify your answer.
$2 x^{2} + 5 y^{2} - 2$

Jefferson Booth 2022-11-05

Make the following conversion in the U.S. system by multiplying the appropriate conversion factor. Write the answer as a reduced mixed number.
57 in. to yards.

Frances Pham 2022-11-05

Why $\frac{\frac{1}{2} \times \frac{k}{k + 7}}{\frac{1}{2} \times \frac{k}{k + 7} + \frac{1}{2} \times \frac{2}{5}} = \frac{k}{k + \frac{2}{5} (k + 7)}$ ?
My attempt:
$\frac{\frac{1}{2} \times \frac{k}{k + 7}}{\frac{1}{2} \times \frac{k}{k + 7} + \frac{1}{2} \times \frac{2}{5}} = \frac{\frac{1}{2} \times \frac{k}{k + 7}}{\frac{1}{2} (\frac{k}{k + 7} + \frac{2}{5})} = \frac{\frac{k}{k + 7}}{\frac{k}{k + 7} + \frac{2}{5}}$

Cael Dickerson 2022-11-04

Simplify the.rational expression.
$\frac{x^{3} - 9 x}{x^{2} + 7 x + 12}$

ajakanvao 2022-11-04

The quantity demanded x each month or Russo Espresso Makers is 250 when the unit price p is $138. The quantity demanded each month is 1000 when the unit price is $108. The suppliers will market 700 espresso makers when the unit price is $78. At a unit price of $108, they are willing to market 2200 units. Both the supply and demand equations are known to be linear.
a) Find the demand equation.
$p = ?$
b) Find the supply equation.
$p = ?$
c) Find the equilibrium quantity and the equilibrium price.
? units
$ ?

Paula Cameron 2022-11-04

Suppose a and b are real numbers. If
$(a - i) (2 + b i) = \frac{a b}{4} + 126 i$
find the values a and b.

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