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3 years ago

Help me 99 points What is the value of x?

Mathematics

2 answers:

pochemuha3 years ago

6 0

Set up a ratio:

12/5x-2 = 16/6x

Cross multiply:

12(6x) = 16(5x-2)

Use distributive property:

72x = 80x - 32

Subtract 80x from both sides:

-8x = - 32

Divide both sides by -8:

X = 4

Fantom [35]3 years ago

5 0

Answer:

Step-by-step explanation:

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Kelly tells you that when variables are in the denominator, the equation one over two plus three over x equals three over four b

Lera25 [3.4K]

1/2 + 3/x = 3/4
3/x = 3/4 - 1/2
3/x = 3/4 - 2/4
3/x = 1/4....this is a proportion, so we cross multiply
(1)(x) = (3)(4)
x = 12

check..
1/2 + 3/12 = 3/4
6/12 + 3/12 = 3/4
9/12 = 3/4
3/4 = 3/4 (correct)

so x = 12

6 0

3 years ago

Read 2 more answers

Which property would be used to first simplify the expression 2 (x+5y+1)-4(3x-y-2)

Mariulka [41]

Answer:

Distributive

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Remember to show work and explain. Use the math font.

MrMuchimi

Answer:

$\large\boxed{1.\ f^{-1}(x)=4\log(x\sqrt[4]2)}\\\\\boxed{2.\ f^{-1}(x)=\log(x^5+5)}\\\\\boxed{3.\ f^{-1}(x)=\sqrt{4^{x-1}}}$

Step-by-step explanation:

$\log_ab=c\iff a^c=b\\\\n\log_ab=\log_ab^n\\\\a^{\log_ab}=b\\\\\log_aa^n=n\\\\\log_{10}a=\log a\\=============================$

$1.\\y=\left(\dfrac{5^x}{2}\right)^\frac{1}{4}\\\\\text{Exchange x and y. Solve for y:}\\\\\left(\dfrac{5^y}{2}\right)^\frac{1}{4}=x\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\\dfrac{(5^y)^\frac{1}{4}}{2^\frac{1}{4}}=x\qquad\text{multiply both sides by }\ 2^\frac{1}{4}\\\\\left(5^y\right)^\frac{1}{4}=2^\frac{1}{4}x\qquad\text{use}\ (a^n)^m=a^{nm}\\\\5^{\frac{1}{4}y}=2^\frac{1}{4}x\qquad\log_5\ \text{of both sides}$

$\log_55^{\frac{1}{4}y}=\log_5\left(2^\frac{1}{4}x\right)\qquad\text{use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\\dfrac{1}{4}y=\log(x\sqrt[4]2)\qquad\text{multiply both sides by 4}\\\\y=4\log(x\sqrt[4]2)$

$--------------------------\\2.\\y=(10^x-5)^\frac{1}{5}\\\\\text{Exchange x and y. Solve for y:}\\\\(10^y-5)^\frac{1}{5}=x\qquad\text{5 power of both sides}\\\\\bigg[(10^y-5)^\frac{1}{5}\bigg]^5=x^5\qquad\text{use}\ (a^n)^m=a^{nm}\\\\(10^y-5)^{\frac{1}{5}\cdot5}=x^5\\\\10^y-5=x^5\qquad\text{add 5 to both sides}\\\\10^y=x^5+5\qquad\log\ \text{of both sides}\\\\\log10^y=\log(x^5+5)\Rightarrow y=\log(x^5+5)$

$--------------------------\\3.\\y=\log_4(4x^2)\\\\\text{Exchange x and y. Solve for y:}\\\\\log_4(4y^2)=x\Rightarrow4^{\log_4(4y^2)}=4^x\\\\4y^2=4^x\qquad\text{divide both sides by 4}\\\\y^2=\dfrac{4^x}{4}\qquad\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\y^2=4^{x-1}\Rightarrow y=\sqrt{4^{x-1}}$

6 0

3 years ago

Suppose James randomly draws a card from a standard deck of 52 cards. He then places it back into the deck and draws a second ca

qwelly [4]

Answer:

1.92%

Step-by-step explanation:

The probability for first case, picking a queen out of deck, will be:

$\frac{4}{52}$

as there will be 4 queens in a deck, one of each suit.

For the second pick, the probability of picking a diamond card, will be:

$\frac{13}{52}$

here the total will remain 52 as he has replaced the first card and not kept it aside and there will be 13 cards in diamond suit (including the three face cards).

Thus the net probability for both cases will be:

$P = \frac{4}{52} * \frac{13}{52}\\ P = \frac{1}{52}\\ P = 0.01923\\P = 1.923\%\\\\P = 1.92\%$

Thus total probability for the combined two cases will be 1.92%

7 0

3 years ago

Abby and Andrew are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of

Slav-nsk [51]

Answer:

$14 for the shiny wrapping paper

Step-by-step explanation:

6x + 4y = 104

8x + 12y = 232

x=8 y=14

4 0

3 years ago