What is the value of x in the system of equations shown below? 5x + 4y = 1 y = 1

Solve the following exponential equations. 10^(x+1) − 10^(x−1) = 1287

Rudiy27

Answer:x=2.114

Step-by-step explanation:

Given

$10^{x+1}-10^{x-1}=1287$

$10\times 10^x-\frac{10^x}{10}=1287$

Let $10^x=y$

$10y-\frac{y}{10}=1287$

$\frac{100y-y}{10}=1287$

$99y=1287\times 10$

$y=\frac{12870}{99}=130$

$10^x=130$

Taking $\log$ both sides

$x\log (10)=\log (130)$

$x=\frac{\log (130)}{1}$

$x=2.114$

7 0

3 years ago

Using base ten blocks subtraction

GREYUIT [131]

Is their any multiple questions

4 0

3 years ago

the ratio of the ages of two children is 2:3. If the younger child is 4 years old, how old is the other child

yKpoI14uk [10]

Answer: The other child is "6 years old".
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Explanation:
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Set up the ratio as a fraction:

→ " 2/3 = 4/x " ; Solve for "x" (the age; in "years", of the "other child") ;

Note: GIven the ratios of two children is: 2:3 ; and there is a younger child among the two children; the number "2" would represent the "younger child; since there are 2 (two) children; and there are 2 (two) numbers in the given ratios; and among the 2 (two) numbers given in the ratio — which are: "2" and "3" ; the given number: "2" is LESS THAN the given number "3" ;

As such:
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→ " 2/3 = 4/x " ; Solve for "x" ;

Cross-multiply;

2x = 3*4 ;

2x = 12 ;

Divide each side of the equation by "2" ;
to isolate "x" on one side of the equation; & to solve for "x" ;

2x/2 = 12/2 ;

to get:
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" x = 6 "
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Alternate method:
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Set up the ratio:
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→ " 2/3 = 4/x " ; Solve for "x" ;

Recognize that: "2/3 = 4/6" ; and that: "x = 6" ;
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Alternate method:
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Set up the ratio:
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→ " 2/3 = 4/x " ; Solve for "x" ;

In the "numerator": → " 2 * [what value?] = 4 ? "
→ To find that value: " 4 ÷ 2 = "2 " .

As such: Multiply the given: "3" in the "denominator" by "2" ; to get:
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"3 * 2 = "x" ; ↔ " x = 6 " .
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Answer: The other child is "6 years old".
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Check our answer:

The given ratio: 2/3 =? 4/6 ? Yes!

{You can even check this using a calculator—if you wish.}.
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5 0

3 years ago

Please answer ! will give brainliest

kotegsom [21]

Answer:

7

Step-by-step explanation:

5 0

3 years ago

Left on together, the cold and hot water faucets of a certain bathtub take 5 minutes to fill the tub. If it takes the hot water

mario62 [17]

Answer:

$\frac{15}{2}=7.5$ minutes.

Step-by-step explanation:

Let t represent time taken by cold water faucet in minutes to fill the tub.

Part of tub filled by cold water faucet in one minute would be $\frac{1}{t}$ .

We have been given that it takes the hot water faucet 15 minutes to fill the tub by itself, so art of tub filled by hot water faucet in one minute would be $\frac{1}{15}$ .

We are also told that left on together, the cold and hot water faucets of a certain bathtub take 5 minutes to fill the tub, so part of tub filled by both faucets in one minute would be $\frac{1}{5}$ .