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2 years ago

CAN SOMEONE PLS HELP ME WITH BOTH OF THESE QUESTIONS

Mathematics

1 answer:

dusya [7]2 years ago

8 0

The amount in the new checking account is 600 dollars

The operation (5 α 3) + (7 α 5) is 46.

<h3>How to find the amount in the checking account?</h3>

She had 1000 dollars in her checking account. she had a loan of 800 dollars to pay.

After paying her loan form her checking account the balance of the loan reduce to half.

Therefore, she paid 800 / 2 = 400 dollars for her loan

Hence,

Her new checking account = 1000 - 400 = 600 dollars

<h3>How to find value of an operation?</h3>

a α b = ab - a + b

Therefore,

(5 α 3) + (7 α 5)

(5 α 3) = 5(3) - 5 + 3 = 13

(7 α 5) = 7(5) - 7 + 5 = 33

Therefore,

(5 α 3) + (7 α 5) = 13 + 33 = 46

Note: I can't use the at symbol because it is a swear word.

learn more on operation and checking account here: brainly.com/question/583664

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The half-life of a radioactive substance is the time it takes for a quantity of the substance to decay to half of the initial am

posledela

Step-by-step walkthrough:

Well a standard half-life equation looks like this.

$N = N_0 * (\frac{1}{2})^{t/p$

$N_0$ is the starting amount of parent element.

$N$ is the end amount of parent element

$t$ is the time elapsed

$p$ is a half-life decay period

We know that the starting amount is 74g, and the period for a half-life is 2.8 days.

Therefore you can create a function based off of the original equation, just sub in the values you already know.

$N(t) = 74g * (\frac{1}{2})^{t/2.8days$

This is easy now that we have already made the function. Here we just reuse it, but plug in 2.8 days.

$N(t) = 74g * (\frac{1}{2})^{t/2.8days} = N(2.8days) = 74g * (\frac{1}{2})^{2.8days/2.8days}\\= 74g * \frac{1}{2} = 37g$

Now we just gotta do some algebra. Use the original function but this time, replace $N(t)$ with 10g and solve algebraically.

$10g = 74g * (\frac{1}{2})^{t/2.8days}\\\\\frac{10g}{74g} = (\frac{1}{2})^{t/2.8days}$

Take the log of both sides.

$log(\frac{5}{37}) = log((\frac{1}{2})^{t/2.8days})$

Use the exponent rule for log laws that, $log(b^x) = x*log(b)$

$log(\frac{5}{37}) = \frac{t}{2.8days} * log(\frac{1}{2})$

$\frac{log(\frac{5}{37})}{log(\frac{1}{2})} = \frac{t}{2.8days}$

$2.8 * \frac{log(\frac{5}{37})}{log(\frac{1}{2})} = t$

slap that in your calculator and you get

$t = 8.1 days$

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2 years ago

Simplify the radical

elena-14-01-66 [18.8K]

Answer:

$\sqrt{108} \sqrt{36 \times 3} \sqrt{36} \sqrt{3} \: \: 6 \sqrt{3} \: \: \: \sqrt{108} = 10.392304845413264$

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3 years ago

How much would you pay for 5 apples at the rate of $6.60 a dozen?

V125BC [204]

Answer:

You would pay $2.75

Step-by-step explanation:

a dozen = 12

6.60 / 12 = $0.55

0.55 x 5 = 2.75

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3 years ago

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The picturre explains the question

Alina [70]

Answer:

x = 47°

Step-by-step explanation:

Since the two angles on a line add up to 180 degrees:

x = 180-133

x = 47°

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3 years ago

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The height of a wooden pole, h, is equal to 20 feet. A taut wire is stretched from a point on the ground to the top of the pole.

kykrilka [37]

ANSWER

D. 25 feet

EXPLANATION

The height of the wall,h, the taut wire and the distance from the base of the pole to the point on the ground, formed a right triangle.

According to the Pythagoras Theorem, the sum of the length of the squares of the two shorter legs equals the square of the hypotenuse.

Let the hypotenuse ( the length of the ) taught wire be,l.

Then

${l}^{2} = {h}^{2} + {b}^{2}$

${l}^{2} = {20}^{2} + {15}^{2}$

${l}^{2} = 400 + 225$

${l}^{2} = 625$

$l= \sqrt{625} = 25ft$

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3 years ago