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3 years ago

-5 solve inequality. put the solution in set notation

Mathematics

1 answer:

Makovka662 [10]3 years ago

7 0

$\tt \to \: - 5 < a + 2$

Move the variable to the left-hand side and change its sign

$\tt \to - 5 - a < 2$

Move the constant to the right-hand side and change its sign

$\tt \to \: - a < 2 + 5$

Add the numbers

$\tt \to \: - a < 7$

Change the signs on both sides of the inequality and flip the inequality sign

$\tt \to \: a > - 7$

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Skylar plans to use $3400 to open a savings account with an annual interest rate of 1.15%. How much more interest will he earn o

Tanzania [10]

Answer:

$ 2.5

Step-by-step explanation:

Given that

Total Amount to be invested = P = $3400

Total Time of investment = t = 13 years

Rate of interest = r = 1.15 %

Lets calculate Simple interest first

As we know formula for simple interest is

$A = P (1 +r)^{t}$

Substituting the values

$A = 3400(1+ \frac{1.15}{100} )^{13}$

A = $ 3944.9

Lets now calculate the compound interest

As we know formula for simple interest is

$A = P (1 + \frac{r}{n})^{nt}$

As compound interest applies every 3 months so n =3

So,

$A = 3400 (1 + \frac{1.15}{100*4} )^{13*4}$

A = $ 3947.4

Now Lets calculate how much more he will earn using compound interest.

It can be found by taking difference of compound interest and simple interest

Amount = 3947.4 - 3944.9 = $ 2.5

So Skyler must have earned 2.5 dollar more using the compound interest.

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3 years ago

Find the value of k given that both points lie on a line passing through the origin.

Bond [772]

Answer:

$k=-3$

Step-by-step explanation:

Since the line passes through the origin, it must be a proportional/direct variation equation.

Direct variation equations have the form:

$y=ax$

Where a is the constant of proportionality.

Let’s solve for a. We know that when x=5, y=40. So:

$40=5a$

Divide both sides by 5:

$a=8$

Therefore, our equation is:

$y=8x$

We want to find the value of k such that y=-24. So, subsitute -24 for y and k for x:

$-24=8k$

Divide both sides by 8:

$k=-3$

Hence, the value of k is -3.

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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Ann Ben and cheyrl share some money in the ratio 3:7:10 Ben receives £650 more than Ann calculate the total amount of money that

k0ka [10]

Let

x------------> Ann's amount of money

y------------> Ben's amount of money

z------------> Cheryl's amount of money

we know that

y=x+650-----> equation 1

x/y=3/7------> y=(7/3)*x-----> equation 2

y/z=7/10-----> equation 3

x/z=3/10-----> equation 4

equate equation 1 and equation 2

x+650=(7/3)*x------> multiply by 3-----> 3x+1950=7x----> 4x=1950

x=1950/4-----> x=487.5

y=x+650-----> y=487.5+650-----> y=1137.5

y/z=7/10------> z/y=10/7------> z=(10/7)*1137.5-----> z=1625

the answer is

Ann's amount of money is £487.5

Ben's amount of money is £1137.5

Cheryl's amount of money is £1625

487.5+1137.5+1625=£3250

The total of money shared is £3250

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Answer:

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Step-by-step explanation:

Multiply 1,852×685

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4 years ago

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