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Musya8 [376]
3 years ago
5

Please help ASAP 15 points

Mathematics
1 answer:
saveliy_v [14]3 years ago
8 0

Answer:

\boxed{\text{(a)}4\sqrt{5} \text{; (b)} -2}

Step-by-step explanation:

(a) Radius of circle

The radius r of the circle is AB.

The coordinates of its ends are (5, 10) and (-3, 6).  

x = x₂ - x₁ = 5- (-3) = 5 + 3 = 8

y = y₂ - y₁ = 10 - 6 = 4

We can use the Pythagorean theorem to calculate its length.

r² = 8² + 4² = 64 + 16 = 80

r = √80 = 4√5

(b) Slope of line l

Slope of AB = 4/8 = ½

Line l⟂AB, so its slope is the negative reciprocal of the slope of AB .

m = -1/½ = -2

The radius of the circle is \boxed{4\sqrt{5}} and the slope of line l is \boxed{-2}.

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Rena spent 6 days reading her book completing the same fraction of the book each day if she had a total of 8/9 of her book after
Artyom0805 [142]

Answer:

The fraction of the book that Rena read every day is \frac{4}{27}

Step-by-step explanation:

Rena spent 6 days reading her book completing the same fraction of the book every day and you want to know the fraction of the book she read each day. Knowing that Rena had a total of 8/9 of her book read after 6 days, then you simply divide the total amount of the book read during those days by 6, the number of days:  

\frac{8}{9}÷6

To divide a fraction by a whole number, you must convert the whole number into a fraction, finding the reciprocal of that fraction, and multiply it by the first fraction. That is, you must find the reciprocal of the number that is after the division symbol; and then you multiply the first number (the one before the division symbol) by the reciprocal of the second number (the one after the division symbol). Remember that to find the reciprocal of a number, you simply have to change the numerator and denominator of the number.

Since 6 can be considered to be a fraction equal to \frac{6}{1}, by inverting the number, then you get \frac{1}{6}

Then:

\frac{8}{9}÷6= \frac{8}{9} *\frac{1}{6}

Now you multiply the numerators and denominators of the fraction to get the new numerator and denominator of the final solution.

\frac{8}{9}÷6= \frac{8}{9} *\frac{1}{6}=\frac{8*1}{9*6} =\frac{8}{54}

Finally, simplifying the fraction:

\frac{8}{9}÷6= \frac{8}{9} *\frac{1}{6}=\frac{8*1}{9*6} =\frac{8}{54}=\frac{4}{27}

So:

\frac{8}{9}÷6= \frac{4}{27}

<u><em>The fraction of the book that Rena read every day is </em></u>\frac{4}{27}<u><em></em></u>

3 0
3 years ago
What value is true of x makes this equation true 0.7x-5=0.2x+1
Sever21 [200]

Answer:

x=12

Step-by-step explanation:

First you make sure x is on both sides of the equation. So you do 0.7x-5-0.2x=0.2x+1-0.2x. Which just simplifies to 0.5x-5=1. You make sure x is the only thing on that side of the equation so you do 0.5x-5+5=1+5 which simplifies to 0.5x=6. Multiply the equation times 2 to just have x. x=12. The value that makes true of x is 12.

7 0
3 years ago
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together the
klasskru [66]

The rate charged per hour by each mechanic was:  x = 75 $ / hr and y = 115 $ / hr.

<h3>What is a system of equations?</h3>

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given;

The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours.

Together they charged a total of $3225.

For this case we have the following variables:

x be the amount of $ / hr that the mechanic obtains 1.

y be the amount of $ / hr obtained by mechanic 2.

An equation to express this would be:

x + y = 190

20x + 15y = 3225

Solving the system of equations we have:

20x + 15(190 -x) = 3225

20x + 2850 - 15x = 3225

5x = 375

x = 75

simililary

y = 190 - x

y = 115

Hence, the rate charged per hour by each mechanic was:

x = 75 $ / hr

y = 115 $ / hr

Learn more about equations here;

brainly.com/question/10413253

#SPJ1

6 0
2 years ago
Using numbers 12,4,5,17,12 make 24. <br> Helllpppp
romanna [79]

Answer: To get 24

Step-by-step explanation

What you would need to do is first multiply 12 x 5 would come out as 60.

Then from 60 you subtract 17 and 12 to get 5. Divide by the 5 that you just got from 17 and 12 and to get 20. Using the 4 add it to the 20 to get 24.

4 0
3 years ago
Please help i don’t really understand this
Andrew [12]

Answer:

g(x) = 1/2x^2

Step-by-step explanation:

6 0
3 years ago
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