MATHEMATICS MIDDLE SCHOOL

Find the equation of the straight line passing through the point (3,5) which is perpendicular to the line y=-3x+2

Answers

Answer 1

Answer:

Answer:

y = $(1)/(3)$ x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = - 3x + 2 is in this form with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

$m_(perpendicular)$ = - $(1)/(m)$ = - $(1)/(-3)$ = $(1)/(3)$

y = $(1)/(3)$ x + c ← is the partial equation

to find c substitute (3, 5 ) into the partial equation

5 = 1 + c ⇒ c = 5 - 1 = 4

y = $(1)/(3)$ x + 4 ← equation of perpendicular line

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How do you solve this problem 5.04÷6

Answers

you would divided 5.04 by 6 to get 0.84

You would divide 5.04 by 6 and when you do this the answer is 0.84.

What is the highest fraction here -3/25, -7 / 20, -27 / 50, -13 / 20, 16 / 25, 53 / 100, -1 / 3

Answers

16/25 is the highest, because if you multiply it by four you get 64/100, and the rest of the fractions are negative.

The stem-and-leaf plot shows the number of home runs Carlos hit in the last five seasons. What is the mean absolute deviation of these values? Carlos home runs

Answers

To find mean, add the numbers then divide by how many numbers there are.

320= how many hundreds/ones? You get

Thanks

Answers

Okay, so the place values are ones, tens, and then then hundreds, from the right to left. Following that pattern, the 0 would be the ones, the 2 would be tens, and the 3 would be the hundreds. So, now you know how to find the place value, you can determine that there are 3 hundreds, 2 tens, and ones, or 20 ones and 3 hundreds.

3 one hundreds and 20 ones

Three quarters of the boats in the marina are white. 4/7 of the remaining boats are blue, and the rest are red. If there are 9 red boats, how many boats are in the marina?

Answers

Answer: 84

Step-by-step explanation:

Let the total number of boats on the marina be x.

Then, The number of white boats= $(3)/(4)x$

then the remaining boats= $x-(3x)/(4)=(x)/(4)$

Now, 4/7 of the remaining boats are blue.

Thus, the number of blue boats= $(4)/(7)*(x)/(4)=(x)/(7)$

The rest of the boats (red boats)= $(x)/(4)-(x)/(7)=(7x-4x)/(28)=(3x)/(28)$

The number of red boats=9

Thus,

$(3x)/(28)=9\n\Rightarrow\ x=(28*9)/(3)\n\Rightarrow\ x=84$

The total number of boats in the marine = 84

There are 84 boats in the marina

Further explanation

Fraction numbers are known as numerator and denominator

On a number line, fractions are expressed in points that lie between two integers

The general form of fractions is

$\large{\boxed{\bold{(a)/(b)} }$

a = numerator

b = denominator

Mixed fractions consist of whole number and proper fractions

There are a number of steps in adding fraction operations

1. the denominators must be the same, if not then

a. Multiply top and bottom of each fraction by the denominator of the other. or

b. we can use Least Common Denominator which is the smallest of all the common denominators.

2. Add the numerators and put over the denominator

3. Simplify the fraction

There are several steps to multiply fractions

1. Multiply the numerators
2. Multiply the denominators
3. Simplify the fraction

Three quarters of the boats in the marina are white

we translate this sentence into equation:

Let x = total boats

$\displaystyle white~boat=\boxed{(3)/(4)x}$

$(4)/(7)$ of the remaining boats are blue

$\displaystyle remaining~boat=x~-(3)/(4)x=(1)/(4)x$

$\displaystyle blue~boat=(4)/(7)*(1)/(4)x=(4)/(28)x=(1)/(7)x$

total boats

$\displaystyle total~boats=x=(3)/(4)x+(1)/(7)x+9$

Because the denominator is not the same, so we can use both multiplying or least common denominator.

let we use least common denominator:

List multiples of 7: 7, 14, 21,28,...

List multiples of 4: 4, 8, 12, 16, 20,24,28, ...

the smallest number that is the same: = 28

then addition operation becomes :

$\displaystyle (21)/(28)x+(4)/(28)x+9=x$

$\displaystyle (25)/(28)x+9=x$

$\displaystyle (3)/(28)x=9$

$\large{\boxed{\boxed{\bold{x=84}}}$

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Keywords : boats, marina, fractions

Use rounding or compatible numbers to estimate the sum 302+412

Answers

i think it would be 710 because you can round the 302 to 300 and then 412 to 410 and then you add the but it asks to estimate so it would probably be 700

well i just looking at the first numbers of each one and added those up that became 700 and since the numbers behind them arent so big it rounds out to 700:))

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