Help this is algebra

loris [4]

<u>The answer is 808/99</u>

7 0

3 years ago

explain how you know that when finding a fractional part of a whole number is the same as multiplying that fraction by a whole n

frosja888 [35]

I know that because my 8th grade math teacher taught us (in 1954)
that when you see the word "of" in a math problem, it almost always
means "times". So part of your question says "... finding a fractional
part times a whole number ...".

7 0

3 years ago

Sonny has entered a reading contest at the local library. After reading two books, he has read 396000 words of text. After five

lutik1710 [3]

Answer:

Please check the expalantion.

Step-by-step explanation:

Let

x is the number of books read

y is the total number of words read

Given that:

After reading two books, he has read 396000 words of text.

Thus, we get the point (2, 396000).

After five books, he has read 990000 words of text.

Thus, we get the point (5, 990000).

As the function is linear, so we take the points

(2, 396000)

(5, 990000)

Determining the slope between (2, 396000) and (5, 990000)

(x₁, y₁) = (2, 396000)

(x₂, y₂) = (5, 990000)

Using the formula

Slope = m = [y₂ - y₁] / [x₂ - x₁]

= [990000 - 396000] / [5 - 2]

= 594000 / 3

= 198000

Thus, the slope of the line = m = 198000

substituting the point (2, 396000) and m = 198000 in the slope-intercept form of the linear equation to determine the y-intercept

y = mx+b

396000 = 198000(2) + b

flipe the equation

198000(2) + b = 396000

396000 + b = 396000

subtracting 396000 from both sides

396000 + b - 396000 = 396000 - 396000

b = 0

now substituting b = 0 and m = 198000 in the slope-intercept form of the linear equation to determine the y-intercept

y = mx+b

y = 198000x + 0

y = 198000x

Therefore, a linear function in slope-intercept form to model his progress is:

y = 198000x

Part b)

How many books will he need to read to reach a total of 10,000,000 words?

As we have already determined a linear function in slope-intercept form to model his progress.

y = 198000x

substituting y = 10,000,000 in the equation

y = 198000x

10,000,000 = 198000x

flip the equation

198000x = 10,000,000

dividing the both equation by 198000

198000x/198000 = 10,000,000/198000

x = 50.5

Thus, Sonny will need to read 50.5 books to read to reach a total of 10,000,000 words.

3 0

3 years ago

WORTH 20 POINTS HELP

vfiekz [6]

Below represents the proof that the quadrilateral QRST is a parallelogram

<h3>How to prove that QRST is a parallelogram?</h3>

The coordinates are given as:

Q = (-1,-1)

R = (2,9)

S = (-4,5)

T = (-7,-5)

Calculate the length of each side using:

$d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}$

So, we have:

$QR = \sqrt{(-1 - 2)^2 + (-1 -9)^2} = \sqrt{109}$

$RS = \sqrt{(-4 - 2)^2 + (5 - 9)^2} = \sqrt{52}$

$ST = \sqrt{(-7 + 4)^2 + (-5 - 5)^2} = \sqrt{109}$

$TQ = \sqrt{(-7 + 1)^2 + (-5 + 1)^2} = \sqrt{52}$

The above computations show that opposite sides are equal.

Next, we determine the slope of each side using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$QR = \frac{9 + 1}{2 + 3} = \frac{10}3$

$RS = \frac{5-9}{-4 - 2} = \frac{2}3$

$ST = \frac{5+5}{-4 + 7} = \frac{10}3$

$TQ = \frac{-5+1}{-7 + 1} = \frac{2}3$

The above computations show that opposite sides are parallel, because they have equal slope

Hence, the quadrilateral QRST is a parallelogram