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3 years ago

It said i need to simplify. how do i

Mathematics

1 answer:

horrorfan [7]3 years ago

4 0

Answer:

The equation relating the volume of water, y to the volume of flour, x is therefore;

y = 1/3×x

The quantity of water per liter of flour = 1/3 liters

The quantity of flour per liter of water = 3 liters

Step-by-step explanation:

The given information from the graph are;

At 0 liters of water, the volume of flour = 0 liters of flour

At 1 liter of water, the volume of flour = 3 liters of flour

The relationship between the volume of water and flour is linear given s follows;

The equation for a linear relationship is y = m·x + c

m = The gradient or slope of the line, c = the y-intercept

In the graph the y-intercept = 0 therefore, c = 0

The slope, m is (change in y-coordinate)/(Change in x-coordinate)

∴ m = (1 - 0)/(3 - 0) = 1/3

The equation relating the volume of water, y to the volume of flour, x is therefore;

y = 1/3×x

Such that when the question asks, how many liter of water is used per liter of flour, we get;

y = 1/3× 1 = 1/3 liters

Similarly when the question asks, how many liter of flour is used per liter of water, we get;

1 = 1/3×x

x = 3 × 1 = 3 liters.

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Can anybody show me how to do this half angle identity problem STEP BY STEP? I always seem to be missing something

klio [65]

Answer: $\bold{-\dfrac{7\sqrt2}{10}}$

<u>Step-by-step explanation:</u>

It is given that θ is between 270° and 360°, which means that θ is located in Quadrant IV ⇒ (x > 0, y < 0). Furthermore, the half-angle will be between 135° and 180°, which means the half-angle is in Quadrant II ⇒ $cos\ \dfrac{\theta}{2}$

It is given that sin θ = $-\dfrac{7}{25}$ ⇒ y = -7 & hyp = 25

Use Pythagorean Theorem to find "x":

x² + y² = hyp²

x² + (-7)² = 25²

x² + 49 = 625

x² = 576

x = 24

Use the "x" and "hyp" values to find cos θ:

$cos\ \theta=\dfrac{x}{hyp}=\dfrac{24}{25}$

Lastly, input cos θ into the half angle formula:

$cos\bigg(\dfrac{\theta}{2}\bigg)=\pm \sqrt{\dfrac{1+cos\ \theta}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{1+\dfrac{24}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{\dfrac{25}{25}+\dfrac{24}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{\dfrac{49}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{49}{50}}\\\\\\.\qquad \quad =\pm \dfrac{7}{5\sqrt2}}\\\\\\.\qquad \quad =\pm \dfrac{7}{5\sqrt2}}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\\\\\\.\qquad \quad =\pm \dfrac{7\sqrt2}{10}$

Reminder: We previously determined that the half-angle will be negative.

6 0

3 years ago

english has 26 different letters. how many consecutive words have to be selected in a book to have at least 5 that start with th

Valentin [98]

The words need not be English language words 142506

What is permutation and combination?

A set of elements can be divided into subsets in two different ways: combination and permutation.

The components of the subset may be arranged in any order when combined. The components of the subset are listed in a permutation in a certain order.

If the word has 5 different letters then it is just 26-choose-5 or (26/5).

If the word has 4 different letters then it is just 26-choose-4 or (26/4)

have 4 options to choose which letter to duplicate twice.

This gives = 4*(26/4)

If the word has 3 different letters then it is just 26-choose-3 or (26/3).

you duplicate one of the three letters 3 times - 3 options for that, or you choose 2 letters and duplicate each one twice - again 3 options. In total this gives = 6*(26/3).

If the word has 2 different letters then it is just 26-choose-2 or (26/2).

The sets of 2 different letters and duplicate either one of the letters 4 times - 2 options; or duplicate one letter 2 times, and the other 3 times - again 2 options. In total this is = 4*(26/2).

The word has just 1 distinct letter you have = (26/1).

we get :

N = (26/5)+ 4*(26/4) + 6*(26/3) + 4*(26/2) + (26/1)

= 142506

The words need not be English language words = 142506

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1 year ago

Find inverse of y=1/2x+8

Molodets [167]

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3 years ago

Answer question 8,9 and 10 with full details.

Lelechka [254]

Answer:

See Explanation

Step-by-step explanation:

8. (1)

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36/3 = x + y

12 = x + y

x + y = 12.... (1)

8(2)

It is given that:

x = 2y....(2)

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Side of square = 1 m

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3 years ago

Choose all that give the correct equation of the line parallel or perpendicular to the given line passing through the point.

andriy [413]

Answer:

A and B

Step-by-step explanation:

Parallel lines are lines which have the same slope. Perpendicular lines have negative reciprocal slopes.

For the options:

A. Both equations have 7/5 as the slope. They are parallel.

B. The slopes are 1 and -1. These are perpendicular.

C. The slopes are 9/2 and are parallel.

D. The slopes are 7/3 and -3/7. They are perpendicular.

The solution is A and B.

7 0

3 years ago