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Eva8 [605]
3 years ago
7

Sonia is hanging up decorations in the ratio of 3red: 2green: 4white . If she hangs up 135 decorations in total , how many of ea

ch colour does she hang up
Mathematics
1 answer:
klasskru [66]3 years ago
8 0

Answer:

She hung 45reds, 30greens and 60whites

Step-by-step explanation:

If Sonia is hanging up decorations in the ratio of 3red: 2green: 4white, the total amount of different she hung is 3+2+4 = 9different colours.

Of she hung 135decorations in total, the number of red = 3/9 × 135 = 45reds

Number of green = 2/9 × 135 = 30greens

Numbe of white = 4/9 × 135= 60whites

She hung 45reds, 30greens and 60whites

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The variance is direct.

Step-by-step explanation:

Since size of the pizza determines the amount of calories.

Let us say that a 2" x4" strip of pizza has 250 calories.

Then a pizza of twice the size (or 4" x 4") will have twice as many calories (500 calories) .

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2 years ago
Andrew pays a monthly membership fee of $10 at his gym. Each time he uses the gym, he pays $5. Last month, Andrew spent a total
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I hope this helps
If you have any questions on my answer please feel free to ask :)
3 0
2 years ago
Read 2 more answers
Can someone please explain how to do this!!!
DedPeter [7]

Hi there!

So we are given that:-

  • tan theta = 7/24 and is on the third Quadrant.

In the third Quadrant or Quadrant III, sine and cosine both are negative, which makes tangent positive.

Since we want to find the value of cos theta. cos must be less than 0 or in negative.

To find cos theta, we can either use the trigonometric identity or Pythagorean Theorem. Here, I will demonstrate two ways to find cos.

<u>U</u><u>s</u><u>i</u><u>n</u><u>g</u><u> </u><u>t</u><u>h</u><u>e</u><u> </u><u>I</u><u>d</u><u>e</u><u>n</u><u>t</u><u>i</u><u>t</u><u>y</u>

\large \displaystyle{ {tan}^{2}  \theta + 1 =  {sec}^{2}  \theta}

Substitute tan theta = 7/24 in.

\large \displaystyle{ {(  \frac{7}{24}) }^{2}  + 1 =  {sec}^{2} \theta }

Evaluate.

\large \displaystyle{ \frac{49}{576}  + 1 =  {sec}^{2}  \theta} \\  \large \displaystyle{ \frac{625}{576}  =  {sec}^{2}  \theta}

Reminder -:

\large \displaystyle{ sec \theta =  \frac{1}{cos \theta} }

Hence,

\large \displaystyle{ \frac{576}{625}  =  {cos}^{2}  \theta} \\  \large \displaystyle{ \sqrt{ \frac{576}{625} }  = cos  \theta} \\  \large \displaystyle{ \frac{24}{25}  = cos \theta}

Because in QIII, cos<0. Hence,

\large \displaystyle \boxed{ \blue{cos \theta =  -  \frac{24}{25} }}

<u>U</u><u>s</u><u>i</u><u>n</u><u>g</u><u> </u><u>t</u><u>h</u><u>e</u><u> </u><u>P</u><u>y</u><u>t</u><u>h</u><u>a</u><u>g</u><u>o</u><u>r</u><u>e</u><u>a</u><u>n</u><u> </u><u>T</u><u>h</u><u>e</u><u>o</u><u>r</u><u>e</u><u>m</u>

\large \displaystyle{ {a}^{2}  +  {b}^{2}  =  {c}^{2} }

Define c as our hypotenuse while a or b can be adjacent or opposite.

Because tan theta = opposite/adjacent. Therefore:-

\large \displaystyle{ {7}^{2}  +  {24}^{2}  =  {c}^{2} } \\  \large \displaystyle{49 + 576 =  {c}^{2} } \\  \large \displaystyle{625 =  {c}^{2} } \\  \large \displaystyle{25 = c}

Thus, the hypotenuse side is 25. Using the cosine ratio:-

\large \displaystyle{cos \theta =  \frac{adjacent}{hypotenuse}}

Therefore:-

\large \displaystyle{cos \theta =  \frac{24}{25} }

Because cos<0 in Q3.

\large \displaystyle \boxed{ \red{cos \theta =  -  \frac{24}{25} }}

Hence, the value of cos theta is -24/25.

Let me know if you have any questions!

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The correct answer is D
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3 years ago
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