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3 years ago

Is 16to 14 and 64to60 equivalent

1 answer:

3 0

NO. They are not.

We can prove this by turning those numbers into fractions:

16 / 14 = 1.1428 ; 64 / 60 = 1.0667

Or simply:

64 / 16 = 4
60 / 14 = 4.29

To get the equivalent of 16 to 14; we must multiply both numbers by 4.

16 * 4 = 64
14 * 4 = 56

The equivalent of 16 to 14 is 64 to 56.

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Cos^2x+cos^2(120°+x)+cos^2(120°-x)<br>i need this asap. pls help me

o-na [289]

Answer:

$\frac{3}{2}$

Step-by-step explanation:

Using the addition formulae for cosine

cos(x ± y) = cosxcosy ∓ sinxsiny

---------------------------------------------------------------

cos(120 + x) = cos120cosx - sin120sinx

= - cos60cosx - sin60sinx

= - $\frac{1}{2}$ cosx - $\frac{\sqrt{3} }{2}$ sinx

squaring to obtain cos² (120 + x)

= $\frac{1}{4}$ cos²x + $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

--------------------------------------------------------------------

cos(120 - x) = cos120cosx + sin120sinx

= -cos60cosx + sin60sinx

= - $\frac{1}{2}$ cosx + $\frac{\sqrt{3} }{2}$ sinx

squaring to obtain cos²(120 - x)

= $\frac{1}{4}$ cos²x - $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

--------------------------------------------------------------------------

Putting it all together

cos²x + $\frac{1}{4}$ cos²x + $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x + $\frac{1}{4}$ cos²x - $\frac{\sqrt{3} }{2}$ sinxcosx + $\frac{3}{4}$ sin²x

= cos²x + $\frac{1}{2}$ cos²x + $\frac{3}{2}$ sin²x

= $\frac{3}{2}$ cos²x + $\frac{3}{2}$ sin²x

= $\frac{3}{2}$ (cos²x + sin²x) = $\frac{3}{2}$

5 0

3 years ago

If 150 empty water bottles weigh 4.5 pounds what do you expect 90 water empty bottles to weigh?

MakcuM [25]

It's 2.7 pounds because I set up a proportion of 150 over 90 = 4.5 over X and multiplied 90 * 4.5 divided by 150

6 0

3 years ago

Read 2 more answers

Two corresponding sides of similar triangles are 2 cm and 5 cm. What is the area of the second triangle if the area of the first

Stella [2.4K]

Answer:

(1) Area of second triangle= 50 cm^2.

(2) Area of ΔABC=98 cm^2.

and Area of ΔDFG=175 cm^2.

Step-by-step explanation:

<em>" For two similar triangles the ratio of sides is equal to the ratio of square of their areas".</em>

i.e. if a,b are the corresponding sides of two similar triangles and let A and B denote the area of two triangles then we have the relation as:

$\dfrac{a^2}{b^2}=\dfrac{A}{B}$

(1)

for the first question:

we have a=2, b=5.

A=8 cm^2.

Hence,

$\dfrac{2^2}{5^2}=\dfrac{8}{B}\\\\\dfrac{4}{25}=\dfrac{8}{B}$

B=50 cm^2.

Hence, the area of second triangle is 50 cm^2.

(2)

In second option we have:

a=6 and b=5.

A-B=77 cm^2.

A=77+B

$\dfrac{6^2}{5^2}=\dfrac{A}{B}\\ \\\dfrac{36}{25}=\dfrac{77+B}{B}\\ \\36B=25\times77+25B\\\\36B-25B=25\times77\\\\11B=25\times77\\\\B=25\times7\\\\B=175$

Hence area of second triangle i.e. ΔDFG is 175 cm^2.

and area of first triangle i.e. ΔABC=175-77=98 cm^2.

8 0

3 years ago

Algebra 2 word problem: Urgent!

vesna_86 [32]

Answer:

180 hours

Step-by-step explanation:

Surfer #1 takes a capsule every 6 hours, but this is also equal to 2 capsules every 12 hours. Surfer #2 takes 1 capsule every 12 hours. Thus, both surfers take a total of 3 capsules every 12 hours.

By dividing 45 total capsules they need to consume by 3, the number of capsules the surfers consume every 12 hour, you get the total number of hours times 12 it takes for them to consume 45 capsules. 45 / 3 = 15, so it takes 15 * 12 hours for them to consume 45 capsules. This is equal to 180 total hours.

6 0

3 years ago

2 y + 4 x = 8, Solve for y

mash [69]

Answer:

y=−2x+4

Step-by-step:

2y+4x=8

Step 1: Add -4x to both sides.

4x+2y+−4x=8+−4x

2y=−4x+8

Step 2: Divide both sides by 2.

2y /2 = −4x+8 /2

y=−2x+4

4 0

3 years ago

Read 2 more answers