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3 years ago

Find the length of the missing side. Leave your answer in simplest radical form.

Mathematics

1 answer:

Mrac [35]3 years ago

4 0

Answer:

a) $\sqrt{69}$

Step-by-step explanation:

this is a right triangle so you can use the Pythagorean Theorem:

the sum of the legs, squared, is equal to the hypotenuse, squared

10² + b² = 13²

100 + b² = 169

b² = 69

b = $\sqrt{69}$

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Ms.Groves has trays of paints for students in her art class.Each tray has5colors one of the colors is purple what fraction of th

Ivahew [28]

The answer is 1/5.

The fraction for 1 tray is 1/5, and when you have 20 trays, you can just simplify to get 1/5.

7 0

4 years ago

A curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordin

Anit [1.1K]

Answer:

$y=5e^{2x}$

Step-by-step explanation:

Let (x,y) represents a point P on the curve,

So, the slope of the curve at point P = $\frac{dy}{dx}$

According to the question,

$\frac{dy}{dx}=2y$

$\frac{1}{y}dy=2dx$

Integrating both sides,

$\int \frac{dy}{y}=2dx$

$ln y=2x+ln C$

$ln y-ln C = 2x$

$ln(\frac{y}{C})=2x$

$\frac{y}{C}=e^{2x}$

$\implies y=Ce^{2x}$

Since, the curve is passing through the point (0, 5),

$5=Ce^{0}\implies C=5$

Hence, the required equation of the curve is,

$y=5e^{2x}$

7 0

4 years ago

What is the first step in estimating 56×27

Free_Kalibri [48]

First you should round the numbers that you are multiplying so.
56 ---> 60
27---> 30
You know that 5 and higher you'll round up.
4 and below you'll round down.

6 0

3 years ago

Read 2 more answers

PLEASE SOLVE QUESTION 13 AND 14 DONT STEAL THE POINTS

Varvara68 [4.7K]

Answer:

See below for solution.

Step-by-step explanation:

$Q13)$ $\frac{\sqrt{11} - \sqrt{5} }{\sqrt{11}+\sqrt{5} }$ = $x - y\sqrt{55}$

LHS :-

= $\frac{\sqrt{11} - \sqrt{5} (\sqrt{11}-\sqrt{5}) }{\sqrt{11}+\sqrt{5} (\sqrt{11}-\sqrt{5}) }$

= $\frac{11-2\sqrt{55}+5 }{11 - 5}$

= $\frac{16-2\sqrt{55} }{6}$

= $\frac{2(8-\sqrt{55}) }{2(3)}$

= $\frac{8-\sqrt{55} }{3}$

=> x = 8/3 and y = 1/3

=> Option B

$Q14)$ $\frac{4}{216^{-2/3} }$ + $\frac{1}{256^{-3/4} }$ + $\frac{2}{243^{-1/5} }$

= 4 x (∛216)² + ( $\sqrt[4]256}$ )³ + 2 x ( $\sqrt[5]{243}$ )

= 4 x 36 + 64 + 2 x 3

= 144 + 64 +6

= 144 + 70

= 214

3 0

2 years ago

A coffee mixture has beans that sell for $0.20 a pound and beans that sell for $0.68. If 120 pounds of beans create a mixture wo

atroni [7]

Let x be the number of pounds of the $1.35 beans. The cost of those beans is $1.35 * x, or 1.35x.
Let y be the number of pounds of the $1.05 beans. The cost of those beans is $1.05 * y, or 1.05y. 
We know that 120 pounds of the mix sells for $1.15/pound, for a total of 120 * 1.15 = $138. 

x + y = 120 
1.35(x) + (1.05)y = 138 

We can rewrite the first as 
x = -y + 120 

Now we can substitute (-y + 120) in for (x) in the second equation, because we just proved they're equal. 

1.35(x) + 1.05(y) = 138 
1.35(-y + 120) + 1.05y = 138 
-1.35y + 162 + 1.05y = 138 
-0.3y + 162 = 138 
-0.3y = -24 
y = 80 

And since x + y = 120, that means x = 40. 

Check: 
40 pounds of x at $1.35 costs 40 * 1.35, or $54. 
80 pounds of y at $1.05 costs 80 * 1.05, or $84. 
Do those add up to our target total, according to the question, of 120 * 1.15 = $138?

3 0

3 years ago