Solve for a side in right triangles

Answer:

(a) [tex]Perimeter = 32.2\ cm[/tex]

(b) 100

Step-by-step explanation:

Solving (a):

Given

Shape: Rectangle

[tex]Area = 64.8[/tex]

Required

Calculate the perimeter.

Area is calculated as:

[tex]Area = L * W[/tex]

Where

[tex]L = Length[/tex] and [tex]W = Width[/tex]

Substitute 64.8 for Area

[tex]64.8 = L * W[/tex]

Make L the subject:

[tex]L = \frac{64.8}{W}[/tex]

Perimeter is calculated as:

[tex]P = 2 * (L + W)[/tex]

Substitute 64.8/W for L

[tex]P = 2 * (\frac{64.8}{W} + W)[/tex]

[tex]P = \frac{129.6}{W} + 2W[/tex]

To solve further, we take the derivative of P and set it to 0, afterwards.

[tex]dP = -\frac{129.6}{W^2} + 2[/tex]

Set to 0

[tex]0 = -\frac{129.6}{W^2} + 2[/tex]

Collect Like Terms

[tex]\frac{129.6}{W^2} = 2[/tex]

Cross Multiply:

[tex]2W^2= 129.6[/tex]

Divide through by 2

[tex]W^2 = 64.8[/tex]

Take square roots

[tex]W = \sqrt{64.8[/tex]

[tex]W = 8.05[/tex]

Recall that:

[tex]L = \frac{64.8}{W}[/tex]

So:

[tex]L= \frac{64.8}{8.05}\\[/tex]

[tex]L= 8.05[/tex]

The perimeter is:

[tex]Perimeter = 2 * (8.05 + 8.05)[/tex]

[tex]Perimeter = 2 * (16.10)[/tex]

[tex]Perimeter = 32.2\ cm[/tex]

Solving (b):

Given

((1 Group of 10 tenths) and (1 group of 8 tenths))/(6 groups of 3 tenths)

Required

Solve

[tex]Tenths = \frac{1}{10}[/tex]

So, the expression becomes:

((1 Group of [tex]10 * \frac{1}{10}[/tex]) and (1 group of [tex]8 * \frac{1}{10}[/tex]))/(6 groups of [tex]3 * \frac{1}{10}[/tex])

This gives:

((1 Group of [tex]\frac{10}{10}[/tex]) and (1 group of [tex]\frac{8}{10}[/tex]))/(6 groups of [tex]\frac{3}{10}[/tex])

Group means product, so the expression becomes:

[tex]\frac{(1 * \frac{10}{10} \ and\ 1 * \frac{8}{10})}{6 * \frac{3}{10}}[/tex]

And, as used here means addition

[tex]\frac{(1 * \frac{10}{10} + 1 * \frac{8}{10})}{6 * \frac{3}{10}}[/tex]

Simplify:

[tex]\frac{(1 * 1 + 1 * 0.80)}{6 *0.30}[/tex]

[tex]\frac{(1 + 0.80)}{1.80}[/tex]

[tex]\frac{1.80}{1.80}[/tex]

[tex]= 1.00[/tex]

Answer:

Find the solution below

Step-by-step explanation:

A) Let the complete power of the phone be 1

If after charging 1/3 of an hour, a phone is at 2/5 of its full power, we can write;

1/3 hr = 2/5 of its full power

To determine the time it will take to phone to charge completely, we will say;

x hr = 1

Divide both expression

(1/3)/x = 2/5

1/3x = 2/5

Cross multiply

1 * 5  = 3x * 2

5 = 6x

x = 6/5

x  = 1.2

Hence it will take 1.2 hour for the phone to charge completely

B) From the expression in A

1/3x = 2/5

Multiply both sides by 3

1/3x * 3= 2/5 * 3

x = 2/5 * 3

Hence the multiplication equation is x = 2/5 * 3

Also divide both sides by 1/3

recall 1/3x = 2/5

1/3x ÷ 1/3 = 2/5÷1/3

x = 2/5÷1/3

Hence the division equation is x = 2/5÷1/3

Answer: n= 80 ×48+ 34×20

Step-by-step explanation:

Given: Number of large boxes = 80

Number of small boxes = 34

Number of markers in each large box = 48

Number of markers in each small box = 20

Total markers = (Number of large boxes)x (Number of markers in each large box) + (Number of small boxes) x (Number of markers in each small box)

Total number of markers = n (given)

Then, n= 80 ×48+ 34×20

Therefore , the equation could be used to find n, the total number of markers in stock: n= 80 ×48+ 34×20

Answer:

y=-5/2*X-3

Step-by-step explanation:

A system has no solutions the lines are parallel

Answer:

620 cm²

Step-by-step explanation:

First I'll describe the net. There are 3 rectangles and 2 triangles. The triangles are identical and 2 out 3 of the rectangles are the same.

So, we know that the two similar rectangles have measurements of 13cm x 10cm. So, that's 130 cm² for one such rectangle. Add the other one and we get 260 cm².

The bottom rectangle has dimensions of 10cm x 24 cm, or 240 cm². Add that to our previous total and we'll get 500 cm².

On to the triangles. Now, we know that 1. these are isosceles triangles, and 2. they have a height of 5 cm. We can pretend to cut them in half at their highest point, which would give us 4 triangles with height 5 and length 12. Now, if you put two identical triangles together, it's a four-sided shape, and you can just multiply length by width. Let's do that.

Now we have 2 rectangles, each with width 5 and length 12. Calculate the area for each, and now we have 2 rectangles with area 60 cm². Add them together....120cm².

Add that to our previous total, and we'll get 620 cm². That should be the surface area of your prism :D

Answer:

Step-by-step explanation:

Given m ∠ Q P S = 4 7 ∘ m∠QPS=47 ∘ m, angle, Q, P, S, equals, 47, degrees m ∠ R P S = 3 x − 3 8 ∘ m∠RPS=3x−38 ∘ m, angle, R, P, S, equals, 3, x, minus, 38, degrees m ∠ Q P R = 7 x − 9 5 ∘ m∠QPR=7x−95 ∘

Sum of angles in a triangle = 180°

47° + 3 x − 3 8 ∘ + 7x - 95° = 180°

10x + 180° = 180°

Answer: 31°

(Attached photo of work)

Answer:

8 ft

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

4ft X 8ft= 32ft

Answer:

u^2+4u-12

Step-by-step explanation:

u x u + 6u -2u - 2 x 6

The answer is no solution

Trapezium I hope you get it right

Total hats = 52 + 13 = 65

Percentage that are baseball = number of baseball/ total hats x 100.

52/65 = 0.8 x 100 = 80%

80% are baseball hats

Answer: 80%

Step-by-step explanation:

First, you would add 52 and 13 together. That would be 65. Then you would divide 52 by 65. The answer is 0.8. That is equal to 80%.

Answer:

638 miles

Step-by-step explanation:

Key skills needed: Proportions, Unit Rates

1) The car can go 464 miles with 16 gallons of gasoline. We need to find how many miles each gallon gasoline results in.

To find the miles per gallon, we would do 464 miles/16 gallons --> 29 mpg

This means each gallon lets the car run 29 miles.

2) To find out how many miles 22 gallons is, we then do 29 x 22, which is 638 miles.

Therefore, your answer is 638.

Hope you understood and have a nice day!!

Answer:

The correct answer is,

[tex]x = 18[/tex]

Answer:

x = 18

Step-by-step explanation:

So first you want to get rid of the fractions, which are 1/2 and 1/3. To do this you can multiply both sides of the equation by 6, so you would get:

3x - 42 = 2(x - 12).

Next, on the right side of the equation you can distribute the 2.

3x - 42 = 2x - 24

You want to get all the x variables on one side so you can subtract 2x from both sides.

x - 42 = -24

And finally you add 42 to both sides

x = 18

Answer:

75.4 ft

Step-by-step explanation:

C=2(pi)r

C=2(pi)12=75.4

Answer:

B

Step-by-step explanation:

It's just B

Answer:

C. y=3x + 1

Step-by-step explanation:

Answer:

2.13

Step-by-step explanation:

.47 would be your probability of randomly selecting but your'e solving geometrically so think how many trials until successful.

use u x(mean)= 1/.47 to get around 2.13

Answer:

2.13

Step-by-step explanation:

.47 is the probability of randomly selecting, you have to find how many trials until successful. x(mean)= 1/.47 to get around 2.13

Answer:

B. Two pairs of opposite sides are congruent

Step-by-step explanation:

This is one of the rules of identifying a parallelogram, and the other ones are false.

Solution:

1)Distance covered by cyclist=3.75 miles.

Time =0.3 hours.

Speed= Distance ÷Time

Speed =3.75÷0.3=12.5 miles per hour.

2) Speed = 12.5 miles per hour, Distance = 4.5 miles .

Time = Distance ÷Speed.

Time = 4.5÷12.5=0.36 hours.

Time taken to cover 4.5 miles is 0.36 hours.

Answer:

a) Speed of the cyclist is (2.75/0.4) = 6.875 miles per hour.

b) It will take (5.5/6.875) = 0.8 hours to travel 5.5 miles at this rate.

Answer:

x=26

Step-by-step explanation:

2x+3x+50=180   add like terms

5x+50=180   subtract both sides by 50

5x=130   divide both sides by 5

x=26

Answer:

x = 26

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

2x + 3x + 50 = 180

5x + 50 = 180 ( subtract 50 from both sides )

5x = 130 ( divide both sides by 5 )

x = 26

Answer:

737 miles

Step-by-step explanation:

So we know that he drove 871 miles in 13 hours so first you want to do 871 divided by 13 and get 67 which means he drove 67 miles in one hour.  Finally you just have to multiply 67 by 11 and get 737.

Answer:

737 miles

Step-by-step explanation:

Since the distance is gonna be less it's gonna be..

11 x 871/ 13

The chart relating to the question can be found in the picture attached below :

Answer:

40%

Step-by-step explanation:

Yoghurt __________ No of responses

Low Fat ___________ 15

Greek_____________24

Whipped __________ 10

Regular ___________ 11

Total number of responses :

(15 + 24 + 10 + 11) = 60

Number of  responses for Greek yogurts = 24

Percentage % :

(Greek Yoghurt responses / total responses) * 100%

= (24 / 60) * 100%

= 0.4 * 100%

= 40%

Answer:

the slope is -2

Step-by-step explanation:

When using rise over run you must divide the Y (in this case it's 2) by the X (which is 1), and in this problem 2 divided by 1 equals 2, but it's a negative line because it's going down which means your answer is -2

Answer:

...........the new price is 22.50

Answer:

James scored 87.5% in the test.

Step-by-step explanation:

7 x 100 : 8 = 87.5%

9514 1404 393

Answer:

  C

Step-by-step explanation:

The problem statement tells you that cost is a function of x minutes. We plot the independent variable (x) on the horizontal axis, so this statement tells you the horizontal axis will be labeled "Minutes." (matches A and C)

When x=0 (no minutes), the function value is ...

  c(0) = 3·0 +2 = 2

For each additional minute, the cost goes up by 3, so we know these things about the line:

The graph of A has a y-intercept of 3, so is incorrect. It also has a slope of 2, so is incorrect on that basis, as well.

The graph of C is the correct choice.

Answer:

-3/2

Step-by-step explanation:

y = - 3/2x + 3

y = mx + b

slope = m

Hope this Helps!!!

Answer:

Not a function

Step-by-step explanation:

because it's not a straight line

Answer:

IT IS A FUNCTION

Step-by-step explanation: did test