What is the length of the hypotenuse of an isosceles right triangle (both legs congruent), if the leg is 8?

Answer: pretty sure it is 56.5

Step-by-step explanation:

Answer: 6 in. x 10 in.

Step-by-step explanation:

Nash is making a framed enlargement of a Mary Cassatt postage stamp to present to a retired postmaster.

1. The scale of enlargement is 2 inches to 1 centimeter.

2. The actual length of the stamp = 3 centimeters

3. The length of frame =   2 x 3 = 6 inches

4. The actual width of the stamp = 5 centimeters

5. The width of frame =  2 x 5 = 10 inches

Conclusion: Because of this, the dimensions for the scale picture would be 6 by 10 inches

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

tan a = [tex]\frac{sina}{cosa}[/tex], cot a = [tex]\frac{cosa}{sina}[/tex]

sec a = [tex]\frac{1}{cosa}[/tex], cosec a = [tex]\frac{1}{sina}[/tex]

Consider the left side

tana + cota

= [tex]\frac{sina}{cosa}[/tex] + [tex]\frac{cosa}{sina}[/tex]

= [tex]\frac{sin^2a+cos^2a}{cosasina}[/tex]

= [tex]\frac{1}{cosasina}[/tex]

= [tex]\frac{1}{cosa}[/tex] × [tex]\frac{1}{sina}[/tex]

= seca . coseca

= right side , thus proven

Answer:

a for 2 b for 3 c for 1 and d is 4

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

xy = 10/5 = 2

the other wrong because

xy = 1

xy = ½

xy = 11

<DSR + <SRD + <RDS = 180° (Angle sum property)

2x + x +3x = 180°

6x = 180°

x = 180°/6

x = 30°

So, <SRD = x = 30°

<RDS = 3x = 3(30°) =90°

<DSR = 2x = 2(30°) = 60°

Hope it helps !

✌️

Jai hind !

Answer:

[tex]3x + 2x + x = 180 \\ 6x = 180 \\ \boxed{x = 30}[/tex]

Angles are 30°,60° and 90°.

Answer:

cotθ = [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

Using the trigonometric identity

cot x = [tex]\frac{cosx}{sinx}[/tex], then

cotθ = [tex]\frac{-0.8}{-0.6}[/tex] = [tex]\frac{8}{6}[/tex] = [tex]\frac{4}{3}[/tex]

Answer:

9

Step-by-step explanation:

when 2 negative signs meet or be multiplied the sign became "+" instead of "- -".

Answer:

As, this question is incomplete and without data we can not answer this question. But we can make it complete by adding our own values. Let's do it and calculate.

Average Time = 23.4 minutes is the time that Mrs Brim wanted to see.

Step-by-step explanation:

As, this question is incomplete and without data we can not answer this question. But we can make it complete by adding our own values. Let's do it and calculate.

Let's suppose, there are 10 students in the class of Mrs. Brim and she took 5 tests on subsequent days and made chart to know the average time her students took to solve the test.

Total time of test = 30 minutes

Average time taken by the students to solve the test on Day 1 = 25 minutes.

Average time taken by the students to solve the test on Day 2 = 27 minutes.

Average time taken by the students to solve the test on Day 3 = 22 minutes.

Average time taken by the students to solve the test on Day 4  = 23 minutes.

Average time taken by the students to solve the test on Day 5 = 20 minutes.

Average Time in all Tests = Sum of all times / total number of days

Average Time = (25 + 27 + 22 + 23 + 20) / 5 days

Average Time = 117/5

Average Time = 23.4 minutes is the time that Mrs Brim wanted to see.

Answer:

t=10

Step-by-step explanation:

4=t/2.5

4=t/25/10

divide 25and10 by 5=5/2

4=t/5/2

4=t×2/5

multiply both sides of the equation by 5

5×4=t×2/5×5

20=t×10/5

20=t×2

— —

2. 2

10=t

Step-by-step explanation:

It's given that A = 30° . Lets find the sin , cos & tan of A

⇒ [tex]\sin A=\sin30 = \frac{1}{2}[/tex]

⇒ [tex]\cos A = \cos 30 = \frac{\sqrt{3} }{2}[/tex]

⇒[tex]\tan A = \tan 30 = \frac{1}{\sqrt{3} }[/tex]

Lets solve the LHS (Left Hand Side) :-

[tex]2(\sin A \times \cos A) = 2(\frac{1}{2} \times \frac{\sqrt{3} }{2}) = \frac{\sqrt{3} }{2}[/tex]

Now lets solve the RHS (Right Hand Side) :-

[tex]\frac{2\tan A}{1+\tan ^{2}A } = \frac{2 \times \frac{1}{\sqrt{3} } }{1 + (\frac{1}{\sqrt{3} } )^{2} } = \frac{2}{\sqrt{3} } \div ( 1 + \frac{1}{3} ) = \frac{2}{\sqrt{3} }\div \frac{4}{3} = \frac{2}{\sqrt{3} } \times\frac{3}{4} =\frac{\sqrt{3} }{2}[/tex]

∴ LHS = RHS ( Proved )

Answer:

240 is the mark down.

Step-by-step explanation:

1 - .20 = 0.8

0.8 x 300 = 240

Answer:

$240

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

7.5 per ticket for every adult and 6 for every child to 7.5a+6c=1267 which is how much they made. Then since the theater sold 180 tickets then a+c=180

9514 1404 393

Answer:

  179/495

Step-by-step explanation:

When the repeating decimal starts at the decimal point, the repeating digits can be turned into a fraction by putting them over the same number of 9s. That is, 0.61616161... is equivalent to 61/99.

Here, the repeating part is 1/10 that value, so is 61/990. This is added to the non-repeating part, which is 0.3 = 3/10.

Then the entire decimal is ...

  0.361_61 = 3/10 + 61/990 = (297 +61)/990 = 358/990 = 179/495

Answer:

f(- 3) = 40

Step-by-step explanation:

To evaluate f(- 3), substitute x = - 3 into f(x), that is

f(- 3) = - 2(- 3) - 9(- 3) + 7 = 6 + 27 + 7 = 40

Answer:

The Width of each side of the bookmark in centimeters = 5cm

Step-by-step explanation:

A bookmark shaped like a rectangle has a total perimeter of38cm the length of the one of its sides is 14 what is the width of each side of the bookmark in centimeters

The formula for perimeter fo a rectangle =

P = 2L + 2W

Where L = Length

W = Width

Hence: From the above question:

38cm = 2 × 14 cm + 2 W

38cm = 28cm + 2W

2W = 38cm - 28cm

2W = 10cm

W = 10cm/2

W = 5cm

Hence, the Width of the rectangle(each side of the bookmark in centimeters) = 5cm

Answer:

[tex](13,-23)[/tex]

Step-by-step explanation:

Given

Translation: [tex](x,y) -> (x-4,y+15)[/tex]

Required

Determine the pre-image of (9,-8)

In (9,8)

[tex]x = 9[/tex] and [tex]y = -8[/tex]

So:

[tex](x,y) -> (x-4,y+15)[/tex]

Becomes

[tex](9,8) ->(x-4,y+15)[/tex]

By comparison:

[tex]x - 4 = 9[/tex]

[tex]y + 15 = 8[/tex]

Solving for (x):

[tex]x - 4 = 9[/tex]

[tex]x = 9 + 4[/tex]

[tex]x = 13[/tex]

Solving for (y):

[tex]y + 15 = -8[/tex]

[tex]y = -8 - 15[/tex]

[tex]y = -23[/tex]

Hence, the pre -image has a coordinate of [tex](13,-23)[/tex]

Answer and Step-by-step explanation:

It's very easy.

If you have two shapes, let's say triangles, the shapes are said to be similar if the corresponding angles are equal. For instance a triangle ABC with angles A = 45, B = 45 and C = 90 if there is another triangle PQR with angles P = 45, Q = 45 and R = 90, we say triangle ABC and triangle PQR are similar because their corresponding angles are equal.

Two triangles are said to be congruent if they are exactly the same in angles and size. All congruent shapes are similar but not all similar shapes are congruent.

To find area of similar shapes, we need what we call the scale factor of the enlargement.

If we have two similar shapes where by one is an enlargement of the other. Let's say the enlargement is in ratio 2:1. This ratio 2:1 is what we call scale factor. If we want to find the area of one shape given the area of a similar one to it, we make use of

Area = (scale factor)². For instance if we have two similar triangles, the area of the bigger is 16cm² and the scale factor is 2:1, we can find the area or the smaller by:

(2/1)² = 16/X = 4/1 = 16/X

4x = 16 and x = 4.

To find volume we use:

Volume = (scale factor)³ and the process is the same.

Answer:

10 kg = 10g = 10 mg

Hope this helped ;)

Answer:

The correct answer is D) 200

Step by step explanation:

Let x be the number:

Then,

→15/100(x)=30

→3/20(x)=30

→3x/20=30

→3x=20⋅30

→3x=600

→x=600/3=200

Hope it helps!

Answer:

D 200

Step-by-step explanation:

Let the number we are find be x. We can write this as an equation:

30 = 15%*x = (15/100)x

Multiplying by 100/15 on both sides to isolate x:

x = 30(100/15) = 2(100) = 200

Therefore, 200 is our answer. I hope this helps! :)

Step-by-step explanation:

Since cosecx = 1 / sinx,

sinФ = 1 / cosecФ = 1 / (4/3) = 3/4.

Answer:

2a + 3c + 4d

Step-by-step explanation:

This is the answer because:

1) Nothing further can be done to this equation since there are no like terms.

Therefore, the answer is 2a + 3c + 4d.

Hope this helps! :D

Answer:

(0,5)

Step-by-step explanation:

Answer:

12%

Step-by-step explanation:

We can get SI of 3 years = 12005 - 9800 = 2205

SI for 5 years = (2205/3)*5 = 3675 [so that we can get principal amount after deducting SI]

Principal = 12005 - 3675 = 6125

So Rate = (100*3675)/(6125*5) = 12%

Answer:

8 minutes

Step-by-step explanation:

Step one:

given

A submarine is 105 feet below the surface of the water

depth of submarine= 105 feet

let the time of ascending be x

Required

The time taken to ascend up to 81 ft

Step two:

the expression for the situation is

81=105-3x

solve for x

3x=105-81

3x=24

divide both sides by 3

x= 24/3

x=8 minutes

Step-by-step explanation:

gradient/slope = 3

y-intercept

2x - 3y = 4

3y = 2x - 4

y = 2/3x - 4/3

so y-intercept is double -4/3 so... -4/3x2 = -8/3

the equation of the line is

y = 3x - 8/3 or 9x - 3y = 8

Answer:

3y=2x-8

Step-by-step explanation:

when y intercept x=0

2(0)-3y=4

-3y=4

y=-4/3

when x intercept y=0

2x -3(0)=4

2x =4

x=2

point (2,-4/3)

gradient

-3y=-2x +4

y=2x/3-4/3

gradient=2/3

equation

y+4/3=2/3(x-2)

3y+4=2x-4

3y=2x-8