The diagram shows a triangle ABC in which AB= 6 cm, BC=8 cm and ABC = 90°.
Calculate the length of AC.

The answer should be 12. please help with explanation and calculation!!!

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Explanation:

We'll involve the nCr combination formula here. This is because order doesn't matter.

There are n = 13 diamonds and we want to select exactly r = 3 of them.

So,

[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{13} C _{3} = \frac{13!}{3!*(13-3)!}\\\\_{13} C _{3} = \frac{13!}{3!*10!}\\\\_{13} C _{3} = \frac{13*12*11*10!}{3!*10!}\\\\_{13} C _{3} = \frac{13*12*11}{3!}\\\\_{13} C _{3} = \frac{13*12*11}{3*2*1}\\\\_{13} C _{3} = \frac{1716}{6}\\\\_{13} C _{3} = 286\\\\[/tex]

There are 286 ways to pick the three diamond cards. Then there are 52-13 = 39 ways to pick the fourth card that is either a spade, club of heart.

So we have 286*39 = 11,154 ways to pick the four cards given the conditions your teacher set.

This is out of 52C4 = 270,725 ways to pick four cards (use the nCr formula above with n = 52 and r = 4).

Divide the two values to get the answer:

(11,154)/(270,725) = 0.04120048019208

that rounds to 0.04 which converts to 4%

So there's roughly a 4% chance of getting exactly 3 diamond cards.

Answer:

4% (four percent)

Answer:

2556

Step-by-step explanation:

Answer:

The minimum number of faces a polyhedron can have is 4 faces.

Step-by-step explanation:

We know that a polyhedron is a shape surrounded by polygons. We also know that we need at least 3 sides to make a polygon. So, at the minimum a polyhedron can be made by using only triangular faces but in order to make a closed figure we need at least four triangular faces (which is a tetrahedron).

Answer:

The values of [tex]a[/tex] and [tex]b[/tex] are [tex]33[/tex] and [tex]\frac{20\sqrt{3}}{3}[/tex], respectively.

Step-by-step explanation:

The statement is equivalent to the following mathematic expression:

[tex]\left(5 + 2\sqrt{2})^{2} = a + b\cdot \sqrt{6}[/tex] (1)

By definition of the perfect square trinomial:

[tex]25 + 20\cdot \sqrt{2} + 8 = a + b\cdot \sqrt{6}[/tex]

[tex]33 + 20\sqrt{2} = a + b\cdot \sqrt{6}[/tex]

And by direct comparison we have the following system:

[tex]a = 33[/tex] (2)

[tex]b\cdot \sqrt{6} = 20\sqrt{2}[/tex] (3)

By (3), we solve for [tex]b[/tex]:

[tex]b = \frac{20}{\sqrt{3}}[/tex]

[tex]b = \frac{20\sqrt{3}}{3}[/tex]

The values of [tex]a[/tex] and [tex]b[/tex] are [tex]33[/tex] and [tex]\frac{20\sqrt{3}}{3}[/tex], respectively.

Answer:

the answer is 35/6 hope it helps:)

Answer:

The answer is 35/6

Step-by-step explanation:

Multiply the denominator by the whole number.

5 x 6 = 30

Then add the Numerator.

30 + 5 = 35

Now the answer is 35/6, you don't change the denominator.

28.7cm²

The sketch of the parallelogram is attached to this response.

As shown in the sketch,

h is the height of the parallelogram

ADC is 125°

AD = 5cm

CD = 7cm

Also

Since the adjacent angles of a parallelogram are supplementary (add up to 180°), it means that;

=> ADC + BCD = 180°

=> 125° + BCD = 180°

=> BCD = 180° - 125°

=> BCD = 55°

The area (A) of a parallelogram is given by;

A = b x h            ----------(i)

Where

b = base of the parallelogram

h = height of the parallelogram

From the sketch,

b = CD = 7cm

h can be found by using the sine trigonometric function as follows

sin BCD = [tex]\frac{h}{BC}[/tex]

=> sin 55° = [tex]\frac{h}{5}[/tex]

=> h = 5 sin 55°

=> h = 5 x 0.8192

=> h = 4.096cm

Now, substitute the values of h and b into equation (i) as follows;

A = 7 x 4.096

A = 28.672

A ≅ 28.7 (to one decimal place)

Therefore, the area of the parallelogram is 28.7cm²

Answer:

45%

Step-by-step explanation:

There are 450 people with over 3 people in their family. There are 1000 total people. 450/1000 is 45%

Answer:

exponent is -3, ceofficiant is 4

(d)

Answer:

A: (x-5.5)^2 + (y-4)^2=12.25

Step-by-step explanation:

Answer:

(⁴√81)⁵

= [tex]81^{\frac{5}{4} }[/tex]

[tex]81^{\frac{5}{4} }[/tex]

= 243

Step-by-step explanation:

(⁴√81)⁵

(3)⁵

= 243

Answer:

the answer is B 81^4/5 I HOPED THIS HELPED

Answer:

The first one, f+2g+3t! :)

Step-by-step explanation:

F is worth 1 point so you don't need to add a number, g is worth 2 points, and t is worth 3 points.

Answer:

.899

Step-by-step explanation:

Answer:

375

Step-by-step explanation:

Applying,

Total surface area of the triangular prism = 3×Area of the rectangular surface + 2×area of the triangular  surface

Assuming the triangular base is an equilateral triangle

A = 3A'+2B.................... Equation 1

Where A = Total  surface area of the prism, A' = Area of the rectangular surface, B = Area of the triangular base.

From the question,

IF  A' = 2B,

Given: A = 3000

Substitute these values into equation 1

3000 = 3(2B)+2B

3000 = 6B+2B

3000 = 8B

8B = 3000

B = 3000/8

B = 375

Answer:

5/6

Step-by-step explanation:

5/6=0.84, 8/10= 0.8

Answer:

Y=6000-400x

Step-by-step explanation:

Y=6000-400x where 6000 is beginning total, x represents how many months have passed, and 400x reduces the total by 400 for x number of months.

Answer:

36

Step-by-step explanation:

She gets 6 question right for every 8 question that means a ratio of 6/8 which is equal to 3/4

so we can say the ratio multiplied by the number of questions equals the correct answers

while x is the number of questions:

solve for x

3/4 * x = 27

x = 27 / (2/3) = 36

Answer:

x = 11.3

Step-by-step explanation:

This is a right isosceles triangle

x² + x² = 16²

2x² = 256

x² = 128

x = 11.3

Exquisite.

All are Correct

My doubts do come from your last answer.

I think the complement should be 60° too

Answer:37.68

Step-by-step explanation:

Do yk the anwser to my question?

Answer:

The percentage discount for the cost of the guitar is 45%.

Step-by-step explanation:

First let's find the difference between the original price and the new price.

80 - 44 = 36

So the actual discount got the price down by $36.

To find the percentage discount we need to ask ourselves the question

36 is what percent of 80?

36 = X percent of 80

In math, of means multiply.

36 = X percent * 80

So to get the "X percent" part alone we divide by 80 on both sides.

36 divided by 80 = 0.45

36 is 45 percent of 80.

The percentage discount for the cost of the guitar is 45%.

Answer:

Explanation:

Hey there!

Here;

f(X) = x²

and g(X) = X+1

To find: gof (2) and fog (2)

For gof (2),

gof = g{f(X)}

= g (x²)

= x²+1

Then;

gof(2) = 2²+1

= 4+1

= 5

Therefore, gof (2) is 5.

For fog(2),

fog (X) = f{g(X)}

= f(X+1)

= (x+1)²

= x²+2x+1

= x²+2x +1

Then;

fog(2) = 2²+2*2+1

= 4+4+1

= 9

Therefore, fog(2) = 9.

Hope it helps!

Answer: 6347.218

Step-by-step explanation:

Answer:6,347.218

Step-by-step explanation:

look at the thousandths place and then look at the number next to it if the number was 5 and above the answer would be 6,347.219 but in this situation it's not so you would keep everything the same but subtract the 0.0004

Answer: 16

Step-by-step explanation: 6400 : 400 = 16

Answer:

You would approximate because the hypotenuse might not be a perfect square.

Step-by-step explanation:

Answer:

9/20

Step-by-step explanation:

There are 40 marbles

18 are white

P( white marble) = number of white marbles / total number of marbles

                            = 18/40  = 9/20

Answer:

positive divided by positive = positive

negative divided by positive = negative

positive divided by negative = negative

negative divided by negative = positive

Step-by-step explanation:

Examples;

8 ÷ 2 = 4

-8 ÷ 2 = -4

8 ÷ -2 = -4

-8 ÷ -2 = 4

You can try these on a calculator

1. positive

2. negative

3. negative

4. positive

The number resulting from the division of one number by another.

The given quotient can be positive or negative can be decide by the facts given below:

1) positive divided by positive = positive

2) negative divided by positive = negative

3) positive divided by negative = negative

4) negative divided by negative = positive

Examples;

Learn more about quotient here:

https://brainly.com/question/27796160

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