a trapezoids longer base is 4 times its shorter base. If the trapezoid has an area of 80 cm squared and a height of 8cm has what is the length of each base ​

Answers

Answer 1
Answer: Long One is 16
Short One is 4!!

A=base+base/2 * height

A=80

16+4/2 = 10

10 * 8 = 80!!

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Can someone please help me :)

Answers

Answer:

90 degree

Step-by-step explanation:

Three points A, B, and C are added and shown in attached picture.

As the property of inscribed angle in circle:

angle BAC = (1/2) x 88 = 44 deg

As the property of complement angle:

angle ABC = 180 - 89 = 91 deg

As the property of sum of three angles in a triangle:

angle ACB + angle ABC + angle BAC = 180 deg

=> angle ACB = 180 - angle ABC - angle BAC = 180 - 44 - 91 = 45 deg

One more time, we use the property of inscribed angle in circle:

x = 2 x angle ACB = 2 x 45 = 90 deg

Hope this helps!

A bag contains 4 red marbles, 1 green one, 1 lavender one, 3 yellows, and 2 orange marbles. HINT [See Example 7.] How many sets of five marbles include at most one of the yellow ones?

Answers

Answer:

266

Step-by-step explanation:

Red marbles = 4

Green marbles = 1

Lavender marbles = 1

Yellow marbles = 3

Orange marbles = 2

To pick 5 marbles with at most 1 yellow, we can pick 5 non-yellow marbles or (4 non-yellow marble and 1 yellow marble).

Picking 5 non-yellow marbles

There are 4 + 1 + 1 + 2 = 8 non-yellow marbles.

The number of ways of picking any 5 is

n_1 = \dbinom{8}{5} = 56

Picking 4 non-yellow marble and 1 yellow marble

The number of ways of picking any 4 non-yellow marbles is

n_2 = \dbinom{8}{4} = 70

The number of ways of picking any 1 yellow marble from 3 is

n_3 = \dbinom{3}{1} = 3

Number of ways for both = 70*3=210

Total number of picking 5 marbles with at most 1 yellow

Therefore, total number of ways = 56 + 210 = 266

Use induction to prove the following formula is true for all integers n where n greaterthanorequalto 1. 1 + 4 + 9 + .. + n^2 = n(n + 1)(2n + 1)/6

Answers

Answer with Step-by-step explanation:

Since we have given that

1+4+9+........................+n² = (n(n+1)(2n+1))/(6)

We will show it using induction on n:

Let n = 1

L.H.S. :1 = R.H.S. : (1* 2* 3)/(6)=(6)/(6)=1

So, P(n) is true for n = 1

Now, we suppose that P(n) is true for n = k.

1+4+9+...................+k^2=(k(k+1)(2k+1))/(6)

Now, we will show that P(n) is true for n = k+1.

So, it L.H.S. becomes,

1+4+9+......................+(k+1)^2

and R.H.S. becomes,

((k+1)(k+2)(2k+3))/(6)

Consider, L.H.S.,

1+4+9+..+k^2+(k+1)^2\n\n=(k(k+1)(2k+1))/(6)+(k+1)^2\n\n=k+1[(k(2k+1))/(6)+(k+1)]\n\n=(k+1)[(2k^2+k+6k+6)/(6)]\n\n=(k+1)(2k^2+7k+6)/(6)]\n\n=(k+1)(2k^2+4k+3k+6)/(6)]\n\n=(k+1)[(2k(k+2)+3(k+2))/(6)]\n\n=((k+1)(2k+3)(k+2))/(6)

So, L.H.S. = R.H.S.

Hence, P(n) is true for all integers n.

To make the cone, melted chocolate is pumped onto a huge cold plate at a rate of 2 ft3/sec. Due to the low temperature, the chocolate forms the shape of a cone as it solidifies quickly. If the height is always equal to the diameter as the cone is formed, how fast is the height of the cone changing when it is 5 ft high?

Answers

Answer:

The height of cone is increasing at a rate 0.102 feet per second.

Step-by-step explanation:

We are given the following in the question:

(dV)/(dt) = 2\text{ cubic feet per second}

Instant height = 5 feet

The height of the cone is always equal to the diameter.

Volume of cone =

V = (1)/(3)\pi (d^2)/(4)h\n\n\text{where d is the diameter and h is the height of cone}\n\nV = (1)/(12)\pi h^3

Rate of change of volume =

(dV)/(dt) = (d)/(dt)((1)/(12)\pi h^3)\n\n(dV)/(dt) =(\pi)/(4)h^2(dh)/(dt)

Putting all the values, we get,

2=(\pi)/(4)(5)^2(dh)/(dt)\n\n\Rightarrow (dh)/(dt) = (8)/(25\pi) =0.102

Thus, the height of cone is increasing at a rate 0.102 feet per second.

Hello can you please help me posted picture of question

Answers

The term of degree 1 in the given polynomial is +9x.

The coefficient is the constant term that is being multiplied to the variable. The variable in this case is x and the constant being multiplied to x is 9. So the coefficient of the term is 9. 

Therefore, the answer to this question is option A
The answer is  A. 9
The leading coefficient for the term of the degree 1 is the number with only one variable (x)

If f(x) = x2 + 2x + 1 and g(x) = 3(x + 1)2, which is anequivalent form of f(x) + g(x)?
O x2 + 4x + 2
O 4x2 + 2x + 4
O 4x2 + 8x + 4
o 10x2 + 20x + 1

Answers

The equivalent form of f(x) + g(x), if  f(x) = x² + 2x + 1 and g(x) = 3(x + 1)² is

4x² + 8x + 4, so option C is correct.

What is a function?

In the case of a function from one set to the other, each element of X receives exactly one element of Y. The function's domain and co-domain are respectively referred to as the sets X and Y as a whole.

Given:

f(x) = x² + 2x + 1 and g(x) = 3(x + 1)²

Calculate the equivalent form as shown below,

f(x) + g(x) = x² + 2x + 1 + 3(x + 1)²

Simplify the above equation,

f(x) + g(x) = x² + 2x + 1 + 3(x² + 2x + 1)

f(x) + g(x) = x² + 2x + 1 + 3x² + 6x + 3

f(x) + g(x) = 4x² + 8x + 4

To know more about function:

brainly.com/question/5975436

#SPJ2

the answer should be C