Determine whether the triangle is acute, right, or obtuse given the sides: 11, 14, 20

Answers

Answer 1

Answer:

Answer:

317 < 400

The Sum of the squares of the smaller 2 sides (121 + 196 = 317) < longest side squared (400) So, it is an OBTUSE SCALENE TRIANGLE.

Source: http://www.1728.org/triantest.htm

Step-by-step explanation:

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Yves bought 420 tropical fish for a museum display. He bought 6 times as many parrotfish as angelfish. How many of each type of fish did he buy? Which is a system of equations to model the problem if x represents the number of angelfish Yves bought and y represents the number of parrotfish he bought?

A.
x + y = 6
y = 420x

B.
x + 6y = 420
y = 6x

C.
x – y = 420
y = 6x

D.
x + y = 420
y = 6x

Answers

Given:
420 tropical fishes
angel fish = x
parrot fish = 6x

x + y = 420
y = 6x Choice D.

x + y = 420
y = 6x

x + 6x = 420
7x = 420
x = 420 / 7
x = 60 number of angelfish

y = 6x
y = 6(60)
y = 360 number of parrot fish

A jar contains 6 chocolate chip cookies and 9 peanut butter cookies. Richard grabs 3 cookies at random to pack in his lunch. What is the probability that he drew 2 chocolate chip cookies and 1 peanut butter cookie?

Answers

The answer is 0.096.

To calculate this, a multiplication rule is used. The multiplication rule calculates the probability that both of two events will occur.

There are in total 15 cookies in the jar:
6 chocolate chip cookies + 9 peanut butter cookies = 15 cookies

The probability to drew 1 chocolate chip cookie is: $P_1= (6)/(15) = (2)/(5)$
The probability to drew 1 peanut butter cookie is: $P_2= (9)/(15) = (3)/(5)$

In this example, we have three events occurring together:
1. The probability that he drew 1 chocolate chip cookie: $P_1= (2)/(5)$
2.The probability that he drew 1 chocolate chip cookie: $P_1= (2)/(5)$
3. The probability that he drew 1 peanut butter cookie: $P_2= (3)/(5)$

By using the multiplication rule, the probability that he drew 2 chocolate chip cookies and 1 peanut butter cookie is 0.096:
$P=P_1*P_1*P_3= (2)/(5) * (2)/(5) * (3)/(5) = (2*2*3)/(5*5*5) = (12)/(125) = 0.096$

2(8n2 + 9n) +
+ 9n) + 3(4n- 7n)

Answers

Answer:

n = 0 or n = -9/16

Step-by-step explanation:

Solve for n:

2 (8 n^2 + 9 n) - 9 n = 0

Hint: | Write the quadratic polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

16 n^2 + 9 n = 0

Hint: | Factor the left hand side.

Factor n from the left hand side:

n (16 n + 9) = 0

Hint: | Find the roots of each term in the product separately.

Split into two equations:

n = 0 or 16 n + 9 = 0

Hint: | Look at the second equation: Isolate terms with n to the left hand side.

Subtract 9 from both sides:

n = 0 or 16 n = -9

Hint: | Solve for n.

Divide both sides by 16:

Answer: n = 0 or n = -9/16

The hypotenuse AB of a right triangle ABC is 5 ft, and one leg, AC, is decreasing at the rate of 2 ft/sec. The rate, in square feet per second, at which the area is changing when AC = 3 is?

Answers

Answer: $-(7)/(4) \quad \text{ft}^(2)/\sec$

Step-by-step explanation:

Since ABC is a right triangle, at any moment it holds that

$5^2=(AC)^2+(BC)^2$

Moreover, the area A of the triangle is given by

$A= (1)/(2)(AC)(BC)$

and we know that the rate of change of the length (AC) is

constant decreasing 2, which may be written using the Leibniz

notation as

$(d(AC))/(dt)=-2$ .

Using the chain rule and the product rule for derivation, the two

first equations tell us

that

$0 = 2 (d(AC))/(dt)(AC) + 2 (d(BC))/(dt)(BC)$

and

$(dA)/(dt) = (1)/(2) \left( (d(AC))/(dt) \cdot (BC) + (d(BC))/(dt) \cdot (AC)\right)$

Moreover, using the first of the last two equations we get

$(AC)(d(AC))/(dt) = -(BC)(d(BC))/(dt) \Rightarrow\n\n\n(AC)(-2) = -(BC) (d(BC))/(dt) \quad \Rightarrow \quad (d(BC))/(dt)=2 ((AC))/((BC))$

Now, when (AC)=3, we have that

$25=(AC)^2 + (BC)^2 \quad \Rightarrow 25 = 9 + (BC)^2\n \n\Rightarrow \quad 16=(BC)^2 \quad \Rightarrow (BC)=4$

and

$(d(BC))/(dt) = 2 ((AC))/((BC))=2 (3)/(4)=(3)/(2)$ .

Hence, at this moment the rate of change of the area of the triangle is

$(dA)/(dt) = (1)/(2) \left( (d(AC))/(dt) \cdot (BC) + (d(BC))/(dt) \cdot(AC) \right)=(1)/(2)\left( -2 \cdot 4 + (3)/(2)\cdot 3\right ) = -(7)/(4)$

okay
we have the rate of change of AC = d(AC)/dt = -2
the rate of change od BC = d(BC)/dt
area = (1/2) *AC) (BC)
taking differential on both sides we ge
d(A)/dt = 1/2){ (BC) d(AC)/dt + (AC) d(BC)/dt)}....(1)
again
when AC= 3
applying pythagorous thm
we get
(5)^2 =(3)^2 +(BC)^2
hence we get BC = 4
now we need to find d(BC)/dt
we have
(5)^2 = (AC)^2 +(BC)^2
taking differenial
0=2(AC) d(AC/dt) +2BC d(BC)/dt
that is
d(BC)/dt = -(3) *(-2)/4 ..(at AC =3)
hence
d(BC)/dt = 3/2
substituting these values in equation (1)
d(A)/dt = (1/2) {4 * -2 + 3 *3/2}

which gives
d(A)/dt = -7/4

The rate, in square feet per second, at which the area is changing when AC = 3 is -7/4 ft/sec.

I hope my answer has come to your help. Thank you for posting your question here in Brainly.

If x = 8 units, y = 6 units, and h = 4 units, then what is the area of the parallelogram shown above? A. 24 square units B. 32 square units C. 28 square units D. 48 square units

Answers

Answer:

Step-by-step explanation:

Convert 18/5 to a mixed number

Answers

your answer would be 3 an 3/5 :) hope i helped ! :D:D:D:D:D:D:D

To convert 18/5 to a mixed number all you have to do is divide 18 by five this would give you 3.6 all you have do do after that would be to change it back into a fraction.

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