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quester [9]
3 years ago
10

On a boat, a cabin's window is in the shape of an isosceles trapezoid, as shown below. What is the area of the window?

Mathematics
1 answer:
Dafna11 [192]3 years ago
3 0

Answer:

196 in ^2

Step-by-step explanation:

Formula for area of trapezium is h ( a + b )/ 2 so.....

14(10 + 18)/2=196

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Find the 6th term of the expansion of (2p - 3q)11. a. -7,185,024p4q7 c. -7,185p4q7 b. -7,185,024p6q5 d. -7,185p6q5
bezimeni [28]
\bf (2p-3q)^{11}\implies 
\begin{array}{llll}
term&coefficient&value\\
-----&-----&-----\\
1&&(2p)^{11}(-3q)^0\\
2&+11&(2p)^{10}(-3q)^1\\
3&+55&(2p)^9(-3q)^2\\
4&+165&(2p)^8(-3q)^3\\
5&+330&(2p)^7(-3q)^4\\
6&+462&(2p)^6(-3q)^5
\end{array}

the coefficient for the first term is 1, the next is 11 and so on... now, notice, the elements of the binomial, the 1st element starts off with 11, and every term it goes down by 1, the 2nd element starts off at 0, and goes up by 1 in each term.

now, to get the next coefficient, you simply, "get the product of the current coefficient and the exponent of the 1st element, and divide that by the exponent of the 2nd element in the next term".

for example, how did we get 165 for the 4th term.... well  (55*9)/3

how did we get 462 for the 6th term? well (330*7)/5.

and then you can just expand it from there.
8 0
3 years ago
Read 2 more answers
If f(x)=3x-2 and g(x)=2x+1,find (f-g)(x) <br><br> A. x - 3<br> B. 5x - 3<br> C. 3 - x<br> D. 5x - 1
Nady [450]

Answer:

A

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= 3x - 2 - (2x + 1)

= 3x - 2 - 2x - 1 ← collect like terms

= x - 3 → A

6 0
3 years ago
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Which of the following numbers could be the sides of a right triangle. A)8,15,17. B)6,8,12 C)9,11,21 D)4,13,16
ArbitrLikvidat [17]

Answer:

A) 8, 15, 17.

Step-by-step explanation:

Right triangle obey the Pythagorean theorem. Thus, we choose the two smaller numbers (being the cathetus) and if after applying the P. Theorem we get the biggest of each option  (the hypotenuse) that means that those numbers could be the sides of a right triangle.

The Pythagorean theorem states that: a^2+b^2=c^2

Thus:

\sqrt{a^2+b^2}=c

Option A:

\sqrt{8^2+15^2}=17 → 17 = 17 OK!

Option B:

\sqrt{6^2+8^2}  = 10 → 10 ≠ 12 NO

Option C:

\sqrt{9^2+11^2} = [tex]\sqrt{202}[/tex] → \sqrt{202} ≠ 21 NO

Option D:

\sqrt{4^2+13^2} = \sqrt{185} → \sqrt{185} ≠ 16 NO

3 0
3 years ago
A bag contains 42 red marbles, 6 white marbles, and 8 gray marbles. You randomly pick out a marble, record its color, and put it
Elanso [62]
For any single draw,

\mathbb P(\text{white})=\dfrac6{42+6+8}=\dfrac6{56}
\mathbb P(\text{gray})=\dfrac8{42+6+8}=\dfrac8{56}

Drawing a white marble or a gray marble are disjoint events; only one of them can happen. So

\mathbb P(\text{white or gray})=\mathbb P(\text{white})+\mathbb P(\text{gray})-\underbrace{\mathbb P(\text{white and gray})}_0
\mathbb P(\text{white or gray})=\dfrac6{56}+\dfrac8{56}=\dfrac{14}{56}

Out of 224 draws, you should expect \dfrac{14}{56}\times224=56 of the marbles to be either white or gray.
6 0
3 years ago
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Given y=2x^2-6x+3. X=-1
konstantin123 [22]
Y=2(-1)^2-6(-1)+3
y=2+6+3
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y=11
5 0
3 years ago
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