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3 years ago

Find the area of triangle ABC with the given side lengths and included angle. 1. B= 124 degrees, a=9, c=11

Mathematics

1 answer:

marishachu [46]3 years ago

8 0

Answer:

Step-by-step explanation:

We can obtain the area of a triangle where two sides and an included angle is given by saying; 1/2 ab sinθ

where a and b are the given sides of the triangle and θ is the included angle.

From the formula for the area of the triangle;

Area of a triangle = 1/2 ac sin B

Area of the triangle = 1/2 * 9 * 11 * sin 124

Area of the triangle = 49.5 * sin 124

Area of the triangle = 41

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Solve irrational equation pls

rusak2 [61]

$\hbox{Domain:}\\
x^2+x-2\geq0 \wedge x^2-4x+3\geq0 \wedge x^2-1\geq0\\
x^2-x+2x-2\geq0 \wedge x^2-x-3x+3\geq0 \wedge x^2\geq1\\
x(x-1)+2(x-1)\geq 0 \wedge x(x-1)-3(x-1)\geq0 \wedge (x\geq 1 \vee x\leq-1)\\
(x+2)(x-1)\geq0 \wedge (x-3)(x-1)\geq0\wedge x\in(-\infty,-1\rangle\cup\langle1,\infty)\\
x\in(-\infty,-2\rangle\cup\langle1,\infty) \wedge x\in(-\infty,1\rangle \cup\langle3,\infty) \wedge x\in(-\infty,-1\rangle\cup\langle1,\infty)\\
x\in(-\infty,-2\rangle\cup\langle3,\infty)$

$
\sqrt{x^2+x-2}+\sqrt{x^2-4x+3}=\sqrt{x^2-1}\\
x^2-1=x^2+x-2+2\sqrt{(x^2+x-2)(x^2-4x+3)}+x^2-4x+3\\
2\sqrt{(x^2+x-2)(x^2-4x+3)}=-x^2+3x-2\\
\sqrt{(x^2+x-2)(x^2-4x+3)}=\dfrac{-x^2+3x-2}{2}\\
(x^2+x-2)(x^2-4x+3)=\left(\dfrac{-x^2+3x-2}{2}\right)^2\\
(x+2)(x-1)(x-3)(x-1)=\left(\dfrac{-x^2+x+2x-2}{2}\right)^2\\
(x+2)(x-3)(x-1)^2=\left(\dfrac{-x(x-1)+2(x-1)}{2}\right)^2\\
(x+2)(x-3)(x-1)^2=\left(\dfrac{-(x-2)(x-1)}{2}\right)^2\\
(x+2)(x-3)(x-1)^2=\dfrac{(x-2)^2(x-1)^2}{4}\\
4(x+2)(x-3)(x-1)^2=(x-2)^2(x-1)^2\\$
$
4(x+2)(x-3)(x-1)^2-(x-2)^2(x-1)^2=0\\
(x-1)^2(4(x+2)(x-3)-(x-2)^2)=0\\
(x-1)^2(4(x^2-3x+2x-6)-(x^2-4x+4))=0\\
(x-1)^2(4x^2-4x-24-x^2+4x-4)=0\\
(x-1)^2(3x^2-28)=0\\
x-1=0 \vee 3x^2-28=0\\
x=1 \vee 3x^2=28\\
x=1 \vee x^2=\dfrac{28}{3}\\
x=1 \vee x=\sqrt{\dfrac{28}{3}} \vee x=-\sqrt{\dfrac{28}{3}}\\$

There's one more condition I forgot about
$-(x-2)(x-1)\geq0\\
x\in\langle1,2\rangle\\$

Finally
$x\in(-\infty,-2\rangle\cup\langle3,\infty) \wedge x\in\langle1,2\rangle \wedge x=\{1,\sqrt{\dfrac{28}{3}}, -\sqrt{\dfrac{28}{3}}\}\\
\boxed{\boxed{x=1}}$

3 0

2 years ago

The probability that Latisha orders french fries at lunch is .32 and the probability that she orders a grilled cheese and fries

EastWind [94]

There is a typo error in the last part of the question. The corrected part is-

"If the probability that she orders just a grilled cheese sandwich is .76, what is the probability that she will order a grilled cheese or fries?"

Answer:

The probability that she will order a grilled cheese sandwich or fries is <u>0.43.</u>

Step-by-step explanation:

Given:

Probability of ordering fries is, $P(F)=0.32$

Probability of ordering cheese sandwich is, $P(S)=0.76$

Probability of ordering both sandwich and fries is, $P(F\cap S)=0.65$

Probability of ordering cheese sandwich or fries is given by the union of both the events 'F' and 'S' given as $P(F\cup S)$ .

Now, using addition theorem of probability, we get:

$P(F\cup S)=P(F)+P(S)-P(F\cap S)\\P(F\cup S)=0.32+0.76-0.65\\P(F\cup S)=0.43$

Therefore, probability of ordering cheese sandwich or fries is 0.43.

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2 years ago

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pickupchik [31]

Answer:

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Step-by-step explanation:

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2 years ago

Read 2 more answers

What point would be reflected across the y-axis to ( − 3, − 9) ?

Aloiza [94]

Answer:

(-3, 9)

Step-by-step explanation:

If a point was reflected across the y-axis, then the y-coordinate would change signs (from negative to positive or from positive to negative). Using this, we could find the original point by changing the sign of the y-coordinate. As you may already see, this is really just reflecting the point across the y-axis again. By doing this, you get the point (-3, 9).

The point would be (-3, 9).

I hope this helps. :)

5 0

2 years ago

Find the value of x for m (arc AB)=23 and m(arc CD)=32 (the answer will be a decimal )

Marta_Voda [28]

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3 years ago