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Amiraneli [1.4K]
3 years ago
8

Which of the following ordered pairs is a solution to y = 2^x?

Mathematics
2 answers:
ss7ja [257]3 years ago
7 0

Answer:

(3,8)

Step-by-step explanation:

Since the answer choices are given we can plug the "x" value and see if it returns the y-value given in the ordered pair (x,y) and so:

y=2^x

Let's use the ordered pair (3,8) meaning that when x=3 y =8 and so:

y=2^3=2\times2\times2=8

y=8

This is correct and so this is a solution, since the solution is unique when x=3 y is always going to return an 8.

worty [1.4K]3 years ago
6 0

Answer:

(3, 8)

Step-by-step explanation:

For x = 3,

. . . y = 2^x

. . . y = 2^3 = 2·2·2 = 8

This is represented by the ordered pair (x, y) = (3, 8).

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Step-by-step explanation:

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2 years ago
Find the area of the given triangle to the nearest square unit. Angle a= 30 degrees, b=10, angle B=45 degrees
storchak [24]

Answer:

A=34\ units^2

Step-by-step explanation:

Suppose we have a general triangle like the one shown in the figure.

We know the angle A, the angle B and the length b.

A = 30\°\\\\B = 45\°\\\\b = 10

By definition I know that the sum of the internal angles of a triangle is always equal to 180 °.

So

A + B + C = 180\\\\30 + 45 + C = 180

We solve the equation and thus we find the angle C.

C = 180 - 30-45\\\\C = 105

We already know the three triangle angles.

Now we use the sine theorem to calculate the sides c and a.

The  sine theorem says that:

\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}

Then

\frac{sin(30)}{a}=\frac{sin(45)}{10}

\frac{sin(30)}{\frac{sin(45)}{10}}=a

a=7.071

Also

\frac{sin(105)}{c}=\frac{sin(45)}{10}

\frac{sin(105)}{\frac{sin(45)}{10}}=c

c=13.660

Finally, we use the Heron formula to calculate the triangle area

A=\sqrt{s(s-a)(s-b)(s-c)}

Where s is:

s=\frac{a+b+c}{2}

Therefore

s=\frac{7.071+10+13.660}{2}

s=15.37

A=\sqrt{15.37(15.37-7.071)(15.37-10)(15.37-13.66)}

A=34\ units^2

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Step-by-step explanation:

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