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3 years ago

Television sizes are labeled by the measure of the diagonal

Mathematics

1 answer:

Fittoniya [83]3 years ago

8 0

Answer:

C. 55 inches

Step-by-step explanation:

a^2 = b^2 + c^2

a^2 = 47.5^2 + 27^2

a^2 = 2985.25

a = 54.637 = 55 inches

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How should I solve for x and what is x?

algol [13]

Answer:

x =12

Step-by-step explanation:

We can use the Pythagorean theorem to solve for x

a^2 + b^2 = c^2

16^2 + x^2 = 20^2

256 +x^2 = 400

Subtract 256 from each side

256-256 +x^2 = 400-256

x^2 =144

Take the square root of each side

sqrt(x^2) =sqrt(144)

x = 12

8 0

3 years ago

What is the range of the equation

a_sh-v [17]

The range of the equation is $y>2$

Explanation:

The given equation is $y=2(4)^{x+3}+2$

We need to determine the range of the equation.

Range:

The range of the function is the set of all dependent y - values for which the function is well defined.

Let us simplify the equation.

Thus, we have;

$y=2 \cdot 4^{x+3}+2$

This can be written as $y=2^{1+2(x+3)}+2$

Now, we shall determine the range.

Let us interchange the variables x and y.

Thus, we have;

$x=2^{1+2(y+3)}+2$

Solving for y, we get;

$x-2=2^{1+2(y+3)}$

Applying the log rule, if f(x) = g(x) then $\ln (f(x))=\ln (g(x))$ , then, we get;

$\ln \left(2^{1+2(y+3)}\right)=\ln (x-2)$

Simplifying, we get;

$(1+2(y+3)) \ln (2)=\ln (x-2)$

Dividing both sides by $\ln (2)$ , we have;

$2 y+7=\frac{\ln (x-2)}{\ln (2)}$

Subtracting 7 from both sides of the equation, we have;

$2 y=\frac{\ln (x-2)}{\ln (2)}-7$

Dividing both sides by 2, we get;

$y=\frac{\ln (x-2)-7 \ln (2)}{2 \ln (2)}$

Let us find the positive values for logs.

Thus, we have,;

$x-2>0$

$x>2$

The function domain is $x>2$

By combining the intervals, the range becomes $y>2$

Hence, the range of the equation is $y>2$

7 0

3 years ago

Solve this equation: 4+k=11

Law Incorporation [45]

Answer:

k=7

Step-by-step explanation:

4+k=11

subtract 4 from both sides to isolate k

k= 7

3 0

3 years ago

Inside an auditorium, 1 out of 5 people wear hats, and 4 out of 5 people do not wear hats. Based on this information, predict ho

Alexxx [7]

Answer:

Step-by-step explanation:

4 0

3 years ago

xand y are light house. y being 20km due east of x and from a ship due south of x the bearing of y was 055°. what is the distanc

leonid [27]

Answer:

I) |xz| ≈ 28.6 km

II) |yz| ≈ 34.8 km

Step-by-step explanation:

Let's assume that the position of ship due south of x is z (aà pictor representation of the question is attached)

|xy| = 20 km, |xz| = ?, |yz| = ?, θ(y) = 55°

Using Trigonometric ratio - SOHCAHTOA

I) Tan θ = |xz| ÷ |xy| ⇒ Tan 55° = |xz| ÷ 20

|xz| = 20 * Tan 55 = 20 * 1.428

|xz| = 28.56 km

|xz| ≈ 28.6 km

II) Cos θ = |xy| ÷ |yz| ⇒ Cos 55° = 20 ÷ |yz|

|yz| * Cos 55° = 20 ⇒ |yz| = 20 ÷ Cos 55°

|yz| = 20 ÷ 0.574 = 34.84 km

|yz| ≈ 34.8 km

4 0

3 years ago