MATHEMATICS HIGH SCHOOL

Two weather tracking stations are on the equator 165 miles apart. A weather balloon is located on a bearing of N 40°E from the western station and on a bearing of N 22°E from the eastern station. How far is the balloon from the western station?

Answers

Answer 1

Answer:

The distance from balloon to the western station is 495 miles.

Explanation:

The distance between two weather stations are 165 miles.

The angle of the regular triangle bearing from the western station is given by

90° - 40° = 50°

The angle of the regular triangle bearing from the eastern station is given by

90° + 22° = 112°

The angle of the balloon is given by

180° - 50° - 112° = 18°

Now, to find the distance of the balloon from the western station, let us use the law of sines formula,

$(a)/(sin a) = (b)/(sin b)$

Let us substitute the values.

Where $a=x, sin a= sin 112$ and $b=165, sin b = sin 18$

Thus, we have,

$(x)/(sin 112) =(165)/(sin 18)$

Multiplying both sides of the equation by sin 112, we get,

$x=sin 112((165)/(sin 18) )$

Simplifying, we have,

$x=0.9272(533.98)\nx=495$

Thus, the distance from balloon to the western station is 495 miles.

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The perimeter of a square garden is to be at least 30 feet but not more than 64 feet. Find all possible values for the length of its sides.

9 is what percent of 25 in percentage form

Answers

9/25=
25*4=100 so,9*4=36
9/25=36%

Which graph represents the following piecewise defined function?

Answers

The graph that represents the following piecewise defined function is of f(x) = x; x <-2 , -2; -2 < or = to x < or = to 1, x-3; x> or = to 1 is the first graph (Image attached)

What is a piecewise function?

A piecewise function is known to be a function that has been formed from pieces of a lot of functions over a lot of intervals.

An example, we can say a piecewise function f(x) where f(x) = -7 when -7 < x ≤ -4, f(x) = 4 when -4 < x ≤ -1, and f(x) = -5 when -1 <x ≤ 7.

The option that best explain the piecewise defined function is the image attached.

Learn more about piecewise defined function from

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Answer:

A on Edge

Step-by-step explanation:

Just took the test and got a 100

What is the discriminant of the quadratic equation 2x + 5x2 = 1?

Answers

$5x^2+2x-1=0$

Delta equation is:

$\Delta =(-b\pm\sqrt(b^2-4ac))/(2a)$

but we are interested in $b^2-4ac$ because it determines the discriminant

$5^2-4*2*(-1)=25+8=33$

$33>0$

which means that discriminant is positive :)

Answer:

The discriminant of the quadratic equation is 24 .

Step-by-step explanation:

Discriminant form of the quadratic equation .

D = b² - 4ac

As the quadratic equation in the form.

2x + 5x² = 1

Simplify the above term

5x² + 2x - 1 = 0

As the quadratic equation in the form

ax² + bx + c =0

Here a = 5 , b = 2 , c= -1

put in the formula

D = 2 × 2 - 4× 5 × -1

D = 4 +20

D = 24

Therefore the discriminant of the quadratic equation 5x² + 2x - 1 = 0 is 24 .

How is (s-t)(s/t) equivalent to (s^2/t) -s

Answers

$(s-t)\cdot(s)/(t)=s\cdot(s)/(t)-t\cdot (s)/(t)=(s^2)/(t)-s$

Explanation:

For the expression (s-t)(s/t) we first use the distributive property:

We can write both s and t as fractions by using a denominator of 1:

$\n=(s)/(1)* (s)/(t)-(t)/(1)* (s)/(t)$

To multiply frations, we multiply straight across:

In the second fraction, st/t, the t will divide out, or cancel, since it is in both the numerator and denominator:

$(s^2)/(t)-s$

Henry took out a 4 year loan for 5,000 and payed 4.2% simple annual interest. Ingrid took out a 6 year loan for 5,000 and payed 3.9% simple annual interest. What is the difference between the mounts of interest Henry and Ingrid payed for their Loans

Answers

Answer:

Ingrid pays 330 more than Henry.

Henry pays 330 less than Ingrid.

Step-by-step explanation:

SI = Simple Interest

P = Principal

R = Rate

T = TIme

Henry

=> SI = P x R x T / 100

=> SI = 5,000 x 4 x 4.2 /100

=> SI = 50 x 4 x 4.2

=> SI = 200 x 4.2

=> SI = 840

Ingrid

=> SI = P x R x T / 100

=> SI = 5,000 x 6 x 3.9 / 100

=> SI = 50 x 6 x 3.9

=> SI = 300 x 3.9

=> SI = 1170

1170 - 840

=> 330

Ingrid pays 330 more than Henry.

840 - 1170

=> -330

Henry pays 330 less than Ingrid.

Ozzie is 6 years older than McKenzie. Theo is Ozzie's dad and is 3 times older than McKenzie. Ozzie is 8 years old. How old is Theo?

Answers

Answer:

If Ozzie is 8 and 6 years older than McKenzie, then McKenzie is 2 years old. So if Theo is 3 times older than McKenzie, then Theo is 6 years old.

Final answer:

Theo's age is calculated by multiplying McKenzie's age by 3. Given that McKenzie is 2 years old (Ozzie's age minus 6), so Theo is 6 years old.

Explanation:

The problem requires the application of basic arithmetic operations, specifically addition and multiplication, to solve an age problem. We know that Ozzie is 8 years old. Since Ozzie is 6 years older than McKenzie, we subtract 6 from Ozzie's age to get McKenzie's age, which is 2. Theo is 3 times older than McKenzie. Thus, to get Theo's age, we multiply McKenzie's age (2) by 3, which results in 6 years old.

Learn more about Age Problem here:

brainly.com/question/31414175

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