MATHEMATICS HIGH SCHOOL

Find the angle measure that makes the statement true.

Sin 25° = Cos ____ °

Answers

Answer 1
Answer:

Answer:

          sin 25° = cos 65°

Step-by-step explanation:

We have trigonometric result

                  sin θ = cos (90 -θ)

Here we asked to convert Sin 25°  in to cosine.

So,

          sin 25° = cos (90 -25) = cos 65°

          sin 25° = cos 65°
Answer 2
Answer: 65. 

You simply have to put cos-1(sin(25))

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What is the solution to the system of equations?

y=3x+6
3x-y=6

Answers

1st equation: y = 3x + 6
2nd equation: 3x - y = 6

Substitute the y in the 2nd equation by its value in the 1st equation.

y = 3x + 6
3x - y = 6

3x - (3x + 6) = 6
3x - 3x - 6 = 6
-6 = 6 NOT A SOLUTION

3x -y = 6
3x = 6 + y
x = (6 + y)/3

y = 3x + 6
y = 3((6+y)/3) + 6
y = 6 + y + 6
y = 12 + y
y - y = 12
0 = 12 NOT A SOLUTION

4x+11<23 solve this equation

Answers

4x + 11 < 23

      - 11  - 11

4x < 12

4x/4 < 12/4

x < 3

What is the value of the dependent variable if the value is 0? f(x)=-13x2+5x-2x+8

Answers

f(0)=-13\cdot0^2+5\cdot0-2\cdot0+8=8

The average reading score on a certain test is given by y=0.150x +255.34 where x is the number of years past 1970 . In what year would the average reading score be 259.24 if this model was accurate

Answers

Answer:

The average was 259.24 in 1996.

Step-by-step explanation:

In order to find the year that the average, "y", is 259.24 we need to apply this value on the given expression, as done below:

259.24 = 0.15*x + 255.34\n0.15*x = 259.24 - 255.34\n0.15*x =3.9\nx = (3.9)/(0.15)\nx = 26

The average was 259.24 after 26 years, therefore it was in 1996.

Consider the function represented by the equation 6c = 2p – 10. Write the equation in function notation, where c is the independent variable.

Answers

we have

6c = 2p - 10

If c is the independent variable

then

p is the dependent variable

so

clear variable p

6c = 2p - 10

Divide by 2 both sides

3c = p - 5

Adds 5 both sides

3c+5 = p - 5 +5

p=3c+5

Write the equation in function notation

f(c)=3c+5

therefore

the answer is

the equation in function notation is equal to f(c)=3c+5
f(c)=3c+5 is the right answer

A projectile is fired straight upward with an initial velocity of 400 feet per second. The height of the projectile, h(t), if represented by the function h(t)=-16t^2+400t, where t is the time in seconds. How long does it take the projectile to reach the maximum height?

Answers

Taking into account the definition of maximum, minimum and vertex of a quadratic function, it takes 12.5 seconds for the projectile to reach maximum height.

A quadratic function is defined in the form:

y= f (x) = ax² + bx + c

Every quadratic function has a maximum or a minimum, which is the vertex of the parabola. If the parabola has an upward concavity, the vertex corresponds to a minimum of the function; whereas if the parabola has concavity downwards, the vertex will be a maximum.

That is, if the coefficient a is positive the parabola is concave and the vertex will be a minimum of the function, while if a is negative the parabola will be convex and the vertex is a maximum.

The maximum or minimum is reached in xv=(-b)/(2a)  

The maximum or minimum value of y is obtained by evaluating the function at xv, this is, f (xv).

In this case, the function is:

h(t)= -16t² + 400t

where t is the time in seconds

Being a = -16 and b = 400, the value of a is negative, so the vertex will be the maximum.

You want to know the time it takes for the projectile to reach the maximum height, that is, the maximum in t. That is, you must calculate t using the expression: t=(-b)/(2a)

So: t=(-400)/(2x(-16))

Solving:

t=(-400)/(-32)

t= 12.5 seconds

It takes 12.5 seconds for the projectile to reach maximum height.

Learn more about cuadratic function with this examples:

Answer:

You can find the answer by using the formula x=-b/2a

Step-by-step explanation:

Remember the maximum height will be at the vertex. The x value of the vertex is your time, so use x=-b/2a. Then if it had also asked what the height was, you would plug that answer into your equation to find the y value of the vertex. Pretty sure your teacher is just asking you to find the x though:)
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