Please help, I'll mark brainliest.

Answer:

2x = 65 + 75

2x = 140

x = 140/2

x = 70

Step-by-step explanation:

Answer:

2x = 65 + 75

2x = 140

x = 140/2

x = 70

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  

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:

So:

Solving:

t= 12.5 seconds

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

Learn more about cuadratic function with this examples:

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• brainly.com/question/19725910?referrer=searchResults
• brainly.com/question/268775?referrer=searchResults

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:)

Answer:

a) Δ ABC is rotated around the origin by angle 180° and then translated 1

unite to the right and 3 units up

b) R (O , 180°) and T (x + 1 , y + 3)

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) rotated about the origin by angle 180° then its image

 is (-x , -y)

- If the point (x , y) translated horizontally to the right by h units

 then its image is  (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 then its image is  (x - h , y)

- If the point (x , y) translated vertically up by k units

 then its image is  = (x , y + k)

- If the point (x , y) translated vertically down by k units

 then its image is  (x , y - k)

* Lets solve the problem

∵ Δ ABC change its place from 2nd quadrant to the 4th quadrant

  and reverse its direction Point A up and its image A" down

∵ No change in its size

∴ Triangle ABC rotates 180° clockwise around the origin

# Remember : There is no difference between rotating 180° clockwise

  or  anti-clockwise around the origin

∵ The vertices of Δ ABC are:

# A = (-3 , 5)

# B = (-3 , 2)

# C = (-1 , 2)

∵ If point (x , y) rotated about the origin by angle 180° then its image

 is (-x , -y)

∴ A'' = (3 , -5)

∴ B'' = (3 , -2)

∴ C'' = (1 , -2)

∴ Triangle ABC rotates 180° around the origin to form ΔA"B"C"

∵ The vertices of Δ A'B'C are:

# A' = (4 , -2)

# B' = (4 , 1)

# C' = (2 , 1)

- By comparing the x-coordinates and y-coordinates of points of

 Δ A''B''C'' and Δ A'B'C' we will find that every x-coordinate add by 1

 and every y-coordinate add by 3

∵ 4 - 3 = 1 and 2 - 1 = 1 ⇒ x- coordinates

∵ -2 - (-5) = -2 + 5 = 3 and 1 - (-2) = 1 + 2 = 3 ⇒ y-coordinates

∴ ΔA''B''C'' translates to the right 1 unite and up 3 units to form

  Δ A'B'C'

a) Δ ABC is rotated around the origin by angle 180° and then

   translated 1 unite to the right and 3 units up

b) R (O , 180°) and T (x + 1 , y + 3)

Answer: If you multiply an inequality by a positive number keep the inequality sign the same

Explanation:  There are certain rules that should be kept in mind while solving the inequality:

1. When a number is added or subtracted from each side of an inequality the direction of the inequality does not change  

2. When each side of an inequality is multiplied or divided by a positive number the direction of the inequality does not change

3. When each side of an inequality is multiplied or divided by a negative number the direction of the inequality does change