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3 years ago

Need the answer for this

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

8 0

Answer:

60 degrees

Step-by-step explanation:

The point at C is a vertical angle.

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Duffy was analyzing the trajectory made after throwing a football. his coach was able to measure that his throw reached a maximu

gregori [183]

Answer:

4.35 seconds.

Step-by-step explanation:

Let x represent the time the independent variable and y be dependent variable (height of the ball).

We are told that Duffy figured that the ball left his hand at a height of 5 feet. This means at x equals 0, y was 5 or initial height of ball is 5 feet.

We have been given that Duffy's coach measured that his throw reached a maximum height of 18 feet after 2 seconds. This means that at x equals 2 y was 18.

As point (2,18) represents maximum height of ball, so it will be vertex of parabola.

Since initial height of ball is less than maximum height, so our parabola will be downward opening and leading coefficient will be negative.

We know that vertex form of a downward opening parabola is in form: $y=-a(x-h)^2+k$

$y=-a(x-2)^2+18$

Let us find value of a using point (0,5).

$5=-a(0-2)^2+18$

$5=-a*4+18$

$5-18=-a*4+18-18$

$-13=-4a$

$\frac{-13}{-4}=\frac{-4a}{-4}$

$\frac{13}{4}=a$

Therefore, the equation $y=-(\frac{13}{4})(x-2)^2+18$ can be used to find the height of ball after x seconds.

To find the time it will take the ball to hit the ground, we will substitute y equals 0 in our equation.

$0=-(\frac{13}{4})(x-2)^2+18$

$0-18=-(\frac{13}{4})(x-2)^2+18-18$

$0-18=-(\frac{13}{4})(x-2)^2$

$-18*(\frac{4}{13})=-(x-2)^2$

$\frac{72}{13}=(x-2)^2$

Taking square root of both sides of our equation we will get,

$\sqrt{\frac{72}{13}}=x-2$

$x-2\pm 2.35339$

$x-2=2.35339\text{ (or) } x-2=2.35339$

$x-2+2=2.35339+2\text{ (or) } x-2+2=-2.35339+2$

$x=4.35339\text{ (or) } x=-0.35339$

$x\approx 4.35\text{ (or) } x\approx -0.35$

Since time can not be negative, therefore, the ball will hit the ground approximately after 4.35 seconds.

7 0

3 years ago

PLEASE HELP! I'm on a time limit!!

QveST [7]

Answer:

P = (2,-4)

Q = (3,9)

R = (-4,2)

Step-by-step explanation:

rotation by 180 degrees means that the points are inverted. the answers would be the opposite of the given

7 0

3 years ago

zlopas [31]

Answer:

Step-by-step explanation:

ΔABC & ΔADE are similar triangles

$\frac{AD}{AB}=\frac{DE}{BC}\\\\\frac{12}{4}=\frac{12}{x}\\$

Cross multiply,

12*x = 12*4

$x=12*\frac{4}{12}\\$

x = 1 * 4

x = 4

8 0

3 years ago

Tammy accidentally wrote a check for more money than she had in her checking account. When she got her statement, she saw that h

sergejj [24]

Answer:

-100

Step-by-step explanation:

1/5 of -125 will be -25.

So, if she deposits 1/5 of what she owes, then she will deposit $25.

Her balance will then become -100 because she paid back 25.

Her new balance is -100

7 0

3 years ago

Help me . With work to plz

Zepler [3.9K]

Answer:

57°

Step-by-step explanation:

Angles EGB and EHD are corresponding angles of two parallel lines cut by a transversal; therefore, they are congruent.

m<EGB = m<EHD = 57°

7 0

3 years ago