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3 years ago

Which of the following statements is the most precise and correct to define an angle?

Mathematics

2 answers:

PolarNik [594]3 years ago

7 0

Answer:

the exact degree of a rotation of a geometric figure in a coordinate plane

Step-by-step explanation:

iragen [17]3 years ago

4 0

Answer:

Step-by-step explanation:

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4(x-6)<-2x+6 what is the solution to the inequality <br> _

Cloud [144]

Simplify both sides if needed. The left-hand side needs simplification.

4(x - 6) $\leq$ -2x + 6
4x - 24 $\leq$ -2x + 6

All is left to do is add and subtract to get the x variable all alone.

4x - 24 $\leq$ -2x + 6
6x - 24 $\leq$ 6 <-- Add 2x to both sides
6x $\leq$ 30 <-- Add 24 to both sides
x $\leq$ 5 <-- Divide both sides by 6

In order to be in the solution set, x has to be less than or equal to 5.

In interval notation: [5, -∞)

7 0

2 years ago

There is only one angle measure , ∡JHF , which is 34 degrees . I have to find the measure of angle ∡FJH .

Minchanka [31]

the assumption here being that both lines JH and FH are tangent lines to the circle, if that's the case the external angle of 34° is the angle made by the equal tangents, meaning the triangle is an isosceles with twin sides.

In an isosceles triangle the twin sides make also twin angles, so the angles at J and F are twins, and they'd be 180° - 34° = 146° total, since they're twins, each one takes half, or 73°.

5 0

2 years ago

Read 2 more answers

The students in Mr. Wilson's Physics class are making golf ball catapults. The

Mnenie [13.5K]

Answer:

Part a) About 48.6 feet

Part b) About 8.3 feet

Part c) The domain is $0 \leq x \leq 48.6\ ft$ and the range is $0 \leq y \leq 8.3\ ft$

Step-by-step explanation:

we have

$y=-0.014x^{2} +0.68x$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

where

x is the ball's distance from the catapult in feet

y is the flight of the balls in feet

Part a) How far did the ball fly?

Find the x-intercepts or the roots of the quadratic equation

Remember that

The x-intercept is the value of x when the value of y is equal to zero

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-0.014x^{2} +0.68x=0$

$a=-0.014\\b=0.68\\c=0$

substitute in the formula

$x=\frac{-0.68(+/-)\sqrt{0.68^{2}-4(-0.014)(0)}} {2(-0.014)}$

$x=\frac{-0.68(+/-)0.68} {(-0.028)}$

$x=\frac{-0.68(+)0.68} {(-0.028)}=0$

$x=\frac{-0.68(-)0.68} {(-0.028)}=48.6\ ft$

therefore

The ball flew about 48.6 feet

Part b) How high above the ground did the ball fly?

Find the maximum (vertex)

$y=-0.014x^{2} +0.68x$

Find out the derivative and equate to zero

$0=-0.028x +0.68$

Solve for x

$0.028x=0.68$

$x=24.3$

<em>Alternative method</em>

To determine the x-coordinate of the vertex, find out the midpoint between the x-intercepts

$x=(0+48.6)/2=24.3\ ft$

To determine the y-coordinate of the vertex substitute the value of x in the quadratic equation and solve for y

$y=-0.014(24.3)^{2} +0.68(24.3)$

$y=8.3\ ft$

the vertex is the point (24.3,8.3)

therefore

The ball flew above the ground about 8.3 feet

Part c) What is a reasonable domain and range for this function?

we know that

A reasonable domain is the distance between the two x-intercepts

$0 \leq x \leq 48.6\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 48.6 feet

A reasonable range is all real numbers greater than or equal to zero and less than or equal to the y-coordinate of the vertex

we have the interval -----> [0,8.3]

$0 \leq y \leq 8.3\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 8.3 feet

8 0

2 years ago

Please Help!!!! Find two consecutive odd numbers whose product is 47 more than their sum.

fenix001 [56]

7 and 9

7 x 9 = 63

7+9=16

63-16 = 47

7 0

2 years ago

Please i need this for finals help me PLEASE

andrey2020 [161]

I believe it is B!!!!!!!!!!

7 0

2 years ago

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