Let x = 20. Which expression has a value greater than 4x−10 ? A. 5x−30 B. 5x−100 C. 8(x−10) D. 5(2x−26)

Two angles of a quadrilateral measure 140° and 80°. The other two angles are in a

aliina [53]

Answer:

Step-by-step explanation :

Ratio = 3x : 4x

<h3>Sum of angle of a quadrilateral = 360</h3><h3>Therefore, 140+80+3x+4x = 360</h3><h3>220+7x = 360</h3><h3>7x = 360-220</h3><h3>x= 140/7</h3><h3>x=20</h3><h3>3x= 3×20=60</h3><h3>4x=4×20=80</h3>

7 0

3 years ago

Read 2 more answers

What is the domain and range of the following graph?

puteri [66]

Using it's concepts, the domain and the range of the graph are given as follows:

Domain: all real values except x = -1.

Range: All real values.

<h3>What are the domain and the range of a function?</h3>

The domain of a function is the set that contains all the values of the input. In a graph, it is given by the values of x, which is the horizontal axis of the graph.

The range of a function is the set that contains all the values of the output. In a graph, it is given by the values of y, which is the vertical axis of the graph.

In this graph, have that the function is defined for all values of x except x = -1, and assumes all real values, hence the domain and the range of the graph are given as follows:

Domain: all real values except x = -1.

Range: All real values.

More can be learned about the domain and the range of a function at brainly.com/question/10891721

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6 0

2 years ago

Fill in the blanks to the picture above

Verdich [7]

The left side was cut out but x will be on top and 5 in the lower square. The last one is the answer.

3 0

3 years ago

Substiution method: y + 9 = 1/5x and

uranmaximum [27]

Y+9=1/5x menjadi y= 1/5x -9
sesudah ini sibtusika n dalam persamaan 4x - 5y = -15x
<span> 4x -5(1/5x-9)= -15 x
4x + x+45=-15x
5x +45 = -15x 45=-20x
x=-45/20
x= -9/4

y+9 =1/5x
y = 1/5(-9/4)-9
y = -189/20
(-</span>9/4,-189/20)

4 0

3 years ago

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

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

so

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

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

so

$0 \leq x \leq 48.6\ ft$

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

so

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

3 years ago