In order to qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches. the inequality 64 < x < 68, where x represents height, can be used to represent the height range which of the following is another way of rewriting inequality?
x > 64 and x < 68 .
x > 64 or x < 68 .
x < 64 and x < 68 .
x < 64 or x < 68

x > 64 and x < 68 is another way of rewriting inequality.

Step-by-step explanation:

To qualify for a role in a play, an actor must be taller than 64 inches but shorter than 68 inches.

⇒The inequality 64 < x < 68, where x represents height,gives the range of height.

⇒In other words range of height can be x > 64 and x < 68 , such that both conditions are applied to single actor.

[with the use of or it will appear to give priority by actor to follow any 1 conditon]

x > 64 and x < 68

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

This is a compound inequality where the intersection of the inequalities is the solution.

These types of inequalities are joined with the word "and ".

In this case 64 < x is equal to x> 64.

So the option that has the same inequalities joined with the word "and” is option a. x > 64 and x < 68 .

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.