Astudent scored 83 and 91 on her first two quizzes. write and solve a compound inequality to find the possible values for a third quiz score that give her an average between 85 and 90,inclusive

81 <= x <= 96

Step-by-step explanation:

To find the score of third quiz which gives her an average between 85 and 90 inclusive, the total divided by 3 should be between the values 255 (85 x 3) and 270 (90 x 3).

Considering the above values, we can form an inequality:

3 x 85 <= 83 + 91 + x  <= 3 x 90

Now solve for x:

255 <= 174 + x <= 270

81 <= x <= 96

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.