Using complete sentences, explain how to find the average rate of change for f(x) from x = 4 to x = 7.

1 answer:

7 0

Even complete sentences are no help if you don't know what the
function f(x) is. Sadly, this is the very situation in which we find
ourselves, searching through the question to find the function,
fruitlessly, and coming up empty-handed.

As both Maimonides and Rashi pointed out more than eight
Centuries ago, you can't find the function's average rate of
change if you've never seen the function.

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Given: △ABC, BC>AC, D∈ AC , CD=CB Prove: m∠ABD is acute

nevsk [136]

I want you to imagine as you read this or you can draw through the help of my explanation and see yourself:

1↪Draw triangle ABC where BC>AC

2↪D is any point on AC such that CD=CB

3↪Roughly drawing , you can assume CD=CB and and join BD

4↪SO triangle ABC which is a big triangle is divided into Triangles ABD and BDC

5↪See in triangle BDC ,CD=CB so, base angles of isosceles triangle are equal:
<CDB=<CBD = x (assume) which means x is acute angle since CDB and CBD are are in same triangle with same measure and there can't be any two obtuse angle in any traingle. So x must be acute.

6↪Now see in traingle ABD,

<ADB=180-<CDB=180-x=obtuse angle
...check yourself ...just subtract any acute angle from 180 you will get only obtuse angle (ie angle greater than 90)
That means in triangle ABD , one angle ADB is obtuse which means remaining <ABD and < BAD are acute. [PROVED]

❇Main Concept Used Here:
↪In any triangle there can be maximum of one obtuse angle...so remaining two must be acute angle otherwise interior angles sum can't be equal to 180.

5 0

2 years ago

Each marble bag sold by Hans's Marble Company contains 8 purple marbles for every 5 green marbles. If a bag has 30 green marbles

gregori [183]

We can set up a proportion since we know the ratio between the # of purple marbles and the # of green marbles.

A ratio is a way to compare two different values: for every 8 purple marbles there are 5 green marbles

<h2> $\frac{8}{5} = \frac{p}{30}$ </h2><h2 /><h2>when we cross multiply, we get 5p = 240 </h2><h2>we divide both sides by 5 to isolate the variable </h2><h2 /><h3><u>There are 48 purple marbles </u></h3>