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Soloha48 [4]
3 years ago
6

A test has thirty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice

questions worth 8 points each. How many multiple choice questions are on the test?
Mathematics
2 answers:
Vika [28.1K]3 years ago
5 0
So let's break this question down.
You need a bit of both, right? Well we need to calculate how many multiple choices we can do whilst having true/false questions, and not going over or under on points.

So, let's pick a random number, 5. So let's do 8x5, that equals 40.
ohmygoditsrightiwasseriouslyjustguessing
Ok so now we have our number, 5 multiple choice questions. 
The true/false questions should be easy, just do 3x20 and you get 60.

ANSWER: 5 
Ilya [14]3 years ago
3 0

Answer:

2 multiple choice problems

Step-by-step explanation:

the equations will be...

x=true/false questions

y=multiple choice problems

x+y=30

3x+8y=100

5y=10

<h2>y=2</h2>
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Let f(x) = x2 and g(x) = x − 3. Evaluate the expression.
vesna_86 [32]

Answer:

B

Step-by-step explanation:

To evaluate (f ○ g)(x)

Substitute x = g(x) into f(x), that is

f(g(x))

= f(x - 3)

= (x - 3)² ← expand using FOIL

= x² - 6x + 9 → B

6 0
3 years ago
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = 7 cos2(x) − 14 sin(x), 0 ≤ x ≤ 2π (a) Find the int
Troyanec [42]

Answer:

[\frac{\pi}{2},\frac{3\pi}{2}]

Step-by-step explanation:

Let me first state that I am assuming your function is

f(x)=7cos^2(x)-14sin(x)

If this is incorrect, then disregard this whole answer/explanation.

In order to find where the function is increasing or decreasing, we need to first find the first derivative, set it equal to 0, and then factor to find the values that cause the derivative to equal 0.  This is where you expect to find a max or a min value in the function itself.  But this function is not going to be easily solved for 0 once we find the derivative unless we make it in terms of either sin or cos right now, before taking the first derivative.  

Let cos^2(x)=1-sin^2(x)

This is a Pythagorean trig identity, and I'm assuming that if you're in calculus solving for the intervals of increasing and decreasing values that you have, at one time, used trig identities.

Rewriting:

f(x)=7(1-sin^2(x))-14sin(x) which simplifies to

f(x)=7-7sin^2(x)-14sin(x) and in order of descending values of x:

f(x)=-7sin^2(x)-14sin(x)+7

Now we can find the derivative.  For the first term, let u = sin(x), therefore,

f(u)=u^2, u' = cos(x), and f'(u) = 2u.  The derivative is found by multiplying f'(u) by u', which comes out to 2sin(x)cos(x)

The derivative for the next 2 terms are simple, so the derivative of the function is

f'(x)=-7[2sin(x)cos(x)]-14cos(x) which simplifies down to

f'(x)=-14sin(x)cos(x)-14cos(x)

We will set that equal to zero and solve for the values that cause that derivative to equal 0.  But first we can simplify it a bit.  You can factor out a -14cos(x):

f'(x)=-14cos(x)(sin(x)+1)

By the Zero Product Property, either

-14cos(x) = 0 or sin(x) + 1 = 0

Solving the first one for cos(x):

cos(x) = 0

Solving the second one for sin(x):

sin(x) = -1

We now look to the unit circle to see where, exactly the cos(x) = 0.  Those values are

\frac{\pi}{2},\frac{3\pi}{2}

The value where the sin is -1 is found at

\frac{3\pi}{2}

We set up a table (at least that's what I advise my students to do!), separating the intervals in ascending order, starting at 0 and ending at 2pi.

Those intervals are

0 < x < \frac{\pi}{2}, \frac{\pi}{2}, and \frac{3\pi}{2}

Now pick a value that falls within each interval and evaluate the derivative at that value and determine the sign (+ or -) that results.  You don't care what the value is, only the sign that it carries.  For the first interval I chose

f'(\frac{\pi}{4})=- so the function is decreasing here (not what you wanted, so let's move on to the next interval).

For the next interval I chose:

f'(\pi)=+ so the function is increasing here.

For the last interval I chose:

f'(\frac{7\pi}{4})=-

It appears that the only place this function is increasing is on the interval

[\frac{\pi}{2},\frac{3\pi}{2}]

3 0
2 years ago
The graph shows a vertical translation of y = x.
iris [78.8K]

Answer:

D is the answer

Step-by-step explanation:

3 0
3 years ago
What is the area of a triangle that has a height of 12 feet and a base length of 6 feet? 24 feet2 36 feet2 48 feet2 72 feet2
Kaylis [27]
It is 36 feet
A=1/2bh
a=1/2*12*6
a=6*6
a=36feet squared
hope this helps!
8 0
3 years ago
Read 2 more answers
How much does a customer pay for an article marked at $50 if a sales tax of 6% is charged? (A) (B) © ថ្មី &gt; $44 547 553 556 (
evablogger [386]

Answer:

53

Step-by-step explanation:

Find the sales tax

50 * 6%

50 * .06

3

Add this to the original price

50 +3

53

7 0
2 years ago
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