Answer: the number of multiple-choice questions in the math test is 35 and the number of open-ended questions in the math test is 3
Step-by-step explanation:
Let x represent the number of multiple-choice questions in the math test.
Let y represent the number of open-ended questions in the math test.
The math test has 38 questions. It means that
x + y = 38
This test consists of multiple-choice questions worth 4 points each and open-ended questions worth 20 points each. The total number of points is 200. It means that
4x + 20y = 200 - - - - - - - - - -1
Substituting x = 38 - y into equation 1, it becomes
4(38 - y) + 20y = 200
152 - 4y + 20y = 200
- 4y + 20y = 200 - 152
16y = 48
48/16
y = 3
Substituting y = 3 into x = 38 - y, it becomes
x = 38 - 3 = 35
9514 1404 393
Answer:
254.8
Step-by-step explanation:
Substitute the numbers where the variables are and do the arithmetic.
4c +2b³ = 4(1.2) +2(5³) = 4.8 +250 = 254.8
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It can also work to let a calculator or spreadsheet do the math for you, once you specify the function.
No because when you add any 2 sides the answer has to be bigger than the 3rd side
ex: 2+7=9
9 is too small, so the tips of the side that is 2ft would not touch the side that is 7ft
What you can put is an obtuse 108 degrees
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We are given with a limit and we need to find it's value so let's start !!!!
But , before starting , let's recall an identity which is the <em>main key</em> to answer this question
Consider The limit ;
Now as directly putting the limit will lead to <em>indeterminate form 0/0.</em> So , <em>Rationalizing</em> the <em>numerator</em> i.e multiplying both numerator and denominator by the <em>conjugate of numerator </em>

Using the above algebraic identity ;


Now , here we <em>need</em> to <em>eliminate (√x-2)</em> from the denominator somehow , or the limit will again be <em>indeterminate </em>,so if you think <em>carefully</em> as <em>I thought</em> after <em>seeing the question</em> i.e what if we <em>add 4 and subtract 4</em> in <em>numerator</em> ? So let's try !


Now , using the same above identity ;


Now , take minus sign common in <em>numerator</em> from 2nd term , so that we can <em>take (√x-2) common</em> from both terms

Now , take<em> (√x-2) common</em> in numerator ;

Cancelling the <em>radical</em> that makes our <em>limit again and again</em> <em>indeterminate</em> ;

Now , <em>putting the limit ;</em>
