Which are similar to triangle JKL? Label each yes or no

what positive number satisfies the condition that twice the number minus three times the reciprocal of the number is equal to 1?

marshall27 [118]

Solve:

"<span>twice the number minus three times the reciprocal of the number is equal to 1."
3(1)
Let the number be n. Then 2n - ------- = 1
n

Mult all 3 terms by n to elim. the fractions:

2n^2 - 3 = n. Rearranging this, we get 2n^2 - n - 3 = 0.

We need to find the roots (zeros or solutions) of this quadratic equation.

Here a=2, b= -1 and c= -3. Let's find the discriminant b^2-4ac first:

disc. = (-1)^2 - 4(2)(-3) = 1 + 24 = 25.

That's good, because 25 is a perfect square.
-(-1) plus or minus 5 1 plus or minus 5
Then x = ------------------------------ = --------------------------
2(2) 4

x could be 6/4 = 3/2, or -5/4.

You must check both answers in the original equation. If the equation is true for one or the other or for both, then you have found one or more solutions.</span>

8 0

3 years ago

There are about 45000 farms in Nebraska using approximately 45 million acres of land. This farmland covers about 9/10 of the sta

yulyashka [42]

9/10 : 1/10 = 45,000,000 : x

x = 45000000/9 = 5,000,000

Answer: 5 million acres

6 0

3 years ago

A recent survey of 128 high school students indicated the following information about release times from school.

Delicious77 [7]

Answer:

A) Interval estimate for those that want to get out earlier = (35%) ± (4%) = (31%, 39%)

Interval estimate for those that want to get out later = (39%) ± (4%) = (35%, 43%)

B) The group that wants to get out of school earlier can win after all the votes are counted if their true population proportion takes on a value that is higher than the closest true population proportion (for the group that wants to get out of school later)

That is, in the (31%, 39%) and (35%, 43%) obtained in (a), a range of (35.1%, 39%) and (35%, 38.9%) show how possible that the group that wants to get out of school earlier can win after all the votes are counted.

Step-by-step explanation:

The Interval estimate for the proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Interval estimate = (Sample proportion) ± (Margin of error)

Margin of Error is the width of the confidence interval about the proportion.

a) Find the interval estimates

i) for those that want to get out earlier and

ii) those that want to get out later.

i) Sample proportion of those that want to get out earlier = 35%

Margin of Error = 4%

Interval estimate for those that want to get out earlier = (35%) ± (4%) = (31%, 39%)

ii) Sample proportion of those that want to get out later = 39%

Margin of Error = 4%

Interval estimate for those that want to get out later = (39%) ± (4%) = (35%, 43%)

b) Explain how it would be possible for the group that wants to get out of school earlier to win after all the votes are counted.

Since the interval estimates represent the range of values that the true population proportion can take on for each group that prefer a particular option, the group that wants to get out of school earlier van have their proportion take on values between 31% and 39%. If their true population takes on a value that is highest (which is very possible from the interval estimate), and the group with the highest proportion in the sample, (the group that wants to get out of school later, whose true population proportion can take between 35% and 43%) has a true population proportion that is less than that of the group that wants to get out of school earlier, then, the group that wants to get out of school earlier can win after all the votes are counted.

Hope this Helps!!!

3 0

3 years ago

What is the vertex of the graph of y = 1/3 (x-9)2 + 5 Question 1 options: (9,5) (3,3) (3,5) (-9,5)

svlad2 [7]

ANSWER

The vertex of the graph of
$y = \frac{1}{3} {(x - 9)}^{2} + 5$
is

$(9,5)$

EXPLANATION

The vertex form of a parabola is given by

$y = a {(x - h)}^{2} + k$

where
$V(h,k)$
is the vertex of the parabola.

The function given to us is

$y = \frac{1}{3} {(x - 9)}^{2} + 5$
This is already in the vertex form.

When we compare this to the general vertex form, we have,

$a = \frac{1}{3}$

$h = 9$
and

$k = 5$

Therefore the vertex of the parabola is

$V(9,5)$

Hence the correct answer is option A.

7 0

3 years ago

Read 2 more answers

The mean score on a set of 17 test is 72. Suppose two more students take the test and score 68 and 63. What is the new mean?

Masja [62]

Answer:

New mean=71.32

Step-by-step explanation:

The expression for the total initial score is;

T=M×S

where;

T=total initial score

M=mean score

S=number in the set

replacing;

T=unknown

M=72

S=17

replacing;

T=72×17=1,224

The total initial score=1,224

Determine the total score by;

total score=total initial score+total final score

where;

total initial score=1,224

total final score=(68+63)=131

replacing;

total score=1,224+131=1,355

Determine the new mean;

New mean=total score/new number

where;

total score=1,355

new number=(17+2)=19

replacing;

new mean=1,355/19=71.32

8 0

3 years ago