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3 years ago

At a competition with 8 runners, 2 medals are awarded for first and second

Mathematics

2 answers:

sashaice [31]3 years ago

7 0

Answer:

A. 56

Step-by-step explanation:

You take 8 and then find the next number down and multiply them.

8*7= 56

(Also, I just did this on APEX)

Dafna1 [17]3 years ago

4 0

Answer: Option 'A' is correct.

Step-by-step explanation :

Since we have given that

Number of medals = 2

Number of runners = 8

We need to find the number of ways to award the medals.

We would use "fundamental theorem of counting" to find the number of ways.

So, number of ways is given by

8 × 7 = 56

Hence, option 'A' is correct.

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P(x)= 3x^3-5x^2-14x-4

nexus9112 [7]

$\displaystyle\\
P(x)=3x^3-5x^2-14x-4\\\\
D_{-4}=\{-4;~-2;~\underline{\bf -1};~1;~2;~4\}\\\\
\text{We observe that } \frac{-1}{3} \text{ is a solution of the equation:}\\
3x^3-5x^2-14x-4=0\\\\
$

$\displaystyle\\
\text{Verification}\\\\
3x^3-5x^2-14x-4=\\\\
=3\times\Big(-\frac{1}{3}\Big)^3-5\times\Big(-\frac{1}{3}\Big)^2-14\times\Big(-\frac{1}{3}\Big)-4=\\\\
=-\frac{1}{9}-\frac{5}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{14}{3}-4=\\\\
=-\frac{6}{9}+\frac{42}{9}- \frac{4\times 9}{9}=\\\\
 =-\frac{6}{9}+\frac{42}{9}- \frac{36}{9}= \frac{42-6-36}{9}=\frac{42-42}{9}=\frac{0}{9}=0\\\\
\Longrightarrow~~~P(x)~\vdots~\Big(x+ \frac{1}{3}\Big)\\\\
\Longrightarrow~~~P(x)~\vdots~(3x+1)$

$\displaystyle\\
3x^3-5x^2-14x-4=0\\
~~~~~-5x^2 = x^2 - 6x^2\\
~~~~~-14x =-2x-12x \\
3x^3+x^2 - 6x^2-2x-12x-4=0\\
x^2(3x+1)-2x(3x+1) -4(3x+1)=0\\
(3x+1)(x^2-2x -4)=0\\\\
\text{Solve: } x^2-2x -4=0\\\\
x_{12}= \frac{-b\pm \sqrt{b^2-4ac}}{2a}=\\\\=\frac{2\pm \sqrt{4+16}}{2}=\frac{2\pm \sqrt{20}}{2}=\frac{2\pm 2\sqrt{5}}{2}=1\pm\sqrt{5}\\\\
x_1 =1+\sqrt{5}\\
x_2 =1-\sqrt{5}\\
\Longrightarrow P(x)= 3x^3-5x^2-14x-4 =\boxed{(3x+1)(x-1-\sqrt{5})(x-1+\sqrt{5})}$

7 0

3 years ago

Ruth is knitting hats to sell at a local fair. The booth costs her $63 and the materials for each hat cost $10. She plans on sel

aev [14]

Answer: Ruth have to make 7 hats to break even.

Step-by-step explanation:

Break even point is a point where Cost = Revenue.

Let x be the number of hats sold.

Given: Cost of booth = $63

Each hat cost = $10

Selling price for each cost = $19

As per given,

Total cost = Cost of booth+ (Cost of each hat)(Number of hats)

= 63+10x

Total selling price = 19x

For break even,

63+10x=19x

9x=63

x=7

Hence, Ruth have to make 7 hats to break even.

7 0

3 years ago

maggie spent 4.50 on cheese and fruit at the farmers market. she bought 1/8 pound of apples, 1/4 pound of pears and 1.25 pounds

serious [3.7K]

The produced answer is 5.5

hope it helps

4 0

3 years ago

3. The area of a square garden is 200 m2. How long is the diagonal?

Step2247 [10]

The answer and explanation in the pic below

Good luck,!

If helped..mark brainliest please ;)

3 0

3 years ago

PLZ HELP ME WITH GEOMETRY

Helga [31]

You just need to use your test-taking skill to eliminate the wrong answers here.

There is no such thing as a "Congruent Angles Postulate," so the last two choices can be eliminated.

The AA Similarity Postulate refers to triangles, not angles, so the second choice can be eliminated.

That only leaves the (correct) first choice.

5 0

3 years ago