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vova2212 [387]
2 years ago
8

the altitude is drawn from the vertex angle of an isosceles triangle and is 15 cm long, if the base of the triangle is 16 cm lon

g, how long are the legs?
Mathematics
1 answer:
erastovalidia [21]2 years ago
5 0
They are about 400cm long just make sure u put that
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Misha Larkins [42]

Answer:

Exact form: 53/10 , Decimal form: 5.3 , Mixed number form: 5 3/10

Step-by-step explanation:

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Giving 100 points.
Nitella [24]

Answer:

1.   <u>Cost per customer</u>:  10 + x

     <u>Average number of customers</u>:  16 - 2x

\textsf{2.} \quad  -2x^2-4x+160\geq 130

3.    $10, $11, $12 and $13

Step-by-step explanation:

<u>Given information</u>:

  • $10 = cost of buffet per customer
  • 16 customers choose the buffet per hour
  • Every $1 increase in the cost of the buffet = loss of 2 customers per hour
  • $130 = minimum revenue needed per hour

Let x = the number of $1 increases in the cost of the buffet

<u>Part 1</u>

<u></u>

<u>Cost per customer</u>:  10 + x

<u>Average number of customers</u>:  16 - 2x

<u>Part 2</u>

The cost per customer multiplied by the number of customers needs to be <u>at least</u> $130.  Therefore, we can use the expressions found in part 1 to write the <u>inequality</u>:

(10 + x)(16 - 2x)\geq  130

\implies 160-20x+16x-2x^2\geq 130

\implies -2x^2-4x+160\geq 130

<u>Part 3</u>

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

\implies -2x^2-4x+160\geq 130

\implies -2x^2-4x+30\geq 0

\implies -2(x^2+2x-15)\geq 0

\implies x^2+2x-15\leq  0

\implies (x-3)(x+5)\leq  0

Find the roots by equating to zero:

\implies (x-3)(x+5)=0

x-3=0 \implies x=3

x+5=0 \implies x=-5

Therefore, the roots are x = 3 and x = -5.

<u>Test the roots</u> by choosing a value between the roots and substituting it into the original inequality:

\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144

As 144 ≥ 130, the <u>solution</u> to the inequality is <u>between the roots</u>:  

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.  

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an <em>increase </em>in cost.  It does not confirm that if the cost is reduced (less than $10) the number of customers <em>increases </em>per hour.]

<u>Cost per customer</u>:  

x =0 \implies 10 + 0=\$10

x=3 \implies 10+3=\$13

Therefore, the possible buffet prices Noah could charge are:

$10, $11, $12 and $13.

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1 year ago
Experts/ace/geniuses helppp asapp
tino4ka555 [31]
Point E is the correct answer! :D
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Answer:

19/5

Step-by-step explanation:

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HELP THIS IS DUE IN 15 MINUTES I DONT KNOW HOW TO SOLVE IT!!!
NARA [144]

Answer:

(x,y)=(-10, -30)

Step-by-step explanation:

x/4 -y/12 = 0

--> x/4 = y/12

substitute into the first eq.

x/4 + y/12 = -5

y/12 + y/12 = -5

2y/12 = -5

y= (-5) * 12/2 = -30

solve for x, x/4 = (-30)/12

x=4* (-30)/12 = -10

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