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MakcuM [25]
3 years ago
11

Deborah has two paintings in her portfolio and paints three more each week.Kai has twelve paintings in her portfolio and paints

two more each week.After how many weeks will Deborah and Kai have the same number of paintings ?
Mathematics
1 answer:
Firdavs [7]3 years ago
4 0
Well, we can set up these equations like this-
Deborah- 2+3w
Kai- 12+2w
w=number of weeks that pass
Now, we set them equal to each other:
2+3w=12+2w

Solve for w
2-12=2w-3w
-10 = -1w
w = 10
10 weeks. Hope this helped!
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The polynomial -x^3-x^2+12x represents the volume of a rectangular aqautic tank in cubic feet. the length of the tank is (x+4).
Verizon [17]

Answer:

<h2>a. It should look for 3 linear factors.</h2><h2>b. There are 3 dimensions.</h2><h2>c. x = 1.7</h2><h2>d. Maximum value is 12.597</h2>

Step-by-step explanation:

a.

-x^{3} - x^{2} + 12 \timesx = -x^{3} - 4 \timesx^{2} + 3 \timesx^{2} +12 \timesx = -(x + 4) \timesx^{2} + 3 \timesx \times(x + 4) = (x + 4) \timesx \times (x + 3)

Hence the factorized form of the volume of the poly is (x + 4) \timesx \times (x + 3)

3 linear factors should needed to be look for.

b.

The 3 dimensions are (x + 4), x, (x + 3).

c.

Let, f(x) = -x^{3} - x^{2} + 12 \timesx

Now, \frac{d  f(x)}{dx} = -3 \timesx^{2} -2 \timesx + 12

Let f1(x) = -3 \timesx^{2} -2 \timesx + 12 and f2(x) = \frac{d f1(x)}{dx} = -3 \timesx -2

The value will be maximum, if f1(x) = 0 and f2(x) < 0.

f1(x) = 0\\ 3 \timesx^{2} + 2 \timesx -12 = 0\\ x = \frac{- 2 + \sqrt{2^{2} + 4 \times3 \times12} }{2 \times3} , \frac{- 2 - \sqrt{2^{2} + 4 \times3 \times12} }{2 \times3}

x = 1.69 ≅ 1.7 or x = -2.36 ≅ -2.4

Now f2(1.7) < 0.

At x = 1.7, the volume will be maximum.

d.

The maximum value is f(1.7) = 12.597(approximately)

8 0
3 years ago
Whats a real world problem for 30x =48+22x
Tamiku [17]

Diving company A charges $30 per hour for diving lessons. Diving company B charges only $22 per hour but they need a $48 down payment. At how many hours would the price for company A be equal to company B?
30x=48+22x
30x-22x=48
8x=48
x=6

Hope this helps!

6 0
3 years ago
The perimeter of a triangle is 51 cm the longest side is twice the length of the Shorty start the third side is 3 cm longer than
Makovka662 [10]

Answer:

The lengths of the sides are 15 cm , 17 cm and 19 cm.

Step-by-step explanation:

Step 1. Perimeter P means adding up all three sides.


Step 2. Let n be an odd integer.


Step 3. Let n+2 and n+4 be the next two consecutive odd integers.


Step 4. Then P=n+n+2+n+4=51.


Step 5. Solving the equation Step 4 yields the following steps


3n%2B6=51


Subtract 6 from both sides of the equation


3n%2B6-6=51-6

3n=45


Divide 45 to both sides of the equation


3n%2F3=45%2F3


n=15 Then n%2B2=17 and n%2B4=19. Also, P=15+17+19=51 which is a true statement.


Step 6. ANSWER: The lengths of the sides are 15 cm , 17 cm and 19 cm.

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3 years ago
Which two techniques are used in constructions with paper
MaRussiya [10]

Answer:

A and B

Step-by-step explanation:

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2 years ago
In order to manually find the pattern of i, simply divide the exponent by four and the
luda_lava [24]
I believe this answer would be true

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3 years ago
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