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ella [17]
3 years ago
14

F(x)=x^2-1 G(x)=x-1 find (f+g)(10).

Mathematics
1 answer:
WARRIOR [948]3 years ago
6 0
<h2>Adding Functions</h2><h3>Answer:</h3>

(f +g)(10) = 108

<h3>Step-by-step explanation:</h3>

Before we can solve for (f +g)(10), we need to know how (f +g)(x) is defined.

(f +g)(x) = f(x) +g(x) \\ (f +g)(x) = (x^2 -1) +(x -1) \\ (f +g)(x) = x^2 -1 +x -1 \\ (f +g)(x) = x^2 +x -2

We can now solve for (f +g)(10):

(f +g)(10) = (10)^2 +(10) -2 \\ (f +g)(10) = 100 +10 -2 \\ (f +g)(10) = 108

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Robert makes 50 litres of green paint by mixing litres of yellow paint and litres of blue paint in the ratio 2:3.
podryga [215]

Answer:

  • 35%

Explanation:

<u>1. Cost of each liter of yellow paint:</u>

Yellow paint is sold in 5 litre tins and ach tin costs £26, thus the cost of one liter is £26 / 5 liters = £5.2 per liter.

<u>2. Cost of each liter of blue paint:</u>

Blue paint is sold in 10 litre tins and each tin costs £48, thus the cost of one liter of blue paint is £48 / 10 liters = £4.8 per liter

<u>3. Cost of each liter of green paint.</u>

Green paint is made by mixing yellow paint and blue paint in the ratio 2:3

Thus, 5 liters of green paint will cost:

2 liters yellow paint: 2 liter × £5.2 / liter = £10.4

3 liters blue paint:     3 liter × £4.8 / liter = £14.4

                                 ==========              ========

5 liters green paint:   5 liter                        £24.8

Cost of one liter of gree paint: £24.8 / 5 liter = £4.96 / liter

<u>4. Profit</u>

Price of each liter of green paint: £66.96 / 10 liters = £6.696 / liter = £6.70 / liter

Profit per liter = price per liter - cost per liter = £6.70/liter - £4.96 / liter = £1.74 / liter

Percentage profit = profit per liter / cost per liter × 100

Percentage profit = (£1.74 / liter) / (£4.96/liter) × 100 =  35.08% = 35%

4 0
4 years ago
Please help I don’t know the answer :(
gogolik [260]

Answer:

When x=8, y=-6. When x=10, y=0

Step-by-step explanation:

y=3x-30\\x^2+y^2=100

You can plug the given y value into the second equation to get:

x^2+(3x-30)^2=100\\x^2+9x^2-180x+900=100\\10x^2-180x+800=0\\10(x^2-18x+80)=0\\10(x-8)(x+10)=0\\x= 8, 10\\y= -6, 0

Hope this helps!

6 0
3 years ago
Read 2 more answers
Fencing a horse corral carol has 2400 ft of fencing to fence in a rectangular horse corral. (a) find a function that models the
Vanyuwa [196]

Here it is given that the width is x ft and total length of the fence is 2400 ft .

Let the length be y ft

So we have

2(x+y) =2400&#10;\\&#10;x+y=1200&#10;\\&#10;y = 1200 -x

Let A represents area, and area is the product of length and width .

So we get

A = x y

Substituting the value of y, we will get

A = x (1200-x)= 1200x -x^2

Second part

The area is maximum at the vertex, and vertex is

x = - \frac{1200}{2(-1)} = 600 feet

And

y=1200-x = 1200-600 = 600 feet

And that's the required dimensions .

8 0
3 years ago
The area of a square piece of cardboard is 81 square inches. What is the length of the cardboard
vredina [299]
9 because the square root of 81 is 9
6 0
3 years ago
John received $300 for his birthday he buys 4 DVDs at $12.95 each. Sales tax is 6.5% how much birthday money does he have left
joja [24]

Answer: $244.83


Step-by-step explanation:

First find the original amount spent on dvds:

    $12.95 * 4 = $51.80

Then, the sales tax (6.5% is converted to decimal form by dividing by 100):

    $51.80 * 0.065 = $3.367

Add the sales tax to the original amount to get the total amount spent:

    $51.80 + $3.367 = $55.167

Round to the nearest hundredth:

    $55.167 -> $55.17

Subtract the total amount from the money received for his birthday:

    $300 - $55.17 = $244.83

4 0
3 years ago
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