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3 years ago

What is (x-8)(x+4)+(x-3)(x+9)?A: 2x²-2x-59B: 2x²+2x-59C: x²-2x-59D: x²+2x-59

Mathematics

1 answer:

Vikki [24]3 years ago

3 0

Answer:

The answer is B. 2x^2 + 2- 59

Step-by-step explanation:

When you simplify (X-8)(x+4)+(x-3)(x+9) your will get the answer i got.

I hope ive helped you :)

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mr. ken's class is collecting empty water bottles. they started with 17 water bottles on day 1. on day 3, they had 30 water bott

Oxana [17]

They had 23 and 38 water bottles on day 2 and day 4 respectively. Also, there will be 68 water bottles on day 7.

Explanation

Suppose, the equation representing the number of bottles is $y= ax^2 +bx+c$ , where $x$ is the number of days.

There are 17 water bottles on day 1, 30 water bottles on day 3 and 47 water bottles on day 5

So, the three points in the form of (x, y) are: (1, 17) , (3, 30) and (5, 47)

Plugging these three points into the above equation, we will get .....

$17=a(1)^2 + b(1) +c\\ a+b+c=17 ............................ (1)\\ \\ 30=a(3)^2+b(3)+c\\ 9a+3b+c=30 ......................... (2) \\ \\ 47=a(5)^2+b(5)+c\\ 25a+5b+c=47 ......................... (3)$

Subtracting equation (1) from equation (2) , we will get .....

$8a+2b=13 ..................... (4)$

Subtracting equation (2) from equation (3) , we will get .....

$16a+2b=17 ...................... (5)$

Now, subtracting equation (4) from equation (5) , we will get ......

$16a -8a = 17-13\\ \\ 8a= 4\\ \\ a=\frac{4}{8}= 0.5$

Substituting this $a= 0.5$ into equation (4) ........

$8(0.5)+2b=13\\ \\ 4+2b=13\\ \\ 2b=9\\ \\ b=\frac{9}{2}=4.5$

Again, substituting $a=0.5$ and $b=4.5$ into equation (1) , we will get ......

$0.5+4.5+c=17\\ \\ 5+c=17\\ \\ c=17-5 =12$

So, the equation will be now: $y= 0.5x^2 +4.5x+12$

For finding the number of bottles on day 2 , day 4 and day 7 , we need to plug $x=2 , 4, 7$ respectively into the above equation.

For $x= 2$ , $y= 0.5(2)^2 +4.5(2)+12 = 2+9+12= 23$

For $x= 4$ , $y= 0.5(4)^2 +4.5(4)+12 = 8+18+12= 38$

For $x= 7$ , $y= 0.5(7)^2 +4.5(7)+12 = 24.5+31.5+12= 68$

So, they had 23 water bottles on day 2 and 38 water bottles on day 4

Also, there will be 68 water bottles on day 7

6 0

3 years ago

A construction company is building the house show below. They need to use a scale of 1 in: 8f. They measured the drawing to find

muminat

Answer:

They would have to multiply 2.5in and 8 ft because the ratio is 1in:8ft and the inches go up and you have to keep the ratio at the same value so you multiply 2.5 and 8

Step-by-step explanation:

3 0

3 years ago

CitiBank recorded the number of customers to use a downtown ATM during the noon hour on 32 consecutive workdays. 39 41 25 17 48

zaharov [31]

Answer:

Mean = 31.22

Midrange = 28.50

Geometric mean = 28.74

Trimmed mean = 31.56

Step-by-step explanation:

Given the data :

39 41 25 17 48 29 31 17 24 36 17 24 40 38 42 11 43 47 27 25 17 23 43 20 32 48 26 26 9 46 44 44

Ordered data :

9, 11, 17, 17, 17, 17, 20, 23, 24, 24, 25, 25, 26, 26, 27, 29, 31, 32, 36, 38, 39, 40, 41, 42, 43, 43, 44, 44, 46, 47, 48, 48

The mean, xbar :

Xbar = Σx / n = 999 / 32 = 31.22

The midrange : (maximum - minimum) / 2

Midrange = (48 + 9) / 2 = 57 / 2 = 28.5

Geometric mean :

(x1*x2*.. xn)^1/n

Geometric mean = (x1*x2*.. xn)^1/32 = 28.74

24% trimmed mean :

24% of 32 = 0.24 * 32 = 7.68 ; this mean cutting off 8 values from the top and bottom and calculating the mean of the remaining values.

Data left :

24, 24, 25, 25, 26, 26, 27, 29, 31, 32, 36, 38, 39, 40, 41, 42

Σx / n = 505 / 16 = 31.5625

Trimmed mean = 31.56

7 0

3 years ago

Find the volume of the solid generated by revolving the region bounded by the lines and curves about the x-axis. y = x, y =1, x

liraira [26]

Answer:

The volume is: $V = \frac{\pi}{3}$ cubic units

Step-by-step explanation:

Volume of a solid:

The volume of a solid, given by the function f(x), over an interval between a and b, is given by:

$V = \pi \int_{a}^{b} (f(x))^2 dx$

y = x, y =1, x = 0

This means that the upper function is y = 1, and the lower function is y = x. So

$f(x) = (1 - x)$

The lower limit of integration is x = 0.

The upper limit is y = x when y = 1, so x = 1.

Then

$V = \pi \int_{a}^{b} (f(x))^2 dx$

$V = \pi \int_{0}^{1} (1-x)^2 dx$

$V = \pi \int_{0}^{1} (1-2x+x^2) dx$

$V = \pi (x-x^2+\frac{x^3}{3})|_{0}^{1} dx$

$V = \pi(1 - (1^2) + \frac{1^3}{3})$

$V = \frac{\pi}{3}$

8 0

3 years ago

Consider f (x) = StartRoot x squared minus 1 EndRoot and g (x) = StartRoot x squared + 1 EndRoot. What value(s) of x would make

dalvyx [7]

Answer:

Any value of x

Step-by-step explanation:

Given

$f(x) = \sqrt{x^2 - 1}$

$g(x) = \sqrt{x^2 + 1}$

Required

What value of x is $f(g(x)) = g(f(x))$

Solving for f(g(x))

$f(x) = \sqrt{x^2 - 1}$

$f(g(x)) = \sqrt{(\sqrt{x^2 + 1})^2 - 1}$

Solve the inner square

$f(g(x)) = \sqrt{(x^2 + 1 - 1}$

$f(g(x)) = \sqrt{x^2 } }$

$f(g(x)) = x$

Solving g(f(x))

$g(x) = \sqrt{x^2 + 1}$

$g(f(x)) = \sqrt{(\sqrt{x^2 - 1})^2 + 1}$

$g(f(x)) = \sqrt{x^2 - 1 + 1}$

$g(f(x)) = \sqrt{x^2 }$

$g(f(x)) = x$

Equate f(g(x)) and g(f(x))

$f(g(x)) = g(f(x))$

$x = x$

This implies that $f(g(x)) = g(f(x))$ at any value of x

8 0

4 years ago

What is (x-8)(x+4)+(x-3)(x+9)?A: 2x²-2x-59B: 2x²+2x-59C: x²-2x-59D: x²+2x-59​

What is (x-8)(x+4)+(x-3)(x+9)?A: 2x²-2x-59B: 2x²+2x-59C: x²-2x-59D: x²+2x-59