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3 years ago

Evaluate -4a + 10 when a = -2

Mathematics

1 answer:

stiks02 [169]3 years ago

4 0

Answer:

18

Step-by-step explanation:

replace a with -2

-4(-2) + 10

multiply the -4 and the -2, the negatives cancel out and leave you with 8

8 +10

just add

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Beakers X and Y contain some water. If 50 ml of water is transferred from Beaker X

eduard

Answer:

140 ml

Step-by-step explanation:

Let x be the amount of water in Beaker X and y be the amount of water in Beaker Y.

Then we get following equations:

First part

x - 50 = 3/7(y + 50)
7x -350 = 3y + 150
7x = 3y + 500

Second part

x + 100 = 4(y - 100)
x + 100 = 4y - 400
x = 4y - 500

Substitute x in first equation:

7(4y - 500) = 3y + 500
28y - 3500 = 3y + 500
28y - 3y = 500 + 3500
25y = 4000
y = 4000/25
y = 160 ml

Then finding x:

x = 4*160 - 500
x = 640 - 500
x = 140 ml

Initial amount of water in Beaker X is 140 ml, in Beaker Y is 160 ml

4 0

3 years ago

The graph of the function showing the path of a soccer ball thrown by a goalie in a video game, f(x) = –0.05x2 + 2.5x + 5.2, is

Tju [1.3M]

Answer:

The correct option is 4.

Step-by-step explanation:

The given function is

$f(x)=-0.05x^2+2.5x+5.2$

Where f(x) is height of the ball and x is the distance.

It is a polynomial function with degree 2. All polynomial functions are defined for all real numbers, therefore the mathematical domain of the function is all real numbers.

$-\infty$

Factorize the given function.

$f(x)=-0.05(x^2-50x-104)$

$f(x)=-0.05(x^2-52x+2x-104)$

$f(x)=-0.05(x(x-52)+2(x-52))$

$f(x) = -0.05 (x - 52) (x + 2)$

Put f(x)=0 to find the x intercepts.

$0 = -0.05 (x - 52) (x + 2)$

Equate each factor equal to 0.

$x=52,-2$

Therefore at x=52 and -2, the graph of f(x) intersects x-axis. Before x=-2 and after x=52 the values of f(x) is negative. Height cannot be negative, therefore reasonable domain is lie between -2 to 52.

Distance cannot be negative, therefore the reasonable domain must be positive.

$0\leq x\leq 52$