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2 years ago

If F(a, b, c, d) = a^b + c \times d, what is the value of x such that F(2, x, 4, 11) = 300?

Mathematics

1 answer:

Greeley [361]2 years ago

5 0

Answer:

x = 8

Step-by-step explanation:

A graphing calculator can show you the answer easily. It works well to define a function whose x-intercept is the solution. We can do that by subtracting 300 from the given equation so we have ...

F(2, x, 4, 11) -300 = 0

The solution is x = 8.

We can solve this algebraically:

F(2, x, 4, 11) -300 = 0

2^x +4·11 -300 = 0 . . . . use the function definition

2^x -256 = 0 . . . . . . simplify

2^x = 2^8 . . . . . add 256

x = 8 . . . . . . . . . match exponents of the same base

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Given the set of vertices, determine whether parallelogram ABCD is a rhombus, rectangle or square. List all that apply. A(7,-4),

Sloan [31]

Given:

Vertices of a parallelogram ABCD are A(7,-4), B(-1,-4), C(-1,-12), D(7, -12).

To find:

Whether the parallelogram ABCD is a rhombus, rectangle or square.

Solution:

Distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using distance formula, we get

$AB=\sqrt{(-4-(-4))^2+(-1-7)^2}$

$AB=\sqrt{(-4+4)^2+(-8)^2}$

$AB=\sqrt{0+64}$

$AB=8$

Similarly,

$BC=\sqrt{(-1-(-1))^2+(12-(-4))^2}=8$

$CD=\sqrt{(7-(-1))^2+(-12-(-12))^2}=8$

$AD=\sqrt{(7-7)^2+(-12-(-4))^2}=8$

All sides of parallelogram are equal.

$AC=\sqrt{(-1-7)^2+(-12-(-4))^2}=8\sqrt{2}$

$BD=\sqrt{(7-(-1))^2+(-12-(-4))^2}=8\sqrt{2}$

Both diagonals are equal.

Since, all sides are equal and both diagonals are equal, therefore, the parallelogram ABCD is a square.

We know that, a square is special case of rectangles and rhombus.

So, parallelogram ABCD is a rhombus, rectangle or square. Therefore, the correct option is c.

7 0

2 years ago

I NEED HELP PLEASE, THANKS.

saveliy_v [14]

Answer:

B. $33.7 mm; 54mm^2$

Step-by-step explanation:

To find the perimeter, use the formula:

P = a + b + c

P = 12 + 12 + 9.7

P = 33.7

To find area, use the formula:

A = $\frac{1}{2} bh$

A = $\frac{1}{2} (12)(9)$

A = $\frac{1}{2} (108)$

A = 54

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2 years ago

a group of 12 runners each drink 64 ounces of water every day how many ounces of water will they drink in 45 days

masha68 [24]

34560 ounces

Step by Step Explanation:

12 x 64 = 768
768 x 45 = 34560 ounces

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3 years ago

if revenue for the week is 2000 and labor cost consist of two workers earning $8 per hour who work 40 hours each week what is la

DerKrebs [107]

The Answer is 32%.
Because for two workers for 40 hours each, it will cost 640
and when you do .32*2000 it equals 640 also
Hope I helped :)

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3 years ago

30 is 60%of what number?

Rom4ik [11]

Answer: 50

Step-by-step explanation:

Step 1: 60% = .60

Step 2: 30 = .60Y

Step 3: Divide both sides of the equation by .30 to isolate the variable Y.

30/.60 = .60/.60Y

50=Y

Therefore, 30 is 60% of 50.

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3 years ago