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jok3333 [9.3K]
3 years ago
7

Let f(x) = 4x+3 and g(x) = -2x +5. Find (f o g)(5)

Mathematics
1 answer:
Sergio [31]3 years ago
8 0
G(5) = -2(5) + 5  = -5

(f o g)(5) = f(-5) =  -20 + 3 = -17 (answer)
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A triangle has 2 sides that equal 6 inches. The other side equals 4 inches. What kind of triangle is this
Tom [10]
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7 0
3 years ago
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A rectangular plot of land that contains 1500 square meters will be fenced and divided into two equal portions by an additional
photoshop1234 [79]
Let the length be x and the width be w

The perimeter will be:
2x+3w=1500

thus
3w=(1500-2x)
w=(1500-2x)/3
w=500-2/3x

The area will be:
A=x*w
A=x(500-2/3x)
A=500x-(2/3)x²

The above is a quadratic equation; thus finding the axis of symmetry we will evaluate for the value of x that will give us maximum area.

Axis of symmetry:
x=-b/(2a)
from our equation:
a=(-2/3) and b=500
thus
x=-500/[2(-2/3)]
x=375
the length will be 375 m

The width will be 250 m

4 0
2 years ago
For a moving object, the force acting on the object varies directly with the objects acceleration. When a force of 35 N acts on
Genrish500 [490]
<h3>Answer:  3 m/s^2</h3>

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

According to Newton's Second Law, we know that

F = m*a

where F is the force applied, m is the mass and 'a' is the acceleration.

We see that this is a direct variation equation for F and a, such that m is the constant of variation. It's similar to how y = kx is also a direct variation equation.

Plug in F = 35 and a = 5 to find m

F = ma

35 = m*5

35/5 = m

7 = m

m = 7

The object has a mass of 7 kg

Our equation F = ma updates to F = 7a

Now plug in the force F = 21 to find 'a'

F = 7a

21 = 7a

21/7 = a

3 = a

a = 3

The acceleration will be 3 m/s^2

Notice how a smaller force applied means that the acceleration has also gone down as well.

8 0
2 years ago
A television screen's width is 1.778 times its height. If its
Nana76 [90]

Answer:

Let a, b, and c be the height, width, and the diagonal of the screen respectively

Since they form a triangle and the angle between a and b is 90 degrees, according to the Pythagorean Theorem a^2 + b^2 = c^2

Let's assume that the aspect ratio is 16:9. Therefore b/a = 16/9

Now we have a system of two equations with two unknowns. We need to express everything in terms of a single unknown, so let's express a in terms of b.

Since, b/a = 16/9, by cross multiplying 16a = 9b. Therefore a=9b/16.

Now we can subsitute 9b/16 for a in the first equation

a^2+b^2=c^2 becomes (9b/16)^2 + b^2 = c^2

Squaring the nominator and the denominator of the fraction yields

81b^2/256 + b^2 = c^2

To perform the addition, we need to express b^2 as a fraction with denominator 256 which is 256b^2/256, Now we have

81b^2/256 + 256b^2/256 = c^2

Adding fractions with the same denominators is now easy and produces

337b^2/256 = c^2

Cross multiply to get

337b^2 = 256c^2

Divide both sides by 337 to get b^2

b^2=256c^2/337

Take the square root of both sides to get b

b = sqrt(256c^2/337)

Lots of complicated Pythagorean responses. This is much simpler to answer with Trigonometry.

TLDR; just multiply the diagonal by the following two coefficients, and add the bezel width, to get the width and height:

w = diag x 0.872 + 2 x bw

h = diag x 0.49 + 2 x bw

(Where diag is the diagonal size of the screen and bw is the bezel width)

Thats all you need to know to do this.

Now here’s the Teig behind it:

First, calculate the angle of the diagonal relative to the base, using tangent, which yields ::

a = tan(9/16)

This will give you an angle of 0.512 radians (or roughly 30 degrees).

Next, calculate the ratio of the height relative to the hypotenuse (the diagonal length) using arc-sine, which yields the relative proportion of opposite length over the hypotenuse for a given angle:

h = asin(0.512)

The result will be roughly h = 0.49, or 49% of the diagonal.

Finally, get the ratio of eidth to hypotenuse using arc-cosine:

w = acos(0.512)

The result is roughly w = 0.872, or 87.2% of the diagonal.

that’s all the math! Enjoy!

6 0
3 years ago
Choose ASA, SAA, or neither to describe this figure
garri49 [273]

ASA

Because the side between two equal angle is equal here. Because "The sides opposite to equal angles of a triangle are equal."

4 0
2 years ago
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