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3 years ago

Consider functions f and g.

Mathematics

1 answer:

MissTica3 years ago

3 0

A function assigns the values. The sum of the two function will be equal to 3[√(x-3) + 5].

<h3>What is a Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.

Given f(x)=√(x-3) and g(x)=[√(4x-12)]+15, therefore, the sum of the two function will be written as,

$(f+g)(x)= \sqrt{x-3} + \sqrt{4x-12}+15\\\\$

$= \sqrt{x-3} + \sqrt{4(x-3)}+3(5)\\\\ = \sqrt{x-3} + 2\sqrt{(x-3)}+3(5)\\\\= 3\sqrt{(x-3)}+3(5)\\\\ = 3[\sqrt{(x-3)}+5]$

Hence, the sum of the two function will be equal to 3[√(x-3) + 5].

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You might be interested in

What is the radius of a circle with a central angle of 4π7 radians that intercepts an arc of length 12π inches?

SCORPION-xisa [38]

Radian measure is given by dividing the length of an arc by the radius of a given circle. Such that an arc that subtends an angle of 1 radian to the center of a circle is equivalent to the radius of the circle.
Therefore; θ = s/r where θ is the angle subtended in radians, s is the length of the arc and r is the radius of the circle.
Hence; r = s/θ
= 12π ÷ (4π/7)
= 12 × (7/4)
= 21 inches

3 0

4 years ago

How do you do this question?

jolli1 [7]

Answer:

Cartesian Equation: y = √(1 - x^2)

Graph: Second one

Step-by-step explanation:

x^2 = sin^2(θ/2),

y^2 = cos^2(θ/2),

According to that theory, by the circle equation, x^2 + y^2 = 1^2.

When θ = -π, x = sin(-π/2) = - 1, and y = cos(-π/2) = 0

When θ = π, x = sin(π/2) = 1, and y = cos(π/2) = 0

The radius is 1 in this case, (x^2 + y^2 = r^2 -> x^2 + y^2 = 1^2 -> x^2 + y^2 = 1) as the semicircle ranges from (- 1, 0) to (1,0). Therefore your graph is the second one;

When theta = 0, x = sin 0 = 0, and y = cos 0 = 1, so the semicircle passes through (0, 1). To determine the equation, let's simply isolate "y" in the equation x^2 + y^2 = 1^2,

In Cartesian form, the equation is y = √(1 - x^2)

8 0

4 years ago

Please guys help me out with this

Kisachek [45]

When you have a negative exponent, you move the variable with the negative exponent to the other side of the fraction to make the exponent positive.

For example:

$x^{-2}$ or $\frac{x^{-2}}{1} =\frac{1}{x^2}$

$\frac{1}{2y^{-3}} =\frac{y^3}{2}$ (you don't move the "2" because "2" has an exponent of 1, only "y" has the negative exponent)

$\frac{5^{-2}}{y}=\frac{1}{(5^2)y} =\frac{1}{25y}$

When you multiply a variable with an exponent by a variable with an exponent, you add the exponents together. (But you can only combine the exponents when the variables are the same)

$x^2(y^3)=x^2y^3$ (You can't combine them because they have different variables of x and y)

$x^3(x^5)=x^{(3+5)}=x^8$

$y^3(y^2)=y^{(3+2)}=y^5$

There's two ways you can do this. Either by first making all the exponents positive then do subtraction, or multiply them then make all the exponents positive. I'm doing the 2nd way.

$2w^7u^{-2}w^{-6}*9y^{-6}*2y^9u$ You can combine the numbers 2 x 9 x 2 = 36

$36w^7u^{-2}w^{-6}y^{-6}y^9u$ Now multiply the terms with the same variables

$36(w^{7+(-6)})(u^{(-2+1)})(y^{(-6+9)})$

$36(w^1)(u^{-1})(y^3)$ Now make all the exponents positive

$\frac{36wy^3}{u}$

If you were to do subtraction, here is what you need to know:

When you divide a variable with an exponent by a variable with an exponent, you subtract the exponents together. (Reminder: they have to be the same variable in order to combine the exponents)

For example:

$\frac{x^3}{x^2} =x^{(3-2)}=x^1$ or x

$\frac{y^2}{y^4} =y^{(2-4)}=y^{-2}=\frac{1}{y^2}$

7 0

3 years ago

The cost of 2 bottles of ketchup is $7.96. What is the cost of each bottle of ketchup?

Evgesh-ka [11]

This is simple division.
You know 2 bottles cost a total of $7.96. You want to find how much each individual bottle costs on it's own. You take 7.96, and divide it by 2 in order to find this. 7.96/2=3.98
Each bottle costs $3.98
The third choice is correct
~Hope this helps!

3 0

4 years ago

Read 2 more answers

Find the number if 1 2/3% of it is 4.75

Alecsey [184]

<h2>Answer:</h2>

The number is:

285

<h2>Step-by-step explanation:</h2>

It is given that:

1 2/3% of a number is 4.75.

Let the number be x.