MATHEMATICS HIGH SCHOOL

If f(x)=x+3 g(x)=2x+6 find (f+g)(x)

Answers

Answer 1

Answer:

Answer:

3x + 9

Step-by-step explanation:

For value of (f+g)(x) add two functions up

x + 3 + 2x + 6 = 3x + 9

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Cindy says that 1/3 is an irrational number because the fraction form doesn't terminate. Construct an argument to support or refute Cindy's position.

Answers

It’s not an irrational number because it can be written as a decimal. It is in an infinite decimal but if anything can be written as a fraction it is not a irrational number. :))

Final answer:

Cindy's argument is incorrect. 1/3 is a rational number because it can be expressed as the ratio of two integers. The fact that the decimal representation of 1/3 does not terminate does not make it irrational.

Explanation:

Cindy's argument is incorrect. A fraction is considered irrational if it cannot be expressed as the ratio of two integers. In the case of 1/3, it can be expressed as the division of the integer 1 by the integer 3, so it is a rational number. The fact that the decimal representation of 1/3 (0.333...) does not terminate does not make it irrational. Irrational numbers are decimal numbers that do not repeat or terminate, such as π (pi) and √2 (the square root of 2).

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Write an algebraic rule to describe the translation C(5, –4) C’(–2, 1)

Answers

Answer:

The required algebraic rule of translation is $(x,y)\rightarrow (x-7,y+5)$ .

Step-by-step explanation:

The coordinates of a point are C(5, –4) and the coordinates of image are C’(–2, 1).

$C(5,-4)\rightarrow C'(-2,1)$ .... (1)

Let the algebraic rule of translation is

$(x,y)\rightarrow (x+a,y+b)$ .... (2)

From (1) and (2) we get

$x=5,y=-4$

$x+a=-2$

$5+a=-2$

$a=-2-5$

$a=-7$

The value of a is -7.

$y+b=1$

$-4+b=1$

$b=1+4$

$b=5$

The value of b is 5.

The algebraic rule of translation is

$(x,y)\rightarrow (x-7,y+5)$

Therefore the required algebraic rule of translation is $(x,y)\rightarrow (x-7,y+5)$ .

We can solve this by using the formula:
(x, y) (x + a, y + b) = (5,-4) (-2,1)

So, plugging in the values and solving for a and b,
5 + a = -2
a = -8

-4 + b = 1
b = 5

Therefore, the translation is
(x,y) (x - 8, y +5)

So a 4 digit number is represented ABCD, they are not multiplied together, each letter represents 1 single , whole numberif ABCD times D=DCBA

solve for the values of A and B and C and D with full workings and solution (this problem is from my 5th grade math book, just for fun)

Answers

$\overline{ABCD}=10^3A+10^2B+10C+D\n\n\overline{ABCD}* D=(10^3A+10^2B+10C+D)* D\n=10^3AD+10^2BD+10CD+D^2\n\n\overline{DCBA}=10^3D+10^2C+10B+A\n\n\overline{ABCD}* D=\overline{DCBA}\n\downarrow\n10^3AD+10^2BD+10CD+D^2=10^3D+10^2C+10B+A$

$one\ of\ the\ solutions\ of\ general:\n\n\#1\ AD=D\n\#2\ BD=C\n\#3\ CD=B\n\#4\ D^2=A\n\nfrom\ \#1\ and\ \#4\nAD=D\ and\ D^2=A\to\ conclusion:A=D=1\n\nfrom\ \#2\ and\ \#3\nBD=C\ and\ CD=B\to conclusion:B=C\n\ntherefore$

$\overline{ABCD}=\n1001\n1111\n1221\n1331\n1441\n1551\n1661\n1771\n1881\n1991$

Rewrite with only sin x and cos x.cos 2x - sin x
Select one:
a. cos2x - sin2x - sin x
b. cos2x - sin3x
c. cos2x + sin2x + sin x
d. cos2x - 3 sin x

Answers

The answer is a. cos2x - sin2x - sin x. Use the rule: cos2x = (cos^2)x - (sin^2)x. So, substitute cos2x in the expression: cos2x - sinx = ((cos^2)x - (sin^2)x) - sinx = (cos^2)x - (sin^2)x - sinx. Therefore, choice a. is correct choice.

$cos^2x - sin^2x - sin x$ is the solution of the given equation.

To rewrite the expression cos 2x - sin x using only sin x and cos x, we can apply trigonometric identities.

Using the identity $cos 2x = 1 - 2sin^2x$ , we can rewrite the expression as:

$1 - 2sin^2x - sin x$

Since,

$sin^2x +cos^2x = 1$

Therefore, the correct answer is:

a. $cos^2x - sin^2x - sin x$

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A football team gained 12 yards on one play, lost 40 yards on another, and gained 34 yards on the last play of the first half. They had already gained 345 already during the half. What was the total yardage gain for the first half?

Answers

351 was the total yardage gain for the first half.

What is addition?

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

A football team gained 12 yards on one play,

lost 40 yards on another,

and gained 34 yards on the last play of the first half.

They had already gained 345 already during the half.

so, we get,

It would be 345+12=357,

then 357-40=317,

and finally,317+34=351

hence. 351 was the total yardage gain for the first half.

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