MATHEMATICS HIGH SCHOOL

Which of the following pairs of numbers contain like fractions? A. 31/2 and 43/4
B. 3/2 and 2/3
C. 6/7 and 15/7
D. 5/6 and 10/12

Answers

Answer 1
Answer: Hi

The same denominator: 6/7 and 15/7

Answer: c)

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The sum of a geometric series of twelve terms with common ratio 2 is 20,475. What is the first term? Needed help please.

Answers

Answer: the first term is 5

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = (ar^n - 1)/(r - 1)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

S12 = 20475

r = 2

n = 12

Therefore,

20475 = (a × 2^(12) - 1)/2 - 1

20475 = (a × 4095)

20475 = 4095a

a = 20475/4095

a = 5

The graph of a function never has two different points with the same x-coordinate because.. A. the graph of a function cannot be a straight line. B. each input value is mapped to a single output value. C. each input value is mapped to more than one output value. D. the graph of a function is a vertical line.

Answers

The best answer to the question that is being stated above would be letter B. The graph of a function never has two different points with the same x-coordinate because the input value of each of the points is mapped to a single output value in the graph. 

Answer:  The correct reason is (B) each input value is mapped to a single output value.

Step-by-step explanation:  The given statement is:

"The graph of a function never has two different points with the same x-coordinate."

We are to select the correct reason for the above statement.

The definition of a FUNCTION is as follows:

In simple language, a function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

That is, if y = f(x) is a function of a variable 'x', then we have

x_1=x_2~~~~\Rightarrow f(x_1)=f(x_2).

(A) The first statement is "the graph of a function cannot be a straight line."

The statement is false. For example, let us consider y = x + 2. Obviously, it is a function because every value of 'x' will result in only one value of 'y'.

Also, the graph here will be a straight line as shown in the attached figure (1).

(B) The first statement is "each input value is mapped to a single output value."

The statement is true according to the definition of a function.

(C) The third statement is "each input value is mapped to more than one output value."

The statement is false by the definition of a function.

(D) The fourth statement is "the graph of a function is a vertical line."

The statement is false. For example, if we consider the vertical line x = 2. Then, we see from the attached figure (2) that the points (x, y) = (2, 1), (2, 0), (2, 3), etc. all lie on the line.

This shows that one input value leads to infinitely many values of 'y'. Hence, this vertical line cannot be the graph of a function.

Thus, (B) is the correct statement.

Find the coordinates of the midpoint of the segment whose endpoints are H(2, 1) and K(10, 7)

Answers

\bf \textit{middle point of 2 points }\n \quad \n \begin{array}{lllll} &x_1&y_1&x_2&y_2\n % (a,b) H&({{ 2}}\quad ,&{{ 1}})\quad % (c,d) K&({{ 10}}\quad ,&{{ 7}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)

you tell us

Answer:

Find the coordinates of the midpoint of the segment whose endpoints are H(2, 1) and K(10, 7).

Step-by-step explanation:

If f(x) = 2x^2 - 10, find f(5).

Answers

sub 5 for every x
f(5)=2(5)^2-10
f(5)=2(25)-10
f(5)=50-10
f(5)=40

Find the LCM of 9 and 12.

Answers

36 because
9 x 4 = 36
12 x 3 = 36

Answer:

36 is the least common multiple of 12 and 9 :)

Step-by-step explanation:

What is the quotient (x^3+8)/(x+2)

Answers

Answer:

Step-by-step explanation:

The easiest way to do this is by using synthetic division (I really hope you know what I'm talking about!)

If the factor is x + 2 = 0, then the solution or the root is x = -2.  We will put -2 outside the "box" and the coefficients from the terms of the polynomial inside the "box":

-2|   1    0    0    8

Bring down the first number and multiply it by the -2.  Put the product up under the first 0 and add:

-2|   1    0    0    8

           -2

      1   -2  

Now multiply the -2 by the -2, put the product up under the next 0 and add:

-2|   1    0    0    8

           -2    4

      1    -2    4

Now multiply the 4 by the -2, put the product up under the 8 and add:

-2|   1    0    0    8

           -2   4    -8

     1    -2   4    0

Those bold numbers are the coefficients to the quotient, which is another polynomial, but is one degree less than the one you started with:

x² - 2x + 4 = 0

Since there is no remainder, then x = -2 is a zero of x³ + 8, and (x + 2) is a factor.

There is a whole world of stuff to learn about quadratics!!
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