MATHEMATICS HIGH SCHOOL

How many solutions are there to the following system of equations?4x – 14y = 6
–2x + 7y = –3

A.
1

B.
2

C.
infinitely many

D.
0

Answers

Answer 1
Answer: 4x-14y=6 \n-2x+7y=-3 \ \ \ |* 2 \n \n4x-14y=6 \n\underline{-4x+14y=-6} \n4x-4x-14y+14y=6-6 \n0=0 \n always \ true \n \n\boxed{\hbox{infinitely many solutions}} \Leftarrow \hbox{answer C}

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What is –3 2/3 · (–2 1/4 )?

A 7/16-inch bolt is used in a machine. Whatis te length of the bolt written as a decimal

Answers

(7)/(16)= (7)/(16)* (625)/(625) = (4375)/(10000)=0.4375

If i is raised to an odd power, then it can not simplify to be

Answers

Answer:

-1

Step-by-step explanation:

If i is raised to an odd power, then it can not simplify to be?

-1

-i

i

Odyssey
i is the square root of -1. It is an imaginary number because you can't find the answer to the square root of a negative number. 
However, the (square root of a number) squared is that number, for example sqrt4 * sqrt4 = 4. 
Likewise, sqrt(i) * sqrt(i) = -1. You can see it as sqrt(-1) * sqrt(-1) = -1. 

If you multiply by another sqrt(i) however, sqrt(i)^3, then the last sqrt(i) will be left and there will still be an imaginary number. You will have -1 * i, which is -i. 
However, if you have sqrt(i)^4, then you have sqrt(-1)*sqrt(-1)*sqrt(-1)*sqrt(-1), which is -1*-1, which equals 1. You see that pairs of sqrt(i)'s balance and take out imaginary numbers. 

So, sqrt(i) to odd powers will still have imaginary numbers, while sqrt(i) to even powers won't have imaginary numbers.

How do i write a fraction or a mixed number as a decimal?

Answers

A decimal is a number divided by 10: 0.x = x/10, whatever the x number might be. If the "decimal" has more digits, then is divided by 100, 1000, and so forth: 0.0y = y/100, 0.00z = z/1000

So the trick for a mixed number to be written as a decimal is first to write the mixed number as a fraction, then, when you have a fraction, you need to make the denominator of the fraction equal to 10, 100, 1000, 10000, etc, and then you have it done.

For example, 4/25 as decimal is:
(4/25) = (4*4)/(25*4)
= 16/100, and that is = 0.16

In the figure below, segment AC is congruent to segment AB.Which statement is used to prove that angle ABD is congruent to angle ACD?
Answer

Angle CAB is congruent to angle CBA.

Angle DAC is congruent to angle DAB.

Triangle ACD is similar to triangle ABD.

Segment AD is congruent to segment AC.

Answers

Answer:

Option B is correct.

Angle DAC is congruent to angle DAB

Step-by-step explanation:

Given: Segment AC is congruent to segment AB.

In  ΔABD and ΔACD

AB \cong AC    [Given]

[Congruent sides have the same length]

AB = AC         [Side]

AD = AD        [Common side]

\angle DAC =\angle DAB      [Angle]

Side Angle Side(SAS) Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Then by SAS,

\triangle ABD \cong \triangle ACD

By CPCT [Corresponding Parts of congruent Triangles are congruent]

then;

\angle ABD \cong \angle ACD

therefore, only statement which is used to prove that angle ABD is congruent to angle ACD is: Angle DAC is congruent to DAB
The right answer for the question that is being asked and shown above is that: "Angle DAC is congruent to angle DAB." The statement that is used to prove that angle ABD is congruent to angle ACD is that Angle DAC is congruent to angle DAB.

Which of the following is a perfect square? A)154 B)169 C)279 D)115

Answers

A) 154 because it's an even number

Answer:

B

Step-by-step explanation:

Multiply two of the same will give you a perfect square like 13 x 13 is 169

Write .48 as a fraction in simplest form

Answers

Answer:

12/25

Step-by-step explanation:

0.48 is read as "forty-eight hundredths," so we can write it as a fraction as

48/100.

Since both 48 and 100 have a common factor, we can reduce the fraction.

48 and 100 are both divisible by 4.

48/100 = 12/25

There are no common factors of 12 and 25, so 12/25 is the answer.

Answer:

12/25

Step-by-step explanation:

48/100 Divide by 2

24/50 Divide by 2 again

12/25 Can not be further simplified.

I hoped this helped you
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