MATHEMATICS HIGH SCHOOL

Which identifies all the integer solutions of |x| = 17?A.
0 only







B.

–17 only








C.
17 only







D.

–17 and 17

Answers

Answer 1
Answer: The answer is D. -17 and 17, for abs(-17) and abs(17) are both equal to 17~

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Choose the two equations you would use to solve the absolute value equation below. Then solve the two equations.|2x + 5| = 3

how would you write this word problem as an equation? When the gas gauge on her car was on the 3/8 mark, Karen pumped 15 gal. of gas into the tank in order to fill it. How many gal. of gas does the tank in Karen's car hold?

Answers

If the tank was 3/8 full, then it was 5/8 empty.
It took 15 gallons to fill those empty 5/8 of a tank.

5/8 x (1 tank) = 15 gallons

1 tank = 15 / (5/8) = 15 x 8/5 =24 gallons

Justin wants to use 188ft. Of fencing to fence off the greatest possible rectangular area for the garden. What dimensions should he use what will be the area of the garden

Answers

Circumference = pie x diameter 188 = pie x d 188/pie = diameter

Which are all the solutions of 5sinθ-4=2sinθ-4, where 0≤θ≤2π

Answers

5sinx-4 =2sinx-4
5sinx-2sinx= 4-4
3sinx=0
sinx=(0÷3)
sinx = 0
x = sin^-1 (0)
x= 0 degrees

And also x = (180- 0 ) = 180 degrees


so x; has 2 answers within the above given interval.

They are;
x= 0 degrees and x=180 degrees

Which one of the following is a Geometric Sequence?

Answers

Answer:

The geometric sequence among following is:

         Option: B

         8 , 4 , 2 , 1 , 1/2 , 1/4 ,.....

Step-by-step explanation:

Geometric sequence--

A sequence is said to be a geometric sequence if each of the number in the sequence is a constant multiple of the preceding term in the sequence.

This constant multiple is known as the common ratio (r)

i.e. the sequence is given by:

a,ar,ar²,ar³,.....

A)

0,1,2,3,......

It is a arithmetic sequence and not a geometric sequence .

Since, each of the term is increasing by 1 as compared to the preceding term of the sequence.

B)

8,4,2,1,1/2,1/4,.....

It is a geometric sequence.

Since, each term of the sequence is a constant multiple of 1/2 of the preceding term of the sequence.

i.e. 8×(1/2)=4

4×(1/2)=2

2×(1/2)=1

1×(1/2)=1/2

and so on.

i.e. the common ratio is: 1/2

C)

-7,10,23,36,.....

This is not a geometric sequence.

Since,

-7* (-10)/(7)=10

but

10* (-10)/(7)\neq 23

D)

2,-3,9/2,-18/4

Here

2* (-3)/(2)=-3

-3* (-3)/(2)=(9)/(2)

but

(9)/(2)* (-3)/(2)=(-27)/(4)\neq (-18)/(4)

Hence, it is not a geometric sequence.

What is the solution to the system of equations?



4x+y=2
x-y=3

Answers

4x+y=2\nx-y=3\n------\n5x=5\nx=1\n\n1-y=3\n-y=-2\ny=2

If -5x=-30, then x=6. What property was applied to get x=6

Answers

Answer:

multiplicative inverses
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