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3 years ago

All points of the step function f(x) are graphed.

Mathematics

1 answer:

mrs_skeptik [129]3 years ago

8 0

Answer:

On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is a closed circle. The right end of each segment is an open circle. The left-most segment goes from (negative 5, 3) to (negative 4, 3). Each segment is 1 unit lower and 1 unit farther to the right than the previous segment. The right-most segment goes from (2, negative 4) to (3, negative 4).

Step-by-step explanation:

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Help! Which choice is the most efficient first step to solve this set of equations?

Dmitry [639]

Answer:

Substitute 3x - 5 for y in the second equation.

Step-by-step explanation:

Generally, to solve the system of linear equations of x and y, the first step would be trying to eliminate x (or y).

Then turn the system into the equation of only y (or x).

Next, try to solve for y (or x).

Then substitute the solved y (or x) into the original system to work out x (or y).

**********

3 options (1 addition, 2 subtractions) do not eliminate x or y (x and y still exist after manipulation).

=> Remaining option relating substitution would be a reasonable choice.

5 0

3 years ago

(4y^2-3y+2)+(5y+12y-4)-(13y^2-6y+20)

Andrews [41]

Answer:

-(9 y^2 - 20 y + 22) or if you need y = 10/9 + (7 i sqrt(2))/9 or y = 10/9 - (7 i sqrt(2))/9

Step-by-step explanation:

Simplify the following:

-(13 y^2 - 6 y + 20) + 4 y^2 + 12 y + 5 y - 3 y - 4 + 2

Grouping like terms, -(13 y^2 - 6 y + 20) + 4 y^2 + 12 y + 5 y - 3 y - 4 + 2 = -(13 y^2 - 6 y + 20) + 4 y^2 + (-3 y + 5 y + 12 y) + (2 - 4):

-(13 y^2 - 6 y + 20) + 4 y^2 + (-3 y + 5 y + 12 y) + (2 - 4)

-3 y + 5 y + 12 y = 14 y:

-(13 y^2 - 6 y + 20) + 4 y^2 + 14 y + (2 - 4)

2 - 4 = -2:

-(13 y^2 - 6 y + 20) + 4 y^2 + 14 y + -2

-(13 y^2 - 6 y + 20) = -13 y^2 + 6 y - 20:

-13 y^2 + 6 y - 20 + 4 y^2 + 14 y - 2

Grouping like terms, 4 y^2 - 13 y^2 + 14 y + 6 y - 20 - 2 = (-13 y^2 + 4 y^2) + (6 y + 14 y) + (-20 - 2):

(-13 y^2 + 4 y^2) + (6 y + 14 y) + (-20 - 2)

4 y^2 - 13 y^2 = -9 y^2:

-9 y^2 + (6 y + 14 y) + (-20 - 2)

6 y + 14 y = 20 y:

-9 y^2 + 20 y + (-20 - 2)

-20 - 2 = -22:

-9 y^2 + 20 y + -22

Factor -1 out of -9 y^2 + 20 y - 22:

Answer: -(9 y^2 - 20 y + 22)

______________________________________________

Solve for y:

-9 y^2 + 20 y - 22 = 0

Divide both sides by -9:

y^2 - (20 y)/9 + 22/9 = 0

Subtract 22/9 from both sides:

y^2 - (20 y)/9 = -22/9

Add 100/81 to both sides:

y^2 - (20 y)/9 + 100/81 = -98/81

Write the left hand side as a square:

(y - 10/9)^2 = -98/81

Take the square root of both sides:

y - 10/9 = (7 i sqrt(2))/9 or y - 10/9 = -(7 i sqrt(2))/9

Add 10/9 to both sides:

y = 10/9 + (7 i sqrt(2))/9 or y - 10/9 = -(7 i sqrt(2))/9

Add 10/9 to both sides:

Answer: y = 10/9 + (7 i sqrt(2))/9 or y = 10/9 - (7 i sqrt(2))/9

4 0

3 years ago

What is the area of the semicircle

kirza4 [7]

Answer:

Apply the formula πr^2/2

6 0

3 years ago

Read 2 more answers

Marco is making mosaic garden Stones using red, yellow ,and blue tiles. He has 45 red tiles,90 blue tiles,and 75 yellow tiles. S

son4ous [18]

The Greatest Common Factor: G C F ( 45, 90 , 75 ) = 15
The greatest number of stones Marco can make is 15.
45 : 15 = 3
90 : 15 = 6
75 : 15 = 5
He will use: 3 red, 6 blue and 5 yellow tiles in each stone.

4 0

3 years ago

Peter has invented a game with paper cups. He lines up 121 cups face down in a straight line from left to right and consecutivel

natita [175]

Answer:

After 121 passes, there will be 11 cups facing up

Step-by-step explanation:

Given that:

Peter initially lines up 121 cups facing down in a straight line from left to right and consecutively labels them from 1 to 121.

We can have an inequality ; i.e 1 ≤ n ≤ 121; if n represents the divisor including n itself for which n = odd number. Thus at the end of this claim, the cup will be facing up.

On the ith pass, he flips over cups i, 2i, 3i, 4i,.... (By "flip," we mean changing the cup from face down to face up or vice versa.)

For each divisor on the ith pass of n;

$i \ th \ pass \ = \ n \ \to \ p |n$ since we are dealing with possibility of having an odds number:

Thus; $p =i$ and $i^2 = n$ where ; n = perfect square.

Thus ; we will realize that between 1 to 121 ; there exist 11 perfect squares. Therefore; as a result of that ; 11 cups will definitely be facing up after 121 passes

3 0

3 years ago