MATHEMATICS HIGH SCHOOL

A) Draw a number line from 0 to 2. Then draw and label the points 2 and 0.2. B) use the number line to explain why 2 is 10 times the value of 0.2​

Answers

Answer 1
Answer:

Answer:

See attachment

Step-by-step explanation:

A) We draw the number line as shown in the attachment with intervals of 0.2 from 0 to 2.

B) Observe that, from 0 to 0.2 you move one units to get to 0.2.

From 0 to 2, on the number line with intervals of 0.2, you move 10 units from 0.

This means that:

2 = 0.2 + 0.2 + 0.2 + 0.2 + 0.2 + 0.2 + 0.2 + 0.2 + 0.2 + 0.2

This gives us:

2 = 0.2(1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1)

Then finally we have:

2 = 0.2(10)

By the commutative property of multiplication:

2 = 10 * 0.2

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Factor completely x^2 - 4x - 12
Explain the steps.
^ = to the power of

Answers

Well x^2 is the same as x-squared (I don't know how to type it). 
So to start off, you have x-squared-4x-12 
Then you just have to combine the x's, and 1x-4x=-3x 
so your final answer would be -3x-squared-12 

Solve for x. 8/9x=32

Answers

Answer:

0.44444444444

Step-by-step explanation:

Which of the following is an equivalent form of the compound inequality −22 > −5x − 7 ≥ −3?A) −5x − 7 < −22 and −5x − 7 ≥ −3
B) −5x − 7 > −22 and −5x − 7 ≥ −3
C) −5x > −22 and −7 ≥ −3
D) −5x − 7 < −22 and −5x − 7 ≤ −3

Answers

The equivalent form of the compound inequality −22 > −5x − 7 ≥ −3 are A) −5x − 7 < −22 and −5x − 7 ≥ −3

What is a solution set to an inequality or an equation?

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Then a Set of such values is called solution set to the considered equation or inequality.

The equivalent form of the given inequality can be obtained by dividing the inequality into two parts.

In this case, we are given -22 > -5x - 7 > -3.

The two parts are; -22 > -5x - 7 and -5x - 7 > -3.

Since the −5x − 7 and −22 have interchanged sides, the inequality sign also changes direction.

For part two, we have  −5x − 7 ≥ −3 remains unchanged.

Therefore, The choice that reflects these parts is A)-5x - 7 < -22 and -5x - 7 -3

Hence, The equivalent form of the compound inequality −22 > −5x − 7 ≥ −3 are A) −5x − 7 < −22 and −5x − 7 ≥ −3

Learn more about inequalities here:

brainly.com/question/27425770

#SPJ2
A) −5x − 7 < −22 and −5x − 7 ≥ −3

Working;
Since the −5x − 7 and −22 have interchanged sides, the inequality sign also changes direction.

For part two,  −5x − 7 ≥ −3 remains unchanged.

Find the sum of the given polynomials.ax + by + c, 2ax - 3by + c, and by - c

3ax - by + c
3a + x - bc
3ax + by - cd
bx - 3bc + a

Answers

  ax +  by + c
2ax - 3by + c
            by - c   
3ax - by + c   First Option.

You must align like terms before adding them. This is to ensure that there will be no confusion in getting the sum of the given polynomials.
If you would like to find the sum of the given polynomials, you can do this using the following steps:

ax + by + c + 2ax - 3by + c + by - c = ax + 2ax + by - 3by + by + c + c - c = 3ax - by + c

The correct result would be 3ax - by + c.

Abigail was skateboarding home when the wheel axle of her skateboard broke. She had already traveled two thirds of the way home and had to walk the rest of the way. Walking the rest of the way home took her twice as long as it took her to ride her skateboard. How many times faster is Abigail on her skateboard than she is walking?

Answers

Answer:

The number of times faster Abigail is on her skateboard than she is walking is 4 times

Step-by-step explanation:

The information given are;

Abigail was skateboarding home (let the distance home = D)

The distance Abigail had traveled when her skateboard broke = 2/3 of D

The distance of the rest (remaining) of the way home = 1 - 2/3 of D = 1/3 of D

The time Abigail took in walking the rest of the way home = 2 × t, Time it will take on the skateboard

Given that t is the time it takes Abigail to arrive home on skateboard alone, we have;

Speed = (Distnce)/(Time)

Speed on skate board, S_t = Distance/Time = D/t

Therefore, the time it took Abigail to travel two thirds (2/3) of D is given as follows;

Time= (Distnce \ covered)/(Speed ) = ((2)/(3) D)/(S_t) = ((2)/(3) D)/((D)/(t) ) = (2)/(3) D * (t)/(D) = (2)/(3) t

The total time it took Abigail to get to her home = Time of walking + Time on skateboard

The question also states that he total time it took Abigail to get to her home by walking and skateboarding because her skateboard broke = 2×t

Therefore, the total time it took Abigail to get to her home = 2×t = Time of walking + Time on skateboard = Time of walking + (2)/(3) t

Which gives;

2×t = Time of walking + (2)/(3) t

Time of walking = 2 * t -(2)/(3) t = (4)/(3) t

∴ The time Abigail walked 1/3·D = (4)/(3) t

Abigail walking speed is then

Walking \ speed= (Distnce \ covered \ walking)/(Time \walking) = ((1)/(3) D)/((4)/(3) t) = ((D)/(3) )/((4 \cdot t)/(3) ) = (D)/(3) } * {(3)/(4 \cdot t) } = (D)/(4 \cdot t) }

To compare how many times faster is Abigail on her skateboard than she is walking, we divide the expression (formula) for the speed of skateboarding with the (formula) for the speed of walking as follows;

The \ number \ of \ times \ faster = ((D)/(t) )/((D)/(4 \cdot t) )} = (D)/(t) * (4 \cdot t)/(D) } = 4

The number of times faster is 4 that is Abigail is four times faster on her skateboard than she is walking.

A zoo has 15 emperor penguins. The emperor penguins make up 30%, percent of all the penguins at the zoo. How many penguins live at the zoo?

Answers

Answer:50 penguins it’s right
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