Factor Completely.
3x^2-75

Proportional reasoning is a form of 'operational reasoning' based on

Piaget's theory.

Proportional reasoning can be used to solve a problem; B. When one

quantity is a constant multiple of the other.

Reasons:

Proportional reasoning is the reasoning based on the cognition that a

relationship exists between the multiples of the variables in the problem,

such that the magnitude of a variable can implied from the changes made

to the relationships connecting the variables.

An example of proportional reasoning is the distance travelled, d, after a

given time, t, at a constant velocity, v;

To judge the distance travelled, a constant, v,  multiplies the time, t, such

that, at a longer time, it can be reasoned that the distance travelled is

much further.

Therefore;

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Options B and C are the correct conditions under which you can use proportional reasoning to solve a problem:

Proportional reasoning is a mathematical concept that involves understanding and solving problems that relate two or more quantities in a proportional manner. It helps us analyze and predict how changes in one quantity affect another based on their proportional relationship.

B: When one quantity is a constant multiple of the other:

In this case, if one quantity is a constant multiple of another, it means that they are directly proportional. For example, if the quantity of oranges you buy is always twice the quantity of apples you buy, then the quantities of oranges and apples are directly proportional. Proportional reasoning can be used to solve problems related to this relationship.

C: When the two quantities multiplied equal a constant:

If the product of two quantities remains constant, regardless of their individual values, they are inversely proportional. For instance, if the time taken to complete a task is inversely proportional to the number of people working on it, as the number of people increases, the time taken decreases. Proportional reasoning can be used to solve problems involving inverse proportionality.

In summary, proportional reasoning is used when two quantities are directly or inversely proportional to each other, i.e., when one quantity is a constant multiple of the other or when the product of the two quantities remains constant.

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Answer:

I believe it would be A

Step-by-step explanation:

Answer:

10.77

Step-by-step explanation:

√(4-0)²+(10-0)²

√4²+10²

√16+100

√116

10.77

Answer:

11

Step-by-step explanation:

For this problem, we simply need to apply the distance formula:

distance = sqrt[ (y2 - y1)^2 + (x2 - x1) ]

distance = sqrt[ (10 - 0)^2 + (4 - 0)^2 ]

distance = sqrt[ (10)^2 + (4)^2 ]

distance = sqrt[ 100 + 16]

distance = sqrt [ 116 ]

distance ~= 10.77

The approximate distance rounded to a whole number is 11.

Cheers.

Answer:

54

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

Start with:

[tex]5x+2=3x+4(2x-1)[/tex]

Distribute the [tex]4[/tex] into [tex](2x-1)[/tex]:

[tex]5x+2=3x+8x-4[/tex]

Combine like terms:

[tex]5x+2=11x-4[/tex]

Add [tex]4[/tex] to both sides of the equation:

[tex]5x+6=11x[/tex]

Subtract [tex]5x[/tex] from both sides of the equation:

[tex]6=6x[/tex]

Divide both sides of the equation by the coefficient of [tex]x[/tex], which is [tex]6[/tex]:

[tex]1=x[/tex]

or

[tex]x=1[/tex]

Answer:

Increase the speed

Step-by-step explanation:

The only way to decrease the time it would take to travel over a distance would be to increase the speed.

Answer:

see below

Step-by-step explanation:

if time decreases.... the velocity will decrease.

ex.

d = v/t

100 m = v/10 sec  v = 1000 m/s

100 m = v/5 sec   v = 500 m/s

100 m = v/1 sec    v = 100 m/s

therefore,

if we decrease the time it takes for a car to travel over the same distance,

the velocity decreases too.

This can be written as -8 + (-10). Subtracting a positive is the same as adding a negative.

One way to think of negatives is to think of debt in money. Writing -8 means you are 8 dollars in debt. Add on 10 more dollars of debt and you'll be 8+10 = 18 dollars in debt total. So this is one way to see how -8-10 = -8+(-10) = -18.

Or you can think of it as if you are in a submarine. The number -8 could represent the idea you are 8 miles below sea level. Then if we subtract 10 from this, or add on -10, it means we're going down another 10 miles to get a total depth of 18 miles below sea level. At this point, we would write -18.

Answer:

f(n+1) = 13

Step-by-step explanation:

Example :When we divide 50 by 100 we get 0.5 (a decimal number). So, to convert from percent to decimal: divide by 100, and remove the "%" sign.

In a flowchart proof, statements and conclusions are connected with arrows.

In terms of mathematics, a statement is simply any sentence in which it can be verifiably true or false. A statement cannot be a subjective opinion. It must be an objective fact and there must not be any ambiguity involved. A conclusion is also a statement that derives from the first statement made.

As an example, you can have the simple argument "if it rains, then it gets wet outside". So the box on the left would be "it rains" and the box on the right would be "it gets wet outside". An arrow connecting the two shows the logical flow of how the argument is set up.

See the diagram below.

Side note: the box on the left is also considered the antecedent because it comes before the conclusion.

Answer:

3 animals

Step-by-step explanation:

     --------------------------

         3x = 9

     2. divide both sides by 3

Answer:

7.2*10⁶

Step-by-step explanation:

0.0000072 =  7.2*10⁶

Answer:

$9.45

Step-by-step explanation:

1.  First, you want to figure out how much one text message costs.  To do this, divide the dollar amount (28.20) by the number of text messages (188).  You get 0.15, or $0.15 per text message.

2. Using this $0.15 per text message, you can calculate how much 63 text messages costs.  You simply multiply $0.15 by 63 to get $9.45, which is your answer.

Hope this helps! :)

Answer:

1

Step-by-step explanation:

1) The equation is 1 1/2 ÷ x = 2/3

2) You can multiply 2/3 with 1 1/2 to get your answer

3) 2/3 × 1 1/2 = 1

Hope this helps!

Answer:

see explanation

Step-by-step explanation:

Given the points (a, c ) and (b, c )

Since the y- coordinates are equal the distance formula simplifies to

d = [tex]\sqrt{(x_{2}-x_{1})^2 }[/tex]

with x₁ = a and x₂ = b

d = [tex]\sqrt{(b-a)^2}[/tex] = b- a

Answer:

Step-by-step explanation:

let the money in her purse be $x

1/3 of the money is 1/3x

Since his father gave him $5 and the total amount became $12

the expression for the total amount would be

12= 1/3x+5

We can now solve for x

12-5= 1/3x

1/3x= 7

cross multiply we have

x= 7*3

x= $21

Therefore the money in joes mother's purse is $21

Slope:

[tex]\sf{\dfrac{2}{5}}[/tex]

Explanation:

Parallel lines have the same slope, so the slope of y = 2/5x + 2 will be the same as the slope of the line which is parallel to it.

The equation is written in slope-intercept form, aka y = mx + b, where m is the slope and b is the y-intercept.

In slope intercept, the slope is always the number that comes before x.

For this equation, the number in front of x is 2/5.

So, I come to the conclusion that the slope of the line parallel to y = 2/5x + 2 is 2/5.

Answer: 16,000,000 years

Step-by-step explanation:

The question already states the formula for time so

1600/0.0001= 16,000,000

Answer:

-2 or -14/7 (they're the same)

Step-by-step explanation:

I hope this helps!

Answer:

Step-by-step explanation:

-3 ²/₇ - ( - ⁵/₇)

- 23 / 7  + 5 / 7

_  23 + 5

       7

_ 18

    7

- 2 ⁴/₇  

Answer:

d = 2[tex]\sqrt{3}[/tex]

Step-by-step explanation:

[tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d= \sqrt{(3-9)^2+(6-2)^2} \\d= \sqrt{(-6)^2+(4)^2} \\d= \sqrt{(36)+(16)} \\d= \sqrt{52} \\d=2 \sqrt{13}[/tex]

Answer:

13. 60

15. 200

Step-by-step explanation:

These are the answers because:

1) Since they are asking us to round to the tens place or the hundreds place we have to look at the ones digit and the tens digit.

2) For 13, the answer is 60 because the rounding digit is 5. Since the digit is 5, we have to round up the digit in the tens place. Therefore, it becomes 60.

3) For 15, the answer is 200 because the rounding digit is 3. Since the digit is 3, we have to keep the same number. Therefore, the answer is 200.

Hope this helps!

Answer:

180000 Meters per hour

Step-by-step explanation:

3 kilometers × 60 minutes (1 hour) = 180 kilometers per hour and then convert kilometers to meters

Answer:

The car's speed is 180,000 meters per hour.

Step-by-step explanation:

(3 km)/min×(1000 m)/(1 km)×(60 min)/(1 hr)=180,000 m/hr

Answer:

√8 and √23

Step-by-step explanation:

The appropriate square root are √7 and √20.

Given that, each number graphed is the square root of a whole number that is not a perfect square.

We need to write the appropriate square root in each box.

The square root of a number is the inverse operation of squaring a number. The square of a number is the value that is obtained when we multiply the number by itself, while the square root of a number is obtained by finding a number that when squared gives the original number.

Now, we can see the decimal numbers marked on the number line are 2.7 and 4.39.

So, 2.62²=6.8644≈7

Then the square root of number is √7

4.39²=19.2721

Then the square root of number is √20

Therefore, the appropriate square root are √7 and √20.

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Answer:

Option C - 0.03 cm

Step-by-step explanation:

The model has a length of 15 cm.

Now, we are told that the scale is 1:500. This means that 1 unit is represents 500 cm on the model.

Since the length on the model is 15 cm which is 15 units, then the true length would be;

15 × 1/500 = 0.03 cm

Therefore, the true length is 0.03 cm.

Option C is correct

Answer:

0.03 cm

Step-by-step explanation:

Answer:

a = 1

Step-by-step explanation:

Step 1: Write equation

a - 2(4 - a) = 7a - 12

Step 2: Solve for a

Distribute -2: a - 8 + 2a = 7a - 12

Combine like terms: 3a - 8 = 7a - 12

Subtract 3a on both sides: -8 = 4a - 12

Add 12 on both sides: 4 = 4a

Divide both sides by 4: a = 1

Step 3: Check

Plug in x to verify if it's a solution.

1 - 2(4 - 1) = 7(1) - 12

1 - 2(3) = 7 - 12

1 - 6 = -5

-5 = -5

Answer:

Step-by-step explanation:

equation given:   a - 2(4 - a) = 7a - 12

distribute and expand the equation

a - 8 + 2a = 7a - 12

combine similar terms:

a + 2a - 7a = -12 + 8

simplify:

-4a = -4

a = -4 / -4

proof that a = 1

a - 2(4 - a) = 7a - 12

1 - 2(4 - 1) = 7(1) - 12

1 - 2(3) = 7 - 12

1 - 6 = -5

-5 = -5  therefore, the a = 1 is correct.