Weekly math review 3:3

Answer:

Step-by-step explanation:

When learning about commutative and associative properties, we learn that ...

  a + b = b + a . . . . . addition is commutative

  ab = ba . . . . . . . . . multiplication is commutative

But we also know that ...

  a - b ≠ b - a . . . . . . subtraction is not commutative

  a/b  ≠ b/a . . . . . . . . division is not commutative

__

We also learn that ...

  a + (b+c) = (a+b) +c . . . . addition is associative

  a(bc) = (ab)c . . . . . multiplication is associative

And of course, ...

  a - (b -c) ≠ (a -b) -c . . . . subtraction is not associative

  a/(b/c) ≠ (a/b)/c . . . . . . . division is not associative

_____

However, you can use associative and commutative properties in problems involving subtraction and division if you write the expression properly:

  a - (b - c) = a +(-(b -c)) = a +((-b) +c) = (a +(-b)) +c . . . . keeping the sign with the value makes it an addition problem, so the associative property can apply

  (a/b)/c = (a(1/b))(1/c) = a(1/b·1/c) = writing the division as multiplication by a reciprocal makes it so the associative property can apply

Answer:

addition

multiplication

Context?                                                                                                                      

??????????????                              

Kim's gross pay for this week is $292.50.

To calculate Kim's gross pay for this week,

we multiply the number of hours she worked by her hourly rate.

In this case, Kim worked 39 hours and her hourly rate is $7.50.

So, we can multiply 39 by $7.50 to find her gross pay.

39 * $7.50 = $292.50

Therefore, Kim's gross pay for this week is $292.50.

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Answer:

1/8

Step-by-step explanation:

Check: 12.5 * 8 = 100

Answer:

1/8 is the simplest form

Step-by-step explanation:

12.5% = 12.5/100 = 125/1000

125/125 = 1

1000/125 = 8

= 1/8

Answer:

[tex]\frac{8}{3}[/tex]

Step-by-step explanation:=

= [tex]\frac{56}{21}[/tex]  ( Divide both sides by 7)

= [tex]\frac{8}{3}[/tex]

21 is 3/8 fraction of 56.

A fraction describes a part of a whole. For example, one slice of a pizza is a fraction of the whole pizza.

Given that, what fraction of 56 is 21,

Finding the fraction, we get,

21 / 56 = 7(3) / 7(8)

= 3 / 8

Hence, 21 is 3/8 fraction of 56.

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Answer: y = 5

Step-by-step explanation:

This triangle is isosceles.

So, ∠ABC = ∠ACB = 75°

Now,

sum of interior angles of a triangle = 180°

∠ABC + ∠ACB + ∠BAC = 180°

75° + 75° + (4y + 10)° = 180°

160° + 4y° = 180°

4y° = 20°

y = 5

Answer: 29 m

Step-by-step explanation: First find the width

Since Area = Length x Width

Width = Area/Length = 232/8 = 29

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Answer:

6

Step-by-step explanation:

Answer:

The equation of the line in point slope form is equal to

[tex]y+2=(x+2)[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

(-2,-2) and (2,2)

substitute the values

[tex]m=\frac{2+2}{2+2}=1[/tex]

step 2

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=1\\(x1,y1)=(-2,-2)[/tex]

substitute the values in the formula

[tex]y-(-2)=(1)(x-(-2))\\y+2=(x+2)[/tex]

Answer:

B, hope this helps you!

The general strategy for solving an equation of the form x/a = b is to multiply both sides by a.

A mathematical statement that two expressions are equal: it is either an identity in which the variables can assume any value, or a conditional equation in which the variables have only certain values (roots) the act of regarding as equal .

Solving equations is computing the value of the unknown variable still balancing the equation on both sides.

The general strategy for solving an equation of the form x/a = b

To solve this equation we will multiply both sides by a

On multiplying

x = ab

Therefore Option B. multiply both sides by a is the correct answer.

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The function that represents the interest on this loan after years is Interest = Principal × Rate × Time.

The function that represents the interest on this loan after years can be calculated using the formula for simple interest:

Interest = Principal × Rate × Time

In this case, the principal is $8,000, the rate is unknown, and the time is 2 years. The interest paid back is $8,160, so we can rewrite the formula as:

$8,160 = $8,000 × Rate × 2

Dividing both sides of the equation by $8,000 × 2 gives:

Rate = $8,160 / ($8,000 × 2)

Solving this equation gives a rate of 0.51, or 51%.

Answer:

when you have two fractions that equal each other you want to solve by using cross multiply

What cross multiply is, is when you multiply diagonally so:

8/x=14/7

you would take 14*x and 8*7

14x=56 (you would then divide each side by 14)

x=4 (14/14=1, 56/14=4)

8/4=14/7

To check your work you could simplify

8/4=2

14/7=2

2=2, which is true

x=4

Hope this helps ;)

Answer:

420 cm

Step-by-step explanation:

Answer:

4 x 11 + 3 = 47

Step-by-step explanation:

n = 11

The equation that represents the situation will be 4n + 3 = 47. And the solution of the equation is 11.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Four times a number, n, added to 3 is 47. Then the equation is given as,

4n + 3 = 47

Simplify the equation, then we have

4n + 3 = 47

4n = 47 - 3

4n = 44

n = 11

The equation that represents the situation will be 4n + 3 = 47. And the solution of the equation is 11.

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Answer:1

Step-by-step explanation:

Answer:

320

Step-by-step explanation:

j u s t a g u e s s b u t i t h i n k i t s r i g h t

To find the area percentage increase when the area of a parallelogram increased from 40 to 128 square centimeters, calculate the percentage change as 220%.

The area percentage increase can be calculated as follows:

Answer:

The area of a the parallelogram is 88meers squared

Answer:

vertex (-3 , 7)

Step-by-step explanation:

vertex (h, k)     f(x) = a | x - h | + k

f(x) = |x + 3|+ 7 ,    h = - 3 and k = 7

vertex (-3 , 7)

The value of vertex of the graph would be,

⇒ (-3 , 7)

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We know that;

Standard form of equation is,

⇒  f(x) = a | x - h | + k

Where, vertex = (h, k)  

Here, The equation of graph is,

f(x) = |x + 3|+ 7 ,    

And, h = - 3 and k = 7

Thus, The value of vertex of the graph would be,

⇒ (-3 , 7)

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Answer:

the answer to the inequality is x>-6

Step-by-step explanation:

x+8>2

x>2-8

x>-6

Answer:

90 yards a minute

Step-by-step explanation:

The way to figure this out is simple. Just do the amount of yards he or she did total, which is 450, then divided it by the amount of time it took him or her to do so, which is 5 minutes, meaning the equation is 450 divided by 5 equaling 90.

Answer:i think its 90

Step-by-step explanation:

450 / 5 = 90

Answer:

Step-by-step explanation:

y - y1 = m(x - x1)

(1,9)...x1 = 1 and y1 = 9

slope(m) = 2

now we sub

y - 9 = 2(x - 1) <===

The point-slope equation of the line with slope 2 that passes through the point (1, 9) is y - 9 = 2(x - 1).

To find the point-slope form equation of a line with a given slope and a point, use the formula y - y1 = m(x - x1),

where (x1, y1) is the point on the line and m is the slope.

In this case, the slope is given as 2 and the point is (1,9).

Substituting these values into the point-slope form formula yields the equation y - 9 = 2(x - 1), which represents the linear relationship between x and y corresponding to the described line.

Answer:

If the input is n then the output f(n) will be 4n - 8.

Step-by-step explanation:

Let the input of the function is denoted by x and the output is denoted by y.

Then, two ordered pairs of the linear function i.e.(x,y) are (2,0) and (3,4).

Therefore, the relation between x and y i.e. the equation of the straight line will be given by

[tex]\frac{y - 4}{4 - 0} = \frac{x - 3}{3 - 2}[/tex]

⇒ y - 4 = 4(x - 3)

⇒ y = 4x - 8

⇒ f(x) = 4x - 8

Therefore, if the input is n then the output f(n) will be 4n - 8. (Answer)

The water will last for 3 days

Solution:

Given that, village having a population of 4000, requires 150 litres of water per head per day

Let us first find the volume of tank

The tank measuring 20m x 15m x 6m

Length = 20 m

Breadth = 15 m

Height = 6 m

[tex]volume\ of\ tank = length \times breadth \times height[/tex]

[tex]Volume\ of\ tank = 20 \times 15 \times 6 = 1800[/tex]

Thus volume of tank is 1800 cubic meter

From given,

Water required per person per day = 150 liters

Therefore, water required for 4000 people per day is:

[tex]\rightarrow 4000 \times 150 = 600000 \text{ liters }[/tex]

Convert to meters

[tex]600000 \text{ liters } = 600000 \times \frac{1}{1000}\ m^3\\\\600000 \text{ liters } = 600\ m^3[/tex]

How many days will the water of this tank last?

[tex]\text{Number of days water will last } = \frac{\text{volume of tank}}{\text{total water required per day}}[/tex]

[tex]\text{Number of days water will last } = \frac{1800}{600} = 3[/tex]

Thus the water will last for 3 days

Answer:

314 mile²

Step-by-step explanation:

area = πr² = 3.14 x 10² = 314 mile²

Answer:

y = x - 4

Step-by-step explanation:

equation of a line can be expressed as

(x - x1)/(x2 - x1) = (y - y1)/(y2 - y1)

(x - 5)/(10 - 5) = (y - 2)/(-3 - 2)

cross multiplying,

-5(x - 5) = 5(y - 2)

clearing the parentheses

-5x + 10 = 5y - 10

hence,

5y = 5x - 20

y = x - 4

Answer:

x = -2

Step-by-step explanation:

Answer: Its 2

Step-by-step explanation: PEMDAS Keep.Change.Flip.

5/6×3/2=15/12=1 3/12

1 3/12+3/4(3/3)

1 3/12+9/12=1 12/12=2. BOOM!

Answer:

Plumber A has greater initial fee

Step-by-step explanation:

Plumber B:

Hourly charge = 160 - 105 = $55

Initial charge = 105 - 55 = $50

Equation: y = 50 + 55x

Answer:

C

Step-by-step explanation:

For plumber A : y = 100 + 30x

For plumber B :

Let the total charge be y

Initial charge be x

Hourly rate be za

For total price = 105 in 1hr

105 = x + a ........(1)

For 160 total charge in 2hrs

160 = x + 2a .........(2)

Substracting (1) from (2)

160 - 105 = 2a - a

55 = a

Substituting a = 55 in (1)

105 = x + a

105 = x + 55

x = 105 - 55

x = 50

:- equation for total charge is

y = 50 + 55a

Answer:

y = 150 - 11x

Step-by-step explanation:

Janelle is starting out with 150 surveys and if she is conducting 11 surveys an hour, then that means you need to subtract 11x from 150 because that will give you how many surveys she has left.