About 365 kg paper can be made from a single
tree. A ream (500 sheets) of paper weighs about
2.3 kg.
(a) How many sheets of paper can a single tree
be made into?

The number of each type of vehicle sold are :

SUVs : 300

Passenger cars : 270

Number of SUVs were sold more than passenger cars = 30

Total number of cars sold = 540

Let the number of Passenger car sold = x

Then, The number of SUVs sold = x + 30

So, Total number of cars sold = Number of Passenger car sold + Number of SUVs sold

     540 = x + (x + 30)

2x + 30 = 540

       2x = 540

         x = 540/2

         x = 270

We got, the number of Passenger car sold (x) = 270

The number of SUV's sold = x + 30

The number of SUV's sold = 270 + 30 = 300

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Answer:3

Step-by-step explanation:

The value of the constant k such that the system has infinitely many solutions is; -2.

It follows from the task content that the system of equations given upon observation are multiples.

Hence, by multiplying the second equation by -2; we have;

-4x +6y = 4

-4x +6y = -2k

Hence, for the system to have infinitely many solutions; 4 = -2k.

Ultimately, k = -2 by dividing both sides of the equation above by -2.

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The catering cost was determined if the cost per person is R225,00. then the cost of 50 people is equal to = 1,125,000 R.

The catering cost was determined if the cost per person is R 225,00.​

The cost per person = 225,00 R

To calculate the cost per unit, add all of your fixed costs and all of your variable costs together and then divide this by the total amount of units you produced during that time period.

Let us assume,

Suppose you can find the cost for 50 people.

Then,

We can write,

Catering cost = x

x = 225,00 * 50

x = 1,125,000 R

Therefore,

The catering cost was determined if the cost per person is R225,00. then the cost of 50 people is equal to = 1,125,000 R.

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The lines are neither, nor perpendicular

The equations of the lines are given as

5x + 2y = 14

y = -5x + 9

Make  y the subject in both equations

So, we have

y = -2.5x + 7

y = -5x + 9

The slopes of the above equations are

m1 = -2.5

m2 = -5

The above slopes are neither equal not opposite reciprocals

Hence, the lines are neither, nor perpendicular

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The 2,722 to the nearest thousand is 3000.

In the given statement is :

What is 2,722 rounded to the nearest thousand

Number is => 2722

Hence, the 2,722 to the nearest thousand is 3000.

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The equation solved for 'd' gives  d =  3f - g³/ 4h

The subject of a formula is defined as the variable expressed in terms of the other variables.

It is also the variable that is worked out in a given equation or expression;

Given the equation;

4hd = 3f - g³

To solve for 'd'

Divide both sides by the coefficients of d, we have;

4hd/ 4h =  3f - g³/ 4h

We then have

d =  3f - g³/ 4h

Thus, the equation solved for 'd' gives  d =  3f - g³/ 4h

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It is true. For all rational numbers a and b, a−b = a + (−b).

Given that,
To determine whether the statement, "For all rational numbers a and b, a−b = a + (−b)." is true or false.

In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.

Here,
= a + (-b)
Since in the parenthesis there is a negative value, when we open the parenthesis the sign of the arithmetic operator will change accordingly,
So,
= a - b
So, the condition is true for all rational numbers.

Thus, It is true. For all rational numbers a and b, a−b = a + (−b).

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Answer: [tex]\frac{1}{\sqrt{2}}[/tex]

Step By Step Explanation:

[tex]=\frac{2\sqrt{2}}{2\cdot \:2}[/tex]

[tex]=\frac{\sqrt{2}}{2}[/tex]

[tex]=\frac{\sqrt{2}}{\sqrt{2}\sqrt{2}}[/tex]

[tex]=\frac{1}{\sqrt{2}}[/tex]

There will be roughly 12,000 bacteria after 12 hours.

So, there are 5300 bacteria  and it gets doubles in 10 hours:

Then,

Therefore, there will be roughly 12,000 bacteria after 12 hours.

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Answer: 2,730

Step-by-step explanation:

Explained in mental math proccess:

In 455, the one value will be multiplied by 6. 5x6= 30.

In 455, the tens value will be multiplied by 6. 50x6= 300.

In 455, the hundreds value will be multipled by 6. 400x6= 2,400.

Find the sums of all products multiplied by 6. 30+300+2,400= 2,730.

455x6= 2,700

Answer:

The equation for this line is (P(x,y)----> P'(2h-x,2k-y), hence h=3 and k=1/2

Step-by-step explanation:

P(x,y)----> P'(2h-x,2k-y)

P(-4,-4)---->P'(8,5)

Now comparing the corresponding sides;

2h+4=8

2h=8-4

2h=4

h=2

Again,

2k-y=5

2k+4=5

2k=5-4

2k=1

k=1/2

Now, checking the answer:

P(-4,-4)----->P'{2*2-(-4),2*1/2-(-4)}

=P'(4+4,1+4)

=P'(8,5)

Answer: 87.96 km

Step-by-step explanation:

10.3% of 853.93km= 87.96 km

Answer: -21

Step-by-step explanation:

x = -3 and y = -2

x²-5xy=

(-3)²-5(-3)(-2)=

9-5(-(-6))=

9-5(6)=

9-30=

-(30-9)=-21

Answer:

$17.20

Step-by-step explanation:

You need to print (130)(17) = 2210 pages.

This means you need 2210/500 reams, which rounds up to 5.

So, the cost is 5(3.44) = $17.20

Answer:

7602.40

Step-by-step explanation:

Based on the given conditions

Formulate:

3.44×30×17

447.2×17

7602.4

Round 7062.4

=7062.40

To get a perfect square, the smallest number to be multiplied by 6300 is 7.

Multiplication is the process of calculating the result when a number is taken times. Each of the numbers is referred to as a factor of the product, which is the outcome of a multiplication.

Consider the number 6300 which can also be written as:

6300 = 2 × 2 × 3 × 3 × 5 × 5 × 7

Now, 2, 3, and 5 are in pairs. Only 7 is not in pair.

Now, we will multiply 6300 by 7.

Then,

6300 × 7 = 44100

Therefore, the number 44100 is the number that makes the perfect square.

Let's say x² = 44100,

Taking square root on each side of the equation:

x² = 44100

√x² = √44100

x = √[ 21 × 21 × 10 × 10 ]

x = 210

Therefore the smallest number by which 6300 is multiplied to get a perfect square is 7.

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The expression of f(x) = -2x² - 10 which is h(x) = -2x² - 6 would be vertically upward by 3 units, it becomes the graph of a function for f(x).

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The function h is defined as follows.

h(x) = -2x² - 6

If the graph of his translated vertically upward by 3 units, it becomes the graph of a function for f(x)

To determine the expression for f(x).

Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.

For example, If shift up by 1 unit,  add 1 to the function

If shift down by 4 units, subtract 4 from the function

Here h + 4 because adding 2 to the h coordinate would shift it up 2

⇒ h(f(x)) = ( x, y +4 )

⇒ f(x) + 4 = -2x² - 6

⇒ f(x) = -2x² - 6 -4

⇒ f(x) = -2x² - 10

Hence, the expression of f(x) = -2x² - 10 which is h(x) = -2x² - 6 would be vertically upward by 3 units, it becomes the graph of a function for f(x).

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Answer:

A negative exponent flips the fraction and turns the exponent positive, and vice versa.

1/121 = 1/1211 = 121-1

As an example, 5-2 = 1/25, and 1/5-2 = 25.

The area of the rectangle is 10x² - 13x - 3.

It should be noted that the area of a rectangle is the length multiplied by the width.

Here, the dimensions of a rectangle are 2x-3 and 5x+1.

The area will be:

= (2x - 3)(5x + 1)

= 10x² + 2x - 15x - 3

= 10x² - 13x - 3

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The length of time that it cost less to move good across town will be more than 2.36 hours.

From the information, ACME movers charges $59 plus $20 per hour to move household goods across town and Hank movers charges $45 per hour.

Let the number of hours be represented by h.

Therefore, the appropriate equation will be:

59 + 20h = 45h

Collect like terms

45h - 20h = 59

25h = 59

h = 59/25

h = 2.36 hours.

Therefore, the length of time that it cost less to move good across town will be more than 2.36 hours.

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ACME movers charges $59 plus $20 per hour to move household goods across town. Hank movers charges $45 per hour. For what length of time does it cost less to move good across town?

Answer:

Answer = (2)n+(2)

Step-by-step explanation:

                    first difference = -2

                    Now,   -2 = -2 × (n) + (0)        if      n = 1          

                        or     -2 = -2 × (n) + (-6)      if       n = -2

                        or     -2 =  |-2| ×(n) + 2   ::::  -2 = 2n +2       if      n = -2

Answer: 79.02

Step-by-step explanation:

set present value to 0

set future value to 300000

set number of time periods to 35 * 12 = 420

set interest rate percent per time period to 10/12 = 0.833333.

Equation:

See attachment

Rounding to an estimate, Sachin will have enough gas to go to both places before he runs out of gas.

An estimate is an equivalent numerical value obtained by rounding off.

The result of an estimate is not an exact value.  The value represents the nearest rounded value.

For instance, 75.9% can be estimated or rounded off to 76%.  32 minutes can be rounded off or approximated to ¹/₂ hour.

Driving distance before getting gas = 110 miles

The distance to his friend's house = 67 miles

The distance to his mom's house = 32 miles

The total distance to be covered on the available gas = 99 miles

Estimated distance to be covered = < 100 miles

Thus, using estimation, Sachin will still have more than 10 miles to drive before he gets gas.

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Answer:

D) b/7 + 18 =16

Step-by-step explanation:

Let's solve your equation step-by-step.

b/7+18=16

Step 1: Simplify both sides of the equation.

1/7b+18=16

Step 2: Subtract 18 from both sides.

1/7b+18−18=16−18

1/7b=−2

Step 3: Multiply both sides by 7.

7*(1/7b)=(7)*(−2)

b=−14

The approximate no . of miles Philip traveled are 4 . 98 * ( 10 ^ 5 ) miles .

Given : the circumference of earth 2.49 x ( 10^4 ) miles

To calculate :  the approximate number of miles Philip traveled

Philip  traveled 20 times

⇒ 20 * circumference of circle

⇒ 20 * [ 2.49 x ( 10^4 ) ]

  ( 2 * 2.49 ) * ( 10 ^ 5 )

= 4 . 98 * ( 10 ^ 5 )

Hence , the approximate no . of miles Philip traveled are 4 . 98 * ( 10 ^ 5 ) miles .

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Answer:

It means that the -4 is one of the solutions for this polynomial. In other words, -4 is a point in the x axis of the graph where the function touches said axis.

The value of the polynomial at P(-4) will be 0.

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

Given that the polynomial function is P(x) = x³ + 11x² + 34x + 24. The value of the function at P(-4) will be calculated as:-

P(x) = x³ + 11x² + 34x + 24

P(-4) = (-4)³ + 11(-4)² + 34(-4) + 24

P(-4) = -64 + 176 - 136 + 24

P(-4) = 200 - 200

P(-4) = 0

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The equation: 1/2 + 1/6 = 2/3

Is true.

Here we have the equation:

1/2 + 1/6 = 2/3

First, we need to find a common denominator for the two fractions, if we multiply and divide the first one by 3 we get:

(3/3)*(1/2) = 3/6

Replacing that in the equation:

3/6 + 1/6 = 2/3

4/6 = 2/3

Now we can simplify the fraction in the left by dividing both numerator and denominator by 2:

4/6 = 2/3

2/3 = 2/3

Thus, the equation is true.

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