The perimeter of a rectangle is twice the sum
of its length and its width. The perimeter is
40 meters and its length is 2 meters more
than twice its width.

Step-by-step explanation:

Monomial = x^2, 1 term

Binomial = x^2 + x, 2 terms

Trinomial = x^2 + x + 3, three terms

Binomial is more than 3 terms

Let's do a 3rd degree polynomial like:

[tex] {x}^{3} + 2x^{2} + 4x + 8[/tex]

[tex] {x}^{2} (x + 2)[/tex]

Now let's factor the second part, the 4x + 8. This can be factored by a 4.

[tex]4(x + 2)[/tex]

Your new equation is:

[tex] \frac{( {x}^{2} + 4)(x + 2)}{x - 2} [/tex]

x^2 + 4 can be factored again down to (x + 2)(x + 2)

YOUR FINAL EQUATION IS:

[tex] \frac{(x + 2)(x + 2)(x + 2)}{x - 2} [/tex]

Answer:

x=2/3

Step-by-step explanation:

(1/2)/3=x/4

(1/2)(1/3)=x/4

1/6=x/4

cross product,

6*x=1*4

6x=4

x=4/6=2/3

x=2/3

3.75 million pounds of aluminium

Step-by-step explanation:

The question requires you to perform division operation

Given that 15 million pounds is processed per month

A month has average 4 weeks.

The aluminium smelted per week will be;

15/4 = 3.75 million pounds of aluminium

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The right answer is Option A.

Step-by-step explanation:

Let,

x be the postcards

y be the large envelops

According to given statement;

14x+5y=12   Eqn 1

10x+15y=24.80   Eqn 2

Multiplying Eqn 1 by 3;

[tex]3(14x+5y=12)\\42x+15y=36\ \ \ Eqn \ 3[/tex]

Subtracting Eqn 2 from Eqn 3;

[tex](42x+15y)-(10x+15y)=36-24.80\\42x+15y-10x-15y=11.20\\32x=11.20\\[/tex]

Dividing both sides by 32

[tex]\frac{32x}{32}=\frac{11.20}{32}\\x=0.35[/tex]

Putting x=0.35 in Eqn 1;

[tex]14(0.35)+5y=12\\4.90+5y=12\\5y=12-4.90\\5y=7.10[/tex]

Dividing both sides by 5

[tex]\frac{5y}{5}=\frac{7.10}{5}\\y=1.42[/tex]

Therefore, one large envelope costs $1.42

The right answer is Option A.

Keywords: linear equations, subtraction

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Answer: A. $1.42

Step-by-step explanation: I did it on the test and got it right!

The right answer is Option D.

Step-by-step explanation:

Let,

Kyle's money = x

Hayden's money = y

Jeremy's money = z

According to statements;

Kyle has three times as much money in his savings account as  Hayden.

x = 3y   Eqn 1

Hayden has twice as much money in his savings account  as Jeremy.

z = 2y   Eqn 2

Combined Kyle, Hayden, and Jeremy have a total of  $612.

x+y+z=612   Eqn 3

Putting value of x and z from Eqn 1 and 2 in Eqn 3

[tex]3y+y+2y=612\\6y=612[/tex]

Dividing both sides by 6

[tex]\frac{6y}{6}=\frac{612}{6}\\y=102[/tex]

Putting in Eqn 1;

[tex]x=3(102)\\x=306[/tex]

Kyle has $306 in his account.

The right answer is Option D.

Keywords: Linear equations, division

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Answer:

5,813 HP

Step-by-step explanation:

P=f*v

f=1/2*p*v^2*C*A

HP=(f*v)/550

Answer:

He needed 3747.61 HP to reach 400 mph.

Step-by-step explanation:

Given data :

P (air density)  =  0.0019 slug/ft³

A (Area)  = 26.72 ft²

C(d) = 0.398

crr = 0.015

V = 400 mph = 587 ft/sec = 178.92 m/sec

weight = 2019 lb = 8980.96 N    [1 pound = 4.44822 N]

[tex]P=\frac{Force\times Displacement}{Time}[/tex]

P =  Force × Velocity = FV

F = F(sum) = F(drag) + F(rolling resistance)

F(drag) = [tex]\frac{1}{2}P\times V^2\times C(d)A[/tex]

F(rolling resistance) = weight × crr

[tex]HP=\frac{P}{1hp}[/tex]   1hp = 745.7 watts

F(drag) = [tex]\frac{1}{2}P\times V^2\times C(d)A[/tex]

[tex]=\frac{1}{2}\times 0.0019\times 587^{2} \times 0.398\times 26.72[/tex]

= 3481.23  [tex]\frac{slug\times ft}{sec^2}[/tex]

convert  [tex]\frac{slug\times ft}{sec^2}[/tex]  to  [tex]\frac{kg\times m}{s^2}[/tex]

1 slug = 14.5939 kg

1 ft = 0.3048 m

[tex]\frac{slug\times ft}{sec^2}[/tex] = 14.5939 × 0.3048 = 4.448 [tex]\frac{kg\times m}{s^2}[/tex]  or newton

Since F(drag) = 3481.23 × 4.448 N

                      = 15484.51 N

P = F(drag) × V

   = 15484.51 × 178.92 N m/s

   = 2770488.529 watts

F rolling resistance = crr × w

                               = 0.015 × 8980.96 N

                               = 134.714 N

Power = (Fdrag + Frolling resistance) × V

            = (15484.51 + 134.714) × 178.92

            = 15619.224 × 178.92

            = 279459.558 watts

Power in HP

[tex]HP=\frac{P}{hp}[/tex]

[tex]=\frac{279459.558}{745.7}[/tex]

= 3747.61 HP

He needed 3747.61 HP to reach 400 mph.

Answer:

The answer to this question is it took him an hour and 27 minute

Answer:

the answer is b

Step-by-step explanation:

Answer:

It's D

Step-by-step explanation:

-3+y=23

To write the equation in standard form, distribute and rearrange the terms. The equation is 3x + y = 23.

To write the equation y - 2 = -3(x - 7) in standard form, we need to expand the expression and rearrange the terms. Starting with the given equation, we can distribute the -3 to the terms inside the parentheses: y - 2 = -3x + 21. Next, we can move the -3x term to the left side of the equation by adding 3x to both sides: 3x + y - 2 = 21. Finally, we can move the constant term (-2) to the right side of the equation by adding 2 to both sides: 3x + y = 23. Therefore, the equation in standard form is 3x + y = 23 (Option D).

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Answer:

If 3 boxes equals $12.00 then 1 box equals $4.00

Step-by-step explanation:

You divide 3 boxes by 3 and 12 dollars by 3 to get 1 box equals 4 dollars

Answer:You have 3 boxes that all cost $12.00. So to find the total of each box you divide $12 by 3 boxes of cookies 12/3=$4.00 each

Step-by-step explanation:

Answer:

ballpoint pen and banana

Step-by-step explanation:

Answer:

We Know, Area = Length * Width

Here, A = 3

W = 1/2

Substitute it into the expression,

3 = L * 1/2

L = 3/ 1/2

L = 3/2 ft²

So, the length of the rectangle would be 3/2 ft²

Hope this helps! :)

The length of the rectangle is found to be 6 feet by using the formula for the area of a rectangle and solving for length.

To compute the length of the rectangle, we need to use the formula for the area of a rectangle which is length times width. Given that the area is 3 square feet and the width is 1/2 foot, we can set up the equation length * 1/2 = 3 square feet. From here, solve for length by dividing both sides of the equation by 1/2.

Therefore, the length of the rectangle is 6 feet.

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Answer:0.17857

Step-by-step explanation:

Step  1  :

           434

Simplify   ———

           25  

Equation at the end of step  1  :

 31   434

 —— ÷ ———

 10   25  

Step  2  :

           31

Simplify   ——

           10

Equation at the end of step  2  :

 31   434

 —— ÷ ———

 10   25  

Step  3  :

        31      434

Divide  ——  by  ———

        10      25  

3.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

31     434       31      25

——  ÷  ———   =   ——  •  ———

10     25        10     434

Final result :

  5            

 —— = 0.17857  

 28          

Answer:

5 = 0.17857

28

Step-by-step explanation:

Change the decimals into fractions.

31   ÷   434

10          25

*They were simplified from their natural fractions.

To divide fractions, write the division as multiplication by the reciprocal of the divisor.

31  ×   25

10       434

Simplify by the greatest common factor.

775  ÷ 155  =  5

4340  ÷ 155     28

Answer:

Yes to both.

Step-by-step explanation:

Similar means the same shape but the sizes may be different.

Right angles are similar and so are equilateral triangle.

Right triangles are not necessarily similar unless they have the same hypotenuse and an acute angle. All equilateral triangles are similar because they have equal angles and sides. This discussion relates to the nature of mathematical truths, which are absolute in their systems, compared to observational truths that rely on variable sensory evidence.

Not all right triangles are similar because they can have different ratios between their sides despite having a right angle. However, if two right triangles have the same length of their hypotenuse and an acute angle correspondingly, they are indeed similar according to a mathematical corollary.

In contrast, all equilateral triangles are similar because they all have equal angles (60 degrees each) and their side lengths are also in the same ratio, which is 1:1:1, making them the same shape, although they can be different sizes.

This connects to the larger questions about mathematical truths. For instance, the statement that the three interior angles of a triangle are equivalent to two right angles is a mathematical truth that is similar to definitional truths, such as 'green is a color,' since both are based on definitions and logical deductions in their respective systems.

However, mathematical truths differ from observational truths like 'there is beer in the refrigerator' because observational truths are subject to sensory evidence which can change, whereas mathematical truths are absolute within the context of their axiomatic systems.

When considering questions that lead to insights into forms, mathematical questions are often better suited over observational ones as they transcend physical reality and provoke a more abstract level of reasoning.

Answer:

25

Step-by-step explanation:

Subtract 17 from 42.

Answer:

42-17=25

Step-by-step explanation:

just subtract 17 from 42

Answer:

2400 milliliters of soup

Step-by-step explanation:

8*300=2400

Final answer:

The average speed of the freight train is found by dividing the distance traveled, 1445 miles, by the time taken, 25 hours, resulting in an average speed of 57.8 mph.

Explanation:

To calculate the average speed of the freight train, we divide the total distance traveled by the time it took to cover that distance. The train travels 1445 miles in 25 hours.

The formula for average speed is:

average speed = total distance / total time

Therefore, the average speed of the train is:

average speed = 1445 miles / 25 hours = 57.8 miles per hour (mph)

Answer:

Step-by-step explanation:

total purchase price = 32*300 = 9600

total selling price = 20*300 = 6000

Net capital loss =total purchase price- total selling price =9600-6000 =  3600. Purchase price of one share is 32

Selling price of one share is 20

Number of shares bought are 300                                                                           Net % loss = (3600*100)/9600=37.5%

Final answer:

The total loss from buying and then selling 300 shares of General Motors stock, which fell from $32 to $20 per share, is $3600. Expressed as a percent of the purchase price, the loss is 37.5%.

Explanation:

To calculate the loss when buying and selling shares, we first find the loss per share and then multiply by the total number of shares. For General Motors, the price fell from $32 per share to $20 per share. This results in a loss of $12 per share. If you bought and sold 300 shares at these prices, your total loss would be:

Loss per share = $32 - $20 = $12

Total loss = $12 × 300 shares = $3600.

To express this loss as a percent of the purchase price:

Loss Percentage = (Loss per share / Purchase price per share) × 100

Loss Percentage = ($12 / $32) × 100 = 37.5%.

Answer:

None.

Step-by-step explanation: 3x does not have the same coefficient as 2y or 7

Answer:

Usally the fastest method to calculating a problem is to do it in your head. With enough practice your brain will be faster then most tools, ganing efficiency with practice.

Answer:

Step-by-step explanation:

In your head:

5 * 7 = 35  so its 5 point something with remainder 5.

7*7 = 49 so its  5.7 approximately.

Answer:16

I think this is the answer

Answer:

10.91

Step-by-step explanation:

The sum of the first 50 terms in this geometric series is 11.00.

When all the terms of a geometric sequence are added, then that expression is called geometric series.

Lets suppose its initial term is f=a , multiplication factor is  r

and let it has total n terms, then, its sum is given as:

[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]

(sum till nth term)

We are given that;

n=50

Series=  1+10/11+100/121

Now,

To find the sum of the first 50 terms in this geometric series, we need to use the formula:

Sum = [tex]a1(1 - r^n) / (1 - r)[/tex]

where a1 is the first term, r is the common ratio, and n is the number of terms. We can identify that the first term is 1, the common ratio is 10/11, and the number of terms is 50. Plugging these values into the formula, we get:

Sum = 1(1 - (10/11)^50) / (1 - 10/11) Sum = (1 - 0.000000000000000000000000000000000000000000000001) / (1/11) Sum = (0.9999999999999999999999) / (0.09090909) Sum = 10.99998

Rounding this result to two decimal places, we get:

Sum = 11.00

Therefore, by the given geometric sequence the answer will be 11.00.

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Answer:

The total cost  of the bill = $36.146

Step-by-step explanation:

Here, the total amount  of the bill = $28.35

Now, the amount of tip = 20%

So, calculating 20% on the bill amount, we get

[tex]\frac{20}{100} \times 28.35  =  5.67[/tex]

or, the amount of 20% tip = $5.67

So, the total bill amount  after 20% tip = Bill Amount + Tip

= $28.35 + $5.67 =  $34.02

Now, the tax is calculated on the amount of  bill $34.02.

[tex]\frac{6.25}{100} \times 34.02  =  2.126[/tex]

or, the amount of tax on the bill = $2.126

So, the total bill amount  after 6.25% tax  = Bill Amount + Tax

=  $34.02 + $2.126 = $36.146

Hence, the total cost  of the bill = $36.146.

Answer:3.80000000000

Step-by-step explanation:

Answer:

$763

Step-by-step explanation:

i got it right on my test

Answer: (1,8) (2,16) (3,24)

Step-by-step explanation:

Because if it takes Trixie 8 minutes per mile then the ratio would be 1:8 and that means every mile you add 8 minutes.

Answer:

15 feet of fencing costs $27

Step-by-step explanation:

We know 15/20 = 3/4 so...

36 x 3/4 = 27

Another way:

36 divided by 20 = 1.8

1.8 x 15 = 27

answer:

$24

Step-by-step explanation:

36 divided by 15 equals 2.4 then 2.4x5 secne 15 is 5 away from 20 equals 12 then 36 - 12 = 24

Answer:

1

Step-by-step explanation:

Answer:

x=30/7

Step-by-step explanation:

7x+12+3x=-6(x-7)+9x

10x+12=-6x+42+9x

10x+12=3x+42

10x-3x+12=42

7x+12=42

7x=42-12

7x=30

x=30/7

Answer:

985 students in the district participate in the school music program.

Step-by-step explanation:

2/5=0.4

394/0.4=985

15%×60=

=15×60/100

=900/100

=9

Answer:

9

Step-by-step explanation:

15/100 = 60/x

Cross Multiply...

100x = 15*60

100x = 900

x = 900/100

x = 9