The area of any rectangular shape is given by the product of its width and length. If the area of a particular
rectangular garden is given by A = 15x°-35x and its width is given by 5x, then find an expression for the
garden's length.

Answer:

x³ - 4x² + 2x + 4 = 0

Here's how I solved this:

You start off by rewriting the zeros into factors:

1 - √3    →    x = 1 - √3    →    (x - 1 - √3)

  2        →    x = 2           →    (x - 2)

1 + √3   →    x = 1 + √3   →    (x - 1 + √3)

Now you want to multiply the factors together:

     (x - 1 - √3) · (x - 2) · (x - 1 + √3)

- Multiply the first two factors together -

                (x - 1 - √3) · (x - 2)

                              ↓

    (x · x - x · 2 - √3 · x + √3 · 2 - x + 2)

   - Combine like terms and simplify -

    (x · x - x · 2 - √3 · x + √3 · 2 - x + 2)

                              ↓

          (x² - 3x - √3 · x + 2√3 + 2)

      - Now multiply the third factor -

   (x² - 3x - √3 · x + 2√3 + 2)(x - 1 + √3)

                              ↓

(x² · x + x² · √3 - x² - 3x · x - 3x · √3 + 3x - √3 · xx - √3 · x · √3 +√3 · x + 2 · √3 · x + 2 · √3 · √3 - 2 · √3 + 2x + 2 · √3 - 2)

                              ↓

(x³ + x² · √3 - x² - 3x² - 3x · √3 + 3x - √3 + 3x - √3 * x² - x · 3 + √3 · x + 2 · √3 · x + 2 · 3 - 2 × √3 + 2x + 2 √3 - 2)

   - Combine like terms and simplify -

(x³ + x² · √3 - x² - 3x² - 3x · √3 + 3x - √3 + 3x - √3 * x² - x · 3 + √3 · x + 2 · √3 · x + 2 · 3 - 2 × √3 + 2x + 2 √3 - 2)

                              ↓

                 x³ - 4x² + 2x + 4

--------------------------------------------------------------------------------------------------------------

And there we get our solution: x³ - 4x² + 2x + 4  

Answer:

Below in bold.

Step-by-step explanation:

1. 165/3.3 = 50 meters/second.

2. In 4 seconds the skydiver will fall 4*50 = 200 meters.

Answer:

Step-by-step explanation:

Simplified this is 9 :)

Answer:

7.5minutes

Step-by-step explanation:

If it travels 2kilometers every 3 min, that means it travels 2/3 kilometer per minute. Then divide 5 kilometers by 2/3kilometers/min, which gets you 7.5minutes

Answer:

D 280

Step-by-step explanation:

Pythagoras theorem

Answer:

a

Step-by-step explanation:

LN=√19＾2 - 9＾2

=√361 - 81

=√280

Answer:

x = 84 y = 59°

Step-by-step explanation:

x = (40/30)×63

x = 84

∆ABC = ∆PQR

so y = 59°

Answer:

1.) 47

2.) 28

Step-by-step explanation:

you just had to use the sin equation for both

Answer:

13.6

Step-by-step explanation:

The distance Jen is from the base of the lighthouse is 86.6 meters.

Trigonometric ratio is used to show the relationship between the sides of a and angles of a right angled triangle.

Let d represent the distance Jen is from the base of the lighthouse.

Using trigonometric ratios:

[tex]tan(30)=\frac{50}{d} \\\\d=\frac{50}{tan(30)} \\\\d=86.6\ m[/tex]

The distance Jen is from the base of the lighthouse is 86.6 meters.

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Answer: look at explanation

Step-by-step explanation:

1st question: 48 / 60 = 80 %

2nd : 1/4 of 60 = 15 people

3rd : If 60% is 48 miles, than 10% is 8 miles. Therefore, 100% (his goal) = 80 miles.

4th: 1/4 of 88 = £22

Answer:

4th option

Step-by-step explanation:

7x(8x² - 4y² + 3y - 5) ← multiply each term in the parenthesis by 7x

= 56x³ - 28xy² + 21xy - 35x

The expression in the expended version will be equal to 56x³ - 28xy² + 21xy - 35x. Hence, option D is correct.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the given expression,

7x (8x² - 4y² + 3y - 5)

Solve the equation by multiplying 7x with the bracket,

56x³ - 28xy² + 21xy - 35x

To know more about the expression:

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Answer:

Option B,option D and option F are the correct statements.

[tex]\boxed{\boxed{\Large \text{Ted will run 60 kilometres in 285 minutes.}}}[/tex]

Using the distance-time-speed relationship:

[tex]\boxed{\Large \text{speed = $\frac{\rm distance}{\rm time}$}}[/tex]

[tex]\boxed{\Large \text{distance = speed $\times$ time}}[/tex]

[tex]\boxed{\Large \text{time = $\frac{\rm distance}{\rm speed}$}}[/tex]

so if Ted can run 20 kilometres (distance) in 95 minutes (time), then his speed = 20 ÷ 95 = 4/19 km/min.

Using this result, to calculate how far Ted will run in 285 minutes, we can say that distance = 4/19 × 285 = 60 kilometres.

∴ Ted will run 60 kilometres in 285 minutes.

[tex]\hrulefill[/tex]

To learn more about speed:

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Answer:

1 1/2 pound

Step-by-step explanation:

If each coin weighs 3/4 ounces and she picked up 6 then you do 3/4 x 6/1 which equals 18/4 and since there is 16 ounces in a pound it simplifies to 1 2/4 or 1 1/2 pounds

Answer:

alr yeah i get it now

Step-by-step explanation:

its A 11/14

Answer:

[tex]\frac{11}{14}[/tex]

Step-by-step explanation:

[tex]\frac{2}{7}[/tex] + [tex]\frac{7}{14}[/tex]

Before adding er require the fractions to have the same denominators.

Multiply the numerator/ denominator of the first fraction by 2

= [tex]\frac{2(2)}{7(2)}[/tex] + [tex]\frac{7}{14}[/tex]

=[tex]\frac{4}{14}[/tex] + [tex]\frac{7}{14}[/tex]  ( now add numerators leaving the common denominator )

= [tex]\frac{4+7}{14}[/tex]

= [tex]\frac{11}{14}[/tex]

Answer:

Step-by-step explanation:

Circumference=72

pi=3.14

Radius=C /2π

72/6.28=11.4649681529

Rounded to the whole would be 11

=11

Answer:

4 fluid ounces

Step-by-step explanation:

A waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of 5 mugs from a full pot of coffee. If her coffee pot holds 8 cups, how many fluid ounces does she have left?

Remember

8 fluid ounces = 1 cup.

First you need to do find out how many fluid ounces she poured in total.

So do,

5 mugs × 12 fluid ounces.

which is 60 fluid ounces.

Now that you now that you need to convert 8 cups into fluid ounces.

Like I said at the top 8 fluid ounces = 1 cup.

So you need to do,

8 cups × 8 fluid ounces.

Which is 64 fluid ounces she can hold in her coffee pot.

Now you subtract,

64 fluid ounces - 60 fluid ounces.

Which is 4 fluid ounces left in her coffee pot.

The number of fluid ounces she has left is 4 fluid ounces if the waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of the 5 mugs from a full pot of coffee.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

It is given that:

A waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of 5 mugs from a full pot of coffee.

Let x be the number of fluid ounces she has left.

4 fluid ounces

As we know,

8 fluid ounces = 1 cup

The total amount of coffee = 5×12

The total amount of coffee = 60

Total amount = 8 cups × 8 fluid ounces.

x = 64 fluid ounces - 60 fluid ounces.

x = 4 fluid ounces

Thus, the number of fluid ounces she has left is 4 fluid ounces if the waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of the 5 mugs from a full pot of coffee.

Learn more about the unit conversion here:

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Answer:

3

Step-by-step explanation:

Answer:

Here is your answer hope I helped! <3

Step-by-step explanation:

t=k/3-p/3

Answer:

C. A rate with one (1) in the denominator

A unit rate is basically a ratio of something to one.

example:

if 10 bananas costs ten dollars then one banana would cost one dollar.

Step-by-step explanation:

Answer:

A.  A rate with one in the numerator

Step-by-step explanation:

We can find the unit rate when given a rate by dividing the unit in the numerator by the quantity in the denominator. For example, if we are given the rate $4.50/5 gallons of milk, we can divide 4.50 by 5 to find the unit price, which is dollars per one gallon of milk. A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

Answer:

155°

Step-by-step explanation:

We know that the sum of the sections must be 360°. So, by removing a section of 75° he leaves the paper circle with a section of 185°, then removes another 130° section, leaving the last section of 155°.

Answer:

b) you need one set of | | for the inside of the logarithm only.

c) pi^2 /56

Step-by-step explanation:

For b, you just need | | instead of ( ) for the inside of the natural logarithm part... .

For c...

Integral( arcsin(7/6x)/sqrt(36-49x^2),x=0..6/7).

Lets go ahead and fix up the the denominator so the multipler on x is the same as it is in numerator.

Factor our sqrt(36) on bottom. Note sqrt(36)=6.

1/6Integral(arcsin(7/6x)/sqrt(1-(7x/6)^2),x=0..6/7)

Let 7/6x=sin(v). Then 7/6 dx=cos(v) dv.

If x=0 then we solve 7/6(0)=sin(v) giving us v=0. Note sin(0)=0.

If x=6/7 then we solve 7/6(6/7)=sin(v) giving us v=pi/2. Note sin(pi/2)=1...and I chose this particular value for v so the sine curve didn't have a chance to make a new or start a new cycle.

1/6×6/7Integral(v/sqrt(1-(sinv)^2) cos(v)),v=0..pi/2)

Next step invokes the Pythagorean Identity sin^2(v)+cos^2(v)=1:

1/7Integral(v/cos(v) cos(v), v=0..pi/2)

1/7Integral(v, v=0..pi/2)

1/7(v^2/2, v=0..pi/2)

1/7((pi/2)^2/2-(0)^2/2)

1/7(pi^2/4/2)

1/7(pi^2/8)

pi^2/56

Answer:

(-4,-5)

Step-by-step explanation:

The coordinates of the midpoint for x = sum of x/2=2

The coordinates of the midpoint for y = sum of y/2=-2

firstly to work out x coordinate:

[tex] \frac{x + 8}{2} = 2[/tex]

rearrange to find x which is -4

work out y coordinate:

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

rearrange to find y which is -5

so coordinates are (-4,-5)

Answer:

I would say either pic 2 or four.

Step-by-step explanation:

Hopes This Helps

Answer:

E= 0 Good luck answering the other questions :)

Step-by-step explanation:

Answer:

11 11/12

Step-by-step explanation:

Answer:

≈ 12

Step-by-step explanation:

To estimate, we'll round these mixed numbers to the nearest whole number, then multiply. Let's start with 4 1/3. 4 1/3 is closest to 4, since 1/3 is smaller than 1/2. Then, we can look at 2 3/4. This mixed number is closest to 3, since 3/4 is greater than 1/2.

Now, the two numbers we have are 4 and 3. What is 4 × 3? Well, that's pretty simple - the answer is 12. So, 4 1/3 × 2 3/4 ≈ 12. Hopefully that's helpful! :)

Answer:

12.4

Step-by-step explanation:

Answer:

1. decrease by 8%

2. decrease by 11%

3. increase by 8%

4. increase by 11%

Step-by-step explanation: