Easy math problem.....

Answer:

width = (21 - 2n) ÷ 2 or 21/2 - n

Step-by-step explanation:

To find Width

let's say width is x

so 2x + 2n = 21

take away 2n from both sides

then 2x = 21 - 2n

Divide both sides by 2 to get x on its own

x = 21 - 2n /2

therefore the width of the rectangle is 21 - 2n /2

Given :

To find :-

Solution :-

First term :-

Second term :-

Third term :-

The height of the escalator is as calculated using trigonometric ratios.

We know that in a right angled triangle the trigonometric ratios are

tan θ = perpendicular ÷ base

For a right angled triangle the tanθ is defined as the ratio of the perpendicular to the base of the triangle . The side opposite the angle θ is the perpendicular and the side adjacent to the θ is the base .

Now it is given that for every 2 feet vertically moved the horizontal distance moved is 3 feet.

Now using the trigonometric ratio of tanθ

tan θ = 2 / 3

Now we will use this ratio to calculate the vertical height for horizontal movement of 90 feet .

Now, the height is given as h .

∴ tan θ = h / 90

or, 2 / 3 = h / 90

or, h = 60 feet

Therefore the height of the escalator is 60 feet.

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Answer:

A

Step-by-step explanation:

The answer is A

The roots of the given quadratic equation are -

x = 2   and   x = 1.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is a quadratic function f(x) defined as -

f(x) = x³ - 3x² + 2

The given quadratic function f(x) is -

f(x) = x³ - 3x² + 2

We can write the roots of the equation as -

x = {3 ± √(9 - 8)}/2

x = {3 + √(9 - 8)}/2    and    {3 - √(9 - 8)}/2

x = (3 + 1)/2   and    x = (3 - 1)/2

x = 2   and   x = 1

Therefore, the roots of the given quadratic equation are -

x = 2   and   x = 1.

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Answer:

40% are boys

Step-by-step explanation:

sum the parts of the ratio, 2 + 3 = 5 parts

Divide number in class by 5 to find value of one part of ratio

30 ÷ 5 = 6 ← value of 1 part of the ratio, then

2 parts = 2 × 6 = 12 ← number of boys in class

percentage = [tex]\frac{boys}{total}[/tex] × 100%

                   = [tex]\frac{12}{30}[/tex] × 100%

                  = 0.4 × 100% = 40%

Answer:

40%   simplify the fraction then divide (boys/total)  then multiply by 100

Step-by-step explanation:                                                                                   2+3 = 5 is the distributer then :                                                                             30/5 = 6  then if 2 are boys  2 x 6 = 12 is the amount of boys                       12/30 = 2/5  simplified and then x 100 to fraction's to find percentage           2/5  x 100 =  40%                                                                                                            

Step-by-step explanation:

1) 3x(6x+5)

= 18x+15x

= 33x Answer

2) 4x(2x-3y)

= 8x-12xy Answer

Cannot be solved because it has unlike terms

Answer:

-1/10

Step-by-step explanation:

-7/24 by the reciprocal of 35/12

The reciproical of 35/12 is 12/35

-7/24 * 12/35

Rewriting

-7/35 * 12/24

-1/5 * 1/2

-1/10

Answer:

Step-1 : Multiply the coefficient of the first term by the constant   1 • 7 = 7  

Step-2 : Find two factors of  7  whose sum equals the coefficient of the middle term, which is   -8 .

     -7    +    -1    =    -8    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  -1  

                    x2 - 7x - 1x - 7

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-7)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-7)

Step-5 : Add up the four terms of step 4 :

                   (x-1)  •  (x-7)

            Which is the desired factorization

Step-by-step explanation:

x = 7 or 1

Answer:

Progression in increments of value 12

Step-by-step explanation:

13 25 37 49 61 73 85 97 .....

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Miss Hawaii

Answer: x=9

Explanation:

8x-13=59

8x-13+(13)=59+(13)

simplify add the numbers

8x=72

Divide both sides of the equation by the same term

8x=72

8x/8=72/8

Simplify

Cancel terms that are in both the numerator and denominator

Divide the numbers

x=9

Answer:

Let P(t) = population t years after 2010

           = 45230e0.02t

Population in 2030 = P(20)

                           = 45230e0.4≈ 6747

Answer:

5

Step-by-step explanation:

Answer:

5 centimeters

Step-by-step explanation:

leaf is 11cm, catepillar is 6.... 11-6=5

Answer:

65 + 5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

5(13 + [tex]\sqrt{2}[/tex]) ← multiply each term in the parenthesis by 5

= 65 + 5[tex]\sqrt{2}[/tex]

the answer is 160% because 1.6×100=160%

Answer:

The area is 49/12 or 4 1/12

Step-by-step explanation:

The area of a triangle is:

a = 1/2 × base × height

a = 1/2 × 3 1/2 × 2 1/3 (4 2/3 is not the height!)

a = 1/2 x 7/2 x 7/3 (I converted all the fractions into improper fractions)

a = 49/12 (1 × 7 × 7 = 49, 2 × 2 × 3 = 12)

You can convert it back to a mixed number:

49/12 = 4 1/12

Hope this helps!

Answer:

-6r^2 + 10

Step-by-step explanation:

2 × 3 + 4 - 6r^2

= 6 + 4 - 6r^2

= -6r^2 + 10

Answer:

- 6r² + 10

Step-by-step explanation:

```````````````````````````

2 × 3 + 4 - 6r²

→ 6 + 4 - 6r²

→ 10 - 6r²

→ - 6r² + 10

```````````````````````````

Answer:

4/3

Step-by-step explanation:

Answer:

The answer is 4/3.

In the United States, the Interstate Highway standards for the Interstate Highway System use a 12 ft (3.7 m) standard lane width, while narrower lanes are used on lower classification roads. In Europe, laws and road widths vary by country; the minimum widths of lanes are generally between 2.5 to 3.25 m (98 to 128 in).

Answer:

9

Step-by-step explanation:

.9*10=10

it's basically simple multiplication with a decimal

Step-by-step explanation:

Miami is approximately 1,054 mi away from Washington DC. assuming the Cortez family is driving in a straight line the time they will be on the road is

[tex]let \: h = hrs[/tex]

[tex] 1054mi \div \frac{55mi}{h } \\ \frac{1054mi}{1} \times \frac{h}{55mi} \\ = \frac{1054mi(h)}{55mi} [/tex]

The miles unit, mi cancels and leaves us with hours, h

[tex] \frac{1054 \: h}{55} \: \: \: \: is \: approx. \: \: \: \: 19.16 \: \: hrs[/tex]

Answer:

54%

Step-by-step explanation:

Answer:

(ii) 1 dollar

Step-by-step explanation:

each pencil costs 17 cents

- thus 3 pencils x 17c is 51c

1.00 dollars minus 0.51 is 49

- 5 pencils x 17c is equal to 85

1.00 dollars minus 0.85 is 15 c

Answer:

12

thStep-by-step explanation:

Answer:

y=-2x+1

Step-by-step explanation:

Just look at photo dap

Answer:

lol

Step-by-step explanation:

to get x in quadratic equations, factor it

Answer: I would say 4

Step-by-step explanation:

Answer:

There are more factories in the city than in the country.

Step-by-step explanation:

Hope this helps!

Step-by-step explanation:

One leg is x, the second leg is 2x and the hypotenuse is:

Perimeter is:

The sides are:

The formula for the circumference of a circle is C = 2πr, where r is the radius and C is the circumference. The equation solved for r is r =c/π2 .

Answer:

A

Step-by-step explanation:

The graph below could be the graph of A) F(x) = 2*[tex](0.7)^x[/tex] exponential function.

The graph of the function F(x) = 2 * [tex](0.7)^x[/tex] is a decreasing exponential function. This is because the base of the exponent, 0.7, is between 0 and 1. As x increases, the value of [tex](0.7)^x[/tex] decreases, so the value of F(x) decreases.

The graphs of the other functions are all increasing exponential functions. This is because the bases of the exponents, 2, 5, and 1.4, are all greater than 1. As x increases, the value of [tex]2^x[/tex], [tex]5^x[/tex], and [tex]1.4^x[/tex] increases, so the value of the functions F(x) = 2 * [tex]2^x[/tex], F(x) = 2 * [tex]5^x[/tex], and F(x) = 2 * [tex]1.4^x[/tex] increases.

Therefore, the graph of the function F(x) = 2 * [tex](0.7)^x[/tex] is the only graph that is decreasing. So the answer is A.

Here is a table that summarizes the properties of the graphs of the four functions:

Function Base of the exponent Graph

F(x) = 2 * [tex](0.7)^x[/tex] 0.7 (between 0 and 1) Decreasing

F(x) = [tex]2^x[/tex] 2 (greater than 1) Increasing

F(x) = 2 * [tex]5^x[/tex] 5 (greater than 1) Increasing

F(x) = 2 * [tex]1.4^x[/tex]  1.4 (greater than 1) Increasing

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