The perimeter of a rectangle is 35 cm. The rectangle's area (in sq. cm) as a function of its length (in cm) is graphed.

What is the approximate average rate at which the area decreases, as the rectangle's length goes from 13 cm to 16 cm?


Options:
1: 10 1/3
2: 10 2/3
3: 11
4: 11 1/3

Answer:

[tex]BC=12.8,\\AC=15.1[/tex]

Step-by-step explanation:

In right triangles only, the tangent of an angle is equal to its opposite side divided by its adjacent side.

Therefore, we have the following equation:

[tex]\tan 58^{\circ}=\frac{BC}{8}[/tex]

Solving, we get:

[tex]BC=8\tan 58^{\circ}\approx \boxed{12.8}[/tex]

Also in right triangles only, the cosine of an angle is equal to its adjacent side divided by the hypotenuse of the triangle.

[tex]\cos 58^{\circ}=\frac{8}{AC},\\AC=\frac{8}{\cos 58^{\circ}},\\AC\approx \boxed{15.1}[/tex]

We can also use the Pythagorean theorem now that we've found BC. However, if you choose to do so, make sure you don't use a rounded value for BC, as that could cause a notable deviation in your final answer.

Using the Pythagorean theorem to verify our answers:

[tex]8^2+(8\tan 58^{\circ})^2=\left(\frac{8}{\cos 58^{\circ}}\right)^2\:\checkmark[/tex]

Answer:

square root of 15 is the answer

Step-by-step explanation:

Answer:It's 1

Step-by-step explanation:

Answer:

the distance is 9.1 inches (please give brainliest)

Step-by-step explanation:

we must use the pythagorean theorem:

5.7^2 + 7.1^2 = c^2

(c being the distance being the two corners)

c^2 = 82.9

c = sqrt(82.9) ≈ 9.1

Answer:

2 2/3 kilometers

Step-by-step explanation:

t = 3y

let t = 8

8 = 3y

Divide each side by 3

8/3 = 3y/3

8/3 = y

2 2/3 kilometers

Answer:

2 2/3 kilometers

Step-by-step explanation:

Step-by-step explanation:

[tex]A = x^2-xy+y^2\\C =x^4+x^2y^2+y^4[/tex]

We will now divide C with A.

[tex]\frac{x^4+x^2y^2+y^4}{x^2-xy+y^2}[/tex]

Divide x^2, -xy, y^2. Remember that dividing exponents results in subtracting.[tex]x^4 / x^2 = x^2\\4 - 2 = 2[/tex]

So:

[tex]\frac{1}{x^2+xy+y^2}[/tex]

Answer:

arts: movement and flexibility  Music: communication and rhythm

Answer: 17%

Step-by-step explanation: 4/25=16/100=16%, so 17% is bigger.

Answer:

gimme pints

Step-by-step explanation:

Answer:

[tex]f = \frac{720}{11}[/tex]

Step-by-step explanation:

Given

[tex]f\ \alpha\ \frac{\sqrt T}{L}[/tex] --- The variation

[tex]f = 60; T = 121; L = 12[/tex]

Required

Find f, when T =81; L = 9

We have:

[tex]f\ \alpha\ \frac{\sqrt T}{L}[/tex]

Express as equation

[tex]f = k\frac{\sqrt T}{L}[/tex]

Make k the subject

[tex]k = \frac{fL}{\sqrt T}[/tex]

When [tex]f = 60; T = 121; L = 12[/tex]

[tex]k = \frac{60 * 12}{\sqrt {121}}[/tex]

[tex]k = \frac{60 * 12}{11}[/tex]

[tex]k = \frac{720}{11}[/tex]

To solve for f, when T =81; L = 9

We have:

[tex]f = k\frac{\sqrt T}{L}[/tex]

[tex]f = \frac{720}{11} * \frac{\sqrt{81}}{9}[/tex]

[tex]f = \frac{720}{11} * \frac{9}{9}[/tex]

[tex]f = \frac{720}{11} * 1[/tex]

[tex]f = \frac{720}{11}[/tex]

Answer:

x =417.6

Step-by-step explanation:

0.5x+78.2=287

Subtract 78.2 from each side

0.5x+78.2-78.2=287-78.2

.5x =208.8

Divide each side by .5

.5x/.5 = 280.8/.5

x =417.6

Answer:

1 sample

Step-by-step explanation:

There is only one sample given for 20%

Answer:

the answer would be

b) 1 sample

Answer:

x=25, 120

Step-by-step explanation:

The two angles form a straight line so they add to 180

60 + 4x +20 =180

Combine like terms

4x+80 = 180

Subtract 80 from each side

4x+80-80 =180-80

4x= 100

Divide by 4

4x/4 =100/4

x= 25

The exterior angle is

4x+20 = 4*25+20 =100+20 =120

Answer:

x=25, 120

Step-by-step explanation:

The two angles form a straight line so they add to 180

60 + 4x +20 =180

Combine like terms

4x+80 = 180

Subtract 80 from each side

4x+80-80 =180-80

4x= 100

Divide by 4

4x/4 =100/4

x= 25

The exterior angle is

4x+20 = 4*25+20 =100+20 =120

Answer:

x = 2

Step-by-step explanation:

Given a line parallel to a side of a triangle and intersecting the other 2 sides then it divides those sides proportionally, that is

[tex]\frac{6}{x+1}[/tex] = [tex]\frac{4}{x}[/tex] ( cross- multiply )

6x = 4(x + 1)

6x = 4x + 4 ( subtract 4x from both sides )

2x = 4 ( divide both sides by 2 )

x = 2

The only table that represents a function is the fourth option.

A function is a relation that maps elements from a set (domain) into elements of another set (range).

Such that each element from the domain can be mapped into only one element from the range.

In the table, the "x" values are from the domain, and the "y" values are from the range.

So, if you see a table with the same value of x being mapped into two different values of y, then that relation is not a function.

With that in mind, the only table that meets this property is table number 4.

If you want to learn more about functions, you can read:

https://brainly.com/question/1770447

Answer:

12 centimetres

Step-by-step explanation:

I looked it up

- 8 / 20 = y / - 4

y = - 4 × - 8 / 20

y = 4 × 8 / 4 × 5

y = 8 / 5

Answer:

11 is the missing number

Answer:

the answer should be 11 your welcome

Answer:

1. 30 desserts

2.42,000

Answer:

0.3

Step-by-step explanation:

When we divide by 10, we want to imagine a decimal point going up a place.

Think of it like this:

03.0

When we divide by 10, the decimal goes up a digit:

0.30 or 0.3

Answer:

(0,3) is the x intercept

(3,0) is the y intercept

Step-by-step explanation:

When it has 0 that means its directly on the line, since x is 0 on (0,3) that means the line is crossing the x intercept

Answer:

In summary, the translation and scale factor are:

Translation: (x,y)↦(x+5,y+4)

Scale factor: 2

Step-by-step explanation:

Answer:

[tex]Volume=56\frac{1}{4}[/tex] cubic feet

Step-by-step explanation:

Given

[tex]L =3\frac{3}{8}ft[/tex] --- Length

[tex]W =13\frac{1}{3}ft[/tex] --- Width

[tex]H =3\frac{3}{4}[/tex] --- Tank

[tex]Water\ level = \frac{2}{3}[/tex]

Required

Space not covered with water

If the water level is:

[tex]Water\ level = \frac{2}{3}[/tex]

Then the empty space is:

[tex]Empty = 1 - Water\ level[/tex] --- Complement rule

[tex]Empty = 1 - \frac{2}{3}[/tex]

Take LCM

[tex]Empty = \frac{3-2}{3}[/tex]

[tex]Empty = \frac{1}{3}[/tex]

So, the volume of the empty space is:

[tex]Volume=L*W*H*Empty[/tex]

[tex]Volume=3\frac{3}{8} *13\frac{1}{3}*3\frac{3}{4}*\frac{1}{3}[/tex]

Express fraction as improper fraction

[tex]Volume=\frac{27}{8} *\frac{40}{3}*\frac{15}{4}*\frac{1}{3}[/tex]

Simplify

[tex]Volume=\frac{9}{8} *\frac{40}{3}*\frac{15}{4}[/tex]

Simplify

[tex]Volume=\frac{3}{8} *\frac{40}{1}*\frac{15}{4}[/tex]

Simplify

[tex]Volume=\frac{3}{1} *\frac{5}{1}*\frac{15}{4}[/tex]

[tex]Volume=\frac{3*5*15}{4}[/tex]

[tex]Volume=\frac{225}{4}[/tex]

[tex]Volume=56\frac{1}{4}[/tex]

The Lewis dot model of an atom has three dots. The statement that is true about the atom is it has three valence electrons. The correct option is A.

Lewis dot model or Lewis structure is a method that was given by Gilbert N. Lewis. It was introduced in 1963. The model is made to put dots around the elements. These dots show the valence electron of the atoms. The model was extended by putting lines around the element.

If an atom has three dots around us, it means the element has three valence electrons. The element is lithium. Lithium has three electrons that are lone or valence, which means it can share and donate three electrons.

Thus, the correct option is A. It has three valence electrons regarding true about the atom.

Learn more about the Lewis dot model, here:

https://brainly.com/question/20300458

#SPJ5

Answer:

Step-by-step explanation:

Answer:

You must find the diameter then half it, so the radius, and then multiply it by 3.14152

Step-by-step explanation:

Answer:

#1

Shaded area:

#2

Shaded area:

219.75cm²

3.14cm²

Answer:

Solution given:

1.

[r]radius of each circle =32/8=4cm

[l]length of square=32cm

Area of shaded region =area of square- area of 16 circle=l²-11*πr²=32²-16*π*4²=219.75cm²

Step-by-step explanation:

radius for big circle [R]=2cm

radius for small circle [r]=1cm

area of shaded region=area of big semi circle -2 area of semi small circle

=½πR²-2*½πr²

=½*π*2²-π*1²

=2π-π

=π=3.14cm²

Answer:

6.34 years

Step-by-step explanation:

Given data

Principal P=$5,000

Rate r= 8%

Final amount A=  $8,303.00

The expression for the time will be

t= ln(A/P)/r

substitute

t= ln(8,303.00/5000)/0.08

t= ln(1.6606)/0.08

t= 0.507/0.08

t= 6.3375

Hence the time is about 6.34 years