The perimeter of a rectangle is 96 feet, and the width is 22 feet. What is the length of the rectangle?

Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here given that the value of,

[tex]\longrightarrow \cos\theta=\dfrac{3}{\sqrt{22}} \\[/tex]

And we know that cosine is the ratio of base and hypotenuse. Therefore,

[tex]\longrightarrow \cos\theta =\dfrac{b}{h} \\[/tex]

So we can also say that,

[tex]\longrightarrow \cos\theta = \dfrac{b}{h}=\dfrac{3}{\sqrt{22}}\\[/tex]

Let us take the given ratio to be 3x:√22x . Now we may find out the value of perpendicular using Pythagoras theorem . The Pythagoras theorem is ,

Pythagoras theorem:-

Mathematically,

[tex]\longrightarrow \boxed{ \boldsymbol{p^2+b^2=h^2}} \\[/tex]

where the symbols have their usual meaning.

On substituting the respective values, we have;

[tex]\longrightarrow p^2+(3x)^2=(\sqrt{22}x)^2 \\[/tex]

[tex]\longrightarrow p^2 = 22x^2-9x^2\\[/tex]

[tex]\longrightarrow p^2=13x^2 \\[/tex]

[tex]\longrightarrow \boldsymbol{ p = \sqrt{13}x} \\[/tex]

Now again , we know that, tangent is defined as the ratio of perpendicular and base. Therefore,

[tex]\longrightarrow \tan\theta = \dfrac{p}{b} \\[/tex]

[tex]\longrightarrow \tan\theta = \dfrac{\sqrt{13}x}{3x}\\[/tex]

[tex]\longrightarrow \boldsymbol{ \tan\theta = \dfrac{\sqrt{13}}{3}}\\[/tex]

Now we may use a identity which is ,

[tex]\longrightarrow\boxed{ \boldsymbol{ \tan (2x)= \dfrac{2\tan x}{1-\tan^2 x}}}\\[/tex]

On substituting the respective values, we have;

[tex]\longrightarrow \tan2\theta = \dfrac{ 2\tan\theta}{1- \tan^2\theta}\\[/tex]

[tex]\longrightarrow \tan2\theta = \dfrac{2\bigg(\dfrac{\sqrt{13}}{3}\bigg)}{1-\bigg(\dfrac{\sqrt{13}}{3}\bigg)^2 } \\[/tex]

[tex]\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{1-\dfrac{13}{9}} \\[/tex]

[tex]\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{\dfrac{9-13}{9}} \\[/tex]

[tex]\longrightarrow \tan2\theta = \dfrac{\dfrac{2\sqrt{13}}{3}}{\dfrac{-4}{9}} \\[/tex]

[tex]\longrightarrow \tan2\theta = -\dfrac{2\sqrt{13}\cdot 9}{3\cdot 4 } \\[/tex]

[tex]\longrightarrow \boxed{\boldsymbol{ \tan2\theta = -\dfrac{3\sqrt{13}}{2}}} \\[/tex]

This is the required answer .

Answer:

1895

Step-by-step explanation:

Answer:

56.6 yd

Step-by-step explanation:

in the picture above

pls mark as brainliest

Answer:

h(0) = 6

h(4) = 38

Step-by-step explanation:

The value of the function at x = 0 will be 10 and the value of the function at x = 4 will be 16.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The function is given below.

h(x) = 2x – 4, x < 0

h(x) = 2x² – 3x + 10, 0 ≤ x < 4

h(x) = (2)ˣ, x ≥ 4

The value of the function at x = 0, will be

The function is valid in the interval of [0, 4) will be h(x) = 2x² – 3x + 10.

Then the value of the function will be

h(0) = 2(0)² – 3(0) + 10

h(0) = 10

Then the value of the function at x = 0 will be 10.

The value of the function, at x = 4, will be

The function is valid in the interval of [4, ∞) will be h(x) = (2)ˣ.

Then the value of the function will be

h(4) = (2)⁴

h(4) = 16

Then the value of the function at x = 4 will be 16.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ5

Answer:

$400

Step-by-step explanation:

Answer:

$1.75

Step-by-step explanation:

2.55÷3=0.85

0.85x2=1.70

8.70-1.70=7

7÷4=1.75

hope this helps

Answer $1.75

Step-by-step explanation

Answer: D

Step-by-step explanation: To reflect each point across the y-axis you take the opposite of the x-coordinate

Answer:

The system has two solutions, but only one is viable because the other results in negative side lengths.

Step-by-step explanation:

Took the plato test and passed it, I don't know what the purpose of the first answer is, but here is the correct answer.

Answer:

200

Step-by-step explanation:

Volume of juice

[tex] = 3.5 \times 6 \times 9 \\ = 189 \\ \approx \: 200 \: {cm}^{3} [/tex]

Answer:

138.16

Step-by-step explanation:

Answer:

144mm²

Step-by-step explanation:

48mm / 4 = 12

12 × 12 = 144mm²

Area = 144mm²

Answer:

200

Step-by-step explanation:

Length*Width*Hight= 4*10*5=200

hope this helps

Answer:  I am pretty sure it is 200

Step-by-step explanation:

I may be wrong sorry if it is have a good day :)

Answer:

18N

Step-by-step explanation:

According to Newtons second law

F ∝ a

F =  ka

k is the constant of proportionality

When a force of 8 N acts on a certain object, the acceleration of the object is 4 m/s2, hence;

8 = 4k

k = 8/4

k = 2

If a = 9m/s², F = ?

Recall F = ka

F = 2 * 9

F = 18N

Hence the force will be 18N

Answer:

2^6 * 3^3

Step-by-step explanation:

1. 6^3 = (2^3) * (3^3)

2. 2^6 = (2^3)^2

3.  ((2^3) * (3^3) * (2^3)^2) / 2^3

4. (3^3) * (2^3)^3 / 2^3

5. (3^3) * (2^3)^2 = (3^3) * (2^6)

Answer:

You need to reword your question , sweetheart!

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sequence you gave is not arithmetic.  I'm assuming the sequence is

21, 6, -9, -24.

d is the common difference between adjacent terms.

a₂ = a₁ + d

6 = 21 + d

d = -15

nth term = a₁ + (n-1)d = 21 - (n-1)15

Step-by-step explanation:

A. r=42/2=21

B.

[tex] {21}^{2} \pi + 60 \times 42 = \\ = 441\pi + 2520[/tex]

C.

[tex]42\pi + 60 \times 2 = \\ = 42\pi + 120[/tex]

Answer:

f(g(-64)) = -190

Step-by-step explanation:

The functions are not well written.

Let us assume;

f(x) = x+1

g(x) = 3x+1

f(g(x)) = f(3x+1)

Replace x with 3x+1 in f(x)

f(g(x)) = (3x+1) + 1

f(g(x)) = 3x + 2

f(g(-64)) = 3(-64) + 2

f(g(-64)) = -192+2

f(g(-64)) = -190

Note that the functions are assumed but same method can be employed when calculating composite functions

Using composite functions, it is found that:

The composite function of functions f(x) and g(x) is given by:

[tex](f \circ g)(x) = f(g(x))[/tex]

Researching the problem on the internet, it is found that the functions are:

[tex]f(x) = (x + 1)^3[/tex]

[tex]g(x) = \sqrt[3]{x} + 1[/tex]

Then, the composite function is:

[tex](f \circ g)(x) = f(g(x)) = f(\sqrt[3]{x} + 1) = (\sqrt[3]{x} + 1 + 1)^3 = (\sqrt[3]{x} + 2)^3[/tex]

At x = -64, we have that:

[tex](f \circ g)(-64) = (\sqrt[3]{-64} + 2)^3 = (-4 + 2)^3 = (-2)^3 = -8[/tex]

Hence:

To learn more about composite functions, you can take a look at https://brainly.com/question/17684028

Answer:

g(-1) = 4

Step-by-step explanation:

Given:

g(x) = [tex] \frac{3x^2 - 2x + 7}{2x + 5} [/tex]

To find g(-1), substitute x = -1

Thus:

g(-1) = [tex] \frac{3(-1)^2 - 2(-1) + 7}{2(-1) + 5} [/tex]

g(-1) = [tex] \frac{3 + 2 + 7}{-2 + 5} [/tex]

= [tex] \frac{3 + 2 + 7}{-2 + 5} [/tex]

= [tex] \frac{12}{3} [/tex]

g(-1) = 4

Answer:

Fraction : 3/9

Decimal : 0.33333333 (the .3 continues)

Percent : 33.33333%

Step-by-step explanation:

Dividing 3 by 9 will give you a continous set of 3.

Answer:

your answer will be P=27

Step-by-step explanation:

hope it helps...

Answer:

345.6

Step-by-step explanation:

Answer:

top=170mm squared

shape 2=76.27 cm squared

shape 3=62.862 cm squared

Step-by-step explanation:

top shape...

(18x15)-4(5x5)=area

270-4(25)=area

270-100=area

170=area

shape 2...

diameter of circle is 6 so radius is 3...

area=pier^2

a=28.27 and their are two half circles so that makes one whole circle

(8x6)+28.27=76.27 cm squared

shape 3...

total of rectangle with a half circle subtracted.  r=4 d=8

so

11x8=88 for rectangle then subtract half circle

a=pie r^2

a=50.27

50.27/2=25.135 subtract this from rectangle total...

88-25.135=62.862 cm squared

pyramid A: 16 + [tex]8\sqrt{5[/tex]

pyramid B: 400 + [tex]8\sqrt{125[/tex]

pyramid A: 4 by 4= 16 cm.

with a height of 1 and length of 2, we use pythagorean theorem to find height of other surfaces to be square root of 5. area of triangle is 1/2 bh

square root of 5 multiplied by 4 and divided by 2 is 2 root 5

multiply this by 4 sides total for 8 root 5

Add the 8 root 5 to 16

To find pyramid B: use ratio of 25:1 and multiply 16 by 25 to find 400, and root 5 to 125

Answer:

5 times

Step-by-step explanation:

1/6·30=5

so your answer is b)5

Can i have a brainliest please or 10 points?

Answer:

37.5

Step-by-step explanation:

16/46 = 20/(20+x)

or, 16(20+x) = 46×20

or, 320 + 16x = 920

or, 16x = 600

or, x = 600/16

x = 37.5

Answer: what are you looking for (d)?  there isnt enough info

Step-by-step explanation: