A rectangular picture frame has length three inches longer than twice it’s width. The perimeter is 36 inches. Find the width of the frame.

a.) 5in
b.) 7in
c.) 10in
d.) 11in

Step-by-step explanation:

Let [tex]x = r\cos{\theta}[/tex] and [tex]y = r\sin{\theta}[/tex]. Substituting these into our equation, it becomes

[tex]\dfrac{r^2\cos^2{\theta}}{25} + \dfrac{r^2\sin^2{\theta}}{9} = 1[/tex]

or

[tex]9r^2\cos^2{\theta} + 25r^2\sin^2{\theta} = 225[/tex]

Let use the identity [tex]\cos^2{\theta} = 1 - \sin^2{\theta}[/tex] to express the equation in terms of sine only:

[tex]9r^2 - 9r^2\sin^2{\theta} + 25\sin^2{\theta} = 225[/tex]

which simplifies to

[tex]r^2(9 + 16\sin^2{\theta}) = 225[/tex]

Taking the square root and solving for r , we get the polar form of the equation as

[tex]r = \dfrac{15}{\sqrt{9 + 16\sin^2{\theta}}}[/tex]

Answer:

x = r\cos{\theta}x=rcosθ and y = r\sin{\theta}y=rsinθ

\dfrac{r^2\cos^2{\theta}}{25} + \dfrac{r^2\sin^2{\theta}}{9} = 1

25

r

2

cos

2

θ

+

9

r

2

sin

2

θ

=1

or

9r^2\cos^2{\theta} + 25r^2\sin^2{\theta} = 2259r

2

cos

2

θ+25r

2

sin

2

θ=225

Let use the identity \cos^2{\theta} = 1 - \sin^2{\theta}cos

2

θ=1−sin

2

θ

9r^2 - 9r^2\sin^2{\theta} + 25\sin^2{\theta} = 2259r

2

−9r

2

sin

2

θ+25sin

2

θ=225

which simplifies to

r^2(9 + 16\sin^2{\theta}) = 225r

2

(9+16sin

2

θ)=225

Taking the square root and solving for r ,

r = \dfrac{15}{\sqrt{9 + 16\sin^2{\theta}}}r=

9+16sin

2

θ

15

Simplifying fractions:

1) [tex]\frac{14}{20} =\frac{7}{10}[/tex]                  2) [tex]\frac{4}{8} =\frac{1}{2}[/tex]

3) [tex]\frac{9}{12} =\frac{3}{4}[/tex]                  4) [tex]\frac{12}{15} =\frac{4}{5}[/tex]

5) [tex]\frac{8}{18} =\frac{4}{9}[/tex]                  6) [tex]\frac{14}{21} =\frac{2}{3}[/tex]

7) [tex]\frac{12}{16} =\frac{3}{4}[/tex]                  8) [tex]\frac{10}{24} =\frac{5}{12}[/tex]

9) [tex]\frac{15}{35}=\frac{3}{7}[/tex]                 10) [tex]\frac{13}{26} =\frac{1}{2}[/tex]

11) [tex]\frac{11}{55}=\frac{1}{5}[/tex]                12) [tex]\frac{9}{21} =\frac{3}{7}[/tex]

13) [tex]\frac{16}{26} =\frac{8}{13}[/tex]              14) [tex]\frac{20}{32} =\frac{5}{8}[/tex]

15) [tex]\frac{18}{24} =\frac{3}{4}[/tex]               16) [tex]\frac{21}{27} =\frac{7}{9}[/tex]

17) [tex]\frac{4}{32} =\frac{1}{8}[/tex]               18) [tex]\frac{25}{40} =\frac{5}{8}[/tex]

Hope this helps :)

9514 1404 393

Answer:

  (g·f)(9) = 496

Step-by-step explanation:

One way to do this is to find the values of g(9) and f(9).

  g(9) = (3x -1)x +14 = (3(9) -1)(9) +14 = 26(9) +14 = 248

  f(9) = -(9) +11 = 2

Then ...

  (g·f)(9) = g(9)·f(9) = 248·2

  (g·f)(9) = 496

Answer:

x≤4 is a closed circle on 4 going left and x≥8 is a closed circle on 8 going right

Step-by-step explanation:

Not sure how to explain it.

Answer:  [tex]18\sqrt{2}\\\\[/tex]

This is the same as saying 18*sqrt(2) or you could say 18√2

============================================================

Explanation:

We'll be using this square root rule: [tex]\sqrt{A}*\sqrt{B} = \sqrt{A*B}[/tex]

So we could have this as our steps:

[tex]3\sqrt{12}*\sqrt{6}\\\\3\sqrt{12*6} \ \text{ ... Apply the rule mentioned}\\\\3\sqrt{72}\\\\3\sqrt{36*2}\\\\3\sqrt{36}*\sqrt{2} \ \text{ ... Apply the rule again, but in reverse}\\\\3*6*\sqrt{2}\\\\18\sqrt{2}\\\\[/tex]

Therefore, [tex]3\sqrt{12}*\sqrt{6} = 18\sqrt{2}[/tex]

The basic idea is to first combine the roots using that rule. From there, we factor the radicand such that we pull out the largest perfect square factor. This will allow us to break the root apart and fully simplify it.

Answer:

[tex] \frac{2n}{3} [/tex]

hope, I'm right

Answer:

[tex] \frac{2n}{3} [/tex]

Step-by-step explanation:

[tex] \frac{ \frac{n}{4} }{ \frac{3}{8} } = \frac{n}{4} \div \frac{3}{8} [/tex]

[tex] \frac{n}{4} \times \frac{8}{3} = \frac{n \times 8}{4 \times 3} [/tex]

[tex] \frac{n \times 2}{3} = \frac{2n}{3} [/tex] ✅

Answer:

which class Of question is this

Answer:

5.264 * 10^4

Step-by-step explanation:

We put a decimal point to the right of the number, so

52640.

Then we move it to the left until we get a number that is between 1 and 10.

5.2640

This was four hops to the left.

We can remove the trailing 0, and write

5.264 * 10^4

10^4 because of the four hops

Answer:

5.264×10^4

Step-by-step explanation:

10^4 = 10,000 x 5.264 = 52,640

Answer: De and Ef

Step-by-step explanation:

Answer:

12 sides

Step-by-step explanation:

its a regular polygon so we can use the formula 180(n-2)/n which finds the angle of the regular polygon, since the exterior angle is 30, the angle of the regular polygon is 180-30=150, so 180(n-2)/n=150.

Answer:

D.  -3/5.

Step-by-step explanation:

6x + 10y = 8

We convert this to slope-intercept form:

Subtract 6x from both sides of the equation:

10y = -6x + 8

Divide through by 10:

y = -6/10 x +  8/10   (Slope-intercept form)

The slope is -6/10

= -3/5.

Answer:

x = 2

Step-by-step explanation:

Equation: 2x + 6 = 10

2x = 4

x = 2

Answer:

let the number be x

then

2x + 6 = 10

2x = 10-6

2x = 4

x = 2

mark me as brainliest

Answer:

x=30 degree is the answer

Answer:

200

Step-by-step explanation:

Answer:

The difference between the height of the mountain and the depth of the trench is 8,271 ft.

Step-by-step explanation:

brainliest plz?

Answer:

He will pay $10

Step-by-step explanation:

35-25=10

The 3 angles form the straight line AB. A straight line equals 180 degrees.

The 3 angles when added together need to equal 180:

2x + 65 + (x + 65) = 180

Simplify by combining like terms:

3x + 130 = 180

Subtract 130 from both sides

3x = 50

Divide both sides by 3

X = 50/3

X = 16 2/3 (16.66667 as a repeating decimal)

Now you have x if you need to solve all the angles replace x with its value and sole:

2x = 2(16 2/3) = 33 1/3

X + 65 = 16 2/3 + 65 = 81 2/3

Step-by-step explanation:

2x+65°+(x+65°)=180° ( sum of angle of straight angle )

3x+65°+65°=180°

3x=180°-130°

3x= 50°

now,

i) 2x=2*50=100°

ii) (x+65°) = 50+65 =115°

plz mark me brainiest and thanks

have a good day ahead...

(-_-)

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]m = 14[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'm'...}}}\\\\(\frac{3}{7}) m=6\\\\-------------\\\rightarrow (\frac{3}{7}m)7 = 6*7\\\\\rightarrow 3m = 42\\\\\rightarrow \frac{3m=42}{3}\\\\\rightarrow \boxed{m= 14}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

9514 1404 393

Answer:

  A.  500 cm²

Step-by-step explanation:

The height of the piece of cardboard is the same as the height of the prism: 20 cm.

The width of the piece of cardboard is the sum of the side lengths of the prism: 7 cm + 9 cm + 9 cm = 25 cm.

The area of the cardboard is the product of its height and width.

  A = HW

  A = (20 cm)(25 cm) = 500 cm²

Answer:

40 000

Step-by-step explanation:

4 thousands = 4000

10 x 4000 = 40 thousands = 40 000

Answer:

40,000

Step-by-step explanation:

Answer:

When we talk about Intercept... We refer to the place where the line touches or Crosses a Mentioned axis.

In this question... We needed the y - Intercept

Know This: At the intercept of a mentioned axis...The other axis is zero at that point.

In other words... If we're asked for intercept at x-axis ... The y value at that point is zero and Vice Versa

So To find the y Intercept... the x value at this point is zero(0).

With this in Mind...

substitute x = 0 into the quadratic eqn

f(x) = 0² +8(0) - 13

f(x) = -13

This is Our Y Intercept .

To get the x intercept(if asked)

substitute y = 0 and solve

0 = x² + 8x - 13

This is a quadratic equation

Solving this would get you two value and those values would be your x intercept.

I hope it helps.

Have a great day.

please mark this answer as brainlist

Answer:

32±b±90=180(being the three angle of a treangle)

32±90±b=180

122±b=180

B=180-122

b=58 answer

90±23±d=180(being three angle of the trangle)

113±d=180

d=180-113

d=78 answer

Answer

:.b=58

:.d=78

Thank you

Answer:

45oz

Step-by-step explanation:

We can find the ratio of white to blue paint he needs by dividing.

10 / 4 = 2.5oz of blue paint for every ounce of white paint

Now, we can multiply to find how much blue paint he needs.

18 * 2.5 = 45oz

Best of Luck!

Answer:

that's cheating, still your indian bro will help _XD

Step-by-step explanation:

ab = 34

bc 33

ac 27

pq 27

qr 27

pr 40