5. Change the following mixed numbers to improper
fractions.
a. 3 5/6
b. 2 7/8
C. 5 1/5
D. 7 1/9

Answer:

Answer:

16 inches

Step-by-step explanation:

2 1/4 = 9/4 inches

Number of pieces = 36 / 9/4

= 36 + 4/9

= 16 inches

If it's a regular nonagon, each exterior angle has measure 360°/9 = 40°, so the supplementary interior angles each have measure 180° - 40° = 140°.

We can split up the nonagon into 9 congruent isosceles triangles whose longer side coincides with the radius of the circle. (The language in the question is a bit ambiguous; I think it's clearler to say the nonagon is itself circumscribed by the circle, so that each of its vertices lie on the circle. See attached image - not mine, but it's in public domain.)

As the image suggests, each triangle will have interior angles measuring 70°, 70°, and 40°.

We can use trigonometry to find the side length of the nonagon, i.e. the length of the shortest side of each triangle - I'll call it x. For example, using the law of cosines,

x² = 4² + 4² - 2 • 4 • 4 cos(40°)   ⇒   x = 4√2 √(1 - cos(40°))

Then the perimeter of the nonagon is

9x = 36√2 √(1 - cos(40°)) in ≈ 24.623 in

The area of a triangle is 1/2 the product of its base and height. The base will be b = x, but to get the height we cut the isosceles triangle in half to produce a right triangle. We use trig again to determine its height h:

tan(70°) = h/(b/2)   ⇒   h = 1/2 x tan(70°)

so each triangle contributes an area of

a = 1/2 bh = 1/4 x² tan(70°) ≈ 5.142 in²

and so the area of the nonagon is

9a = 9x²/8 tan(70°) ≈ 46.281 in²

Answer:

208

Step-by-step explanation:

A coin can have 2 total outcomes

A card deck can have 52 total outcomes

Im flipping 2 coins and then drawing a card

2 x 2 x 52 = 208

Answer:

1. -5+3

2. -6+4

3. -8+6

Step-by-step explanation:

they all will equal -2

Answer:

12/20=3/5   5/20=1/4 so the answer would be 12/20 + 5/20

Answer:

The area of figure is 29.

Step-by-step explanation:

By counting the square box.

Answer:

28.5 square units

Step-by-step explanation:

Spit it into a triangle and a rectangle.

The Triangle is

(3 * 3) / 2

= 9 / 2

= 4.5

The Rectangle is

3 * 8

=24

The total is 4.5 + 24 = 28.5

Answer:

38

Step-by-step explanation:

|-7|×|5|+18÷|-6|

First take the absolute value of each number, which means take the positive value

7×5+18÷6

Multiply and divide from left to right

35 + 3

Then add

38

Answer:

14.20669 years

Roughly 14 years and 2.5 months.

Step-by-step explanation:

Assuming this is compound interest.

The formula is [tex]A=P(1+\frac{r}{n})^{nt}[/tex]

[tex]A=[/tex] Final Amount

[tex]P=[/tex] Principal Amount

[tex]r=[/tex] Interest Rate

[tex]n=[/tex] # of times interest is compounded per year

[tex]t=[/tex] Time in years

We are looking for the times in years to double the money so

[tex]2500*2=5000[/tex]

[tex]A=5000[/tex]

[tex]P=2500[/tex]

[tex]r=0.05[/tex]

[tex]n=1[/tex]

[tex]t=?[/tex]

Lets solve for [tex]t[/tex] .

Step 1.

Plug in our numbers into the compound interest formula.

[tex]5000=2500(1+\frac{0.05}{1}) ^{1*t}[/tex]

Step 2.

Simplify the equation.

Evaluate [tex]1+\frac{0.05}{1}=1.05[/tex]

Evaluate [tex]1*t=t[/tex]

[tex]5000=2500(1.05) ^{t}[/tex]

Step 3.

Divide both sides of the equation by [tex]2500[/tex]

[tex]\frac{5000}{2500}=1.05 ^{t}[/tex]

Evaluate [tex]\frac{5000}{2500}=2[/tex]

[tex]2=1.05 ^{t}[/tex]

Step 4.

Take the natural log of both sides of the equation and rewrite the right side of the eqaution using properties of exponents/logarithms.

[tex]ln(2)=t*ln(1.05)[/tex]

Step 5.

Divide both sides of the equation by [tex]ln(1.05)[/tex]

[tex]\frac{ln(2)}{ln(1.05)}=t[/tex]

Step 6.

Evaluate

[tex]t=14.20669[/tex]

Roughly 14 years and 2.5 months.

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

Work Shown:

[tex]2\sqrt{b} + 5 = 11 - \sqrt{b}\\\\2x + 5 = 11 - x\\\\2x+x = 11 - 5\\\\3x = 6\\\\x = 6/3\\\\x = 2\\\\\sqrt{b} = 2\\\\b = 2^2\\\\b = 4\\\\[/tex]

What I did for a good portion of the early steps is replace [tex]\sqrt{b}[/tex] with x. Then I solved for x like with any normal equation. Once x is isolated, plug in [tex]x = \sqrt{b}[/tex] and isolate b itself.

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

Let's check the answer:

[tex]2\sqrt{b} + 5 = 11 - \sqrt{b}\\\\2\sqrt{4} + 5 = 11 - \sqrt{4}\\\\2*2 + 5 = 11 - 2\\\\4 + 5 = 11 - 2\\\\9 = 9 \ \ \ \ \checkmark\\\\[/tex]

The answer of b = 4 is confirmed.

It's always a good idea to check the answer with any equation. This is especially true with square root equations because the solution might be extraneous (meaning that it works in some equations but not in the original starting equation).

Answer:

Tama po

Yan

Step-by-step explanation:

Enjoy po

Godbless

Answer:

-36-128b

Step-by-step explanation:

Simply take -36 out of the parentheses to get -36-128b.

3 cm/h easy peasy

Step-by-step explanation:

Answer:

4r ^2 +9r + 12

Step-by-step explanation:

Hope this helps! :)

Answer:

11/15

Step-by-step explanation:

sum the two 1/3+2/5=11/15

Answer:

See below

Step-by-step explanation:

z  = uncle's age

1/2z +3   = Sam's age

[tex]10^3 = 10 \times 10 \times 10 = 1000[/tex]

Answer:

c/d

Step-by-step explanation:

The value of π is the ratio of the circumference of any circle to it's diameter, irrespective of it's size.

Answer:

[tex]\dfrac12 < p < 5[/tex]

Step-by-step explanation:

To solve this, we need to use the discriminant.

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]

If the given equation has 2 real roots, then we need to use:

[tex]b^2-4ac > 0[/tex]

Given equation:  [tex]8x^2-4x+1-p=0[/tex]

[tex]\implies a=8, \quad b=-4, \quad c=(1-p)[/tex]

Substituting these values into [tex]b^2-4ac > 0[/tex] and solve for p:

[tex]\implies (-4)^2-4(8)(1-p) > 0[/tex]

[tex]\implies 16-32(1-p) > 0[/tex]

[tex]\implies 16-32+32p > 0[/tex]

[tex]\implies -16+32p > 0[/tex]

[tex]\implies 32p > 16[/tex]

[tex]\implies p > \dfrac{16}{32}[/tex]

[tex]\implies p > \dfrac12[/tex]

For the roots to be less than 1, first find the value of p when the root is 1.

If the root is 1, then [tex](x-1)[/tex] will be a factor, so [tex]f(1)=0[/tex]

Substitute [tex]x=1[/tex] into the given equation and solve for p:

[tex]\implies 8(1)^2-4(1)+1-p=0[/tex]

[tex]\implies 5-p=0[/tex]

[tex]\implies p=5[/tex]

Therefore, the values of p for which the given equation has two different real roots less than 1 are:

[tex]\dfrac12 < p < 5[/tex]

Answer: D

Step-by-step explanation:

Answer:

D. 95 ≤ u ≤ 155

Step-by-step explanation:

Answer:

E. 4/6 = 18/x

Step-by-step explanation:

4 hour using 6 logs

18 hours using x logs

Answer:

Step-by-step explanation:

Formula

Volume = L * w * h

Givens

L = 7 feet

w = 4 feet

h = 5 feet

Solution

V = L * w * h             Substitute values into the formula

V = 7 * 4 * 5

V = 140 cubic feet.

Answer

140 ft^3

Answer:

D) 140 cubic feet

Step-by-step explanation:

The given information is,

→ Length (l) = 7 ft

→ Breadth (b) = 4 ft

→ Height (h) = 5 ft

Formula we use,

→ Volume of cuboid = l × b × h

Let's solve the problem,

→ l × b × h

→ 7 × 4 × 5

→ [ 140 ft³ ]

Hence, the volume is 140 ft³.

Answer:

The answer is 50.

Step-by-step explanation:

Set up a proportion: [tex]\frac{41}{y} =\frac{82}{100}[/tex]
Step 2- Multiply 41 by 100 to get 4100
Step 3. Divide 4100 by 82 to get 50.
Hope this helps! :)

Answer:

1.35 square miles I think

Step-by-step explanation:

Answer:

Julie travels 1.35 miles on the same path every day.

Area = 1.35 miles

Step-by-step explanation:

What we know so far:

- It takes 2.4 miles to walk from house to school.

- The distance from the park to school is 2.1 miles.

- It takes 1.5 miles to walk from your house to the park.

The area of a triangle is 0.5 or 1/2 x base x height.

As a result, 1.5 x 1.8 divided by two equals 1.35.

So, Julie walks 1.35 miles every day on the same route.

Area = 1.35 miles

Hope this helps! :D Brainliest?

This exercise is about optimization and seeks to prove that if the new strategy of packing the discs is adopted, then h/r = [tex]\sqrt[4]{3}[/tex]/n ≈2.21.

We must determine the amount of metal consumed by each end, or the area of each hexagon.

The hexagon is divided into six congruent triangles, each of which has one side (s in the diagram) in common with the hexagon.

Step I

Next, let's derive the length of s = 2r tan π/6 = (2/([tex]\sqrt{3}[/tex])r². From this we can state that the area of each of the triangles are 1/2(sr) = (1/[tex]\sqrt{3}[/tex])r²

while the total area of the hexagon is 6 * (1/[tex]\sqrt{3}[/tex])r² = (2/[tex]\sqrt{3}[/tex])r².

From the above, we can state that the quantity we want to minimize is given as:

A =  2πrh + 2* (2/[tex]\sqrt{3}[/tex])r²

Step 2

Next, we substitute for h and differentiate. This gives us:

da/dr = - (2V/r²) + [tex]\sqrt[8]{3r}[/tex].

Let us equate the above to zero.

[tex]\sqrt[8]{3r} ^{3}[/tex] = 2V = 2πr²h ⇒  h/r =[tex]\sqrt[4]{3}[/tex]/n  

The above is approximately 2.21

Because d²A/dr²=[tex]\sqrt[8]{3}[/tex] + 4V/r[tex]^{3}[/tex] > 0 the above minimizes A.

Learn more about Optimization at:

https://brainly.com/question/17083176

#SPJ1

Expanding the cube, we have

[tex]\dfrac1{(a+b+c)^3} = \left(\dfrac1{a+b+c}\right)^3 \\\\ = \dfrac1{a^3} + \dfrac1{b^3} + \dfrac1{c^3} + 3 \left(\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2}\right) + \dfrac6{abc}[/tex]

so it remains to be shown that

[tex]3 \left(\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2}\right) + \dfrac6{abc} = 0[/tex]

Factorize the grouped sum on the left as

[tex]\dfrac1{a^2b} + \dfrac1{a^2c} + \dfrac1{ab^2} + \dfrac1{b^2c} + \dfrac1{ac^2} + \dfrac1{bc^2} = \dfrac1{abc} \left(\dfrac ca + \dfrac ba + \dfrac cb + \dfrac ab + \dfrac bc + \dfrac ac\right)[/tex]

so that with simplification, it remains to be shown that

[tex]\dfrac ca + \dfrac ba + \dfrac cb + \dfrac ab + \dfrac bc + \dfrac ac + 2 = 0[/tex]

With a little more manipulation, we have

[tex]\dfrac ba + \dfrac ca = \dfrac{a+b+c}a - 1[/tex]

[tex]\dfrac cb + \dfrac ab = \dfrac{a+b+c}b - 1[/tex]

[tex]\dfrac bc + \dfrac ac = \dfrac{a+b+c}c - 1[/tex]

so that our equation simplifies to

[tex]\dfrac{a+b+c}a + \dfrac{a+b+c}b + \dfrac{a+b+c}c - 1 = 0[/tex]

which we can factorize as

[tex](a+b+c)\left(\dfrac1a+\dfrac1b+\dfrac1c\right) - 1 = 0[/tex]

Finish up by using the hypothesis:

[tex]\left(\dfrac1{\frac1{a+b+c}}\right)\left(\dfrac1a+\dfrac1b+\dfrac1c\right) - 1 = 0[/tex]

[tex]\underbrace{\left(\dfrac1{\frac1a+\frac1b+\frac1c}\right)\left(\dfrac1a+\dfrac1b+\dfrac1c\right)}_{=1} - 1 = 0[/tex]

and the conclusion follows.

Answer

Write properties of function:

x intercept/zero: [tex]x_1=-7[/tex]; [tex]x_2=-1[/tex]; [tex]x_3=2[/tex]

factorized form: [tex]f(x)=(x+1)(x-2)(x+7)[/tex]

Explanation

Write properties of function: Write properties of function:

x intercept/zero: [tex]x_1=-7[/tex]; [tex]x_2=-1[/tex]; [tex]x_3=2[/tex]

factorized form: [tex]f(x)=(x+1)(x-2)(x+7)[/tex]

Answer: Write properties of function:

x intercept/zero: [tex]x_1=-7[/tex]; [tex]x_2=-1[/tex]; [tex]x_3=2[/tex]

factorized form: [tex]f(x)=(x+1)(x-2)(x+7)[/tex]

Answer

3*9=27

27/ 1/5

5.25

Step-by-step explanation:

5.25=5 1/4

Answer:

4,569,760 different passwords

Step-by-step explanation:

[tex]26 \times 26 \times 26 \times 26 \times 10 = 4569760[/tex]

Digits can be repeated means repeatation is allowed

So

Total ways