Solve for x


There’s no options sorry ya’ll please answer I’m desperate

Due to the symmetry of the paraboloid about the z-axis, you can treat this is a surface of revolution. Consider the curve [tex]y=x^2[/tex], with [tex]1\le x\le2[/tex], and revolve it about the y-axis. The area of the resulting surface is then

[tex]\displaystyle2\pi\int_1^2x\sqrt{1+(y')^2}\,\mathrm dx=2\pi\int_1^2x\sqrt{1+4x^2}\,\mathrm dx=\frac{(17^{3/2}-5^{3/2})\pi}6[/tex]

But perhaps you'd like the surface integral treatment. Parameterize the surface by

[tex]\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+u^2\,\vec k[/tex]

with [tex]1\le u\le2[/tex] and [tex]0\le v\le2\pi[/tex], where the third component follows from

[tex]z=x^2+y^2=(u\cos v)^2+(u\sin v)^2=u^2[/tex]

Take the normal vector to the surface to be

[tex]\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial u}=-2u^2\cos v\,\vec\imath-2u^2\sin v\,\vec\jmath+u\,\vec k[/tex]

The precise order of the partial derivatives doesn't matter, because we're ultimately interested in the magnitude of the cross product:

[tex]\left\|\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right\|=u\sqrt{1+4u^2}[/tex]

Then the area of the surface is

[tex]\displaystyle\int_0^{2\pi}\int_1^2\left\|\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right\|\,\mathrm du\,\mathrm dv=\int_0^{2\pi}\int_1^2u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv[/tex]

which reduces to the integral used in the surface-of-revolution setup.

The length of the side d would be 77/18.

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or

[tex]\dfrac{a}{b}[/tex]

If triangles DEF and NPQ are similar, then

7/9 = d/ (11/2)

By cross multiply

9d = 7 x 11/2

d = 77/2 ÷ 9

d = 77/18

Thus, The length of the side d would be 77/18.

Learn more about ratios here:

brainly.com/question/186659

#SPJ2

Answer:

C

Step-by-step explanation:

Given

x + 10 = 3(x - 1)² ← expand (x - 1)² using FOIL

x + 10 = 3(x² - 2x + 1) ← distribute

x + 10 = 3x² - 6x + 3 ← subtract x + 10 from both sides

0 = 3x² - 7x - 7 → C

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The associative property lets you move parentheses in a sum or product. That is, it doesn't matter which sum or product you compute first.

The commutative property lets you swap the order of operands in a sum or product.

The identity property says the operation using the identity element gives the original value, unchanged.

Answer:

Step-by-step explanation:

Answer:

[tex]271.3 mm^3\\[/tex]

Step-by-step explanation:

We have to find the volume of the hole and subtract it from the volume of the cylinder.

The volume of a cylinder is given as:

[tex]V = \pi r^2h[/tex]

where r = radius

h = height

A cylindrical metal pipe has a diameter of 8.4 mm and a height of 10 mm.

Its radius is 4.2 mm. Therefore, its volume is:

[tex]V = 3.14 * 4.2^2 * 10 = 553.9 mm^3[/tex]

A hole cut out of the center has a diameter of 6 mm. Its height is also 10 mm.

Its radius is 3 mm. Therefore, its volume is:

[tex]V = 3.14 * 3^2 * 10 = 282.6 mm^3[/tex]

Therefore, the volume of metal in the pipe is:

[tex]553.9 - 282.6 = 271.3 mm^3[/tex]

Answer:

B

Step-by-step explanation:

a) The percentage of women meeting the height requirement is approximately 99.99%.

b) The percentage of men meeting the height requirement is approximately 99.95%.

c) The new height requirements are at least 58.5 inches and at most 71.8 inches.

a) To find the percentage of women meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we need to calculate the proportion of women within this range using the normal distribution.

First, we standardize the height requirement using the formula:

Z = (X - μ) / σ

where X is the value (height), μ is the mean, and σ is the standard deviation.

For the lower limit (57 inches):

Z_lower = (57 - 63.3) / 2.7 ≈ -2.33

For the upper limit (76 inches):

Z_upper = (76 - 63.3) / 2.7 ≈ 4.70

Using a standard normal distribution table or calculator, we can find the area between -2.33 and 4.70. This represents the percentage of women meeting the height requirement.

The percentage of women meeting the height requirement is approximately 99.99%.

b) Similarly, for men meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we standardize the values:

For the lower limit (57 inches):

Z_lower = (57 - 67.3) / 2.8 ≈ -3.68

For the upper limit (76 inches):

Z_upper = (76 - 67.3) / 2.8 ≈ 3.11

Using the standard normal distribution table or calculator, we find the area between -3.68 and 3.11.

The percentage of men meeting the height requirement is approximately 99.95%.

c) To find the new height requirements that exclude the tallest 5% of men and the shortest 5% of women, we need to determine the corresponding Z-scores.

For men:

Z_upper_men = Z(0.95) ≈ 1.645

For women:

Z_lower_women = Z(0.05) ≈ -1.645

Using these Z-scores, we can calculate the new height requirements:

For the new lower limit:

X_lower = Z_lower_women * σ + μ

For the new upper limit:

X_upper = Z_upper_men * σ + μ

Substituting the values:

X_lower = -1.645 * 2.7 + 63.3 ≈ 58.53 inches

X_upper = 1.645 * 2.8 + 67.3 ≈ 71.78 inches

Therefore, the new height requirements are at least 58.5 inches and at most 71.8 inches.

For more such question on percentage visit:

https://brainly.com/question/24877689

#SPJ8

a) The percentage of women meeting the height requirement is 99.99%.

b) The percentage of men meeting the height requirement is 99.95%.

c) The new height requirements are at least 58.5 inches and at most 71.8 inches.

a) For women meeting the height requirement:

Given: Mean (μ) = 63.3 in.

Standard Deviation (σ) = 2.7 in.

So, Minimum height requirement:

= 4 ft 9 in

= 4 * 12 + 9

= 57 inches

and, Maximum height requirement:

= 6 ft 4 in

= 6 * 12 + 4

= 76 inches

We will calculate the Z-scores for these heights using the formula:

Z = (x - μ) / σ

For the minimum height requirement:

[tex]Z_{min[/tex] = (57 - 63.3) / 2.7 ≈ -2.33

For the maximum height requirement:

[tex]Z_{max[/tex] = (76 - 63.3) / 2.7 ≈ 4.70

So, the the area between -2.33 and 4.70.

Thus, the percentage is  99.99%.

b) For men meeting the height requirement:

Given: Mean (μ) = 67.3 in., Standard Deviation (σ) = 2.8 in.

Minimum height requirement: 4 ft 9 in = 57 inches

Maximum height requirement: 6 ft 4 in = 76 inches

For the minimum height requirement:

[tex]Z_{min[/tex]= (57 - 67.3) / 2.8 ≈ -3.68

For the maximum height requirement:

[tex]Z_{max[/tex] = (76 - 67.3) / 2.8 ≈ 3.11

So, the area between -3.68 and 3.11.

Thus, the percentage is 99.95%.

c) For the new height requirements:

For men:

[tex]Z_{upper_{men[/tex] = Z(0.95) ≈ 1.645

For women:

[tex]Z_{lower_{women[/tex] = Z(0.05) ≈ -1.645

For the new lower limit:

[tex]X_{lower} = Z_{lower}_{women} \sigma+ \mu[/tex]

For the new upper limit:

[tex]X_{upper} = Z_{upper}_{men} \sigma+ \mu[/tex]

Substituting the values:

[tex]X_{lower} = -1.645 * 2.7 + 63.3[/tex]

           = 58.53 inches

and, [tex]X_{upper} = 1.645 * 2.8 + 67.3[/tex]

                     = 71.78 inches

Therefore, the new height at least 58.5 inches and at most 71.8 inches.

Learn more about z score here:

https://brainly.com/question/31871890

#SPJ6

Answer:

The simple interest rate is 5%.

This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex]

Joshua has $4,200 to invest for college. If Joshua invests $4,200 for 3 years and earns $630, what is the simple interest rate?

We have that [tex]P = 4200, E = 630, t = 3[/tex]. We have to find I.

[tex]E = P*I*t[/tex]

[tex]630 = 4200*I*3[/tex]

[tex]I = \frac{630}{4200*3}[/tex]

[tex]I = 0.05[/tex]

The simple interest rate is 5%.

Joshua’s goal is to have $5,000 after 4 years. Is this possible if he invests with a rate of  return of 6%?

We have to find T when [tex]P = 4200, t = 4, I = 0.06[/tex]

So

[tex]E = P*I*t[/tex]

[tex]E = 4200*0.06*4[/tex]

[tex]E = 1008[/tex]

[tex]T = E + P = 4200 + 1008 = 5208[/tex]

This is possible with a rate of 6%, since in this case, his amount earned will be $5,208.

Answer:

66%

Step-by-step explanation:

15% of homes have both features.

The percentage of homes that have a pool and no garage is:

Pool only = 19% - 15% = 4%

The percentage of homes that have a garage and no pool is:

Garage only = 62% - 15% = 47%

Therefore, the percentage of homes that have a pool, a garage or both is:

[tex]P = 4\%+47\%+15\%\\P=66\%[/tex]

Answer:

Step-by-step explanation:

hey

(f*g)(x) = f(g(x)) = f(2) = 2

second answer is correct

thanks

Answer: 363 cm squared

Step-by-step explanation:

So we can split the shape into 1 triangle and 3 rectangles.

We can start with the top right rectangle which is a 4 by 5.

4*5 = 20 cm squared

We can now do the horizontal rectangle. We need to find the dimensions firs by subtracting 4 from 31 to find the length and add 4 and 5 to find the height.

This means the dimensions are 27 by 9.

27 * 9 = 243 cm squared

Now the final square toward the bottom left will be a 10 by 7.

10 * 7 = 70 cm squared.

Now for the final piece is the triangle in the bottom left. We need to first find the height which we can determine by taking the the right hand side values of 10 , 4 and 5 and adding those together then subtracting that number by 13 to get the missing length that will add to 6 to find the height.

10 + 4 + 5 = 19

19 - 13 = 6

6 + 6 = 12

Now that we have the height and base of the triangle we solve for the area.

0.5 * 5 * 12 = 30 cm squared

Now we add all the areas together to find the total area.

20 + 243 + 70 + 30 = 363 cm squared

Answer:

The 95% confidence interval for the difference of means is (7.67, 16.33).

The estimate is Md = 12.

The standard error is sM_d = 2.176.

Step-by-step explanation:

We have to calculate a 95% confidence interval for the difference between means.

The sample 1 (this year's sales), of size n1=36 has a mean of 53 and a standard deviation of 12.

The sample 2 (last year's sales), of size n2=49 has a mean of 41 and a standard deviation of 6.

The difference between sample means is Md=12.

[tex]M_d=M_1-M_2=53-41=12[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{12^2}{36}+\dfrac{6^2}{49}}\\\\\\s_{M_d}=\sqrt{4+0.735}=\sqrt{4.735}=2.176[/tex]

The degrees of freedom are:

[tex]df=n_1+n_2-1=36+49-2=83[/tex]

The critical t-value for a 95% confidence interval and 83 degrees of fredom is t=1.989.

The margin of error (MOE) can be calculated as:

[tex]MOE=t \cdot s_{M_d}=1.989 \cdot 2.176=4.328[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M_d-t \cdot s_{M_d} = 12-4.328=7.67\\\\UL=M_d+t \cdot s_{M_d} = 12+4.328=16.33[/tex]

The 95% confidence interval for the difference of means is (7.67, 16.33).

Answer:

For a given output value, there is, at most, one input value

Step-by-step explanation:

Given: the concept of function

To find: the statement that best describes the concept of a function

Solution:

A function is a relation in which every value of the domain has a unique image in the codomain.

Input value belongs to the domain and output value belongs to the codomain.

The statement ''For a given output value, there is, at most, one input value'' describes the concept of a function

The statement best describes the concept of a function is

For a given output value, there is, at most, one input value.

A relation is a function when each input has exactly only one output

Domain x is the input and range y is the output

In a function , each input x must have exactly only one output.

Input x cannot have two outputs.

The statement best describes the concept of a function is

For a given output value, there is, at most, one input value.

Learn more information about 'functions' here :

brainly.com/question/1593453

it is age heart rate and weather

Answer:

Step-by-step explanation:

Note that 28 + 110 + 42 = 180, and that 28 + 42 + 110 = 180 also.

Since all three angles of one triangle are the same as the corresponding angles of the other triangle, the triangles are similar.

Answer:

Rs 75,000

Step-by-step explanation:

Let the total value of property be x

If one-fifth of that is given to son

property with son = 1/5 of total value of property = 1/5 of x = x/5

If one-third of that is given to daughter

property with daughter = 1/3 of total value of property = 1/3 of x = x/3

remaining property after giving the portions to son and daughter

= total value of property - property with son -property with daughter

= x - x/5 - x/3

taking LCM of 5 and 3 (15)

= (15x - 3x - 5x)/15

= 7x/15

Given that remaining property was given to wife

property with wife = 7x/15

it is given that wife got 35000 Rs

thus,

7x/15 = 35,000

7x = 35,000*15 = 525,000

x =  525,000/7 = 75,000

Thus, total worth of property =Rs 75,000 Answer

Answer:

Rs 75,000

Step-by-step explanation:

Let the total value of property be x

If one-fifth of that is given to son

property with son = 1/5 of total value of property = 1/5 of x = x/5

If one-third of that is given to daughter

property with daughter = 1/3 of total value of property = 1/3 of x = x/3

remaining property after giving the portions to son and daughter

= total value of property - property with son -property with daughter

= x - x/5 - x/3

taking LCM of 5 and 3 (15)

= (15x - 3x - 5x)/15

= 7x/15

Given that remaining property was given to wife

property with wife = 7x/15

it is given that wife got 35000 Rs

thus,

7x/15 = 35,000

7x = 35,000*15 = 525,000

x =  525,000/7 = 75,000

Thus, total worth of property =Rs 75,000 Answer

Answer:

12x+40

Step-by-step explanation:

A=l*w

A=20(3/5x+2)

A=4*3x+20*2

A=12x+40

Answer:

[tex] = 12x + 40[/tex]

Step-by-step explanation:

[tex]area = l \times b \\ = 20 \times (\frac{3}{5} x + 2) \\ = \frac{60x}{5} + 40 \\ = 12x + 40[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

3.67 units

Step-by-step explanation:

The central angle is at the point (0,0).

Then it's at the point (1,0)

Then it moved 210 degrees.

Let's bear in mind that we start moving the degree from it's current position.

So moving 210 degrees is moving 180 degrees plus 30 degrees.

Moving 180 degrees I like transforming linearly.

Now the location is at (-1,0)

But the distance covered will be

= 2πr*210/360

r = 1

= 2*3.142*1*(210/360)

= 6.144*0.5833333

= 3.67 units

Answer:

[tex] P= 2*Lenght + 2*Width[/tex]

Since the perimeter is 56 inches we can solve for the lenght with this equation:

[tex] 56 in = 2*12in + 2*Length[/tex]

And solving for the length we got:

[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]

So then the lenght = 16 inhes and the width of 12 inches

Step-by-step explanation:

For a rectangle of width 12 inches and lenght y inches we know that the perimeter is given by:

[tex] P= 2*Lenght + 2*Width[/tex]

Since the perimeter is 56 inches we can solve for the lenght with this equation:

[tex] 56 in = 2*12in + 2*Length[/tex]

And solving for the length we got:

[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]

So then the lenght = 16 inhes and the width of 12 inches

Answer:

2 times the square root of 10

Step-by-step explanation:

If you make a right triangle and solve for the hypotenuse (the distance between P1 and P2), you will get 2 times the square root of 10.

Please mark this brainliest.

Answer: [tex]2\sqrt{10}[/tex]

Step-by-step explanation:

if you draw a triangle starting from P1 and go up to the y value of P2, the change in y is equal to 6.

From that point, go to the right until you hit P2 to get a change in x of 2.

Youre basically missing the hypotenuse of this triangle that you drew. Which is where the distance formula is derived from. 6^2 + 2^2 = s^2

You get √40 = s. It appears that they want you to simplify this square root. What are the two greatest numbers that multiply to equal 40 and atleast one of them has a perfect square root? That's 10 and 4. you can perfectly take the square root of 4, so go ahead and do that. Put that 2 outside of the square root. That gives you [tex]2\sqrt{10}[/tex]

Answer:

c, Z

Step-by-step explanation:

x+y=4

y+z=5

y=4-x

4-x+z=5

-x+z=1

z=1+x

Answer:

  19.8 cm

Step-by-step explanation:

Angle B is the complement of angle A, so we have this relation for the angles:

  B/A = 3/2 = (90°-A)/A

  2(90° -A) = 3A . . . . . cross multiply

  180° = 5A . . . . . . . . . eliminate parentheses, add 2A

  36° = A . . . . . . . . . . . divide by 5

The relations expressed by the mnemonic SOH CAH TOA remind you that ...

  Cos = Adjacent/Hypotenuse

  cos(A) = AC/AB

  AB = AC/cos(A) = (16 cm)/cos(36°)

  AB ≈ 19.8 cm

Answer:

Step-by-step explanation:

let the height height of the tree be "h"

Hence the tree's height h=9 ft

one year later,let the height of the tree increased by x ft

hence

[tex]9 + x = 16[/tex] --------This is the equation for the growth of the tree

In order to solve for the added height(growth) of the tree we need to solve for x

[tex]9 + x = 16\\x=16-9\\x=7ft[/tex]

Answer:

[tex] P(t) = A (1+r)^t [/tex]

Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:

[tex] P(t)= 6(1.7781)^t [/tex]

And replacing t=4 we got:

[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]

So then after 4 days we would expect about 60 protzoa

Step-by-step explanation:

For this case we can use the following function to model the population of protzoa:

[tex] P(t) = A (1+r)^t [/tex]

Where P represent the population after t days. a the initial amount on this case 6 and r the growth factor rate of 0.7781. so then our model would be given by:

[tex] P(t)= 6(1.7781)^t [/tex]

And replacing t=4 we got:

[tex] P(4) = 6(1.7781)^4 =59.975 \approx 60[/tex]

So then after 4 days we would expect about 60 protzoa

Answer:

The total price of the shoes including tax is 51.45

Step-by-step explanation:

You could go about this 2 ways.

One way is if the shoes originally cost $70 and they are now 30% off, it basically means that the discounted price of the shoes is 70% of the original cost, which is $49. Then to find the total price including tax, you need to find 105% of 49, because you are adding 5% to the discounted price(100). When you do the math, you should get the answer 51.45.

The other way to do it is by first finding 30% of 70, which is 21, and then subtracting that from the original price(70) to get the discounted price, $49. Then you need to find 5% of 49 and then add that to 49 to find the total cost w/ tax, which is 51.45.

Answer:

76

Step-by-step explanation:

The two angles are vertical angles so they are equal

3x+7 = 4x-16

Subtract 3x from each side

3x-3x+7 = 4x-3x-16

7 = x-16

Add 16 to each side

7+16 = x-16+16

23 =x

We want YAX

YAX = 3x+7

3*23+7

69+7

76

Answer:

Next two numbers are 15 and 32 respectively.

Step-by-step explanation:

The given pattern is  

45, 15, 44, 17, 40, 20, 31, 25, …

Here, we have two patterns.

Odd places : 45, 44, 40, 31,...

Even places : 15, 17, 20, 25,...

In series of odd places, we need to subtract square of integers.

[tex]45-(1)^2=45-1=44[/tex]

[tex]44-(2)^2=44-4=40[/tex]

[tex]40-(3)^2=40-9=31[/tex]

So, 9th term of given pattern is  

[tex]31-(4)^2=31-16=15[/tex]

In series of even places, we need to add prime numbers.

[tex]15-2=17[/tex]

[tex]17+3=20[/tex]

[tex]20+5=25[/tex]

So, 10th term of given pattern is  

[tex]25+7=32[/tex]

Therefore, the next two numbers in the pattern of numbers are 15 and 32 respectively.

Answer:

s = 4.43

Step-by-step explanation:

Using formula for bigger circle

s =r∅

Where s is the Arc length, r is rdius and ∅ is theta(angle)

8.84=5∅

∅= 8.84/5

Angle = 1.77 radians

So both angles equal to 1.77 radians

Now again

Using formula

s = r∅

Where s is the Arc length, r is rdius and ∅ is theta(angle)

s = (2.5)(1.77)

s ≈ 4.43

Answer:

I assume Josh and Peyton are his friends and both gave him advice on what to do with half of the money from the big lottery win.

Let's say Josh said "save it or invest it for your retirement" and Peyton said "use it to keep playing the lottery.

We will now look at the sense in each piece of advice!

Step-by-step explanation:

JOSH

By investing the $250,000 (half of the money won), Patrick will be sure that the money is available for him anytime and would even have gotten interest, by the time he's ready to use it.

PEYTON

By playing the lottery continuously, Patrick could get lucky once in a while and win big again. How big though?

Analyzing with the figures given,

$20 gets Patrick a lottery ticket.

$250,000 will get him 12,500 lottery tickets!

Whether he's buying the tickets at once or he'll play the lottery once in a while, I'll say he has good chances of winning big again.

So if the probability of winning big after purchasing up to 12,500 tickets is close to 1, Patrick should play the lottery with the $250,000

If the probability of winning big after purchasing 12,500 lottery tickets is close to 0 (closer to 0 than it is to 1) then Patrick should invest the $250,000 in retirement.

Answer:

see below

Step-by-step explanation:

To find the x intercept set y =0 and solve for x

6x+5y = -30

6x = -30

Divide by 6

x = -30/6 = -5

The x intercept is (-5,0)

To find the y intercept set x =0 and solve for y

6x+5y = -30

5y = -30

Divide by 5

y = -30/5 = -6

The y intercept is (0,-6)

To find the x-intercept set y =0. Solve for x.

6x+5y=-30

6x+5(0)=-30

6x+0=-30

6x=-30

x=-30/6

x=-5

The x-intercept is at (-5, 0)

To find the y-intercept set x =0. Solve for y.

6x+5y=-30

6(0)+5y=-30

0+5y=-30

5y=-30

y=-30/5

y=-6

The y-intercept is at (0, -6)

Answer:

d: please note I am not sure about this but look at my reasoning and maybe you can find your own answer that you are sure about.

D: i am sure about this.

Step-by-step explanation:

From what I looked up, i believe what you are talking about is deductive reasoning, which is based off of facts. It can't be a or b because that wasn't defined in the statement. Squares and rectangles are not the same thing since you can have a square that is a rectangle, but a rectangle that is not a square, so D is correct.

corresponding angles i believe since they are matching

I know that the 2 lines are parallel because 5 and 6 are alternate interior angles since they are on opposite sides.

4 and 6 are not vertical or right angles, so it must be d, also they follow what a corresponding angle is, which is them being matching.

Answer:

13. B

14. D

Step-by-step explanation:

13. Law of Detachment says that if two statements are true then we can derive a third true statement. So, for example, say the first statement is that you are a human. Say the second statement is that you breathe. You can write this as: if you are a human, you breathe. In this case, if you have a square, then you have a rectangle. You have a quadrilateral.

14. 4 and 6 are corresponding angles, since you can tell that there are two parallel lines from angle 5 = angle 6. You can also use angle addition theorem.