James and Martha are discussing special right triangles. James believes that a 30-60-90 triangle with a hypotenuse of 10 feet has a greater perimeter than a 45-45-90 triangle with a hypotenuse of 10 feet. Martha disagrees. Who is correct?​

Answers

Answer 1

Answer:

Step-by-step explanation:

Disclaimer  it is up the student to verify all the geometry algabra and mathematical formulas and calculation .

cosФ = opp/hyp     sinФ = adj/hyp        hyp = 10      perimeter = a + b + c

for the 45° right triangle

a = b     so      2a² = hyp²                       perimeter 45 = a + a + hyp    

P45 = 2a + hyp         a = sin(45) (hyp)  = [1/2√2)] (hyp)        sin(45) = (√2)/2

P45 = 2([1/2√2)] (hyp) + hyp

P45  = hyp (√2 + 1)

for the 30° right triangle

a = hyp×sin(30)     b = hyp×cos(30)           perimeter 30 = a + b + hyp    

            sin(30) = 1/2       cos(30) = (√3)/2

a  = hyp(1/2)           b = hyp(1/2)(√3)

P30 =        a        +      b         + hyp

        =  hyp(1/2)  +  hyp(1/2)(√3) + hyp

        =  hyp[ 1/2  +  (1/2)√3  + 1]

        =  hyp[ 1/2  +  (1/2)√3  + 1]             factored out the hyp

        =  (1/2)hyp[ 1 + √3 + 2]                  factored out a 1/2

P30  =  (1/2)hyp[ 3 + √3]

which is greater  P45 or P30?   vso I set both perimeters equal to each other

              P45           vs             P30

      hyp (√2 + 1)     =    (1/2)hyp[ 3 + √3]            the hyp cancel

               (√2 + 1)     =    (1/2)[ 3 + √3]                    still tough to tell  needed

               1.414 + 1    =    (1/2)[ 3 + 1.732]                to go to the calsulator

                 2.414      vs    1/2( 4.732)

                 2.414      >     2.366        thus P45 > P30    < -----  Final Answer

Disclaimer  it is up the student to verify all the geometry algabra and mathematical calculation.

Answer 2

Answer:

what he said

Step-by-step explanation:


Related Questions

A 10 METER PIECE OF WIRE IS CUT IN TO TWO PIECES ONE PIECE IS 2 METERS LONGER THAN THE OTHER HOW LONG ARE THE PIECES

Answers

one piece is 6m and the other is 4m

one piece is 2m

one is 8m

Find a solution to the equation 4(x + 7) = 38

Answers

Answer:

4(x+7)=38

4x+28=38

4x=38-28

4x=10

(divide by 4)

x=2whole number 2/4

=2whole number 1/2

or x=2.5


Circle the volume, in cm^3, of a cylinder with radius 5 cm and height 8 cm
[1 mark]
A)40π
B)80π
C)200π
D)1600π

Answers

Answer:

C

Step-by-step explanation:

Volume of a cylinder is πr²h

V = π * 5² * 8

V = π * 25 * 8

V = π * 200

V = 200π

The final price of an iPhone 12 Pro Max was $1072.85 after a 7.5% sales tax was applied. What was the original cost of the phone? Please explain

Answers

Answer:

992.39

 Step-by-step explanation:

sales tax was 80.46 subtract from 1072.85 get 992.39 original price.

Help please!!

Rogelio has $34 and he wants to buy a jacket for $75. He works with
his uncle on the weekends for $8 an hour.
Which inequality represents the number of hours (h) Rogelio could
work to earn at least enough money to buy the jeans?

Answers

The answer to this problem is B

Write an equation of the line that passes through the given point and has the given slope.
(4, 3); slope 1/2

Answers

Answer:

y = 1/2x + 1

Step-by-step explanation:

m = 1/2

Slope-intercept:

y - y1 = m(x - x1)

y - 3 = 1/2(x - 4)

y - 3 = 1/2x - 2

y = 1/2x + 1

What’s the answer!???

Answers

answer is $30

looks like u cheating

In the diagram, the measures of 22, 23 and 26 are 40°. The measure of 21
is 140°. Are lines cand d parallel?

Answers

Answer:

c. Yes because ∠2 and ∠6 are congruent.

Step-by-step explanation:

From the picture attached,

m(∠2) = m(∠3) = m(∠6) = 40°

m(∠1) = 140°

Since (∠2 ≅ ∠6) (corresponding angles)

Therefore, by the converse theorem of corresponding angles lines c and d are parallel.

Option c is the answer.

PLEASE HELP ASAP
find JL

Answers

Answer:

7

Step-by-step explanation:

Need help ill give brainliest to the correct answer

Answers

Answer:

i think that the answer is y = 3x- 1

I need help with this question

Answers

Answer:

Part A

D

Part B

76

Step-by-step explanation:

I don't know how to explain it

Solve
7 + x/3 = 2x - 5

Answers

Answer:

Exact form: x = 36\5

Decimal form: 7.2

Mixed number form: 7 1\5

Giving brainliest!!!Please help.. :(

Select the statement that describes this expression: 5 x (3 + 4) − 4.

A) 5 times the sum of 3 and 4, then subtract 4
B) 5 times 3 plus 4 minus 4
C) 5 more than the sum of 3 and 4, and then subtract 4
D) 5 times 3 plus the difference of 3 and 4

Answers

A is the answer 5 times the sum of 3 and 4 then subtract 4

Answer:

A

Step-by-step explanation:

A the anser is A deal with it...

please help me i really need it

Answers

Answer:

top right is the hypotenuse, top left is a leg, bottom right is a leg

Step-by-step explanation:

Every triangle has 2 legs and 1 hypotenuse. The hypotenuse is always the longer side and across the 90 degree angle. All of the other sides would be called the legs because they are not the hypotenuse

What is the percent decrease from 20 to 11?​

Answers

Answer:

The decrease from 20 to 11 is 9, and that is 45% of 20.

Hope this helps!

It should be 9, sorry if it’s wrong tho

HELP NEED THIS FOR A TEST!!! 20 POINTS!!

Diego's family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when remaining fuel is 1.5 gallons or less.

Answers

Answer:

a.

capacity of car = 14 gallons

consumption of fuel in one day = 0.6 gallons

consumption of fuel in 14 days = 14 x 0.6 = 8.4 gallons

fuel remaining in car = 14 - 8.4 = 5.6 gallons

so they can drive the car without warning.

b.

consumption of fuel in one day = 0.6 gallons

consumption of fuel in 25 days = 25 x 0.6 = 15 gallons

fuel remaining in car = 14 - 15 = -1 gallons

so they can't drive the car without warning.

c.

the expression 14 - 0.6t represents remaining fuel in the vehicle, where t represents number of days.

d.

14 - 0.6t = 1.5

or - 0.6t = 1.5 - 14 = - 12.5

or t = -12.5 / - 0.6

or t = 20.8333 days

so he can drive 20 days without warning.                                                                                         E.

14 - 0.6t < 1.5

or t < 20.8333

here t represents number of days car can drive without warning light.

Step-by-step explanation:

The inequality is  

The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days

14 gallons-1.5 gallons=12.5 gallons  

we know that

If the remaining fuel is greater than  1.5 gallons Diego's father can drive the car without the warning light coming on  

so

Let

x ----> the number of days

 ----> inequality that represent the situation

Solve for x

The maximum number of days that Diego's father can drive the car without the warning light coming on is 20 days

You told your friend that you could eat 3/5 of a large pizza. If you only ate 1/2 of what you said you could eat, what fraction of a large pizza did you eat?

Answers

Answer:

3/10

Step-by-step explanation:

3/5 is equal to 6/10, and half of 6/10 is 3/10

Answer:

3/10

Step-by-step explanation:

Amount of pizza u told= 3/5

Amout u could eat of  wht u told = 1/2

Amount u could eat of pizza = 3/5 x 1/2 = 3/10

(calculation attached below)

I hope im right!!

Which of these is a function please answer.

Answers

Answer:

1 and 3

Step-by-step explanation:

Answer:

Options 1 and 4

Step-by-step explanation:

Option 1

x-values are different and y-values are sameThis is a function

Option 2

x-values are repeated (3) with different y-valuesThis is not a function

Option 3

x-values are repeated and y-values are differentThis is not a function

Option 4

x- values are different, y-values are differentThis is a function

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Answers

1. 15 - 5 / 18 - 6 / 21 - 7 / 24 - 8 / 27 - 9 / 30 - 10

The diagram below shows a banquet hall’s plans to install a new dance floor.

What is the area of the new dance floor in square feet?

Answers

Answer:

333 ft squared

Step-by-step explanation:

18 x 18.5 = 333

Linda made $228 for 12 hours of work. At the same rate, how many hours would she have to work to make $133?​

Answers

Step-by-step explanation:

228 ÷12 =19

So 19 dollars per hour

Now 133÷19= 7 hours

I NEED HELP ILL GIVE BRAINLEST

Answers

The last 2 options are correct

Answer:

5,0

10,0

( I'm sorry if this wasn't helpful to you) ;(

Reflect across the y-axis. Fill in the new coordinates below:

Answers

Answer:

A(-1,2)

B(-4,4)

C(-3,1)

Step-by-step explanation:

simply reflect across the y-axis. pls give brainliest

To decide if 12.5 centimeters is greater than 140 millimeters, the first step is to set up a proportion. Which of the following proportions are correct?


A. 10mm/1cm = x/140mm
B. 1cm/10mm = 12.5cm/x
C. 10mm/1cm = 140mm/x
D. 12.5mm/1cm = 140mm/x

Answers

The answer is The one option C

A. f(x) =1/2 (4,000)^x

B. f(x) = 4,000(2)^x

C. f(x) = 2,000 (1/2)^x

D. f(x) = 4,000 (1/2)^x

Answers

the answer is b sit

hi i would rly appreciate ur help on this. I need to write these expressions as products:
1. ((a+1)^3)+(x^3)
2. ((y-2)^3)-27
3.((a-b)^3)+b^3
4. (8x^3)+((x-y)^3)
5. (27a^3)-((a-b)^3)
Thank you so much i rly appreciate it

Answers

Answer:

1.)   ((a+1)^3)+(x^3)  = a^3 + 3a^2 + 3a + x^3 + 1

2.)  ((y-2)^3)-27  =   (y^2-y + 7) x ( y - 5 )

3.)   ((a-b)^3)+b^3  = a (a^2 - 3ab + 3b^2 )

4.)   (8x^3)+((x-y)^3)  =  9x^3 -3x^2 y + 3xy^2 - y^3

5.)   (27a^3)-((a-b)^3) = 26a^3 + 3a^2 b - 3ab^2 + b^3

5) factor = (a+b)(a+b)^ 2    if a is squared and if b is cubed and moved over to = 0 then we can find (a+b)(a+b)^2 but in all cases of quadratics you can set (x -1 ) = 1 and (x-1 ) = 1  so they are always positive. Which is the same if they start of negative.

For question 5 we have a factor solved (a+b)(a+b)^ 2

Which means the same as this expansion

(

Of 120 owners of reptiles surveyed, 27 own snakes as pets. What percent of
the reptile owners own snakes as pets?

Answers

Answer:

22.5%

Step-by-step explanation:

Find the number of possible outcomes. A coffee shop offers small, medium, and large sizes. Customers can choose between French roast, Italian roast, and American roast

PLS HELP! ASAP!!!

Answers

Answer:

9

3 different sizes times 3 different flavors.

3x3=9

What is the volume of a sphere with a radius of 6.9 ft

Answers

V=4/3 π•r^3
r=6.9 ft
V=4/3 π• (6.9)^3
V=4/3 π • 328.509 ft^3
V= π•438.012 ft^3
V= 1,375.35768 ft^3
V~ 1,375 ft^3

find the inverse of y=100-x^2

Answers

Answer:

The inverse  is ±sqrt(100-x)

Step-by-step explanation:

To find the inverse, exchange x and y

x = 100 -y^2

Solve for y

Subtract 100 from each side

x - 100 = -y^2

Divide by -1

-x +100 = y^2

Take the square root of each side

±sqrt(100-x) = sqrt(y^2)

±sqrt(100-x) =y

The inverse  is ±sqrt(100-x)

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