A triangle has sides with lengths of 31 feet, 72 feet, and 78 feet. Is it a right triangle?
yes
no

Part 1

Focus on triangle ABC.

Since AB is a diameter of the circle, this means angle ACB is 90 degrees. Refer to Thale's Theorem. Or you could use the inscribed angle theorem. Thale's theorem is a special case of the inscribed angle theorem.

Minor arc CB is 48 degrees. Use the inscribed angle theorem to see that angle CAB is 48/2 = 24 degrees.

Therefore, angle CBA = 90 - (angle CAB) = 90 - 24 = 66 degrees

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

Part 2

Inscribed angle CBA was found to be 66 degrees back in part 1.

This doubles to 132 degrees to represent minor arc AC.

Or you could note that:

minor arc AC = 180 - (minor arc CB) = 180 - 48 = 132

Inscribed angle BCD is 48 degrees. This doubles to 96 degrees when using the inscribed angle theorem, and this is the measure of minor arc CBD.

-----------

Here's what we know about the arc measures of the circle

These three arcs, along with minor arc AD, will add up to get a full 360 degree circle. Check out the diagram below.

Adding those 3 pieces gets us 132+48+96 = 276

This means minor arc AD has to be 360 - 276 = 84 degrees

Then use the inscribed angle theorem one more time to divide the minor arc AD in half to get the inscribed angle ACD

84/2 = 42

The approximate value of x in the square that the diagonals meets to form four right angles is 5.7 units

Using Pythagoras theorem the value of x can be found as follows:

c² = a² + b²

where

Therefore,

8² = x² + x²

64 = 2x²

x² = 64 / 2

x = √32

x = 5.65685424949

x = 5.7 units

learn more on square here:https://brainly.com/question/12338379

#SPJ4

Answer: 5.7 units

Step-by-step explanation:

Answer:

8.625 or 8 5/8

Step-by-step explanation:

to find area you multiply length times width.

first, change 2 7/8 to an improper fraction to make multiplying easier. 2 7/8= 23/8.

then, multiply 3/1 (or 3) by 23/8. multiply across to get 69/8. Simplify the fraction to get 8 5/8 or 8.625.

Answer:

6 hours

Step-by-step explanation:

Subtract saved amount from required amount :

Divide by the pay rate :

Tyrone must work at least 6 hours to have $100 saved.

Answer:

x = -2/7

Step-by-step explanation:

The excluded values of the given expression are all the values of x that will make the denominator (7x + 2) = 0. This is because you cannot divide by 0...at least in algebra.

1. 7x + 2 = 0

7x = -2

x = -2/7

Therefore, x = -2/7 is the excluded value.

Answer:

3rd option

Step-by-step explanation:

[tex]\frac{14x}{7x+2}[/tex]

the denominator cannot be zero as this would make the expression undefined. Equating the denominator to zero and solving gives the value that x cannot be.

7x + 2 = 0 ( subtract 2 from both sides )

7x = - 2 ( divide both sides by 7 )

x = - [tex]\frac{2}{7}[/tex] ← excluded value

Answer:

Alleles because genes come in all different varieties.

I Hope This Helps!!!

Answer:

15.9

Step-by-step explanation:

The unfilled volume inside the cylinder is determined as 640π cubic units.

The volume of the cylinder is determined as follows;

V = πr²h

where;

V = π(8²)(15)

V = 960 π cubic units

V = ¹/₃πr²h

where;

V = ¹/₃π(8)²(15)

V = 320 π cubic units

ΔV = 960 π - 320 π = 640 π cubic units

Learn more about volume of cylinder here: https://brainly.com/question/9554871

#SPJ4

Answer:

It’s C

Step-by-step explanation:

i got a 100% on my quiz so trust me

ur wlcm :)

Answer:

Step-by-step explanation:

39-27=12

51-39=12

63-51=12

It’s clear that ,in this sequence we add 12 each time to a term to get the next term.

This means that this is an arithmetic sequence with a common difference of 12.

Therefore,

Term1 = 27  ; Term2 = 39  ; Term3 = 51  ; Term4 = 63

Term5 = 75

Term6 = 87

Term7 = 99

Term8 = 111

Method 2 :

Un = U1 + (n-1)r

r is the common difference = 12

U1 = 27 is the first term

Then

U8 = 27 + (8-1)×12

     = 27 + 7×12

     = 27 + 84

     = 111

There are seven "0"s between the decimal point and the digit "6".

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

Explanation:

The number [tex]6.51 \times 10^{-8}[/tex] is in scientific notation.

The exponent -8 tells us to move the decimal point exactly 8 spots to the left to get the answer 0.0000000651

In other words, we'll move the decimal point one spot to the left to go from 6.51 to 0.651

Then we move it another seven spots to the left to arrive at 0.0000000651

This is why there are seven "0"s between the decimal point and the digit "6".

Answer:

,

Step-by-step explanation:

answer. is in the image

Answer:

it's c

Step-by-step explanation:

Answer: it is c

Step-by-step explanation:

i took the test it was right<3

brainiest please and thx :)

Answer:

2 15/28

Step-by-step explanation:

First we will convert both mixed fractions into improper fractions.

5 1/4 becomes 21/4

2 5/7 becomes 19/7

21/4 - 19/7 does not work, so we must make the denominator the same

147/28 - 76/28 = 71/28

Now we convert back to a mixed number:

2 15/28

Answer: [tex]-11\frac{15}{28}[/tex]

Step-by-step explanation:

Convert to Improper fractions

[tex]5\frac{1}{4} = \frac{21}{4} \\2\frac{5}{7} = \frac{19}{7} \\[/tex]

Find a lowest common multiple

lcm(4,7) = 28 (7 * 4)

since they are just multiplying each other, we can cross multiply

[tex]\frac{(21*7) - (19*4)}{4*7} = \frac{147-76}{28} \\= \frac{71}{28} \\=2\frac{15}{28}[/tex]

Answer:

D.94 square centimeters

Step-by-step explanation:

(10×4) + (8×6) + (1/2×6×2)

= 94 cm^2

Answer:

D. 94 square centimeters

Step-by-step explanation:

It mentions the composite figure is made up of three simpler shapes.

Area (figure) = Area (parallelogram) + Area (rectangle) + Area (triangle)

Answer:

-32

Step-by-step explanation:

-2^2 is 4

-2^3 is -8

So 4•-8

=-32

Hope this helps. Brainliest would be appreciated.

We need a maximum enlargement of n = 18 terms in order to guarantee this level of accuracy for Simpon's Rule.

The estimation of Simpson's rule follows an approach where the value of the definite integral [tex]\int\limits^a_b f{x} \, dx[/tex] is approximated by using a parabolic method of approximation for each subinterval of the interval [a, b].

The formula for calculating Simpon's rule can be expressed as:

[tex]\mathbf{\int ^b_a f(x) d \simeq \dfrac{\Delta x}{3}[y_o+4y_1+2y_2+4y_3+2y_4+...+4{y_{n-1} +y_n}}[/tex]

Given that:

[tex]\mathbf{\int ^1_0 7ex^2 dx }[/tex],

We need to determine the fourth derivative; i.e.

[tex]\mathbf{f'(x) = 14xe^{x^2}}[/tex]

[tex]\mathbf{f''(x) = 14ex^2 +28x^2e^{x^2} = (14+28x^2)e^{x^2}}[/tex]

[tex]\mathbf{f'''(x) = 56xe^{x^2} +2(14+28x^2)e^{x^2} = (84x+48x^3)e^{x^2}}[/tex]

[tex]\mathbf{f^{iv}(x) = (84+144x^2)e^{x^2} +2x(84x+48x^3)e^{x^2} = (84x+312x^2+96x^4)e^{x^2}}[/tex]

The maximum value of the 4th derivative on the interval [0,1] is:

[tex]\mathbf{f^{iv}(1) = 624e}[/tex] and the error is bounded by:

[tex]\mathbf{\Bigg| \dfrac{f^{iv}(1) (1-0)^5}{180n^4} \Bigg| = \dfrac{624e}{180n^4}=\dfrac{52e}{15n^4}}[/tex]

Now for the error to be less than 0.0001; we have:

[tex]\mathbf{\dfrac{52e}{15n^4} < 0.0001}[/tex]

[tex]\mathbf{52e < 0.0015n^4}[/tex]

[tex]\mathbf{n^4 > \dfrac{52e}{0.0015}}[/tex]

[tex]\mathbf{n > \sqrt[4]{ \dfrac{52e}{0.0015}}}[/tex]

n ≅ 17.52.

Therefore, we can conclude that we need a maximum of n = 18 terms in order to guarantee this level of accuracy for Simpon's Rule.

Learn more about Simpson's Rule here:

https://brainly.com/question/13107531

#SPJ4

Answer:

It will make 4 90° turns, because each 1/4 turn or 15 minutes is 90°.

Answer:

Here is the ans...hope it helps

Answer:

1326 cm²

Step-by-step explanation:

1) Identify the equation of the surface area of a rectangular prism

       [tex]A = 2(wl + wh + hl)[/tex]

2) Input the corresponding values [tex]l=15 cm[/tex]; [tex]w=22 cm[/tex]; and [tex]h=9 cm[/tex] into the equation, and solve for the area

       [tex]A=2(wl+wh+hl)\\A=2((22)(15)+(22)(9)+(9)(15))\\A=2(330+198+135)\\A=2(663)\\A=1326 cm^{2}[/tex]

3) ∴ [tex]A=1326cm^2[/tex]

Answer:

81.055 ft²

Step-by-step explanation:

A full circle has a central angle of 360°.

A sector with a central angle is 72° is 72/360 = 1/5 of a circle.

A full circle has 5 times the area of a sector with a 72° central angle.

A = 5 × 16.211 ft²

A = 81.055 ft²

The function that could be the function h is option A.

This refers to the type of function that can be defined by a rational fraction and contains polynomials.

Hence, we can see that option A is correct because x²+16 never turns 0, and this makes this function continuous and both the numerator and denominator are both polynomials of the second degree.

Read more about rational functions here:

https://brainly.com/question/1851758

#SPJ4

Step-by-step explanation:

since he was already on time on the first day, the question is reduced to the probability of being on time on exactly one of the next 2 days.

the probability to be on time on exactly one day means to be on time on one day and to be late on the other.

the probability to be late is the opposite of the probability to be on time, so

1 - 0.7 = 0.3

so, the probability for this combined event for one of the day combinations is

0.7 × 0.3 = 0.21

how many day combinations (1 day on time, the other late) can we have ? 2 (either on time on the first and late on the second, or late on the first and on time on the second).

so, we need to multiply this with the basic probability and get

0.21 × 2 = 0.42

so, b. is the right answer.

The total surface area of the cylinder in terms of π is 96π cm². The correct option is the second option 96π cm²

From the question, we are to determine the total surface area of the cylinder

The total surface area of a cylinder can be calculated by using the formula,

T.S.A = 2πr² + 2πrh = 2πr(r +h)

Where r is the radius

and h  is the height

From the given information,

h = 8 cm

r = 4 cm

Putting the parameters into the formula, we get

T.S.A = 2π×4(4 +8)

T.S.A = 8π(12)

T.S.A = 96π cm²

Hence, the total surface area of the cylinder in terms of π is 96π cm². The correct option is the second option 96π cm²

Learn more on Calculating Total surface area of a Cylinder here: https://brainly.com/question/15389804

#SPJ1

Answer:

For each object, choose an appropriate scale for a drawing that fits on a regular sheet of paper. Not all of the scales on the list will be used.

Step-by-step explanation:

The closest integer value of x where both functions are equal is 1

The equations are given as:

y = 12x + 12

y  = (14)^x

Next, we plot the graph of both equations.

From the attached graph, both functions intersect at:

x = 1.249

Approximate this value

x = 1

Hence, the closest integer value of x where both functions are equal is 1

Read more about system of equations at:

https://brainly.com/question/14323743

#SPJ1

The value of the trigonometry equation (sin 60)(cos 30)+(cos 60)(sin 30) is sin (60+30). Option J is correct.

The formula of sum of sin (a+b) is the trigonometry identity which is used to solve and simplify the problem based on trigonometry equation.

The formula of sum of sin (a+b),

Sin(A+B)=(sin A)(cos B)+(cos A)(sin B)

Here, (A and B) are the measure of angles.

The trigonometry equation given in the problem is,

(sin 60)(cos 30)+(cos 60)(sin 30)

Compare this expression with the above formula we get,

A=60

B=30

Thus, the value of the given expression is,

(sin 60)(cos 30)+(cos 60)(sin 30)=sin (60+30)

Thus, the value of the trigonometry equation (sin 60)(cos 30)+(cos 60)(sin 30) is sin (60+30). Option J is correct.

Learn more about the sum of sin (a+b) here;

https://brainly.com/question/13094664

#SPJ1

The factor of the polynomial 18x³ + 6x²y - 9x² - 3xy will be 3x(6x² - 2xy - 3x - y). Then the correct option is C.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The polynomial is given below.

⇒ 18x³ + 6x²y - 9x² - 3xy

Then the factor of the polynomial will be

⇒ 18x³ + 6x²y - 9x² - 3xy

⇒ 3x(6x² - 2xy - 3x - y)

More about the factorization link is given below.

https://brainly.com/question/6810544

#SPJ1