Determine sin(S) and sin(T).

Answer:

4 and 3/4 is the 5th shortest piece

a third of 4 and 3/4 is 1 and 7/12

the answer is: 1   7/12  in.

Step-by-step explanation:

4 and 3/4 is 19/4

19/4 divided 3 is 19/4 *1/3 = 19/12 = 1 7/12

Answer:

(-1, 4) and (2, 7)

Step-by-step explanation:

Answer:

3/16 of the class share guitars today.

Step-by-step explanation:

1/4 x 3/4 = 3/16! :)

Answer: 39.34

Step-by-step explanation:

Answer:

5x² ( x² - 2x + 2 ) ( x² + 2x + 2 ) ( x² + 2 ) ( x² - 2 )

Step-by-step explanation:

→ Find the highest common factor from 5 and 80

5

→ Find the highest common factor of x¹⁰ and x²

x²

→ Write the partially factored form

5x² ( x⁸ - 16 )

→ Factor down ( x⁸ - 16 )

( x⁴ + 4 ) ( x⁴ - 4 )

→ Factor down ( x⁴ + 4 ) ( x⁴ - 4 )

( x² - 2x + 2 ) ( x² + 2x + 2 ) ( x² + 2 ) ( x² - 2 )

Answer:

Step-by-step explanation:

The greatest common factor is that factor that includes every prime factor that is found in both expressions. Once that is removed, the formula for the factorization of the difference of squares is needed.

__

Each expression factors as ...

  5x^10 = 5·x^2·x^8

  80x^2 = 5·x^2·16

The common factors in these expressions are 5, x^2, so the expression with the greatest common factor factored out is ...

  5x^2(x^8 -16)

__

The remaining factor is the difference of squares, which factors as ...

  a² -b² = (a -b)(a +b)

Here, we have a=x^4 and b=2^2, so the factors of the difference are ...

  x^8 -16 = (x^4 -4)(x^4 +4)

The first of these factors is also recognizable as a difference of squares, so it can be factored further:

  x^4 -4 = (x^2 -2)(x^2 +2)

The second factor can also be cast as the difference of squares, allowing it to be factored further:

  x^4 +4 = (x^4 +4x^2 +4) -(4x^2) = (x^2 +2)^ -(2x)^2

  = (x^2 +2x +2)(x^2 -2x +2)

So, the complete factorization of the original expression is ...

  5x^10 -80x^2 = 5x^2(x^2 +2x +2)(x^2 -2x +2)(x^2 +2)(x^2 -2)

_____

Additional comment

We could factor to linear terms if we wanted to use radicals and complex numbers. This is the factorization in integers.

Answer: The final balance is $4,734.73

Answer:

in the picture

Step-by-step explanation:

the sign you see at the corners with arrows (see drawing) indicate a right angle

Explanation:

The area of a parallelogram is equal to base times height.

The base and height are always perpendicular to one another. Usually the base is horizontal along the ground (if not then you'd need to rotate your paper until it is, but that step is optional).

The base is 6 meters and the height is 7 meters.

Therefore, area = base x height = 6 x 7

The side of 11 meters is not used at all. It's likely put in there as a distraction.

Answer:

A = 6 * 7

Step-by-step explanation:

A parallelogram follows the same rules as a regular quadrilateral, as the only difference is that both its sides have been moved along.

Probability helps us to know the chances of an event occurring. The probability of getting a double card in a row is 0.311.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The probability of drawing a single double turn card for the first time, therefore,

Probability = 29/52

Further, given the card is replaced and reshuffled, therefore, the probability of getting a double card again will be,

Probability = 29/52

Thus, the probability of getting a double card in a row can be written as,

Probability = (29/52)×(29/52) = 0.311

Hence, the probability of getting a double card in a row is 0.311.

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Answer:

Sherlyn swam 42 minutes on Saturday

Step-by-step explanation:

danced for 3 2/4 hours on Saturday

3 2/4 hours is equivalent to 3.5 hours

1 / 5 of (that time) 3.5 hours is (1 / 5) * 3.5 = 0.7 hours

Because one hour is equal to sixty minutes, in order to change the units you have to multiply the number of hours, 0.7, by 60.

0.7 x 60 = 42 minutes

Let me know if you have any questions !

AND WELCOME TO BRAINLY :)

Answer:

We are given the dimension of the side being 5 inches and it states that we need to determine the surface area.  The first step that we must do is find the area of one side and then we multiply it by 6 because we have 6 same sides.

[tex]A = s^2[/tex]

[tex]A = (5\ in)^2[/tex]

[tex]A = 25\ in^2[/tex]

Now that we have the area of one side we can multiply it by 6 to get the total surface area.

[tex]A = 25\ in^2 * 6[/tex]

[tex]A = 150\ in^2[/tex]

Therefore, our final answer is that the surface area is 150 inches squared

Hope this helps!

Answer:

150 square inches

Step-by-step explanation:

find the area of 1 square face

5*5=25

multiply by 6 faces

25*6=150

Part A

To shift the curve 3 units to the right, we'll replace x with x-3. What this does is move the xy axis 3 units to the left. If we held the curve in place as the axis moves, then it gives the illusion the curve is moving 3 units to the right.

[tex]f(x) = x^2 + 5\\\\f(x-3) = (x-3)^2 + 5\\\\g(x) = (x-3)^2 + 5\\\\[/tex]

Do not expand out the (x-3)^2 term, because you want to keep the function in vertex form. The old vertex of (0,5) moves three units to the right to arrive at (3,5)

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

Part B

We use the same idea as before. This time we're moving the curve 10 units to the left, so we'll replace x with x+10

[tex]f(x) = x^2 + 5\\\\f(x+10) = (x+10)^2 + 5\\\\g(x) = (x+10)^2 + 5\\\\[/tex]

Answer:

a) 19.63 mm (2 dp)

b) 245.44 mm²  (2 dp)

Step-by-step explanation:

Formula

[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)[/tex]

[tex]\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]

[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}[/tex]

Calculation

Given:

[tex]\begin{aligned}\implies \textsf{Arc length} &=2 \pi (25)\left(\dfrac{45^{\circ}}{360^{\circ}}\right)\\ & = 50 \pi \left(\dfrac{1}{8}\right)\\ & = \dfrac{25}{4} \pi \\ & = 19.63\: \sf mm \:(2\:dp)\end{aligned}[/tex]

[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{45^{\circ}}{360^{\circ}}\right) \pi (25)^2\\& = \left(\dfrac{1}{8}\right)\pi \cdot 625\\& = \dfrac{625}{8} \pi\\& = 245.44\: \sf mm^2 \:(2\:dp)\end{aligned}[/tex]

Please note:  As you have not specified if π should be approximated, I have not used an approximation for π.

Answer:

[8] Area is = to 1017.36            Circumference is = to 113.04

[9] Area is = 490.625             Circumference is = 78.5

[10] D  = 16                                R = 8

Step-by-step explanation:

[8]

Area is = to 1017.36

Circumference is = to 113.04

Formula:

Area = πr²

Circumference = 2πr

Solve:

A =  πr²

A = 3.14(18) ²

A = 3.14(324)

A = 1017.36

C= 2πr

C = 2(3.14)(18)

C = 113.04

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

Area = 490.625

Circumference is = 78.5

Formula:

Area = πr²

Circumference = 2πr

Solve:

Area = πr²

A = 3.14(12.5)²

A = 3.14(156.25)

A = 490.625

Circumference = 2πr

C = 2(3.14)(12.5)

C = 78.5

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

[10]

Circle area = π * r² = π * 64 [cm²] ≈ 201.06 [cm²]

π ≈ 3.14159265 ≈ 3.14

d = r * 2 = 8 [cm] * 2 = 16 [cm]

Hence,

D  = 16

R = 8

⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻

Kavinsky

Step-by-step explanation:

scientific notation is

a.b × 10^c

with a being <> 0.

0.0002 cm = 2.0×10^-4 cm (the "2" moves 4 positions to the right for the actual number).

so, this is between 1.0×10^-4 cm and 1.0×10^-3 cm.

0.02 cm = 2.0×10^-2 cm (the "2" only need to move 2 positions to the right for the actual number).

so, this is between 1.0×10-2 cm and 1.0×10^-1 cm.

200 cm = 2.0×10² cm (now the "2" needs to move 2 positions to the left for the actual number).

so, this is between 1.0×10² cm and 1.0×10³ cm.

20,000 cm = 2.0×10⁴ cm (the "2" has to move 4 positions to the left for the actual number).

so, this is between 1.0×10⁴ cm and 1.0×10⁵ cm.

Answer:

each pair of pants was $20 each

Step-by-step explanation:

75-15=60

60/3=20

The measures for the given angles B and E are 12° .

Triangles are similar when the correspondent angles and the ratio of correspondent sides are equal. Also, it must present the same shape, but it is not mandatory the same dimension.

Like the triangles are similar,  ∠B=∠E. Then,

∠B=∠E

3y=6y-12

3y-6y=-12

-3y=-12

y=4

You can write too:

AC=DF

7a+5=5a+9

7a-5a=9-5

2a=4

a=2

Therefore,

∠B=3y= 3* 4 =12

m∠E=6y-12=6*4-12=21-12=12

AC=7a+5= 7*2+5=14+5=19

DF=5a+9=5*2+9=10+9=19

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Answer:

1 560

Step-by-step explanation:

If no digit (from the digits 3, 4, 5, 6, 7, 8) can be used more than once :

we can form 6P5 = 720 (five-digit numbers) and they are all > 7000

we can form 6P6 = 720 (six-digit numbers) and they are all > 7000

if our number has four digits ,then the digit in the ten-thousands place of it must be 7 or 8 :

In this case :

we can form 5P3=60 number where the digit in the ten-thousands place of it is 7.

and we can form 5P3=60 number where the digit in the ten-thousands place of it is 8.

Final answer :

We can form 720+720+60+60 = 1 560 number greater than 7000

Answer:

y = - 2x

Step-by-step explanation:

the equation of a line passing through the origin is

y = mx ( m is the slope )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 1, 2) ← 2 points on the line

m = [tex]\frac{2-0}{-1-0}[/tex] = [tex]\frac{2}{-1}[/tex] = - 2 , then

y = - 2x ← equation of line

The price of each comb is $0.5, and the total income from selling x plastic combs is y = x/2

An equation is an expression that shows the relationship between two or more number and variables.

The linear equation y = x/2 models the income, in dollars, from selling x plastic combs. Hence:

Price of each comb = (x/2) / x = 0.5

The price of each comb is $0.5, and the total income from selling x plastic combs is y = x/2

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Answer: B. $0.50

Step-by-step explanation:

Took the Test/Exam

Answer:

b) g(x) = x + 7

it may seem like its x - 7, but it's actually x + 7 since it shifts up the graph 7 units.

The quadratic model that represents the data will be A. -16x² - 99x + 6.

It should be noted that a quadratic model simply means a model that is represented by a quadratic equation in the form of y = ax² + bx + c.

From the complete question, the quadratic model that represents the data will be -16x² - 99x + 6.

In conclusion, the correct option is A.

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Answer:

Step-by-step explanation:

The sides and angles of the right triangle area as follows:

m∠C = 28°

m∠A = 62°

AC = 17 units

Using trigonometric ratios,

cos C = 15 / 17

m∠C = cos⁻¹ 0.88235294117

m∠C = 28.0726015272

m∠C = 28°

m∠A = 180 - 28 - 90 = 62°

AC = 17 units

AC is the hypotenuse of the right angle triangle.

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a =80 vertically oposite angle

a+b=180 angle of the same side of transversal are 180 degree

so b=180-80

=100

c=b vertically oposite angle

b=100=c

c= 100

Answer:

a=80, b=100, c=100

Step-by-step explanation:

Because A is directly across from 80 degrees, A is also 80 degrees. They are alternate angles, and so they equal the same thing. B is 100, because it is on the same line as 80, and a line equals 180 degrees. C is also 100 degrees, because it is across from B and on the same line as A, which is 80 degrees.

Hope this helps!

Answer:

0.13

Step-by-step explanation:

2/3×1/5 = 0.13

The probability of exactly 3 of the containers being defective is given as 0.1468

We have to set p as the  probability of container being non- defective

We have p as the  probability of container being defective 50 - 10 = 40

p = 40/50

= 0.8

q = 10/50

= 0.2

P(3) = 8c3 * 0.2² * 0.8⁵

= 0.1468

Hence the probability that the container has exactly 3 defective containers is 0.1468

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Based on the rate of decrease and the acres of undeveloped land, the equation to determine the number of years till 900 acres is remaining is B)900 = 3,400(0.827)^t.

As 900 acres is the target number of acres to remain, this will be on the left side of the equation as the y value.

The right side of the equation would be:

= Current number of acres remaining x ( 1 - rate of decrease) ^ number of years

= 3,400 x ( 1 - 17.3%) ^ number of years

Putting them together:

900 = 3,400(0.827)^t.

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Answer:

1

Step-by-step explanation:

7^0 = 1

Note : -

( Any number )^0 = 1

Factor 2x from 6x².

2x (3x)+14x

Factor 2x from 14x.

2x (3x) + 2x (7)

Factor 2x from 2x (3x) + 2x (7).

2x(3x+7) ====> Answers

Answer:

(2x)(3x + 7)

Step-by-step explanation:

Hello!

We can factor this expression by taking out the GCF of both the terms.

The GCF is 2x, because it is the largest factor that is in common between 6x² and 14x

The factored expression is (2x)(3x + 7)