what's the numerator for the following rational expression? 6/t+7/t=?/t

The exact value of sin θ  and cos θ  is: sinθ =(√105)/19 and cosθ =16/19

The terminal side of an angle is the angle at the standard position. The terminal side of an angle θ drawn in angle standard position is the side which isn't the initial side.

Given that the point of intersection of the terminal side of θ an the unit circle is:

(16/19,y)

The exact value of sin θ  and cos θ  is: sinθ =(√105)/19 and cosθ =16/19

The given parameters is represented by:

(16/19,y)

This means that :

(cosθ ,sinθ )=(16/19,y)

Using the following trigonometric identity:

cos²θ +sinθ =1

We have:

(16/19)²+y²=1

Expand fraction:

(256/361)+y²=1

Collect like terms:

y²=1-(256/361)

Take LCM:

y²=(361-256)/361

y²=105/361

Take square roots

y=(√105)/19

Substitute value for y in

(cosθ ,sinθ )=(16/19,y)

By comparison:

cosθ =16/19

sinθ =(√105)/19

So the exact value of sin θ  and cos θ  is: sinθ =(√105)/19 and cosθ =16/19

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The probability that the contestant wins at least one car is 3/5.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

For 1 car, we consider two possible outcomes:

P(1 car) = 2/6 x 4/5 + 4/6 x 2/5

P(1 car) = 8/15

For no car in either door

P(no car) = 4/6 x 3/5

P(no car) = 2/5

The probability that the contestant wins at least one car is the sum of the probability of one car and the probability of two cars:

P(2 cars) = 2/6 x 1/5

= 1/15

P(1 car) + P(2 cars) = 8/15 + 1/15

= 3/5

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Answer:

first H(8)= 2×8+1=16+1=17

and G(17)= 4×17-5=68-5=63

Answer:

y < x + 1

Step-by-step explanation:

identify 2 points along the line (-1,0) and (0,1)

gradient = [tex]\frac{0-1}{-1-0} =1\\\\the \ y \ intercept = 1\\\\y=x+1\\\\[/tex]

let us choose point (0,0) which is within our origin and substitute

0 = 0 +1

0 = 1

but we know 0 < 1

so the region is well represented by : y < x + 1

Answer:

y > x + 1

Step-by-step explanation:

→ As the line is upward sloping we can eliminate the 2 negative equations options

y < x + 1 or y > x + 1

→ As the region shaded is above the line y = x + 1, it must be y > x + 1

The attached graph represents the graph of the function g(x)

The function f(x) is an absolute value function.

An absolute value function is represented as:

y = a|x - h| + k

Where

Vertex = (h, k)

From the graph, we have:

(h, k) = (-3, -2)

So, we have:

y = a|x + 3| - 2

Also, we have:

(x, y) = (-1, 0)

So, we have:

0 = a|-1 + 3| - 2

This gives

0 = 2a - 2

Solve for a

a = 1

Substitute a = 1 in y = a|x + 3| - 2

y = |x + 3| - 2

This means that

f(x) = |x + 3| - 2

We have:

g(x) = 2f(x)

This means that:

g(x) = 2(|x + 3| - 2)

So, we have:

g(x) = 2|x + 3| - 4

See attachment for the graph of g(x)

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Answer:

It is cosine theorem

Step-by-step explanation:

It is cosine theorem.

The two expression 2(10x +15) and -5x ( x+6) are equivalent to given expression

Expressions are the mathematical statement consisting of variables , constants and mathematical operators .

The expression given is

-20x -30

-2(10x +15)

-20x -30

-5x ( x+6)

Therefore these two expression 2(10x +15) and -5x ( x+6) are equivalent to given expression.

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The expression for hypotenuse is √4x^4 + y^4.

A theorem stating that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides.

Given:

one leg = 2x²- y²

another leg = 2xy

H² = (2x²- y²)² + (2xy)²

H² = 4x^4 + y^4 - 4x²y² + 4x²y²

H²= 4x^4 + y^4

H= √4x^4 + y^4

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Answer:

35 degrees

Step-by-step explanation:

Given all 3 angles add up 180(Sum of angles in a straight line)

[tex]2x + 30 + 40 + 40 = 180 \\ 2x + 110 = 180 \\ 2x = 180 - 110 \\ 2x = 70 \\ x = 35deg[/tex]

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Solve for x in the diagram below.

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

Notice that all 3 of those angles together make a linear pair, or a [tex]\bf{180^\circ}[/tex] angle.

This is the key to solving this problem, because the sum of these angles is 180 degrees.

[tex]\bf{2x+30+40+40=180}[/tex] | arrange the like terms

[tex]\bf{2x+30=180-40-40}[/tex] | arrange the like terms

[tex]\bf{2x+30=100}[/tex] | subtract 30

[tex]\bf{2x=70}[/tex] | divide by 2

[tex]\bf{x=35}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                    [tex]\bf{=m\angle x=35^\circ}[/tex]

[tex]\LARGE\boxed{\bf{aesthetics \not1\theta l}}[/tex]

The factorization if the given expression 128 + 2d³ is 2(64 + d³).

128 + 2d³

There are two parameters in the expression;

The common factors between 128 and 2d³ is 2

So,

128 + 2d³

= 2(64 + d³)

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An equation is formed of two equal expressions. The number of questions that Lesley answered correctly is 20.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of correct questions answered be x, while the number of questions incorrectly answered be y.

The total number of questions can be written as,

x + y = 25

Solving the equation for y,

y = 25 - x

The total marks can be written as,

3x - 1y = 55

Substitute the value of y,

3x - 25 + x = 55

4x = 80

x = 20

Hence, the number of questions that Lesley answered correctly is 20.

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The best representation for the point I is that Chana's distance from the starting line at a time when she is behind Josiah.

The point I is the distance of Chana at a particular point in time. This distance is the line a.

At point a, the speed is more so below it, it shows a speed that is less than the distance which Josiah has covered.

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Answer:

184 m²

Step-by-step explanation:

lateral area of a prism = perimeter of base × height

A = 2(14 m + 9m) × 4 m

A = 184 m²

Answer:

The answer is A)

Step-by-step explanation:

There is a domain restriction meaning the denominator should not equal to zero. If you substitute 6 and -1 into x for A) :

(1-1)(-6+6)=0

The Denominator can't be zero

Hope it helps!

3,2

because each input only has one output and 2 has 0 and 3 so it is not a function that leaves 3,2.

Answer:

33 %

Step-by-step explanation:

3200 - 2400 = 800

800 / 2400 x 100

1 /3 x 100

100/ 3

33 %

The maximum pounds of celery she can buy is  3.25 pounds.

1.5c = o equation 1

1.50o + 1.80c = 8.10 equation 2

Where:

o = pounds of onions

c = pounds of celery

How many pounds of celery can she buy?
Substitute for o in equation 2 using equation 1

1.50(1.50) + 1.80c = 8.10

2.25 + 1.80c = 8.10

1.80 = 8.10 - 2.25

1.80c = 5.85

c = 5.85 / 1.80

c = 3.25 pounds

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Answer:

2x² + 6x + 20

Step-by-step explanation:

See the picture

Answer:

6,569 pounds

Step-by-step explanation:

Ton= 2,000 pounds each

Therefore, 3 x 2,000 (pounds) = 6,000(pounds). You can use a shortcut by multiplying 3 x 2 and adding the three zeros at the end. 6,000 pounds + 569 pounds will result in 6, 569 pounds.

The probability that a point is chosen randomly inside the rectangle is either in the circle or in the trapezoid is 0.23 option first is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The area of the rectangle = 30×21 = 630 square m

The total outcomes = 630 square m

The favorable outcomes = area of the circle + area of the trapezoid

= π(5)² + [(11+15)/2]×5

= 78.53 + 65

= 143.53 square m

Probability(a point chosen randomly inside the rectangle is either in the circle or in the trapezoid):

= 143.53/630

= 0.227 ≈ 0.23

Thus, the probability that a point is chosen randomly inside the rectangle is either in the circle or in the trapezoid is 0.23 option first is correct.

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Answer:

0.13

Step-by-step explanation:

I guessed and got it correct. Sorry, I cant show work, I hope it helped!! <3

Answer:

y= -2x+2.

Step-by-step explanation:

1) according to the condition interception is '2' (point (0;2));

2) slope is: (2+4)/(0-3)= -2;

3) finally the required equation is: y=-2x+2.

P.S. the suggested option is not the only one.

The expression that is equivalent to  Balin's expression is 5/6 x 1/10.

Division is the mathematical operation that is used to determine the quotient of a number.

In order to determine the distance ran by each member, divide the total distance ran by the total number of people.

5/6 ÷ 10

5/6 x 1/10

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The expression is equivalent to Balin’s expression is StartFraction 5 Over 6 EndFraction divided by 10

Distance each member ran = Combined distance ÷ Number of Balin’s soccer team

= 5/6 ÷ 10

= 5/6 × 1/10

= 5/60

= 1/12 mile

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Answer:

y=⅔m-8 or 3y=2m-8

Step-by-step explanation:

put both equations in the form y=mx+c and solve simultaneously. when done, you will recive values for m and c. replace those values into y=mx+c

Answer:

Step-by-step explanation:

7 = (y+2)/(x-1)

Parallel lines have equal slopes.

You can "massage" the form into any form you need.

Answer:

2

Step-by-step explanation:

The first table represents the linear function.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The first table represents a linear function because the slope remains constant through out the function

Hence, the first table represents the linear function.

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Answer:

125cm³

Step-by-step explanation:

To find volume, we multiply length × width × height

(length × breadth × height)

here, we know our length to be 5cm, our width to be 5cm, and our height to be 5cm

length : 5cm

width/breadth: 5cm

height: 5cm

so, we can multiply our values together (we can plug in our known values to the volume formula of length × width × height)

length × width × height

5  ×   5  ×  5= 125

*note: we write volume as cubed (unit³)

So, we know our volume is 125cm³

hope this helps! have a lovely day :)

If the linear function has the domain (-2, -1, 0, 1, 2). Then the range of the function h(x) = 2x + 3 will be (-1, 1, 3, 5, 7).

The domain means all the possible values of x and the range means all the possible values of y.

The function is given as

h(x) = 2x + 3

The linear function has the domain (-2, -1, 0, 1, 2).

For x = -2

h(-2) = 2 (-2) + 3

h(-2) = -1

For x = -1

h(-1) = 2 (-1) + 3

h(-1) = 1

For x = 0

h(0) = 2 (0) + 3

h(0) = 3

For x = 1

h(1) = 2 (1) + 3

h(1) = 5

For x = 2

h(2) = 2 (2) + 3

h(2) = 7

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Answer: (-∞,∞)

Step-by-step explanation:

f(x)=4x+19

g(x)=12x+14

f + g=  4x +19 + 12x + 14 = 16x + 33

Domain of 16x + 33 = (-∞,∞)

Answer:

Recognize the equation as that of a horizontal line passing through the y-axis at −3