This circle is centered at the origin, and the length of its radius is 8. What is
the circle's equation?
or +
5
8
5
OA. x+y=8
OB.x²2² +2²=8
OC. x + y = 64
OD. x² + y² = 64
4

All of these questions require one thing: trigonometric functions.

There are 3 main trigonometric functions, which can only be used on right triangles: sine, cosine, and tangent.

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Tangent = opposite / adjacent

When trying to figure out what function to use, we always start by looking from the angle. Take problem a, for example. Looking from angle E, of which the value is not given, we have the side opposite and the side adjacent. Therefore, we should use the tangent function.

---The hypotenuse is always the longest side of the triangle. It is never considered the opposite or adjacent side.

Let's set up our function with the given information from problem a.

tan(x) = 9.7 / 5.2

---The tangent of an unknown angle is equal to the quotient of the opposite side and the adjacent side.

Now, solving for the value of x will require a calculator. We'll need to use what's called an inverse trigonometric function. Most calculators have these directly above the regular trigonometric functions, and the inverse functions are accessed using a "second" key.

---Ensure that your calculator is in degrees, not radians!

x = tan^-1(9.7 / 5.2)

x = 61.805 = 62 degrees

Next, let's take a look at problem b. This time, we're solving for a side length instead of an angle. But, we're still going to start by looking from our angle.

Looking from the 38 degree angle, we are given the adjacent side and an unknown hypotenuse. Therefore, we should use the cosine function.

cosine(38) = 53.1 / r

---The cosine of a 38 degree angle is equal to the quotient of 53.1 and an unknown hypotenuse, r.

Use your algebra skills to isolate the variable r.

r * cosine(38) = 53.1

r = 53.1 / cosine(38)

---From here, all you need to do is plug this into your calculator. Since we are solving for a side length (and given an angle), we are just using the regular trigonometric function buttons on the calculator.

r = 67.385 = 67.4 units

Hope this helps!

The odds in favor of the Cougars losing the toss in exactly two of three games is 3:8 option second 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.

We have:

A coin toss is used to determine which team will receive the ball at the beginning of a football game.

The Cougars always choose tails in the toss.

There will total of 8 cases and in 8 cases there will be three cases in which exactly two heads will come so,

3:8

The cases = {TTT, TTH, THT, HTT, HHT, HTH, HHT, HHH}

Thus, the odds in favor of the Cougars losing the toss in exactly two of three games is 3:8 option second is correct.

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Answer:

x=1, y=1. (1, 1).

Step-by-step explanation:

y=-5x+6

y=3x-2

------------

-5x+6=3x-2

-5x-3x+6=-2

-8x+6=-2

-8x=-2-6

-8x=-8

8x=8

x=8/8=1

y=3(1)-2=3-2=1

Answer:

y = -x + 2

Step-by-step explanation:

*Assuming the slope given is -1*

Applying point-slope formula :

1) The equation of the line passing through (−4, 4) and parallel to the line whose equation is 7x − 9y − 8 = 0 is; y - 4 =  ⁷/₉(x + 4)

1) We are told that the line passes through (−4, 4) and is parallel to the line whose equation is 7x − 9y − 8 = 0

Thus, let us rearrange to find the slope.

7x − 9y − 8 = 0

⇒ 9y = 7x - 8

⇒ y = ⁷/₉x - ⁸/₉

Slope; m = ⁷/₉

Now,  the point slope formula is;

y − y₁ = m(x − x₁)

where;

y₁ is the y-coordinate

x₁ is the x-coordinate

m is the slope

Thus the line Passing through (−4,4) is;

y - 4 =  ⁷/₉(x + 4)

2) The equation in general form is;

y = 4 + ⁷/₉x + ²⁸/₉

y = ⁷/₉x + ⁶⁴/₉

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Answer:

-1

Step-by-step explanation:

From 10 to 8.5   is  - 1.5  

   this is -1   S.D.   below the mean

(8.5 - 10)/1.5 = -1

The number of rows of seats needed to seat the greatest possible number of participants in each row is 5

The highest common factor is the highest number that divides the numbers given.

On the basis of given data

Total number of children = 26

Total number of adults = 39

The highest common factor of both the number is 13 ,

Therefore the highest possible number of people that can sit in one row so that the number is in constant in all the rows.

So 2 rows of children of 13 each and

3 rows of adult of 13 each

Which makes the total number of rows = 5

Therefore the number of rows of seats needed to seat the greatest possible number of participants in each row is 5

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Answer:

[tex]\dfrac 5{13}[/tex]

Step-by-step explanation:

[tex]\sin \theta =\dfrac{\text{Perpendicular}}{\text{Hypotenuse}} = \dfrac{5}{\sqrt{5^2 +12^2}} = \dfrac 5{\sqrt{169}} = \dfrac 5{13}[/tex]

The equation best models the situation 100 + 0.8(x - 100) = 250.

The correct option is (D)

An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.

The complete question is:

An ongoing promotion at a department store gives customers 20% off the portion of their bill that is over $100. Ruby's total bill at the department store after the promotion has been applied is $250. If x represents the amount of money Ruby would have spent on the same purchase at the department store without the promotion, which of the following equations best models the situation?

A. 0.2x + 100 = 250

B. 0.8x + 100 = 250

C. 100 + 0.2(x - 100) = 250

D. 100 + 0.8(x - 100) = 250

Given:

Department store gives 20 % off the portion of the bill that is over 100 dollars.

Total bill = 250

let x is the amount of money she would have spent without the promotion.

Then, cost after discount applies = 0.8 ( x - 100 ).

Hence, the equation is 100 + 0.8 (x - 100) = 250.

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Based on the image description, the quantity that is equal to cos W is sin P.

The image is known to be showing an object on a ramp. Based on it, we can therefore take the angle a to the complementary angle of angle w.

Note that the angle w and angle b are said to be the same via alternate interior angles. Therefore,  the quantity that is equal to cos W is sin P.

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Answer:

20 mph

Step-by-step explanation:

First problem:

The new speed is 26 mph.

The old speed was x.

The new speed is 30% higher than the old speed.

1.3x = 26

x = 20

Answer: 20 mph

Second problem:

A number, perhaps a percent or a fraction, is missing from the problem.

The choice trigonometric ratio is tangent and the distance is 3. 98 meters.

The given angle is 86

The opposite side is given as 57 meters

The distance is in the adjacent

Thus, trigonometric ratio to use is the tangent

Tangent = opposite/ adjacent

We have,

tan 86 = 57/x

14. 300 = 57/x

x = 57/ 14. 300

x = 3.i 98 meters

Thus, the choice trigonometric ratio is tangent and the distance is 3. 98 meters.

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Answer:

5

Step-by-step explanation:

Divide 200 by 40 to get 5.

Answer:

ig 5 Apples can be Brought with Rs. 200

Step-by-step explanation:

Rs. 40 = 1 apple

Rs. 200 = ? Apple

therefore 5 apples can be brought...

Hope it Helps!!!

Answer:

[tex]\huge\boxed{\sf Option \ D}[/tex]

Step-by-step explanation:

[tex]\displaystyle =\frac{36}{25} \\\\[/tex]

36 and 25 have no common factor as:

and

So, No factor can be cancelled out and thus, the expression can not be simplified further. So, It will remain the same.

[tex]\rule[225]{225}{2}[/tex]

Answer:

d

Step-by-step explanation:

i did it

Answer:

[tex]\sf r^6[/tex]

Step-by-step explanation:

         [tex]\boxed{\bf \dfrac{a^m}{a^n}=a^{m-n}}[/tex]

In exponent division, if bases are same, subtract the powers.

 [tex]\sf \dfrac{r^9}{r^3}=r^{9-3}=r^{6}[/tex]

Answer:

Yes

Step-by-step explanation:

Answer:

2: no

3: no

4: no

5: yes

6: no

8: no

9: no

10: no

11: yes

Step-by-step explanation:

there are some simple divisibility rules that we can utilize here:

a number is divisible by __ if...

2: ends in [last digit] 0, 2, 4, 6, 8

so 275 is not divisible by 2

3: sum of digits is 3

2 + 7 + 5 = 14 [14 is not divisible by 3]

so 275 is not divisible by 3

4: last two digits are divisible by 4

75 is not divisible by 4

so 275 is not divisible by 4

5: last digit is 0 or 5

so 275 is divisible by 5

6: number is divisible by both 2 and 3

we know that 175 is not divisible by 2 or 3, so 275 is not divisble by 6

8: last three digits are divisible by 8

>> we also know that any number that 8 goes into, 4 also goes into [not always the other way around], meaning that because 175 is not divisible by 4, it must not be divisible by 8

so, 275 is not divisible by 8

9: sum of digits is divisible by 9

>> we also know that 9 only can go into numbers that 3 can go into, so because 175 is not divisible by 3, it must not be divisible by 9

so, 275 is not divisible by 9

10: last digit is 0

so, 275 is not divisible by 10

11 is a bit complicated:

sum of digit in odd places and sum of digit in even places has a difference is divisible by 11 [or is 0]

2 7 5

odd places: 2, 5 (2 + 5 = 7)

even places: 7 (7 = 7)

difference between 7 and 7 is 0 (7-7 = 0),

so, 275 is divisible by 11

hope this helps!! :)

Step-by-step explanation:

The graph is shown in the image above.

Answer: Draw a line through the two points (5,-3) and (7,-4)

See the diagram below.

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

Explanation:

Start at (5,-3). Then move down 1 and to the right 2 units to arrive at (7,-4)

The motion of "down 1, right 2" is from the slope of -1/2

slope = rise/run = -1/2

rise = -1 = go down 1 unit

run = 2 = go 2 units to the right

Two points are the minimum amount needed to draw any line. Plot the two points (5,-3) and (7,-4) and draw a straight line through them as shown in the diagram below. I used GeoGebra to make the graph. Desmos is another tool you could use.

Each step of the proof are:

The given parameter is:

Lines a and b are parallel.

This is represented as; a || b

Corresponding angles are equal.

∠1 and ∠5 are corresponding angles.

So, we have: ∠1 ≅ ∠5

Also, they are congruent.

So, we have ∠1 ≅ ∠5

Vertical angles are equal.

∠5 and ∠7 are vertical  angles.

So, we have: ∠5 ≅ ∠7

Also, they are congruent.

So, we have ∠5 ≅ ∠7

According to the transitive property;

If ∠1 ≅ ∠5 and ∠5 ≅ ∠7, then ∠1 ≅ ∠7

Hence, it has been proved that ∠1 ≅ ∠7

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Answer:

x= -10 , x= -5 , x=5

Step-by-step explanation:

we are given function as

x^3+10x^2-25x-250

We are given one of zero is x=-10

we can find all possible factors of 250

so, we will check zeros at x=-5 and x=5

At x=-5:

we can plug x=-5

At x=5:

we can plug x=5

So, other zeros are

x=-5 and x=5

All zeros are

x=-10 , x=-5 , x=5

We can see that the area of the triangle is: 5.65in².

A triangle is actually known to be a shape that has three sides, three angles and three vertices. It's also known as a plane shape.

In order to find the area of the triangle, we will use Pythagorean Theorem: c² = a² + b².

Where c = hypotenuse = 6in.

b = 2in.

6² = a² + 2²

36 = a² + 4

a² = 36 - 4 = 32

a = √32

Area of the triangle = ½ × base × height.

Where base = √32

height = 2

Thus: A = ½ × √32 × 2

A = √32 = 5.65in².

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The solution to the given compound inequality 2x - 3 < x + 2 ≤ 3x + 5 is 5 > x ≥ -3/2

2x - 3 < x + 2 ≤ 3x + 5

solve differently

2x - 3 < x + 2

2x - x < 2 + 3

x < 5

x + 2 ≤ 3x + 5

x - 3x ≤ 5 - 2

-2x ≤ 3

x ≥ 3/-2

x ≥ -3/2

Therefore, the solution of the compound inequality is 5 > x ≥ -3/2

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Using linear function concepts, it is found that a set of ordered pairs with a slope of 3 is perpendicular to the set (12,3), (9,4).

A linear function is modeled by:

y = mx + b

In which:

If two lines are perpendicular, the multiplication of their slopes is of -1. The set (12,3), (9,4) has the slope given by:

m = (4 - 3)/(9 - 12) = -1/3.

Hence, for the perpendicular set:

[tex]-\frac{1}{3}m = -1[/tex]

m = 3.

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2.5 miles/hour

Simply 15/6

Answer:

Colin walks an average speed of 2.5 miles per hour.

Step-by-step explanation:

15/6= 5 miles/2 hours

2.5

Subdivide the interval [0, 3] into 6 subintervals of equal length, ∆x = (3 - 0)/6 = 1/2. Then the partition is

[tex]\left[0,\dfrac12\right] \cup \left[\dfrac12,1\right] \cup \left[1,\dfrac32\right] \cup \cdots \cup \left[\dfrac52,3\right][/tex]

The right endpoint of the [tex]i[/tex]-th subinterval is

[tex]r_i = \dfrac12 + (i-1)\times\dfrac12 = \dfrac i2[/tex]

with [tex]i\in\{1,2,3,\ldots,6\}[/tex].

Then the area under the [tex]y=x^2[/tex] on the interval [0, 3] is approximately

[tex]\displaystyle \int_0^3 x^2 \, dx \approx \sum_{i=1}^6 (r_i)^2 \Delta x = \frac18 \sum_{i=1}^6 i^2[/tex]

Recall that

[tex]\displaystyle \sum_{n=1}^N n^2 = \frac{N(N+1)(2N+1)}6[/tex]

Then the approximate value of the area is

[tex]\displaystyle \int_0^3 x^2 \, dx \approx \frac{6\times7\times13}{48} = \boxed{\frac{91}8}[/tex]

The actual value of the area is 9, so this approximation is an overestimation, as is always the case when using a right endpoint sum for an increasing function.

Unit conversion is a way of converting some common units into another without changing their real value. The correct option is D.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

The complete question is mentioned in the below image.

Given that 2 inches are 5 centimeters. Therefore, the ratio of an inch to centimeters are,

2 inches = 5 centimeters

1 inch = 5/2 centimetes

Now, if using the ratio, the measurements are converted then,

A.) 7 inches = 7 × (5/2)centimeters = 17.5 centimetes

B.) 5 inches = 5 × (5/2)centimeters = 12.5 centimetes

C.) 8 inches = 8 × (5/2)centimeters = 20 centimetes

D.) 3 inches = 3 × (5/2)centimeters = 7.5 centimetes

As it can be observed that the correct statement is D If 2 inches is 5 centimeters, then 3 inches is 7.5 centimeters. Hence, the correct option is D.

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The time spent by the repairman there will be 3 hours so the correct answer is option D.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

A roof repairman charges a $60 consult fee, and then $45 per hour to complete repairs. if the homeowner pays a total of $195.

The time will be calculated as:-

Total amount =  $195

Now the fixed consulting cost will be $60 and will be deducted from the

total amount.

Variable cost = 195 - 60 = 135

The $45 per hour charge so for $145 the time will be:-

Time = 135 / 45

Time =  3 Hours

Therefore the time spent by the repairman there will be 3 hours so the correct answer is option D.

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