Find an equation of the circle having the given center and radius.Center (-3, 3), radius 16

Answer

KM = 30 units

Tan M = (8/15)

Explanation

The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.

The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.

The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,

a² + b² = (hyp)²

For this question,

a = KM = ?

b = KL = 16

hyp = LM = 34

a² + b² = (hyp)²

KM² + 16² = 34²

KM² + 256 = 1,156

KM² = 1,156 - 256

KM² = 900

Take the square root of both sides

√(KM²) = √(900)

KM = 30 units

In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.

Using M as the given non-right angle,

Hypotenuse = LM = 34

Opposite = KL = 16

Adjacent = KM = 30

Using trignometric identities, we know that TOA means

Tan M = (Opp/Adj)

Tan M = (16/30)

Divide numerator and denominator by 2

Tan M = (16/30) = (8/15)

Hope this Helps!!!

Given that,

A car drove 300 miles in four hours.

We can simply put it in this way.

In 4 hours, a total distance covered by the car = 300 miles

In 1 hour, a total distance covered by the car = 300/4 miles = 75 miles.

Hence, the car was traveling at a speed of 75 miles per hour.

Answer:

145 miles

Step-by-step explanation:

870 ÷ 6 = 145

The total company's net operating income (NOI) is $103,500.

In accounting, a Net operating income refers to the figure that equals to all revenue from the property minus all reasonably necessary operating expenses.

The computation of the Net operating income is as follows:

= Gross Income - Operating Expenses

= (Sales+Sales) - [(variable expenses + variable expenses) + (fixed expenses + fixed expenses) + 137,200]

= (320,000+630,000) - [(158,100 + 343,800) + (72,300 + 135,100) + 137,200]

= 950,000 - (5,01,900 + 2,07,400 + 137,200)

= 950,000 - 8,46,500

= $1,03,500

In conclusion, the total company's net operating income (NOI) is $103,500.

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Step 1: Problem

To determine the equation of a circle with centre (5, -3) and radius 7

Step 2: Substitute the centre value and radius to the equation

Step 3: Simplify the above equation

Hence the equation of the circle is

In a unit circle, given the (x,y) coordinate, x corresponds to cosine, and y corresponds to sine.

Then use the trigonometric identity to solve for tangent.

We therefore have the following ratios for sin, cos, and tan.

Solving for the reciprocal of sin, cos, and tan we have

He spend $260 on 4 chairs:

To know how much he spent on each chair he must:

You first pick the firt digit of the dividend (260) and look if you can divide that digit into the divider (4) as in this case the firt digit 2 cannot be divided into 4 you take the first and secon digit (26) and divide it into 4 (how many times fix 4 in 26), this is equal to 6 times (this is the first digit of the quotient), then you multiply the 6 by 4 (6*4=24)and put the result under the 26 to substract it:

Now you lower the zero (of the 260) next to the result of the previous subtraction:

And divide 20 into 4 (how many times fix 4 in 20) this is equal to 5 times (this is the second digit of the quotient ) then you multiply the 5 by 4 (5/4 =20) and put the result under the 20 to substract it:

The remainder of 0 means the division has not decimal result, the result of 260 into 4 is an interger number (65)

The firt digit of the quotient is 6 because 26 into 4 is 6.

We are given that there are 20 students and an unknown number of adult chaperones.

Let x denotes the unknown number of adult chaperones.

The bus holds at most 35 people

We know that 20 students plus x number of adult chaperones should be at most 35

at most 35 means equal or less than 35

So we can write

Now we can easily solve for x

The total track lap time of the runner is 4 11/15 and it has been written as a mixed number or a fraction in lowest terms.

Mixed fraction:

The fraction represented with its quotient and remainder is known as mixed fraction.

Given,

A runner has a track lap time of 3 minutes while at a run, 5 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/2 at a jog, and 1/10 at a walk.

Here we need to find the total track lap time of the runner.

Here we can compute the Total Lap Time by multiplying each fraction by its associated lap time, then we get,

   Run Lap Time = (2/5)(3) = 6/5 minutes

   Jog Lap Time = (1/3)(5) = 5/3 minutes

   Walk Lap Time = (4/15)(7) = 28/15 minutes

So, the total lap time is, written as,

   Total Lap Time = 6/5 + 5/3 + 28/15

Now, we have to make the fraction equal to each other,

=> (6x3)/(5x3) + (5x5)/(3x5) + (28 x 1)(15 x1)

=> 18/15 + 25/15 + 28/15  

=> (18 + 25 + 28)/15 = 71/15

Now, we have to convert this into mixed fraction then we get,

=> 71/15 = 4 11/15

Therefore, the total Lap Time is 4 11/15 minutes.

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The height of the building is 38.85 ft.

Given;

length of the ladder, x = 39 ft

the angle between the ground and the ladder, θ = 85°

let the height of the building be h.

Construct this triangle, the ladder forms the hypotenuse side of the right angle triangle, the height of the triangle is the opposite side of the triangle while the base of the triangle is the adjacent side of the triangle.

Apply the following trig ratio to determine the height of the triangle;

sin(θ) = opposite/hypotenuse

sin(85°) = h/39

h = 39sin(85°)

h = 38.85 ft

Therefore, the height of the building is 38.85 ft (approx.).

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Answer:

Trusting peoples

Be happy

make friends

Hello there. To solve this question, we have to remember some properties about the representation of a complex number in the complex or Argand-Gauss plane.

Given the complex plane with the point A representing a complex number:

We have to remember that in the complex plane, a complex number z:

has coordinates

And it is more commonly represented by a vector starting at the origin and with the tip on this point.

In this case, we find that the coordinates of the point A are:

Which means that the complex number is

And this is the answer contained in the last option.

Solution:

Given:

The only acceptable first step in simplifying the expression from the options that would not change or alter the values of the expression is by multiplying (1 + sin x) to both the numerator and the denominator.

Therefore, the correct answer is OPTION B.

The tent is pentagonal , this means it has 5 sides. The tent have a side length of 5.13 meters.

The area of the pentagon can be calculated below

Each interior angle of a pentagon is

The given function is

f(x) = 5x - 2

If we are given a function f(x), the x is called argument of the function.

You just have to pass argument x to get the value of f(x).

7 out of every 500 Americans aged 13 -17 years are vegetarians

This implies that in a group of 500 Americans , 7 Americans that are within the age range of 13 - 17 years are vegetarians

7 ======== 500

x ======== 350

Introduce cross multiplication

7 x 350 = x * 500

2450 = 500x

Divide both sides by 500

2450/500 = 500x/ 500

x = 4.9

Approximately, 5

5 vegetarians aged 13 - 17 years will be present is in a group of 350 Americans

The answer is 5

The total points that the four students score in round 1 is 75 points.

Based on the information given, it's important to convert the numbers to while numbers and then add.

John has 19.5. This will be 20.

Adam had 21.2. This will be 21.

Peter has 23.8. This will be 24.

Grace has 10.2. This will be 10.

The total points will be:

= 20 + 21 + 24 + 10

= 75

The complete question is given below.

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The points of four students are:

John 19.5

Adam 21.2

Peter 23.8

Grace 10.2

About how many points did the four students score in round 1. Estimate by rounding each point total to the nearest whole number

In order to convert from fluid ounce to pint, we need to know that 16 fluid ounces is equivalent to 1 pint.

Then, to find how many pints is 24 fluid ounces, we can use a rule of three:

So 24 fluid ounces is equivalent to 1 1/2 pints, therefore the correct answer is C.

In the given figure, angle ABC is formed by a tangent and a secant.

The angle formed by tangent and secant is given by

Where mAD and mAC are the intercepted arcs.

For the given case,

Let us substitute the given values into the above formula and solve for x

The value of x is 9

So, the measure of angle ABC is

Therefore, the measure of angle ABC is 51°

You have G(x) = x².

take into account that G(x) can be considered as an streched of the F(X), moreover, F(x) is a translation of G(x) downward 3 units. If G(x) is an strech of F(x), then, G(x) is multipled by a constant lower than 1.

Then, based on the previous considerations, you have that the form of F(x) is:

F(x) = 0.2x² - 3

A rhombus have 4 sides and angles

it first must be proven to have 4 sides, or 4 angles

thats a definition for Quadrilateral

then correct option is D

If the ratio of zinc to copper is 4 to 11. A jar of the chemical contains 528 grams of copper. Then 192 grams of zinc does it contain

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that,

In a certain​ chemical, the ratio of zinc to copper is 4 to 11.

i.e 4:11 or 4 /11

If A jar of the chemical contains 528 grams of copper

We need to find how many grams of zinc does it contain.

Let us consider it as x.

Form a equation,

4/11=x/528

4×528=11x

2112=11x

Divide both sides by 11

192=x

Hence 192 grams of zinc does it contain.

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ANSWER :

0.1785

EXPLANATION :

35% will receive an incentive and (100% - 35% = 65%) will NOT receive an incentive.

So an employee has 65% chance of NOT receiving an incentive.

The probability that among 4 employees do not receive the incentive is :

GCF of 4,8 and 24

is. = 4

Then new expression is

y = 4• (x^2 + 2x + 6)

The rate of increase in water pressure in atm/km = 992 atm/km

Pressure can be defined as the external or internal force that acts on an area of an object which can be measured in atmosphere per meter.

The rate at which Mustafa dives = 0.992atm/meter.

That is,

0.992 atm = 1 meter

X atm = 1 km

But 1000m = 1 km

make X atm the subject of formula;

x atm = 0.992 × 1000

X atm = 992 atm/km

Therefore, the rate in atm/ km would be = 992 atm/km

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Answer:  [tex]6 \times 10^6[/tex] which is choice B

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

Method 1

5,846,000 rounds to 6,000,000 aka "6 million".

This converts to the scientific notation [tex]6 \times 10^6[/tex]

The first 6 is from "6 million", while the 6 as the exponent tells us to move the decimal point that many places to the right to go from 6.0 to 6,000,000

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

Method 2

Place a decimal point between the first two digits of 5,846,000 and erase the zeros at the end.

So we get 5.846

We must move the decimal point 6 spaces to the right to go from 5.846 back to 5,846,000 again

Therefore, [tex]5,846,000 = 5.846 \times 10^6[/tex]

Then the 5.846 rounds to 6.0 or simply 6 when rounding to the nearest whole number. This leads to [tex]6 \times 10^6[/tex]

Answer:

• 17, 20, 25, 29 and 40

• IQR=9

Explanation:

(a)Given the set of values:

{17, 20, 21, 25, 25, 29, 40}​

• The minimum value = 17

The first quartile

The first quartile is the median of the lower half of the data set.

The lower half of the data set = 17, 20, 21

• Therefore, the first quartile =20

The Median

The median is the number in the middle of the set of values.

The number in the middle is 25, therefore:

• Median = 25

The third quartile

The third quartile is the median of the upper half of the data set.

The upper half of the data set = 25, 29, 40

• Therefore, the third quartile =29

Finally, Maximum Value = 40.

The five-number summary of the set of values is: 17, 20, 25, 29 and 40

(b)Interquartile Range

Interquartile Range = Third Quartile - First Quartile

=29 - 20

IQR=9

First, let's sum the single costs of each item.

Because they are buying 1 jacket, 2 pairs of jeans, and 1 vest. So, the subtotal of these items is $84. (At Discount Heaven)

Then, we apply a 7% sales tax.

As you can observe, the sales tax is $5.88 for all the items purchased, and the total cost they have to pay is $89.88.

Answer:

There were 378 students who chose to study French their freshman year. This means that 72% of the total number of students chose to study French their freshman year. Therefore, the total number of students must be 378 / 0.72 = 527.5. This means that there were 148.5 students who chose not to take French their freshman year.

Step-by-step explanation:

The volume of a cone is given by the formula:

From the question, we are provided with following:

We have to use the given parameters to obtain the radius of the cone.

Thus, we have:

Therefore, the volume of the cone is:

Hence, the correct option is option BH