Plot the point given by the following polar coordinates on the graph below. Each circular grid line is 0.5 units apart.(2, -1)

For this type of questions you just have to substitute x by the given number ( in this case 1) anywhere x shows in the equation

f(1)= -1+7 = 6

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(lengthe + width)

Given that the perimeter = 14, it means that

2(lenght + width) must be equal to 14

Looking at the options,

2(1 + 6) = 14

2(2 + 5) = 14

2(3 + 4) = 14

2(4 + 3) = 14

2(5 + 2) = 14

2(6 + 1) = 14

Thus, the correct options are A, B, C, D, E, F

We know that Jamal paid 4061 of taxes and

where P is Jamal's income and 6.2% correspond to 0.062. Now, we must isolate P. It yields,

this means that Jamal's income was $65500 last year

Solution

Now

The final answer

It took 1.5 hour for Leo to clean the room .

In the question ,

it is given that

Leo and Oliver clean their their room

time taken by Oliver to clean the room is = 3/4 of an hour = 0.75 hours .

and also given that Leo takes twice as long as Oliver

which means

time taken by Leo to clean the room = 2*(time taken by Oliver to clean the room )

On substituting the values

we get ,

time taken by Leo to clean the room = 2*(0.75 hours)

= 1.5 hours

Therefore , Leo takes 1.5 hours to clean the room .

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You have the equation -4y=28

To solve this equation you need to clear the value of the unknown variable y, meaning, you have to simplfy the equation until you reach y=

For this, since y is multiplied by -4 you have to divide it by -4 to leave y alone, and what you do in one side of the equation must be done to the other side to keep the equality:

The value of y=-7

Step-by-step explanation: move down 1 and right 2 because it has to be a negative slope.

Answer: See attached, or read below.

Step-by-step explanation:

    First, we see there is no b value, so there is no y-intercept. The line will intercept the graph at (0, 0), also known as the origin.

    Next, we see a negative slope of -1/2. This means, starting at the origin, we will move down one unit and right two. Then repeat. Lastly, draw a straight line through all three points for our graph.

9452

Explanation

an exponential function is given by:

so

Step 1

Set the equations

a) initial population = 2363

time=0

replace

b) If the number of bacteria doubles every 157 minutes

so, the function is

Step 2

what will the population be 314 minutes from now?

Let

time=x =314

replace

therefore, the answer is

9452

I hope this helps you

x + y = 2 is the equation of the line that the hat will follow if we ignore the gravity and air resistance.

Given, we are riding in a roller coaster which follows the curve in the graph and when we reach the point (1 , 1) our hat falls off.

Now, we have to find the equation of the line that the hat follow,

The slope of the tangent to the curve x³ + y³ = 2xy  is given by,

3x² + 3y²y' = 2y + 2xy'

at the point (1 , 1)

3 + 3y' = 2 + 2y'

y' = -1

Now, the slope of the line perpendicular to the tangent of the curve is,

-1

Now, the equation of the line that hat follows is,

(y - 1)/(x - 1) = -1

y -1 = 1 - x

x + y = 2

Hence, x + y = 2 is the equation of the line that the hat will follow if we ignore the gravity and air resistance.

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Explanation

When two lines are crossed by another line (called the Transversal): Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.

so, the angle is

I hope this helps you

Recall that the simple interest means that you will calculate interest only based on the initial deposit amount. This means that the generated interests do not generate any interests.

To find the number of years James has had this account, we will first find a formula for the amount available in the account each year.

At year 0, James deposits 12500. So, at year 0 the account has 12500

At year 1, James earns 1.5% over the 12500. So we add to what we had at year 0, the interest. That is

where i is the interest annual rate of 1.5%.

At year 2, James earns 1.5% over 12500 again. So we add this value to what we had at year 1, so at year 2 he has

Finally, at year 3, James earns another 1.5% over the 12500. So we add this value to what he had at year 2, so he has

In general, from this we can see a pattern. At year n, the amount available would be

In this formula the amount of interest is given by the expression

We are told that this amount is 1687.5. So we have the following equation

so, if we divide both sides by 12500*i, we get

we know that i=1.5%. = 0.015. So we have

so James has had the account for 9 years.

the coordinate of point B is (-3,2)

In order to dilate the point with a scale factor of 1/2 we need to multiplicate the scale factor by the coordinate-x and the coordinate-y

coordinate x

coordinate y

the coordinate dilate is

B'(-1.5,1)

the correct answer is b

Given the figure of the circle Q

As shown, ST is tangent to circle Q

So, ST is perpendicular to the radius QS

So, the triangle QST is a right-angle triangle

We can apply the Pythagorean theorem where the legs are QS and ST

And the hypotenuse is QT

The side lengths of the triangle are as follows:

QS = r

ST = 48

QT = r + 36

So, we can write the following equation:

Expand then simplify the last expression:

Combine the like terms then solve for (r):

So, the answer will be r = 14

5x + 4 = x + 44

x is adding on the right, then it will subtract on the left

4 is adding on the left, then it will subtract on the right

5x - x = 44 - 4

4x = 40

4 is multiplying on the left, then it will divide on the right

x = 40/4

x = 10

The sum of 3 times a number and another number is 34. Five times the first number minus the other number is 38. What are the two numbers. The numbers are 3 and 11. The numbers are 9 and 7.​

Let

x -----> first number

y -----> another number

we have that

3x+y=34 -------> equation A

5x-y=38 -----> equation B

solve by elimination

Adds the equations

so

8x=72

x=72/8

x=9

substitute

3(9)+y=34

y=34-27

y=7

therefore

absolute change is determined by the absolute value of the subtraction of the number of refugees in both years:

absolute change = | 16.1 million - 8.7 million | = 7.4 million

Relative change is given by the quotient between final value and initial value, just as follow:

relative change = final value / initial value

= 16.1 million / 8.7 million

= 1.85

Hence, the absolute change is 7.4 million and relative change is of 1.85

We have the equation

Let's complete the square, to do it let's add and subtract 25 on the right side

Now we can have y in function of x

Now we can already identify the vertex because it's in the vertex form:

Where the vertex is

As we can see, h = 5 and k = -2, then the vertex is

Now we can continue and find the focus, the focus is

We have a = 1/20, therefore

The focus is

And the last one, the directrix, it's

Then

Hence the correct answer is: vertex (5, -2); focus (5, 3); directrix y = -7

ANSWER

B. False

EXPLANATION

We want to identify if the statement is true or false.

A function is a type of relation in which each input value is mapped directly to only one output value. In other words, each value of x has only one value of y.

To identify the graph of a function, if a vertical line can be drawn at any value of x such that it connects more than one point on the graph, then, the graph does not represent a function.

From the given graph, we see that a vertical line can be drawn to touch more than one point at several values of x.

This implies that the graph does not represent a function, hence, the statement is false.

The answer is option B.

Answer:

0.79

Explanation:

Given a binomial experiment with 18 trials; and

By the conditions required for a binomial experiment, the probability of success (or failure) remains the same throughout the experiment and for each and every trial.

Therefore:

The answer is 0.79

half the diameter is the radius, so

now we can calculate the total area of the circle , and then will calculate the area for the angle

the area of the circle is 225pi, this is the corresponding area for the complete angle of the circle, therefore it is equivalent to 2pi

now we create a relation to find the area corresponding to the indicated angle

if 225pi is equal to 2pi how much is 3pi / 5

where x is the area covered by the angle

we solve ussing cross multiplication, x is equal to: multiply the values ​​that are found diagonally and make them equal

and solve for x

The rounded area is 212.0575 square feet

Answer:

P(1+rY) (r=Interest in Decimal Form) (Y=Number of years investing)

Step-by-step explanation:

The expression you want to use for simple interest is P(1 + rY), where r = the interest (in decimal, so 0.07) and Y = the number of years you are investing.

100(1+(0.07)(20))

This turns into

100(1+1.4)

100(2.4)

And with simple multiplication (100 x 2.4) you would receive 240 as an answer.

Hope that helps.

Given in the scenario:

a.) Mary made 1/5 of a batch of cookies in 1/10 of an hour.

Let's determine how many batches of cookies can she make in one hour.

Step 1: Let's convert the given into a ratio and proportion.

Mary made 1/5 of a batch of cookies in 1/10 of an hour = 1/5 : 1/10

At x = number of batches of cookies in one hour, we get = x : 1

Step 2: Let's determine the value of x.

Therefore, Mary can make 2 batches of cookies in one hour.

Solution

For this case we have two points given :

(-2,5) and (2,-3)

We can find the slope on this way:

And the intercept would be:

5 = -2(-2)+b

5 = 4 +b

b= 1

Then the original equation is:

y= -2x+1

And we need to find equivalent equations so we can analyze one by one the options like this:

A. y+3 = -2(x-2)

y+3 = -2x+4

y =-2x+1

B. y-5 = -2(x+2)

y-5 =-2x-4

y = -2x +1

C. y=2x+1

D. y= -0.5x +1

E. y-5 = -2(x-2)

y-5 = -2x +4

y= -2x+9

Then the correct options are A and B

Given the function f(x);

When the function is flipped across the x-axis, we'll have the sign reversed.

So, the new function formed is;

To get a probability in a given set, we need to count the events we want to happen and divide by the total possibilities.

a) Here, we have a set that goes from 1 to 12, so there is 12 possibilities. We want to pick a prime number, so we need to count how many primes we have in this set.

1 is not prime.

Also, 4, 6, 8, 9, 10 and 12 are not primes.

So, we have the primes: 2, 3, 5, 7 and 11. There are 5.

So, the probability will be:

b) Assuming the die are 6-sided going from 1 to 6, we can obtain the numbers from 1 + 1 = 2 until 6 + 6 = 12. However, there are differento number of possibilities. We still are looking for 2, 3, 5, 7 and 11, however now we have a total of 6 times 6 possibilities:

And we have to calculate the combinations for each prime and add them.

2: there is only 1 + 1, so:

3: We can do 1 + 2 and 2 + 1, so there are 2:

5: We have 1 + 4, 2 + 3, 3 + 2 and 4 + 1, so 4 possibilities:

7: We have 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2 and 6 + 1, 6 possibilities:

11: We have 5 + 6 and 6 + 5 only. 2 possitilities:

In total, we have:

So, the probability will be:

It ended up being the same.

Answer:

Mr. Smith gave $1110.7 to the agency

Explanation:

Given that the job Mr. Smith took pays $76k per year.

In his first 4 weeks, taking the number of weeks per year to be 52, he is paid:

4 × ($76000)/52

= 4 × $1461.5 (Approximately)

= $5846

He is charged 19% of this earnings:

19% of $5846 is:

0.19 × $5846

= $1110.7

What he has in the end is:

$17000 - $1110.7

= $15889.3

Part A

Find out the slant height of the cone

Applying the Pythagorean Theorem

AC^2=AB^2+BC^2

we have

AC ----> slant height

AB=4/2=2 in

BC=6 in

substitute given values

AC^2=2^2+6^2

AC^2=40

AC=2√10 in

Part B

Find out the measure of the angle formed between the base and the slant height

we have that

tan( by opposite side divided by adjacent side

tan(mm

Part C

see the figure below to better understand the problem

we have that

AC and DC are slant height

triangle ADC is an isosceles triangle

because AC=DC

that means

mmmmthe answer part C is 36.86 degrees

The five-number summary of a distribution consists of

1)The minimum(smallest observation)

2)The maximum ( Largest observation)

3)median

4)Two quartiles( The first quartile and the third quartile)

That is option C

To find out if Omar made a mistake, we must solve the equation step by step.

Step 1

Step 2

Simplify the final part in step 1

Since, we have gone through all the steps and gotten exactly the same steps and solution as Omar, we can conclude that Omar did not make a mistake.

Answer:

[tex]3x = 2(x - 1)[/tex]