Find the center and the radius of the circle whose equation is x^2+y^2+8x-10y-23=0

We have the next polynomial function

In order to find the zero we punt the function equal to zero

We have a given zero that is 1-i

x=1-i

than means that we need the conjugate of the zero given is also a zero

x=1+i

and then we need a third zero because the polynomial has third-degree it can be calculated if we factorize the polynomial given

Therefore the zeros are

x=-1

x=1-i

x=1+i

Explanation: There are different ways to solve this problem but let's focus on just one. When we have a division multiplied by a number we can always consider the following

Step 1: Once we understand that we can solve by models as follows

First, let's solve the numerator (our multiplication)

Step 2: Once our numerator 3 x 12 = 36 now we have

Now we can solve our division as follows

As we can see above, we have 36 blue boxes divided into 4 red larger boxes equally which gives us 9 blue boxes for each of the red boxes. It means 36/4 = 9.

Final answer: So our final answer is

.

6 square box, each of length 3.5 inches:

Area of the original box = 6 x area of the smaller box = 6 x L x L

Area of the original box = 6 (3.5 x 3.5) = 6 (12.25) = 73.5 square inches

Apr = 2.5% every 6 months

Use formula

N = N1 ( 1+ 2.5/100)^ 2

APY= (1 + r/2) ^2 - 1

. = ( 1 + 2.5/2) ^2 - 1

. = (2.25)^2 - 1

. = 4.0625

Then answer is

Annual percentage yield

APY = 4.06 %

In order to calculate the distance between A and C, we can use the Pythagorean Theorem, since we have a right triangle:

So the distance between A and C is 13 meters.

Answer

Percentage of students that are freshman = 23%

Explanation

Total number of students in a club = 100

Number of freshman = 23

Percentage of students that are freshman = [(Number of freshman)/(Total number of students in a club)] x 100

Percentage of students that are freshman = (23/100) x 100

Percentage of students that are freshman = 23%

First, calculate each velocity:

so:

Now calculate the average between the 3 velocities:

The answer is 126.67 m per minute.

Answer:

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

The mean is:

Simplify and solve for x:

Answer:

x = 45

Step-by-step explanation:

Formula we use,

→ (Sum of numbers/Total numbers) = 35

Now the value of x will be,

→ (Sum of numbers/Total numbers) = 35

→ (20 + 30 + 45 + x)/4 = 35

→ (95 + x)/4 = 35

→ 95 + x = 35 × 4

→ x = 140 - 95

→ [ x = 45 ]

Hence, the value of x is 45.

Answer:

Febuary -2.25

Explanation:

We are told that the negative values indicate the amount of data that was under the plan. Therefore, the more negative the value, the less of the data Emmanuel used.

With this in mind, looking at the table we note that in the month of febuary Emmnuel used -2..25 of data (2.25 untis less than his plan ) which is the least amount of data used in any month.

The two triangles are not similar

Here, we want to check the if the given triangles are similar

From the diagrams given, we can see that the only similarity between the two is the presence of an angle 100 at the top vertex

This does not give any other proof of similarity between the two triangles

Thus, we have it that the triangles cannot be similar based on the given point

Hence, we can conclude that the two triangles are not similar

notice that we have one factor of the complete expression, then, we can make the following division:

therefore, the missing factor is 7y+4

We will solve as follows:

From the information given we can deduce that the triangle is Isosceles. We also have from theorem that angles that are opposite to congruent sides are also congruent, therefore angle

Using this, and the fact that the sum o all internal angles of a triangle add to 180°, the following is true:

Now, we replace the values we know:

So, the value of angle

SOLUTION

Tom wants to get to the playground at 2:30 p.m

if it take him 2

Given that :

We can prove that :

is it's inverse doing the following:

Step 1. Set y = f(x):

Step 2. Switch the variables:

Then we solve for y:

Step 3. The inverse of :

can be found in a similar way.

This tells us that f(x) and g(x) are one to one functions are f(x) is the mirror image of g(x)

From the figure given;

Observe that, side AB is congruent to EF.

Side AC is congruenct ED

side BC is congruent to FD

From the above, we can deduce that Δ ABC ≅ Δ EFD

Answer:

[tex]\sqrt{122}\approx{11.05}[/tex]

Step-by-step explanation:

In any right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. This is commonly represented by the equation [tex]a^2+b^2=c^2[/tex].

In the triangle on the left:

[tex]a^2+b^2=c^2[/tex]

[tex]5^2+9^2=c^2[/tex]

[tex]25+81=c^2[/tex]

[tex]106=c^2[/tex]

[tex]\sqrt{106}=c[/tex]

The hypotenuse of the triangle on the left becomes a leg of the triangle on the right, so we repeat the process:

[tex]a^2+b^2=c^2[/tex]

[tex]4^2+(\sqrt{106})^2=c^2[/tex]

[tex]16+106=c^2[/tex]

[tex]122=c^2[/tex]

[tex]\sqrt{122}=c[/tex]

[tex]c\approx{11.05}[/tex]

Given:

(a) The parent function of p(x) is the cubic function:

(b) To produce p(x) from y, we need to perform the following transformations in order:

* Shift to the left 3 units. This gives the function:

* Stretch vertically by a factor of 3. This gives the function:

* Shift upward 2 units. This gives the final function:

(c) The graphs of the parent function (in blue) and the transformed function (in red) are shown below:

Answer:

Step-by-step explanation:

We have the following:

solving by substitution:

now, for x

The solution is

An order of magnitude is the class of scale of any amount in which each class contains values of a fixed ratio to the class preceding it. Usually, the amount scaled is 10, and the scale is the exponent applied to this amount.

Question 5

The weight of each car is 3,000 pounds. There are 5 cars in total. Therefore, the total weight is given to be:

Writing the calculated weight in standard form, scaling to 10, we have:

Therefore, the order of magnitude is 4.

Question 6

The number of people that voted per county is 20,000. There are 7 counties in total. Therefore, the total number of people that voted is:

Writing the calculated number in standard form, scaling to 10, we have:

Therefore, the order of magnitude is 5.

Given:

Total number of candy in a bag is 15.

Number of orange flavored candy is 2

Number of cherry flavored candy is 6

Let A be the event of picking an orange or a cherry flavored candy from the bag.

ANSWER;

The fraction of the time she worked was 7/9 of the time the polls were opened

EXPLANATION;

Here, we want to get the fraction of the time in which Marlene worked

What we have to do here is to calculate the total time the pool was opened, then calculate the total time in which she went for break. Then we divide the break time by the total opening time

We proceed as follows;

From 7 : 30 am to 9pm

7:30 am to 9:30 pm is 14 hours

Kindly note that we are to subtract 30 minutes, so we have the total time as 13 hours and 30 minutes

For ease of calculations, we shall have all the time in minute

Recall, 60 minutes are in an hour

So, in 13 hours, we have 13(60) = 780 minutes

Added to the 30, we have a total of 780 minutes + 30 minutes = 810 minutes

Break Times

The first break is 10; 30 am to 12 pm; that is a total time of 1 hour 30 minutes

The second break is from 5:30 pm to 7 pm; that is another 1 hour 30 minutes

Total time spent on breaks is 3 hours

Converting to minutes, we simply multiply by 60 and that will give 3(60) = 180 minutes

Thus, we can now proceed to divide;

The above is the fraction spent on breaks. To get the farction worked, we simply subtract the above fraction from 1

We have this as;

In the given circle, The diameter of the circle is 8 in

Radius is the half of the diameter,

Radius = Diameter/2

Radius = 8/2

Radius = 4 in

Area of the circle with radius r is express as :

Substitute the value of radius = 4in

Area of the circle is 50.27 in²

Answer : Area of the circle is 50.27 in²

Given:

a.) Solution A is 65% salt

b.) Solution B is 90% salt

c.) She wants to obtain 140 ounces of a mixture that is 85% salt.

Let x = the number of ounces of Solution A

Let y = the number of ounces of Solution B

x + y = 140

y = 140 - x (Eq. 1)

0.65x + 0.90y = 0.85(140)

0.65x + 0.90y = 119

(0.65x + 0.90y = 119) x 100

65x + 90y = 11,900 (Eq. 2)

Substitute Eq. 1 to Eq. 2

65x + 90y = 11,900

65x + 90(140 - x) = 11,900

65x + 12,600 - 90x = 11,900

65x - 90x = 11,900 - 12,600

-25x = -700

-25x/-25 = -700/-25

x = 28 ounces

y = 140 - x

y = 140 - 28

y = 112 ounces

Therefore, you will be needing 28 ounces of Solution A and 112 ounces of Solution B.

The given function is expressed as

f(x) = 2^(x + 1)

The domain of a function is the set of all the possible values of x that would satisfy the function.

The range of a function is the set of all the possible values of y that would satisfy the function.

Since the fuction has no denominator or even root, the values of can be all real numbers. This means that the domain would be between - infinity and infinity

For the range, no matter how small the value of x that we input into the function, the value of f(x) or y would never be lesser than zero. Also, there is no limit to the value of f(x) even if we input very large values of x. Thus, the range is between 0 and infinity. Thus,

the correct option is the second one

Looking at the Algorithm

We can see that

A) True

2 is one of the roots and the divisor of that Divison

B) False

When we plug into the function (x) the root the result is going to be zero

Since f(-2) = 5(-2)² -16(-2) +12 f(-2) = 20 +32 +12 f(-2) = 64 not equal to zero, then x = -2 is not the root

f(x) = -5x² -16x +12 has x_1= 2 and x_2= 6/5

C) False

Factoring f(x) = -5x² -16x +12 we'll have f(x) = (5x -6)(x-2)

D) True

For the previous explanation

E) True

Rewriting as a factored form we'll have f(x) = (5x -6)(x-2)/(x-2) = 5x -6

F) False

We can't find the same result as the previous one. by dividing by (x+2)

This implies that

Combining them we have

-4.4

Now to the graph