What is the value of the dot shown on the number line below? If the answer is not an integer, enter it as a fraction or mixed number. ​

Answer:

  p(x) = x⁴ -7x³ +59x² -343x +490

Step-by-step explanation:

Each root is the zero of a binomial factor. That is, for root x = a, the polynomial has a factor (x -a). Complex roots come in conjugate pairs, so if there is a root 7i, there is also a root -7i.

__

The given roots mean the polynomial can be written in factored form as ...

  p(x) = (x -2)(x -5)(x -7i)(x -(-7i))

We can combine multiply these factors together to simplify the polynomial.

  p(x) = (x² -7x +10)(x² +49)

  p(x) = x⁴ -7x³ +59x² -343x +490

_____

Additional comment

Combining the conjugate complex roots uses the special form for the factoring of the difference of squares.

  a² -b² = (a -b)(a +b)

  (x -7i)(x +7i) = x² -(7i)² = x² -49i² = x² +49 . . . . . where i = √(-1)

reflection on x-axis

then translations right 3 units & down 2 units

Answer:

$17 ( 17 USD )

Step-by-step explanation:

C(x)=11.00+0.15x

40 copies:

C(40) = 11+0.15(40)

C(40) = 11+6

C(40) = $17

Therefore, the total cost for an order of 40 copies is $17.

Hope this helps!!!

Please mark as brainliest!!!

P.S. I guess you don't have to change schools now?

Answer:

x^-2 = 1/36

x^-1 = 1/6

x^0 = 1

x^1 = -6

x^2 = 36

#1

#2

#3

#4

#5

Answer:

(- 2, 0 )

Step-by-step explanation:

5x - 4y = - 10 → (1)

- 4x + 5y = 8 → (2)

multiplying (1) by 4 and (2) by 5 and adding result will eliminate x

20x - 16y = - 40 → (3)

- 20x + 25y = 40 → (4)

add (3) and (4) term by term to eliminate x

9y = 0 , thus

y = 0

substitute y = 0 into either of the 2 equations and solve for x

substituting into (1)

5x - 4(0) = - 10

5x - 0 = - 10

5x = - 10 ( divide both sides by 5 )

x = - 2

solution is (- 2, 0 )

Using the normal distribution, it is found that the desired measures are given by:

a. Z = -0.67.

b. X = 2.2.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In item a, we have that [tex]X = 36, \mu = 40, \sigma = 6[/tex], and want to find Z, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{36 - 40}{6}[/tex]

Z = -0.67.

In item b, we have that [tex]\mu = 1.3, \sigma = 0.6, Z = 1.5[/tex], and want to find X, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.5 = \frac{X - 1.3}{0.6}[/tex]

X - 1.3 = 0.6 x 1.5

X = 2.2.

More can be learned about the normal distribution at https://brainly.com/question/24663213

#SPJ1

Answer:

x=45, y=45, z= 131

Step-by-step explanation:

x and y makes up a right angle (90). You can even;y split them in half, which is 45 degrees. Therefore, x= 45 and y also = 45.

Now that there are 2 right angles, that makes up 180. 180+49=229

A full rotation is 360, so you subtract that. 360-229=131
z=131.

Answer:

Step-by-step explanation:

The relevant relations are ...

__

The angle marked 49° and the one marked "y" are vertical angles, so have the same measure.

  y = 49°

The angle marked "x" and the angle marked "y" together make up a right angle, so total 90°.

  x + y = 90°

  x + 49° = 90°

  x = 41° . . . . . . . . . subtract 49°

The angle marked z and the one marked 49° together make up a straight angle, so total 180°. (They are a "linear pair.")

  49° +z = 180°

  z = 131° . . . . . . . subtract 49°

The measures of the marked angles are ...

  x = 41°

  y = 49°

  z = 131°

The time taken by the bacterias to reach 3,700 will be 2.81 days.

It is given in the question that:-The the number of bacteria, B left parenthesis d right parenthesis, in a certain population increases according to the following function, where time, d, is measured in days:

[tex]B(d)=2425\ e^{0.15d[/tex]

[tex]3700= 2425\ e^{0.15d}\\\\\\e^{0.15d}=\dfrac{3700}{2425}\\\\\\0.15d=ln\dfrac{3700}{2425}\\\\\\[/tex]

d   =   2.81  days

Hence the time taken by the bacteria to reach 3,700 will be 2.81 days.

To know more about exponential questions follow

https://brainly.com/question/2456547

#SPJ1

The probability that the spinner is multiple of 4 or multiple of 7 is 1/3

Probability is the likelihood or chance that an event will occur, Mathematically;

Probability = expected/total

If a game has a spinner with 15 equal sectors labeled 1 through 15, the total outcome is 15

P(multiple of 4) = 3/15 =1/5

Pr(multiple of 7 )= 2/15

p(multiple of 4 or multiple of 7) = 1/5 + 2/15
p(multiple of 4 or multiple of 7) = 5/15 =1 /3

Hence the probability that the spinner is multiple of 4 or multiple of 7 is 1/3

Learn more on probability here: https://brainly.com/question/25870256

#SPJ4

Answer:

42 meters

Step-by-step explanation:

if his math teacher is 6 meters ahead of him and his science teacher is 7 meters to the right of him than you multiply to get the area of distance from each other.

6 x 7 = 42

the teachers are 42 area meters away from each other

Answer:

temperature > -15

Question 1 True or False: A sector of a circle with a measure of 72 and radius of 12 cm has an arc length of about 15cm. True O False

Step-by-step explanation:

its false

The given statement about the sector of the circle is true.

A circle is a shape or a curve in a plane that has a fixed distance, called the radius, from a given point, called the centre. A circle is also the set of all points that are equidistant from the centre.

Given that we need to check whether a sector of a circle with a measure of 72° and radius of 12 cm has an arc length of about 15cm, or not,

Arc length = central angle / 360° × 2π × radius

= 72/ 360° × 2(3.14) × 12

= 0.2 × 6.28 × 12

= 15.072

≈ 15

Therefore, yes the sector of a circle with a measure of 72° and radius of 12 cm has an arc length of about 15cm.

Hence, the given statement about the sector of the circle is true.

Learn more about circle, click;

https://brainly.com/question/29142813

#SPJ2

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C.

The two triangles can be made as shown below, the bigger triangle will be an equilateral triangle with each side measuring 10 units, while the smaller triangle will be an isosceles triangle and the measure of the same length side will be equal to the radius of the circle.

Learn more about Triangle:

https://brainly.com/question/2773823

#SPJ1

Answer:

See below

Step-by-step explanation:

You don't give any options, but here's the information you can get from just the equation itself:

Look for these characteristics and find the appropriate graph.

Using it's concept, it is found that the desired probability is given as follows:

P(Head, Diamond AND Head, Heart) = 1/64.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, for each trial, there are 8 equally as likely outcomes, hence:

Hence the probability of both outcomes is given by:

P(Head, Diamond AND Head, Heart) = 1/8 x 1/8 = 1/64.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

Candy is 21 years old

Step-by-step explanation:

If Alisa is 16 years old, that would mean that Barbara would be 8, since she is half of Alisa's age.

If we add 5 to Alisa's age, we get 21. To find the average of their ages, we add them all up, and divide by how many people there are (3).

16+8+21=45

45÷3=15

Hope this helps!

Age of Ailsa is 20 years. Then Candy's age will be 15 years.

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

Ailsa is twice as old as Barbara. Ailsa is 5 years younger than Candy. The average age of Candy, Ailsa, and Barbara is 15.

Let 'x' be the age of Ailsa, 'y' be the age of Barbara, and 'z' be the age of Candy. Then the equations are given as,

x = 2y                                    ...(1)

x - 5 = z                                 ...(2)

(x + y + z) / 3 = 15                  ...(3)

From equations (1), (2), and (3), then

x + x / 2 + x - 5 = 45

(5/2) x = 50

x = 20

Then the age Candy is calculated as,

z = 20 - 5

z = 15

Age of Ailsa is 20 years. Then Candy's age will be 15 years.

More about the solution of the equation link is given below.

https://brainly.com/question/22613204

#SPJ3

The measure of the angle is 205°. Then the correct option is A.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

There are 4 quadrants and each quadrant has a measure of 90° angle.

The fact that the orientation is positive indicates that the arm is moving from the first to the second quadrant.

90° + 90° = 180°

The arm has been in the third quadrant due to the additional 25° rotation.

180° + 25° = 205°

The measure of the angle is 205°.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ1

Answer:

  10∠126.87°

  r = 10; θ = 126.87°

Step-by-step explanation:

The coordinate conversion from (x, y) or (x +yi) to (r; θ) can be done using the relations ...

  r = √(x² +y²)

  θ = arctan(y/x) . . . . paying attention to quadrant

__

For the given complex number, we have ...

  r = √((-6)² +8²) = √(36 +64) = √100 = 10

  θ = arctan(8/(-6)) = arctan(-4/3) . . . . in the 2nd quadrant

  θ ≈ -53.13° +180° = 126.87°

The equivalence is ...

  -6 +8i  ⇔  10∠126.87° . . . . . in the form r∠θ

_____

Additional comment

Many scientific and graphing calculators are equipped to work with complex numbers, including their conversion to or from polar form.

Answer:

-7.75

Step-by-step explanation:

[tex]\text{if}\ x = 8 \rightarrow y = 124\\y \propto x\\y = kx\\\\124 = k \times 8 = 8k\\\frac{124}{8} = \frac{8k}{8}\\15.5 = k\\\\\text{We've now found the formula}\\y \propto x\\y = kx = 15.5x\\\\x = -\frac{1}{2} \rightarrow y = ?\\y = 15.5x = 15.5 \times -\frac{1}{2} = -7.75[/tex]

Answer:

x = 42

Step-by-step explanation:

a striaght line = 180°

z + y + x = 180

103 + 135 + x = 180

138 + x = 180

subtract 138 from both sides

138 - 138 + x = 180 - 138

x = 42

Answer:

what shape it is

Step-by-step explanation:

wat is the shape

Answer:

The radius of the circle r=12.

The area of a circle is 144π.

Step-by-step explanation:

The radius of the circle is r where 2πr=24π, r=12.

The area of a circle with radius 12 is

A=πr², A=π12², A=144π.

The possible value of x is 2, and the possible dimensions are 8 ft by 11 ft

The equation is given as:

(6 + x) * (9 + x) = 88

Express 88 as a product of two factors

(6 + x) * (9 + x) = 8 * 11

Express 8 and 11 as a sum

(6 + x) * (9 + x) = (6 + 2) * (9 + 2)

By comparison, we have:

6 + x = 6 + 2

9 + x = 9 + 2

This means that

x = 2

So, we have:

The possible value of x is 2, and the possible dimensions are 8 ft by 11 ft

Read more about area at:

https://brainly.com/question/24487155

#SPJ4

Answer: D) two possible amounts by which the dimensions were changed

Step-by-step explanation:

Edg 2022

Answer: 3 square inches

Step-by-step explanation:

   See attached for how I broke the shape up. Since each square is equal to 1 square inch, and the shape is about 3 squares, the answer should be;

O 3 square inches

Please note that different people may estimate differently.

   Learn more about estimating area from a grid here:

https://brainly.com/question/12178325

Answer:

17

Step-by-step explanation:

10=7-m

m=???

so if you do 10+7 which equal 17 and then do 17-7 you will get ten

m=17

have a good day

Answer:

the answer is -3

Step-by-step explanation:

10 = 7 -m

swap sides so that all the variable terms are on the left hand side

7 - m =10
subtract 7 from both sides

-m + 10 - 7

subtract 7 from 10 to get 3

multiply both sides by -1

m = -3

Answer:

6.28 meters

Step-by-step explanation:

Circumference is D[tex]\pi[/tex]

D=2 meters

2*3.14 = 6.28

Answer

the range is the spread of your data from the lowest to the highest value in the distribution

Answer:

9

Step-by-step explanation:

To find the range, subtract the biggest number (here it's 9) and the smallest number (here it's 0).

9 - 0 = 9