Simplify the expression.(4+2i)-(1-i)

Answer:

The center is (1,4)

Step-by-step explanation:

The coordinates of the center of an ellipse are the coordinates that are in the middle of the two focus.

Then if we have a focus on [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], we can say that the coordinates for x and y can be calculated as:

[tex]x=\frac{x_1+x_2}{2}\\ y=\frac{y_1+y_2}{2}[/tex]

So, replacing [tex](x_1,y_1)[/tex] by (-4,4) and [tex](x_2,y_2)[/tex] by (6,4), we get that the center is:

[tex]x=\frac{-4+6}{2}=1\\ y=\frac{4+4}{2}=4[/tex]

Answer:isosceles is the correct

Step-by-step explanation:

According to the given conditions the triangle ABC is an isosceles triangle.

An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.

Given that, BD is median and altitude in the triangle ABC, and we are asked to find that what type of the triangle ABC will be if we prove triangles  ADB and CBD congruent by SAS rule,

So, the proof is as follows,

AD = CD [definition of median]

∠ ADB = ∠ CDB [definition of altitude]

BD = BD [reflexive property]

∴ Δ ADB ≅ Δ CBD by SAS rule

AB = BC by CPCT

According to the definition of an isosceles triangle we can say that, ABC is an isosceles triangle.

Hence, according to the given conditions the triangle ABC is an isosceles triangle.

Learn more about isosceles triangles, click;

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Answer:

h = 7.1 cm

Step-by-step explanation:

To find the height of the triangle, we can first find the area of the triangle using the Heron's formula:

[tex]S = \sqrt{p(p-a)(p-b)(p-c)}[/tex]

Where a, b and c are the sides of the triangle and p is the semi perimeter of the triangle:

[tex]p = \frac{a+b+c}{2} = \frac{15 + 8 + 17 }{2} = 20\ cm[/tex]

So the area of the triangle is:

[tex]S = \sqrt{20(20-15)(20-8)(20-17)}[/tex]

[tex]S = 60\ cm^2[/tex]

Now, to find the height, we can use the following equation for the area of the triangle:

[tex]S = base * height/2[/tex]

The height draw in the figure is relative to the side of 17 cm, so this side is the value of base used in the formula. So we have that:

[tex]60 = 17 * h/2[/tex]

[tex]h = 120/17[/tex]

[tex]h = 7.06\ cm[/tex]

Rounding to the nearest tenth, we have h = 7.1 cm

Answer:

7.1 cm

Step-by-step explanation:

:D

Answer:

Hey there!

The circumference of a circle is [tex]\pi(d)[/tex], where d is the diameter, and [tex]\\\pi[/tex] is a constant roughly equal to 3.14.

The diameter is 16, so plugging this into the equation, we get 3.14(16)=50.24.

The circumference of the circle is 50.24 yards.

Hope this helps :)

Answer:

6[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

y + 1[tex]\frac{1}{6}[/tex] = 7[tex]\frac{5}{6}[/tex]

y + [tex]\frac{7}{6}[/tex] = [tex]\frac{47}{6}[/tex]

y = 40/6 = 20/3 = 6[tex]\frac{2}{3}[/tex]

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is [tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex].

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be [tex]z (x) = \cos x[/tex] the base formula, where [tex]x[/tex] is measured in sexagesimal degrees. This expression must be transformed by using the following data:

[tex]T = 180^{\circ}[/tex] (Period)

[tex]z_{min} = -4[/tex] (Minimum)

[tex]z_{max} = 5[/tex] (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of [tex]2\pi[/tex] radians. In addition, the following considerations must be taken into account for transformations:

1) [tex]x[/tex] must be replaced by [tex]\frac{2\pi\cdot x}{180^{\circ}}[/tex]. (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

[tex]\Delta z = \frac{z_{max}-z_{min}}{2}[/tex]

[tex]\Delta z = \frac{5+4}{2}[/tex]

[tex]\Delta z = \frac{9}{2}[/tex]

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

[tex]z_{m} = \frac{z_{min}+z_{max}}{2}[/tex]

[tex]z_{m} = \frac{1}{2}[/tex]

The new function is:

[tex]z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)[/tex]

Given that [tex]z_{m} = \frac{1}{2}[/tex], [tex]\Delta z = \frac{9}{2}[/tex] and [tex]T = 180^{\circ}[/tex], the outcome is:

[tex]z'(x) = \frac{1}{2} + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)[/tex]

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

Answers:

sin a=12/15=4/5

step by step explanation:

AB=9, and BC=12

find c: hyp.=√12²+9²=c²

c=15

sin a=opp/hyp.=12/15=4/5 ( convert to degrees)

a=41.10

Answer:

Hey there!

A=1/2bh

14=1/2(28)h

14=14h

h=1

Hope this helps :)

Answer:

Step-by-step explanation:

Area of a triangle is

[tex] \frac{1}{2} \times b \times h[/tex]

where b is the base

h is the height

From the question

Area = 14in²

b = 14 inches

So we have

[tex]14 = \frac{1}{2} \times 28 \times h[/tex]

which is

[tex]14 = 14h[/tex]

Divide both sides by 14

That's

[tex] \frac{14}{14} = \frac{14h}{14} [/tex]

We have the final answer as

h = 1

Therefore the height is 1 inch

Hope this helps you

The complete question is;

The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

(a) less than 10 minutes

(b) longer than 5 minutes

(c) between 8 and 15 minutes

Answer:

A) P (x < 10) = 0.6700

B) P (x > 5 ) = 0.9406

C) P (8.0000 < x < 15.0000) = 0.6332

Step-by-step explanation:

A) we are given;

Mean;μ = 8.9 minutes

Standard deviation;σ = 2.5 minutes

Normal random variable;x = 10

So to find;P(x < 10) we will use the Z-score formula;

z = (x - μ)/σ

z = (10 - 8.9)/2.5 = 0.44

From z-distribution table and Z-score calculator as attached, we have;

P (x < 10) = P (z < 0.44) = 0.6700

B) similarly;

z = (x - μ)/σ =

z = (5 - 8.9)/2.5

z = -1.56

From z-distribution table and Z-score calculator as attached, we have;

P (x > 5 ) = P (z > -1.56) = 0.9406

C)between 8 and 15 minutes

For 8 minutes;

z = (8 - 8.9)/2.5 = -0.36

For 15 minutes;

z = (15 - 8.9)/2.5 = 2.44

From z-distribution table and Z-score calculator as attached, we have;

P (8.0000 < x < 15.0000) = P (-0.36 < z < 2.44) = 0.6332

Answer:

5 games

Step-by-step explanation:

To find how many games the team scored at least 70 points, we need to look at the 7 on the stem side. The 7 means 70, and we add the digits on the leaf side. For example, 7 | 2 is 72. The numbers on the leaf side are: 1, 1, 2, and 3.

There are no points for the 8 on the stem side, but on 90, there is one digit on the leaf side: 1. So, the points they scored over 70 are 71, 71, 72, 73, and 91, which equals to five games.

Answer:

[tex]\boxed{\mathrm{5 \ games}}[/tex]

Step-by-step explanation:

At least 70 points makes it 70 and more. It should be at least 70 and at most anything above then 70.

So, In 5 games, the team scored at least 70. (71,71,72,73 and 91)

Answer: hundredths place

Step-by-step explanation:

Answer:

- greater than Upper Q 3 plus 1.5 (IQR)

- less than Upper Q 1 minus 1.5 (IQR)

Step-by-step explanation:

To identify outliers the interquartile range of the dataset can be used

Outliers can be identified as data values that are

- greater than Upper Q 3 plus 1.5 (IQR)

- less than Upper Q 1 minus 1.5 (IQR)

Using the interquartile range concept, it is found that:

The interquartile range​ (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.

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

[tex]v < Q1 - 1.5IQR[/tex] or [tex]v > Q3 + 1.5IQR[/tex]

Thus:

The interquartile range​ (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.

A similar problem is given at https://brainly.com/question/14683936

Answer:

(D)R: x+2=7

Step-by-step explanation:

Given the statement P:x=5

An equivalent statement will be a statement whose result is exactly x=5.

From the given options:

R: x+2=7

R: x=7-2

R: x=5

Therefore, R is an equivalent statement.

The correct option is D.

Question:

Diners frequently add a​ 15% tip when charging a meal to a credit card. What is the price of the meal without the tip if the amount charged is ​$20.70? How much was the​ tip?

Answer:

Price of meal = $18

Tip price = $2.70

Step-by-step explanation:

Let the price of the meal be y;

Let the tip be t

From the question;

15% of y is the tip charge (t). i.e

t = 15%y

=> t = 0.15y          --------(i)

The total amount charged is $20.70  (This means that the sum of the price of the meal and the tip is $20.70)

=> y + t = 20.70            [substitute the value of t=0.15y from equation (i)]

=> y + 0.15y = 20.70

=> 1.15y = 20.70

=> y = [tex]\frac{20.70}{1.15}[/tex]

=> y = $18

Therefore the price of the meal, y, is $18.

From equation (i),

t = 0.15y           [substitute the value of y = $18]

t = 0.15(18)

t = $2.70

Therefore the tip was $2.70

Answer:  m = -5

Step-by-step explanation:

[tex]\dfrac{m+3}{m^2+4m+3}-\dfrac{3}{m^2+6m+9}=\dfrac{m-3}{m^2+4m+3}\\\\\\\dfrac{m+3}{(m+3)(m+1)}-\dfrac{3}{(m+3)(m+3)}=\dfrac{m-3}{(m+3)(m+1)}\quad \rightarrow m\neq-3, m\neq-1[/tex]

Multiply by the LCD (m+3)(m+3)(m+1) to eliminate the denominator. The result is:

(m + 3)(m + 3) - 3(m + 1) = (m - 3)(m - 3)

Multiply binomials, add like terms, and solve for m:

(m² + 6m + 9) - (3m + 3) = m² - 9

    m² + 6m + 9 - 3m - 3 = m² - 9

                  m² + 3m + 6 = m² - 9

                           3m + 6 =  -9

                                  3m = -15

                                    m = -5  

Answer:

Step-by-step explanation:

g(x) = |x – 8| + 6 was transformed from the parent function g(x) = |x|:

8 unit right

6 units up

a parent absolute value function has a vertex at (0,0)

if the function is moved so is the vertex:

(0+8,0+6)

(8,6)

So, the vertex of this function is at (8,6)

Answer:  vertex = (8, 6)

Step-by-step explanation:

The Vertex form of an absolute value function is: y = a|x - h| + k   where

g(x) = |x - 8| + 6 is already in vertex form where

h = 8 and k = 6

so the vertex (h, k) = (8, 6)

Answer:

Correlation Coefficient

Step-by-step explanation:

Answer:

[tex] x = 2 [/tex]

Step-by-step explanation:

Given a right-angled triangle as shown above,

Included angle = 60°

Opposite side length = 3

Adjacent side length = x

To find x, we would use the following trigonometric ratio as shown below:

[tex] tan(60) = \frac{3}{x} [/tex]

multiply both sides by x

[tex] x*tan(60) = \frac{3}{x}*x [/tex]

[tex] x*tan(60) = 3 [/tex]

Divide both sides by tan(60)

[tex] \frac{x*tan(60)}{tan(60} = \frac{3}{tan(60} [/tex]

[tex] x = \frac{3}{tan(60} [/tex]

[tex] x = 1.73 [/tex]

[tex] x = 2 [/tex] (approximated to whole number)

Answer:

The first statement is incorrect. They have to be complementary.

Step-by-step explanation:

You can't say the measure of angle B is congruent to theta because it is possible for angles in a right triangle to be different.

You can only say that what he said is true if the angle was 45 degrees, but based on the information provided it is not possible to figure that out.

The other two angles other than the right angle in a right triangle have to add up to 90 degrees, which is the definition of what it means for two angles to be complementary. A is the correct answer.

Answer:

[tex]\boxed{\sf A}[/tex]

Step-by-step explanation:

The first statement is incorrect. The angle B is not equal to theta θ. The two acute angles in the right triangle can be different, if the triangle was an isosceles right triangle then angle B would be equal to theta θ.

Answer:

Nx = λx

Nx = 0, with x≠0

if N is nilpotent matrix, then the system Nx = 0 has non-trivial solutions

Step-by-step explanation:

given that

let N be a square matrix in order of n

note: N is nilpotent matrix with [tex]N^{k} = 0[/tex], k ∈ N

let λ be eigenvalue of N and let x be eigenvector corresponding to eigenvalue λ

Nx = λx (x≠0)

N²x =  λNx = λ²x

∴[tex]N^{k}x[/tex] =  (λ^k)x

[tex]N^{k}[/tex] = 0, (λ^k)x = [tex]0_{n}[/tex], where n is dimensional vector

where x = 0, (λ^k) = 0

λ = 0

therefore, Nx = λx

Nx = 0, with x≠0

note: if N is nilpotent matrix, then the system Nx = 0 has non-trivial solution

Answer:

[2.5 ,4]

Step-by-step explanation:

The graph in this interval has a vertex while opening up wich means it's a minimum

Answer:

2√137

Step-by-step explanation:

To find AB, we can use the Pythagorean Theorem (a² + b² = c²). In this case, a = 22, b = 8 and we're solving for c, therefore:

22² + 8² = c²

484 + 64 = c²

548 = c²

c = ± √548 = ± 2√137

c = -2√137 is an extraneous solution because the length of a side of a triangle cannot be negative, therefore, the answer is 2√137.

Answer: 32

Step-by-step explanation:

Answer:

105.6

Step-by-step explanation:

If the mean is 8.8, than that means that in total the sum must be (8.8 * 12) which equals 105.6.

This is because the sum of all the numbers in a list divided by the amount of numbers in a list equals the mean.

Answer:

option: D

51200

Step-by-step explanation:

64000 x 80/100 = 51200

Answer:

Hi there!!!

your required answer is option D.

explanation see in picture.

I hope it will help you...

Answer:

3

Step-by-step explanation:

Use this equation

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] substitute

-6-3/0-3 subtract

-9/-3 simplify

-3/-1 two negitives cansle out

3/1=3

Hope this helpes, if it did, please consider giving me brainliest, it will help me a lot. If you have any questions, feel free to ask.

Have a good day! :)

Answer:

3

Step-by-step explanation:

To find the slope, we use the slope formula

m= ( y2-y1)/(x2-x1)

   = ( -6 -3)/(0 -3)

    = -9/-3

    = 3

Answer:

26 × 26 × 10 × 10 × 10 = 676 , 000  possibilities

Step-by-step explanation:

There is nothing stating that the letters and numbers can't be repeated, so all  26  letters of the alphabet and all  10

digits can be used again.

If the first is A, we have  26  possibilities:

AA, AB, AC,AD,AE ...................................... AW, AX, AY, AZ.

If the first is B, we have  26  possibilities:

BA, BB, BC, BD, BE .........................................BW, BX,BY,BZ

And so on for every letter of the alphabet.  There are  26  choices for the  first letter and  26  choices for the second letter. The number of different combinations of  2  letters is: 26 × 26 = 676

The same applies for the three digits. There are  10  choices for the first,  10

for the second and  10  for the third:

10 × 10 × 10 = 1000  

So for a license plate which has  2  letters and  3  digits, there are:  26 × 26 ×  10 × 10 × 10 = 676 , 000  possibilities.

Hope this helps.

Answer:

Step-by-step explanation:

Given the shape of the equation -2(x+3) = -10. Since x is being multiplied by -2, the first step would be to divide by -2, which is equivalent to multiply by (-1/2) on both sides. Hence the answer is B

Answer:

14 Quarters and 28 dimes

Step-by-step explanation: 14 quarters $3.50

28 dimes is $2.80 total is $6.30