Evaluate (10 – 4i) ÷ (5 + i).
Fifty-four twelfths minus fifteen twelfths i
Twenty-three twelfths minus fifteen twelfths i
Fifty-four thirteenths minus fifteen thirteenths i
Twenty-three thirteenths minus fifteen thirteenths i

Answer:

A.

Step-by-step explanation:

x^2+11x+28

first get the product and sum by using

a=1

b=11

c=28

and then

p=a multiplied by c

b=11

p=28

s=11

find any number that can be multiplied by

7&4 are the numbers

(x^2+7x)+(4x+28)

x(x+7)+4(x+4)

(x+7)(x+4)

The linear function is y = x + 7 and it has it domain and range at  (-∞, ∞) respectively while it x and y - intercepts are (-7, 0) and  (0, 7) respectively.

A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

The linear function always model the form of y = mx + c

Taking the points, we can find the slope of the line

m = y₂ - y₁ / x₂ - x₁

m = 8 - 0 / 1 - (-7)

m = 8 / 8

m = 1

The slope of the line is 1

Using the slope to find the y - intercept;

y = mx + c

8 = 1(1) + c

8 = 1 + c

c = 8 - 1

c = 7

The linear function is y = x + 7

The range of this function is (-∞, ∞) and the domain of the function is

(-∞, ∞).

The x and y -intercept of the function are

x - intercept = (-7, 0)

y - intercept = (0, 7)

Learn more on linear function here;

https://brainly.com/question/15602982

#SPJ1

Answer:

Given :

The diagonal of a rectangle is 2 ✓13 cm.

The length and breadth are in the ratio

3:2.

To find :

The Area of the rectangle.

Solution :

Given that

The ratio of the length and breadth of a rectangle = 3:2

Let they be 3X cm and 2X cm

We know that

The diagonal of a rectangle = √(1²+b³)

units

The diagonal of the rectangle

= √[(3X)³+(2X)³] cm

= √(9x³+4x²) cm

=> √(13X²) cm

=> √13 X cm

According to the given problem

The diagonal of the rectangle = 2√13 cm

=> ✓13 X = 2 √13

=> X = 2√13/√13

=> X = 2 cm

If X = 2 cm then 3X=3(2) = 6 cm

If X = 2 cm then 2X = 2(2)=4 cm

Length = 6 cm

Breadth = 4 cm

We know that

Area of a rectangle = length breadth sq.units

Area of the given rectangle = 6 cm x 4 cm

= 24 cm²

Answer:

$19.90

Step-by-step explanation:

Cost at Best Computers

Cost at Val-U-Mart

Money saved

Answer:

Domain- {-2,0,2}

Range- {0,6,12}

Step-by-step explanation:

Answer:

Domain- {-2,0,2}

Range- {0,6,12}

Step-by-step explanation:

domain is x and range is y

Step-by-step explanation:

Absolute error=14.7-13.0

=1.7m

Percentage error = 1.7/14.7 x 100%

=11.56462

=11.6%

Answer:

Both distances are radii of the smaller circle and must be equal by the definition of a circle.

Answer is in the image, proof also has given

A graph of the exponential function \(f(n)=37000(1.06)^n\) is shown in the image attached below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x)=a(b)^x\)

Where:

Based on the information provided above, your salary can be modeled or represented by the following exponential function;

\(f(n)=37000(1.06)^n\)

Lastly, we would use an online graphing calculator to plot the given exponential function as shown in the graph attached below.

In conclusion, the rate of change of this exponential function is equal to 1.06.

Read more on a graph here: brainly.com/question/4546414

#SPJ1

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

For more questions on trigonometric form

https://brainly.com/question/31744474

#SPJ8

Assuming Jerry can save $1,200 per month for the next year, he will have a total of $14,400 saved in his account.

Amount is a term used to refer to a quantity, amount can refer to a monetary value, a unit of measurement, a number of items, or any other type of quantity. Amount is often used to refer to the total of a certain kind of item or the sum of money involved in a transaction. Amount can also refer to a number of different things, such as the number of people in a group or the number of items in a collection.

After making the down payment, he will have $13,200 left in his account. If Jerry continues to save for a longer period of time, the balance of his account will increase.

To know more about the amount click-
https://brainly.com/question/19104371
#SPJ1

Answer: 120 yds

Step-by-step explanation:

48+30+24+18+120 yds

we know that

Any triangle has three interior angles, and their sum must be equal to 180 degrees

so

If there is a triangle with two right angles, then the third angle is equal to zero

therefore

Is not exist a triangke with two right angles

Answer:

B! Pls mark brainiest!

Step-by-step explanation:

Answer:

Theyre right the answer is B. expirment

Step-by-step explanation:

Took the test just confirming

It took Emily 33.4 minutes to make dinner.

A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.

To solve the problem, we have to convert the mixed number  \(9 \frac{1}{10}\)   to a decimal number:

⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)

⇒ \(\frac{91}{10}\)  =  9.1

This means that Emily finished making dinner 9.1 minutes sooner than the cake.

To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:

⇒ 42.5 - 9.1 = 33.4 minutes

Therefore, it took Emily 33.4 minutes to make dinner.

To know more about mixed number, visit:
https://brainly.com/question/414559
#SPJ1

The two statements about risk and return that are true or potentially true are:

What is risk and return?

The risk connected to a particular investment and its returns are known as risk and return in financial management. High-risk investments typically produce higher financial returns, and low-risk investments typically produce lower returns. In other words, a given investment's risk and return are directly correlated.

As the risk of an investment increases, so does the potential for a higher return because there is a direct correlation between risk and return.

Also, holding stocks of companies of different sizes and from different sectors reduces investment risk in a portfolio because on diversifying the portfolio, risk also gets divided thus, giving a satisfactory return to the investor.

Hence, the above two statements are true.

Learn more about risk and return from the given link

https://brainly.com/question/3161133

#SPJ1

Answer: As the risk of an investment increases, so does the potential for a higher return. and Holding stocks of companies of different sizes and from different sectors reduces investment risk in a portfolio.

Step-by-step explanation: Increased price fluctuation, upward or downward, increases risk and the possibility of a high return or a huge loss. When the risk, or price fluctuation, is low, so is the return potential. Diversification helps decrease the risk of a group of investments because the value of individual investments will increase or decrease at different time periods and help to lessen value fluctuation in the overall portfolio.

Answer:

\(-\frac{2}{9}\)

A: The linear equations are x + y = 125 and x = y + 45.

B: Everyday Angela spends 40 minutes in playing golf.

C: No, it is not possible for Angela to spend 80 minutes playing soccer every day.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Part A:

Let x be the number of minutes Angela plays soccer every day

Let y be the number of minutes Angela plays golf every day

According to the problem statement the linear equations are -

x + y = 125 (total time playing both sports is 125 minutes)

x = y + 45 (Angela plays 45 more minutes of soccer than golf)

Part B:

Substitute x = y + 45 into the first equation -

(y + 45) + y = 125

Use the addition operation -

2y + 45 = 125

2y = 80

y = 40

Angela spends 40 minutes playing golf every day.

Part C:

If Angela spends 80 minutes playing soccer every day, then

x = 80

y + 45 = 80 (using the equation x = y + 45)

y = 35

But this would mean that she plays golf for 35 minutes and soccer for 80 minutes, which adds up to a total of 115 minutes.

This is not possible since the problem states that Angela plays both sports for a total of 125 minutes every day.

Therefore, it is not possible for Angela to have spent 80 minutes playing soccer every day.

To learn more about linear equation from the given link

https://brainly.com/question/2226590

#SPJ1

Applying the Angle Addition Postulate, the measure of angle BDC is calculated as: 57 degrees.

The Angle Addition Postulate establishes that when two angles are adjacent, the measure of the resulting angle formed by their combination is equal to the sum of their individual measures.

Therefore, according to the Angle Addition Postulate, we would have:

(-6x + 11) + (-7x + 15) = 104

Solve for x:

-6x + 11 - 7x + 15 = 104

-13x + 26 = 104

-13x = 104 - 26

-13x = 78

x = -6

Measure of angle BDC = -7x + 15

Plug in the value of x:

Measure of angle BDC = -7(-6) + 15 = 57°

Learn more about the Angle Addition Postulate on:

https://brainly.com/question/24746945

#SPJ1

During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:

P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes

The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.

For more such questions on population

https://brainly.com/question/29885712

#SPJ8

Answer:

80

Step-by-step explanation:

155-75=80

Step-by-step explanation:

I answered that already.

Answer: The sum of money shared is 3700.00 php, Y’s share is 740.00 php, and M receives 45% of the total.

Step-by-step explanation:

=1295/7 • 20

=3700

= 1295/7 • 4
= 185(4)

= 740

Answer:

Equation that represents the line passing through the point -3, -1 with a slope of 4 is

\(y= 4x+11\)

Step-by-step explanation:

Equation of line in point slope form is

\(y-y_1=m(x-x_1)\) -------(1)

Here

\(m=4 \ \ \ and \ \ \ (x_1, y_1) = (-3, -1)\)

Substituting values in equation (1)

\(y+1=4(x+3)\\ y= 4x+11\)

Answer:  the longest poster that could fit in the box is approximately 22.56 inches long.

Step-by-step explanation: Utilizing the Pythagorean theorem, able to calculate the corner to corner as takes after:

diagonal^2 = 11^2 + 18^2 + 8^2

diagonal^2 = 121 + 324 + 64

diagonal^2 = 509

inclining = sqrt(509)

corner to corner ≈ 22.56 inches

9514 1404 393

Answer:

  s ≤ 4(0.20×80)

Step-by-step explanation:

The maximum Jason spends each week is 0.20 × $80. Then the amount (s) he spends in 4 weeks will be less than or equal to 4 times this product.

  s ≤ 4(0.20×80)

The cylinder's surface area is S = 452.4 cm²

Given data ,

Let the surface area of the cylinder with one base be S

Now , Surface area of cylinder = 2πr ( r + h )

To find the surface area of a cylinder, we need to calculate the sum of the areas of the curved surface (lateral surface) and the two circular bases.

where r = 8 cm

h = 5 cm

The formula for the lateral surface area of a cylinder is given by:

Lateral Surface Area = 2πrh

where r is the radius of the cylinder and h is the height.

The formula for the area of a circle is given by:

Base Area = πr²

Now , S = πr² + 2πrh

On simplifying , we get

S = π ( 8 )² + 2 ( π ) ( 8 ) ( 5 )

S = 64π + 80π

S = 452.389 cm²

Hence , the surface area is S = 452.4 cm²

Click here to find out more about cylinder.

https://brainly.com/question/16134180

#SPJ1

The lengths of the other two sides of the right triangle are 24m and 25m, respectively.

Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.

According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Using this theorem, we have the equation:

\(7^2 + x^2 = (x + 1)^2\)

Expanding and simplifying this equation, we get:

\(49 + x^2 = x^2 + 2x + 1\)

Now, we can cancel out \(x^2\) from both sides of the equation:

49 = 2x + 1

Next, we can isolate 2x:

2x = 49 - 1

2x = 48

Dividing both sides by 2, we find:

x = 24

Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.

Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.

For more question on lengths visit:

https://brainly.com/question/28322552

#SPJ8

Answer:

angle ced is a right ange

so the m angels debate =135 m angle aeb =35

so the answer is 135+35 =170

180 is a all side sim

=180-170=10 answer

Answer:

∠CED is a right angle.

∠CEA is a right angle.

m∠CEB = m∠BEA

m∠DEB = 135°