D^2=290^2+2030^2
How Do i simplify this

The simplified expression of (7 + 9i)(8 - 10i) is 146 + 2i

The expression is given as:

(7 + 9i)(8 - 10i)

Expand the bracket

7 * 8 + 9i * 8 -7 * 10i - 9i * 10i

Evaluate the products

56 + 72i -70i - 90(i²)

Evaluate the difference

56 + 2i - 90(i²)

In complex numbers;

i² = -1

So, we have:

56 + 2i - 90(-1)

Evaluate

56 + 2i + 90

Add the like terms

146 + 2i

Hence, the simplified expression of (7 + 9i)(8 - 10i) is 146 + 2i

Read more about complex numbers at:

https://brainly.com/question/10662770

#SPJ1

Yes the ladder be safe at this height.

The angle formed by the line of sight and the horizontal plane for an object above the horizontal.

Given:

ladder = 15 ft long.

top of the ladder is 14.2 ft above the ground.

Using trigonometry,

sin x = 14.2/15

sin x = 0.947

x= 71.262°

As, 78 > 71.262°

Hence, it would be safe to use the ladder of 15 ft long.

Learn more about angle of elevation here:

https://brainly.com/question/21137209

#SPJ1

The measure of each of the angles ∠P,∠Q,∠R, ∠S are 45°,72°,135° and 98° respectively.

A quadrilateral is a polygon having four sides. The measure of the opposite angle of quadrilateral inside circle is 180°.

From the figure:

∠P=x+15

∠Q=3x-8

∠R=?

∠S=3x+8

∠Q+∠S=180

3x-8+3x+8=180

6x=180

x=30°

∠P+∠R=180°

x+15+∠R=180

30+15+∠R=180

∠R=180-45

∠R=135°

∠P=30+15=45

∠Q=3x-8=3(30)-8=72

=135

∠S=3x+8=3(30)+8=98

Hence,the measure of each of the angles ∠P,∠Q,∠R, ∠S are 45°

,72°,135° and 98°.

To learn more about the quadrilateral refer:

https://brainly.com/question/13805601

#SPJ1

[tex]\text{Let,}\\\\~~~~~~~~~y = e^{\ln 8}\\\\\implies \ln y = \ln \left( e^{\ln 8} \right)\\\\\implies \ln y = \ln 8( \ln e)\\\\\implies \ln y = \ln 8\\\\\implies y = 8\\\\\implies e^{\ln 8} = 8\\\\\text{Hence,}~~ e^{\ln 8 } = 8[/tex]

Answer:

8

Step-by-step explanation:

One of the properties of natural logs is that

[tex]e^{lnx} = x\\\\So,\\\\e^{ln8} = 8[/tex]

Answer:

Initial balance$1000

interest rate 8%

Term 20yrs

Step-by-step explanation:

The final balance is $4,926.8.The total compound interest is $3,926.8.

The value of r is 2 %.

Simple Interest can be defined as the sum paid back for using the borrowed money, over a fixed period of time. Compound Interest can be defined as when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time. Formula. S.I. = (P × T × R) ⁄ 100.

Given:

Principal(P)= $4540

Rate = ?

Time=10  years

CI=$1328.54

We have to find the value of r.

According to given question we have

By the use of compound interest we have

[tex]CI=p((1+\frac{r}{100} )^{10} -1)\\\\1328.54 =4540 ((1+\frac{r}{100} )^{10} -1)\\\\\0.292= ((1+\frac{r}{100} )^{10} -1)\\[/tex]

After simplifying we get,

r=2 %

Therefore, the value of r is 2 %.

Learn more details about simple & compound interest here:

https://brainly.com/question/22621039

#SPJ1

Answer:

  -448

Step-by-step explanation:

The sum of 28 terms of the arithmetic sequence with first term 92 and common difference -8 can be found using the formula for the sum of an arithmetic series.

  Sn = (2a1 +d(n -1))(n/2) . . . . sum of n terms with first term a1, difference d

__

Using the above formula with a1=92, d=-8, and n=28, the sum is ...

  S28 = (2·92 -8(28 -1))/(28/2) = (184 -216)(14) = -448

The sum of the first 28 terms of the sequence is -448.

Finding the correlation coefficient, it is found that the regression line shows a:

negative trend line with a strong relationship.

Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is of -0.85, which is negative and strong.

More can be learned about correlation coefficients at https://brainly.com/question/25815006

#SPJ1

Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85,

The table contains data for six students in a running club: time run in minutes, x, and the corresponding average speed in mph, y.

Finding the correlation coefficient, it is found that the regression line shows a: negative trend line with a strong relationship.

It is an index that measures the correlation between two variables, assuming values between -1 and 1.

If it is positive, the relationship is positive, that is, they are directly proportional. If it is negative, they are inversely proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.

Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85, which is negative and strong.

To learn more can about correlation coefficients visit: brainly.com/question/25815006

#SPJ1

Answer:

Step-by-step explanation:

for 1

area=2x×3x=6x²

for 2

l=3x+2x=5x

b=2x

area=5x×2x=10x²

total area=6x²+10x²=16x²

The solution to the given system of equation is (4, 4)

From the solved steps, the final quadratic functions is given as;

x^2 - 8x + 16 = 0

Factorize to have;

x^2 - 4x - 4x + 16 = 0

x(x-4)-4(x-4) = 0
(x-4)(x-4) = 0

x = 4 and 4

Hence the solution to the given system of equation is (4, 4)

Learn more on system of equation here: https://brainly.com/question/847634

#SPJ1

Answer:

8= 24b

8/8=24b/8

b=3

Step-by-step explanation:

Based on my own learning

Answer:

The answer is

" THe middle triangle is scalene"

and "the right and left triangle are isosceles"

Step-by-step explanation:

This is because B, and D are wrong.

B is wrong because all three sides are different lengths

D is wrong because the right and left triangles are not equalateral

give brainliest please!

hope this helps :)

Answer:

Choice C

Step-by-step explanation:

Given equation,

To Find:

Solution:

=>x/-3=-6

Transpose 3 from LHS to RHS,make sure to change the sign from ÷ to *.

=>x = -6*-3

=>x = 18

Hence, the value of x is 18.

Answer:

6

Step-by-step explanation:

hope it helps

a) [tex](a+b)(x)=a(x)+b(x)=7x+10+12x-18=\boxed{19x-8}\\[/tex]

b) [tex](a-b)(x)=a(x)-b(x)=(7x+10)-(12x-18)=7x+10-12x+18=\boxed{-5x+28}[/tex]

c) [tex](a-b)(x)=a(x)-b(x)=(7x+10)-(12x-18)=7x+10-12x+18=\boxed{-5x+28}[/tex]

d) [tex]a(b(x))=a(12x-18)=7(12x-18)+10=84x-126+10=\boxed{84x-116}[/tex]

Answer:

the length of the third side is 26

Step-by-step explanation:

By Pythagoras theorem

AC² = AB² + BC²

AC² = 10² + 24²

AC² = 100 + 576

AC² = 676

AC = √676

AC = 26

Answer:

Radio
r=4.5cm

Area
63.62cm2

Perímetro
C≈28.27cm

The elimination method is the process of removing the variable from the system of equations, whereas the substitution method is the process of replacing a variable with a value to find the solution for the system of equations.

For instance, the system of two equations with two unknown values, the solution can be obtained by using the below steps. Here, the list of steps is provided to solve the linear equation. They are

Answer:

The Area is 25

Step-by-step explanation:

You will need distance formula for this questions

for AD, (0,4) and (4,7)

The formula is here

[tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

which gives you

[tex]\sqrt{\left(4-0\right)^2+\left(7-4\right)^2} = 5[/tex]

for AB

(0,4),(3,0)

[tex]\sqrt{\left(3-0\right)^2+\left(0-4\right)^2}=5[/tex]

The answer will be 5*5, which is 25

If 5x - 17 ≥ 0, then |5x - 17| = 5x - 17 and the equation reduces to

-8 - 2 (5x - 17) = -14

-8 - 10x + 34 = -14

-10x = -40

x = 4

If 5x - 17 < 0, then |5x - 17| = -(5x - 17) = -5x + 17 and we have

-8 - 2 (-5x + 17) = -14

-8 + 10x - 34 = -14

10x = 28

x = 2.8

Answer:

1.43

Step-by-step explanation:

12 tenths ⇒ 1.2

23 hundredths ⇒ 0.23

0.23 + 1.2 = 1.43

Answer:

Step-by-step explanation:

3a 2b ×2a 6b = (3 × 2)×(a × b) × (2 × 6)×(a × b)   [commutative property]

                      = (6×ab) × (12×ab)  [associative property]

                      = (6×12) × (ab×ab)  [commutative + associative]

                      = (72) × (ab)²

                      = 72× (ab)²

                      = 72a²b²  [exponent property]

The solutions to the systems of equations are:

1. (2, 3) (see attachment below). [one solution]

2. no solution

3. (3, 13) [one solution]

The solution to a system of equations is the x-value and y-value that will make both equations true. It can be found either using a graph, by elimination method, or substitution method as explained below.

1. Using graph to solve y = 2x - 1 and y = 4x - 5:

The solution is the point where both lines intersect which is: (2, 3) (see attachment below). [one solution]

2. Solving using substitution method:

x = -5y + 4 ---> eqn. 1

3x + 15y = -1 ---> eqn. 2

Substitute x = -5y + 4 into eqn. 2

3(-5y + 4) + 15y = -1

-15y + 12 + 15y = -1

-15y + 15y = -1 - 12

0 = -13 (this shows that there is no solution)

3. Using elimination method:

14x = 2y + 16 ---> eqn. 1

5x = y + 2 ---> eqn. 2

1(14x = 2y + 16)

2(5x = y + 2)

14x = 2y + 16 ----> eqn. 3

10x = 2y + 4 -----> eqn. 4

Subtract

4x = 12

x = 12/4

x = 3

Substitute x = 3 into eqn. 2

5(3) = y + 2

15 = y + 2

15 - 2 = y

13 = y

y = 13

The solution is: (3, 13).

Learn more about the solution of a system of equations on:

https://brainly.com/question/13729904

#SPJ1

The perimeter of the composite figure shown in the figure is equal to 5 · [2 + √2 · (1 + √5)] units (approx. 32.882 units) and the total area is 33.5 square units.

In this case we have a composite figure formed by six triangles and two rectangles. The perimeter is the sum of the side lengths and the area is the sum of the areas of the triangles and rectangles. The perimeter of the entire figure is described below:

p = AB + BC + CD + DE + EF + FG + GA

p = 5√2 + √10 + √10 + 5 + √10 + 5 + 2√10

p = 10 + 5√2 + 5√10

p = 10 + 5 · (√2 + √10)

p = 10 + 5√2 · (1 + √5)

p = 5 · [2 + √2 · (1 + √5)]

And the area of the composite figure is determined by the following expression:

A = 0.5 · (3) · (1) + (3) · (4) + 0.5 · (3) · (1) + 0.5 · (3) · (1) + 0.5 · (3) · (1) + (3) · (2) + 0.5 · (7) · (1) + 0.5 · (6) · (2)

A = 2 · (3) · (1) + (3) · (4) + (3) · (2) + 0.5 · (7) · (1) + 0.5 · (6) · (2)

A = 33.5

The perimeter of the composite figure shown in the figure is equal to 5 · [2 + √2 · (1 + √5)] units (approx. 32.882 units) and the total area is 33.5 square units.

To learn more on composite figures: https://brainly.com/question/27234680

#SPJ1

Answer:

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Step-by-step explanation:

The common ratio of the sequence is -1.5

The sequence is given as:

1,-1.5,2.25,-3.375

Divide the second term by the first to determine the common ratio (r)

r = T2/T1

This gives

r = -1.5/1

Evaluate

r = -1.5

Hence, the common ratio of the sequence is -1.5

Read more about common ratio at

https://brainly.com/question/2488421

#SPJ1

Answer:D. x^2+7

Step-by-step explanation:

If f(x) = 2x² +5 and g(x)=x2-2, find (f-g)(x).A. x^2+3B. 3x^2+3C. 3x^2+7D. x^2+7