(2+i)-(5-4i)

Find the difference of the following expression

Answer: 77 yd^2

Step-by-step explanation:

S=Area of Square. s=side length of square. w=width of rectangle

l=length of rectangle. R=Area of Rectangle

S=s^2

S=7^2

S=49 yd^2

R=l*w

R=9*14

R=126 yd^2

R-S=

126-49=77 yd^2

Answer:

  E.  a^(1/3)b^(1/6)

Step-by-step explanation:

You want an expression equivalent to (a^(2/3)b^(1/3))^(1/2).

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

  (ab)^c = (a^c)(b^c)

The given expression simplifies to ...

  [tex](a^{2/3}b^{1/3})^{1/2}=a^{(2/3)(1/2)}b^{(1/3)(1/2)}=\boxed{a^{1/3}b^{1/6}}[/tex]

set, in mathematics and logic, any collection of objects (elements), which may be mathematical (e.g., numbers and functions) or not. A set is commonly represented as a list of all its members enclosed in braces. The intuitive idea of a set is probably even older than that of number.

Let C=15, 16, 17, 18, and 19) and U=x | x is a full number and 0 x 19). Use the listing technique to write U U C.

UUC=

D U E = { 16, 18, 19, 20, 21 }

U stands for the union of sets.

We combine all of the components from the two groups.

16, 19, 21, and 16, 18, 19, 20 are the elements in sets D and E, respectively.

Therefore, we combine all of their components. The shared components of both sets are written just once.

As a result, there are 16, 18, 19, 20, and 21 elements in the set D U E.

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An equation that relates T to N can be written as T = 750 + 630N.

An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

A function can be defined as a mathematical expression which can be used to define and represent the relationship that exist between two or more variables in a population (data set).

Since the total amount saved by using both plans (functions A and B) is represented by T, an equation that relates T to N can be written as follows:

T = A + B

Substituting the given parameters into the formula, we have;

T = (750 + 135N) + 495N

T = 750 + 135N + 495N

T = 750 + 630N.

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Complete Question:

Raina and her husband are each starting a saving plan. Deshaun will initially set aside $750 and then add $135 every month to the savings. The amount A (in dollars) saved this way is given by the function A=750+135N , where N is the number of months he has been saving. Her husband will not set an initial amount aside but will add $495 to the savings every month. The amount B (in dollars) saved using this plan is given by the function B=495N. Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N.

Simplify your answer as much as possible.

Answer: x=2

Step-by-step explanation:

x=z/4+7

x=z/4+3+4

x=(z/4+3)+4

x=-2+4

x=2

5 is at the one-place value, and 0.5 is at the tenth-place value. 5 is ten times the value of 0.5.

For the given question;

The speed of the world's biggest submarine is 25.5 miles per hour on the surface.

Thus, in the value of 25.5, the digit 5 lies on the once place.

The value 0.5 lies on the tenth place.

Now, it is clear that the 5 is the 10 times the value of 0.5, which is the required relation.

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Answer:

[tex]\dfrac{7}{8} \textsf{ and } -\dfrac{5}{8}[/tex]

Step-by-step explanation:

To find numbers that are [tex]\dfrac{3}{4}[/tex] units distance from [tex]\displaystyle \dfrac{1}{8}[/tex] , add and subtract [tex]\dfrac{3}{4}[/tex] to and from [tex]\displaystyle \dfrac{1}{8}[/tex]

One of the points is at [tex]\displaystyle \dfrac{1}{8} + \dfrac{3}{4}[/tex] units away and the other at [tex]\displaystyle \dfrac{1}{8} - \dfrac{3}{4}[/tex] units away

Answer:

5 days.

Step-by-step explanation:

The food will last her 5 days.
[tex]3\frac{1}{2}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}[/tex]
[tex]=1\frac{5}{8}-\frac{5}{8}-\frac{5}{8}[/tex]
[tex]=1-\frac{5}{8}[/tex][tex]=\frac{3}{8}[/tex]

Answer: -5<=x≤3   ==> 3rd option

Step-by-step explanation:

(x-3)(x+5)≤0

x-3>=0 and x+5≤0

x>=3 and x≤-5      ==> Not possible since a number subtracted by 3 can't be greater than the same number added by 5.

x-3≤0 and x+5>=0

x≤3 and x>=-5 ==> -5<=x≤3   ==> 3rd option

The solution to the inequality is {x | -5 ≤ x ≤ 3}, option C is correct.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is (x-3)(x+5) ≤0

To solve this inequality, we first find the critical points by setting the expression inside the inequality to zero:

(x-3)(x+5) = 0

This gives us two critical points: x=3 and x=-5.

We want to find where the expression is less than or equal to zero, so we include the endpoints of the intervals where the expression is zero or negative.

Hence,  the solution to the inequality is {x | -5 ≤ x ≤ 3}, option C is correct.

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Answer:

33.33

Step-by-step explanation:

    Well, we already know the amount of time it takes to make the lemonade, and we know the rate as well.

We need to find out how many pitchers you can make in an hour. If you can make one pitcher in 10 minutes, then you can make 6 pitchers in 60 minutes, AKA an hour.

So we make 6 pitchers per hour.

If we make 6 an hour, then we multiply 6 by 200 to get the number of pitchers we can make in 200 hours.

We can make 33.33 pitchers in 200 hours

According to the image, the figure moved four times to return to its initial position.

The starting position of the figure is in the lower left corner of the frame.

The movement made by the figure from position 1 to position 2 is that it moves from the lower left corner to the lower right corner.

The movement made by the figure from position 2 to position 3 is that it moves from the lower right corner to the upper right corner. Additionally, the figure rotates to the left 180°.

The movement that the figure performs from position 3 to position 4 is that it moves from the upper right corner to the upper left corner.

The movement made by the figure from position 4 to position 5 is that it moves from the upper left corner to the lower left corner. Additionally, the figure is rotated 180° to the left again.

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Answer: v=M^3

Step-by-step explanation:

Answer:642

Step-by-step explanation:

Look at the book and solve it

To earn $100 profit Manu should get the order of 22 glasses.

Given that, the cost price of a drinking glass=$8 and the selling price = $13.

When, in a transaction, the selling price is greater than the cost price, it means we earn a profit. The basic formula used for calculating the profit is Profit = Selling Price - Cost Price.

Let x = the number of glasses and y = profit from selling x glasses.

Now, y=(13-8)x-10

Assumed that the order is x glasses to earn a profit of $100.

(13-8)x-10=100

⇒5x-10=100

⇒5x=110

⇒x=22

Therefore, to earn $100 profit Manu should get the order of 22 glasses.

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The numbers are -3 and 6

From the information given, let the number be x;

the expression is given as;

(√3x + 2) = x - 4

To determine the number, find the square of both sides, we have;

(√3x + 2) ^2 = (x - 4)^2

Find the square of both sides

3x + 2 = ( x - 4)(x + 4); difference of two squares

expand the bracket

3x + 2 = x^2 + 4x - 4x - 16

collect like terms

x^2 - 3x - 16 - 2

x^2 - 3x - 18

x^2 - 6x + 3x - 18

Factorize the expression

x( x - 6) + 3( x - 6)

(x + 3) or (x - 6)

x = -3 or x = 6

Thus, the numbers are -3 and 6

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The equation of this linear equation is f(x) = 9/7(x - 1) + 2

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are

f(−6) = −7, f(1) = 2

Start by calculating the slope (m) using

m = [f(-6) -f(1)]/[-6 - 1]

This gives

m = [-7 - 2]/[-6 - 1]

Evaluate

m = 9/7

The linear equation is then calculated as

f(x) = m(x - x1) + f(1)

So, we have

f(x) = 9/7(x - 1) + 2

Hence, the equation of this linear equation is f(x) = 9/7(x - 1) + 2

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The error of interval for x will be [12.25, 12.35) for rounding off to 12.3 to 1 decimal place

In the given question, a number supposed to be 'x' is rounded off to the 1 decimal place, so that the number rounded off becomes 12.3. So, it is given that the number x is rounded off to 12.3 by 1 decimal place.

From this, we get that x should be greater than or equal to 12.25 and x should be smaller than 12.35. The equations will be :

     =>  x ≥ 12.25   and x < 12.35

So, the x lies between 12.25 and 12.35 which defines the error of interval for x.

Hence, the error of interval for x will be [12.25, 12.35)

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Answer:

12

Step-by-step explanation:

3*4 = 12

12/6 = whole number

6/4 is not a whole number

12 is the lowest it could be.

Also those kids have issues.

a baby blue whale weigh= 2000 kg

Simple equation :

A linear equation that involves only one variable is known as a simple equation or a linear equation in one variable. For example, \(3x + 2 = 23,x = 7,2x + 6 = 3x – 4,\)etc., are simple equations.Let us assume a situation, in which you go to the market to buy mangoes in a supermarket. Your mother gave you Rs.100 and said that you can keep Rs.40 for buying chocolates and for the remaining amount, you need to buy mangoes. When you went to the market, you found out that the price of one kg of mangoes was Rs.12. So, the final question is how many mangoes you should buy, so that everyone is satisfied. Recall the concept of simple equations from previous classes and proceed. Let us assume that you have to purchase kg of mangoes, so the total amount of money that you will be spent on buying mangoes will be Rs.12x. Now, you have Rs.40 for yourself, so you have an equation:

12 x + 40 = 100

12x = 100 – 40

12x = 60

x = 60/12 = 5, This is the same equation as above. Now when you will solve this, you will get to know the value of 5kg of mangoes. It means that you can buy 5 kg mangoes and spend Rs.40 on buying chocolates

weigh: to measure how heavy something is, especially by using a machine (scales)

given :

A baby American bison weighs=20kg

The solution according to Question  =

Let the weight of baby blue whale = b

the baby blue whale weighs =100(a baby American bison)

b=100(20)

b=2000 weigh

a baby blue whale weigh= 2000 kg

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Answer: 18.25

Step-by-step explanation:

5.5*4=22

401.5/22=18.25

Answer:

$18.25

Step-by-step explanation:

Since area is given as A=LW, and we are given the values of the dimensions of the floor, we get:

5.5×4=22

So, the area is 22 yards, and it costs $401.5 to carpet it. Now, We simply need to divide the cost by the area to get the "cost per-square yard" as needed in the question. We get:

401÷22=18.25

So, the cost of the carpet per square yard is $18.25

The gross income will be $5,800.

It is given that per month salary of an individual is $4000 and from a side job he makes $20 per hour for 10 hours a week for 4 weeks and rent he got is $1000.

We have to calculate the gross income.

What do you mean by gross income ?

Gross income refers to the total income of a person or business from all resources.

As per the question ;

Per month salary = $4000

Earning from side job is given $20 per hour for 10 hours a week for 4 weeks.

i.e.,

= 20 × 10 × 4

= $800 for 4 week

and

the rent they receive = $1000

So ;

The gross income will be ;

= 4000 + 800 + 1000

= $5,800

Thus , the gross income will be $5,800.

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Pedro requires [tex]1\frac{1}{2}[/tex] cups oatmeal for a single batch of granola bars as calculated by division of fractions.

A fraction is a piece of a whole or, to put it more broadly, any number of equal portions.

Total batches required [tex]= 3 \frac{1}{2} = \frac{7}{2} = \frac{14}{4}[/tex] cups

Total oatmeal required [tex]= 5 \frac{1}{4} =\frac{21}{4}[/tex] cups

Therefore now to calculate the amount of oatmeal needed for single

batch we divide the fraction [tex]\frac{21}{4}[/tex]  by  [tex]\frac{14}{4}[/tex] cups

1 batch requires = [tex]=\frac{21}{4}\div\frac{14}{4}=\frac{3}{2} = 1\frac{1}{2}[/tex] cups.

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Answer:

Absolute error = 20.2m

% error = 6.73%

Step-by-step explanation:

Absolute error = 300-279.8= 20.2m

% error = 20.2 ÷ 300 = 6.73%

Step-by-step explanation:

the constant k of proportionality is defined by

y = kx

or in our case

b = ka

so, let's see

14 = k×2

k = 14/2 = 7

this also works for the other data pairs :

7×5 = 35

7×9 = 63

7 × 1/3 = 7/3

perfect.

so, the constant of proportionality is 7.

The coordinate of the pointed that represented the weighted average of A and B is: 1

Note that X = [x1w1 + x2w2 +.......xnwn]/w1+w2 +....wn

Where x is the numbers and w is the weight.

Given,

A = - 4  : Weight = 2

B= 3    : Weight = 5

Hence, average is given as;

([-4 x 2] + [3 x 5])/2+5

= (-8 + 15)/7

= 7/7

= 1

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Answer:

I believe R is congruent to U

Step-by-step explanation:

I don't exactly remember much about these types of problems but I hope it helps! =D

Answer:

∠VS is congruent to ∠UR

Step-by-step explanation:

congruent means same size or shape and the markings are the little lines

the little curves over the angles are congruent as well

Answer:

eueueue

Step-by-step explanation:

1) a + b = ?

→ (9i − 4j + 3k) + (6i − 9k)

→ 15i - 4j - 6k

2) 9a + 3b = ?

→ 9(9i − 4j + 3k) + 3(6i − 9k)

→ (81i - 36j + 27k) + (18i - 27k)

→ 99i - 36j

3) |a| = ?

→ |9i − 4j + 3k|

→ 9i + 4j + 3k

4) |a − b| = ?

→ |(9i − 4j + 3k) - (6i − 9k)|

→ |3i - 4j + 12k|

→ 3i + 4j + 12k

Answer:

[tex]a+b=15i-4j-6k[/tex]

[tex]9a+3b=99i-36j[/tex]

[tex]|a| = 9i+4j+3k[/tex]

[tex]|a-b| = 3i+4j+12k[/tex]

Step-by-step explanation:

Given:

[tex]\begin{cases}a = 9i-4j+3k\\b=6i-9k\end{cases}[/tex]

[tex]\begin{aligned}a+b & = (9i-4j+3k)+(6i-9k)\\& = 9i-4j+3k+6i-9k\\& = 9i+6i-4j+3k-9k\\& = 15i-4j-6k\\\end{aligned}[/tex]

[tex]\begin{aligned}9a+3b & = 9(9i-4j+3k) + 3(6i-9k)\\& = 81i-36j+27k+ 18i-27k\\& = 81i+ 18i-36j+27k-27k\\& = 99i-36j\end{aligned}[/tex]

[tex]\begin{aligned}|a| & = |9i-4j+3k|\\& = 9i+4j+3k\end{aligned}[/tex]

[tex]\begin{aligned}|a-b| & = |(9i-4j+3k)-(6i-9k)|\\& = |9i-4j+3k-6i+9k|\\& = |9i-6i-4j+3k+9k|\\& = |3i-4j+12k|\\& = 3i+4j+12k\end{aligned}[/tex]