(01.01 MC)
Which value of x would make the expression (75)* equal to 5?
a
b
3
12
C 4
5
d 5
4

Answer:

-12 - 51i

Step-by-step explanation:

[tex]original:(-6-3i)*(5+6i)\\FOIL:(-6)(5)+(-6)(6i)+(-3)(5)+(-3i)(6i)\\Multiply:(-30)+(-36i)+(-15i)+(18i^2)\\Combine\ Like\ Terms:(-30) + (-51i)+(-18i^2)\\i^2\ =\ -1:(-30)+(-51i)+(-18)(-1)\\Multiply:(-30)+(-51i)+(18)\\Combine\ Like\ Terms:(-12) + (-51i)\\Simplify:-12-51i[/tex]

Thing to remember:

[tex]i = \sqrt{-1} \\i^2 = \sqrt{-1}*\sqrt{-1} = \sqrt{-1}^2 = -1\\i^3 = \sqrt{-1}*\sqrt{-1}*\sqrt{-1} = i^2 * i = (-1)*i = -i\\i^4 = \sqrt{-1}*\sqrt{-1}*\sqrt{-1}*\sqrt{-1} = \sqrt{-1}^2*\sqrt{-1}^2 = (-1)*(-1) = 1\\[/tex]

And all powers over 4 repeat such that [tex]i^x\ such\ that\ x\mod4 = y[/tex] is the same as [tex]i^y\\[/tex]:

i.e.:

[tex]i^6 = i^{4+2}= i^4*i^2 = 1*-1 = -1\\\\i^9 = i^{4+4+1}=i^4*i^4*i^1=(1)(1)(i) = i[/tex]

NOTE: x mod 4 simply means the remainder when x is divided by 4.

i.e.:

[tex]7\mod4 = 3\\8\mod4 = 0\\13\mod4 = 1[/tex]

The least common multiple of 10 and 4 is 20.

L.C.M is defined as Least Common multiple. The Least Common multiple of two numbers is the least possible number that can be divisible by both the numbers. Or, in simple words, the least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers.

We need to find the L.C.M of two numbers which are 10 and 4

First we will find out few multiples of 10 and 4which are:

       multiples of 10 : 10,20,30,40,50,60,70,80.....

       multiples of 4 : 4,8,12,16,20,24,28,32,36,40,......

Then we will filter out the common multiple.

common are : 20 and 40

From these two number the least number is 20.

Hence the least common multiple of 10 and 4 is 20.

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Answer:

See below

Step-by-step explanation:

Look for where the vertical line x = -2 crosses the graph.....the value is shown below.....

check image for answer po

Some of the 20th century's biggest market shifts were sparked by technological breakthroughs that impacted market supply curves.

The supply curve illustrates the relationship between the price of an item or service and the volume delivered over a specific time period.

In a typical scenario, the amount supplied will be shown on the horizontal axis and the price will be shown on the left vertical axis.

It should be noted that some of the 20th century's biggest market shifts were sparked by technological breakthroughs that impacted market supply curves.

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The factors are 17 and 3.

The given conditions are two factors of the first number, 51 such that their product is 51 and the sum is the second number 20.
let say, the factors are x and y.

therefore, we can write, x.y = 51 ... (1)  and x + y = 20 .... (2)

Putting  the value of x from equation (2) in  equation (1) we get,

(20 - y).y = 51

or, 20y - y² = 51

or, y² - 20y + 51 = 0

or, y = 17, 3

then x = 3,17

Therefore, The factors are 17 and 3.

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Answer:

124.4 pounds

Step-by-step explanation:

We have:

651 + 95.4 = 6.B

=> 746.4 = 6.B

=> B = 746.4/6

=> B = 124.4

Answer:

I think the answer is 7/16 hope it's correct

Answer:

Step-by-step explanation:

unit place can be selected in ways=5

ten's place can be selected in ways=5

total numbers=5×5=25

but if the numbers at two places is different then number of ways=5×4=20

Answer:1200

Step-by-step explanation:

Answer:

x = 1, x = 4

Step-by-step explanation:

First, let x = u^(2/3)

The problem given has a third power and also a 1.5 power. That is just oof! So choosing "u to the 2/3 power" to substitute in for x will make this equation be a straightforward quadratic that you can factor and solve.

see image.

Substitute

x = u^(2/3)

This gives you:

u^2 - 9u + 8 = 0

Factor.

(u - 1)(u - 8) = 0

Solve.

u-1 = 0 and u-8=0

u = 1 and u = 8

Substitute back into

x = u^(2/3)

x = 1^(2/3) and

x = 8^(2/3)

Remember some exponent rules and definitions. The 2 in the 2/3 will square the base number and the 3 (actually 1/3) will cuberoot the base number. See image. Hope this helps.

Answer: 23100 voters

Step-by-step explanation:

42*55000=2310000

2310000/100=23100 voters

The measure of segment AB from the given question is 25

In line geometry, a line is the distance between two points while an angle is the point where two lines intersect.

Given the following parameters

AC = 31

BC = 6

Required

AB

Using the addition postulate

AB + BC = AC

Substitute

AB = AC - BC

AB =  31 - 6

AB = 25

Hence the measure of segment AB from the given question is 25

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Answer:

1.5 g are in that bottle.

Step-by-step explanation:

100 soft gels × 15 mg each = 1500 mg of vit. E

1500 mg = 1.5 g

Answer:

3x+2 = 14.12

f(4) = 0

Answer: EVALUATE

3x+8f

f(x)=3x+2f(4)=

Multiply 2 and 4 to get 8.

3x+8f

DIFFERENTIATE W.R.T. X

3

Step-by-step explanation:

Answer:

  speed × time = 100 miles

Step-by-step explanation:

The graph shows an inverse relation between speed and time. You want to know what is true about the product of speed and time.

Two quantities are inversely proportional when one is proportional to the inverse of the other. A constant of proportionality will be involved. The relation can be written ...

  y = k(1/x)

where x and y are the quantities inversely related, and k is the constant of proportionality.

In the present case, we have a graph of the relation ...

  time = distance/speed

where the distance is 100 miles.

Comparing this to the above inverse proportion relation, we see that "distance" is the constant of proportionality (k):

  time = (100 miles)/speed

The times at various speeds are ...

Multiplying both sides of this equation by speed, we get ...

  speed × time = speed × (100 miles)/speed

  speed × time = 100 miles

The product of speed and time is always 100 miles in this scenario.

Step-by-step explanation:

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The total cost of the used cell phone in Canadian dollars is C$130.16.

Su Mei should buy the used cell phone because it is cheaper than the new cell phone.

The exchange rate is the rate at which one unit of a currency is exchanged for another currency. For example, if the exchange rate of the US dollar and the Canadian dollars is 1.00903. It means that 1 unit of the US dollar would buy 1.00903 of the Canadian dollars.

The first step is to determine the total cost of the used cell phone in US dollar. The total cost would be the sum of the used cell phone and the shipping cost.

Total cost of the used cell phone = $99 + $30 = $129

The next step is to convert the cost of the used cell phone that is priced in the US dollar to Canadian dollars.

129 x 1.00903 = $130.16

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Interval notation

(-5,-3) U [22,00)

• Interval notation in mathematics is a method to represent an interval of a number on the number line. In simpler words, interval notation is a way of writing subsets of the real number line .

• An interval comprises of the numbers lying between two specific given numbers. For example a set of numbers lying between 0 and 3 is an interval that contains 1,2.The way to represent interval notation is by using square bracket or round brackets, square brackets for both value included and round brackets for both value not included.

We are given that x is a real number which lies between -3 and -5 or any real number greater than or equal to 22

Firstly, x lies between -3 and -5

-5< x <-3

x = (-5,-3)

Secondly, x is greater than 22

x>=22

x = [22,00)

Interval notation

(-5,-3) U [22,00)

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If 8/9 is multiplied by 3/7 then the product will not be greater than either of the two factors.

According to the question

on multiplying 8/9 by 3/7 we get

=8/9*3/7

=(8*3)/(9*7)

=24/63

=0.38095         ...(i)

On comparing it with two factors,

8/9 = 0.88888         .....(ii)

and

3/7 = 0.42857        ......(iii)

As we can see that on comparing equation (i) with equation (ii) and

equation (i) with equation (iii)    , we get that the product of 8/9 and 3/7 is less than both 8/9 and 3/7 .

Therefore , if 8/9 is multiplied by 3/7 then the product will not be greater than either of the two factors.

The given question is incomplete , the complete question is

If 8/9 is multiplied by 3/7 , will the product be greater than either of the 2 factors ?

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When only 4 players remain, the fewest number of matches that can be played is 37.

Given information:

When only four players remain, the smallest number of matches that can be played is calculated as follows:

Now, divide both sides by 3 as follows:

Therefore, when only 4 players remain, the fewest number of matches that can be played is 37.

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Answer:

4) Larger/smaller, Size

5) Whichever are larger then the original, depends on if green or blue is original

Step-by-step explanation:

Answer:

After 4 weeks: $45, After w weeks: 5w + 25

Step-by-step explanation:

5 per week is 20 for 4 weeks. $25 + $20 = $45.

5w is 5 times the week. +25 because he had 25 to begin with. 5w+25.

The lateral area of the cone is 394 square inches

The formula for lateral area of a cone is expressed as;

Lateral area = πr √h² + r²

Given that;

Substitute the values into the formula

Lateral area = 3. 142(6) √20² + 6²

Lateral area = 18. 85 √436

Lateral area = 18. 85 × 20. 8

Lateral area = 394 square inches

Thus, the lateral area of the traffic cone is 394 square inches

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The length of the square in centimetres in algebraic expression is 25m

The perimeter of a square is m meters.

The length of the each side of the square in centimetres can be represented in an algebraic expression as follows:

Therefore,

perimeter of a square = 4l

where

Therefore,

m = 4l

where

l = m / 4 meters.

Therefore, the side length of the square in centimetres is as follows:

1 meters = 100 cm

m / 4 meters  = ?

cross multiply

length of the square in meters = m / 4 × 100

length of the square in meters = 100m / 4

length of the square in meters = 25m

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Answer:
10 Probability of blue is 2/10%

Step-by-step explanation:

scale factor of triangle is 20/7 = 2.8571 .

To get the scale factor of two triangles, follow these steps:

1. Check that the two triangles are similar.

2-If the triangles are similar, identify the sides that match.

3. Subtract any known angle from the triangle and multiply the result by the matching (also known) angle in the second triangle.

As a result,

4- the scale factor is equalized by the division.

∵ To find scale factor of two triangle we divide the sides of the both sides

∴ the scale factor of triangle given will be 20/7 = 2.8571 .

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a. It takes the robot 4/35 hour to complete one tasks

b. The number of tasks the robot can complete in one hour is 8 3/4 tasks

From the question, we are to determine how long it takes the robot to complete one task

From the given information,

A robot can complete 7 tasks in 4/5 hour

If the robot can complete 7 tasks in 4/5 hour

Then,

The robot will complete 1 task in 4/5 ÷ 7 hour

4/5 ÷ 7

= 4/5 × 1/7

= 4/35  

Hence, it takes the robot 4/35 hour to complete one tasks

b.

Let the number of tasks the robot can complete in one hour be x

If the robot can complete 7 tasks in 4/5 hour

Then,

The robot will complete x tasks in 1 hour

4/5 × x = 7 × 1

4/5 × x = 7

4 × x = 7 × 5

4x = 35

x = 35/4

x = 8 3/4

Hence, the number of tasks the robot can complete in one hour is 8 3/4 tasks

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The next step that Michael could use to evaluate the expression is count 3 units to the left of -8

The expression is given as

-8 - 3

The first step is given as

Locating –8 on the number line

The other term of the expression is a negative number i.e. -3

This means that Michael needs to count 3 units to the left of the first number

Hence, the next step that Michael could use to evaluate the expression is count 3 units to the left of -8

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Thus the profit of the manufacturer is 240000$ per month

It is given that a product costing 60 cents per unit to produce had been selling at the average rate of 1,200,000 units per month.

After the product was improved, sales increased to an average of 2,000,000 units per month.

It is also given that the new product cost five percent more to produce.

If the manufacturer's selling price in each instance was 75 cents per unit, We are required to find what was the manufacturer's added profit per month with the newer product.

Cost price is the price which the manufacturer pays for each unit

It is given that the cost price of new version is 5 percent more than the previous one.

Thus, the cost price of each unit of product = 60 cents +5 percent of 60 cents = 60+5/100*60=63 cents

It is also given that selling price of each unit is 75 cents

Profit=selling price- cost price

        = 75-63= 12 cents

Thus, total profit on selling the 2000000 products= 2000000x12cents

Now we know that 100 cents = 1 dollar

Thus the profit in dollars will be = 2000000*12/100=240000

Thus the profit of the manufacturer is 240000$ per month

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