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[tex](3-9i)(6-i)=18-3i-54i+9i^2=18-57i-9=\boxed{9-57i}[/tex].

Hope this helps.

Answer:

5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

The diagonal divides the square into 2 right triangles.

let s be the side of the square with the diagonal being the hypotenuse.

Applying Pythagoras' identity to one right triangle, gives

s² + s² = 10² , that is

2s² = 100 ( divide both sides by 2 )

s² = 50 ( take the square root of both sides )

s = [tex]\sqrt{50}[/tex] = [tex]\sqrt{25(2)}[/tex] = [tex]\sqrt{25}[/tex] × [tex]\sqrt{2}[/tex] = 5[tex]\sqrt{2}[/tex]

Answer:

T = - 3.2e + 80

Step-by-step explanation:

Given the following :

e = elevation in thousands of feets

T = temperature (°F)

e1 = 5 ; e2 = 10 (in thousands of feet)

T1 = 64° ; T2 = 48°

y = mx + c ; T = me + c

y = ; m = slope, c = intercept

64 = m5 + c - - - - (1)

48 = m10 + c - - - - (2)

From (1)

c = 64 - m5

Substitute c = 64 - m5 into (2)

48 = m10 + c - - - - (2)

48 = m10 + 64 - m5

48 - 64 = 10m - 5m

-16 = 5m

m = - 16 / 5

m = - 3.2

Substitute the value of m into c = 64 - m5

c = 64 - 5(-3.2)

c = 64 - (-16)

c = 64 + 16

c = 80

Inserting our c and m values into T = me + c

T = - 3.2e + 80

Where e is in thousands of feet

T is in °F

Answer:

128 Apples

Step-by-step explanation:

Answer:

128 apples

Elaborated:

Your first multiple 16 and 7 which is 112. Your than multiply 2 and 8 since the remaining boxes are half full which is 16. 112+16 is 128. Hope this helps!

Answer:

You get 12$ per B and 15$ per A.  Thus, the answer is A) $282

Step-by-step explanation:

4A+4B=108

Divide by 4

A+B=27

Subtract B

A = 27 - B

3A+5B=105

Substitution

3(27-B)+5B = 105

Distribute

81-3B+5B=105

Combine like terms

81+2B=105

Subtract 81

2B=24

Divide by 2

B = 12

A = 15

14(15)+6(12)=x

210+72=x

282=x

Hope it helps <3

Answer:

a) A quadrilateral with 4 right angles

Answer:

I think the answer is b

I'm sorry if I'm not correct

Hey there! I'm happy to help!

To find the volume of a cone, we multiply the base by the height and then divide by three.

First, we find the area of the base, which is a circle. To find a circle, you square the radius and then multiply by pi (or 3.14 in our case).

Radius is half of the diameter.

3/2=1.5

We square this.

1.5²=2.25

We multiply by 3.14

2.25×3.14=7.065

Now, we multiply this base area by the height.

7.065×7=49.455

We divide by 3.

49.455/3=16.485

Therefore, if we round this, our answer is 16.49 in³.

Now you can find the volume of a cone! Have a wonderful day! :D

Answer:

16.49

Step-by-step explanation:

Answer:

x= 24, y= 33°

Step-by-step explanation:

MJ is part of the diameter of the circle and there is right angle between the diameter and HK

As the diameter and HK are perpendicular, HM=MK and mHJ= mJK

So,

and

Answer:

The probability is 0.0053861

Step-by-step explanation:

To answer this question, the best thing to do is to put the wordings in a mathematical expression.

Thus what we have is;

P(z < 2.55)

Now since we have the mathematical expression, the next thing to do here is to use the standard normal distribution table.

From the standard normal distribution table, we can get the probability value that equals the given z-score value

Mathematically this is;

P(z<2.55) = 0.0053861

Answer:

I think it doesnt have solution.

Answer: The probability that she will visit them in the exact order ABCD or DCBA =  [tex]\dfrac{1}{12}[/tex]

Step-by-step explanation:

Given: Jennifer wants to visit 4 different cities A,B,C and D on her vacation.

If she visits in an order , total such orders will be [tex]4![/tex] = 4 x 2 x 3 x 1 =24.

Since probability = [tex]\dfrac{\text{Favourable outcomes}}{\text{total outcomes}}[/tex]

In this case favorable outcomes ( ABCD ,  DCBA)=  2

Total outcomes = 24

Required probability = [tex]\dfrac{2}{24}=\dfrac{1}{12}[/tex]

Hence, the probability that she will visit them in the exact order ABCD or DCBA =  [tex]\dfrac{1}{12}[/tex]

Complete question :

The table shows the total number of student applications to universities in a particular state over a period of 12 semesters. States base their decisions on data like this. Suppose they decide that if fewer than 200,000 students apply during 6 or more semesters, the state will make a special effort to promote university education. Using this data, what is the population proportion of semesters for which the number of student applications is less than 200,000?

Semester Student Applications (in thousands)

1 106

2 137

3 285

4 120

5 202

6 195

7 327

8 139

9 307

10 318

11 212

12 217

Answer:

42%

Step-by-step explanation:

Given the above data in thousand :

Proportion of students

1 - - - - 106, 000

2 - - - -137, 000

3 - - - - 285, 000

4 - - - 120, 000

5 - - - 202, 000

6 - - - 195, 000

7 - - - 327, 000

8 - - - 139, 000

9 - - - 307, 000

10 - - - 318, 000

11 - - -212, 000

12 - - - 217, 000

Therefore, proportion of semesters with student application below 200,000

= (Number of semesters below 200,000 / total number of semesters)

Semesters below 200,000 :

(106000, 137000, 120000, 195000, 139000) = 5

(5 / 12) = 0.416666

= 0.42

In terms of percentage :

0.42 * 100 = 42%

Answer:

log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x.

Log₂ 9 + 3Log₂ x

Step-by-step explanation:

Log subscript 2 baseline 9 x cubed can be written as:

Log₂ 9x³

Now, let us simply Log₂ 9x³.

This is illustrated below:

Log₂ 9x³

Recall: LogMN = Log M + Log N

Log₂ 9x³ = Log₂ 9 + Log₂ x³

Recall: Log Mⁿ = nLog M

Log₂ 9x³ = Log₂ 9 + 3Log₂ x

Therefore, the answer is log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x.

The equivalent expression of [tex]\log_2(9x^3)[/tex] is [tex]\log_2(9) + 3\log_2(x)[/tex]

The logarithmic expression is given as:

[tex]\log_2(9x^3)[/tex]

Apply the quotient law of logarithm

[tex]\log_2(9x^3) = \log_2(9) + \log_2(x^3)[/tex]

Apply the power rule of logarithm

[tex]\log_2(9x^3) = \log_2(9) + 3\log_2(x)[/tex]

Hence, the equivalent expression of [tex]\log_2(9x^3)[/tex] is [tex]\log_2(9) + 3\log_2(x)[/tex]

Read more about equivalent expressions at:

https://brainly.com/question/2972832

Answer:

I think

x y

2

3

4

6

6

9

Step-by-step explanation:

but i don't see any table

Answer:

3²

Step-by-step explanation:

We have to use BPEMDAS Order of Operations:

B - Brackets

P - Parenthesis

E - Exponents

M - Multiply

D - Divide

A - Addition

S - Subtraction

We use this order left to right. Since we have parenthesis, we look at that first. Inside, we have division and exponents. Since exponents come first, we have to evaluate 3² first.

Answer:

square the 3

Step-by-step explanation:

In the order of operations, you must do the exponent inside the parentheses first, so the first step is:

4(27 ÷ 3²) =

= 4(27 ÷ 9)

Answer: square the 3

Answer:

108

Step-by-step explanation:

To find x, you need the geometric mean. First, find the second part of 225 by doing 225 - 144 = 81. Now, to find geometric mean, do 81 x 144 = 11,664; [tex]\sqrt{11,664} = 108[/tex].

The missing length in the right triangle as given in the task content is; 108.

It follows from the complete question that the triangle given is a right triangle and the missing length can be calculated as;

First, find the second part of 225 by

225 - 144 = 81.

Now, to find geometric mean,

81 × 144 = x²

11,664 = x²

x = 108

Thus, The missing length in the right triangle as given in the task content is; 108.

Read more on missing length;

https://brainly.com/question/28040679

#SPJ2

Answer:

[tex] area = 10x^2 - 4x + 6 [/tex]

Step-by-step explanation:

Given that the rectangle has a height = 2, and width of [tex] 5x^2 - 2x + 3 [/tex]

Area of the whole rectangle can be calculated as:

[tex] area = 2(5x^2 - 2x + 3) [/tex]

Use the distributive property of multiplication by using 2 to multiply each term in the expression, [tex] (5x^2 - 2x + 3) [/tex]

[tex]area =2(5x^2) +2 (-2x) + 2(3)[/tex]

[tex] area = 10x^2 - 4x + 6 [/tex]

Answer:

4107 cells

Step-by-step explanation:

From the question, we have the following values:

Day 1 : 113 cells

Number of cells increases by day by 82%

Hence,

Day 2

113 × 82% = 92.66cells

Hence, Total number of bacteria cells for Day 2 = 113 + 92.66 = 205.66cells

Day 3

205.66 × 82% = 168.6412 cells

Hence, Total number of bacteria cells for Day 3 = 168.6412 + 205.66 = 374.3012 cells

Day 4

374.3012 × 82% = 306.926984 cells

Hence, Total number of bacteria cells for Day 4 = 306.926984 + 374.3012 = 681.228184 cells

Day 5

681.228184 × 82% = 558.60711088 cells

Hence, Total number of bacteria cells for Day 5 = 558.60711088 + 681.228184 = 1239.8352949 cells

Day 6

1239.8352949 × 82% = 1016.6649418 cells

Hence, Total number of bacteria cells for Day 5 = 1016.6649418 + 1239.8352949 = 2256.5002367 cells

Day 7

2256.5002367 × 82% = 1850.3301941 cells

Hence, Total number of bacteria cells for Day 7 = 1850.3301941 + 2256.5002367 = 4106.8304308 cells

Approximately to nearest whole number, the total number of bacteria cells that would be present after 7 days = 4107 cells

Answer:

[tex]\boxed{d = 54 yards}[/tex]

Step-by-step explanation:

Formula for diagonal is as follows:

[tex]d = \sqrt{l^2+w^2}[/tex]

Where d is diagonal, l is length (50 yards) and w is width (20 yards)

[tex]d = \sqrt{(50)^2+(20)^2}[/tex]

[tex]d = \sqrt{2500+400}[/tex]

[tex]d = \sqrt{2900}[/tex]

d = 53.85 yards

d ≈ 54 yards

Answer:

[tex]\boxed{\mathrm{54 \: yards}}[/tex]

Step-by-step explanation:

The shape of the pool is a rectangle.

The diagonal of a rectangle can be found through a formula by using Pythagorean theorem.

[tex]d^2=l^2 +w^2[/tex]

[tex]d=diagonal\\l=length\\w=width[/tex]

The length is given 50 yards, and width is given 20 yards. Find the diagonal.

[tex]d^2 =50^2 +20^2[/tex]

[tex]d^2 =2500+400[/tex]

[tex]d^2 =2900[/tex]

[tex]d=\sqrt{2900}[/tex]

[tex]d \approx 53.851648[/tex]

[tex]d \approx 54[/tex]

Answer:

1 / 3^1

Step-by-step explanation:

3^-1 • 3^0

When multiplying exponents with the same base, we add the exponents

3^ (-1+0)

3 ^-1

We know that a^ - b = 1/a^b

3 ^ -1 = 1/3^1

Answer:

y = 2x + 4

Step-by-step explanation:

y = mx + b

b = y-intercept = 4

m = slope = rise/run = 4/2 = 2

y = 2x + 4

Answer:

[tex]\bold {3.25+5.50S \le 30}[/tex] is the correct answer.

Step-by-step explanation:

Given that

Chocolate milk already ordered for the cost of $3.25.

Maximum bill that Benjamin wants = $30

Cost of a stack pancake = $5.50

Number of stacks of pancakes bought = S

It is given that all the money available is to be spent on 1 chocolate milk and S number of stacks of pancakes.

Cost of 1 pancake = $5.50

Cost of S number of stacks of  pancakes = [tex]\text{Number of stacks of pancakes} \times \text{Cost of each pancake}[/tex]

i.e. [tex]S \times 5.50 = 5.50S[/tex]

So, total money spent = $3.25+5.50S

Now, this money should be lesser than or equal to $30 because maximum bill that Benjamin wants is $30.

So, the inequality can be written as:

[tex]\bold{3.25+5.50S \le 30}[/tex]

Answer:

120 mg

Step-by-step explanation:

20% of  100 is 20 so that would be 20mg  plus the 100mg they just took

100+20=120mg

i hope this helps you!

Answer:

B

Step-by-step explanation:

When you plug it in, another form could be y=-3x+2

Answer:

y=-3x+2

Step-by-step explanation:

y=-3x+7

parallel lines have the same slope but different y intercept which is b in the equation y=mx+b

since it passes through (2,-4) then x=2 and y=-4, m(slope)=-3

y=mx+b

-4=-3(2)+b

b=-4+6

b=2

y=-3x+2

Answer:

125 degrees

Step-by-step explanation:

Using a theorem, you know that angle a is half of 110. Also, in all quadrilaterals   inscribed in a circle, the opposite angles are supplimentary. So then, knowing that angle a is 55 degrees, you can come to the conclusion that b is 125 degrees.

Hope this is helpful! :)

The residual value is the distance between where the line is and the dot is.

At x = 2, the line crosses at y = 2, and the dot is at y = 1

The difference is: 2-1 = 1

BeUse the dot is below the line it becomes a negative value.

The answer would be -1

Answer:

[tex]\dfrac{74}{20}=3.7 meters[/tex]

Step-by-step explanation:

Hello!

1) Since no other data has been given. Suppose Natasha is in the center and the beagle is to the right.

[tex]\dfrac{25}{4} \:meters[/tex]  

2) The labrador is [tex]\dfrac{51}{20}\: to\: the\: left.[/tex]

[tex]\dfrac{25}{4} -\dfrac{51}{20} =\dfrac{(5*25)-51}{20} \\\dfrac{(125-51}{20} =\dfrac{74}{20}[/tex]

Answer:

The answer is B :D hope this helps

Step-by-step explanation:

Answer:

340 liters

Step-by-step explanation:

357/1.05=340

[tex](2+3)^{-1}\equiv5^{-1}\pmod7[/tex] is the number L such that

[tex]5L\equiv1\pmod7[/tex]

Consider the first 7 multiples of 5:

5, 10, 15, 20, 25, 30, 35

Taken mod 7, these are equivalent to

5, 3, 1, 6, 4, 2, 0

This tells us that 3 is the inverse of 5 mod 7, so L = 3.

Similarly, compute the inverses modulo 7 of 2 and 3:

[tex]2a\equiv1\pmod7\implies a\equiv4\pmod7[/tex]

since 2*4 = 8, whose residue is 1 mod 7;

[tex]3b\equiv1\pmod7\implies b\equiv5\pmod7[/tex]

which we got for free by finding the inverse of 5 earlier. So

[tex]2^{-1}+3^{-1}\equiv4+5\equiv9\equiv2\pmod7[/tex]

and so R = 2.

Then L - R = 1.