is 1+isqrt3 a complex number

Answer:

3,060

Step-by-step explanation:

Given:

18C4

nCr=n! / r!(n-r)!

=18! / 4!(18-4)!

18!=18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1

=6,402,373,705,728,000

4!=4*3*2*1

=24

(18-4)!=14!

=14*13*12*11*10*9*8*7*6*5*4*3*2*1

=87,178,291,200

18! / 4!(18-4)!

=6,402,373,705,728,000 / 24*87,178,291,200

=6,402,373,705,728,000 / 2,092,278,988,800

=3,060

Answer:

5x43

it can only be divided by 1, 5, and 43.

When 215 is written as a product of its prime factor, the result is 5 × 43.

To find the prime factorization of 215, we'll divide it by its smallest prime factor and continue the process until we get all the prime factors. Here's the step-by-step breakdown:

Divide 215 by the smallest prime number, which is 5. We get:

215 ÷ 5 = 43

43 is a prime number, so we stop here.

Now, the prime factorization of 215 is:

215 = 5 × 43

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Answer:

Step-by-step explanation:

  We already establish an understand  that, for Brooke to graduate she needs nothing less than 132 credit hours.

Now a semester has 15 credit hours, she has 4 semester completed already.

Hence 15*4= 60 credit hours done and dusted

This means that she has 132-60 = 72 credit hours to go

Since "c" is the number of credit hours that Brooke needs to complete in order to graduate college.

The inequality can be modeled as,

60 + c > 132

c= 132-60

c= 72

Answer:

9x3 - 2x - 3.

Step-by-step explanation:

(6x3 − 8x − 5) + (3x3 + 6x +2)

=  6x3 − 8x − 5 + 3x3 + 6x + 2

= 6x3 + 3x3 - 8x + 6x - 5 + 2

= 9x3 - 2x - 3.

Answer:

9x-2x-3

Step-by-step explanation:

I took the test

2. 3x+2y= 1 and 5x+3y=-8

solution: In picture.

Answer: C.V=C1.V1 +C2.V2

Step-by-step explanation: C=(C1V1 + C2V2)/V -> C=(20%.V+25%V)/2V-> C=22,5%

Answer:

TRUE

Step-by-step explanation:

Length of other leg [tex]= \sqrt {12^2 - 8^2} \\

= \sqrt {144 -64} \\

= \sqrt {80} \\

= 4\sqrt {5} \\[/tex]

Since, [tex] \sqrt 5[/tex] is an irrational number, hence Perimeter of triangle will also be irrational.

TRUE

Answer:

True.

Step-by-step explanation:

The length of the other side = sqrt ( 12^2 - 8^2)

= sqrt (144 - 64)

= sqrt ( 80) which is irrational so the perimeter is also irrational.

(The sum of a rational number and an irrational is irrational).

Answer:

1 meter = 3.28 feet

Step-by-step explanation:

The unit of conversion from meters to feet is given as follows;

By convention

1 yard = 09144 meters

1 yard = 3 feet

Therefore, we have;

1 foot = 0.9144/3 = 0.3048 m

Alternatively we can get;

1 inch = 0.0254 meters

1 foot = 12 inches

Therefore, we have;

1 foot = 12 × 0.0254 = 0.3048 meter

Which gives;

1 foot = 0.3048 meter

Given that 0.3048 meter = 1 foot, to find the measure of 1 meter, we proceed by dividing both sides of the equation by 0.3048 to get

0.3048/0.3048 meter = 1/0.3048 foot = 3.28084 feet

1 meter = 3.28084 feet. ≈ 3.28 feet to the nearest hundredth

Answer:

x = 20

Step-by-step explanation:

Hello!

What we do to one side we have to do to the other

3x/4 - 5 = 10

Add 5 to both sides

3x/4 = 15

Multiply both sides by 4

3x = 60

Divide both sides by 3

x = 20

The answer is x = 20

Hope this helps!

Answer:

20

Step-by-step explanation:

3x/4 - 5 = 10

3x/4      = 10 + 5

3x/4      = 15

3x         = 15 * 4

3x         = 60

x           = 60/3

x           = 20

Answer:

P = 57°

Step-by-step explanation:

Given the following :

PQ = 17

QR = 15

PR = 14

Using the cosine formula since the length of the three sides are given:

a2 = b2 + c2 – 2bccos(A)

To find P:

QR^2 = PQ^2 + PR^2 – 2(PQ)(PR)cos(P)

15^2 = 17^2 + 14^2 – 2(17)(14)cos(P)

225 = 289 + 196 - 476 cosP

476*CosP = 485 - 225

476*CosP = 260

CosP = 260/476

CosP = 0.5462184

P = Cos^-1(0.5462184)

P = 56.892029

P = 57°

Answer:

57 degrees

Step-by-step explanation:

just took the test on edg2020

====================================================

Explanation:

A drawing may be helpful to see what's going on. Check out the diagram below. This is one way of drawing out the two triangles. The locations of the points don't really matter, and neither does the the orientation of how you rotate things. What does matter is we have the right points connected to form the segments mentioned.

----------

For now, focus on triangle TIP only. In order to have this be isosceles, we must make TP = 5 or TP = 7.

If TP = 5, then it's the same length as TI.

If TP = 7, then it's the same length as PI.

In either case, we have exactly two sides the same length (the other side different) which is what it means for a triangle to be isosceles.

----------

Let's consider triangle TOP. For it to be isosceles, we must have two sides the same length. We already locked in TP to be either 5 or 7 in the previous section above. So there's no way that TP could be 11 units long to match up with PO = 11.

If TP = 5, then OT must also be 5 units long so that triangle TOP is isosceles.

If TP = 7, then OT = 7 for similar reasoning.

Either way, TP only has two choices on what it could be.

----------

In short, we basically just write the first two values given to us to get the two triangles to be isosceles. We can't use TP = 11 as it would make triangle TIP to be scalene (all sides are different lengths).

Answer:

So we all cheat AOPS huh

Step-by-step explanation:

Answer:

Weak positive correlation

Answer:

Yes!

Step-by-step explanation:

Answer:

first answer

Step-by-step explanation:

(8x³ - 22x² - 4) / (4x - 3)

when you do long division you get the first answer

Answer:

D) y = x - 1

Step-by-step explanation:

First we need the general equation of point slope form:

(y - y0) = m(x - x0)

Where y0 is the y coordinate and x0 is the x coordinate and m is the slope.

For the line to be perpendicular, we need the slope to be the negated opposite of the other equation.  So the negated opposite of -1 is 1.

So our m = 1, y0 = -2, and x0 = -1.  Now let's plug this into the equation and reform the equation into slope-intercept form

(y - (-2)) = 1 (x - (-1))

y + 2 = 1 (x + 1)

y + 2 = x + 1

y = x - 1

So the equation of the line that goes through the point (-1,-2) and is perpendicular to the line y = -x -1, is y = x - 1.

Cheers.

Answer:

B) y = -x - 3

Step-by-step explanation:

slope = -1

y = mx + b

-2 = -1(-1) + b

-3 = b

y = -x - 3

Answer:

a. You can find the value of 4w by using inverse operations. Subtract 8 from both sides in the equation 4w+8=32. You will get 4w=24. Now, you divide 4 by both sides to get w by itself. You will soon get 6. Now multiply 6 and 4, coming to the conclusion that 4w=24.

b. To find the value of w using the value of 4w, which is 24, simply use inverse operations once more. Using the equation 4w=24, we can use division and divide 4 by both sides, leaving us with w by itself. We end up with w=6. The value of w is 6.

c. You can check if the value of w is correct by plugging in your number back into the equation. Our equation is 4w+8=32, so we replace w with 6, the value for w that we found. We end up with 4(6)+8=32. Multiply 4 by 6, ending up with 24, then add it to 8, coming up with 32. 4(6)+8=32, which shows us that 6 is the correct value for w.

Answer:

2 pi •10•210

Step-by-step explanation:

Khan academy

Answer:

Segment addition postulate

Step-by-step explanation:

It’s the Segment addition postulate.

ab+bc=ac

Answer:

She sold 10 pounds of peaches and 45pounds of grapes

Step-by-step explanation:

X= pounds of peaches

x+35=pounds of grapes

2x+4(x+35)=200

2x+4x+140=200

6x=200-140

6x=60

x=10

She sold 10 pounds of peaches and 45pounds of grapes. (Sorry, can’t help you graph it.)

Function 1 = negative y intercept

Function 2 = positive y intercept

====================================================

Explanation:

A. This is false because function 2 has a positive y intercept. Each time x goes up, y goes down. Reverse this and decreasing x leads to increasing y.

B. False. Function 1 has a negative y intercept. The y intercept occurs where the diagonal line crosses the y axis.

C. True. The graph shows a negative y intercept. The y intercept of function 2 is (0,2).

D. False. This contradicts choice C.

Since the interest is compounded, we will have to use the compound interest formula.

We Weill plug 7500 in for A, because that's the amount of money that we want to have at the end of some amount of time.

5000 will go in for P because that's the starting amount.

2.7% will be converted into a decimal percentage form. You can do this by dividing by 100, which you will get .027, and then plug that in for r, the rate.

Since the interest is compounded quarterly, n = 4.

After a bit of number crunching, you will get to the point where you have to solve for an exponent. You can easily do this by using the natural log ln(). One property of logarithm is that you can take the exponent and place it in front of the log. Now you can divide both sides to separate and solve for t.

It take 10.5 years for the investment to grow to $7,500 in the account with a 2.7% annual interest rate compounded quarterly.

Given:

P = $5000

r = 2.7% = 0.027 (as a decimal)

n = 4 (quarterly compounding)

A = $7500

The formula for compound interest:

[tex]\[ A = P\left(1 + \frac{r}{n}\right)^{nt} \][/tex]

Substituting these values into the formula

[tex]\[ 7500 = 5000\left(1 + \dfrac{0.027}{4}\right)^{4t} \][/tex]

Dividing both sides of the equation by $5000, we have:

[tex]1.5 = (1.00675)^{(4t)[/tex]

Assuming a natural logarithm (ln), we have:

ln(1.5) = [tex]ln((1.00675)^{(4t))[/tex]

Using the logarithm property,[tex]ln(a^b) = b * ln(a)[/tex], simplify the equation:

[tex]ln(1.5) = 4t * ln(1.00675)[/tex]

Now, dividing both sides of the equation by 4 * ln(1.00675):

t = ln(1.5) / (4 * ln(1.00675))

t = 10.5 years.

Therefore, it will take 10.5 years for the investment to grow.

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Answer: 10

Step-by-step explanation:

4(x+2)=48

4x+8=48

4x=40

x=10

Answer:

x=10

Step-by-step explanation:

4(x+2)=48

Divide each side by 4

4/4(x+2)=48/4

x+2 = 12

Subtract 2 from each side

x+2-2= 12-2

x = 10

Answer:

722059884 if there are 232323 students

if there are 23 students its 71484

Step-by-step explanation:

hope this helps

Answer: The answer is 644

Step-by-step explanation:

23x4x7=644

Answer:

Frankie will have created 161 drawings.

Step-by-step explanation:

Answer:

161

Step-by-step explanation:

your welcome

Answer:

f₁(x) = -3x + 2

f₂(x) = x - 4

f₃(x) = x + 8

f₄(x) = -2x - 6

f₅(x) = -3x

Step-by-step explanation:

1). Since function f₁ (blue line) passes through a point (0, 2) and (-2, 8)

Let the equation of the blue line is,

y = mx + b

Since slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{8-2}{-2-0}[/tex]

m = -3

Y-intercept 'b' = 2

Therefore, equation of the line will be,

y = -3x + 2

Linear function representing the line will be,

f₁(x) = -3x + 2

2). Let the equation of the red line passing through (0, -4) and (2, -2) is,

y = mx + b

Slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{-4+2}{0-2}[/tex]

m = 1

y-intercept 'b' = -4

Therefore, the linear function will be,

f₂(x) = x - 4

3). Let the equation of the green line passing through (-6, 2) and (-2, 6) is,

y = mx + b

Slope of the line 'm' = [tex]\frac{6-2}{-2+6}[/tex]

m = 1

y-intercept 'b' = 8

Therefore, linear function will be,

f₃(x) = x + 8

4). Let the equation of the yellow line passing through (-6, 6) and (-4, 2) is,

y = mx + b

Slope of the line = [tex]\frac{6-2}{-6+4}[/tex]

m = -2

y-intercept of the line 'b' = -6

Therefore, function representing the line will be,

f₄(x) = -2x - 6

5). Let the equation of the pink line is passing through (0, 0) and (-2, 6) is,

y = mx + b

Since the line is passing through origin, y-intercept 'b' = 0

Slope of the line = [tex]\frac{6-0}{-2-0}[/tex]

m = -3

Therefore, equation of the linear function will be,

f₅(x) = -3x

Answer:

They are similar because corresponding sides are not proportional

Answer:

about 11.03 million

Step-by-step explanation:

Use the equation I = P(1+r/100)^n - P (I is the compound interest, P is the principle, r is the rate percent, and n is the number of years):

Substitute the values given:

I = 70,000,000(1 + 5/100)^3 - 70,000,000

Use a calculator to solve and you will get ~11.03 million.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

The interest the company paid is $11 million.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

P = $70 million

r = 5%

t = 3 years

n = 1

A = 70 ( 1 + 0.05)³

A = 70 ( 1.05)³

A = 70 x 1.05 x 1.05 x 1.05

A = $81 million

The amount of interest.

= A - P

= 81 - 70

= $11 million

Thus,.

The interest the company paid is $11 million.

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Answer:

false

Step-by-step explanation:

correlation doesn't mean causation-

one doesn't necessarily affect the other, can just be conditions (such as weather) or coincidence

[tex]g(f(x))=(x-7)^3=x^3 - 21 x^2 + 147 x - 343[/tex]

Answer:

X= 128degrees

Step-by-step explanation:

As, angles 52,38,142and X making 360 degree

52 +38+142+x=360

X=128

⇛ ∠ x° and ∠ 52° (Both are linear pairs).

A linear pair is a pair of adjacent angles formed when two lines intersect.

[tex] \bf \large \implies \: \angle \: x \: + \: \angle \: 52 \: = \: 180 \degree[/tex]

[tex]\bf \large \implies \: \angle \: x \: = \: \: 180 \degree \: - \: \angle \: 52 \:[/tex]

[tex]\bf \large \implies \: \angle \: x \: = \: 128 \degree[/tex]