Two complex numbers have a sum of 14 and a product of 74. Write either of the two numbers.

Answer:

There are a few rules that we can use here:

ln(a^x) = x*ln(a)

ln(a) - ln(b) = ln(a/b)

ln(1) = 0

So here we want to expand:

ln(1/49^k)

First we can use the second property to get:

ln(1/49^k) = ln(1) - ln(49^k)

using the third property, we have:

ln(1/49^k) = ln(1) - ln(49^k) = 0 - ln(49^k)

ln(1/49^k) =  - ln(49^k)

Now we can use the first property to get:

ln(1/49^k) =  - k*ln(49)

Now we can use the fact that:

49 = 7*7 = 7^2

then:

- k*ln(49) = -k*ln(7^2) = -2*k*ln(7)

So we have:

ln(1/49^k) = (-2*ln(7))*k

We can expand it anymore because this is a real number  "(-2*ln(7))" times a variable k.

Answer:

a)

d)

Step-by-step explanation:

It's easiest to reduce each statement to its simplest form for comparison

Our test statement can be reduced by combining like terms

16x - 12 -24x + 4 = -8x - 8

this becomes our new gold standard

a) 4 + 16x - 12(1 + 2x)

apply the distributive property by multiplying terms in parenthesis by -12

4 + 16x - 12 - 24x

combine terms

-8x - 8     Yeaah, We have a winner as it exactly matches our gold standard.

b) 40x - 16 is already in simplest terms and does NOT match the gold standard.

c) 16x - 24x - 4 + 12

has the same cardinal values as the original, but differing signs, reducing gives -8x + 8

Not quite the same as a plus sign occurs where a negative exists in our gold standard.

d) -8x - 8  is already in simplest terms and exactly matches our gold standard. Yeah!

e) 10(1.6x - 1.2 - 2.4x + 4)

apply distributive property by multiplying each term in parenthesis by 10

16x - 12 - 24x + 40

combine like terms

-8x + 28 does NOT match our gold standard

Answer:

Fraction form: 7/-13

Decimal form:-0.53846153846154

Hello!

Out equation is: [tex]A=P(1+\frac{r}{n} )^t^n[/tex]

A= 6000

P=5000

N=1

T=5

R= What we are trying to find

This means we will have [tex]6000=5000(1+r)^5[/tex]

Divide both sides by 5000:

[tex]\frac{6000}{5000} = (1+r)^5[/tex]

Move the power to the other side by rooting both sides:

[tex]\frac{6000}{5000} ^1^/^5 = 1+r[/tex]

Subtract 1 from both sides:

[tex]\frac{6000}{5000} ^1^/^5 -1 = r[/tex]

Now we just need to calculate: R = 0.03713728...

I don't know how many decimal places you can have, but I will round to 2. This will give you an Interest Rate of 3.71%.

I hope this helps! :)

Answer:

z = 110

Step-by-step explanation:

The measure of an angle created by the intersection of two secants outside a circle is half the difference of the angles it intercepts. In this it would be:

2x + 15 = 1/2 * (10x + 20 - 80)

We can now solve:

4x + 30 = 10x - 60

30 = 6x - 60

6x = 90

x = 15

This means the values of 10x + 20 is 10(15) + 20, which is 170.

Now, we can add up all the arcs in a circle, which sum to 360 degrees:

360 = z + 170 + 80

360 = z + 250

z = 110

Answer:

[tex]A)\ \ z = 110[/tex]

Step-by-step explanation:

One is given a circle with two secants. Please note that a secant is a line that intersects a circle in two places. The secant exterior angle theorem states that when two secants intersect each other outside of a circle, the measure of the angle formed is half the of the positive difference of the intersecting arcs. One can apply this theorem here by stating the following:

[tex]2x+15=\frac{(10x+20)-(80)}{2}[/tex]

Simplify,

[tex]2x+15=\frac{(10x+20)-(80)}{2}[/tex]

[tex]2x+15=\frac{10x-60}{2}[/tex]

[tex]2x+15=5x-30[/tex]

Inverse operations,

[tex]2x+15=5x-30[/tex]

[tex]15=3x-30[/tex]

[tex]45=3x[/tex]

[tex]15=x[/tex]

Substitute this value into the equation for one of the intersecting arcs to find the numerical value of that intersecting arc:

[tex]10x+20\\x = 15\\\\10(15) + 20\\= 150 + 20\\= 170[/tex]

The sum of all arc measures in a circle is (360) degrees. One can apply this here by stating the following:

[tex]80 + 170 + z = 360[/tex]

Simplify,

[tex]80 + 170 + z = 360[/tex]

[tex]250 + z = 360[/tex]

Inverse operations,

[tex]250 + z = 360[/tex]

[tex]z = 110[/tex]

Answer:

x = 57

y = 57

Step-by-step explanation:

because of the two parallel lines :

41+y+8+74 = 180 add like terms

y + 123 = 180 subtract 123 from both sides

y = 57

x - 3 + 41 + y + 8 = 180 because they make a straight line

x + y + 46 = 180

x + 57 + 46 = 180

x + 123 = 180 subtract 123 from both sides

x = 57

Answer: 24 people earnt As

Step-by-step explanation:

1. We know that 18 people are the other 3/7 of the class

2. We first find out 1/7, which is calculated by dividing 3/7 by 3, which is 18 / 3 so 6

3. We can then find 4/7 by multiplying the amount of 1/7 by 4, so 6 x 4 = 24

Answer:

(3, 1)

Step-by-step explanation:

A circle with radius √10 and centre at (0, 0) will have a point (3, 1) on its circumference.

I guess the chef is making the mixture for the sheriff... Let x be the amount of dressing with 5% vinegar that is required, and y the amount of 15% vinegar dressing (both amounts in mL).

The sheriff wants 390 mL of the mixed dressing, so that

x + y = 390

x mL of the 5% dressing contains 0.05x mL of vinegar, while y mL of the 15% dressing contains 0.15y mL of vinegar. The resulting mixture should have a concentration of 9% vinegar, so that it contains 0.09 (390 mL) = 35.1 mL of vinegar. This means

0.05x + 0.15y = 35.1

Solve for x and y :

y = 390 - x

0.05x + 0.15 (390 - x) = 35.1

0.05x + 58.5 - 0.15x = 35.1

23.4 = 0.10x

x = 234

y = 156

Answer:

A. As the sample size is appropriately large, the margin of error is ±0.032.

Step-by-step explanation:

The margin of error is ±0.032 and the sample size is appropriately large. Therefore, the correct option is A.

Answer:

B

Step-by-step explanation:

(-2/3x)-10<1/3

(-2/3x)<1/3+10

(-2/3x)<31/3

x>-31/2, -31/2=-15 (1/2), x> - 15 (1/2)

Answer:

a

Step-by-step explanation:

Answer:

Incorrect, it's actually B.

Step-by-step explanation:

Look at the Non-Sporting Group and Herding Group. The sizes of the slices are different (NSG being smaller than HG)

Answer:

27

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

-9 × -3

= 27

Note: When you multiply two integers with same sign, then their product is positive.

Answer:

see below

Step-by-step explanation:

a x (b+c) = a x b + a x c

Let A= -35 , B = 10 , C= -5

-35 * ( 10 -5) = -35 *10 + -35 * -5

-35 *(5) = -350 + 175

-175 = -175

Answer:

Step-by-step explanation:

y = x³

x = ∛y

Switch x and y:

y = ∛x

f⁻¹(x) = ∛x

f⁻¹(12) = ∛12 ≅ 2.29

check:

x = 2.29

f(x)  = 2.29³ ≅ 12

Answer:

there is a 20% chance of getting a red marble

Step-by-step explanation:

Answer:

there is a 1/5 percent chance or 20%

Step-by-step explanation:

Hope this helps!

Step-by-step explanation:

Recall that 1 dozen = 12 so 4 dozen cookies has a total of 48 cookies. We are going to use the following ratios to solve the problem:

[tex]\left(\dfrac{3\:\text{eggs}}{48\:\text{cookies}}\right)[/tex] and [tex]\left(\dfrac{48\:\text{cookies}}{3\:\text{eggs}}\right)[/tex]

a) [tex]12\:\text{eggs}×\left(\dfrac{48\:\text{cookies}}{3\:\text{eggs}}\right) = 192\:\text{cookies}[/tex]

b) 18 dozen cookies = 216 cookies

[tex]216\:\text{cookies}×\left(\dfrac{3\:\text{eggs}}{48\:\text{cookies}}\right) = 13.5\:\text{eggs}[/tex]

Answer:

(4) 644,000

Step-by-step explanation:

643,581

The 3 is in the thousands place

We look at the hundreds place

5

It is 5 or greater so we round the thousands place up 1

644000

Answer:

48 ÷ 60 = 4/5

Step-by-step explanation:

4/5 is the answer

Answer:

[tex]\frac{1}{30}[/tex]

Step-by-step explanation:

We require the number of minutes in a day.

i hour = 60 minutes

24 hours = 24 × 60 = 1440 minutes ( 24 hours in 1 day )

Then

fraction = [tex]\frac{48}{1440}[/tex] ( divide numerator/ denominator by 12 )

            = [tex]\frac{4}{120}[/tex] ( divide numerator/ denominator by 4 )

            = [tex]\frac{1}{30}[/tex]

Answer:

3 hours 30 minutes

Step-by-step explanation:

Jan :2 hours

her husband : 1 hour 30 minutes

2hr + 1 ½ hrs = 3 ½ hrs...that is 3 hours 30 minutes....?

Answer:

Sin X = 12 / 37

Step-by-step explanation:

Given a right angled triangle, we are to obtain the Sin of the angle X ;

Using trigonometry, the sine of the angle X , Sin A is defined as the ratio of the angle opposite X to the hypotenus of the right angle triangle.

In the right angle triangle :

Sin X = opposite / hypotenus

Opposite = 12 ; hypotenus = 37

Sin X = 12 / 37

Answer:

B opition is right

Step-by-step explanation:

The domina a function of

Answer:

general term - 7n+4

5th term - 7(5) + 4 = 39

6th term - 7(6) + 4 = 46

Answer:

1050

Step-by-step explanation:

Let x = full capacity

[tex]\frac{3}{5} x=\frac{2}{7} x+330[/tex]

Move the variable to the left side by subtracting both sides by [tex]\frac{2}{7} x[/tex]

[tex]\frac{3}{5} x-\frac{2}{7}x=\frac{2}{7} x+330 -\frac{2}{7}x[/tex]

[tex]\frac{3}{5} x-\frac{2}{7} x=330[/tex]

Combine the like terms (don't forget about common denominator)

[tex]\frac{21}{35} x-\frac{10}{35} x=330[/tex]

[tex]\frac{11}{35} x=330[/tex]

Multiply both sides by [tex]\frac{35}{11}[/tex] to isolate the x

[tex](\frac{35}{11})\frac{11}{35} x=330(\frac{35}{11})[/tex]

[tex]x = 1050[/tex]

Answer:

-8 and 3

Step-by-step explanation:

The slope of the line will be - 8, the equation is y=-8x+3

Answer : 19.6cm

I hope this helps you! Have a good day!

Answer:

Amanda's box is in this case, the bigger one. Then subtract the Amanda's by Mary's. The Larger box is 70cm^3 larger then the smaller box.

Step-by-step explanation:

Amanda's box: 13.5*10*10= 1350cm^3

Mary's box: 20*8*8= 1280cm^3

1350-1280=70

The larger box is 70cm^3 larger then the smaller box.

If you have any questions regarding my answer tell me in the comments, i will come answer them. Have a good day.

Answer:

y<=(-2x+4)

Step-by-step explanation:

The equation of line is y=-2x+4. For the region left of it, y<=(-2x+4)