Katherine invested $86,000 in an account paying an interest rate of 52%
compounded daily. Michael invested $86,000 in an account paying an interest rate of
5% compounded continuously. After 13 years, how much more money would
Katherine have in her account than Michael, to the nearest dollar?

Answer:

2. Definition of supplementary angles

3. [tex]\angle 1 + \angle 2 = \angle 1 + \angle 3[/tex]

4. [tex]\angle 2 = \angle 3[/tex]

5. Definition of congruent angles

Step-by-step explanation:

Required

Fill in the gaps

1. Given

Supplementary angles: [tex]\angle 1[/tex] and [tex]\angle 2[/tex]

Supplementary angles: [tex]\angle 1[/tex] and [tex]\angle 3[/tex]

2. Supplementary angles add up to 180.

So:

[tex]\angle 1 + \angle 2 = 180[/tex]

[tex]\angle 1 + \angle 3 = 180[/tex]

3. Apply transitive property on (2)

[tex]\angle 1 + \angle 2 = 180[/tex] and [tex]\angle 1 + \angle 3 = 180[/tex], then

[tex]\angle 1 + \angle 2 = \angle 1 + \angle 3[/tex]

4. Subtract [tex]\angle 1[/tex] from both sides

[tex]\angle 1 - \angle 1 + \angle 2 = \angle 1 + \angle 3 - \angle 1[/tex]

[tex]\angle 1 - \angle 1 + \angle 2 = \angle 1 - \angle 1+ \angle 3[/tex]

[tex]\angle 2 = \angle 3[/tex]

This property is called the subtraction property

5. If [tex]\angle 2 = \angle 3[/tex],

Then [tex]\angle 2[/tex] and [tex]\angle 3[/tex] are congruent

Answer:

the measure of angle sbt is 95 degrees

Step-by-step explanation:

50+35=85

180-85+95

Answer:

133 bucks can i get brainliest

Step-by-step explanation:

Answer:

.17 per once for the smaller box and .15 for the bigger box

Step-by-step explanation:

Answer:

The answer is 5

Step-by-step explanation:

Step-by-step explanation:

let c=x1, y1 and d=x2,y2

Then distance=√(4-2)²+(1-1)²

= √4+0

=2

ans is 2 units

Step-by-step explanation:

2 !!!

hope it helps

have a great day:))

Answer:

2 :D

Step-by-step explanation:

......thank you....

Answer:

y = 15 + 7.50x

Step-by-step explanation:

It is given that, At a park, the cost to rent a bike has an initial fee of $15.00 plus $7.50 per hour.

Let the number of hours is x and the total cost is y.

When the bike is rented for x hours, its cost will be 7.50x.

Total cost (y) in terms of number of hours is given by :

y = 15 + 7.50x

Hence, this is the required equation.

Answer:

Both are correct

Step-by-step explanation:

All the angles are equal, therefore causing the triangles to be similar.

Answer:

0.33333333

Step-by-step explanation:

4 divided by 12 would be written like this: 4/12

it's always good to simplify if possible, so it should look like this: 1/3

3 which is the denominator would be divided by 10, so 3/10 = 0.33333333

0.33333333 is the answer because the numerator is how many times you multiply it, and 1*0.33333333 = 0.33333333

Answer:

Bet

Step-by-step explanation:

An imaginary number is denoted by i.

The value of i is √-1.

Imaginary number.

i= √-1

i² = -1

i³ = -i = -√-1

The product of 3i (5 - 3i) in the form of a + bi is

9 + 15i.

An imaginary number is denoted by i.

The value of i is √-1.

We have,

Imaginary number.

i= √-1

i² = -1

i³ = -i = -√-1

Now,

3i (5 - 3i)

Removing the parenthesis.

= (3i x 5) - (3i x 3i)

= 15i - 9(-1)

= 15i + 9

= 9 + 15i

This is in the form of a + bi

Thus,

The product of 3i (5 - 3i) in the form of a + bi is

9 + 15i.

Learn more about imaginary numbers here:

https://brainly.com/question/6748860

#SPJ2

Answer:

c=74

Step-by-step explanation:

Let c represent how many contacts Joy had on her phone before she updated it.

Because Joy added 26 new contacts, we can say that c+26 is equal to her new total of 100 contacts.

c+26=100

Therefore, the equation that represents this situation is c+26=100

Now, we can use our equation to solve for c.

c+26=100

Subtract both sides by 26 to isolate c

c+26-26=100-26

c=74

Therefore, Joy had 74 contacts on her phone before she updated it.

I hope this helps!

Answer:

The measure of one of the acute angles is 22 degrees, and the measure of the other acute angle is 68 degrees.

Step-by-step explanation:

The angles of a triangle add up to 180 degrees; we know this by the Sum of Angles of a Triangle Theorem.

Then one angle is marked as a right angle meaning it has a measure of 90 degrees.

Using this information and the labels on the diagram we can set up an equation:

x+3x+2+90=180

Now we can solve for x.

4x+92=180

4x=88

x=22 degrees

The measure of one of the acute angles is 22 degrees.

Now to solve for the measure of the other acute angle.

Subsitute the value of x first.

x=22

(3x+2)=?

3*22+2=68 degrees

The measure of the other acute angle is 68 degrees.

In the right-angled triangle given, the measure of each of the acute angles in the given diagram are:

[tex]\mathbf{22^{\circ}}\\\\\mathbf{68^{\circ}}[/tex]

The triangle given is a right triangle having an angle tat is 90 degrees and two other acute angles given as: x and (3x + 2)

Thus:

[tex]x + (3x + 2) + 90 = 180^{\circ}[/tex] (sum of triangle)

[tex]x + 3x + 2 + 90 = 180[/tex]

[tex]4x + 92 = 180\\\\[/tex]

[tex]4x = 180 - 92\\\\4x =88[/tex]

x = 22

Measure of one of the acute angles is 22 degrees.

To find the second acute angle measure, substitute the value of x

3x + 2 = 3(22) + 2 = 68 degrees

Therefore, in the right-angled triangle given, the measure of each of the acute angles in the given diagram are:

[tex]\mathbf{22^{\circ}}\\\\\mathbf{68^{\circ}}[/tex]

Learn more here:

https://brainly.com/question/347922

Answer:

∫(x) = [tex]\frac{2}{3}[/tex]x - 3

Answer:

f(x)=2/3x-3

Step-by-step explanation:

f(x) is the same as y, so the function would be f(x)=2/3x-3.

Hope this helps! :)

Answer:

I believe it is y=1/4x.

Answer: yes

Step-by-step explanation:

Answer:

Probability = [tex]\frac{22}{31}[/tex]

Step-by-step explanation:

Number of students working part time, living in dorm = 22

Total number of students working part (either living in dorm or not in dorm)

= 22 + 9

= 31

Probability of the students working part time and living in dorm,

P = [tex]\frac{\text{Favorable event}}{\text{Total outcomes}}[/tex] = [tex]\frac{\text{Students working part time either living in dorm}}{\text{Total number of students working part time either living in dorm or not}}[/tex]

P = [tex]\frac{22}{31}[/tex]

Therefore, probability of the students chosen that he/she is working part time given that he/she lives in dorm is [tex]\frac{22}{31}[/tex].

Answer:

x + 1

y = 9

Step-by-step explanation:

In order to solve this question we need to represent "y "in terms of "x" in the first equation, and the plug in the "y" value in the first equation into the second one. Luckily for us in the first equation it already shows what "y" is equal to in terms of "x" (based on the first equation y = -x + 10). Now we just need to plug in the value that we got instead of "y" in the second equation, and so we get....

y = 7x + 2

(plug in the y value and get the following ….)

-x + 10 = 7x + 2

(now just solve the following equation)

-x + 10 + x = 7x + 2 + x

10 = 8x + 2

10 - 2 = 8x + 2 - 2

8 = 8x

8/8 = 8x/8

1 = x

Now that we know the value of "x", all we need to do now is substitute the value of "x" into any of the equations and we will get the value of "y". So we do the following.....

y =  7x + 2

y = 7(1) + 2

y = 7 + 2

y = 9

Answer:

1. b =1/2 (4)(3.5)

v=(14)(8)

2.b= 1/2 (9)(12)

V=(54)(13)

3.b= 1/2(7)(6.1)

v= (21.35)(9)

Answer:

a=3.63

Step-by-step explanation:

Isolate the variable by dividing each side by factors that contain the variable.

Answer:

Percent air is calculated as:

Solve for total amount of air:

Substitute the values in hand to get the answer

Step-by-step explanation:

4x - 5 > 4

4x > 9

x > 2.25

Hence the integer values of x that satisfy are 3, 4, 5, 6, 7 and 8.

Answer:

81 1/2

Step-by-step explanation:

We plug a and c in to get: 9^2+1/2

9^2=81 and 81+1/2 is 81 1/2

Answer:

4 and 6

Step-by-step explanation:

Judging by the table and how x = 1 and y = 2, you can estimate that y is twice as much as x.

This is supported by the equation, if you take 2 and multiply it by x (1) and take 3 and multiply it by y (2), then add the 2x1 (2) and 3x2 (6), you should get 8.

Answer:

A compound inequality contains at least two inequalities that are separated by either "and" or "or". ... A number is a solution to the compound inequality if the number is a solution to both inequalities. It can either be written as x > -1 and x < 2 or as -1 < x < 2.

Hope this helped! :}