Elizabeth invested $970 in an account paying an interest rate of 6\tfrac{5}{8}6 8 5 ​ % compounded daily. Matthew invested $970 in an account paying an interest rate of 6\tfrac{3}{4}6 4 3 ​ % compounded continuously. After 8 years, how much more money would Matthew have in his account than Elizabeth, to the nearest dollar?

Answer:

lines are perpendicular

Step-by-step explanation:

• Parallel lines have equal slopes

• The product of the slopes of perpendicular lines = - 1

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange the given equations into this form and extract the slope

3x - 2y = - 6 ( subtract 3x from both sides )

- 2y = - 3x - 6 ( divide through by - 2 )

y = [tex]\frac{3}{2}[/tex] x + 3 ← in slope- intercept form

with slope m = [tex]\frac{3}{2}[/tex]

----------------------------------

4x + 6y = 2 ( subtract 4x from both sides )

6y = - 4x + 2 ( divide through by 6 )

y = - [tex]\frac{4}{6}[/tex] x + [tex]\frac{2}{6}[/tex] , that is

y = - [tex]\frac{2}{3}[/tex] x + [tex]\frac{1}{3}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{2}{3}[/tex]

--------------------------------------

[tex]\frac{3}{2}[/tex] ≠ - [tex]\frac{2}{3}[/tex] , then lines are not parallel

[tex]\frac{3}{2}[/tex] × - [tex]\frac{2}{3}[/tex] = - 1

Thus the lines are perpendicular to each other

Answer:

Option D

Hope this helps!

Answer:

6×3×4= 72 unit cubes

................................

Answer:

x² + 8x + 15

Step-by-step explanation:

(x +3)(x+5)

=> x² + 5x + 3x + 15

=> x² + 8x + 15

So, after simplifying, we can conclude that x² + 8x + 15 is our answer. Hoped this helped.

Answer:

Step-by-step explanation:

Facts to know :

-diagonals of rhombus are angle bisector so angle A is double 28

∡A = 28*2 = 56°

-opposite angles in a rhombus are congruent so angle A and angle C have the same measure

∡C = 56°

-the sum of angles in a rhombus is 360°

360 - 2*56 = 360-112 = 248

248 /2 = 124

∡B = ∡D = 124°

Answer:

Buy from Tickets Inc.

Step-by-step explanation:

Answer:

130542

Step-by-step explanation:

FV=48000(2.7196)

FV=130542

Answer:

5n-4

Step-by-step explanation:

The rule of the sequence is 5n-4.

If n=1 then 5(1)-4=1 because 5x1=5 and 5-4=1

If n=2 then 5(2)-4=6 because 5x2=10 and 10-4=6

If n=2 then 5(3)-4=11 because 5x3=15 and 15-4=11

If n=2 then 5(4)-4=16 because 5x4=20 and 20-4=16

Answer:

Well lucy has a 50/50 chance to get a odd card so that is it

Step-by-step explanation:

The ratio of even cards to odd cards that Lucy has is 3:4 in its simplest form.

Let's denote the number of even cards as "x" and the number of odd cards as "y".

The probability of choosing an even card is given as [tex]\frac{3}{7}.[/tex]

The probability of choosing an even card is calculated by dividing the number of even cards by the total number of cards:

Probability of choosing an even card = Number of even cards / Total number of cards

Therefore, we have:

[tex]\frac{3}{7} = \frac{x}{x+y}[/tex]

To find the ratio of even cards to odd cards, we can set up the equation:

[tex]\frac{x}{y} = \frac{3}{4}[/tex]

Therefore, the ratio of even cards to odd cards that Lucy has is 3:4 in its simplest form.

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Answer:

i think its 16 but im not sure

Step-by-step explanation:

6+6+2+2= 16 but im not sure if that how u do it or not

it's been so long since i've done that stuff. 12 in i think

Answer:

44 home runs

Step-by-step explanation:

550 ÷ 25

= 22

22 x 2

= 44

Answer:

Perimeter: 4x+14

Step-by-step explanation:

The Formula for perimeter is P = 2L + 2W

So apply it:

L = x+7

W = x

[tex]P=2x+2\left(x+7\right)[/tex]

[tex]P=4x+14[/tex]

Answer:

333

666

Step-by-step explanation:

333 / 9 = 37

666 / 9 = 74

yeah-ya...... right?

Answer:

333

Step-by-step explanation:

we see that all three digits are the same so heres a list of numbers it could be 222 333 444 555 666 777 and we know that numbers divisible by nine mean all the digits added up have to be divisible by nine and we can see that 333 equals 9 when the digits are added together so this is the answer.

Answer:

x=16.9+34.6

x=51.5

.............................

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Answer:

6x + 13 = 12x - 20

Step-by-step explanation:

6x + 13 = 12x - 20

Answer:

I think if you haven't hung out with her a lot, you should start hanging out with her, getting along, until you have built up courage to tell her you have feelings for her.

If I earned $2 more than Andrew at the end of the day, then the value of t  is [tex]1\frac{2}{3}[/tex]

Number of hours that I used to work = 1 hour

My hourly pay =  $3t - 3

My total pay at the end of the day = Number of hours x hourly pay

My total pay at the end of the day = 1 (3t - 3)

My total pay at the end of the day = $ 3t - 3

Number of hours that Andrew used to work = 3t -5 hour

Andrew's hourly pay =  $2

Andrew's total pay at the end of the day = Number of hours x hourly pay

Andrew's total pay at the end of the day = 2 (3t - 5)

Andrew's total pay at the end of the day = $ 6t - 10

At the end of the day, I earned $2 more than Andrew

My total pay = Andrew's total pay + 2

3t - 3   =  6t - 10  +  2

6t  -  3t  =  -3 +10 - 2

3t  =  5

t  =  5/3

[tex]t = 1\frac{2}{3}[/tex]

If I earned $2 more than Andrew at the end of the day, then the value of t  is [tex]1\frac{2}{3}[/tex]

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Answer:

Step-by-step explanation:

total # of families=15

families that own 0 cars=2

families that own 1 cars=5

families that own 2cars=4

families that own 3 cars=3

families that own 4 cars=1

so 2+5+4+3+1=15

total# of families/ sum of cars = 15/15=1

Answer: C ≈ 94.25 in

Step-by-step explanation:

Answer:

3 2 /5 ×3

change 3 2 /5 into an improper fraction

then you will get 17 /5

after that you say 17/5 ×3/1

=(17×3)/ (5x1)

=51/5 (51÷5)

=10.2/ 10 1/5

[tex]3 \frac{2}{5} \times 3 \\ = \frac{17}{5} \times 3 \\ = \frac{51}{5} \\ = 10 \frac{1}{5} [/tex]

[tex]10 \frac{1}{5} [/tex]

Hope it helps.

Do comment if you have any query.

Answer:

See Below:

Step-by-step explanation:

So, first of all. to find the equation of the line, the equation has to be in [tex]y=mx+b[/tex] form. In this for the following are:

Solving

So, first of all, to find the equation of the line, we can get two points from the line, you can pick any points you want, but for this case, I will be using (0,-2) and (-2,0).

To solve for the slope, we can use rise over run to find the equation.

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Upon inserting our points into the equation, we get a slope of -1.

[tex]\frac{0-(-2)}{-2-0}=\frac{2}{-2}=-1[/tex]

Creating The Equation

To create the equation in [tex]y=mx+b[/tex] form, we need to know what the intercept and the slope are, for which we solved above. We can now put in the things we found to get our final equation.

[tex]y=-1x-2[/tex]

We know the slope has to be -1 as we solved for that, and because the line is decending downwards, we can interpret the slope as down 1 right 1.

We know that b is -2 because the y intercept is -2 and b is equal to the y intercept. Therefore the b cation is -2.

Cheers!

Answer:A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour.

Step-by-step explanation:

had this question

Answer:

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

[tex]1/3(3)(12)[/tex]

The 1/3 and 3 cancel and you are left with

[tex]12[/tex]

Answer:

  -1

Step-by-step explanation:

The expression evaluates to the indeterminate form -∞/∞, so L'Hopital's rule is appropriately applied. We assume this is the common log.

  d(log(x))/dx = 1/(x·ln(10))

  d(log(cot(x)))/dx = 1/(cot(x)·ln(10)·(-csc²(x)) = -1/(sin(x)·cos(x)·ln(10))

Then the ratio of these derivatives is ...

  lim = -sin(x)cos(x)·ln(10)/(x·ln(10)) = -sin(x)cos(x)/x

__

At x=0, this has the indeterminate form 0/0, so L'Hopital's rule can be applied again.

  d(-sin(x)cos(x))/dx = -cos(2x)

  dx/dx = 1

so the limit is ...

  lim = -cos(2x)/1

  lim = -1 when evaluated at x=0.

_____

I find it useful to use a graphing calculator to give an estimate of the limit of an indeterminate form.

Answer:

$1,270

Step-by-step explanation:

let x be the total amount of ice cream sold without tax

x + (x*0.0635)=21270

1.0635x=21270

x=20,000

so the amount he needs to send to state is

21270-20000

1,270

Total cost of icecream without cost be x

[tex]\\ \sf\longmapsto x+0.0635x=21270[/tex]

[tex]\\ \sf\longmapsto 1.0635x=21270[/tex]

[tex]\\ \sf\longmapsto x=21270/1.0635=20000[/tex]

Amount to be paid

[tex]\\ \sf\longmapsto 21270-20000=1270[/tex]

Answer:

6x - 6

Step-by-step explanation:

(2x + 6) + (4x - 12) ← remove parenthesis

= 2x + 6 + 4x - 12 ← collect like terms

= (2x + 4x) + (6 - 12)

= 6x + (- 6)

= 6x - 6

Answer:

17/4

Step-by-step explanation:

add the fractions

[tex]\dfrac{\tfrac 27}8 = \dfrac 2{7 \times 8} = \dfrac 2{56} = \dfrac 1{28} = 1:28[/tex]