How many years will it take Mr. Arnold to make $600 in interest if he invested $729 at a 5.8% interest rate? Round to the nearest whole year.

Step-by-step explanation:

It's just asking you to find the slope

Plug in x=2 into given function. Then you will get f(2). Do the same to find f(5).

Then you can use slope formula to find the answer

Question 4

Explanation:

If the initial point is the origin, the coordinates of the terminal point form the vector itself in component form. We go from (-8,6) to <-8,6>. The notation change is from ordered pair to vector format.

We have a right triangle with legs of 8 and 6 units. The pythagorean theorem will help us determine the hypotenuse is 10. Therefore, the vector length is 10 units and we would say ||v|| = 10. We have a 6-8-10 right triangle.

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Question 5

Explanation:

Vector v starts at (2,5) and ends at (-3,-2).

The x component of the vector is x2-x1 = -3-2 = -5 meaning we move 5 units to the left when going from the start point to the endpoint.

At the same time we move 7 units down because y2-y1 = -2-5 = -7 which is the y component of the vector.

The component form of vector v is

v = <-5, -7>

it says "move 5 units left, 7 units down".

Apply the pythagorean theorem to find the length of the vector.

a^2+b^2 = c^2

c = sqrt(a^2 + b^2)

||v|| = sqrt( (-5)^2 + (-7)^2 )

||v|| = 8.602 which is approximate.

Now let's use the arctangent function to find the angle

theta = arctan(b/a)

theta = arctan(-7/(-5))

theta = 54.462 which is also approximate.

There's a problem however. This angle is in Q1 but the vector <-5,-7> is in Q3. An easy fix is to add on 180 to rotate to the proper quadrant.

54.462+180 = 234.462

which is the proper approximate angle for theta.

Answer:

This is the answer.

Step-by-step explanation:

but I think you dont write the question fully.

answer: it's literally -3

37 * 9 = 333

333 + 555 = 888

888/9 = 98.666666666666666666666666666667

Hope that helps!

Answer:

98.67

Step-by-step explanation:

Step 1 :

37 x 9 = 333

Step 2 :

333 + 555 = 888

Step 3 :

888 / 9 = 98.67

#1

[tex]\\ \rm\rightarrowtail x+1=9[/tex]

[tex]\\ \rm\rightarrowtail x=9-1[/tex]

[tex]\\ \rm\rightarrowtail x=8[/tex]

#2

[tex]\\ \rm\rightarrowtail 8+1=9[/tex]

Hence verified

[tex]x + 1 = 9[/tex]

[tex]x = 9 - 1[/tex]

[tex]x = 8[/tex]

[tex]8 + 1 = 9[/tex]

[tex]9 = 9[/tex]

Hence, Verified!

Total layers=6

Total volume:-

Answer:

D. 18 ÷ 2 = 9

Step-by-step explanation:

The equation matches the equation 18 ÷ 9 = 2

The other equations do not match the previous equations because the previous three equations didn't have a 36 or the number six

I hope this helps!

Answer:

d 18÷2=9

Step-by-step explanation:

The answer is d because the fact family contains 2,9and18.

2×9=18, 18÷9=2and 9×2=18 are already solved. so all you need to do is to study the question and the answer very well.

To find the answer you need to look at the numbers in the question carefully an look for it in the answer.

Answer:

y = -12

Step-by-step explanation:

any equation with only an x or y value present will either be a vertical or horizontal line. Because the y axis is vertical, a line that is present on y=-12 will sit on y=-12 forever, and therefore be a horizontal line

Answer:

[tex]\displaystyle y = -12[/tex]

Step-by-step explanation:

If any quantity is set equivalent to y, then it is a horisontal line. In other wourds, it is considered a zero rate of change [slope].

I am joyous to assist you at any time.

Answer:

A) 3/4

B) 1/4

C) 1/2 / 2/4

Step-by-step explanation:

Using simple interest, it is found that the monthly payments are of $739.00.

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

In this problem:

Then, the total amount will be of:

[tex]A(t) = A(0)(1 + rt)[/tex]

[tex]A(t) = 85000[1 + 30(0.071)][/tex]

[tex]A(t) = 266050[/tex]

In 30 x 12 = 360 monthly payments, hence:

266050/360 = 739.

The monthly payments are of $739.00.

More can be learned about simple interest at https://brainly.com/question/25296782

Answer:

8n-4n +(6x2)-6-8n

24n+8 - 20n -(2n x 4n)-2

Step-by-step explanation:

#1

Take -8n+5 and 4n+1

#2

Take -2n+4 and -2n+2

Answer:

24/35

Step-by-step explanation:

Answer:

the answer is 3

Step-by-step explanation:

function notation is the way a function is written.

Answer:

They had 7,618.8 subscribers last year.

Let me know if this helped :)

Step-by-step explanation:

We need to find 40% of 12,698

To do that, we need to multiply 12,698 by the decimal form of 40%.

12,698*0.40=5,079.2

Then, we need to subtract 5,079.2 from the amount of subscribers we had this year.

12,698-5,079.2= 7,618.8

Step-by-step explanation:

MN and JK are parallel lines. So those two angles are going to be corresponding angles which means their measurements are the same

4x+56 = 7x +53

3=3x

x=1

LKJ = 4(1)+56= 60

Michelle's investment balance after 8 years is $10,790.48.

Kristen's investment balance after 8 years is $3,770.55.

Gabriella's investment balance after 8 years is $24,780.42.

Judy's investment balance after 8 years is $3618.62.

The person with the highest amount of money at the end of the 8 years is Gabriella. If I were to choose one of the investment options, I would choose Gabriella's option.

The formula that can be used to determine the future value of the investment with compounding is:

FV = P (1 + r)^nm

Where:

Future value with continuous compounding =  : A x e^r x N

Where:

Future value with monthly compounding = $2000 x ( 1 + 0.035/12)^(12 x 8) = $2645.18

Future value with continuous compounding: 1000 x e^0.018 x 8 = $8,145.30

Total = $8,145.30 + $2645.18 = $10,790.48

Future value with quarterly compounding = 2500 x (1 + 0.012 / 4)^(4 x 8) = $2,751.50

Future value with quarterly compounding = 500 (1 .0225)^(8x4) = $1019.05

Total = $3,770.55

$3000 x e^0.032 x 8 = $24,780.42

Future value with exponential increase = 1050 x (1.015)^8 = $1,182.82

Future value with biannual compounding = 1950 x (1 + 0.028/2)^(8 x 2) = $2435.80

Total = $3618.62

To learn more about future value, please check: brainly.com/question/18760477

Answer:

0.4

Step-by-step explanation:

I can't draw a model, but I will give you an equation!

Two items are going to be divided amongst five people:

2/5=0.4

Each person will get 0.4 OR 4/10 of the two items.

Here's a math problem you could use:

Henry and his 4 friends want to eat some chocolate, but there's only two bars, Henry suggests that they just split it equally. If everyone get's an equal share, how much did each get? Everyone got 0.4 of the two chocolate bars.

Each person will get 0.4 OR 4/10 of the two items.

Since it varies directly as q and partly inversely as q^2 it is represented has this below

p = aq + b/q^2

The constants of proportionality here are a and b

11 = 2a + b/4 ----- i x 5

25.16 = 5a + b/25 ------ ii x 2

Multiply equation i by 5 and equation ii by 2

55 = 10a + 5b/4 ----- iii

50.32 = 10a + 2b/25 ----- iv

Subtract equation iv from equation iii

b = 4

Put the value of b in equation iv

50.32 = 10a + 8/25

Multiply through by 25

1258 = 250a + 8

a = 5

p =5q + 4/q^2

Therefore using this equation put into the equation the value of q which is 7

p = 5(7) + 4/(7)^2

p = 35 +4/49

p = 35.082

hope this helped.

Answer:

2 times a number, plus 1, plus 2 times a number, is equal to 4x + 2.

The way they factored ↓

2 x 2 = 4

4x = 4 times a number or itself multiple times

4 + 2 is the same as a number times 1 equals 2.

If that's the case, x = 2.

Answer:

First choice

Step-by-step explanation:

He must ride 60 - 12 miles during the 6 days

Every day he rides x miles, 6 days, 6x miles

so 60 - 12 = 6x

First choice

Answer:

91°

Step-by-step explanation:

We first add 75 and 14 which is equal to 89°. Now, we know that a full triangle angle is 180° . We then calculate 180°-89° which gives us the final answer 91°.

Ps: 91 rounded to the nearest tenth is equal to: 91.0

Answer:

27 is ta value of x because.. first of all add allthose threee sides

3(x+2)+ 35+ 52=180(the sum of triangle)

or, 3x+6+35+52=180

or,3x=180-93

or,x=87/3

Therefore, the value of x is 29

Step-by-step explanation:

mark me as main brainliest please

Answer:

2.129

Step-by-step explanation:

So, 3.157 - ______ = 1.028

Add the blank to the other side:

3.157 = 1.028 + ______

Now subtract the 1.028

3.157 - 1.028 = ______

3.157 - 1.028 = 2.129

Nice handwriting, if that's yours.

Answer:

2.129

Step-by-step explanation:

The residual is the difference between the observed etching rate and the predicted etching rate

The residual of a room temperature of 25 degrees Celsius is [tex]- 2\dfrac{\mu\text{m}}{\text{min}}[/tex]

The least squares regression equation for predicting the etching rate from the room temperature is given as:

[tex]\hat y = 2 +\dfrac{1}{5} x[/tex]

When the room temperature is 25 degrees Celsius, the regression equation becomes

[tex]\hat y = 2 +\dfrac{1}{5} *25[/tex]

Evaluate the product

[tex]\hat y = 2 +5[/tex]

Evaluate the sum

[tex]\hat y = 7[/tex] --- this represents the predicted etching rate

The residual is calculated as:

Residual = Observed - Predicted

From the question, the observed etching rate is [tex]5\dfrac{\mu\text{m}}{\text{min}}[/tex]

So, the residual equation becomes

[tex]r = 5\dfrac{\mu\text{m}}{\text{min}} - 7\dfrac{\mu\text{m}}{\text{min}}[/tex]

Evaluate the difference

[tex]r = - 2\dfrac{\mu\text{m}}{\text{min}}[/tex]

Hence, the residual of a room temperature of 25 degrees Celsius is [tex]- 2\dfrac{\mu\text{m}}{\text{min}}[/tex]

Read more about residuals at:

https://brainly.com/question/2732316

Step-by-step explanation:

she walked 5 2/3 miles in 2 2/3 hours.

so, the unit rate (speed) is 5 2/3 miles / 2 2/3 hours.

for the regular miles/hour speed we need to this back to x miles/ 1 hour.

we start by creating full fractions :

17/3 miles / 8/3 hours = 17/3 × 3/8 miles/hour =

(17×3)/(3×8) = 17/8 = 2 1/8 miles/hour

and for hours/mile we need to flip this upside-down:

8/3 / 17/3 = 8/3 × 3/17 = 8/17 hours/mile

Answer:

See answers below

Step-by-step explanation:

Problem 1

Recall that [tex]tan(A+B)=\frac{tanA+tanB}{1-tanAtanB}[/tex] and that [tex]tan(\frac{\pi}{4})=1[/tex]. Using these two facts, we can rewrite the expression:

[tex]\frac{1+tanx}{-1+tanx}\\\\-\frac{1+tanx}{1-tanx}\\ \\-\frac{tan(\frac{\pi}{4})+tanx}{1-tan(\frac{\pi}{4})tan(x)}\\ \\-tan(x+\frac{\pi}{4})\\ \\tan(\frac{3\pi}{4}-x)[/tex]

Hence, the first choice is correct

Problem 2

[tex]cos(\frac{x}{2})=\sqrt{3}-cos(\frac{x}{2})\:;\: 0\leq x < 360^\circ\\\\2cos(\frac{x}{2})=\sqrt{3}\\ \\cos(\frac{x}{2})=\frac{\sqrt{3}}{2}\\\\\frac{x}{2}=\frac{\pi}{6}+2\pi n,\frac{11\pi}{6}+2\pi n\\ \\ x=\frac{\pi}{3}+4\pi n,\frac{11\pi}{3}+4\pi n\\ \\ x=60^\circ+720n^\circ, 660^\circ+720n^\circ\\\\x=60^\circ[/tex]

It's helpful to use the unit circle to solve these kinds of problems. Therefore, the third answer is correct.

Problem 3

Because [tex]sin\theta=-\frac{5}{13}[/tex] and our parameters are [tex]\pi < \theta < \frac{3\pi}{2}[/tex], the triangle must be in Quadrant III where [tex]sin\theta < 0[/tex] and [tex]cos\theta < 0[/tex].

You may recall the double angle formula [tex]sin2\theta=2sin\theta cos\theta[/tex]. We can find [tex]cos\theta[/tex] using [tex]sin\theta[/tex] with the Pythagorean Identity [tex]sin^2\theta+cos^2\theta=1[/tex] keeping our parameters in mind:

[tex]sin^2\theta+cos^2\theta=1\\\\(-\frac{5}{13})^2+cos^2\theta=1\\ \\\frac{25}{169}+cos^2\theta=1\\ \\cos^2\theta=\frac{144}{169}\\ \\cos\theta=-\frac{12}{13}[/tex]

Thus, [tex]sin2\theta=2sin\theta cos\theta=2(-\frac{5}{13})(-\frac{12}{13})=2(\frac{60}{169})=\frac{120}{169}[/tex], which means the third option is correct.

Answer:

I think it is A≈225.77

Step-by-step explanation:

The scale factor of the dilation can either be increased or decreased or enlarged or reduced but for the given parameters, the scale factor of the dilation is; 1.5

In dilation, the figure or image could be either enlarged or reduced. Now, we are told that OB' = 5cm and it was dilated to BB' which is 7.5 cm.

We can see that the length increased from 5 cm to 7.5cm. Thus, we can find the scale factor of dilation from;

Scale Factor = BB'/OB' = 7.5/5

Scale Factor = 1.5

Read more about scale factor at: https://brainly.com/question/10253650