The Campbells are saving up to go on a family vacation in 5 years. They invest $2800
into an account with an annual interest rate of 1.46% compounded monthly. Assuming no withdrawals are made, how much money is in the Campbells' account after 5 years?

Answer:

1.5 or 1 1/2

Step-by-step explanation:

2*9 = 18

4*3 = 12

18/12 = 3/2

1.5 or 1 1/2

Answer: Choice C

4/(3*sqrt(3))

which is the same as writing [tex]\frac{4}{3\sqrt{3}}[/tex]

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

Explanation:

We have the line [tex]\left(\sqrt{2}\right)x+y +2 = 0[/tex] in which points B and C are on this line. In other words, all of segment BC is on that line.

Point A is somewhere off that line as the diagram below indicates. We need to find the line through A that is perpendicular to the given line.

Recall that for any line of the standard form [tex]Px+Qy+R = 0\\\\[/tex], any perpendicular line will look like this: [tex]Qx-Py+S = 0\\\\[/tex]. Note the swap and sign change for the P,Q coefficients.

So anything perpendicular to [tex]\left(\sqrt{2}\right)x+y +2 = 0[/tex] will be of the form [tex]x-\left(\sqrt{2}\right)y+S = 0[/tex]. The sub-goal here is to find what S is equal to.

If you plugged in the origin point (x,y) = (0,0), then you should find that S = 0.

Therefore, the equation [tex]x-\left(\sqrt{2}\right)y = 0[/tex] is perpendicular to the given line and it passes through point A(0,0).

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

The reason why we computed that perpendicular line is to help determine the point D as shown in the diagram below. This point is at the intersection of the green perpendicular lines. This is at the base of the triangle such that BC is the base.

To find the location of point D, you need to solve this system of equations

[tex]\begin{cases}\left(\sqrt{2}\right)x+y +2 = 0\\\\x-\left(\sqrt{2}\right)y = 0\end{cases}[/tex]

Let's isolate x in the second equation

[tex]x-\left(\sqrt{2}\right)y = 0\\\\x=\left(\sqrt{2}\right)y\\\\[/tex]

Then substitute that into the other equation. Solve for y.

[tex]\left(\sqrt{2}\right)x+y +2 = 0\\\\\left(\sqrt{2}\right)*\left(\sqrt{2}\right)y+y +2 = 0\\\\2y+y +2 = 0\\\\3y +2 = 0\\\\3y = -2\\\\y = -2/3\\\\[/tex]

Now we can find x like so

[tex]x=\left(\sqrt{2}\right)y\\\\x=\left(\sqrt{2}\right)*(-2/3)\\\\x=\frac{-2\sqrt{2}}{3}\\\\[/tex]

The point D is located at the exact coordinates of

[tex]D=(x,y) = \left(\frac{-2\sqrt{2}}{3},\frac{-2}{3}\right)\\\\[/tex]

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

Next, we use the distance formula to compute the distance between point A and point D.

I'll use lowercase d to represent distance.

[tex]A = (x_1,y_1) = (0,0)\\\\D = (x_2,y_2) = \left(\frac{-2\sqrt{2}}{3},\frac{-2}{3}\right)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{\left(0-\left(\frac{-2\sqrt{2}}{3}\right)\right)^2 + \left(0-\left(\frac{-2}{3}\right)\right)^2}\\\\d = \sqrt{\left(\frac{2\sqrt{2}}{3}\right)^2 + \left(\frac{2}{3}\right)^2}\\\\d = \sqrt{\frac{8}{9} + \frac{4}{9}}\\\\d = \sqrt{\frac{12}{9}}\\\\d = \sqrt{\frac{4}{3}}\\\\d = \frac{\sqrt{4}}{\sqrt{3}}\\\\d = \frac{2}{\sqrt{3}}\\\\[/tex]

This represents the exact length of segment AD.

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

Since triangle ABC is equilateral, this means triangles ADB and ADC are identical mirrored copies of each other. Those two smaller triangles are equal in area and combine to form triangle ABC back again. Furthermore, they are right triangles. This last fact mentioned will allow us to use the pythagorean theorem like so

[tex]a^2+b^2 = c^2\\\\\left(\text{AD}\right)^2+\left(\text{DC}\right)^2=\left(\text{AC}\right)^2\\\\\left(\frac{2}{\sqrt{3}}\right)^2+\left(\frac{x}{2}\right)^2=\left(x\right)^2\\\\[/tex]

where x represents the lengths of AB, BC and AC.

After skipping a bit of steps, solving that said equation should lead to these two solutions

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

Because x is a side length, we ignore the negative solution.

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

We can now compute the area of triangle ABC

[tex]\text{area of triangle} = \frac{1}{2}*\text{base}*\text{height}\\\\\text{area of triangle ABC} = \frac{1}{2}*\text{BC}*\text{AD}\\\\\text{area of triangle ABC} = \frac{1}{2}*\frac{4}{3}*\frac{2}{\sqrt{3}}\\\\\text{area of triangle ABC} = \frac{1*4*2}{2*3*\sqrt{3}}\\\\\text{area of triangle ABC} = \frac{8}{6\sqrt{3}}\\\\\text{area of triangle ABC} = \frac{4}{3\sqrt{3}}\\\\[/tex]

which points us to choice C as the final answer.

When writing this on a keyboard, we would write "4/(3*sqrt(3))" without quotes. The use of parenthesis is needed to ensure we divide by all of 3*sqrt(3). Otherwise, the computer might mistake it for [tex]\frac{4}{3}\sqrt{3}[/tex] which is entirely different.

Answer:

-9

Step-by-step explanation:

Think about the Keep and change rule, since this is negative, the more negative numbers there are the more it will go deeper. -4 - 5 is -9 because just create a number line and place -4 one it, then jump backwards 5 times.

Answer:

Solution for What is 38 percent of 95: 38 percent *95 = (38:100)*95 = (38*95):100 = 3610:100 = 36.1. Now we have: 38 percent of 95 = 36.1.

Step-by-step explanation:

Answer:

percent grade

89%, 70%, 60%

Step-by-step explanation:

2, 98.2, 2/8, 4/6

Answer:

[tex]216[/tex]

Step-by-step explanation:

Remember that [tex]a^{b}=a*a*a*a*... b~~times[/tex].

So, [tex]6^3=6*6*6=(6*6)*6=36*6=\boxed{216}[/tex]

Answer:

6.02

Step-by-step explanation:

Answer:

Step-by-step explanation:

Suppose we decide to solve for y first.  y will then be in terms of x AND a real and an imaginary term:

48-5i=-4x+10yi

The goal here is to solve for y.  Adding 4x to both sides yields

48 - 5i + 4x = 10yi

and then we divide both sides by 10i to isolate the variable y:

48 - 5i + 4x

----------------- = y                 This result is "y in terms of the constant 48, the

      10i                               imaginary terms 5i and 10i, and the expression 4x.

We solve the original equation for x in a similar manner:

48-5i=-4x+10yi becomes 48 - 5i - 10yi = -4x, so that:

      -(48 - 5i - 10yi)

x = ------------------------

                 4

Next time, please specify which variable (x or y) you're solving for.  Thank you.

Answer:

[tex]y = - \frac{2}{3} x + 1[/tex]

Step-by-step explanation:

2x +3y= 5

3y= -2x +5

Divide both sides by 3:

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

[tex]y = - \frac{2}{3} x + 1 \frac{2}{3} [/tex]

Now that the equation is in the slope-intercept form (y= mx +c), the slope of the given line is the coefficient of x.

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

Parallel lines have the same slope.

Slope of unknown line= -⅔

y= -⅔ +c

To find the value of c, substitute a pair of coordinates into the equation.

When x= 3, y= -1,

[tex] - 1 = - \frac{2}{3} (3) + c[/tex]

-1= -2 +c

c= -1 +2

c= 1

Thus, the equation of the line is y= -⅔x +1.

Answer:

Next, in 1630, the Puritans used the royal charter establishing the Massachusetts Bay Company to create a government in which “freemen”—white males who owned property and paid taxes and thus could take on the responsibility of governing—elected a governor and a single legislative body called the Great and General Court ...

Answer:

Questions and answers about the Massachusetts Bay Colony. The Puritans established a theocratic government with the franchise limited to church members.

Questions and answers about the Massachusetts Bay Colony. The Puritans established a theocratic government with the franchise limited to church members.Related Places: United States British Empire Massachusetts American colonies

Questions and answers about the Massachusetts Bay Colony. The Puritans established a theocratic government with the franchise limited to church members.Related Places: United States British Empire Massachusetts American coloniesRelated Topics: Western colonialism Puritanism theocracy “Bay Psalm Book”

You are correct!

20 Characters

Answer:

99

Step-by-step explanation:

 64

+ 35

= 99

Answer:

[tex]{ \rm{ {a}^{ \frac{b}{c} } \: \dashrightarrow \: ( {a}^{b}) {}^{ \frac{1}{c} } }} \\ \\ { \boxed{ \rm{ \boxed{} \: \: \sqrt[c]{ {a}^{b} } }}} \\ [/tex]

Answer:

4 3 4 4 4 2 3 4 5 5 3.5 5

Just divide the number by 4

Sry if the list is kinda confusing

Answer:

[tex]f(x) = {sec}^{ - 1} x \\ let \: y = {sec}^{ - 1} x \rightarrow \: x = sec \: y\\ \frac{dx}{dx} = \frac{d(sec \: y)}{dx} \\ 1 = \frac{d(sec \: y)}{dx} \times \frac{dy}{dy} \\ 1 = \frac{d(sec \: y)}{dy} \times \frac{dy}{dx} \\1 = tan \: y.sec \: y. \frac{dy}{dx} \\ \frac{dy}{dx} = \frac{1}{tan \: y.sec \: y} \\ \frac{dy}{dx} = \frac{1}{ \sqrt{( {sec}^{2} \: y - 1}) .sec \: y} \\ \frac{dy}{dx} = \frac{1}{ |x | \sqrt{ {x }^{2} - 1} } \\ \therefore \frac{d( {sec}^{ - 1}x) }{dx} = \frac{1}{ |x | \sqrt{ {x }^{2} - 1} } \\ \frac{d( {sec}^{ - 1}5x) }{dx} = \frac{1}{ |5x | \sqrt{25 {x }^{2} - 1} }\\\\y=arccos(\frac{1}{x})\Rightarrow cosy=\frac{1}{x}\\x=secy\Rightarrow y=arcsecx\\\therefore \frac{d( {sec}^{ - 1}x) }{dx} = \frac{1}{ |x | \sqrt{ {x }^{2} - 1} }[/tex]

-3.6

Step-by-step explanation:

z/(-2) + -5 = -3.2 → times -2

z + 10 = 6.4

z = 6.4 - 10

z = -3.6

9514 1404 393

Answer:

  (b)  Hiking 10 feet due north, then hiking 10 feet due south

Step-by-step explanation:

Any pair of numbers that totals zero will be a pair of opposites. The offered choices are ...

  +6 -4 = 2 . . . not zero

  +10 -10 = 0

  +2 -3 = -1 . . . not zero

  +5 -3 = 2 . . . not zero

Hiking 10 feet due north, then hiking 10 feet due south is a situation involving opposite numbers adding up to zero.

Answer:

[tex]T(x)=\begin{cases}\frac{3x+1}{2} & x\text{ is odd} \\ \frac{x}{2} & x\text{ is even}\end{cases} \\ for \: instance \: start \: with \: 7 \: \\ which \: is \: an \: odd \: number \\ \frac{21 + 1}{2} = \frac{22}{2} = 11 \\ 11 \: is \: odd \\ \frac{11 + 1}{2} = 6\\ 6 \: is \: even \\ \frac{6}{2} = 3 \\ 3\: is \: odd \\ \frac{9 + 1}{2} = 5 \: \\ 5 \: is \: odd\\ \frac{15 + 1}{2} = 8 \\ 8 \: is \: even \\ \frac{8}{2} = 4 \\ 4 \: is \: even \\ \frac{4}{2} = 2 \: then \: 1 \\ [/tex]

Step-by-step explanation:

Can we connect to 1 for all numbers?

A general proof for a simple pattern seems almost impossible, probably a new branch of mathematics maybe needed to tackle this conjecture...

Answer:

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

Answer:

10 to 15 (simplified: 2 to 3)

10/15 (simplified: 2/3)

10 : 15 (simplified: 2 to 3)

Answer:

[tex]2x + 5 \geqslant 27 \\ = 2x \geqslant 27 - 5 \\ = 2x \geqslant 22 \\ = x \geqslant 22 \div 2 \\ x \geqslant 11 \\ x[11 \: \infty ) \\ thank \: you[/tex]

Step-by-step explanation:

Hope this help you

If this help you then mark me as a brainliest

Answer:

12

Step-by-step explanation:

you reverse the operations, you multiply LxWxH to get the volume, so you can do V/L/H to get the width. 2880 divided by 24 equals 120, and 120 divided by 10 equals 12, so therefore the width is 12. Hope this helps!

Answer:

f(x)=4−(x−7)

3

Let y=f(x)

So, x=f

−1

(y) ---- ( 1 )

y=f(x)

⇒ y=4−(x−7)

3

⇒ (x−7)

3

=4−y

⇒ x−7=

3

4−y

⇒ x=7+

3

4−y

⇒ f

−1

(y)=7+

3

4−y

.................. [ From ( 1 ) ]

∴ f

−1

(x)=7+

3

4−x

Hi there!

What we need to know:

The three main trigonometric ratios are sine, cosine and tangent:

[tex]\displaystyle sin\theta=\frac{opposite}{hypotenuse}[/tex]     [tex]\displaystyle cos\theta=\frac{adjacent}{hypotenuse}[/tex]    [tex]\displaystyle tan\theta=\frac{opposite}{adjacent}[/tex]

"Opposite" refers to the side opposite the angle that is not the hypotenuse.

"Hypotenuse" refers to the side opposite the right angle of a right triangle.

"Adjacent" refers to the side next to the angle that is not the hypotenuse.

"θ" is read as "theta". It just represents the angle.

Keep in mind that these three ratios only apply to right triangles.

You can use the mnemonic "soh-cah-toa" to help you remember these ratios.

First question

For the first question, we're given the angle with a measure of 56 degrees and the length of the hypotenuse. We must calculate a, which represents the side adjacent to the given angle.

Given the hypotenuse and the adjacent side, we know that we must use the cosine ratio:

[tex]\displaystyle cos\theta=\frac{adjacent}{hypotenuse}[/tex]

Plug in the given information:

[tex]\displaystyle cos56=\frac{a}{13}[/tex]

Isolate a by multiplying both sides by 13:

[tex]13\displaystyle cos56=a[/tex]

Solve using a calculator:

[tex]a=7.3[/tex]

Therefore, a is equal to 7.3 when rounded to 1 decimal place.

Other information you will need to know:

In the above question, we needed to solve for a side. But what if we were given two sides and we needed to solve for an angle? For example:

[tex]\displaystyle sin\theta=\frac{5}{8}[/tex]

In this case, we will use the inverse sine ratio:

[tex]\displaystyle \theta=sin^-^1(\frac{5}{8})[/tex]

Solve using a calculator:

[tex]\displaystyle \theta=39[/tex]

Therefore, the angle would equal approximately 39 degrees.

I hope this helps!

Answer:

1. y = 3x - 1

2. y = -3x

3. y = 2x + 4

4. y = 2.5x - 4

5. y = 4x

6. y = -3/4x -0.25

7. uhhh two lines  since one definitlye doesn’t work

Step-by-step explanation: I couldn’t add more than 5 pics it’s the limit sadly.

Answer:

75

Step-by-step explanation:

15 is 20% of the total.

The total is x since it is unknown.

20% of the total = 15

20% of x = 15

0.2x = 15

Multiply both sides by 5.

x = 75

Answer:

16.5 minutes

Step-by-step explanation:

2508/152 = 16.5

Check: 152 x 16.5 = 2508

Answer:

x=135/13

Step-by-step explanation:

9/13 × 15 = x

9 × 15/13 = x

135/13 = x

x = 135/13

I hope this helps :)

Answer:

2. 4y-2xy

Step-by-step explanation:

6y-2y(x+1)=6y-2xy-2y

=4y-2xy

Answer:

3102.12

Step-by-step explanation:

add the starting weight 788.52 plus the weight he gained 2.313.6

788.52 + 2.313.6 = 3102.12