How much would $500 invested at 5% interest compounded continuously be worth after 4 years? Round your answer to the nearest cent

Answer:

33 units

Step-by-step explanation:

AB = BC

2x + 7 = 23

2x = 16

x = 8

DC = DA

DC = 4x + 1

DC = 4(8) + 1

DC = 33

Given:

Values of a polynomial P(x).

[tex]P(-5)=-2[/tex]

[tex]P(-3)=6[/tex]

[tex]P(3)=7[/tex]

[tex]P(5)=-1[/tex]

To find:

The remainder when P(x) is divided by (x+5).

The remainder when P(x) is divided by (x-3).

Solution:

If a polynomial P(x) is divided by (x-a), then the remainder is P(a).

If the polynomial P(x) is divided by (x+5), then the remainder is P(-5).

[tex]P(-5)=-2[/tex]

Therefore, the remainder is -2 when P(x) is divided by (x+5).

If the polynomial P(x) is divided by (x-3), then the remainder is P(3).

[tex]P(3)=7[/tex]

Therefore, the remainder is 7 when P(x) is divided by (x-3).

Answer:

194

Step-by-step explanation:

Rectangles :

7 x 10 = 70

6 x 10 = 60

4 x 10 = 40

Triangles

[tex]\frac{6x4}{2}[/tex] = 12   (two of them = 24)

70 + 60 + 40 + 24 = 194

Answer: 21, 28

Step-by-step explanation:

Use the Pythagorean Theorem [tex]a^{2}+b^{2}=c^{2}[/tex]:

Substitute in the values & solve:

[tex]x^{2}+(x+7)^{2}=35^{2}\\x^{2}+x^{2}+14x+49=1225\\2x^{2}+14x+49-1225=0\\2x^{2}+14x-1176=0\\2(x^{2}+7x-588)=0\\2(x + 28)(x - 21)=0\\x_{1}=-28, x_{2}=21[/tex]

-28 is not a possible solution since you can't have negative inches...

Answer:

200

Step-by-step explanation:

Substitute 15 for y

[tex] \frac{1}{5} x - \frac{2}{3} (15) = 30[/tex]

[tex] \frac{1}{5} x - 10 = 30[/tex]

[tex] \frac{1}{5} x = 40[/tex]

[tex]x = 200[/tex]

5a) 3x3x13

b) 3x7x7

c)11x5x2x2

d)3x3x3x5x2

6a)2x2x2x131

7a)5x5x2x2

b) 3x2x17

c)5x2x2x2x2x2x2

d)5x5x5x3

e) 2x2x103

f)5x3x137

g) 2x2x2x2x2x2x2x2x2

h)5x5x7x7x3

Answer:

11.3

Step-by-step explanation:

first we find angle F.

remember, all angles in a triangle always sum up to 180 degrees.

so,

F = 180 - 90 - 61 = 29 degrees

now we use the law of sines.

EF/sin(D) = ED/sin(F) = DF/sin(E)

DF = x

sin(E) = sin(90) = 1

5.5/sin(29) = x/1 = x

x = 11.3

Answer:

The last table (the bottom one)

Step-by-step explanation:

The ingredients having the same ratio means that, for every number of servings, we should have:

Y/X = constant.

So, for the first table when we have 1 serving, the quotient is:

Y/X = 2/1 = 2

when we have two servings:

Y/X = 3/2 = 1.5

The ratios are different.

Then this is not the correct option.

For the second table, when we have 1 serving the ratio is:

Y/X = 2/1 = 2

when we have two servings:

Y/X = 4/2 = 2

when we have 3 servings:

Y/X = 8/3 = 2.66

This is not the correct option.

For the third table:

1 serving:

Y/X = 2/1 = 2

2 sevings

Y/X = 3/2 = 1.5

This is not the correct option.

fourth table:

1 serving:

Y/X = 2/1 = 2

2 servings

Y/X = 4/2 = 2

3 servings

Y/X = 8/4 = 2

Here we can see that the ratio is always the same, then the ratio remains constant.

This is the table that shows a possible ratio for ingredients X and Y,

Answer:

c = - 4

Step-by-step explanation:

Nothing else matters except that the number associated with the y value in equation one = 1 and the number in front of x is known in equation 1. Then we'll get around to looking at c

Add 2y to both sides of equation 1 (the top equation)

3x - 2y + 2y = 3 + 2y

3x = 2y + 3        

Now divide both sides of the equation by 2

3x/2 = y + 3/2

What's in front of x? It is (3/2)

So divide both sides of 6x + cy = 4       by c

6x/c + y = 4/c

Now put 6x/c on the right hand side so y is by itself.

y = -6x/c + 4/c

What do you have to do now?

You must equate -6x/c = 3/2x

Why?

The slopes have to be the same so the lines are parallel and never cross. That will give no solutions.

-6x/c = 3x / 2     Divide both sides by x

-6/c = 3/2           Cross multiply

3c = - 6 * 2        Combine

3c = - 12             Divide by 3

c = - 12/3

c = - 4

Answer:

[tex]m=6[/tex]

Step-by-step explanation:

Exponent properties:

We can use exponent property [tex]a^{b^c}=a^{(b\cdot c)}[/tex] to solve this problem.

Rewrite [tex]8[/tex] as [tex]2^3[/tex], then apply exponent property [tex]a^{b^c}=a^{(b\cdot c)}[/tex] to simplify:

[tex]2^{3^5}=2^{2m+3},\\2^{15}=2^{2m+3}[/tex]

If [tex]a^b=a^c[/tex], then [tex]b=c[/tex], because of log property [tex]\log a^b=b\log a[/tex]. Using this log property, you can take the log of both sides and divide by [tex]\log a[/tex] to get [tex]b=c[/tex]

Therefore, we have:

[tex]15=2m+3[/tex]

Subtract 3 from both sides:

[tex]12=2m[/tex]

Divide both sides by 6:

[tex]m=\frac{12}{2}=\boxed{6}[/tex]

Alternative:

Given [tex]8^5=2^{2m+3}[/tex], to move the exponent down, we'll use log properties.

Start by simplifying:

[tex]\log 32,768=2^{2m+3}[/tex]

Take the log of both sides, then use log property [tex]\log a^b=b\log a[/tex] to move the exponent down:

[tex]\log(32,768)=\log 2^{2m+3},\\\log (32,768)=(2m+3)\log 2[/tex]

Divide both sides by [tex]\log2[/tex]:

[tex]2m+3=\frac{\log (32,768)}{\log(2)}[/tex]

Subtract 3 from both sides:

[tex]2m=\frac{\log (32,768)}{\log(2)}-3[/tex]

Divide both sides by 2:

[tex]m=\frac{\log (32,768)}{2\log(2)}-\frac{3}{2}=\boxed{6}[/tex]

Answer:

2, 3, 7 or 8

Step-by-step explanation:

Answer:

The slope is Negative three-halves and contains the point (0, 2).

Step-by-step explanation:

(-3,-4)(3,0)

M= -4/-6 = 2/3

⊥M = -3/2

0 = 2/3(3) + B

B=2

Answer:

(101/42, 19/14)

Step-by-step explanation:

Given the following equations

3x+5y=14 ..... 1 * 2

6x-4y=9 ... 2 * 1

__________________

6x+10y=28

6x-4y=9  

Subtract

10y+4y = 28 - 9

14y = 19

y = 19/14

Get the value of x

Since 3x+5y = 14

3x+5(19/14) = 14

3x + 95/14 = 14

3x = 14 - 95/14

3x = 101/14

42x = 101

x = 101/42

Hence the solution is (101/42, 19/14)

Answer:

-9

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

-8 +___= - 17

___=-17 +8

___=-9

=-9

Answer:

The answer is C

Step-by-step explanation:

Switch x and y

[tex]x = \frac{2y}{7} + 4[/tex]

Solve for y

[tex]y = \frac{7(x - 4)}{2} [/tex]

Answer:

slope= -3/1

y-intercept= 4

Answer:

m = -3

y intercept = 4

Step-by-step explanation:

The given equation of the line is ,

[tex]\implies y = -3x+4[/tex]

We know that the Standard equation of Slope Intercept Form of the line is,

[tex]\implies y = mx + c[/tex]

Where ,

On comparing to the Standard form of the line we get ,

[tex]\implies Slope = -3 [/tex]

[tex]\implies y - intercept= 4 [/tex]

Answer:

x = 0

Step-by-step explanation:

This is a vertical line, in fact the y- axis

The equation of a vertical line is

x = c

where c is the value of the x- coordinates the line passes through

All of the x- coordinates on the y- axis are zero, then

x = 0 ← equation of line

Answer:

exact form: x=-1/2

decimal form: x=-0.5

Answer:

Sue candy = 13 - x

Tony candy = 9 + 1/2x

Step-by-step explanation:

Sue candy = 18

Tony candy = 18

Let x = some candy gives to tony

Sue candy = 18 - x

Tony candy = 18 + x

sue then eats five of hers

Sue candy = 18 - x - 5

= 13 - x

tony eats half of his

Tony candy = 1/2(18 + x)

= 18/2 + x/2

= 9 + 1/2x

Expressions for the number of pieces candy sue and tony now have:

Sue candy = 13 - x

Tony candy = 9 + 1/2x

Hermes is incorrect. The opposite of 9 is -9 if Hermes says that the opposite of 9 is 9 since each number is 9 units from zero on the number line.

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

To find the same distance away from zero in the opposite direction to determine the opposite number.

The distance from zero in this situation is 9. nine times in the opposite direction from zero.

Thus, Hermes is incorrect. The opposite of 9 is -9 if Hermes says that the opposite of 9 is 9 since each number is 9 units from zero on the number line.

Learn more about the number line here:

brainly.com/question/13189025

#SPJ2

Hi there!

We know that the angles ∠B and ∠A are supplementary because they are both interior angles. Therefore:

180 = ∠A + ∠B

Rewrite:

180 = (6x - 48) + (4x + 38)

Combine like terms:

180 = 10x - 10

Solve for x:

190 = 10x

x = 19

Solve for ∠B by plugging in this value of x:

∠B = 4(19) + 38

∠B = 76 + 38

∠B = 114

The correct answer is to drag The Plus sign (+)

This has to do with the use of symbols to denote mathematical equations such as addition, subtraction, etc.

Hence, we can see that the correct position to put the operator on the image to result in a binomial is to drag the plus sign (+) so that the equations can be solved,.

Read more about operators here:

https://brainly.com/question/25974538

#SPJ2

Answer:.

Step-by-step explanation:

Step-by-step explanation:

a vector multiplied by a scalar is equal to it's image. The expression above gives an equation and after solving, it gives you the image

Answer:

yes.. they are

Step-by-step explanation:

because

Answer:

B

Step-by-step explanation:

To find which ordered pairs are solutions to the inequalities we can simply plug in the x and y values of the ordered pairs into the inequalities and if the equation is true for both inequalities then the ordered pair is a solution to the inequalities.

For (0,0)

x = 0

y = 0

y > x + 5

Substitute 0 for y and x

0 > 0 + 5

Simplify right side

0 > 5

The inequality is not true as 5 is greater than 0, not less than. So immediately we can eliminate answer choice A.

For (5,1).

x = 5

y = 1

y > x + 5

Substitute 5 for x and 1 for y

1 > 5 + 5

Simplify right side

1 > 10

Again, the equation is not true as 1 is not greater than 10. This means that c cannot be the answer

For (3,7)

x = 3

y = 7

y > x + 5

Substitute 3 for x and y for 7

7 > 3 + 5

Simplify right side

7 > 8

7 is not greater than 8 meaning that (3,7) cannot be a solution to the inequalities

None of the ordered pairs created true equations hence the answer is B

Answer:

3/5

Step-by-step explanation:

Remember that odds for plus odds against must be 1. Therefore, 20 out of 50 of the DVRs are defective, so 30 out of 50 would work.

30/50

simplifies into 3/5 so that would be the probability of you picking out a DVR that works, and the probability of picking one that does not work would be the leftover 2/5 . Or, if you're answering with a percent, you would have a 60% chance of picking a working DVR.

I hope this helps, I know the explanation isn't really clear, but I can't really think of another way to explain it.

Answer:

Step-by-step explanation:

The formula for this is the one we use when we are given the ratio the directed line segment is separated into as opposed to the point being, say, one-third of the way from one point to another. The 2 equations we use to find the x and y coordinates of this separating point are:

[tex]x=\frac{bx_1+ax_2}{a+b}[/tex]  and  [tex]y=\frac{by_1+ay_2}{a+b}[/tex] where x1, x2, y1, y2 come from the coordinates of A and B, and a = 1 (from the ratio) and b = 2 (from the ratio). Filling in for x first:

[tex]x=\frac{2(2)+1(-4)}{1+2}=\frac{4-4}{3}=0[/tex] and then y:

[tex]y=\frac{2(-3)+1(9)}{1+2}=\frac{-6+9}{3}=\frac{3}{3}=1[/tex]

The coordinates of point E, then, are (0, 1).

Answer:

(-1,3)

Step-by-step explanation:

Mathematically, what we have to do here is to get the coordinates of the midpoint of the line AB

we have this as;

(x,y) = (x1 + y1)/2, (y1 + y2)/2

(x,y) = (-4+2)/2, (9-3)/2 = (-1, 3)

Answer: The function M if derived from the integral of the derivative of the function. This is valid by the fundamental theorem of calculus.

M(x)=43x32−7x+C

Step-by-step explanation: not 100 about this but it's what I got