ALGEBRA 2 - Exponential and Logarithmic Functions
April invests $500 in an account that is compounded continuously at an annual interest rate of 5%. Approximately how many years will it take for April’s money to double?

Answer:

C only

Step-by-step explanation:

C is the only one which is correct as in all the other options x is cancelled out as both sides have 2x which gets cancelled leaving the equation with something like:

31=31 which is true but it's not considered a "solution" and as A, B and D end up with stuff like this they are all not 1 solution. For c, as c doesn't have a power on top of it, like [tex]x^{2}[/tex] does, its equation can only have 1 solution (or in some cases 0 solutions but this isn't one of them) so it is the correct answer.

A. all real numbers

B. x = 0

C. all real numbers

D. no solutions

the explanation is in imagine

Answer:

1) 12.2425 square meters

2)$288

Step-by-step explanation:

According to the problem, we have a rectangle bedroom with 415cm long by 295cm width.

We know that 1cm = 0.01 m

Length of bedroom: 415 x 0.01 = 4.15m

of bedroom: 295 x 0.01 = 2.95m

area of rectangle: Length x Width

Area: 4.15 x 2.95 = 12.2425 square meters

We have a cost of carpet 24 per square meter is given from the problem.

we now know that it is in a whole number so we divide by 2 to get it square

A= 12m (squared)

now we multiply 12 and 24

we get $288

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The cost of each box of candy is 31 cents and the cost of each bag of chips is 69 cents.

To find the cost of each box of candy, we first need to find the total cost for all items. We know that Rafael and his sister spent a total of $3.82 + $2.69 = $6.51 on snacks. Since Rafael bought 3 boxes of candy and 1 bag of chips, and his sister bought 2 bags of chips and 1 box of candy, there were a total of 3 + 2 = 5 bags of chips and 3 + 1 = 4 boxes of candy bought.

To find the cost of each box of candy, we divide the total cost for all boxes of candy by the number of boxes of candy: $6.51 / 4 = $1.63 or 163 cents. To find the cost of each bag of chips, we divide the total cost for all bags of chips by the number of bags of chips: $6.51 / 5 = $1.30 or 130 cents.

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Answer:

The sum is 2635

Step-by-step explanation:

I did this problem

Answer:

81/100 is the answer I believe if I'm wrong my bad

Answer:

81/100

Step-by-step explanation:

brainliest pls

We can tell if a number is rational or irrational by Venn Diagram

Both irrational and rational numbers are exact, yet they have different properties. Any number that can be expressed as P/Q, where P and Q are both integers and Q is more than zero, is considered to be reasonable. Simple fractions, however, cannot be used to express an irrational number. An illustration of a rational number is 2⅔ 3, while an irrational number is √2.

All integers, fractions, and repeating decimals are included in the concept of a rational number. We may represent every rational number as p/q, where p and q are integer numbers.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]2y=6-2x\implies 2y=-2x+6\implies y=\cfrac{-2x+6}{2} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-1}x+3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -1 \implies \cfrac{-1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-1} \implies 1}}[/tex]

so we're really looking for the equation of a line whose slope is 1 and it passes through (6 , -7)

[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{ 1}(x-\stackrel{x_1}{6}) \implies y +7= 1 (x -6) \\\\\\ y+7=x-6\implies {\Large \begin{array}{llll} y=x-13 \end{array}}[/tex]

The equation of the function in the form y=mx+b is y = 110x-2020

Adaptation of function speed

A line's equation is written as mx + b = y, where m denotes the rate of change or slope.

The intercept is B.

utilizing the coordinates

Calculate the slope.

m = 550/5

m = 110

The intercept for

280 + 110(20) + b

280 = 2200 + b

b = 180 - 2200

b = -2020

The equation for the function of the type y=mx+b is hence y = 110x-2020.

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The complete question would be:

The table shows the distance Penelope is from the park as she walks to soccer practice. Assume the relationship between the two quantities is linear. Find and interpret the rate of change and initial value. Then write the equation of the function in the form y=mx+b

Answer:

= -0.7x-11+4.6g

Step-by-step explanation:

hope this helps :)

Answer:

−0.7x − 11 + 4.6g

Step-by-step explanation:

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Answer:

=9-3b

Step-by-step explanation:

i hope this helps :)

Answer:

5,859,375

Step-by-step explanation:

a10 = 3×5^9 = 3×1,953,125

= 5,859,375

Answer:

5,859,375

Step-by-step explanation:

Given :-

And we need to find out the 10th term of the sequence. Here firstly we should find the Common Ratio and then we can substitute the respective values in the formula to find the nth term of a geometric sequence .

Common Ratio :-

[tex]:\implies[/tex] CR = 15 ÷ 3 = 5

The 10 th term :-

[tex]:\implies[/tex] T_n = arⁿ - ¹

[tex]:\implies[/tex] T_10 = 3 × 5 ¹⁰ - ¹

[tex]:\implies[/tex] T_10 = 3 × 5⁹

[tex]:\implies[/tex] T_10 = 3 × 1953125

[tex]:\implies[/tex] T_10 = 5859375

Hence the 10th term is 5,859,375

Answer:

Step-by-step explanation:

5. P-4=-4

P-4+4=-4+4=0

P=0

The percent error in the amount of water Rich added is 15.93%.

When compared to the actual value, the percent error is the difference between the estimated and actual values.

The difference between the estimated value and the actual value in relation to the actual value is given as a percentage and is known as the percent error. In other words, the relative error times 100 equals the percent error.

Given that Rich added water to a solution in science class is 26.2 milliliters

Whereas the directions said to add water is 22.6 milliliters

The amount of water that is added more is 26.2 -22.6 = 3.6 milliliters

The percent error is = (3.6/22.6)*100%

The percent error is = 15.9292*100%

Therefore, the correct answer is option b) 15.93%.

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Answer:

please join my meeting

Answer:

The error interval for x is:

                 [3.65,3.74]

Step-by-step explanation:

The number after rounding off is obtained as:

                         3.7

We know that any of the number below on rounding off the number to the first decimal place will result in 3.7:

  3.65     3.66    3.67    3.68    3.69    3.70    3.71   3.72    3.73    3.74

( Because if we have to round off a number present in decimals to n place then if  there is a  number greater than or equal to 5 at n+1 place then it will result to the one higher digit  at nth place on rounding off and won't change the digit if it less than 5 )

        Hence, the error interval is:

            [3.65,3.74]

The dilation of the circle with a scale factor 1/r and center at (a,b) will transform the circle into a point at (a,b).

A dilation is a transformation that results in an image with the same shape as the original but a different size. • An enlargement is a dilation that produces a larger image. • A reduction is a dilation that produces a smaller image.

To solve this we will use the transformation formula for a dilation with center (a,b) and scale factor

k, (x,y) --> (a + k(x-a), b + k(y-b)).

Substituting in our values, we get

(x,y) --> (a + (1/r)(x-a), b + (1/r)(y-b)).

Setting this equal to (a,b), we get

(a + (1/r)(x-a) = a, b + (1/r)(y-b) = b).

Solving for x and y gives x = a and y = b. Therefore, the dilation of the circle with a scale factor of 1/r and center at (a,b) will transform the circle into a point at (a,b).

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Answer:

16.8 inches

Step-by-step explanation:

Perimeter =2(length+width) so 2·(5.6+2.8)≈16.8

Answer and Step-by-step explanation:

First, write down what we know.

Length of Rectangle = [tex]5\frac{3}{5}[/tex]

Width = [tex]\frac{Length}{2}[/tex]

2 ways to solve this:

1st way:

If we convert the fraction into a decimal, then we can easily find the width.

[tex]5\frac{3}{5}[/tex] can be solved by making the mixed number into a improper fraction.

Multiply the denominator (5) by the whole number (5), then add the numerator (3). This number is 28. Replace the 3 with the 28, and now we have [tex]\frac{28}{5}[/tex]. This number is equal to 5.6.

Now, we have to divide this number.

5.6 divided by 2 is equal to 2.8.

So, the width is equal to 2.8.

Now, we add the width and length together twice to get the perimeter of the rectangle.

2.8 + 2.8 + 5.6 + 5.6 = 16.8

So, the answer is A. 16.8 inches.

2nd way:

Since we know that the width is half of the length, we can just add the length by itself 3 times, since two of the widths combined will equal the length.

5.6 + 5.6 + 5.6 = 16.8

So, the answer is A. 16.8 inches.

#TeamTrees #PAW (Plant And Water)

Step-by-step explanation:

it means that the graph of the function above y=x must be the mirrored image of the graph under y=x.

it means that the function applied to itself gives x.

f(f(x)) = x

e.g.

f(x) = 5 - x

f(f(x)) = 5 - (5 - x) = 5 - 5 + x = x

so, this f(x) is its own inverse.

Answer:

possible

Step-by-step explanation:

the question asks what is the likelyhood of making a free throw 70% of the time, whcih is possible beacuase you can make it, you can also miss it. there are several professional basketball players that have that percentage. but it is not likely that someone could just shoot 70 percent. so i would stick with possible

Answer:

400sq.ft

Step-by-step explanation:

Let Area of smaller rectangle be x

➝2:3=x:600

➝2/3=x/600

➝2×600=3x

➝3x=1200

➝x=1200/3

➝x=400sq.ft

Answer:

has a maximum value

Step-by-step explanation:

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

Answer:

maximum value

Step-by-step explanation:

Answer:

a.  The total cost of fixing the drain is $198

b. The plumber spend 13 hours fixing the drain

Step-by-step explanation:

We know the equation is

C=25h+73

C = the total cost

h = the number of hours

Let's solve question a by putting 5 in for h

C=25(5)+73

C = 125 + 73

C = $198

So, the total cost of fixing the drain is $198

Let's solve question b by butting 398 in for c

398=25h+73

325 = 25h

h = 13 hours

So, the plumber spend 13 hours fixing the drain

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Answer:

120

Step-by-step explanation:

So there are two ways of doing this.

The easiest, we know that the biggest of 30, 60 and 90 degrees is 90.

We know that a right angle is 90 degrees.

The 1 angle is clearly bigger than 90 degrees.

So it must be 120.

The actual way of solving:

The mini trinalge that has the 90 degree angle in it is a 30, 60, 90 trinalge.

We know that the 3 is the 30 degree angle on the trinalge.

We know that the angle on the opposite side of the dotted line must be 30 as well.

Since thats 30, the opposite side of the dotted part of thr traingle must be 30 as well.

This means that the other two angles are 60 which you subtract from 180

This leaves 120

So 120 degree angle is the answer

Sorry if this is confusing I hope this helps!

Mrs. Smith will be responsible for paying $75.00

The normal monthly charge is $40.00 and the current balance is $110.00,

so the difference is $110.00 - $40.00 = $70.00.

Mrs. Smith negotiated a 50% credit, so she will receive

$70.00 x 0.50 = $35.00 credit.

To find the amount she is responsible for paying, we subtract the credit from the current balance

$110.00 - $35.00 = $75.00

Thus, the amount Mrs. Smith will be responsible for paying is $75.00

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Solving for X in a Right Triangle

Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees. Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X

Answer$250

Step-by-step explanation:

6.25 x 8 = 50 x 5 = 250

Answer:

$1,050

Step-by-step explanation:

6.25 x 24 x 7 = $1,050

6.25 x 24 represents the amount per hour multiplied by a days total hour (24) which is then multiplied by 7 to represent a week.... which equals $1,050

Answer:

Cot(theta) = - 0.75 or -3/4

Step-by-step explanation:

The hypotenuse is 5

The y value is 4

We need to find the corresponding x value.

x^2 + y^2 = z^2

X = ?

y = 4

z = 5

x^2 + 4^2 = 5^2

x^2 + 16 = 25

x^2 = 9

Now in this case, you are in quadrant 2, so the x value is - 3

sqrt(x^2) = sqrt(9)

x = - 3

The cot value is the adjacent (x value) / the opposite ( y ) value

Cot(theta) = -3/4

cot(theta) = -0.75

Answer:

cotθ = -3/4

Step-by-step explanation:

Given:

sinθ = 4/5

θ is in Quadrant II, so cosθ < 0

Recall:

cotθ = cosθ/sinθ

cos²θ + sin²θ = 1

Determine cosθ:

cosθ = -√(1-sin²θ) = -√(1-(4/5)²) = -√(1-16/25) = -√(9/25) = -3/5

Determine cotθ:

cotθ = cosθ/sinθ = (-3/5)/(4/5) = (-3/5)(5/4) = -15/20 = -3/4

Answer:

50x + 19.5 ≤ 130

Step-by-step explanation:

X is the number of days Mei Mei plans to rent the car

For driving 100 miles, Mei Mei will be charged $19.50. [130 times 0.15]

Mei Mei has a maximum budget of $130, so the inequality will have a less than or equal to sign

50x + 19.5 ≤ 130