An account earns 1.5% interest compounded annually. The balance after 2 years is $8241.80. What is the principal?

Answer:

Alternative A

Step-by-step explanation:

2x(x² + 2x - 6)

2x³ + 4x² - 12x

I hope I helped you

Answer: A

Step-by-step explanation:

 2x(x² + 2x - 6)

= 2x(x²) + 2x(2x) + 2x(-6)

= 2x³ + 4x² - 12x

Answer:

Step-by-step explanation:

Alright, lets get started.

Suppose one side of the kite is x

One side of a kite is 5 cm less than 2 times the length of another.

So, another side of the kite will be = [tex]2x-5[/tex]

So, the all 4 sides of the kite will be x, x , 2x-5 and 2x-5

The perimeter of the kite will be = [tex]x+x+2x-5+2x-5=6x-10[/tex]

As per given in question, perimeter is 14, so

[tex]6x-10=14[/tex]

Adding 10 in both sides

[tex]6x=24[/tex]

Dividing 6 in both sides

[tex]x=4[/tex]

So, another side is [tex]2*4-5=3[/tex]

So, the sides are 4 cms and 3 cms   :   Answer D

Hope it will help :)

Answer:

D) 4 cm, 3 cm  

Step-by-step explanation:  

Since we know that kite is made of two sets of equal sides.

Let x be the length of one of equal sides and y be length of another side of equal sides.      

We have been given that one side of a kite is 5 cm less than 2 times the length of another. We can represent this information as:

[tex]x+5=2y...(1)[/tex]

We are also told that the perimeter is 14 cm. We can represent this information as:

[tex]2(x+y)=14...(2)[/tex]

From equation (1) we will get,

[tex]x=2y-5[/tex]

Substituting this value in equation (2) we will get,

[tex]2(2y-5+y)=14[/tex]

[tex]2(3y-5)=14[/tex]

[tex]6y-10=14[/tex]

[tex]6y-10+10=14+10[/tex]

[tex]6y=24[/tex]

[tex]y=\frac{24}{6}[/tex]

[tex]y=4[/tex]

Therefore, length of one side of kite is 4 cm.  

Upon substituting y=4 in equation (1) we will get,

[tex]x+5=2*4[/tex]

[tex]x+5=8[/tex]

[tex]x+5-5=8-5[/tex]

[tex]x=3[/tex]

Therefore, the length of another side of kite is 3 cm and option D is the correct choice.

Answer: D.

A horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180° rotation.

The transformations that can map a strip onto itself in geometry are reflection, rotation, and translation. Reflection flips the shape over an axis, rotation turns it around a central point, and translation moves it along a vector without changing its orientation.

In mathematics, particularly geometry, there are several types of transformations that can map a figure onto itself. Probably you are referring to a strip as in a planar shape, such as a rectangle or square. The main transformations that can map this strip onto itself are: reflection, rotation, and translation.

Reflection is like flipping the strip over an axis. If the strip is symmetrical, it will map onto itself. Rotation means turning the strip around a central point. For instance, rotating a square shape 90, 180, 270, or 360 degrees about its center will map it onto itself. Lastly, translation keeps the strip in the same orientation and moves it along a vector direction. As long as it doesn't interfere with its setting, it would still map onto itself.

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Answer:

The length of RT is 5. The length of RS and ST is either 7 or 3.

Step-by-step explanation:

The Law of Cosine is defined as

[tex]a^2=b^2+c^2-2bc\cos(A)[/tex]

It is given that, the law of cosine for triangle RST can be set up as

[tex]5^2=7^2+3^2-2(7)(3)\cos(S)[/tex]

Therefore the length of opposite side of angle S is 5. The opposite side of angle S is RT, therefore the length of RT is 5.

The length of two other sides are either 7 or 3.

Therefore length of RT is 5. The length of RS and ST is either 7 or 3.

Answer:

answer is d on edge

Step-by-step explanation:

Answer:

$3.4875

Step-by-step explanation:

AS the ride is completed and according the rule the person have to give a tip on the total taxi ride

according to the given

tip given 15%

Total ride cost = $23.25

To find is the total tip given in dollars

Solution:

Total tip in dollars = 15 % of total ride cost

Putting the values of the given

Total tip in dollars = 15 % of 23.25

it can be written as

                             = [tex]\frac{15*23.25}{100}[/tex]

                              =[tex]\frac{348.75}{100}[/tex]

                               =$ 3.4875

So the total tip would be $3.4875

Answer:

3.50 cent

Step-by-step explanation:

I take 10% and 20% of the number. For this ride, that would be about $2.33 and 4.66.

Then I estimate what is about half way between those two numbers. It looks like about $3.50 would be about 15%.

Answer:

The answer  =

Step-by-step explanation:

Answer:

This system of linear equations represents parallel lines.

The system of equation 1 and the equation 20y = 12x + 88 represents coincidental  lines

Step-by-step explanation:

-3x + 5y = 22 (equation 1)

Lets solve the equation for y

Add 3x on both sides

5y= 3x+22

Now divide by 5 on both sides

[tex]y=\frac{3x}{5}+ \frac{22}{5}[/tex]

Slope of equation 1 is [tex]\frac{3}{5}[/tex]

20y − 11 = 12x (equation 2)

solve for y

Add 11 on both sides

20y = 12x + 11

Divide by 20 on both sides

[tex]y=\frac{12x}{20}+ \frac{11}{20}[/tex]

simplify the fraction

[tex]y=\frac{3x}{5}+ \frac{11}{20}[/tex]

Slope of equation 2 is [tex]\frac{3}{5}[/tex]

Slope of equation 1  and equation 2  are same , so the lines are parallel

This system of linear equations represents parallel lines.

-3x + 5y = 22 (equation 1) and 20y = 12x + 88

Solve both equations for y

-3x + 5y = 22 (equation 1)

[tex]y=\frac{3x}{5}+ \frac{22}{5}[/tex]

Slope of equation 1 is [tex]\frac{3}{5}[/tex] and y intercept is 22/5

20y = 12x + 88

Divide by 20 on both sides and simplify the fraction

[tex]y=\frac{3x}{5}+ \frac{22}{5}[/tex]

Slope of 20y=12x+88 is [tex]\frac{3}{5}[/tex] and y intercept is 22/5

Slope and y intercepts are same so the lines are coincidental

The system of equation 1 and the equation 20y = 12x + 88 represents coincidental  lines

See the attached picture:

The fraction 7/25 translates to the decimal 0.28 in mathematics.

In the question, we are to translate the fraction 7/25 to a decimal. This is a straightforward conversion in the field of mathematics. To convert this fraction to a decimal, we divide the numerator (the top number) by the denominator (the bottom number), yielding 7 ÷ 25 = 0.28. Therefore, the fraction 7/25 is equivalent to the decimal number 0.28 when rounded to two decimal places.

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Hey there.

To do this, we simply just subtract. 88,003-87,845

Once we do this, we get 158. Miguel traveled 158 miles that week.

-TheOneandOnly003

Answer:

87,845-88,033= -188 so he traveled 188 miles that week.

x - price of one pair socks

The equation:

[tex]5(2x)+5\times12=125[/tex]

[tex]10x+60=125[/tex]       subtract 60 from both sides

[tex]10x=65[/tex]      divide both sides by 10

[tex]\boxed{x=6.5}[/tex]

5(2x) - five sisters · two pairs of socks

5 · 12 - five scraves

125 - total cost

Answer:

11 3/8 watts

Step-by-step explanation:

1 7/8 converts to 1.875

4 3/4 converts to 4.75

4.75 * 2 = 9.5

9.5 + 1.875 = 11.375

11.375 converts to 91/8 or 11 3/8

Answer:

The loose sweets at ?0.89 for 100 g.

Step-by-step explanation:

First, calculate the price per gram. You do this by dividing the price by the grams.

?1.49 / 120 g =  1.49 / 120 = 0.0124 (4 dp)

Because the answer was very long, I have rounded it to 4 decimal places (4 dp).

?0.89 / 100 g = 0.89 / 100 = 0.0089

Next, you must calculate both pre-packed and loose sweets to the same weight. I am calculating them both to 100 g.

0.0124 x 100 = 1.24

0.0089 x 100 = 0.89

Finally, the cheapest product for 100 g will be the better value. In this case, it is the loose sweets.

Answer:

$245

Step-by-step explanation:

Orignal price for shirt was 105

Original price for shoe sizes was 140

105+140=245

Answer:

6 miles

Step-by-step explanation:

AS Mike took the taxi from his home to airport and covered a distance

Initial fee of the ride was $ 6 which is fixed

Now with each mile he has to pay $3

Total he paid = $ 24

Now we have to find the total no of miles traveled  by Mike

The tip given is 0

Now from the given we can make an equation

Initial fee + 3 * miles traveled =  total Paid

Let total no of miles traveled are x

Putting all the values in the given equation

6 + 3 * x = 24

6 + 3x = 24

3x = 24-6

3x = 18

Dividing both sides by 3

x = 18 /3

x =6 miles

So the total miles traveled by him is 6 miles

The equation is $6 + $3 *m = $24, where m represents the number of miles traveled. Solving this, Mike traveled 6 miles.

The student's question concerns calculating the distance Mike traveled by taxi, given the initial fee and the per mile charge, as well as the total fare. To solve this, we can set up a simple algebraic equation. The initial fee is $6, and the charge per mile is $3. Since the total fare was $24, our equation becomes:

Initial fee + (charge per mile * number of miles) = Total fare

$6 + $3 * m = $24

Where m represents the number of miles Mike traveled. We will solve for m to find the distance Mike traveled

Thus, Mike traveled 6 miles by taxi on this ride.

Answer:

m ≤ 27  or m > 11

m is all real number since we have the or

Step-by-step explanation:

m − 11 ≤ 16 or 15 − 2m < −7

Lets solve the one on the left first

m − 11 ≤ 16

Add 11 to each side

m-11+11 ≤ 16 +11

m ≤ 27

Now lets solve the one on the right

15 − 2m < −7

Subtract 15 from each side

15 −15- 2m < −7 -15

-2m < -22

Divide by -2, remembering to flip the inequality

-2m/-2 > -22/-2

m > 11

Answer:

AD>EC

Step-by-step explanation: If you look at the two traingles, angle AD is a bit larger than angle EC, this is due to the degrees of the angles, EC-> 25,

AD-> 30, this makes the triangle of AD, greater than EC.

To know if a dilation is an expansion ( bigger) r a contraction ( smaller) ignore the negative sign.

If the number is larger than 1, it is an expansion, if the number is smaller than 1 it is a contraction.

-4 is an expansion

2.5 is an expansion

2/3 is a contraction

-3/4 is a contraction

The length of {MZ} will be equivalent to -

MZ = 4 - 2x.

Given is that M is the midpoint of YZ. Also, it is given that YM = x + 3, and YZ = 3x - 1.

We can write -

YM + MZ = YZ

(x + 3) + MZ = (3x - 1)

MZ = (x + 3) - (3x - 1)

MZ = x + 3 - 3x + 1

MZ = 4 - 2x

Therefore, the length of {MZ} will be equivalent to -

MZ = 4 - 2x.

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Answer:

Final answer is y=3x-2.

Step-by-step explanation:

We have been given a graph and using that graph we need to find the equation of line.

Equation of line is given by formula y=mx+b

Where b is the y-intercept.

We see that graph crosses y-axis at (0,-2) so that means b=-2

Now plug b=-2 into formula y=mx+b. We get:

y=mx-2 ...(i)

Now find any point from the graph say (1,1) and plug into (i) to find value of slope m

1=m*1-2

1=m-2

1+2=m

3=m

Now plug m=3 into (i). We get:

y=3x-2

Hence final answer is y=3x-2.

By establishing and solving the equation c + 23 = 42, where c represents the number of cows in the barn, it is demonstrated that c = 19 is indeed a correct solution to the problem.

The student needs to determine if c=19 is a solution for the equation representing the number of cows still in the barn. To represent the total number of cows with those seen outside and those inside, we can write the equation c + 23 = 42. This equation sums the number of cows outside (23) with those still in the barn (c) to get the total number of cows (42).

Calculating the Unknown

Firstly, define the symbol c as the number of cows still in the barn. Then, using our equation c + 23 = 42, we can solve for c by subtracting 23 from both sides of the equation, getting c = 42 - 23, which simplifies to c = 19.

Evaluating the Solution

Substituting c = 19 back into the original equation to check if it makes sense, we get 19 + 23 = 42, which is a true statement, confirming that the value of c is indeed 19 and it is the correct solution.

Answer:

Option C -M'K' is the same length as MK

Step-by-step explanation:

Given : Line segment MK has endpoints at (2, 3) and (5,4)

               M'K' is the reflection of MK over the y-axis

By definition of reflection: reflection of point (x,y) across the the y-axis is the point (-x,y)

which implies M'K' has end points (-2,3) and (-5,4)

Now, we find the length of MK

let [tex](x_1,y_1)=(2,3)\\\\(x_2,y_2)=(5,4)[/tex]

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

⇒ [tex]d=\sqrt{(2-5)^2+(4-3)^2}[/tex]

⇒[tex]d=\sqrt{9+1}[/tex]

⇒[tex]d=\sqrt{10}[/tex]   ....(1)

Now, we find the length of M'K'

let [tex](x_1^{'},y_1^{'})=(-2,3)\\\\(x_2^{'},y_2^{'})=(-5,4)[/tex]

[tex]d^{'}=\sqrt{(x_2^{'}-x_1^{'})^2+(y_2^{'}-y_1^{'})^2}[/tex]

⇒ [tex]d^{'}=\sqrt{(-2+5)^2+(3-4)^2}[/tex]

⇒[tex]d^{'}=\sqrt{9+1}[/tex]

⇒[tex]d^{'}=\sqrt{10}[/tex] .....(2)

from (1) and (2) we simply show that the length of MK and M'K' is equal

we can also refer the figure attached for reflection of MK and M'K'

therefore, Option C is correct

Answer:

M'K' is the same length as MK.

Step-by-step explanation:

A reflection is a rigid transformation. Rigid transformations do not affect the length of the line segment

Answer:

Two sevenths

Step-by-step explanation:

Final answer:

To find the probability that everyone in the group is a girl, we use the combination formula to calculate the number of ways to choose a group of 3 from 7 students and the number of ways to choose 3 girls from the 5 available. The probability is 2/7.

Explanation:

To find the probability that everyone in the group is a girl, we need to consider the total number of ways to choose a group of 3 from the 7 students, and the number of ways to choose 3 girls from the 5 available.

The total number of ways to choose a group of 3 from 7 is given by the combination formula, which is:

C(7, 3) = 7! / (3! * (7-3)!) = 35

The number of ways to choose 3 girls from 5 is:

C(5, 3) = 5! / (3! * (5-3)!) = 10

Therefore, the probability that everyone in the group is a girl is:

P(girls) = C(5, 3) / C(7, 3) = 10 / 35 = 2/7

Answer:

Go to graphing website desmos.com and plug the equation in to see graph

Step-by-step explanation:

1) Starting graph: Linear Graph (x)  

Translations:

|x| erase left and copy right, in this case it makes an absolute value graph or a "V graph" informal term

-3(move right)

-2(down 2)

2) Order goes as follows: "||", -3, -2

Graph: see attached

Translations:

The parent graph is y = |x|

a horizontal shift 3 units to the right makes a new graph of: y = |x - 3|

a vertical shift 2 units down makes a newer graph of: y = |x - 3| - 2

Translations are as follows:

Answer:

1 1/4 mph

Step-by-step explanation:

Distance = rate x time

1/2 mile = R x 2/5 hour

1/2=2/5R

/2/5 /2/5

R=1/2 x 5/2

R=1 1/4

I hope this helps :)

Answer: Their balance at the beginning of their second month is $2803.86.

Step-by-step explanation:

Since we have given that

Amount on credit card = $2745.69

APR on credit card = 12.75%

Late fee = $29

According to question, they miss their minimum payment .

So, their balance at the beginning of their second month is given by

[tex]2745.69\times \frac{12.75}{12\times 100}\\\\=29.17\\\\\text{After late fees }=29.17+29\\\\=58.17\\\\\text{ Amount in the beginning of their second month }\\\\=\$2745.69+58.17\\\\=2803.86[/tex]

Hence, their balance at the beginning of their second month is $2803.86

Answer:

2,803.86

Step-by-step explanation:

Answer: (9 CDs)

If she has $45 and the CDs cost $5. The most she can buy is 9 CDs

The number of maximum CDs that Jennifer can buy is 9.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Division = divide any two numbers or variables called division.

As per the given,

Cost of one CD = $5

Jennifer budget = $45

Number of CDs can buy = Jennifer's budget/cost of one CD

Number of CDs can buy = 45/5 = 9

Hence "The number of maximum CDs that Jennifer can buy is 9".

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Answer:

23

Step-by-step explanation:

46 divided by 2

equals:23