can someone help me with this question please

Ronald opened a savings account and deposited 100.00 as principal the account 2% interest compounded annually. What is the balance after 8 years?

_____________________________________________________________

Interest compounded

A = P(1 + r/n)^nt

A= final amount (P + Interest )

P= incial amount

r= Interest

n= compounding periods (year)

t= time

________________________

Data

A = P(1 + r/n)^nt

P= 100.00

r= 0.02

n= 1 (compounded annually)

t= 8

_______________

A = 100.00 (1 + 0.02 /1)^1* 8

A = 117.17

_______________

Answer

The balance after 8 years is 117.17

________________

Do you have any questions regarding the solution?

If you don’t need further explanation on this question, we can end the session.

I want to remind you this answer will always be saved in your profile. I’d really appreciate you letting me know how I did by rating our session after you exit. Thanks and have a great day!

A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.

One possible set could be 3 cm, 4 cm, and 5 cm.

To verify if this set forms a right triangle, we can apply the Pythagorean theorem.

Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.

Adding these two values together gives us 25.

Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.

It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.

There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.

These sets are known as Pythagorean triples.

Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.

In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

For similar question on hypotenuse's.

https://brainly.com/question/30390037  

#SPJ8

Answer:

1 - 9/16

Step-by-step explanation:

The whole is 1 or 16/16. The number of blue tiles is 9. It's represented as 9/16.

so we take 9/16 from the whole.

1 - 9/16

To calculate the total surface area of a triangular prism, we need to find the area of each face and add them up.

The triangular faces have base 5cm and height 12cm, so each one has an area of:

(1/2) x 5cm x 12cm = 30cm²

There are two of these faces, so their combined area is:

2 x 30cm² = 60cm²

The rectangular faces have dimensions 5cm x 10cm and 5cm x 13cm, so their areas are:

5cm x 10cm = 50cm²

5cm x 13cm = 65cm²

Again, there are two of these faces, so their combined area is:

2 x (50cm² + 65cm²) = 230cm²

Finally, we add up the areas of all the faces to get the total surface area:

60cm² + 230cm² = 290cm²

Therefore, the total surface area of this triangular prism is 290cm².

9514 1404 393

Answer:

  y = 8

Step-by-step explanation:

You will get the same value for y whether you approach the problem by making corresponding angles equal, or by making corresponding sides equal. The equation for the sides takes less work to solve.

  2y -3 = y +5

  y = 8 . . . . . . . . add 3-y to both sides

_____

Check

This value of y makes the angles ...

  (6y -5)° = (6·8 -5)° = 43°

  (4y +11)° = (4·8 +11)° = 43°

Corresponding angles and the side between them have the same measures, so the triangles are congruent by ASA.

Answer:

-16

Step-by-step explanation:

Step 1: Solve absolute value of |-4|

Step 2: Multiply -4 by 4.

Therefore, the answer is -16.

Answer:

-16

Step-by-step explanation:

the number on the inside always becomes positive so it should be -4|4|

then multiply -4×4=-16

Answer:

2y2+9y−10

Step-by-step explanation:

Distribute the Negative Sign:

=−2y2+6y−1+−1(−4y2−3y+9)

=−2y2+6y+−1+−1(−4y2)+−1(−3y)+(−1)(9)

=−2y2+6y+−1+4y2+3y+−9

Combine Like Terms:

=−2y2+6y+−1+4y2+3y+−9

=(−2y2+4y2)+(6y+3y)+(−1+−9)

=2y2+9y+−10

Answer

5k dollars

Step-by-step explanation:

The midpoint is 26.

Midpoint in this scenario = mean

(23+29)/2 = 26

Answer:

-6

Step-by-step explanation:

The probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To find the probability that Greg winds up wearing the white shirt and tan pants while getting dressed in the dark, we need to find out all the possible outfit options. According to the question given, first we nned to find out number of outfit combinations possible.

Total number of Outfit Combinations:

There are 4 shirts: a white one, a black one, a red one, and a blue one and also two pairs of pants, one blue and one tan. So, total number of possible outfit combinations would be 4 * 2 = 8.

No of favourable options:

As given in the question, Greg wears white shirt and tan pants. There is only one white shirt and one tan pant. So, number of favourable options would be only 1 .

Probability = Number of favourable outcomes/Total no. of combinations

Probability = 1/8

Probability = 0.125 or 12.5%

Therefore, the probability, if Greg gets dressed in the dark, that he winds up wearing the white shirt and tan pants is 0.125 or 12.5%.

To study more about Probability:

https://brainly.com/question/13604758

https://brainly.com/question/251701

Answer:

Step-by-step explanation:

-4x-3=y

Answer:

For the LCM : 80 and the GCF is 8

Step-by-step explanation:

Answer:

For the LCM : 80 and the GCF is 8

Step-by-step explanation:

Want free points?! Want free brainliest?! Come to my profile and just answer one of my questions. I am YOUR community builder who gives free things. ("Thanks" on ur profile, points, hacks, brainliest, etc.)

Put me as brainliest so I can receive 50% more points!

Answer:

32 units squared

Step-by-step explanation:

Split up the figure into easy to find area parts. So, theres 2 triangles, and in the middle of those, you can make a square. And that would make the top part a large triangle! Now find the area of these

Large triangle: 1/2 (4)(10) = 20

Smallest triangle: 1/2(2)(2) = 2

Medium triangle: 1/2(6)(2) = 6

Square: 2*2 = 4

Now add them all up! 20+2+6+4 = 32 units squared!

Answer:6.25

Step-by-step explanation:1.25x5=6.25

Answer:

$6.25

Step-by-step explanation:

1.25 × 5 = 6.25

hope this helps...

Answer:

x > 5

Step-by-step explanation:

add 3 to both sides

9x-3>5x+17

+3      +3

9x>5x+17+3

Simplify

9x > 5x + 20

Subtract 5x from both sides

9x > 5x + 20

-5x      -5x

= x = 5

Hope This Helped

Answer:

200

Step-by-step explanation:

factors of 125 are 1, 5, 25, 125

factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100 and 200.

Based on the number of factors of the two numbers, the number with more factors is 200.

The factors of 125 are:

The factors of 200 are:

The factors of 200 are 12 in total while that of 125 are only 4.

In conclusion, 200 has more factors than 125.

Find out more about factors at https://brainly.com/question/596862.

Answer:

B

Step-by-step explanation

We have

using a graph tool

see the attached figure

The solution of the system is the shaded area

we know that

The line is solid

The line passes through points and and is shaded above the line.

The line is solid

The line passes through points and and is shaded below the line

The two lines intersect at one point

therefore

the answer is the option

B) Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded above the line.

The square of a binomial, when the binomials are subtracted, is defined as follows:

(a - b)² = a² - 2ab + b².

When the two binomials are added, the square is given as follows:

(a + b)².

Expanding the square, we have that:

(a + b)² = (a + b) x (a + b).

(a + b)² = a² + ab + ab + b².

(a + b)² = a² + 2ab + b².

Which is the result presented in this problem.

Now, when the binomial has a minus sign, involving a subtraction, the pattern is obtained as follows:

(a - b)² = (a - b) x (a - b).

(a - b)² = a² - ab - ab + b².

(a - b)² = a² - 2ab + b².

More can be learned about the square of a binomial at https://brainly.com/question/12336181

#SPJ1

Explanation:

On the third line is where the student went from -12-3 to -9. This is not correct. Instead, it should be -12-3 turning into -15.

Think of it like being 12 feet under water (the number -12) and then moving 3 more feet deeper under water. You'll move down 3 to get to -15 to represent being 15 feet under water. Use a vertical number line if needed.

You can also compute -12-3 like 12+3 = 15, then just make everything negative. So -12-3 = -15

It is recommended that you visit your courses on D2L frequently, ideally at least once a day, to stay up-to-date with any new announcements or assignments posted by your instructor. This will help you stay on track with your coursework and prevent you from falling behind. Additionally, regular visits to your courses can help you participate in discussions with your peers and ask questions if you are unsure about any of the material. It's important to remember that online learning requires a high level of self-discipline and responsibility, so making a habit of checking in on your courses regularly can contribute to your overall success in the class.

Triangle ADC also has a right angle at D, making it a right-angled triangle.

The exact value of x be 2.25.

The hypotenuse's square is equal to the sum of its two other side squares of a right-angled triangle, according to the Pythagoras theorem.

Triangle ADB exists even a right-angled triangle with right-angle at D.

Therefore, Base of Triangle ADB = BD = 4,

Height of Triangle ADB = AD = 3,

Hypotenuse of Triangle ADB = AB

Using the Pythagoras Theorem, we get,

\($\left[(A D)^2+(B D)^2\right]=(A B)^2$\)

substitute the values in the above equation, we get

or,\($(A B)^2=\left[(3)^2+(4)^2\right]$\)

simplifying the equation, we get

or, \($(A B)^2=[9+16]$\)

or, \($(A B)^2=25$\)

or, \($\sqrt{(A B)^2}=\sqrt{25}$\)

or, AB = 25

Triangle ADC is also a right-angled triangle with right-angle at D.

Therefore, Base of Triangle ADC = DC = x

Height of Triangle ADC = AD = 3,

And, Hypotenuse of Triangle ADC = AC

Using the Pythagoras Theorem, we get,

\(& {\left[(D C)^2+(A D)^2\right]=(A C)^2} \\\)

simplifying the equation, we get

\(& \text { or },(A C)^2=\left[(3)^2+(x)^2\right] \\\)

\(& \text { or },(A C)^2=\left[9+x^2\right]\)

Triangle ABC is also a right-angled triangle with right-angle at A. Therefore, Base of Triangle ABC = AC,

Height of Triangle ABC = AB = 5,

And, Hypotenuse of Triangle ABC =  BC = (4 + x)

Using the Pythagoras Theorem, we get,

\(& {\left[(A C)^2+(A B)^2\right]=(B C)^2} \\\)

\(& \text { or, }(B C)^2=\left[(A C)^2+(A B)^2\right] \\\)

substitute the values in the above equation, we get

\(& \text { or, }(4+x)^2=\left[\left(9+x^2\right)+(5)^2\right] \\\)

simplifying the equation, we get

\(& \text { or, }\left[4^2+(2 \times 4 \times x)+x^2\right]=\left[9+x^2+25\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]=\left[(9+25)+x^2\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]=\left[34+x^2\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]-\left[34+x^2\right]=0 \\\)

\(& \text { or, },(16-34)+8 x+\left(x^2-x^2\right)=0 \\\)

8x - 18 = 0

8x = 18

\(& \text { or, } x=\frac{18}{8} \\\)

\(& \text { or, } x=\frac{9 \times 2}{4 \times 2} \\\)

\(& \text { or, } x=\frac{9}{4} \\\)

Therefore, the value of x be 2.25.

To learn more about Pythagoras Theorem refer to:

https://brainly.com/question/343682

#SPJ1

The true statements are;

1) AB + BC = AC

Length of BC = |6 - 1|

2) ∠JMK = 50°

∠KML = 35°

1) From the given number line interval, we can deduce the interpretation as follows;

AB + BC = AC

Length of BC = 5 units or |6 - 1|

Length of B = 3 Units

2) We can see that ∠JML is an angle triangle. Thus, ∠JML = 85°. Thus;

6x + 2 + 4x + 3 = 85

10x + 5 = 85

10x = 85 - 5

10x = 80

x = 80/10

x = 8°

Thus;

∠JMK = 6(8) + 2

∠JMK = 50°

∠KML = 85° - 50°

∠KML = 35°

Read more about Number Line Intervals at; https://brainly.com/question/27998235

#SPJ1

Answer:

160

Step-by-step explanation:

Using Exterior angle theorem

30+130=160

Step-by-step explanation:

21x²-2x +1/2 = 0

x² - 2x ×21 + 1/2× 21 = 0

By considering these rules and properties of integers, the correct result of 6 was obtained.

When writing the response, I considered the following information:

The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.

To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.

To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.

This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.

By considering these rules and properties of integers, the correct result of 6 was obtained.

for such more question on integers

https://brainly.com/question/22008756

#SPJ8

Step-by-step explanation:

6.

the sum of all internal angles in a polygon is

(n-2)×180

n is the number of sides of internal angles.

now, that means that one internal angle of a regular polygon is

(n-2)×180/n

and we know that is 170°.

so,

170 = (n-2)×180/n

170n = 180n - 360

-10n = -360

10n = 360

n = 36

the polygon has 36 sides.

7.

a. is a rectangle or a square, as the fact that all 4 segments of the diagonals are equally long solid to both. after all, a square is just a special rectangle.

but given the picture that suggests different Legrand and widths it is a rectangle.

b.

parallelogram.

the 2 lengths are equal, and the 2 widths are equal. and therefore, both lengths are parallel and both widths are parallel.

but the angles are not 90°. so, it is not a rectangle, but still a parallelogram.

c.

isoceles trapezoid.

top and bottom sides are parallel, but if different size.

the left and right sides are equally long and inclined inwards.

8.

as explained in 7. : the 2 lengths are equal and parallel, and the 2 widths are equal and parallel.

also the diagonals intercept each other at their midpoints. so, both segments of a diagonal are equal.

the sum of all angles is still 360°, and the opposing angles are equal, while every pair of neighboring angles are together 180°.

and - the sum of all angles in a triangle is always 180°.

a. AD = BC = 7

b. DC = AB = 16

c. AC = 2×EC = 2×7 = 14

d. EB = ED = 10.2

angle DAB = angle BCD = 120°

angle ADC = angle ABC = 43 + x

e.

180 = 120 + 43 + x

60 = 43 + x

17° = x

so,

angle ABC = angle ADC = 43 + 17 = 60°

f. angle CDB = x = 17°

g. angle CBD = angle ADB = 43°.

because

180 = CDB + BCD + CBD

180 = 17 + 120 + CBD

43° = angle CBD

h. angle BCD = angle DAB = 120°.

Answer:

Question 6:

Question 7:

Question 8:

Step-by-step explanation:

The formula for calculating the interior angle of a regular polygon is:

\(\text{Interior angle}=\dfrac{(n - 2) \times 180^\circ}{n}\)

where n is the number of sides of the regular polygon.

To calculate the number of sides a regular polygon has if its interior angle is 170°, substitute this angle into the formula and solve for n.

\(\implies 170^{\circ}=\dfrac{(n - 2) \times 180^{\circ}}{n}\)

\(\implies 170n=180(n - 2)\)

\(\implies 170n=180n-360\)

\(\implies -10n=-360\)

\(\implies n=36\)

Therefore, a regular polygon with an interior angle of 170° has 36 sides.

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

Congruent lines are shown by placing the same number of tick marks on each congruent line segment.

Parallel lines are shown by placing the same number of arrows on each parallel line.

Shape a is a rectangle because the diagonals bisect each other and the length of the diagonals is equal, indicated by the tick marks.

Shape b is a parallelogram because it has two pairs of parallel opposite sides.

Shape c is an isosceles trapezoid because one pair of sides is parallel and the remaining sides are non-parallel and equal in length.

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

A parallelogram has opposite sides that are of equal length. Therefore:

The diagonals of a parallelogram bisect each other. Therefore:

Therefore, AC = AE + EC = 7 + 7 = 14

Same-side interior angles sum to 180°. Therefore:

⇒ m∠DAB + m∠ABC = 180°

⇒ 120° + m∠ABC = 180°

⇒ m∠ABC = 60°

The opposite angles of a parallelogram are equal. Therefore:

As m∠ADC = 60° and m∠ADE = 43° then:

According to the alternate interior angles theorem:

Answer:

10.74666666666667 per quart

Step-by-step explanation3 divided 36.24