The sum of three consecutive odd numbers is 39. What is the smallest of these numbers?

"Which shapes are topologically equivalent to Choice 2?

DanielleElmas [232]

<span>Which shapes are topologically equivalent to Choice 2? D. NONE

Choice 1, 3, and 4 are topologically equivalent. These figures each have two holes.

Choice 2 has three holes and is different from the other.

Topologically equivalent figures are figures that can be rearranged to form another shape without breaking.</span>

8 0

3 years ago

Nicolas has $6,500 to deposit into an account which earns 3.25% interest compounded annually. How interest will he have earned a

agasfer [191]

We have been given that Nicolas has $6,500 to deposit into an account which earns 3.25% interest compounded annually. We are asked to find amount of interest earned at the end on 8 years.

We will use compound interest formula to solve our given problem.

$A=P(1+\frac{r}{n})^{nt}$ , where,

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years.

$3.25\%=\frac{3.25}{100}=0.0325$

$A=6500(1+\frac{0.0325}{1})^{1\cdot 8}$

$A=6500(1+0.0325)^{8}$

$A=6500(1.0325)^{8}$

$A=6500(1.2915775352963673)$

$A=8395.253979$

Now we will subtract principal amount from final amount to find amount of interest as:

$\text{interest}=8395.253979-6500$

$\text{interest}=1895.253979\approx 1895.25$

Therefore, Nicolas would have earned $1895.25 in interest at the end of 8 years.

7 0

3 years ago

A farmer has a square garden that has an area of 100 feet squared. He needs to

stellarik [79]

Answer:

40ft

Step-by-step explanation:

The shape of the garden (square) tells you that both the length and the width of the garden are the same measure.

If the area is 100sqft, you can determine that side * side = 100. To find this answer, you can take the square root of 100. side=10, because 10 * 10= 100 (the area).

Now, we know that each side measures 10 feet. Try drawing and labeling a picture to help you visualize the garden. Next, label each side of the square garden 10ft. To find the feet of fencing is needed to enclose the garden,

We need to find the perimeter, so we can calculate

10ft * 4 sides = 40 feet of fencing.

5 0

3 years ago

There is a 12-ft fence on one side of a rectangular garden. The gardener has 44 ft of fencing to the enclose the other three sid

Morgarella [4.7K]

Answer:

16 ft

Step-by-step explanation:

One of the other three sides is 12 ft. After that fence is subtracted from the total, there are 32 ft of fence left for the other two sides of the rectangle. That allows those sides to be 32 ft/2 = 16 ft long.

The rectangle can be 12 ft by 16 ft. The longer dimension is 16 ft.

7 0

3 years ago

Some students are trying to write an expression with fewer terms that is equivalent to 8 - 3(4 - 9x). Noah says, "I worked the p

Irina-Kira [14]

Answer: Yes I agree with Jada. His approach is correct.

Step-by-step explanation: The question requires the student to write an equivalent equation with fewer terms. Nonetheless, this does not prevent applying a mathematically correct approach.

(1) Noah is wrong and the reason is that the initial step is mathematically incorrect. The expression on the right hand side reads 3(4 - 9x), therefore starting with "8 - 3" is very wrong. The right step was to take one side which is 8 and take the other side which is 3(4 - 9x).

(2) Lin is wrong and the reason is that she started inside the parenthesis and this also is mathematically incorrect. The digits inside the parenthesis are "not like terms" and hence calculating 4 - 9x = -5x is very incorrect (the same way you cannot correctly calculate 500 metres minus 200 inches. You must make sure they are both in meters or in inches, that is both must be like terms).

(3) Jada is very correct in using the distributive property and ended up with the only correct solution. The digits on the right hand side of the expression was solved first and that resulted in -12 + 27x. The reason being that the number outside the parenthesis which is -3, multiplied both digits inside the parenthesis. The minus sign had a major effect, and after simplifying the right hand side the expression now becomes;

8 - 12 + 27x

Since the like terms are 8 and 12, you can simplify further to become

- 4 + 27x OR the expression can be rearranged as 27x - 4

(4) Andre is not correct and the reason is that although he used the distributive property, he made a slight mistake while solving for the right side of the expression. What Andre did was

-3(4 - 9x)

-12 - 27x

Remember that when a negative value multiplies another negative value the answer is positive. Therefore -3 times -9x should have been +27x, just like Jada did as shown above.

From that point onward, his answer would be incorrect.

5 0

3 years ago