What is the volume of a cuboid measuring 5cm by 6cm by 7cm

Answers

Answer 1
Answer: Volume of a cuboid:

a x b x c = abc

5 cm * 6 cm * 7 cm = 210 cm³

hope this helps!

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The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain? A. {5, 8} B. {-5, -8} C. {3, 8} D. {4, 7} E. {4, 8}

Answers

Answer:

Option D

The domain of the function is: {4, 7}

Step-by-step explanation:

We know that for polynomial functions like f(k) = k^2 + 2k + 1 its domain and its rank are all real numbers. However, for this case we are told that the function range is: the set {25, 64}

This means that the function is bounded.

Then the domain of f(k) are all possible values of k such that f(k) belongs to the interval {25, 64}.

To find the limit values of k then we do f(k) = 25

k^2 + 2k + 1 = 25

k^2 + 2k -24 = 0

Now we factor the expression:

(k + 6)(k-4) = 0

Then k = 4 and k = -6.

Now we do f(k) = 64

k ^ 2 + 2k +1 = 64\n\nk ^ 2 + 2k -63 = 0

We factor the expression:

(k + 9)(k-7) = 0

k = -9 and k = 7.

Finally we search between the options given an interval that matches.

The option that matches is option D {4, 7}

Finally, the domain of the function is: {4, 7}

29 feet = how many yards and how many feet?

Answers

All you do is divide by three to get 9.667 which is 9 and 1/3 feet
29 feet = 29 feet

29 feet = x yards

1 foot = 0.333333 yard

0.333333 × 29 = 9.666657

SO 

29 feet ≈ 10 yards (about)

Hope I helped ya!!

amber invested 25000 at 2% for 3 years compound simiannually.Find future value at the end of 3 years?

Answers

Use the compound interest formula:

A = P(1+r/n)^(nt). Here, P = $25000, r = 0.02, t = 3 and n = 2.

Then:

A = $25000(1 + 0.02/2)^(3*2)

= $25000(1.01)^6

= $26538.00 (future value at the end of 3 years)

First you use the compound interest formula which is: A = P(1+r/n)^(nt).

Plug in the number in this case being P = $25000, r = 0.02, t = 3 and n = 2.

A = $25000(1 + 0.02/2)^(3*2)

= $25000(1.01)^6

= $26538.00 (future value at the end of 3 years)

A square is drawn inside a circle so that its vertices touch the circle.if the radius of the circle is 15cm, what is the perimeter of the square?

Answers

Answer:

the perimeter of the square is 60cm

Step-by-step explanation:

because 15 X 4 =60cm

Please help me with these questions

Answers

Besides posting the answers, I also included the solution to solve similar simplification of algebraic expressions questions. :)

A triangle has an angle that measures 80°. The other two angles are in a ratio of 7:13. What are the measures of those two angles?

Answers

The angles are B and C.


The three angles add up to 180º
A=80º
B
C

A+B+C=180º
80º+B+C=180º
B+C=180º-80º
B+C=100º  (1)

The ratio between A and B is 7/13 ; therefore:
B/C=7/13  ⇒B=7C/13    (2)

With the equations (1) and (2), we make a system of equations:

B+C=100
B=7C/13

We can solve this system of equations by substitution method:
7C/13  + C=100
least common multiple=13
7C+13C=1300
20C=1300
C=1300/20
C=65

B=7C/13
B=7*65/13
B=455/13
B=35º

Answer: The measures of those two angles are 65º and 35º.