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2 years ago

The area of a rectangular table top is square meters. If the top of the table is meter long, what is its width?

Mathematics

1 answer:

TEA [102]2 years ago

6 0

Ok
so i think you would need to add around the table and then you got the answer

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Write an explicit rule in function form for the sequence represented by the given terms.

hram777 [196]

Answer:

The general relation about a geoemtric sequence is

$a_{n}=a_{1}r^{n-1}$

For the first sequence, we have

$3=a_{1}r^{5-1}$

$147=a_{1}r^{7-1}$

Which is a system of equations. We can isolate a variable in the first equation to replace that expression into the second equation.

$a_{1}=\frac{3}{r^{4} }$

$147=\frac{3}{r^{4} }r^{6}$

$r^{2}=\frac{147}{3}\\ r=\sqrt[2]{49}\\r=7$

Now, we replace this value to find the other one

$3=a_{1}(7)^{4}\\ a_{1}=\frac{3}{2401}$

Therefore, the explicit rule function is

$a_{n}=\frac{3}{2401} \times (7)^{n-1}$

Now, we use the same process for the second sequence.

$10=a_{1}r^{3-1} \\a_{1}=\frac{10}{r^{2} }$

The second equation is

$1440=a_{1}r^{5-1}\\a_{1}=\frac{1440}{r^{4} }$

Now, we solve the following expression

$\frac{10}{r^{2} }=\frac{1440}{r^{4} }$

We solve for $r$

$\frac{r^{4} }{r^{2} }=\frac{1440}{10}\\r^{2}=144\\ r=\sqrt{144} \\r=12$

Then

$a_{1}=\frac{10}{(12)^{2} } =\frac{10}{144}=\frac{5}{72}$

Therefore, the function that models the second sequence is

$a_{n}=\frac{5}{72} \times (12)^{n-1}$

Notice that $a_{n}$ is the dependent variable and $n$ is the independent variable.

5 0

3 years ago

Consider the circle with an equation in standard form: ( x – 4)² + ( y + 2)² = 36 . Explain in 2-3 sentences or explain the step

iragen [17]

Answer:

The center of this circle is found at (4, -2) and the radius is 6.

Step-by-step explanation:

The equation for a circle in standard for is ( x – h)² + ( y - k)² = r². In this equation, (h, k) is the center of the circle and r is the radius.

From the given equation, ( x – 4)² + ( y + 2)² = 36, h is already subtracted from x, so h = 4, but the k is not subtracted, so (y + 2) = [y - (-2)], and we see that k is -2. Therefore, the center of the circle is (4, -2) and 36 = r². By taking the square root of 36, we find that r = 6.

The center of this circle is found at (4, -2) and the radius is 6.

4 0

2 years ago

A student is attempting to factor a polynomial. Sample mathematical work is shown below. Which statement best applies to the sam

Murljashka [212]

Answer:

I believe it is B. The student incorrectly divided each term by the greatest common factor.

Step-by-step explanation:

3 is the correct greatest common factor of 3x+6, but it wouldn't be 3(x+3). If the student correctly divided each term, it would be 3(x+2). I hope this helps!

4 0

2 years ago

What are the numbers between 8 and 9

madreJ [45]

Answer:

The numbers between 8 and 8

9 is 8.5

8, 8.5, 9

5 0

1 year ago

Read 2 more answers

If the hypotenuse is 41 and one of the legs is 40 what is the length of the other leg

-Dominant- [34]

The length of the other leg is 9 inches

4 0

2 years ago