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3 years ago

An arithmetic sequence is defined by the recursive formuala t1=9,tn=tn-1-4 where n enand n>1 the seuence s

1 answer:

8 0

It's not clear what you're supposed to do, but I would guess that you're asked to find a certain term in the sequence.

Given

$\begin{cases}t_1=9\\t_n=t_{n-1}-4&\text{for }n>1\end{cases}$

you can do that by solving for $t_n$ explicitly.

$t_n=t_{n-1}-4=t_{n-2}-2\times4=t_{n-3}-3\times4=\cdots=t_1-(n-1)\times4$

So the explicit formula for the $n$ th term is

$t_n=9-4(n-1)=13-4n$

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David and Karen are building a treehouse in the shape of a rectangular prism for their daughter.If the treehouse is going to 5 f

Serga [27]

The space left inside the tree is 300 cubic feet.

David and Karen have to paint 275 square feet on the outside.

Explanation:

It is given that the length of the tree house is 7.5 feet

The width of the tree house is 8 feet

The height of the tree house is 5 feet

The tree house is in the shape of a rectangular prism.

The volume of the rectangular prism is given by

$\text {Volume}=\text {length } \times \text {width} \times \text {height}$

Substituting the values, we have,

$Volume$=7.5 \times 8 \times 5$\\Volume $=300$$

Thus, the volume of the rectangular prism is 300 cubic feet

Hence, the space left inside the tree is 300 cubic feet.

The area they have to paint on the outside can be determined using the formula for surface area of the prism .

$Area=2(w l+h l+h w)$

Substituting the values, we get,

$Area=2[(8*7.5)+(5*7.5)+(5*8)]$

Multiplying the terms within the bracket, we get,

$Area=2(60+37.5+40)$

Adding the terms, we have,

$Area=2 \times 137.5$

Multiplying, we get,

$Area =275$

Thus, David and Karen have to paint 275 square feet on the outside.

6 0

3 years ago

Write the following inequality in slope-intercept form -6x+2y is greater than on equal to 42

andreyandreev [35.5K]

Answer:

$\large\boxed{y\geq3x+21}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

$-6x+2y\geq42\qquad\text{add}\ 6x\ \text{to both sides}\\\\2y\geq6x+42\qquad\text{divide both sides by 2}\\\\y\geq3x+21$

4 0

4 years ago

There are 12 pieces of candy in a bowl. 6 are mints, 4 are Butterscotch, and 2 are Cinnamon.

Alecsey [184]

Answer:

6/12

Step-by-step explanation:

I think that's right because once you put that mint back it's not decreasing in value so it would stay as 6/12

3 0

3 years ago

When you divide 7.7 by 700, how many decimal places will the quotient have?

Nikolay [14]

The answer would be 0.011 so there would be three decimal places

4 0

3 years ago

Write the equation of the hyperbola with foci at (1, 5) and (7, 5) and with vertices at (2, 5) and (6, 5).

mash [69]

If you plot the points given on a coordinate plane you see that this is a hyperbola that is is horizontal in nature, meaning it opens side to side, not up and down. We can determine the center of it by taking the point equidistant from the vertices, which is (4, 5), the h and k of our center, respectively. Also, the equation looks like this when it is horizontal: $\frac{(x-h) ^{2} }{ a^{2} } - \frac{(y-k) ^{2} }{ b^{2} } =1$ . a is the distance between the center and the vertices, so our a = 2, and c is the distance between the center and the foci, so our c = 3. We need to find b now, using Pythagorean's theorem. $( 2)^{2} + b^{2} =( 3)^{2}$ and $b= \sqrt{5}$ . Now we have everything we need to rewrite the equation: $\frac{(x-4) ^{2} }{4} - \frac{(y-5) ^{2} }{5} =1$

6 0

3 years ago