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2 years ago

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A group of students is arranging squares into layers to create a project. The first layer has 5 squares. The second layer has 10

squares. Which formula represents an arithmetic explicit formula to determine the number of squares in each layer?

1 answer:

nignag [31]2 years ago

3 0

Answer:

$a_n=5n$

Step-by-step explanation:

They gave us the first two terms in the sequence which is 5,10.

They then tell us the sequence is arithmetic which means all you need to do to get the next term is add/subtract.

To get from 5 to 10, you would need to add 5.

So that is what we are doing every time here.

5,10,15,20,25,... so on...

Now we want to make an equation for this.

When you see arithmetic sequence, you should think linear equations.

x | y

-----------

1 5

2 10

3 15

4 20

Can you see the relationship between y and x?

Slope is 5 because that is what the sequence is going up by.

y=5x+b

Maybe you can already see b is 0. If not, you can use a point on the line to find b.

Let's use (1,5).

5=5(1)+b

5=5+b

0=b

So b=0.

The equation is y=5x.

Our since we are talking about sequences maybe you prefer to say $a_n=5n$

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On a coordinate plane, 2 quadrilaterals are shown. Quadrilateral Q R S T has points (negative 1, 0), (5, 0), (3.5, negative 6) a

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Answer:

$\dfrac{1}{3}$ .

Step-by-step explanation:

In quadrilateral QRST, Q(-1,0), R(5,0), S(3.5,-6), T(-2.5,-6).

In quadrilateral Q'R'S'T', Q'(-1,2), R'(1,2), S'(0.5,0), T'(-1.5,0).

Distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using distance formula , we get

$QR=\sqrt{(5-(-1))^2+(0-0)^2}=\sqrt{6^2}=6$

$Q'R'=\sqrt{(1-(-1))^2+(2-2)^2}=\sqrt{2^2}=2$

Now,

$\text{Scale factor}=\dfrac{Q'R'}{QR}$

$\text{Scale factor}=\dfrac{2}{6}$

$\text{Scale factor}=\dfrac{1}{3}$

Therefore the scale factor is $\dfrac{1}{3}$ .

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A map of Colorado says that the scale is 1 inch to 20 miles or 1 to 1,267,200. Are these two ways of reporting the scale the sam

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Answer:

1,267,200

Step-by-step explanation:

Given that the map reported that the scale is 1 inch to 20 miles.

Recall that there are 63,360 inches in 1 mile, thus, in 20 miles, we have 20 x 63,360 = 1,267,200

Therefore, the scale of 1 inch to 20 miles can also be represented as 1 to 1,267,200

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A study was conducted on the effects of divorce. Researchers gathered data from a random sample of 5,125 adults and measured qui

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Answer:

We can infer a cause-and-effect relationship because multiple variables were included.

Step-by-step explanation:

The multiple attributes for the divorced ones are

1) less physically active

2) an unhealthy weight,

3) smokers.

The attribute showing the % of the married is

1) death

So when we compare the two groups married and divorced we see different variables are involved in evaluating the percentage.

This shows a cause and effect involving multiple variables.

In cause and effect one variable is dependent and the other is independent.

The cause is the independent variable and effect is the dependent variable.

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2) an unhealthy weight,

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A symmetrical binomial distribution with large sample size can be approximated by a __________

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Typical distribution?

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Line segment JL is an altitude in triangle JKM. Which statement explains whether JKM is a right triangle? Round measures to the

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Answer:

C. JKM is not a right triangle because KM ≠ 15.3.

Step-by-step explanation:

We can see from our diagram that triangle JKM is divided into right triangles JLM and JLK.

In order to triangle JKM be a right triangle $KM^{2}=JK^{2}+JM^{2}$ .

We will find length of side KM using our right triangles JLM and JLK as $KM=KL+LM$ .

Using Pythagorean theorem in triangle JLM we will get,

$LM=\sqrt{JM^{2}-JL^{2}}$

$LM=\sqrt{8^{2}-5^{2}}$

$LM=\sqrt{64-25}$

$LM=\sqrt{39}=6.244997998\approx 6.24$

Now let us find length of side KL.

$KL=\sqrt{JK^{2}-JL^{2}}$

$KL=\sqrt{13^{2}-5^{2}}$

$KL=\sqrt{169-25}$

$KL=\sqrt{144}=12$

Now let us find length of KM by adding lengths of KL and LM.

$KM=12+6.24=18.24$

Now let us find whether JKM is right triangle or not using Pythagorean theorem.

$KM^{2}=JK^{2}+JM^{2}$

$18.24^{2}=13^{2}+8^{2}$

$18.24^{2}=169+64$

$18.24^{2}=233$

Upon taking square root of both sides of equation we will get,

$18.24\neq 15.264337522473748$

$18.2\neq 15.3$

We have seen that KM equals 18.2 and in order to JKM be a right triangle KM must be equal to 15.3, therefore, JKM is not a right triangle and option C is the correct choice.

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