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3 years ago

Find the nth term of the following sequence: 7, 13, 19, 25,

Mathematics

2 answers:

Natalija [7]3 years ago

8 0

The answer of the next term is 31

katen-ka-za [31]3 years ago

5 0

Answer:

Tn = 7 + (n - 1)*(6)

Step-by-step explanation:

The explicit rule is in the form: Tn = a + (n - 1)*(d), where 'a' is the first term and d is the common difference.

The first term in the sequence is 7, so 'a' is 7. The common difference is 6

(13 - 7) = 6, hence 'd' is 6.

Therefore, Tn = 7 + (n - 1)*(6)

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Nat2105 [25]

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.. I = Prt
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.. tax+license + down payment + loan repayment
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4 0

3 years ago

We have seen that isosceles triangles have two sides of equal length. The angles opposite these sides have the same measure. Use

Naddik [55]

Question has missing figure, the figure is in the attachment.

Answer:

The measure of ∠1 is 65°.

The measure of ∠2 is 65°.

The measure of ∠3 is 50°.

The measure of ∠4 is 115°.

The measure of ∠5 is 65°.

Step-by-step explanation:

Given,

We have an isosceles triangle which we can named it as ΔABC.

In which Length of AB is equal to length of BC.

And also m∠B is equal to m∠C.

ext.m∠C= 115°(Here ext. stands for exterior)

We have to find the measure of angles angles 1 through 5.

Solution,

For ∠1.

∠1 and ext.∠C makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

$\angle1+ext.\angle C=180\°$

On putting the values, we get;

$\angle 1+115\°=180\°\\\\\angle1=180\[tex]\therefore m\angle2=65\°$ -115\°=65\°[/tex]

Thus the measure of ∠1 is 65°.

For ∠2.

Since the given triangle is an isosceles triangle.

So, $m\angle1=m\angle2$

Thus the measure of ∠2 is 65°.

For ∠3.

Here ∠1, ∠2 and ∠3 are the three angles of the triangle.

So we use the angle sum property of triangle, which states that;

"The sum of all the angles of a triangle is equal to 180°".

$\therefore \angle1+\angle2+\angle3=180\°$

Now we put the values and get;

$65\°+65\°+\angle3=180\°\\\\130\°+\angle3=180\°\\\\\angle3=180\°-130\°=50\°$

Thus the measure of ∠3 is 50°.

For ∠4.

∠4 and ∠2 makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

$\angle2 +\angle 4 =180\°$

Substituting the values of of angle 2 to find angle 4 we get;

$65\°+ \angle 4 = 180\°\\\\ \angle 4 = 180\°-65\°\\\\\angle 4= 115\°$

Thus the measure of ∠4 is 115°.

For ∠5.

∠4 and ∠5 makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

$\angle4 +\angle 5 =180\°$

Substituting the values of of angle 4 to find angle 5 we get;

$115\°+ \angle 5 = 180\°\\\\ \angle 5 = 180\°-115\°\\\\\angle 5= 65\°$

Thus the measure of ∠5 is 65°.

Hence:

The measure of ∠1 is 65°.

The measure of ∠2 is 65°.

The measure of ∠3 is 50°.

The measure of ∠4 is 115°.

The measure of ∠5 is 65°.

6 0

3 years ago

Find the range of possible lengths of the third side using the given side lengths <br> 10, 7

Tomtit [17]

Answer:

3 < x < 17

Step-by-step explanation:

Given 2 sides then the possible range of the third side x is

difference of 2 sides < x < sum of 2 sides , that is

10 - 7 < x < 10 + 7

3 < x < 17

8 0

3 years ago

A charter airline finds that on its Saturday flights from Philadelphia to London, all 120 seats will be sold if the ticket price

Nataliya [291]

Answer:

a) $P=3(120-s)+200$

b) $215 \leq P \leq 290$

Step-by-step explanation:

For this case we can use a linear model to solve the problem.

s) Create an equation to express the increase on the price tickets and the number of seats sold

$s$ number of seats, if w analyze the info given the number of seats after increase the price is given by $120-s$ .

And let P the price for the ticket. So after the increase in ticket price the expression for the increase is P-200.

We have an additional info, for each increase of $3 the number of setas decrease 1. And the equation that gives to us the price change in terms of the increase of price is:

$P-200=3(120-s)$