What is the solution to the system of equations below ?

I'm lazy and dont feel like doing math myself. So pls help me!

s2008m [1.1K]

Answer:

55

Step-by-step explanation:

Well you just plug in 10 as n.. and you get the equation:

$\frac{10(10+1)}{2} \\\frac{10(11)}{2}\\\\\frac{110}{2}\\\\55$

8 0

2 years ago

What is the 308th term of the sequence 11,12.5,14,15.5,17...

Alecsey [184]

$\huge\boxed{471.5}$

The formula for an arithmetic sequence is as follows:

$a_n=a_1+(n-1)d$

In this formula, $a_n$ represents the $n$ th term of the sequence and $d$ represents the common difference between each term.

Plug in the known values.

$a_{308}=11+(308-1)1.5$

Subtract.

$a_{308}=11+307*1.5$

Multiply.

$a_{308}=11+460.5$

Add.

$a_{308}=\boxed{471.5}$

6 0

3 years ago

What other information do you need in order to prove the triangles congruent using the SAS congruence postulate

iren [92.7K]

AC is perpendicular to BD.

<h3>Further explanation</h3>

We observe that both the ABC triangle and the ADC triangle have the same AC side length. Therefore we know that $\boxed{ \ \overline{AC} \cong \overline{AC} \ }$ is reflexive.
The length of the base of the triangle is the same, i.e., $\boxed{ \ \overline{BC} = \overline{CD} \ }$ .
In order to prove the triangles congruent using the SAS congruence postulate, we need the other information, namely $\boxed{ \ AC \bot BD \ }$ . Thus we get ∠ACB = ∠ACD = 90°.

Conclusions for the SAS Congruent Postulate from this problem:

$\boxed{ \ \overline{BC} = \overline{CD} \ }$
∠ACB = ∠ACD
$\boxed{ \ \overline{AC} = \overline{AC} \ }$

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The following is not other or additional information along with the reasons.

∠CBA = ∠CDA no, because that is AAS with ∠ACB = ∠ACD and $\boxed{ \ \overline{AC} \cong \overline{AC} \ }$
∠BAC = ∠DAC no, because that is ASA with $\boxed{ \ \overline{AC} \cong \overline{AC} \ }$ and ∠ACB = ∠ACD.
$\boxed{ \ \overline{BC} = \overline{CD} \ }$ no, because already marked.

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Notes

The SAS (Side-Angle-Side) postulate for the congruent triangles: two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle; the included angle properly represents the angle formed by two sides.
The ASA (Angle-Side-Angle) postulate for the congruent triangles: two angles and the included side of one triangle are congruent to two angles and the included side of another triangle; the included side properly represents the side between the vertices of the two angles.
The SSS (Side-Side-Side) postulate for the congruent triangles: all three sides in one triangle are congruent to the corresponding sides within the other.
The AAS (Angle-Angle-Side) postulate for the congruent triangles: two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.

<h3>Learn more</h3>

Which shows two triangles that are congruent by ASA? brainly.com/question/8876876
Which shows two triangles that are congruent by AAS brainly.com/question/3767125
About vertical and supplementary angles brainly.com/question/13096411

9 0

3 years ago

Read 2 more answers

A triangle has an angle that measures 90°. What type of triangle could it be? (Choose all that apply)

valentinak56 [21]

Answer:

The triangle could be a right triangle.

Step-by-step explanation:

Right triangles have right angles. (90 degrees). All triangles have 3 angles that add up to 180 degrees. So as long as one of the angles is 90 degrees, it's a right triangle.

8 0

3 years ago

Read 2 more answers

A life insurance policy costs $13.58 for every $1,000 of insurance. At this rate, what is the cost of $80,000 of insurance?

oee [108]

Answer:

80 times 13.58 =1086400

Step-by-step explanation:

7 0

3 years ago