Answer:
225
Step-by-step explanation:
The sum of this series is given by the formula:
![S_n=\frac{n}{2}[2a+(n-1)d]](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D)
Where
S_n is the sum
a is the first term (we get this by plugging in n = 1 into "2n-1", we have 2(1) - 1 = 1)
n is the number of terms (the sum is defined for n = 1 to n = 15, so 15 terms)
d is the common different (the difference is successive terms. Here, 2nd term would be 2(2) - 1 = 3, and first term was 1, so d = 3 -1 = 2)
<em>plugging in the info, we will get the sum:</em>
<em>![S_n=\frac{n}{2}[2a+(n-1)d]\\S_{15}=\frac{15}{2}[2(1)+(15-1)(2)]\\=225](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D%5C%5CS_%7B15%7D%3D%5Cfrac%7B15%7D%7B2%7D%5B2%281%29%2B%2815-1%29%282%29%5D%5C%5C%3D225)
</em>
<em>The sum is 225</em>
<span>B. ∠E and ∠H are alternate exterior angles</span>
Answer:
A. a + c ≥ 70; 15a + 4c ≤ 1000
Step-by-step explanation:
<u>Given data:</u>
A community action committee is planning a block party
The party will be successful if at least 70 adults (a) and children (c) attend
Their budget for the party is $1,000
The cost for each adult will be $15
And the cost for each child will be $4
<u>Solution:</u>
<u />
At least 70 adults and children attend.
So the inequality here is a + c ≥ 70
The budget for the party is $1,000.
So the cost for all adults plus the cost for all children cannot exceed $1,000
And hence the inequality here is; 15a + 4c ≤ 1,000
Answer: IDK im here for the points
Step-by-step explanation: Srry bud
<h3>Answer: Choice B) 8.57</h3>
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Explanation:
The triangles are similar through the AA (angle angle) similarity rule. Note how the angle markers correspond and match up. Example: angle C and angle F both have triple angle markers to indicate these angles are congruent.
The corresponding sides pair up to form equal fractions. AB and DE form AB/DE which is equal to AC/DF, as these two sides correspond as well.
Therefore: AB/DE = AC/DF
Let's plug in the given values and isolate x
AB/DE = AC/DF
11/7 = (15+x)/15 ...... substitution
11*15 = 7*(15+x) ....... cross multiply
11*15 = 7*15+7*x ...... distribute
165 = 105+7x
165-105 = 105+7x-105 ..... subtract 105 from both sides
60 = 7x
7x = 60
7x/7 = 60/7 ............ divide both sides by 7
x = 8.57142857142858
x = 8.57 ..... rounding to the nearest hundredth
