Answer:
Step-by-step explanation:
slope = m = (10-7)/4+3) = 3/7
y=3x/7+b
plug in either point to solve for b=y intercept
10=(3/7)/4+b =12/7+b
b =10-12/7 = 58/7
y=3x/7 + 58/7 or
eliminate the fractions
multiply by 7 to get
7y=3x + 58
Nickels n
quarters q
I: 3.15=n*0.05+q*0.25
II: n+q=23
isolate n in II:
n+q=23
n=23-q
substitute n in I:
3.15=n*0.05+q*0.25=
3.15=(23-q)*0.05+q*0.25
3.15=(23-q)*(1/20)+(q/4)
3.15=(23/20)-q/20+(q/4)
3.15=1.15-(4*q/20)
2=q/5
10=q
insert q=10 into II:
n+q=23
n+10=23
n=13
so c) 3 more nickels than quarters
Step-by-step explanation:
standard form of
1 . = x⁴-2x ²+3
2. = 5m³- 3m²+ 9m -7
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Answer:
![S_{15}= 50](https://tex.z-dn.net/?f=S_%7B15%7D%3D%2050)
Step-by-step explanation:
Given
![a_7 = \frac{14}{3}](https://tex.z-dn.net/?f=a_7%20%3D%20%5Cfrac%7B14%7D%7B3%7D)
![d = -\frac{4}{3}](https://tex.z-dn.net/?f=d%20%3D%20-%5Cfrac%7B4%7D%7B3%7D)
![n = 15](https://tex.z-dn.net/?f=n%20%3D%2015)
Required
The sum of n terms
First, we calculate the first term using:
![a_n = a + (n - 1)d](https://tex.z-dn.net/?f=a_n%20%3D%20a%20%2B%20%28n%20-%201%29d)
Let ![n = 7](https://tex.z-dn.net/?f=n%20%3D%207)
So, we have:
![a_7 = a + (7 - 1)d](https://tex.z-dn.net/?f=a_7%20%3D%20a%20%2B%20%287%20-%201%29d)
![a_7 = a + 6d](https://tex.z-dn.net/?f=a_7%20%3D%20a%20%2B%206d)
Substitute
and ![d = -\frac{4}{3}](https://tex.z-dn.net/?f=d%20%3D%20-%5Cfrac%7B4%7D%7B3%7D)
![\frac{14}{3} = a + 6*\frac{-4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B14%7D%7B3%7D%20%3D%20a%20%2B%206%2A%5Cfrac%7B-4%7D%7B3%7D)
![\frac{14}{3} = a -8](https://tex.z-dn.net/?f=%5Cfrac%7B14%7D%7B3%7D%20%3D%20a%20-8)
Collect like terms
![a =\frac{14}{3} +8](https://tex.z-dn.net/?f=a%20%3D%5Cfrac%7B14%7D%7B3%7D%20%2B8)
Take LCM and solve
![a =\frac{14+24}{3}](https://tex.z-dn.net/?f=a%20%3D%5Cfrac%7B14%2B24%7D%7B3%7D)
![a =\frac{38}{3}](https://tex.z-dn.net/?f=a%20%3D%5Cfrac%7B38%7D%7B3%7D)
The sum of n terms is then calculated as:
![S_n = \frac{n}{2}(2a + (n - 1)d)](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%282a%20%2B%20%28n%20-%201%29d%29)
Where: ![n = 15](https://tex.z-dn.net/?f=n%20%3D%2015)
So, we have:
![S_n = \frac{15}{2}(2*\frac{38}{3} + (15 - 1)*\frac{-4}{3})](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7B15%7D%7B2%7D%282%2A%5Cfrac%7B38%7D%7B3%7D%20%2B%20%2815%20-%201%29%2A%5Cfrac%7B-4%7D%7B3%7D%29)
![S_n = \frac{15}{2}(2*\frac{38}{3} + 14 *\frac{-4}{3})](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7B15%7D%7B2%7D%282%2A%5Cfrac%7B38%7D%7B3%7D%20%2B%2014%20%2A%5Cfrac%7B-4%7D%7B3%7D%29)
![S_n = \frac{15}{2}(2*\frac{38}{3} - 14 *\frac{4}{3})](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7B15%7D%7B2%7D%282%2A%5Cfrac%7B38%7D%7B3%7D%20-%2014%20%2A%5Cfrac%7B4%7D%7B3%7D%29)
![S_n = \frac{15}{2}(\frac{2*38}{3} - \frac{14 *4}{3})](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7B15%7D%7B2%7D%28%5Cfrac%7B2%2A38%7D%7B3%7D%20-%20%5Cfrac%7B14%20%2A4%7D%7B3%7D%29)
Take LCM
![S_n = \frac{15}{2}(\frac{2*38-14 *4}{3})](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7B15%7D%7B2%7D%28%5Cfrac%7B2%2A38-14%20%2A4%7D%7B3%7D%29)
![S_n = \frac{15}{2}(\frac{20}{3})](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7B15%7D%7B2%7D%28%5Cfrac%7B20%7D%7B3%7D%29)
Open bracket
![S_n = \frac{15*20}{2*3}](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7B15%2A20%7D%7B2%2A3%7D)
![S_n = \frac{300}{6}](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7B300%7D%7B6%7D)
![S_n = 50](https://tex.z-dn.net/?f=S_n%20%3D%2050)
Hence,
![S_{15}= 50](https://tex.z-dn.net/?f=S_%7B15%7D%3D%2050)
![d=37\](https://tex.z-dn.net/?f=d%3D37%5C)
<u>Step-by-step explanation:</u>
Here , we have In August, Cory begins school shopping for his triplet daughters. One day, he bought 10 pairs of socks for $2.50 each and 3 pairs of shoes for d dollars each. He spent a total of $135.97. We need to find What does d equal . Let's find out:
One day, he bought 10 pairs of socks for $2.50 each
Following is the equation for this info:
⇒ ![Money = 10(2.50)](https://tex.z-dn.net/?f=Money%20%3D%2010%282.50%29)
⇒ ![Money = 25\](https://tex.z-dn.net/?f=Money%20%3D%2025%5C)
3 pairs of shoes for d dollars each
Following is the equation for this info:
⇒ ![Money = 3(d)](https://tex.z-dn.net/?f=Money%20%3D%203%28d%29)
⇒ ![Money = 3d\](https://tex.z-dn.net/?f=Money%20%3D%203d%5C)
He spent a total of $135.97
Following is the equation for this info:
⇒ ![Total-Money = 135.97](https://tex.z-dn.net/?f=Total-Money%20%3D%20135.97)
⇒ ![25+3d=135.97](https://tex.z-dn.net/?f=25%2B3d%3D135.97)
⇒ ![3d=135.97-25](https://tex.z-dn.net/?f=3d%3D135.97-25)
⇒ ![d=37\](https://tex.z-dn.net/?f=d%3D37%5C)
Therefore ,
.