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Marysya12 [62]
3 years ago
10

What is the 32nd term of the arithmetic sequence where a1 = 14 and a13 = -58?

Mathematics
1 answer:
liq [111]3 years ago
5 0
The nth term of an arithmetic sequence is found from:
n_{th}\ term=a+(n-1)d
Plugging in the given values, we get for the 13th term:
-58=14+12d
12d =-58 - 14 = -72
d = -6
So, the 32nd term is:
a_{32}=14+(32-1)-6=-172
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Connexus: C,D,C,A,A.

Step-by-step explanation:

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4 years ago
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4-x and y = 2x + 3 intersect are the s
ale4655 [162]
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4-x and y = 2x + 3 intersect are the solutions of the equation 4-x = 2x + 3.

Because the point where the graphs intersect is a point that meets both rules (functions) y = 4 - x and y = 2x + 3 meaning that y from y = 4 - x equals y from 2x + 3 and also both x have the same value.

Part B: Make tables to find the solution to 4-x = 2x + 3. Take the integer values of x between -3 and 3.

x values    4 -x         2x + 3

-3              4-(-3)=7     2(-3)+3 =-3
-2              4-(-2)=6     2(-2)+3 =-1
-1              4-(-1)=5     2(-1)+3 = 1
0                4-0=4        2(0)+3 = 3
1                4-1=3         2(1)+3=5
2                4-2=2        2(2)+3 = 7
3                4-3=1        2(3)+3 = 9

The the solution is between x = 0 and x =1

Part C: How can you solve the equation 4-x = 2x + 3 graphically?

Draw in a same graph both functions  y= 4 - x and y = 2x +3.

Then read the x-coordinates of the intersection point. That is the solution.

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Step-by-step explanation:

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Step-by-step explanation:

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5 0
3 years ago
Exercise
Maurinko [17]
X - nominator
y - denominator

\frac{3x}{y+12}=\frac{3}{4}\\
\frac{x+7}{3y}=\frac{1}{2}\\\\
3(y+12)=12x\\
2(x+7)=3y\\\\
3y+36=12x\\
2x+14=3y\\\\
2x+14+36=12x\\
10x=50\\
x=5\\\\
3y=2\cdot5+14\\
3y=10+14\\
3y=24\\
y=8\\\\
\frac{x}{y}=\boxed{\frac{5}{8}}
6 0
4 years ago
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