Answer: - 7.2 , 2.6 , 12.4 and 22.2
Step-by-step explanation:
Let the arithmetic means be p , q , r ,s , therefore , the sequence becomes:
-17 , p , q , r , s , 32
The first term (a ) = -17
Last term (L) = 32
common difference (d) = ?
number of terms (n ) = 6
We will use the formula for calculating the last term to find the common difference. That is
L = a + (n - 1 ) d
Substituting the values , we have
32 = -17 + (6-1) d
32 = -17 + 5d
32 + 17 = 5d
49 = 5d
Therefore: d = 9.8
We can therefore find the values of p , q , r , and s
p is the second term , that is
p = a + d
p = -17 + 9.8
p = -7.2
q = a + 2d
q = - 17 + 19.6
q = 2.6
r = a + 3d
r = - 17 + 29.4
r = 12.4
s = a + 4d
s = - 17 + 39.2
s = 22.2
Therefore : the arithmetic means are : - 7.2 , 2.6 , 12.4 and 22.2
Let's solve your equation step-by-step.
3
(
3
x
−
4
)
=
−
2
(
1
−
4
x
)
Step 1: Simplify both sides of the equation.
3
(
3
x
−
4
)
=
−
2
(
1
−
4
x
)
(
3
)
(
3
x
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+
(
3
)
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−
4
)
=
(
−
2
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(
1
)
+
(
−
2
)
(
−
4
x
)
(Distribute)
9
x
+
−
12
=
−
2
+
8
x
9
x
−
12
=
8
x
−
2
Step 2: Subtract 8x from both sides.
9
x
−
12
−
8
x
=
8
x
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2
−
8
x
x
−
12
=
−
2
Step 3: Add 12 to both sides.
x
−
12
+
12
=
−
2
+
12
x
=
10
We use the pythagorean theorem and information about the rectangular prism to find the length of the hypotenuses that the spider walks along. Adding them together (5.39+5+5.83+3.91) gives us 20.13cm, the answer.
Answer:
13/4
Step-by-step explanation:
Given that total number of pounds of grass seed needed = 9
Let number of pounds of Bermuda seeds used = x
Let number of pounds of Fescue seeds used = y
Then sum of both gives equation:
x+y=9
or y=9-x...(i)
Given that cost of 1 pound of Bermuda seed = $4.80
Then cost of x pound of Bermuda seed = $4.80x
Given that cost of 1 pound of Fescue seed = $3.50
Then cost of y pound of Fescue seed = $3.50y
total cost will be 4.80x+3.50y
Given that cost of 1 pound of mix seed = $4.02
Then cost of 9 pound of mix seed = $4.02*9
combining all three parts, we get equation:
4.80x+3.50y=4.02*9
4.80x+3.50y=36.18...(ii)
plug (i) into (ii)
4.80x+3.50y=36.18
4.80x+3.50(9-x)=36.18
4.80x+31.5-3.50x=36.18
4.80x-3.50x=36.18-31.5
1.3x=4.68
x=3.6
Now plug x=3.6 into (i)
y=9-x=9-3.6=5.4
Hence final answer is given by:
Let number of pounds of Bermuda seeds he should buy = 3.6 pounds
Let number of pounds of Fescue seeds he should buy = 5.4 pounds
