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alisha [4.7K]
4 years ago
7

Which statement is true?

Mathematics
1 answer:
ANTONII [103]4 years ago
8 0

Answer:

the answer is b

Step-by-step explanation:

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in this particular arithmetic sequence, a6 = 36 and a17 = 113. what is the value of a23 a23=101 a23=155 a23=162 a23=167
il63 [147K]
Determine first the common difference (d) of the arithmetic sequence using the given terms,
                             d = (a17 - a6) / (17 - 6) 
                               d = (113 - 36) / 11 = 7
Using the 17th term, 113, we get the value of a23 by,
                             a23 = a17 + (23 - 17) x 7
                                    a23 = 113 + 42 = 155
Thus, the 23rd term is 155. 
5 0
3 years ago
One side of a triangle is increasing at a rate of 9 cm/s and a second side is decreasing at a rate of 2 cm/s. if the area of the
LenKa [72]
Use the attached figure to guide yourself through the explanation. In the figure:
a=21cm, b=36cm, \widehat{C}=\frac{\pi}{6}.
We know that:
 \frac{da}{dt}=9,\frac{db}{dt}=-2
Also remmeber that the area of a triangle is:
A=\frac{Base\times Height}{2}
The hegiht is shown in the figure in red, the base is just the b side.
Using the angle C the area of the triangle is:
A=\frac{1}{2}ab\cos(\widehat{C})\implies2A=ab\cos(\widehat{C})
Now taking the derivative of the area 2A with respect to t we have:
2\frac{dA}{dt}=b\cos(\widehat{C})\frac{da}{dt}+a\cos(\widehat{C})\frac{db}{dt}-ab\sin(\widehat{C})\frac{d\widehat{C}}{dt}

Replacing with the right values:
\frac{dA}{dt}=0\\
\\
\cos({\widehat{C}})=\frac{\sqrt{3}}{2}\\ \\
\sin({\widehat{C}})=\frac{1}{2}\\ \\


yields:
0=36\frac{\sqrt{3}}{2}.9-21\frac{\sqrt{3}}{2}.2-\frac{1}{2}.21.36.\frac{d\widehat{C}}{dt}\implies \frac{d\widehat{C}}{dt}=\frac{141}{378}\sqrt{3}

5 0
4 years ago
One lap around the track is 400 meters. If Sean ran around the track 5 and 1/2 times, how far did Sean run?
telo118 [61]
2200 meters...I think
7 0
3 years ago
Read 2 more answers
Need help on numbers 6, 7, and 8 ill mark brainliest if they are right
Andrei [34K]

Answer:

1st one is B

Step-by-step explanation:

2nd one is the 1st one

7 0
3 years ago
Solve the inequation 2x -3(3x-4)>_8​
svlad2 [7]

Answer:

x≤47

Step-by-step explanation:

2x−3(3x−4)≥8

Step 1: Simplify both sides of the inequality.

−7x+12≥8

Step 2: Subtract 12 from both sides.

−7x+12−12≥8−12

−7x≥−4

Step 3: Divide both sides by -7.

−7x−7≥−4−7x≤47

Answer:x≤47

8 0
3 years ago
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