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USPshnik [31]
3 years ago
10

If a sequence of 8 consecutive odd integers with increasing values has 9 as its seventh term. What is the sum of the terms of th

e sequence?​
Mathematics
1 answer:
klemol [59]3 years ago
8 0

Answer:

Sum = 32

Step-by-step explanation:

Given

Sequence = Consecutive Odds

T_7 = 9

Required

The sum of the terms

A sequence of odd number has a difference of 2. So, the sequence is represented as:

S = \{-3,-1,1,3,5,7,9,11\}

Add up all terms in the sequence

Sum = -3-1+1+3+5+7+9+11

Sum = 32

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If cos(x) = Three-fourths and tan(x) < 0, what is cos(2x)?
makvit [3.9K]

Step-by-step explanation:

The value of sin(2x) is \sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−

8

15

How to determine the value of sin(2x)

The cosine ratio is given as:

\cos(x) = -\frac 14cos(x)=−

4

1

Calculate sine(x) using the following identity equation

\sin^2(x) + \cos^2(x) = 1sin

2

(x)+cos

2

(x)=1

So we have:

\sin^2(x) + (1/4)^2 = 1sin

2

(x)+(1/4)

2

=1

\sin^2(x) + 1/16= 1sin

2

(x)+1/16=1

Subtract 1/16 from both sides

\sin^2(x) = 15/16sin

2

(x)=15/16

Take the square root of both sides

\sin(x) = \pm \sqrt{15/16

Given that

tan(x) < 0

It means that:

sin(x) < 0

So, we have:

\sin(x) = -\sqrt{15/16

Simplify

\sin(x) = \sqrt{15}/4sin(x)=

15

/4

sin(2x) is then calculated as:

\sin(2x) = 2\sin(x)\cos(x)sin(2x)=2sin(x)cos(x)

So, we have:

\sin(2x) = -2 * \frac{\sqrt{15}}{4} * \frac 14sin(2x)=−2∗

4

15

∗

4

1

This gives

\sin(2x) = - \frac{\sqrt{15}}{8}sin(2x)=−

8

15

6 0
2 years ago
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Michelle has to find the decimal equivalent of 15 yards. How can she do
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Answer:

15.0 yards

Step-by-step explanation:

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3 years ago
A 17.7-inch-thick layer of ash and pumice has already settled onto the Forum, which is 520 feet long by 109 feet wide. What is t
valentinak56 [21]

Answer:

so if im right, and i dont think i am, the volume should be 83603 feet^3

Step-by-step explanation:

7 0
2 years ago
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If the area of a circle is 58 square feet, find the circumference
enyata [817]
Hi there! C=2πa=2*π*58=26.99621 ft. Therefore, the answer is 27 ft.
3 0
3 years ago
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Consider a line whose slope is 6 and which passes through the point (8.–2).
Zolol [24]

Answer:

y=6(x-8)-2\qquad\text{point-slope form}

y=6x-50\qquad\text{slope-intercept form}

Step-by-step explanation:

The equation of a line can be written in several forms. Two of the most-used forms are the point-slope and the slope-intercept forms.

The point-slope form requires to have one point (xo, yo) through which the line passes and the slope m. The equation expressed in this form is:

y=m(x-xo)+yo

The slope-intercept form requires to have the slope m and the y-intercept b, or the y-coordinate of the point where the line crosses the y-axis. The equation is:

y=mx+b

The line considered in the question has a slope m=6 and passes through the point (8,-2). These data is enough to find the point-slope form of the line:

\boxed{y=6(x-8)-2\qquad\text{point-slope form}}

To find the slope-intercept form, we operate the above equation:

y=6x-48-2

\boxed{y=6x-50\qquad\text{slope-intercept form}}

3 0
3 years ago
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