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neonofarm [45]
3 years ago
5

The first term of an arithmetic sequence is -3 and the fifteenth term is 53. What is the common difference of the sequence?

Mathematics
1 answer:
Maru [420]3 years ago
4 0

C: 4 is the right answer

Step-by-step explanation:

Given

a1 = -3

a15 = 53

We know that explicit formula for the arithmetic sequence is:

a_n=a_1+(n-1)d

For the 15th, term it will be

a_{15}=-3+(15-1)d\\53=-3+14d

Adding 3 on both sides

53+3 = -3+3 + 14d\\56 = 14d

Dividing both sides by 14

\frac{56}{14}=\frac{14d}{14}\\d=4

Hence,

C: 4 is the right answer

Keywords: Arithmetic sequence, Common Difference

Learn more about arithmetic sequence at:

  • brainly.com/question/12896802
  • brainly.com/question/12973601

#LearnwithBrainly

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4p + 1 = 10 what is the value of p?
fredd [130]

Answer:

p = 9/4 or 2.25

Step-by-step explanation:

4p + 1 = 10

      -1     -1

4p = 9

Divide 4 on both sides

p = 9/4 or 2.25

5 0
3 years ago
Read 2 more answers
Carrie and brent leave home at the same time. carrie drives due east at a rate of 30 mph, while brent drives due south at a rate
Helga [31]

<h3>They are 268 miles far apart after 4 hours</h3>

<h3>Further explanation</h3>

Acceleration is rate of change of velocity.

\large {\boxed {a = \frac{v - u}{t} } }

\large {\boxed {d = \frac{v + u}{2}~t } }

<em>a = acceleration ( m/s² )</em>

<em>v = final velocity ( m/s )</em>

<em>u = initial velocity ( m/s )</em>

<em>t = time taken ( s )</em>

<em>d = distance ( m )</em>

Let us now tackle the problem !

<u>Given :</u>

v₁ = 30 mph due east

v₂ = 60 mph due south

t = 4 hours

<u>Unknown :</u>

displacement = d = ?

<u>Solution :</u>

d_1 = v_1 \times t

d_1 = 30 ~ mph \times 4 ~ h

d_1 = \boxed {120 ~ miles}

d_2 = v_2 \times t

d_2 = 60 ~ mph \times 4 ~ h

d_2 = \boxed {240 ~ miles}

d^2 = (d_1)^2 + (d_2)^2

d^2 = 120^2 + 240^2

d^2 = 72000

d = \sqrt{72000}

d = 120\sqrt{5} ~ miles

d \approx \boxed {268 ~ miles}

<h2>Conclusion :</h2><h3>They are 268 miles far apart after 4 hours</h3>

<h3>Learn more</h3>
  • Velocity of Runner : brainly.com/question/3813437
  • Kinetic Energy : brainly.com/question/692781
  • Acceleration : brainly.com/question/2283922
  • The Speed of Car : brainly.com/question/568302

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate

6 0
3 years ago
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Need help with 13 14 and 15
ad-work [718]

Answer:

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Step-by-step explanation:

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6 0
3 years ago
C
Volgvan

The arc angle AC is measured as 55 degrees.

<h3>How to find arc angle?</h3>

If two secant intersect in the exterior of a circle, then the measure of the angle formed is half the positive difference of the arcs intercepted.

Therefore, the secants intersect outside the circle at point E.

The arc angle AC can be found as follows:

Therefore,

m∠BED = 1 / 2 (arc angle AC - arc angle BD)

arc angle AC = x

arc angle BD = 23 degrees.

m∠BED = 16 degrees.

m∠BED = 1 / 2 (arc angle AC - arc angle BD)

16 = 1 / 2 (x - 23)

16 = 1 / 2x - 23 / 2

16 + 11.5 = 0.5x

27.5 = 0.5x

x = 27.5 / 0.5

x = 55 degrees.

Therefore,

arc angle AC = 55 degrees.

learn more on arc angle here: hhttps://brainly.com/question/23117081

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7 0
1 year ago
Which of the following are measurements of the sides of a right triangle?
Anna [14]

the answer is D. all of the above

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