1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mezya [45]
3 years ago
12

find the 20th term of an arithmetic sequence with a first term of 3 and a common difference of 5. a. 87 b. 98 c. 101 d. 130

Mathematics
1 answer:
Nady [450]3 years ago
3 0
The formula for the nth term of an arithmetic sequence is:
n_{th} \ term=a+(n-1)d
where a is the first term and d is the common difference.
Plugging the given values into the formula, we get:
20th\ term=3+(20-1)5=98
The answer is b. 98.

You might be interested in
What is a fraction has both a negative denominator and numerator?
liubo4ka [24]
Negative divided by negative makes a positive
6 0
3 years ago
Given that triangle ABC is congruent to triangle DEF find x and y
Charra [1.4K]
X will equal 12, and y will equal 18.
6 0
3 years ago
A cylinder and its dimensions are shown. Which equation can be used to find V, the volume of the cylinder in cubic centimeters?
Basile [38]
D the formula is v=(pie)(r)2(h)
Sorry I don’t have the right tools to do the equation right. But it’s D
8 0
2 years ago
Read 2 more answers
June’s portfolio includes 177 shares of parchar special effects, 213 shares of giaco household goods, and 152 shares of raxin ac
givi [52]
Junes is it a joke or not even a cheer leader for the last year of her and I can’t bc
5 0
2 years ago
∆ABC has vertices A(–2, 0), B(0, 8), and C(4, 2)
Natali [406]

Answer:

Part 1) The equation of the perpendicular bisector side AB is y=-\frac{1}{4}x+\frac{15}{4}

Part 2) The equation of the perpendicular bisector side BC is y=\frac{2}{3}x+\frac{11}{3}

Part 3) The equation of the perpendicular bisector side AC is y=-3x+4

Part 4) The coordinates of the point P(0.091,3.727)

Step-by-step explanation:

Part 1) Find the equation of the perpendicular bisector side AB

we have

A(–2, 0), B(0, 8)

<em>step 1</em>

Find the slope AB

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{8-0}{0+2}

m=4

<em>step 2</em>

Find the slope of the perpendicular line to side AB

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

therefore

The slope is equal to

m=-\frac{1}{4}

<em>step 3</em>

Find the midpoint AB

The formula to calculate the midpoint between two points is equal to

M(\frac{x1+x2}{2},\frac{y1+y2}{2})

substitute the values

M(\frac{-2+0}{2},\frac{0+8}{2})

M(-1,4)

<em>step 4</em>

Find the equation of the perpendicular bisectors of AB

the slope is m=-\frac{1}{4}

passes through the point (-1,4)

The equation in slope intercept form is equal to

y=mx+b

substitute

4=(-\frac{1}{4})(-1)+b

solve for b

b=4-\frac{1}{4}

b=\frac{15}{4}

so

y=-\frac{1}{4}x+\frac{15}{4}

Part 2) Find the equation of the perpendicular bisector side BC

we have

B(0, 8) and C(4, 2)

<em>step 1</em>

Find the slope BC

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{2-8}{4-0}

m=-\frac{3}{2}

<em>step 2</em>

Find the slope of the perpendicular line to side BC

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

therefore

The slope is equal to

m=\frac{2}{3}

<em>step 3</em>

Find the midpoint BC

The formula to calculate the midpoint between two points is equal to

M(\frac{x1+x2}{2},\frac{y1+y2}{2})

substitute the values

M(\frac{0+4}{2},\frac{8+2}{2})

M(2,5)

<em>step 4</em>

Find the equation of the perpendicular bisectors of BC

the slope is m=\frac{2}{3}

passes through the point (2,5)

The equation in slope intercept form is equal to

y=mx+b

substitute

5=(\frac{2}{3})(2)+b

solve for b

b=5-\frac{4}{3}

b=\frac{11}{3}

so

y=\frac{2}{3}x+\frac{11}{3}

Part 3) Find the equation of the perpendicular bisector side AC

we have

A(–2, 0) and C(4, 2)

<em>step 1</em>

Find the slope AC

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{2-0}{4+2}

m=\frac{1}{3}

<em>step 2</em>

Find the slope of the perpendicular line to side AC

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

therefore

The slope is equal to

m=-3

<em>step 3</em>

Find the midpoint AC

The formula to calculate the midpoint between two points is equal to

M(\frac{x1+x2}{2},\frac{y1+y2}{2})

substitute the values

M(\frac{-2+4}{2},\frac{0+2}{2})

M(1,1)        

<em>step 4</em>

Find the equation of the perpendicular bisectors of AC

the slope is m=-3

passes through the point (1,1)

The equation in slope intercept form is equal to

y=mx+b

substitute

1=(-3)(1)+b

solve for b

b=1+3

b=4

so

y=-3x+4

Part 4) Find the coordinates of the point of concurrency of the perpendicular bisectors (P)

we know that

The point of concurrency of the perpendicular bisectors is called the circumcenter.

Solve by graphing

using a graphing tool

the point of concurrency of the perpendicular bisectors is P(0.091,3.727)

see the attached figure

5 0
3 years ago
Other questions:
  • Which measurements are the greatest 6kilometers 60 meters 600 centimeters 6000 milimeters
    14·2 answers
  • How will removing the wheel of cheese affect the mean and median
    11·1 answer
  • how much would 200 invested at 6% interest compounded annually be worth after 6 years? round your answer to the nearest cent
    12·1 answer
  • (7-4n) x 6= I need the answer as quick as possible
    10·2 answers
  • Amy is sewing some pants for herself.
    12·1 answer
  • find the indicated limit, if it exists. limit of f of x as x approaches 8 where f of x equals x plus 10 when x is less than 8 an
    5·1 answer
  • Solve this problem thanks
    5·2 answers
  • Decide whether the statement is a valid dennltion.
    10·1 answer
  • Only a couple more questions!! Help please
    5·1 answer
  • A number is chosen at random from 1 to 25. find the probability of selecting a number less than 3?​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!