Find the common difference for an arithmetic series with
a1=5 and S10 = 320.

Answers

Answer 1

Answer:

6

Step-by-step explanation:

Let [tex]n = a_{10}[/tex]. We know the formula for the sum of an arithmetic sequence is:

[tex]S_{n} = \frac{n(a_{1}+a_{n} )}{2}[/tex]

Where n is the number term you are finding the sum up to, a1 is the first term, and an is the nth term. We can substitute what we have:

[tex]320=\frac{10(5 + n)}{2}[/tex]

[tex]640=10(n+5)\\64=n+5\\n=59[/tex]

The formula to find the nth term of an arithmetic series is:

[tex]a_{n} = a_{1} + (n-1)d[/tex]

Where d is the common difference. Again, we can plug in what we have;

[tex]59 = 5 + 9d\\9d = 54\\d = 6[/tex]


Related Questions

What is an equation of the line that passes through the point (-6,-8) and is parallel to the line x-2y=6?

Answers

Answer:

[tex]y=\frac{1}{2}x-5[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines always have the same slope and different y-intercepts

1) Determine the slope (m)

[tex]x-2y=6[/tex]

Rearrange this equation into slope-intercept form (this will help us find the slope)

Subtract x from both sides

[tex]x-2y-x=6-x\\-2y=-x+6[/tex]

Divide both sides by -2

[tex]y=\frac{1}{2} x-3[/tex]

Now, we can identify clearly that the slope of the given line is [tex]\frac{1}{2}[/tex] since it's in the place of m. Because parallel lines always have the same slopes, the line we're currently solving for would therefore have a slope of [tex]\frac{1}{2}[/tex] as well. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\frac{1}{2}x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=\frac{1}{2}x+b[/tex]

Plug in the given point (-6,-8)

[tex]-8=\frac{1}{2}(-6)+b\\-8=-3+b[/tex]

Add 3 to both sides to isolate b

[tex]-8+3=-3+b+3\\-5=b[/tex]

Therefore, the y-intercept is -5. Plug this back into [tex]y=\frac{1}{2}x+b[/tex]:

[tex]y=\frac{1}{2}x-5[/tex]

I hope this helps!

Write the expressions for the following:

(i) 3 added with the product of x and y.

(ii) 4 subtracted from the product of -2 and m.​

Answers

Answer:

i) (xy)+3 or 3+(xy)

ii) (-2×m)-4

Answer:

3+xy

-2m-4

Step-by-step explanation:

What is the arithmetic mean of the following
numbers?
4,9,6, 3, 4,2

Answers

Step-by-step explanation:

the arithmetic mean are 14

the arithmetic value is 14

In a 3-digit number, the hundreds is one more than the ones digit and tens digit is twice the hundred digit. If the the sum of the digits is 11, find the number.

Answers

Answer:

362

Step-by-step explanation:

Let u = the units digit

2(u + 1) = the tens digit

u + 1 = the hundreds digit

u + 2(u + 1) + u + 1 = 11

u + 2u + 2 + u + 1 = 11

4u + 3 = 11

4u = 8

u = 2 = ones digit

u + 1 = 3 = hundreds digit

2(u + 1) = 2(3) = 6

The number is 362

Which of the following is not a triangle similarity theorem

Answers

Answer:

D. SSA

Step-by-step explanation:

The SSA postulate does not exist because an angle and two sides does not guarantee that the two triangles are congruent. This is because if two triangles have two congruent sides but a non-included congruent side, this does not indicate that it is necessarily congruent.

A snow cone cup is 12cm tall and has a diameter or 8cm find the volume of the flavored ice that can be held inside the snow cone cup

Answers

Answer:

200.96 cm³

Step-by-step explanation:

Volume of a cone = πr²h/3

Pi, π = 3.14

Radius, r = diameter/2

= 8 cm/2

= 4 cm

Height, h = 12 cm

Volume of a cone = πr²h/3

= 3.14 * (4 cm)² * 12 cm / 3

= 3.14 * 16 cm² * 12 cm / 3

= 602.88 cm³/3

= 200.96 cm³

Volume of a cone = 200.96 cm³

In the coordinate plane, what is the length of the line segment that connects points at (5,4) and (-3,-1)
Enter your answer in the box. Round to the nearest hundredth.
units

Answers

Answer:

9.434 units

Step-by-step explanation:

Given data

points (5,4) and (-3,-1)

x1= 5

y1= 4

x2= -3

y2= -1

The expression for the distance between two points is

d=√((x_2-x_1)²+(y_2-y_1)²)

substitute

d=√((-3-5)²+(-1-4)²)

d=√((-8)²+(-5)²)

d=√64+25

d=√89

d=9.4339

d= 9.434 units

Hence the distance between the points is 9.434 units

Please help. Thank you....

Answers

The answer is B

Hopefully this helps

Find the range of the relation {(-8,1),(-3,-6),(-7,-5),(9,5),(-2,9)}

Answers

Answer: (11,-4)
Explanation: the range is to subtract the maximum and the minimum. The maximum is 9,5 and the minimum is -2,9

I need to find this angle please help i know it is adjacent but i need the angle.

Answers

Answer:

148 degrees!

Step-by-step explanation:

They are 180 degrees together so just subtract 32. 180- 32 = 148.

Answer:

148°

Step-by-step explanation:

A flat angle measures 180°

180° - 32° = 148°

If you have 5 questions and get an 80% how many questions did you get wrong?

Answers

Answer:

4

Step-by-step explanation:

you got 1 question wrong

The area of a rectangular piece of plastic is 10 square millimeters. The perimeter is 22 millimeters. What are the dimensions of the piece of plastic?

Answers

2789 dimensions because it’s simple u multiple them

What is the perimeter of the garage if d=3

I’m marking branliest

Answers

Answer:

perimeter= 46

Step-by-step explanation:

(3(3)-2) + (3(3)-2) + (5(3)+1) + (5(3)+1)

7 + 7 + 16 + 16

= 46

I need help solving this problem. 15-1(12÷4+1)​

Answers

the answer would be 11

Answer:

11

Step-by-step explanation:

1. First do the brackets because BEDMAS

So, (12÷4+1) = 4

2. 15 - 1 x 4

3. 15 - 4

4. 11

Hope this helps! :)

Use the symbolab website/app it's really helpful

(5. solve for x )
2/5 + x = 1

Answers

X=3/5 for exact form of decimal it is x=0.6

What is the mesure of angle AXB?

Answers

The answer is 180 degrees
180 degrees your welcome !

Please help 15 points!!!

Answers

Answer:

20 m²

Step-by-step explanation:

Figure 1: 4 x 4 = 16

Figure 2: 2 x 2 = 4

16 + 4 = 20

PLEASE ANSWER THIS IS DUE TOMORROW!!!!!!!!!!!

Answers

Answer:

x-intercept: 15

y-intercept: -6

The slope is positive because 2/5 (the slope) is positive.

Step-by-step explanation:

The x-intercept is where the line crosses the x-axis.

The y-intercept is where the line crosses the y-axis.

LABEL THE TRIANGLE!! PLEASE HELP!!

Answers

Answer:

Determination of HYP,OPP,ADJ with respect to x.

Opposite side of right angle:Hypotenuse: AC

Opposite side of given angle: Opp:BC

remaining side of a triangle: Adjacent:AB.

ALRIGHT 66% WE NEED AT LEAST AN 80, WHAT WONDERFUL PERSON IS GONNA HELP!?

Answers

Answer:

I got 45

Step-by-step explanation:

so I did the triangle first I did 5 times 6 divided by 2 and got 15 then I did 5 times 6 and got 30 then I added the 30 and 15 together.

Answer:

Formula of trapezoid:

B1(base 1) + B2(base 2) x Height(h) x 1/2

Area of Trapezoid:

10(base 1) + 6(base 2) = 16

16 x 5 = 80

80 x 1/2 = 40

A bag contains 4 blue marbles, 6 red marbles, 3 yellow marbles, and 5 black marbles. What is the probability that you choose two marbles, without replacement, that are both black? Answer as a decimal to the nearest thousandths place (3 after the decimal).

Answers

Answer:

.065

Step-by-step explanation:

The total number of marbles is

4 blue marbles+ 6 red marbles+ 3 yellow marbles+5 black marbles=18

P(1st black) = Black/total = 5/18

You keep the marble

The total number of marbles is

4 blue marbles+ 6 red marbles+ 3 yellow marbles+4 black marbles=17

P(2st black) = Black/total = 4/17

Multiply the probabilities together

P(black,black)= 5/18 * 4/17 =10/153=.065359477 =.065

I need help ASAP PLEASE
What is the sum of the first 47 terms of the sequence?
-215,-201,-187,-173,...

Answers

Answer:

5029

Step-by-step explanation:

There is a common difference between consecutive terms, that is

d = - 201 - (- 215) = - 187 - (- 201) = - 173 - (- 187) = 14

This indicates the sequence is arithmetic with sum to n term

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = - 215 and d = 14 , then

[tex]S_{47}[/tex] = [tex]\frac{47}{2}[/tex] [ (2 × - 215) + (46 × 14) ]

     = 23.5 (- 430 + 644)

    = 23.5 × 214

    = 5029

A laptop is in the shape of a rectangular prism. The laptop has a length of 14
inches, a width of 10 inches, and a height of 1.5 inches.
What is the volume of the laptop?

Answers

Answer:

V=210 square inches

Step-by-step explanation:

Volume formula for a rectangular prism is V=lwh

So Volume=Length x Width x Height

V= 14 x 10 x 1.5

V=210 square inches

Dan bought a new computer for $900. Each year, the value of the computer decreased by 25% of the previous year’s value.
At this rate, what can Dan expect the approximate value of the computer to be after 12 years?
A $73
B. $90
C. $29
D. $85

Answers

Answer:

$29, that is the answer for this question

can some one help me plzz!! No links!!​

Answers

The answer is C.0,3 because One of Y equal 0 for X

Multiple Rules (Condense)
You can also use multiple rules at a time to condense
multiple log expressions to one.
2 log(x) +3 log(y) – 4 log(z)
Would condense to which of the following?
2 3
log
4
log
23
log
1,3,4
log(x21324)

Answers

Answer:

A

Step-by-step explanation:

Log poperties

What is the slope for y = - 6x + 12 on a graph

Answers

Answer:

For question A)  y = -6 , b = 12

For question B) x = 2

Step-by-step explanation:

Find the distance between the two points in simplest radical form.
(-9,3) and (-3,-5)

Answers

Answer:

10

Step-by-step explanation:

Distance Formula: sqrt_/(x1-x2)^2 + (y1-y2)^2

sqrt_/(-9-(-3))^2 + (3-(-5))^2

sqrt_/(-6)^2 + (8)^2

sqrt_/36+64

sqrt_/100

Simplify and you get the number 10.

Find the measure of each angle indicated. It’s two questions.
11)
A) 41
B) 45
C) 49
D) 42

12)
A) 68
B) 85
C) 70
D) 71

Answers

The first one is 49
The second one is 68

The radius of a circle is 11 meters. What is the circle's area?

Answers

Answer:

379.94 m²

Step-by-step explanation:

3.14×11²= 379.94 m²

Step-by-step explanation:

The area of a circle is

π[tex]r^{2}[/tex]

The r is 11 so we get 11^2 * π

121π is our exact area,

380.13 m^2 is our approximate area

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