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

Answers

Answer 1

Answer:

53=-3+14d

56=14d

d=4 that is the common difference


Related Questions

If 12 is the greatest common factor of y and 36, how many possible values for y are in between 20 and 80 ?

Answers

Answer: 3

Step-by-step explanation: I don’t have an explanation but I got the same question on a quiz and 3 was the correct answer.

the possible values for y are in between 20 and 80 will be 3.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

If 12 is the greatest common factor of y and 36.

The value of y will be a multiple of 12 and greater than 36.

Then the numbers will be

12 x 4 = 48

12 x 5 = 60

12 x 6 = 72

Then the possible values for y are in between 20 and 80 will be 3.

More about the Algebra link is given below.

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Tony runs 100 meters in 10.36 seconds and neal runs the same distance in 10.26 seconds who is the faster runner?​

Answers

Neal. 10.26 is faster than 10.36

On a world ​, the distance between city A and city B is 5,625 inches. The two cities are actually 1688 miles apart. On the same ​, what would be the distance between city C and city​ D, two cities that are actually 1296 miles​ apart? Use a proportion to solve this problem.

Answers

Answer:

The distance between C and D is 4.2768 inches.

Step-by-step explanation:

As from A to B the distance is 5.625 inches and actual is 1688 miles

so,

1 mile = 5.625/1688 = 0.0033 inches

So, the distance between C and D is 1296 miles

= 1296 x 0.0033 inches = 4.2768 inches  

which expression is equivalent to 13-(-18)

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{13 - (-18)}[/tex]

[tex]\huge\textsf{= 13 + 18}[/tex]

[tex]\huge\textsf{= \bf 31}[/tex]

[tex]\boxed{\boxed{\huge\text{Therefore, your answer is most likely: \textsf{31}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\huge\text{Amphitrite1040:)}[/tex]

Answer:

[tex] \displaystyle 31[/tex]

Step-by-step explanation:

we want to simplify the following expression:

[tex] \displaystyle 13 - ( - 18)[/tex]

remove parentheses and change its sign because we know that two negatives make positive Thus:

[tex] \displaystyle 13 + 18[/tex]

finally simplify addition:

[tex] \displaystyle\bf \fbox{31}[/tex]

hence,

[tex] \displaystyle 13 - ( - 18) = \boxed{31}[/tex]

Question 2 of 10
The function Fx) = log 0.5 x is decreasing. true or false ​

Answers

Answer:

True

Step-by-step explanation:

log0.5= -1.6990

so,anwer is negative than the statement is true

Someone plz help me on this one

Answers

Answer:

76

Step-by-step explanation:

Since this is a right triangle, we  can use  trig functions

tan ? = opp side/ adj side

tan ? = 40 / 10

tan ?  = 4

Taking the inverse  of each side

tan ^ -1 (tan ?) = tan ^-1(4)

? =75.96375653

To the nearest degree

? = 76

What is Index Law 2?
please give definition

Answers

LAW 2: The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In algebraic form, this rule is as follows . The a represents the number that is divided by itself and m and n represent the powers.

Answer:

The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. The a represents the number that is divided by itself and m and n represent the powers. Here is an example for this rule.

If the value of a is 8 in f(x)=ax^2, what does the graph look like?

Answers

Step-by-step explanation:

the answer is in the image above

pleasee help asapp:)

Answers

They gave you the length of the two sides of the triangular part. Calculate the circumference of the semi circle on top.

Circumference of a semi circle is 1/2 x 2 x radius x PI

The radius is given as 3 ft.

Circumference  = 1/2 x 2 x 3 x 3.14 = 9.42ft

Perimeter is the length of the circumference of the semi circle plus the side lengths of the triangle:

5 + 5 + 9.42 = 19.42 feet

Answer: 19.42 feet

Answer:

10 + 3[tex]\pi[/tex]

19.42

Step-by-step explanation:

here are the first five terms of a quadratic sequence (1 8, 21, 40, 65). the nth term of this sequence can be written in the form (an2 + bn). where a and b are integers. work out the value of a and the value of b

Answers

Answer:

a=3 and b=-2

Step-by-step explanation:

We are given that five  terms of a quadratic sequence are

1 8, 21, 40, 65.

The nth term of this sequence

=[tex]an^2+bn[/tex]

We have to find the value of a and b where a and b are integers.

For n=1

[tex]a+b=1[/tex]   ......(1)

For n=2

[tex](2)^2a+2b=8[/tex]

[tex]4a+2b=8[/tex]

[tex]2a+b=4[/tex]   .....(2)

Subtract equation (1) from (2) we get

[tex]2a-a=4-1=3[/tex]

[tex]a=3[/tex]

Using the value of a=3 in equation (1)

[tex]3+b=1[/tex]

[tex]b=1-3=-2[/tex]

Hence, the value of

a=3 and b=-2

please help!! 15 points! I need 5 and 9 answered

Answers

Answer:

B: Subtraction property of equality

5 and 9 are subtraction property of equality

Instructions: Find the missing side. Round your answer to the nearest
tenth.
49
х
66°
X

Answers

[tex]\sin(66) = \frac{49}{x} \\ 0.913 = \frac{49}{x} \\ x = 53.6 \\ x = 54[/tex]

The missing side is 53.6 units for the given right triangle.

What is the right triangle?

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The right triangle is given in the question, as shown.

The ratio of the length of the side opposite the angle to the length of the hypotenuse of the triangle. The sine function is denoted by the symbol "sin" and is defined as follows:

sin(θ) = opposite / hypotenuse

Here, θ = 66°

Using the sine ratio in the given triangle, we get

sin 66° = perdenicular/hypertanuas

Substitute the known values in the above ratio,

sin 66° = 49/x

x = 49/sin 66°

x = 53.63717

Rounded to the nearest tenth,

x ≈ 53.6

Thus, the missing side is 53.6 units for the given right triangle.

Learn more about the right triangle here:

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Which of the following is an example of rigid transformations?
A. Moving the glass from one place to other
B. Cutting a piece of bread
C. Squeezing the cherry
D. All of the choices

Answers

Answer:

Moving the glass from one place to other is rigid transformation.

Step-by-step explanation:

The rigid transformation includes rotation, translation, reflection or their combination.

So, Moving the glass from one place to other place is translation. It is example of rigid transformation.

Now, cutting a piece of bread is not rotation or translation or reflection. So, it is NOT rigid transformation.

Squeezing the cherry is not rotation or translation or reflection. So, it is too NOT rigid transformation.

see ss below
please explain each step ​

Answers

Answer:

p(x) = (x - 5)(x + 1)(x + 4)

General Formulas and Concepts:

Algebra I

Terms/CoefficientsFactoring

Algebra II

Factoring Cubes:                                                                                           [tex]\displaystyle (a \pm b)(ax^2 \mp bx + c)[/tex]Long DivisionSynthetic Division

Step-by-step explanation:

*Note:

Please excuse my bad handwriting :)

Step 1: Define

Identify

p(x) = x³ - 21x - 20

Linear factor (x - 5)

Step 2: Factor

Option 1: Factoring cubes formula

Factor [Factoring Cubes]:                                                                            p(x) = (x - 5)(x² + 5x + 4)Factor:                                                                                                          p(x) = (x - 5)(x + 4)(x + 1)

Option 2: Long Division

See Attachment

Option 3: Synthetic Division

See Attachment #2

Can someone help me with this please

Answers

Answer:

.574

Step-by-step explanation:

This can be inputted in a calculator to achieve .57357643

To three decimal places that is .574

With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is rejected if there is at least one defective unit. The ABCD Electronics Company has just manufactured 4500 write-rewrite CDs, and 150 are defective. If 4 of these CDs are randomly selected and tested, what is the probability that the entire batch will be rejected

Answers

Answer:

0.1269 = 12.69% probability that the entire batch will be rejected.

Step-by-step explanation:

CD's are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

4500 CDs, which means that [tex]N = 5000[/tex]

150 defective, which means that [tex]k = 150[/tex]

4 are selected, which means that [tex]n = 4[/tex]

What is the probability that the entire batch will be rejected?

At least 1 defective, which is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,4500,4,150) = \frac{C_{150,0}*C_{4350,4}}{C_{4500,4}} = 0.8731[/tex]

So

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.8731 = 0.1269[/tex]

0.1269 = 12.69% probability that the entire batch will be rejected.

Find the slope.
Directions: For problems 1 through 3, graph the line by using the given X values and find its slope.​

Answers

Answer:

Answer is in the picture.

Find the volume of this solid.

Answers

Answer:

Step-by-step explanation:

area of side surface=50×20+20×35=1000+700=1700 m²

voume of solid=1700×12=204,00  m³

the inverse of f(x) is a function true or false

Answers

the answer is true, the inverse of f(x) IS a function !

Write as an equation: a triangle has two equal sides and a third side that is 15cm long. How long is each of the equal sides if the perimeter is 50?

Answers

Answer:

Step-by-step explanation:

X+x+15=50

The robotics team purchased 3 androids for the purpose of programming. Each of the robots was $398, which included tax. If the tax rate is 8%, what is the TOTAL TAX to be paid?

Answers

Answer:

$95.52

Step-by-step explanation:

Number of robots = 3

Cost of each robots = $398

Tax rate = 8%

Amount of tax of each robots = 8% of $398

= 8/100 × $398

= 0.08 × $398

= $31.84

TOTAL TAX to be paid = Amount of tax of each robots × Number of robots

= $31.84 × 3

= $95.52

TOTAL TAX to be paid = $95.52

A rectangular park of length 60 m breadth 50 m encloses w volleyball court of length 18 m and breadth 10 m. Find the area of the park excluding the court at the rate of Rs 110 per square meter.​

Answers

Given

A rectangular park of length 60 m breadth 50 m encloses with volleyball court of length 18 m and breadth 10 m.

To find:

The area of the park excluding the court at the rate of Rs 110 per square meter.​

Solution:

Area of a rectangle is:

[tex]Area=length \times breadth[/tex]

Area of whole park is:

[tex]A_1=60 \times 50[/tex]

[tex]A_1=3000[/tex]

Area of volleyball court is:

[tex]A_2=18 \times 10[/tex]

[tex]A_2=180[/tex]

Now, the area of the park excluding the court is:

[tex]A=A_1-A_2[/tex]

[tex]A=3000-180[/tex]

[tex]A=2820[/tex]

Therefore, the area of the park excluding the court is 2820 square meter.

anyone know the answer?

Answers

Answer:

26.97

find side km using cos,after you find km you can then use tan to find the angle

hope this helps

Which of the following are true statements about the expression 12^5?
Check all that apply.
A. 12 is the base.
B. 12 is the exponent and tells us how many times we should
multiply 5 by itself.
C. 5 is the exponent and tells us how many times we should multiply 12 by itself.
D. 5 is the base.

Answers

C because 5 is the exponent and so you multiply 12 by itself 5 times

Need helppppp I’m stuckkkk

Answers

Answer:

b) 94

Step-by-step explanation:

The Total Degree of a Triangle is 180 degrees. Knowing this, set up an equation.

68+26+x=180.

x is the complementary angle of the "?" angle.

Solve the equation.

94+x=180

x=86

Then Subtract 86 from 180 to find "?"

180-86=94

I hope this helps!

Answer:

94;b

Step-by-step explanation:

68+26=94. 180-94=86. 180-86=94.

please help me solve the equations, I re-wrote the question under each of them so you can read it better. Ty ​

Answers

I think these are the correct answers
45. 13/36
46. 86/63
47. 19/42
48. 17/30

Answer:

45:13/36

46:86/63

47:19/42

48:9/10

49:1/12

The heights of 200 adults were recorded and divided into two categories
Which two-way frequency table correctly shows the marginal frequencies

Answers

Answer:

C

Step-by-step explanation:

male total= 98

female total =102

total total=200

see screenshot below

Answers

Answer:

4x^2 +2x +1

Step-by-step explanation:

(4x^3 -14x^2 -7x-4) / (x-4)

Using synthetic division

Bringing  down the 4  and multiplying  and adding

4      4   -14  -7  -4

       ↓   16   8   4

-------------------------------

      4     2    1   0

The quotient is  4x^2 +2x +1  and the remainder is 0

Answer:

[tex] {4x}^{2} + 2x + 1[/tex]

Step-by-step explanation:

the most handy way to solve the question is Polynomial long division which is done below:

[tex] \begin{array}{ccc} \qquad {4x}^{2} + 2x + 1 \\ \hline x - 4 \Bigg)4 {x}^{3} - {14x}^{2} - 7x - 4 \\ - {4x}^{3} + 16 {x}^{2} \\ \hline \qquad \qquad \qquad {2x}^{2} - 7x - 4 \\ \qquad \qquad- {2x}^{2} + 8x \\ \hline \qquad \qquad \qquad \qquad \qquad x - 4 \\ \qquad \qquad \qquad \qquad \qquad - x + 4 \\ \hline\qquad \qquad \qquad \qquad \qquad0 \end{array}[/tex]

since our remainder is 0 we'll put the answer in P(x) form only

note: please see the answer in the brainly app for a better view

simplify.
[tex] {y }^{ - 3} [/tex]
Options:
3/y

-1/y^3

-3y

1/y^3​

Answers

Answer:

Rewrite the expression using the negative exponent rule   [text]{b}^{-n } = 1/bn

Step-by-step explanation:

1/y^3

If 8 is 8% of S, what does S equal?

Answers

Answer: S=100.

Step-by-step explanation:

Since 8 is 8% of 100 we know this is right.

Answer:

S = 100

Step-by-step explanation:

The equation is 8/? = 8/100

Multiply 8 x 100 to get 800, then divide by 8% to get 100.

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