The start of an arithmetic sequence is
17, 21, 25, 29,
21,
The rule for the sequence can be written in the form
In
= en + d, where c and d are numbers.
a) By first calculating the values of c and d, work out the rule
for the sequence.
b) What is the value of 211?

Answer:x=16

Step-by-step explanation:

just divide both sides by negative 1

Answer:

m∠TQS = 137°

m∠RQS = 43°

Step-by-step explanation:

It is given that ∠RQT is a straight angle
That means that this angle is 180° and RQT is a straight line

Therefore m∠TQS + m∠RQS = m∠RQT = 180°

Given
m∠TQS = (6x + 20)° and m∠RQS = (2x + 40)°

adding the two angles together will imply
(6x + 20)° +  (2x + 40)° = 180°

=> 6x + 20 + 2x + 4 = 180
=> 6x + 2x + 20 + 4 = 180

=> 8x + 24 = 180

=> 8x = 180 - 24= 156

=> x = 156/8 = 19.5

Substitute for x in  the angle expressions
m∠TQS = 6x + 20 = 6(19.5) + 20 = 117 + 20 = 137°

m∠RQS  2x + 4 = 2(19.5) + 4  = 39 + 4 = 43°
(or we could subtract m∠TQS from 180 to get 180 - 137 = 43°)

Check if they add up to 180°
137° + 43° is indeed 180°

A power function has the formula f(x) = kxⁿ,

A power function is a function that has a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real value. (A coefficient is a value that increases an exponent by a variable.)

Monomial functions:

Linear: y=3x+5

Quadratic: y = x²

Constant: y = 6

Cubic: y = x³+5

Quartic : y = x⁴

Quantic : y = x⁵

Therefore the function with a power function is given by y = k xⁿ

To learn more about power function visit:

https://brainly.com/question/24364138

#SPJ1

Julia must sell 21 tacos to meet the requirement .

Given: Price of each taco = $ 3.75

Price of each burrito = $ 6

Total amount of money she needs to earn = $ 330

Also the number of burritos sold= 42.

So the total amount earned on selling these burritos= 42× 6 = $ 252

And as it is given that total money she needs to earn is $ 330 .

so required money= $ 330- $ 252

=$ 78

Thus the total number of tacos she needs to sell = 78/ price of 1 taco

= 78/ 3.75

= 20.8 ≈ 21

Thus Julia must sell 21 tacos to meet the requirement .

To know more about selling and buying refer to:

https://brainly.com/question/27681817

#SPJ13

Answer:

is there a picture because this can't be solved without a picture

The quadratic function has an equation of f(x) = 2x²+ x - 4

From the question, the ordered pairs are given as

(-1, -3), (0, -4), (2, 6)

A quadratic function is represented as

f(x) = ax²+ bx + c

Using the point (0, -4), we have

a(0)²+ b(0) + c = -4

So, we have

c = -4

This gives

f(x) = ax²+ bx - 4

Using the point (-1, -3), we have

a(-1)²+ b(-1) - 4 = -3

So, we have

a - b = 1

Using the point (2, 6), we have

a(2)²+ b(2) - 4 = 6

So, we have

4a+ 2b  = 10

So, we have

a - b = 1

This gives

a = b + 1

Substitute a= b + 1 in 4a+ 2b  = 10

4(b + 1) + 2b  = 10

This gives

4b + 4 + 2b  = 10

Evaluate

6b = 6

Divide

b = 1

So, we have

a = 1 + 1

a = 2

So, we have

f(x) = 2x²+ x - 4

Hence, the equation is f(x) = 2x²+ x - 4

Read more about quadratic function at

https://brainly.com/question/1214333

#SPJ1

Here, we are given;

P(A)=0.6

P(B)=0.42

P(B/A)=0.63

We have to find;

Now,

This is the formula for finding conditional probability.

From here,we can see that we have values of P(B/A) and P(A) and we can easily find P(Aand B) from here.

Since P(A)>0 so we can use this formula.

Therefore,

The equation have infinitely many solution when n is equal to -15.41.

A linear equation in one variable is an equation which has a maximum of one variable of order 1. It is of the form ax + b = 0, where x is the variable. This equation has only one solution.

Given equation is;

24( mx + n ) = 3x + 17

where; m and n are real numbers.

Part 1.  If m = 14 and n = 13 then

Putting the value of m and n in the equation we get;

= 24( 14.x + 13 ) = 3x + 17

=  336x + 312 = 3x + 17

=  336x - 3x = 17- 312

=  333x = -295

x = 0.886

Hence,  x = 0.886  the equation having one solution .

part 2.  if m = 18 then to find n .

put m = 18 in the given equation;

= 24(18.(0.886) + n ) = 3(0.886) + 17

= 24(15.94) + 24n = 2.658 + 17

= 382.56 + 24n = 19.658

= 24n = 19.658 - 382.56

n = -15.41

Hence, The equation have infinitely many solution when n is equal to -15.41.

TO learn more details about the types of solution click the given below.

brainly.com/question/21400387

#SPJ1

The complete question is;

PART A: Rosie writes the equation 24(mx+n)=3x+17, where m and n are real numbers.

If m=14 and n=13, does the equation have one solution, infinitely many solutions, or no solutions? Explain your answer.

Answer:

7b + 6

Step-by-step explanation:

Given expression,

→ 5b + 10 + 2b - 4

Let's solve the expression,

→ 5b + 10 + 2b - 4

→ (5b + 2b) + (10 - 4)

→ 7b + 6

Hence, answer is 7b + 6.

The problems with a difference of 10.2 are:

We are given some subtraction problems for which we need to find the ones with a difference of 10.2.

The problems are:

12.05 - 2.03

16.29 - 6.09

36.1 - 25.9

22.09 - 21.07

10.82 - 9.8

We find the difference for each of them one-by-one after subtraction.

The question is incomplete. Find the complete question below:

Circle the two subtraction problems that have a difference of 10.2.

12.05 - 2.03

16.29 - 6.09

36.1 - 25.9

22.09 - 21.07

10.82 - 9.8

Learn more about subtraction at https://brainly.com/question/17301989

#SPJ1

Answer:

7.63 x 10⁷

Step-by-step explanation:

To convert to scientific notation you have to move the decimal place to where there is only one number in front of it. In this cause the number in front is 7. You have to maintain the same number of significant figures which in this case was 3 then multiply by 10 to the exponent of how many times you moved the decimal place.

Answer:

=76.3×10⁶

Step-by-step explanation:

=76,300,000÷1,000,000

=76.3×10⁶

Answer: 4√2-0.5

Step-by-step explanation:

[tex]\sqrt{(2\sqrt{2}-3)^2 } +|2\sqrt{2}+5|-|-2.5|=\\\\|2\sqrt{2}-3|+(2\sqrt{2}+5)-(2.5 )=\\\\2\sqrt{2}-3+2\sqrt{2}+5-2.5 =\\\\4\sqrt{2} -0.5[/tex]

If the coordinates of the vertex of a parabola are known [tex]V(p,k)[/tex], the equation for that parabola can be written by the following formula;7

Now let's find the vertex of the given equation.

We've found our vertex.

Let's substitute the unknowns in the formula I've given.

Let's expand the expression and find the coefficient p.

Finally;

[tex]q=\frac{7}{4}[/tex]

[tex]p=2[/tex]

Step-by-step explanation:

100% = 1028

1% = 100%/100 = 1028/100 = 10.28

the decrease was

1028 - 755 = 273

these 273 were how many % ?

as many % as how often 1% fits into 273 :

273 / 10.28 = 26.55642023... %

this was a 26.55642023...% decrease.

Answer:

96

Step-by-step explanation:

If Y is directly proportional (or in this case varies directly) then whatever you do to one value you do to the other.

So in this case, when Y = 8 and X = 4 that means that Y is double of X (cause 8 is double 4).

So when X = 48 all you need to do is double X which will give you 96.

Answer:

AB = 12cm

Step-by-step explanation:

ABC is the right triangle, that means we can use theorem: AC²=AB²+BC²

AB²=AC²-BC²=13²-5²=169-25= 144

AB=√144

AB=12cm

Answer: -8°

Step-by-step explanation: the temperature dropped by 64 degrees over the span of 8 hours. 64/8 = 8.

Answer:

The answer is most definitely A. It is the only answer that reaches the correct value of 190, which is what 5 * 38 equals. However, to put it into perspective...

Step-by-step explanation:

When we use the distributive property we are breaking down something sometimes, and in this case, very simple into a more extended form.

5 * 38 is the same as saying 5(40 - 2). We also know that if we subtract the sum of 5 * 2 from 5 * 40, it will end up the same as 5 * 38 because you are multiplying 5 two times less.

5 * 40 = 200

5 * 2 = 10

200 - 10 = 190

The answer is A

;)

Step-by-step explanation:

Q.1

6×sqrt(27) + 11×sqrt(75) =

= 6×sqrt(3×9) + 11×sqrt(3×25) =

= 3×6×sqrt(3) + 5×11×sqrt(3) =

= 18×sqrt(3) + 55×sqrt(3) = 73×sqrt(3)

Q.2

53×sqrt(5) × (-103×sqrt(50)) =

= 53×-103 × sqrt(5)×sqrt(50) =

= -5459 × sqrt(5×50) = -5459 × sqrt(250) =

= -5459 × sqrt(10×25) = -5459 × 5×sqrt(10) =

= -27,295 × sqrt(10)

Q.3

1/4 + 1/2 rational (as both terms are rational)

sqrt3 + 4 irrational (as sqrt(3) is not rational)

sqrt4 + 7 rational (sqrt(4) = 2, 2+7 = 9)

2 x sqrt9 rational (sqrt(9) = 3, 2×3 = 6)

7 x sqrt6 irrational (sqrt(6) is not rational)

4x2sqrt3 irrational (sqrt(3) is not rational)

3. 7 x (1/3) rational (all terms are rational)

7 x sqrt81 rational (sqrt(81) = 9, 7×9 = 63)

A model of a famous statue is  [tex]3\frac{1}{2}[/tex]inches tall. The actual statue is  [tex]5\frac{1}{4}[/tex] feet tall, the ratio of the height of the model to the height of the actual statue in simplest​ form is  [tex]3\frac{1}{2}[/tex]:63

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of the lemons to oranges is 6:8 (or 3:4). (or 4:7).

A ratio can have any number of quantities, such as counts of people or things or measurements of the length, weight, time, etc. Both the numbers must be positive in most situations.

You can specify a ratio by either writing out both of the integers that make it up, "a to b" or "a:b", or by giving just the value of their quotient a/b. Equal quotients correspond to the equal ratios.

A ratio can therefore be thought of as an ordered pair of integers, a fraction with first number in the numerator and the second in the denominator, or as the value represented by this fraction. Ratios of the counts that are expressed in terms of (non-zero) natural numbers are rational numbers and occasionally natural numbers as well. The ratio of the two numbers is a dimensionless number when they are measured using the same unit, which happens frequently. A rate is product of two quantities that are divided by their respective units of measurement.

Given,

A model of a famous statue is [tex]3\frac{1}{2}[/tex] inches tall.

The actual statue is [tex]5\frac{1}{4}[/tex] feet tall

1 feet = 12 inches

21/4 ft = 12*21/4 inches = 63 inches

Therefore the ratio is

[tex]3\frac{1}{2}[/tex]:63

To know more about ratio visit: https://brainly.com/question/13419413

#SPJ9

Answer:

An hour is a unit of time.

Step-by-step explanation:

An hour is a period of 60 minutes.

1 hour = 60 minutes.

Answer:

an hour is the si unit of time

1 hour = 60 minutes

1 minutes = 60 seconds

pls mark as brainliest

Step-by-step explanation:

The average rate for the entire walk of hiker is 3.75 miles per hour by the concept of average speed.

The instantaneous speed is the upper limit of the average speed as the duration of the time interval approaches zero. An object's average speed during a certain period of time is equal to its distance traveled over that period divided by its duration. Speed and velocity are distinct concepts.

The whole distance traveled divided by the total time results in the average rate for the entire walk, expressed in miles per hour.

Given that:

Distance A = 12.8 miles

Distance B = 17.2 miles

Total distance = Distance A + Distance B

Total distance= 12.8 + 17.2

Total distance= 30 miles

Time A = 9:00 a.m. to noon = 3 hours

Time B = 1:00 p.m. to 6:00 p.m. = 5 hours

Total time = Time A + Time B

Total time= 3 + 5

Total time= 8 hours

Average rate = Total distance/Total time

Average rate= 30 miles/8 hours

Average rate= 3.75 miles per hour

Therefore, the average rate for the entire walk of hiker is 3.75 miles per hour.

To know more about average rate visit:

https://brainly.com/question/12322912

#SPJ13

The minimum additional information needed in order to be able to state that the triangles are congruent by AAS is . Option A

[tex]\angle A B C=\angle A D C[/tex]

This is further explained below.

Generally, The triangles are said to be congruent if they satisfy the AAS (Angle-Angle-Side) condition, which states that if two angles and a non-included side in one triangle are congruent to two angles and the equivalent non-included side in another triangle, then the triangles are congruent.

In conclusion, The following pieces of knowledge are the bare minimum that is required in order to be able to make the assertion that the triangles are congruent according to AAS:

[tex]\angle A B C=\angle A D C[/tex]

Read more about a congruent  angle

https://brainly.com/question/16448127

#SPJ1

Answer:

-3(12g)

Step-by-step explanation:

Because if we simplify the 7+5g to 12g because 7+5=12.

Therefore,

-3(7+5g)= -3(12g)

Answer:

a=5

Step-by-step explanation:

1/3(6a-15)=(a-2)+2

1/3(6a-15)=a

6a-15=3a

3a=15

a=5

:]

Step-by-step explanation:

1.multiply in first bracket

[tex]2a - 5 = a + 0[/tex]

2.Take unknowns to left and constants to the right

[tex]2a - a = 5[/tex]

3.solve for a

[tex]a = 5[/tex]

Answer:

y = 7

eight grade math comes back to haunt me

Answer:

21

Step-by-step explanation:

7x - 7

=> substituting x = 4

=> 7(4) - 7

=> 28 - 7

=> 21

We know that the equation of a line is given by

y = mx + b, where m and b are numbers:

m is the slope of the line and b is the y intercept.

In this case we have the equation:

6 - 2y = - 6

We clear y so we can identify m and b

6 - 2y = -6​

6 = -6​ + 2y

6 + 6​ = 2y

12 = 2y

12/2 = y

6 = y

In this case

y = 6

Then m=0 and b = 6

The situation that is best represented by an exponential distribution is given by the following option:

Tafadzwa runs between 10 and 16 laps every day. his times get slower as he gets tired, but his daily average is 48.2 s per lap. what is the probability that his mean lap time tomorrow will be less than 45 s?.

The exponential probability distribution, with mean m, is described by the following mass function:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

From this, we get that the exponential distribution is used when we want to study the time between events in a distribution, and only the first option in this problem gives it.

As for the other options, the distributions are as follows:

More can be learned about the exponential distribution at https://brainly.com/question/16371214

#SPJ1

1. Solve s in the second equation:

2. Substitute the s in the first equation by the value you get in the previous step:

3. Solve t:

4. Use the value of t to solve s: