If the nth term of a sequence is
28-3n what is the 7th term?

Answer:

[tex]x = \sqrt{-2} = 2i[/tex]

Step-by-step explanation:

[tex]5x^2-2=-12[/tex]

[tex]5x^2 =-10[/tex]

[tex]x^2 =-2[/tex]

[tex]x = \sqrt{-2} = 2i[/tex]

Answer:

A. x=2 y=7

Step-by-step explanation:

-12x -3 = 3y

6x + 3y = 33

sooo you add them up...

so its

-6x = -12

x=2

and then you plug in the x value into one of the equations

6x + 3y = 33

6(2) + 3y = 33

12 + 3y = 33

3y = 33 - 12

3y = 21

21/3=7

y=7

Answer:

wheres the underline pls let me know what is underlined ill answer it on comment

Given:

The sum of the first three terms = 12

The sum of the first six terms = (−84).

To find:

The third term of a geometric progression.

Solution:

The sum of first n term of a geometric progression is:

[tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]

Where, a is the first term and r is the common ratio.

The sum of the first three terms is equal to 12, and the sum of the first six terms is equal to (−84).

[tex]\dfrac{a(r^3-1)}{r-1}=12[/tex]               ...(i)

[tex]\dfrac{a(r^6-1)}{r-1}=-84[/tex]               ...(ii)

Divide (ii) by (i), we get

[tex]\dfrac{r^6-1}{r^3-1}=\dfrac{-84}{12}[/tex]

[tex]\dfrac{(r^3-1)(r^3+1)}{r^3-1}=-7[/tex]

[tex]r^3+1=-7[/tex]

[tex]r^3=-7-1[/tex]

[tex]r^3=-8[/tex]

Taking cube root on both sides, we get

[tex]r=-2[/tex]

Putting [tex]r=-2[/tex] in (i), we get

[tex]\dfrac{a((-2)^3-1)}{(-2)-1}=12[/tex]

[tex]\dfrac{a(-8-1)}{-3}=12[/tex]

[tex]\dfrac{-9a}{-3}=12[/tex]

[tex]3a=12[/tex]

Divide both sides by 3.

[tex]a=4[/tex]

The nth term of a geometric progression is:

[tex]a_n=ar^{n-1}[/tex]

Where, a is the first term and r is the common ratio.

Putting [tex]n=3,a=4,r=-2[/tex] in the above formula, we get

[tex]a_3=4(-2)^{3-1}[/tex]

[tex]a_3=4(-2)^{2}[/tex]

[tex]a_3=4(4)[/tex]

[tex]a_3=16[/tex]

Therefore, the third term of the geometric progression is 16.

Answer:

45.9

Step-by-step explanation:

Answer:

(5) c

(6) c

(7) b

(8) a

Step-by-step explanation:

(5) The multiplicative inverse of a number n, is the number which when multiplied by n will give a result of 1 which is a multiplicative identity. The multiplicative inverse of a number is actually the reciprocal of that number. For example, the multiplicative inverse of n is 1/n. The multiplicative inverse of 5 is 1/5. The multiplicative inverse of 5/6 is 6/5.

Therefore, the multiplicative inverse of [tex]\frac{-11}{15}[/tex] is [tex]\frac{-15}{11}[/tex]

(6) To solve 7m + 12 = -4m + 78, follow these steps;

i. Collect like terms by putting terms with m on the left hand side and the terms without m on the right hand side as follows;

7m + 4m = 78 - 12

ii. Now solve both sides;

11m = 66

iii. Divide both sides by 11;

[tex]\frac{11m}{11} = \frac{66}{11}[/tex]

m = 6

(7) Let the number be x;

10 more than twice number is 22 implies that

10 + 2x = 22

Now solve the equation;

2x = 22 - 10

2x = 12

x = 6

(8) The interior angles of a given polygon are the angles of its vertices that are within or inside of the polygon.

The sum of the interior angles of a polygon is given by;

(n-2) x 180°

where;

n = number of sides of the polygon.

For example;

For a triangle, which has n = 3 sides, the sum of these interior angles is (3 - 2) x 180° = 180°

For a rectangle/square, which has n = 4 sides, the sum of these interior angles is (4 - 2) x 180° = 360°.

For a pentagon, which has n = 5 sides, the sum of these interior angles is (5 - 2) x 180° = 540°

Therefore, depending on the number of sides n, the sum of the interior angles of a given polygon is given by;

(n-2) x 180°

============================================================

Explanation:

The number 8 from "8 year old boy" can be completely ignored. In my opinion, this is an (un)intentional distraction on your teacher's part.

There are 6 toys to arrange. The order is important.

We have this countdown: 6,5,4,3,2,1

Those values multiply out to 6*5*4*3*2*1 = 720

There are 720 ways to arrange the 6 different toys. Order matters.

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

An alternative approach is to use the nPr permutation formula with n = 6 and r = 6. We use a permutation because order matters.

The nPr formula is

[tex]_{n} P _{r} = \frac{n!}{(n-r)!}\\\\[/tex]

where the exclamation marks indicate factorial. For example, 6! = 6*5*4*3*2*1 = 720.

Answer:

hour= 1.25

MINUTES ANSWER= 75 minutes

Step-by-step explanation:

hope that helps>3

Answer:

5/4 hour= 75 minutes

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

[tex]\textbf{HOPE IT HELPS}[/tex]

[tex]\textbf{HAVE A GREAT DAY!!}[/tex]

Answer:

0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Proportion of 0.6

This means that [tex]p = 0.6[/tex]

Sample of 46

This means that [tex]n = 46[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.6[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.6*0.4}{46}} = 0.0722[/tex]

Probability of obtaining a sample proportion less than 0.5.

p-value of Z when X = 0.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.5 - 0.6}{0.0722}[/tex]

[tex]Z = -1.38[/tex]

[tex]Z = -1.38[/tex] has a p-value of 0.0838

0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.

Answer:

[tex]8^{3(n-1)+1}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

hope it will help u

Answer:

2x + y

Step-by-step explanation:

x² + xy - y² = 4

→ Remember the rule, bring the power down then minus 1

2x + y

Answer:

3/14

Step-by-step explanation:

it takes 3 days to construct a porch and 14 days to construct a family room

so porch/family room = 3/14

Brainliest if this was correct

AnsweStep-by-step explanation:

lol

[tex]option(c) \: cylinder[/tex]

Step-by-step explanation:

You can see that in the figure, this is rectangle. Here, ABCD is rotated around the vertical line through A and D. So, you will get Cylinder shape as you rotate it.

Answer:

Step-by-step explanation:

> the equation given is x-y =0

> three points that will solve the equation could be

if x= -2 , y = -2 then x-y = 0 is -2 -(-2) =0 so it works point (-2,-2)

if x=1, y = 1 then x-y = 0 is 1-1 =0 is true so we have point (1, 1)

if x=2 ,y= 2 then x-y = 0 is 2-2 =0 is true so we have point (2, 2)

Answer:

4.076

Step-by-step explanation:

tan27°= |AC|/8

8*tan27°= 4.076

Use the tangent to find the unknown side lengths.

This is the answer

Ac= 4.07

Ab=8.97

Answer:

30 minutes

Step-by-step explanation:

that problem description is imprecise.

I think what is meant here : they each keep jogging at their own same speed.

Diane's speed is 1/3 miles / 10 min.

Jack's speed is 2/3 miles / 10 min.

now, to bring this to regular miles/hour format, we need to find the factor between 10 minutes and an hour (60 minutes) and multiply numerator and denominator (top and bottom of the ratio) by it.

60/10 = 6.

so, we need to multiply both speeds up there by 6/6 to get the miles/hour speeds.

Diane : (1/3 × 6) / hour = 2 miles / hour

Jack : (2/3 × 6) / hour = 4 miles / hour

since Jack is running twice as fast as Diane, she will finish one length in the same time he finishes a round trip (back and forth).

Diane running 1 mile going 2 miles/hour takes her 30 minutes.

Jack running 2 miles (back and forth) going 4 miles/hour will take him also 30 minutes.

so, they will meet at his starting point after 30 minutes.

Answer: Definition: Ratio of the size of the map to its subject: Scale ... so scale = 1 cm / 100,000 cm = 1/100,000. - Scale ... STEP 1: - 2 cm represents 5 km

Step-by-step explanation:

STEP 1: - 2 cm represents 5 km - (write in full)

- STEP 2: - 1 cm represents 2.5 km - (divide so left side = 1)

- STEP 3: - 1 cm represents 250,000 cm - (convert to same units)

- STEP 4: - scale is 1 : 250,000 - (express as a representative fraction)

Answer:

1/2

Step-by-step explanation:

The largest value in fraction it is 1/2 because the fraction is small amount .while the 3/4 is least amount .and 3/5 is greatest amount fractions

C={ check example in book}

Answer:

[tex]A = 200,000(1+.025) ^{t}[/tex]

[tex]A = 200,000(1+.025) ^{10}[/tex]

Step-by-step explanation:

Answer:

Smallest: 18° Middle: 54° Largest: 108°

Step-by-step explanation:

We can start by writing out what we know in a series of equations:

s= smallest angle, m= medium angle, L= largest angle.

Since the largest is 6 times the smallest we have:

L=6s

Since the middle is 3 times the smallest we have:

m=3s

Since the 3 interior angle measures of a triangle always must equal 180°, we have:

s+m+L=180

Then we plug in our L and m into the third equation:

s+3s+6s=180

Combining like terms and solving:

10s=180

s=18

Then we plug in 18 for s into the first 2 equations to get:

L= 6* 18

L= 108

and

m= 3* 18

m= 54

So s= 18, m= 54, and L=108.

To check the answer we can:

Answer:

A

Step-by-step explanation:

Hello,

if B ⊂ A then A∩B=B

So B={1,4,5}

As per the given value of sets, B is (1,4,5).

A set is a collection of one or multiple data.

Given,

B ⊂ A

[tex]A[/tex] ∩  [tex]B = (1,4,5)[/tex]

[tex]A[/tex] ∪ [tex]B = (1,2,3,4,5,6)[/tex]

As B ⊂ A, therefor, B is a subset of A.

Therefore, [tex]A[/tex] ∩ [tex]B = B[/tex] and [tex]A[/tex] ∪ [tex]B = A[/tex]

Hence, [tex]B = A[/tex] ∩ [tex]B = (1,4,5)[/tex].

Learn more about a set here:

https://brainly.com/question/20516078

#SPJ2

Answer:

2<X ,this is because opened and facing towards x

and

–3≤X this is because the circle is closed and also facing towards x

Answer:

No.

Step-by-step explanation:

y/x has to be the same number no matter what except at point (0 0) which it must also include for it to be a direct variation.

*y=2x+3 is not a direct variation because you can not write it as y/x=k where k is some constant number. If we were y=2x, then yes since y/x=2.

*You could also take two points and see if they are proportional. That is, you can see if y2/x2 gives the same value as y1/x1 where (x1,y1) and (x2,y2) are points on the line y=2x+3. This must work for every pair of points on the linear relation except at x=0 (where you would or should have y=0 if it is directly proportional).

Let's try it out. If x=1, then y=2(1)+3=5.

5/1=5

If x=2, then y=2(2)+3=7

7/2=3.5

As you can see 5 doesn't equal 3.5.

*For it to be a direct variation, it also must contain the point (0,0) and be a diagonal line when graphed. It can also be written in form y=kx where k is a constant number. This fails two of the the things I mentioned. It doesn't contain point (0,0) because y=2(0)+3=3 not 0. It cannot be written in form y=kx because of the plus 3.

If it were y=2x, then the answer would be yes.

Answer:

Step-by-step explanation:

[tex]4(x+y)^{2} - 9(x-y)^{2}=4[x^{2}+2xy+y^{2}]-9[x^{2}-2xy+y^{2}]\\\\=4x^{2}+4*2xy + 4y^{2}-9x^{2}-2xy*(-9)+y^{2}*(-9)\\\\= 4x^{2}+8xy+4y^{2}-9x^{2}+18xy-9y^{2}\\\\= 4x^{2}-9x^{2} + 8xy + 18xy +4y^{2} - 9y^{2}\\\\= -5x^{2} + 26xy - 5y^{2}[/tex]

= -5x² + 25xy + xy - 5y²

= 5x(-x + 5y) - y(-x +5y)

= (-x + 5y)(5x - y)