Change x^2-2x-3 to intercept form

the first four terms of a geometric progression are 2,10,50,250 a) write down the common ratio of the progression b) write down

VLD [36.1K]

Answer:

The common ratio is 5 and the 5th term is 1250

Step-by-step explanation:

The common ratio is given by

r=U(2)/U (1)

=10/2

=5

The fifth term

U (n)=ar^n-1

U(5)=2(5)^5-1

=2×5^4

=2×625

=1250

3 0

3 years ago

The perimeter of the rectangle she below is 24feet

maxonik [38]

This is really obvious but the answer is 4 feet.

6 0

2 years ago

Which simplifications of the powers of i are correct? There may be more than one correct answer.

fredd [130]

$\bf i^2=-1\qquad\qquad i^3=-i\qquad \qquad i^4=1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ i^{22}\implies i^{(4\cdot 5)+2}\implies i^{4\cdot 5}i^2\implies (i^4)^5 i^2\implies 1^5(-1)\implies -1~\dotfill \bigotimes \\\\\\ i^{11}\implies i^{(2\cdot 5)+1}\implies (i^2)^5 i\implies (-1)^5(i)\implies -i~\dotfill \checkmark$

$\bf i^{21}\implies i^{(4\cdot 5)+1}\implies (i^4)^5 i\implies 1^5(i)\implies i~\dotfill \checkmark \\\\\\ i^{12}\implies i^{3\cdot 4}\implies i^3 i^4\implies (-i)(1)\implies -i\dotfill \bigotimes \\\\\\ i^{20}\implies i^{4\cdot 5}\implies (i^4)^5\implies 1~\dotfill \checkmark \\\\\\ i^{26}\implies i^{(4\cdot 6)+2}\implies (i^4)^6 i^2\implies 1^6(-1)\implies -1\dotfill \checkmark \\\\\\ i^{27}\implies i^{(4\cdot 6)+3}\implies (i^4)^6 i^3 \implies 1^6(-i)\implies -i\dotfill \bigotimes$

6 0

2 years ago

A child is hopping along a sidewalk. The ratio table below shows the comparison between the number of hops and the distance trav

natima [27]

First we rewrite the table:
20 30
50 75
80 120
150 ?
We observe that for each 30 number of hops, the distance increases by 45 feet.
We must find the slope of the line:
m = (y2-y1) / (x2-x1)
m = (75-30) / (50-20)
m = 1.5
Then, the line is:
y = 1.5x
We substitute x = 150
y = 1.5 * (150)
y = 225
Answer:
Find the ratio of hops to distance traveled (1: 1.5), then multiply 150 by 1.5.

3 0

2 years ago

Read 2 more answers

An educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an est

MrRa [10]

Answer:

85% level of the confidence interval is

(26.337, 26.662)

Step-by-step explanation:

Explanation:-

Given the size of the sample 'n' = 295

Mean of the sample x⁻ = 26.5

The Standard deviation of the Population = 2.7

85% level of the confidence interval is determined by

$(x^{-} - Z_{0.15} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.15} \frac{S.D}{\sqrt{n} })$

Critical value Z₀.₁₅ = 1.036

85% level of the confidence interval is determined by

$(x^{-} - Z_{0.15} \frac{S.D}{\sqrt{n} } , x^{-} + Z_{0.15} \frac{S.D}{\sqrt{n} })$

$(26.9 -1.036 \frac{2.7}{\sqrt{295} } , 26.5 + 1.036 \frac{2.7}{\sqrt{295} })$

( 26.5 - 0.1628 , 26.5+0.1628)

(26.3372,26.6628)

7 0

2 years ago