[tex] \green{\large\underline{\sf{Solution-}}}[/tex]
Given expression is
[tex]\rm :\longmapsto\:\dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } [/tex]
can be rewritten as
[tex]\rm \: = \: \dfrac{5 \times { {(5}^{2} )}^{n + 1} - {5}^{2} \times {5}^{2n} }{5 \times {5}^{2n + 3} - {( {5}^{2} )}^{n + 1} } [/tex]
We know,
[tex] \purple{\rm :\longmapsto\:\boxed{\tt{ {( {x}^{m} )}^{n} \: = \: {x}^{mn}}}} \\ [/tex]
And
[tex] \purple{\rm :\longmapsto\:\boxed{\tt{ \: \: {x}^{m} \times {x}^{n} = {x}^{m + n} \: }}} \\ [/tex]
So, using this identity, we
[tex]\rm \: = \: \dfrac{5 \times {5}^{2n + 2} - {5}^{2n + 2} }{{5}^{2n + 3 + 1} - {5}^{2n + 2} } [/tex]
[tex]\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 4} - {5}^{2n + 2} } [/tex]
can be further rewritten as
[tex]\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 2 + 2} - {5}^{2n + 2} } [/tex]
[tex]\rm \: = \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2} - 1)} [/tex]
[tex]\rm \: = \: \dfrac{4}{25 - 1} [/tex]
[tex]\rm \: = \: \dfrac{4}{24} [/tex]
[tex]\rm \: = \: \dfrac{1}{6} [/tex]
Hence,
[tex]\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } = \frac{1}{6} }}[/tex]
Betty was charged 15 1/2% interest for the year
on her loan of £2 400. James was charged 12% interest for the year on his loan of £4 000.
How much more interest did James pay for the
year?
HELP PLEASE
Answer: James was charged with $180 more for the year that Betty
Step-by-step explanation: So I dont know how your money currency works sorry, also Ive never done this kind of math problem so I dont know if its right
can somebody help me with these 2 questions plz
Answer:
1) 14/3 (D)
2) -0.6 (C)
Step-by-step explanation:
1) 5-(2/3)*(2/3//4/3)
2)|-1.2-2.03|-2.03/-2
Jim and his friends went out for dinner at a restaurant and the bill was $68.50 if Jim wants to tip 18% what should the tip be
Answer:
$12.33
Step-by-step explanation:
Since the bill is $68.50, and Jim wants to tip 18%, it will be $80.83 in total
18% = 0.18
since you don't want to DECREASE the bill, it's 1.18
1.18 x 68.5 = 80.83
hope this helped :)
Jerry played with 3 friends today, all at different times. He played with Tommy for 1 7/8 hours, then Nathan for 1 3/4 hours, then Chris for 3/2 hours.
How many hours did Jerry play with his 3 friends today?
Answer:
4hrs 7 minutes and 30 seconds
Step-by-step explanation:
1 7/8 = (1=60) + (7/8 * 60) = 1 : 52:50 time played with Tommy 1 3/4 = (1=60 ) ( (3/4 * 60) = 1:45:00 time played with Nathan 3/2 = (3/2 *60) = 90 = 1:30:00 time played with Chris Total played with 3 friends = 1:52:50 + 1:45:00+1:30:00= 4:07:50 = 4hrs 7 minutes and 30 seconds
A negative correlation means ________. a third variable eliminates a correlational relationship one variable decreases as the other increases there is a relationship between two variables, but it is not statistically significant two variables increase together, but they are associated with an undesirable outcome
Answer:
A negative correlation means one variable decreases as the other increases.
Suppose you have $20 in a bank account. You start saving $5 each week. Your friend has $5 in his account and is saving $10 each week. Assume that neithet you nor your friend makes any withdrawls.
a) After how many weeks will you and your friend have the sane amount of money
b) How much money will you have when your balances are the same?
Answer: y = $35 & 3 weeks
Step-by-step explanation:
Answer:
A) 3 week
B) $35
Step-by-step explanation:
$20-$5=15
$20+$15=35
Think about all the ways in which a circle and a parabola can intersect.
Select all of the number of ways in which a circle and parabola can intersect.
0
1
2
3
4
5
Answer:
3
Step-by-step explanation:
Answer:
0,1,2,3,4
Step-by-step explanation:
trustttttt meee
Find the sample standard deviation and the population standard deviation of the data set.
17, 37, 56, 16, 12, 16, 19, 45, 14, 37, 21, 26, 43, 46, 42
a.
5 - 13.97
5 - 3.73
0= 14.46
0 - 3.61
b.
d.
5 - 14.46
5-3.61
0-13.97
0 - 3.73
Please select the best answer from the choices provided
А
Answer:
Step-by-step explanation:
a
Which type of parent function is f(x) = ?
A. Square root
B. Reciprocal
C. Quadratic
D. Cube root
SUNMIT
Answer:
Write properties of function:
x intercept/zero: x = 0
Step-by-step explanation:
Write properties of function: Write properties of function:
x intercept/zero: x = 0
Answer: Write properties of function:
x intercept/zero: x = 0
Evaluate x(y+3)/(3+y)z for x = 2, y = 5, and z = 1.
4
3
2
1
Answer:
2
Step-by-step explanation:
hope this helps
Whose sequence proves triangle ABC is congruent to triangle DEF? Why?
Answer:
If you are doing the same assignment as me then you probably have to choose between either Chanel or Preston and if my math is correct than the right answer would be Chanel.
how to solve
2(x+6)=4
x=?
Answer:
[tex]x=-4[/tex]
Step-by-step explanation:
[tex]2(x+6)=4~(Given)\\\\2x+12=4~(Distribute~2~to~x+6)\\\\2x+12-12=4-12~(Subtract~12~on~both~sides)\\\\2x=-8~(Simplify)\\\\\frac{2x}{2}=\frac{-8}{2}~(Divide~2~on~both~sides)\\\\x=-4~(Simplify)[/tex]
Answer:
[tex]\boxed {x=-4}[/tex]
Step-by-step explanation:
[tex]2(x+6)=4[/tex]
Divide both sides by 2 :
[tex]\cfrac{2\left(x+6\right)}{2}=\cfrac{4}{2}[/tex][tex]x+6=2[/tex]Subtract 6 from both sides:
[tex]x+6-6=2-6[/tex][tex]x=-4[/tex]______________________
what is the volume of the prism?
Answer:
Step-by-step explanation:
h = 3 ft
l*b = 25 sq.ft
Volume = l*b *h
= 25 * 3
= 75 cubic feet
Answer:
75ft
Step-by-step explanation:
First you mupilply [tex]25 x 3 = 75ft[/tex]
and that is it.
A laboratory is testing a product by heating or cooling it at different rates. The table shows the results of four tests. Drag a number to each empty cell to complete the table.
ill give brainliest
Answer:Cell content
Started at 20° and dropped 4° each minute -4
Cell content
Started at −20° and rose 1° each minute 1
Cell content
Started at 20° and dropped 1° each minute -1
Cell content
Started at −20° and rose 4° each minute 1
Step-by-step explanation:
Answer:
Cell content
Started at 20° and dropped 4° each minute -4
Cell content
Started at −20° and rose 1° each minute 1
Cell content
Started at 20° and dropped 1° each minute -1
Cell content
Started at −20° and rose 4° each minute 1
Step-by-step explanation:
the line through (6, 1) and (-3,5) in
slope-intercept form
Answer: y = -4/9x + 11/3
Step-by-step explanation:
PLSSS HLEPP ME OUTT ITS URGENTTTT
Answer:
[tex]P(B) = \frac{4}{18} = \frac{2}{9} = 0.2[/tex]
Step-by-step explanation:
Sample space 2+5+7+4=18
Answer:
4/18 or 2/9
Step-by-step explanation:
The total number of balls = 2 + 5 + 7 + 4 = 18
4 out of the 18 balls are blue ∴ the probability is 4/18 or 2/9
Hope this helps!
6) Which numbers are irrational?
7.27, 5/9, square root of 15 , square root of 196
Answer:
The square route of 15 is irrational
May I please receive help?
Please????
Answer:
<1=23
Step-by-step explanation:
If WXZ contains both <1 and <2, and <2 is 4 times <1, then we can set this up as x + 4x = 115
This is easily simplified to 5x = 115
Divide both sides by 5 and you will get x=23
Helppppppp pleaseee tyy smmm
Answer: 56
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Round each number to the nearest ten 24. 311. 107
Answer:
24-20 311-310 107-110
Step-by-step explanation:
Answer:
nearest tenth
......
24= 20
311=310
107=110..........
Help please due today
Answer:
Line a. goes to table 3, line b. goes to table 2, and line c. goes to table 1.
Step-by-step explanation:
Here are the 3 lines graphed (I even labeled each for you) so you can have a bit of a visual.
Hopefully you can find the points on each graph.
(Hint: The x row represents the x coordinate of an ordered pair, and the y row represents the y coordinate of an ordered pair.)
Ordered pairs look like this btw (x,y)
Hope this helps :)
The types Flowers on the table make up an arrangement. What percent of the flowers in the arrangement her roses
Answer:
60%
Step-by-step explanation:
You could make a fraction to help solve for the answer. The denominator is 25 because you add 4 + 15 + 6. The numerator is 15, because it is the number of roses. 15/25 as a percent is 60% because you just times both the numerator and denominator by 4.
How do you solve for x and y. Thanks!!
Kinda urgent sorry..
Answer:
x= 17.5
y= 35
Step-by-step explanation:
Steps are in attachment.
Answer:
• For x (Acute angle property)
[tex]{ \rm{(2x + 10) \degree + 30 \degree + 6x=180 \degree}} \\ \\ { \rm{8x + 40=180}} \\ \\ { \rm{8x = 140}} \\ \\ { \boxed{ \underline{ \rm{ \: \: x =17.5 \: \: }}}}[/tex]
• For y ( Interior angle sum of triangles )
[tex]{ \rm{(y + 10) \degree + 6x \degree + 30 \degree = 180 \degree}} \\ \\ { \rm{y + 10 + 30 + (6 \times 17.5) = 180}} \\ \\ { \rm{y +145 = 180 }} \\ \\ { \boxed{ \underline{ \rm{ \: \: y = 35 \: \: }}}}[/tex]
if x=1 and y =-2 what's 3(2-x)+4(3-y)
explanation please
Answer:
23
Step-by-step explanation:
3/4+x=2x-x+ ?(need answer)
Answer:(x - 4)(2x + 3)
FOIL = first,outside,inside,last
F -- so multiply first terms in each set....(x)(2x)
O -- multiply outside terms in each set...(3)(x)
I -- multiply inside terms in each set....(-4)(2x)
L -- multiply last terms in each set.......(-4)(3)
Step-by-step explanation:
Show that:
[tex]\bigg(\frac{ \sqrt{7} + i \sqrt{3} }{\sqrt{7} - i \sqrt{3} } + {\frac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } } \bigg) \: is \: real \\ [/tex]
Please answer this question.
Step-by-step explanation:
[tex]\large\underline{\sf{Solution-}}[/tex]
Consider,
[tex]\rm \longmapsto\:\dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } [/tex]
On taking LCM, we get
[tex]\rm \: = \: \dfrac{ {( \sqrt{7} + i \sqrt{3})}^{2} + {( \sqrt{7} - i \sqrt{3})}^{2} }{( \sqrt{7} + i \sqrt{3})( \sqrt{7} - i \sqrt{3})} [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}}} \\ [/tex]
and
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ (x + y)(x - y) = {x}^{2} - {y}^{2} \: }}} \\ [/tex]
So, using these Identities, we get
[tex]\rm \: = \: \dfrac{2\bigg[ {( \sqrt{7})}^{2} + {(i \sqrt{3}) }^{2} \bigg]}{ {( \sqrt{7}) }^{2} - {(i \sqrt{3})}^{2} } [/tex]
[tex]\rm \: = \: \dfrac{2(7 + 3 {i}^{2})}{7 - {3i}^{2} } [/tex]
We know,
[tex] \purple{\rm \longmapsto\:\boxed{\tt{ {i}^{2} = - 1}}} \\ [/tex]
So, using this, we get
[tex]\rm \: = \: \dfrac{2(7 - 3)}{7 + 3} [/tex]
[tex]\rm \: = \: \dfrac{2 \times 4}{10} [/tex]
[tex]\rm \: = \: \dfrac{4}{5} [/tex]
Hence,
[tex] \red{\rm\implies \:\boxed{\sf{ \dfrac{ \sqrt{7} + i \sqrt{3} }{ \sqrt{7} - i \sqrt{3}} + \dfrac{ \sqrt{7} - i \sqrt{3} }{ \sqrt{7} + i \sqrt{3} } \: is \: purely \: real}}}[/tex]
Solve the quadratic equation numerically (using tables of x- and y-values).
x2 + 9x + 18 = 0
a. x = 6 or x = 2
c. x = -6 or x = -3
b. x = 6 or x = -3
d. X = 6 or x = -1
Answer:
Third Option: [tex]x=6[/tex] or [tex]x=-3[/tex]
Step-by-step explanation:
[tex]x^2+9x+18=0[/tex]
[tex](x+6)(x+3)=0[/tex]
[tex]x=6[/tex] or [tex]x=-3[/tex]
Can anyone help me, I can’t find the answer.
Answer:
(p = 2) = -2
Step-by-step explanation:
HELP ME PLEASEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
Commutative Property
Step-by-step explanation:
Hope it helps. Please mark me brainliest if you would :D
If you translated the point a (4,-3) left 2 units and down 6 units where is A