Answer:
a. 1/2
b. 512
c. 1024
Step-by-step explanation:
The nth term of a geometric progression can be written as;
Tn = ar^n-1
where a is the first term, r is the common ratio and n is the term number
From the question;
Fifth term = ar^4 = 32
Eight term = ar^7 = 4
a. We want to find the common ratio
What to do here is that we can divide the 8th by the 5th term
ar^7/ar^4 = 4/32
r^3 = 1/8
r^3 = (1/2)^3
Thus r = 1/2
b. First term
we can make a substitution in any of the two given terms
Let’s use the fifth term
ar^4 = 32
a * (1/2)^4 = 32
a * 1/16 = 32
a = 16 * 32
a = 512
C. Sum of the first 50 terms
To calculate this, we use the sum of terms formula
Sn = a(1- r^n)/1-r
a = 512 , n = 50 and r = 1/2
Making the substitution;
Sn = 512(1-(1/2)^50)/1-1/2
Kindly note that (1/2)^50 will be infinitesimally small and will be close to zero
So we can approximate (1/2)^50 to be zero
Hence;
Sn = 512(1-0)/0.5
Sn = 512/0.5
Sn = 1024
Find 2 equivalent fractions to 4/6
Plane zwv and plane tuv intersect at
Answer:
Option (1)
Step-by-step explanation:
Planes ZWV (shaded side) and plane TUV (Top of the box) are the two sides of the given cube or box in the picture attached,
Common edge of the given planes is side SV.
Common edge or the line where two planes meet is the line of intersection of two planes.
Therefore, line SV will be the line of intersection of the given planes.
Option (1) will be he answer.
Brad's checking account starts off with a balance of $126.50. Throughout the week, Brad pays a bill for $87.21, and pays $5.64 for breakfast. He deposits $15.00 but then pays another bill for $55.25. At the end of the week, he gets a notice from the bank that he has a negative balance. How much does Brad need to deposit into his account to get to a $0 balance?
Answer:
$6.6
Step-by-step explanation:
Let's find out what his balance is after those transactions.
Initial balance: 126.50
After bill:
126.50 - 87.21 = 39.29
After breakfast:
39.29 - 5.64 = 33.65
After deposit (we're adding money now!):
33.65 + 15 = 48.65
After 2nd bill:
48.65 - 55.25 = -6.6
We find that his balance is negative $6.6. Thus, to get to $0, he needs to deposit an additional $6.6.
Answer: $6.6
What is the domain of the given relation?
{(0, – 1), (2, - 3), (3, - 2)}
A
{0, 2, 3}
B
{ -3, - 2, - 1}
C
{ - 3, – 2,3}
D
{ - 1,0,2}
Answer:
Option (A) : {0,2,3} is the domain
Emily owns 10.2 shares of stock in a company. On Friday, the stock dropped by $1.35/share. What was the total change in value of Emily’s stock? −$13.77 −$7.56 +$7.56 +$13.77
Answer:
-$13.77
Step-by-step explanation:
cube root of 0.18125
Answer:
0.005954345703125
Step-by-step explanation:
0.18125^3 = 0.005954345703125
So I need help with this because I had did it but the teacher said to redo it but I forgot the answers,
Please help !
Solve it
it's easy
take as much time you need☺️
Step-by-step explanation:
101^2= [100+1]^2
[100]^2 +1^2+2×100×1
=10000+1+200
=10201
HOPE IT HELP.......
The candle maker makes a total of 454545 orange candles. This is 30\%30%30, percent of all the candles she made this week. How many candles did the candle maker make this week?
Answer:
150 candles
Step-by-step explanation:
Convert this rational number
to its decimal form and round
to the nearest thousandth.
7/8
Answer:
.875
Step-by-step explanation:
Guys I really need help!
The general equation for the geometric sequence -1, -2, -4, ... is a n = -1 · 2 n - 1 .
TrueFalse
Answer: false
Step-by-step explanation:
Answer:
Yes absolutely true i took the lesson
Step-by-step explanation:
Is 4 - 4x and 4(1 - x) equivalent expressions? Why or why not?
Hey there!
ANSWER:Yes
EXPLANATION:Is 4 - 4x and 4(1 - x) equivalent expressions? Why or why not?
If you want to know whether they are equivalent, let's first find the value of both of them.
[tex]4-4x[/tex]
[tex]-4x+4[/tex]
[tex]4(1-x)[/tex]
Let's add parenthesis to 4 and (1-x) and add negative to x.
[tex](4)(1+-x)[/tex]
Now separate all with parenthesis.
[tex](4)(1)+(4)(-x)=4-4x\\-4x+4(ANSWER)[/tex]
Since both had the same value, they are equivalent.
Hope this helps!
[tex]\text {-TestedHyperr}[/tex]
What is m
50
65
140
155
Answer:
65 degrees.
Step-by-step explanation:
Since angle JLG is 115 degrees, andgle JLH must be 65 because the two angles are supplementary, which means they add up to 180 degrees.
Which are the roots of the quadratic function f(b) = 62-75? Select two options,
b=53
b= -573
Ob=35
b = -315
b = 256
Answer:b=573
Step-by-step explanation:
help me i have no clue
Answer:
It seems like D if I eyeball it.
Encuentren dos números cuyo cociente sea -1 y que la resta del primero menos el segundo sea -3/2
Answer:
[tex]\dfrac{3}{4}\ \text{and}\ \dfrac{-3}{4}[/tex]
Step-by-step explanation:
Find two numbers whose quotient is -1 and the subtraction of the first minus the second is -3/2
Let two numbers are x and y. When they are divided the quotient is -1. So,
[tex]\dfrac{x}{y}=-1[/tex]
It can also be written as :
x = -y ....(1)
The subtraction of first minus the second is -3/2 .
[tex]x-y=\dfrac{-3}{2}\ .....(2)[/tex]
Use equation (1) in (2),
[tex]-y-y=\dfrac{-3}{2}\\\\-2y=\dfrac{-3}{2}\\\\y=\dfrac{3}{4}[/tex]
From equation (1) : [tex]x=\dfrac{-3}{4}[/tex]
Hence, two numbers are [tex]\dfrac{3}{4}\ \text{and}\ \dfrac{-3}{4}[/tex].
if α,β are the roots of the equation x^{2}-3x+2=0 form an equation whose roots are (α+β)² & (α-β)²
Solution:-
Let's find roots of x² - 3x + 2
=> x² - 3x + 2 = 0.
=> x² - x - 2x + 2 = 0.
=> x ( x - 1 ) -2 ( x - 1) = 0.
=> ( x - 1 ) ( x - 2 ) = 0.
=> x = 2, 1.
Now
( a + ß )² = (2+1)²=3²=9( a - ß )² = ( 2 - 1 )² = 1² = 1.So , equⁿ would be ,
=> x² - ( 9 + 1)x + 9×1=0.
=> x² - 10x + 9=0.
Here are two five-pointed stars. A student said, “Both figures A and B are polygons. They are both composed of line segments and are two-dimensional. Neither have curves.” Do you agree with the statement? Explain your reasoning.
Answer:A
Step-by-step explanation:
Bcnitsreksbeux
A store sells candles.
• The retail price was a 45% markup
over the manufacturer price.
• A month later, the store reduced the
retail price of the candles by 20
percent.
What percent markup is the new retail
price over the manufacturer price?
Answer:
25%
Step-by-step explanation:
If you start at 45% and it reduces by 20% you are just doing 45-20 which equals 25. (Please let me know if im wrong)
16 percent markup is the new retail price over the manufacturer price.
Here,
A store sells candles.
Retail price will be 45% marked-up
A month later, store reduced the retail price of the candles by 20%.
We have to find the percent markup.
What is the percentage?
The percentage is the value per hundred.
Now,
Consider the manufacturer price = 100x
Retail price will be 45% marked-up
Hence, 100x+45% of 100x = 145x
Reduced retail price of the ladder after one month = 145x-145x*20/100
Reduced retail price of the ladder after one month = 116x
Percentage markup of the reduced retail price over the manufacturer price will be:
={(reduced retail price - manufacturer price)/manufacturer price} *100
=[ (116x-100x)/100x ] *100 = 16%
Hence, 16 percent markup is the new retail price over the manufacturer price.
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2+2x + x^2 +XY
What would be the answer to this question simplified
Hey there!
ANSWER: [tex]x^2+xy+2x+2[/tex]EXPLANATION:[tex]2+2x+x^2+x*y[/tex]
To solve, you will need to simplify.
[tex]x^2+xy+2x+2[/tex]
Hope this helps!
[tex]\text {-TestedHyperr}[/tex]
A conditional statement can be written as "If hypothesis, then conclusion". How can "your phone is set to vibrate so it will not disturb others" be written as a conditional statement?
Answer:
If your phone is set on vibrate, then it will not disturb others.
Step-by-step explanation:
It's an if then statement.
plz help!!!! (click on the pic)
Answer:
x^2+8x
Step-by-step explanation:
instructions included above :)
Answer....
[tex] \boxed{ {x}^{2} + 8x}[/tex]
[tex] \boxed {\tt{Step-by-step \: explanation:-}}[/tex]
(6x²+10x-1)+(-5x²-2x+1)
=6x²+10x-1-5x²-2x+1
=6x²-5x²+10x-2x-1+1
=x²+8x
Is -5 a integer or rational or irrational?
Answer:
irrational
Step-by-step explanation:
Answer:
It's rational because it isn't a decimal with no end. To simplify it even more, it is an integer.
Step-by-step explanation:
f(x) = -2x, g(x)= -2x-1
Answer:
I graphed the two points on a graph in the attachment! Hope this helps! :)
Step-by-step explanation:
Hi! I need help on this one. Hope there's someone willing to help!!
2 of 5 is a 40% chance
40% * 40 = 16
He should expect to be stopped 16 times.
what is the answer 2(3x-4)+3(7-12x)
Answer:
-30x+13
Step-by-step explanation:
6x-8 + 21 - 36x
-30x+13
Follow the guided instructions below to rotate the figure 90° clockwise about the
point (-1,1).
Click and drag to draw a line through the yellow center and the vertex on
the circle.
y
10
9
8
7
6
5
3
2
0 1
-1
3
4
-5 4 3
5
6
7
8
9
10
-10-9-8
-3
-4
-5
-6
Answer:
1111111111111111
Step-by-step explanation:
222222222222
You pick one card from a standard deck of 52 cards. What is the probability that the card will be a two?
Answer:
4 out of 52 or simplified 2 out of 26
Step-by-step explanation:
There are 4 suites of cards, spades, hearts, clubs, diamonds and there is one card for two in each suite, so we therefore know that the probability of picking a two out of a 52 card deck will be four out of 52 or the simplified answer would be 2 out of 26. Hope this helps, have a great day!
what is the value of x?
Answer: 4
Step-by-step explanation:
subtract 10 from 18 , thats 8 then divide 8 by 2 and get 4.
The coordinates of points A and B are A(4, -2) and B(12, 10). What are the coordinates of the point that is 1/4 of the way from A to B?
Answer:
Step-by-step explanation:
(4 + 12)/4 = 16/4 = 4
(-2 + 10)/2= 8/4 = 2
(4, 2) is 1/4 of the way from A to B
The coordinates of the point that is 1/4 of the way from A to B is (28/5, 2/5) if the coordinates of points A and B are A(4, -2) and B(12, 10).
What is an ordered double?It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
It is given that:
The coordinates of points A and B are A(4, -2) and B(12, 10)
The coordinates of the point that is 1/4 of the way from A to B
The above statement means that the line segment AB is divided in the ratio of 1:4 internally.
Using the section formula:
Let C be the new coordinate point:
C(x) = [1(12) + 4(4)]/(1+4)
C(x) = 28/5
C(y) = [1(10) + 4(-2)]/(1+4)
C(y) = 2/5
Thus, the coordinate of the point that is 1/4 of the way from A to B is (28/5, 2/5) if the coordinates of points A and B are A(4, -2) and B(12, 10).
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