Answer:
The sum of the first 8 terms will be:
[tex]\frac{1288991}{7776}[/tex]Step-by-step explanation:
Given the sequence
[tex]36, 30, 25, ...[/tex]
A geometric sequence has a constant ratio and is defined by
[tex]a_n=a_0\cdot r^{n-1}[/tex]
computing the common ratio
[tex]\frac{30}{36}=\frac{5}{6},\:\quad \frac{25}{30}=\frac{5}{6}[/tex]
[tex]r=\frac{5}{6}[/tex]
As the first element is
[tex]a_1=36[/tex]
so the nth term will be:
[tex]a_n=a_0\cdot r^{n-1}[/tex]
[tex]a_n=36\left(\frac{5}{6}\right)^{n-1}[/tex]
Geometric sequence sum formula
[tex]a_1\frac{1-r^n}{1-r}[/tex]
Plugin the values to determine the sum of the first 8 terms
[tex]n=8,\:\spacea_1=36,\:\spacer=\frac{5}{6}[/tex]
[tex]=36\cdot \frac{1-\left(\frac{5}{6}\right)^8}{1-\frac{5}{6}}[/tex]
[tex]=\frac{\left(1-\left(\frac{5}{6}\right)^8\right)\cdot \:36}{1-\frac{5}{6}}[/tex]
[tex]=\frac{36\left(-\left(\frac{5}{6}\right)^8+1\right)}{\frac{1}{6}}[/tex]
[tex]=\frac{36\left(-\frac{390625}{1679616}+1\right)}{\frac{1}{6}}[/tex]
[tex]=\frac{\left(1-\frac{390625}{1679616}\right)\cdot \:36\cdot \:6}{1}[/tex]
[tex]=\frac{216\left(-\frac{390625}{1679616}+1\right)}{1}[/tex]
[tex]=\frac{216\cdot \frac{1288991}{1679616}}{1}[/tex]
[tex]=216\cdot \frac{1288991}{1679616}[/tex]
[tex]=\frac{1288991\cdot \:216}{1679616}[/tex]
[tex]=\frac{278422056}{1679616}[/tex]
[tex]=\frac{1288991}{7776}[/tex]
Therefore, the sum of the first 8 terms will be:
[tex]\frac{1288991}{7776}[/tex]4x + 6y - z=-18
3x +2y - 4z = -24
- 5x + 3y + 2z = 15
find x y and z
Answer:
x = -2, y = -1, z = 4
Step-by-step explanation:
4x + 6y - z=-18
z = 18 + 4 x + 6 y
3x +2y - 4z = -24
z = 6 + (3x)/ 4 + y /2
- 5x + 3y + 2z = 15
z = 15/2 + (5x)/2 - (3y)/2
18 + 4 x + 6 y = 6 + (3x)/ 4 + y /2 = 15/2 + (5x)/2 - (3y)/2
x = -22y/13 - 48/13
4(-22y/13 - 48/13) + 6y - (15/2 + (5(-22y/13 - 48/13))/2 - (3y)/2) = -18
Compute the output value of the variables x and y with respect to the input values of x, y, and z coefficients.
Tracy is borrowing $10,700 on a six-year, %, add-on interest loan. What will Tracy's monthly payments be?
Answer:
Step-by-step explanation:
Use the formula I=prt. (Interest = principle x rate x time)
So, I = 10700 x 0.07 (7% as a decimal) x 6
So, I = 749(6)
I = 4494
Now, divide 4494 by 6(12)
4494/71
This = 63.3 dollars.
Therefore, she is paying 63 dollars per month.
Tracy's monthly payments is $62.41.
What is Simple Interest?The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.
Amount (A) = Principal (P) + Interest (I)
and, Simple Interest = PRT/100
Given:
P= 10700
Time= 6 year
Interest = 7%
Now, using simple interest
SI = P x R x T/100
SI = (10700 x 0.07 x 6)
SI = $4494
So, Tracy's yearly payments
= 4494/6
= 749
and, Tracy's monthly payments
= 749 / 12
= 62.41
Hence, Tracy's monthly payments is $62.41.
Learn more about Simple interest here:
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What is the equation of a line parallel to y=7x-8 that passes through (5, 22)?
Answer:
y = 7x - 13
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 7x - 8 ← is in slope- intercept form
with slope m = 7
Parallel lines have equal slopes, thus
y = 7x + c ← is the partial equation
To find c substitute (5, 22) into the partial equation
22 = 35 + c ⇒ c = 22 - 35 = - 13
y = 7x - 13 ← equation of parallel line
answer this strenuous question
A factory makes 300 sheets of construction paper per hour. How many sheets of construction paper will the factory make in 2 hours?
Answer: 600 sheets
Step-by-step explanation:
300/1 -> 300 sheets per 1 hour
To find the number in two hours, multiply the numerator and the denominator by 2.
300 x 2 = 600
1 x 2 = 2
Thus, the factor makes 600 sheets in 2 hours.
Write an equation for the graph in the form Y=KX
Answer:
Step-by-step explanation:
y=8x
ill give the right answer brainliest!
Answer:
C=84, D=80,b=99 and a=81
Step-by-step explanation:
In a quadrilateral, it's opposite measurements has to be equal to 180 degrees. So, for example if one side is 100 then the opposite side has to be equal to 80 so that if you add them there sum would be 180 degree.
Sorry, but I am not sure about a but you can try 81 degrees if you want. Hope this helps you!
The difference between two numbers is 3.50. The lesser number is 1.65.
What is the other number?
Answer:
5.15
Step-by-step explanation:
you add 3.50 and 1.65 to get the other number
You are adding to rational numbers with different signs. How can you tell if the sum will be positive, negative, or zero? #24
Answer:
it would be positive
Step-by-step explanation:
Answer:
Step-by-step explanation:
A positive plus a negative equals a negative:
4 + (-3) = 1
A positive plus a positive equals a positive:
4 + 4 = 8
A negative plus a negative equals a negative:
(-2 )+ (-2) = -4
If two number have the same absolute value, they will equal zero:
-3 + 3 = 0
- 2 + 2 = 0
Write a system of equations with the solution (4,-3). Show your work.
Answer:
4x4 then dived by 8you will get 4x4=16 dived by 8=8
What is the slope of the line shown on the graph?
Pick two points on the line, then use the slope formula.
The slope is
Answer:
the slope is 1/2
Step-by-step explanation:
You are packing a canoe for a
river trip. The canoe weighs 45 pounds and each supply pack weighs 12 pounds. How many supply packs can you put in the canoe if your total weight must be under 117 pounds?
Answer:
12x + 45 < 117
What is -4 1/2 - (-1.07)
Answer:
The answer is -3.43
Step-by-step explanation:
7x-5=8(x*3) what value of x makes this equation true
The given equation is:
[tex]\displaystyle 7x-5=8(x+3)[/tex]
The first step you need to do is open the parentheses and distribute the 8 to x+3. It will be 8 times x and 3 times x.
[tex]8(x+3)=8 \times x+ 8 \times 3\\\\8 \times x=8x\\8 \times 3=24[/tex]
[tex]8(x+3) \rightarrow 8x+24[/tex]
Rewrite the equation:
[tex]7x-5=8x+24[/tex]
Now you need to move one of the variables to the other side.
If you move 7x to the other side, then:
You can move the variable by doing the opposite of it. Since 7x is positive, you can move it by subtracting 7x, which is negative. Subtract 7x on both sides:
[tex]7x-5-7x=8x+24-7x\\-5=x+24[/tex]
Now you need to leave x alone. x is being added to 24, so remove it by subtracting both sides by 24. Remember that when you're subtracting from a negative number, you're actually adding while keeping the negative sign.
[tex]-5-24=x+24-24[/tex]
Subtract:
[tex]\bf-29=x[/tex]
If you move 8x to the other side, then:
8x is positive, so you can move it by subtracting 8x, which is negative. Subtract 8x on both sides:
[tex]7x-5-8x=8x+24-8x\\-x-5=24[/tex]
You need to leave the variable alone, so move -5 to the other side. You can do this by adding 5 to both sides.
[tex]-x-5+5=24+5\\-x=29[/tex]
Lastly, x is negative, but you're looking for the value of positive x. Divide both sides by -1 to remove the negative sign.
[tex]\displaystyle \frac{-x}{-1} =\frac{29}{-1}[/tex]
Remember that a positive number divided by a negative number is negative. Divide:
[tex]\bf x=-29[/tex]
The answer to your question is x = -29.
Step-by-step explanation:
Question:-Solve for x
[tex]\\ \tt{:}\leadsto 7x-5=8(x+3)[/tex]
SOLUTION:-[tex]\\ \tt{:}\leadsto 7x-5=8(x+3)[/tex]
[tex]\\ \tt{:}\leadsto 7x-5=8x+24[/tex]
[tex]\\ \tt{:}\leadsto 7x-8x=24+5[/tex]
[tex]\\ \tt{:}\leadsto -x=29[/tex]
[tex]\\ \tt{:}\leadsto x=29[/tex]
Buying three tires at $80 each and getting a fourth tire free
Answer
3 x 80=240
240 / 4=$60 effective unit rate for each tire.
Step-by-step explanation:
mark me as brainliest!
the awnser is 15 i did it by steep like there is 16 ones then you multiply and thye awnser i got was 15.
there you go :D
Answer:
What is the question
Step-by-step explanation:
Upload a picture
y=+/-√bx+c+d Use the inverse of the function y= x2 -18x to find the unknown values.
Answer:
a=1
b=81
c=9
Step-by-step explanation:
here you go, have a great day!
The length of a cell phone is 1.8 1.8 inches and the width is 4.4 4.4 inches. The company making the cell phone wants to make a new version whose length will be 1.17 1.17 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone
can you help me again UwU
Answer:
Upper Left
Bigger slopes means steeper lines.
Good luck!
Find the slope of the line through each pair of points. (2,5) and (6, 8)
Which point is the y-intercept of the line represented by the equation y-3=13(x+6)?
(0,9)
(0,5)
(5,0)
(0,2)
Answer:
The equation for a zero slope line is one where the X value may vary but the Y value will always be constant. An equation for a zero slope line will be y = b, where the line's slope is 0 (m = 0).
The y-intercept of the equation will be at (0, 81). Then the correct option is A.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given below.
y - 3 = 13(x + 6)
Convert the linear equation into slope-intercept form. Then the equation is written as,
y - 3 = 13x + 78
y = 13x + 78 + 3
y = 13x + 81
The y-intercept of the equation will be at (0, 81). Then the correct option is A.
More about the linear equation link is given below.
https://brainly.com/question/11897796
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The options are wrong. Then the correct options are given below.
A. (0, 81)
B. (0, -81)
C. (-81, 0)
D. (81, 0)
Tell me if this is correct?
How many parts is the
whole divided into?
Solve this too?
Divided into ____ Equal Parts
Answer:
Divided into five equal parts
2(x+3)=x-4
help!
45 points!
What is the area of the above trapezoid? Please help
I will cash app if you help out
Answer:
b should be correct
Step-by-step explanation:
no need to cash app me its been a while since ive done math so i dont even know if this is right
What is an equation of the line that passes through the point
(6,7) and is parallel to the line
2x−3y=9?
Answer:
The equation of line parallel to given line passing through (6,7) is: [tex]y = \frac{2}{3}x+3[/tex]
Step-by-step explanation:
Given equation of line is:
[tex]2x-3y = 9[/tex]
We have to convert the equation in slope-intercept form. The slope-intercept form is given by:
[tex]y= mx+b[/tex]
Adding 3y on both sides and subtracting 9 from both sides
[tex]2x-3y+3y-9 = 9+3y-9\\2x-9 = 3y\\3y = 2x-9[/tex]
Dividing whole equation by 3
[tex]\frac{3y}{3} = \frac{2x-9}{3}\\y = \frac{2}{3}x - \frac{9}{3}\\y = \frac{2}{3}x-3[/tex]
Let m be the slope of given line then
m = 2/3
Let m1 be the slope of line parallel to given line. Slopes of two parallel lines is equal that means:
m = m1 = 2/3
The equation of line will be:
[tex]y = m_1x +b\\y = \frac{2}{3}x+b[/tex]
Putting the point (6,7) in equation
[tex]7 = \frac{2}{3}(6) +b\\7 = 2(2) +b\\7 = 4+b\\b = 7-4\\b = 3[/tex]
Putting the value of b
[tex]y = \frac{2}{3}x+3[/tex]
Hence,
The equation of line parallel to given line passing through (6,7) is: [tex]y = \frac{2}{3}x+3[/tex]
What is the equation of the line through the points (3, 2), (8, 5), (13, 8) and (18, 11)? HELP ASAP I WILL MAKR BRAINLIEST PLSSSSSSS
Is it multiple choice?
Answer:(it might be)
y=5/3x+1/3
Step-by-step explanation:
The graph shows how much money Priya has in her savings account weeks after she started saving on a regular basis. How much money does Priya have in the account after 10 weeks? How long did it take her to save $200? How much money did Priya have in her savings account when she started to save regularly? Write an equation to represent the dollar amount in her savings account and the number of weeks of saving. Be sure to specify what each variable represents.
Answer:
How much money does priya have after 10 weeks? 320
How long did it take her to save 200? 5
How much did priya have in her savings account when she started to save regularly? 80
someone please answer these for me i’ll mark brainlist
1. Belinda has a box of 48 bananas.
5/8 if them are ripe.
How many bananas does she have?
Find the following amounts:
A) 2/3 of 12=
B) 5/6 of 24=
C) 4/9 of 45=
D) 3/5 of 55=
E) 2/7 of 35=
F) 9/10 of 40=
Answer:
She has 30 ripe bananas.
A) 8
B) 20
C) 20
D) 55
E) 10
F) 36
Is -4pi a rational number
Answer:
no
Step-by-step explanation:
Pi is irrational
Answer:
No it is a irrational number
Step-by-step explanation:
-4pi is not a whole number, integer number, or a rational number. It is only a irrational number.
TRUE OR FALSE: Determine whether the figure is a parallelogram for the given values of the variables
Answer:
True
Step-by-step explanation:
jrhudoakueieeisp
Answer:
A: True
B: False
Step-by-step explanation:
8a: x=5 and y=11
A= 84°
B= 96°
C= 96°
D= 84°
8b: x=4 and y=2
A= 66°
B= 6°
C= 15°
D= 64°