Answer:
Step-by-step explanation:
(3x + 4)(x + 3)
3x^2 + 9x + 4x + 12
3x^2 + 13x + 12
The fifth term of a geometric sequence is 32 and the eighth term is 4.
(a) Find the ratio. (2 marks)
(b) Find the first term. (2 marks)
(C) Find the sum of the first 50 terms of the sequence. (3 marks)
What is the first term?
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
1. Minti can do a piece of work in 12 days. Minti and Rinki together can finish the work in 8 days.
Find: (a) the number of days in which Rinki alone can finish the work.
(b) the work left if Rinki alone works on it for 4 days.
Answer:
Minti - 12 days
Minti & Rinki - 8 days
Use Formula 3
time= (12 * 8) / (12 -8)
time = 96 / 4
time for Rinki alone = 24 Days
*****************************************************
Rinki alone for 4 days will leave 20 days of work to be done.
Step-by-step explanation:
What is the inverse of the following function? y = 12x −6
Answer:
f ^−1(x)=x/12+1/2
Step-by-step explanation:
help me please! don’t right nonsense! i have 15 minutes left!
Answer:
let M(-3,-4) be (x1, Y1)
T(5,0) be (x2,y2)
m:n = 2 : 3
using section formula
Q(x,y) = {mx2 + nx1/(m+n), my2 + ny1/(m+n)}
{ ( 10 -9)/5, (0 -12)/5}
(1/5, -12/5)
This could be answer if internally
What is the solution to the equation -6x + 9 – 4x = 14? I need some more help
Answer:
x= - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
- 6x + 9 - 4x = 14, that is
- 10x + 9 = 14 ( subtract 9 from both sides )
- 10x = 5 ( divide both sides by - 10 )
x = [tex]\frac{5}{-10}[/tex] = - [tex]\frac{1}{2}[/tex]
X+y=-4
2x+4y=-12
Stop by substitution
Answer:
X=4-y
2(4-y)+4y=12
8-2y+4y=12
2y=12-8
2y=4
y=4/2
y=2
x=4-y
x=4-2
x=2
if it is 9:39 what time would it be a hour and a half later
Answer:
It would be 11:09
Answer:
11:09
Step-by-step explanation:
30 mins after 9:30 is 10pm,add an hour that's 11 pm plus the 9 additional minutes its 11:09
80iu612345678909876533456
.
Answer:
weird
Step-by-step explanation:
Each year, the science club puts on a science show for the students in the elementary school. Luis is planning demonstrations to show properties of metals. For one property, he decides to use a ball of pizza dough and a rolling pin.
Which property of metals is Luis most likely going to demonstrate using these materials
luster
opacity
conductivity
malleability
Answer:
D. Malleability because he is most likely going to show how you can easily roll pizza dough
Step-by-step explanation:
Answer:
malleability or D
Step-by-step explanation:
Find the distance between the points L(7, -1) and M(-2, 4).
Answer:
(5-5)
Step-by-step explanation:
hope this helped
Answer:Not correct
Step-by-step explanation:
3/2a-8=11 URGENT ANSWERRRRRRR
Answer:
38/3
Step-by-step explanation:
3/2a-8=11
3/2a=19 add 8 to each side
i forget the rest of the steps smh
Answer:
38/3
Step-by-step explanation:
3/2A-8=11
3A/2=11+8
3A/2=19 CROSS MULTIPLY
3A=38
A=38/3
3/5(1 + p) = 21/20
find the solution to p
Answer:
3/4
Step-by-step explanation:
3/5(1+p)-21/20
3/5+3/5p=21/20
3/5p=21/20-3/5
3/5p=21/20-12/20
3/5p=9/20
p=9/20÷3/5
p=9/20*5/3
p=45/60
p=3/4
5(1-b)=8(b+2) solve for b
Step-by-step explanation:
Hey there!!
Here,
[tex]5(1 - b) = 8(b + 2)[/tex]
[tex] \: \: \: \: \: 5 - 5b = 8b + 16[/tex]
[tex] \: \: \: \: \: \: \: 8b + 5b = 5 - 16[/tex]
[tex] \: \: \: \: \: \: \: 13b = - 11[/tex]
[tex] \: \: \: \: \: \: \: b = \frac{ - 11}{13} [/tex]
Therefore the value of b is -11/13.
Hope it helps...
Step-by-step explanation:
first open up the brackets according to BODMAS to get
5-5b=8b+16
then collect like terms together and make sure to change the sighns eg - becomes +
5-16=8b+5b
you get
-11=13b
then divide both sides with 13 to get b
-11/13=b ( you can leave as a negative decimal according to the question)
Help please solve by factoring
We know that 6x(-7) is -42 and we also know that 6+(-7) is -1.
So we can write
[tex]x^2+6x-7x-42[/tex]
[tex]x(x+6)-7(x+6)[/tex]
[tex](x-7)(x+6)[/tex]
So our solutions are [tex]x=7,-6[/tex]
−2π
Is this rational or irrational
It is irrational.
π is an irrational number.
It follows that -2π is also irrational number.
What is the solution to the equation 3x + 2(x − 9) = 8x + x − 14? (5 points)
Answer:
x= -1
Step-by-step explanation:
Answer:
x = -1
Step-by-step explanation:
3x+2(x-9)=8x+x-14 ;; equation
simplify the equation to the form
3x+2(x-9)=8x+x-14
reorder the terms in parentheses
3x+(+2x-18)=8x+x-14
remove unnecessary parentheses
+3x+2x-18=+8x+x-14
move all terms containing x to the left and all other terms to the right.
+3x+2x-8x-1x=-14+18
simplify left and right side of the equation.
-4x=+4
divide both sides of the equation by -4 to get x.
x=-1
How do you solve 2 1/3 + 5y = 4
Answer:
Not sure but that's my answer
1) 3(3x - 4) = -2(1 – 4x)
Answer:
x = 10
Step-by-step explanation:
3(3x - 4) = -2(1 - 4x)
9x - 12 = -2 + 8x
9x - 8x = -2 + 12
x = 10
Hope this helps!
Three sisters have ages that are consecutive odd integers. Their combined ages is 51.
How old is the youngest sister?
Enter the decimal 1.18 as an improper fraction in simplest form.
Answer:
59/50
Step-by-step explanation:
118/100 divided by 2/2
=59/50
Mr.Joseph recently received a notice that his average gas and electric bill would increase at the beginning of the year. He went online to see the amount of his last 12 bills. If his average bill over the past 12 month goes up 17%, what can he expect to pay on average next year.
Answer:
about 2,546
Step-by-step explanation:
what is 6.257 x 10^-7
Answer:
-62570000
Step-by-step explanation:
6.257× -10000000
-62570000
The property can be used to remove the parentheses in the expression 1.7(x + 9).
Answer: Distributive property
3/4 of a cup of pasta sauce for every 12 ounces whats the unit rate
Answer:
the unit rate is 1/4 every 4 ounces
Step-by-step explanation:
12/3=4 3/3=1 so 1/4 of a cup every 4 ounces.
Write 821 in scientific notation
Answer:
8.21 x 102
Step-by-step explanation:
cus thats the answer
The afternoon temperature in Biscoff Bay was – 2°F. By midnight, a warm front moved in and the temperature rose to 11°F. What was the change in temperature from afternoon to midnight? To solve the problem, Ross subtracted 11–( – 2) and came up with an answer of 13°F. Is Ross correct? Why or why not?
Answer:
Ross is correct. He is right because if you do 11- (-2) the double negatives turn into a positive and the answer is 13.
The answer is "Yes", Ross is right, and the temperature change will be 13 °F.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the mentioned data in the question,
The afternoon temperature in Biscoff Bay = -2 °F
The temperature rose at midnight = 11 °F
Then, the change in temperature will be,
It is changing from -2 °F to 11 °F then,
= 11 - (-2) = 13 °F
To know more about arithmetic operations:
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Jordan will hike a 10 mile trail at a rate of 2 mi/h. Write a linear equation to represent the distance of the trail that Jordan still has to hike after x hours. What does the y-intercept of the equation represent?
Answer:
y = 10 -2x; 10 is the length of the trail
Step-by-step explanation:
Jordan's remaining distance starts at 10 miles, and decreases 2 miles each hour:
y = -2x +10
The y-intercept is the length of the trail.
A teacher spends $354 on costumes and microphones for six cast members in a play. Each cast member receives a costume that costs $38 and a microphone that costs $c What did the teacher spend on each microphone? The teacher spent $ ___on each microphone. Question 2 Justify your answer.
The teacher spend some amount on buying costumes and microphones for 6 cast members.
GiveN:
Cost of each costume = $38Cost of each microphone = $cTotal money spent = $354Let's frame the equation. Total money is the total amount spent for 6 cast members.
Money spent on costumes = $38 × 6
Money spent on microphone = $c × 6
Equation:
[tex]6 \times 38 + 6 \times c = 354[/tex]
Taking 6 as common,
[tex]6(38 + c) = 354[/tex]
Dividing 6 from both sides,
[tex] \dfrac{6(38 + c)}{6} = \dfrac{354}{6} [/tex]
[tex]38 + c = 59[/tex]
Solving further,
[tex]38 + c - 38 = 59 - 38[/tex]
[tex]c = 21[/tex]
So, the cost of each microphone = $21
The teacher spent this much on each microphone.
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The teacher spent $21 on each microphone.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
The total amount of teachers have = $354
Cost of costume for all 6 members ;
6 × 38 = $228
Cost of microphone for all 6 members ;
6 × c = 6c
Now,
Cost of microphone + Cost of costume = total amount
6c + 228 = 354
6c = 126
c = 21
Hence "The teacher spent $21 on each microphone".
For more about the equation,
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Jamal drew the function below. Which explains whether or not his function is linear?
His function is linear because it graphs out a straight line. If you were to pick any two points on that line, and find the slope, you should find that the slope is the same no matter which two points you picked.
Answer:
linear
Step-by-step explanation:
there's a constant rate of change/constant slope and the function is a straight line
Find the measure of