The sum of first four terms is a G.P. is 30 and that of the last four terms is 960. if its first term is 2 find the common ratio .
If the sum of first four terms in a G.P. is 30 and that of the last four terms is 960, then the sum of the first 8 terms is 990
We also know that a = 2
sum of first 4 terms
= 2(r^4 - 1)(r-1) = 30
r^4 - 1 = 15r - 15
r^4 - 15r + 14 = 0
r = 1 works for the equation , but r = 1 would make all the terms of the
GP the same, so clearly not a solution
r^4 - 15r + 14 = 0 , a bit of trial and error ....
(r-1)(r - 2)(r^2 + 3r + 7) = 0
so r = 2 or r = not real
check: sum(4) = 2(2^4 - 1)/(2-1) = 30 , as needed
so r = 2 , BUT it does not work for sum(8)
sum(8) = 2(2^8 - 1)(2-1) = 510 , not 990 as necessary according to your second part of the question.
check your question.
The transformation shown is a rotation.
true or false
Answer:
True
Step-by-step explanation:
Actually, I'm pretty sure it can also be a reflection! :) Have a good day!!!
A bag contains 12 identical marbles consisting of an equal number of red, green and yel low marbles. A marble is picked at random from the bag. a) Are all the outcomes equally likely? Give a reason for your answer?
Answer:
yes the outcomes are equally likely
Step-by-step explanation:
12 = red yellow green
12 = 3
12/3
4
red balls are 4
yellow balls are 4
green balls are 4
so the outcome is equal for all the colour of the balls
Can you help me with my work select the best estimate of the product of 18*31 =
I need help with my homework… plz
{Find the number that is missing from the equation}
Question 1 →3 + __________ = (-7)
Question 2 → Solve : (-9) + 18 + (-2) + (-5) + 9.
Answer:
-10
and I think it's 11 or 7
Please help Please thank you
Answer: C) The student made an error in step 3.
Step-by-step explanation:
When dividing by a negative while working with inequalities, you must "flip the sign." Thus, there is an error in step 3.
N.B. The answer could very well be interpreted as B), but I believe C) is the best and most defensible answer.
Hope it helps :) and let me know if you want me to elaborate.
Answer:
nvm
Step-by-step explanation:
What’s the answer, I will mark brainless
Answer:
68x
Step-by-step explanation:
you first of all find the area
1/2b×h=
1/2x×34
1/2×1/34x
68x
A train goes at a constant speed. It can travel 150 miles in 2 1/2. How long will it take that train to travel 100 miles
Answer:
1 2/3 hours
Step-by-step explanation:
At constant speed, the time is proportional to the distance.
time/distance = 2.5 h/150 mi = x /100
x = 100(2.5/150) h = 5/3 h = 1 2/3 h
It will take the train 1 2/3 hours to travel 100 miles.
Which product is represented by the hundredths grid A. 0.5 X 0.02 = 0.01
B. 5 X 0.2=1
C. 0.5 X 0.2 = 0.1
D. 0.05 X 0.02 = 0.001
Answer:
The product of A would be the answer
Please help me please 38
Answer:
8 inches
Step-by-step explanation:
Area of a triangle:
[tex]a=bh/2[/tex]
We're given 2 variables already, area and base, so we just need to plug those in and solve for the 3rd variable.
[tex]40=10h/2\\40=5h\\8 = h\\h = 8[/tex]
Answer:
8
Step-by-step explanation:
a right triangle is half of a square, so (10*8)/2=10*4=40.
If given DG ≅ JK, which congruence postulate or theorem must you use before proving FG ≅ HK?
Answer:
the correct answer choice is marked (AAS)
Step-by-step explanation:
All the corresponding angles are marked congruent. If one corresponding side is marked congruent, you can claim AAS or ASA congruence for the triangles: one side and two angles. Of these, AAS is among the answer choices.
You must use AAS to show triangle congruence before claiming FH ≅ HK by CPCTC.
1. 4x^2 +3x+2 and 7x^2+7x+3
Answer:
-x2 + 9x - 15
—————————————
3
Step-by-step explanation:
-x2 + 9x - 15
—————————————
3
What is slope ? Help me please
Answer:
Step-by-step explanation:
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x). there you go.
hi i need the answer to this now plz
2 divided by 3
plz explain how you got answer like show work
What is the value of y? y = 40 y = 80 y = 100 y = 120.
Answer:
I think it is 80. But I am also not sure because this question is not briefly described.
Answer:
80
Step-by-step explanation:
got it right on edge
umm i have an answer but not sure help
Answer:
tan A = 8/15
sin A = 8/17
cos A = 15/17
Step-by-step explanation:
Follow "SOH-CAH-TOA"
SOH---> sin A = (opposite of the angle mentioned) / hypotenuse
CAH---> cos A = (adjacent of the angle mentioned) / hypotenuse
TOA---> tan A = (opposite of the angle mentioned) / (adjacent of the angle mentioned)
Note: Hypotenuse is the side opposite of 90° of a right-angled triangle.
Question in Image Rearranging Algebra expressions Will give brainliest.
Owen is driving to a concert and needs to pay for parking. There is an
automatic fee of $12 just to enter the parking lot, and when he leaves the lot,
he will have to pay an additional $3 for every hour he had his car in the lot.
How much total money would Owen have to pay for parking if he left his car
in the lot for 5 hours? How much would Owen have to pay if he left his car in
the lot for t hours?
Cost of parking for 5 hours:
Cost of parking for t hours:
Answer:
$39
Step-by-step explanation:
because 12 enter and leave is 24 then 3 per he that is 39$
Can someone please do this for me?
Answer:
x= 105
y= 40
Step-by-step explanation:
3y=4y-40 because they are alternate interior
Solve for y.
y=40
4y-40=x+15 because they are vertical angles.
Substitute 40 in for y.
4(40)-40=x+15
Solve.
x=105
Answer:
y = 40 and x = 105
Step-by-step explanation:
4y-40 = 3y
y = 40
4(40)-40 = 120
x+15 = 120
x = 105
Quadrilateral ABCD has the following
vertices:
A(2, 7)
B(8,1)
C(1, -9)
D(-6, -2)
Is quadrilateral ABCD a parallelogram, and
why?
Answer:
Yes
Step-by-step explanation:
Because it’s a trapezoid and those can be trapezoid because they have one pair of parallel sides and a parallelogram has two pairs of parallel sides so a parallelogram is also a trapezoid.
answer to this question please
Answer:
Volume is 21
Explanation
Base length is 4.5
Widgth is 3.5
and height is 4 (I can't tell if its 2 because picture is blurry)
V=lwh/3=4.5·3.5·4= 21
2. A number 'a' is equal to the square of the number 'b' plus three times the
number'c
o Write a formula for 'a'
Answer:
a = b² + 3c
Step-by-step explanation:
The square of the number b is b² and 3 times c is 3c , then
a = b² + 3c
What is the rate of 13 inches of snow in 8 hours?
Answer: 1.625 inches of snow per hour
Step-by-step explanation:
13 divided by 8 is 1.625
Write a recursive formula for the explicit formula
A(n) = -1 + (n-1)(-2)
Answer:
see explanation
Step-by-step explanation:
A recursive formula allows a term in the sequence to be found by adding a common difference to the previous term
Given the explicit formula
A(n) = - 1 + (n - 1)(- 2)
This is an arithmetic sequence with explicit formula
A(n) = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
For the given explicit formula, then
a₁ = - 1 and d = - 2
The recursive formula is then
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] - 2 ; a₁ = - 1
a farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. no fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. if the fencing costs per linear foot to install and the farmer is not willing to spend more than , find the dimensions for the plot that would enclose the most area.
The constraint for the maximum enclosed area is the amount the farmer is
willing to spend on fencing.
The width of the plot that will give the most area, y = 83.[tex]\underline{\overline 3}[/tex] feet
The length of the plot that will give the most area, y = 125 feet
Reasons:
The given parameters are;
The cost of fencing per foot = $20
The maximum amount the farmer is willing to spend = $5000
Number of sides of fencing = 3 sides
Cost of the west side of the = Split with neighbor
Solution:
Let, y, represent the length of the fence, and let x represent the width of
the fence, we have;
Length of fence required = y + 2·x
Cost of the fence = 20·y + 20·x + (20÷2)·x = 20·y + 30·x
Therefore;
Maximum amount to be spent on the fence, 5000 = 20·y + 30·x
[tex]\therefore y = \dfrac{5000 - 30 \cdot x}{20} = 250 - \dfrac{3}{2} \cdot x[/tex]
[tex]y = \mathbf{250 - \dfrac{3}{2} \cdot x}[/tex]
Area of a rectangle = Length × Width
The enclosed rectangular area of the fencing, A = y × x
[tex]\therefore A = \left(250 - \dfrac{3}{2} \cdot x\right) \cdot x = 250 \cdot x - \dfrac{3}{2} \cdot x^2[/tex]
[tex]\therefore A = -\mathbf{ \dfrac{3}{2} \cdot x^2 + 250 \cdot x}[/tex]
The leading coefficient of the quadratic function of the area is negative,
therefore, the function only has a maximum point.
At the point of the most area, the slope, [tex]\dfrac{dA}{dx} = 0[/tex]
Finding the value of x at the maximum point, we get;
[tex]\dfrac{dA}{dx} = \mathbf{ \dfrac{d}{dx} \left( 250 \cdot x - \dfrac{3}{2} \cdot x^2\right)} = 250- 3 \cdot x = 0[/tex]
Therefore;
[tex]\mathrm{ The \ width \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ x = \dfrac{250}{3} \ feet = \underline{83.\overline 3 \ feet}[/tex]
[tex]\mathrm{ The \ length \ of \ the \ plot \ that \ will \ enclose \ the \ area}, \ y = 250 - \dfrac{3}{2} \times \dfrac{250}{3} = 125[/tex]
The length of the plot that will give the most area, y = 125 feet
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hurry please im dead meat if i cant do this picture below
Answer:
4 divided by 1/8
hope it helps
Step-by-step explanation:
Write 5×100+9×1+3×1/100+7×1/1000 in standard form
Answer:
512.017
Step-by-step explanation:
Just multiply all the numbers and add them as you go along to make one number.
Work out
(
7
×
10
−
3
)
−
(
4
×
10
−
5
)
Give your answer in standard form.
Answer:
32
let me know if its correct!
Your visually impaired friend asked you to enlarge your notes from class so he can study. You took notes on 8.5-inch by 11-inch paper. The enlarged copy has a smaller side with a length of 10 inches. What is the scale factor of this dilation?
Find the scale factor.
Answer:FINDING A SCALE FACTOR Your visually impaired friend asked you to enlarge your notes from class so be can study. You took notes on 8.5-inch by 11-inch.
Step-by-step explanation:thank you
The scale factor is 20/17.
According to the question, you took notes on a paper with dimensions 8.5 inches × 11 inches.
the breadth of the paper is 8.5 inches
the length of the paper is 11 inches
Now, to make an enlarged copy, you used a paper that has its smaller side dimension of 10 inches.
Which means the breadth of the new paper is 10 inches.
So, if we calculate the ratio of the breadths we get the scale factor.
k = 10 / 8.5
k = 20/17 is the scale factor of dilation.
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