The sum using summation notation will be - 312. The sum of the following progression is found by the formula as [tex]S_n = \frac{a(1 - r^n)}{(1 - r)}[/tex].
What is geometric progression?Geometric Progression (G.P.) is a sort of sequence in which each successive phrase is obtained by multiplying the prior term by a set number known as a common ratio.
This progression is also known as a pattern-following geometric sequence of integers. Here you may also learn about mathematical progression.
A non-zero value is obtained by multiplying the common ratio by each phrase to obtain the next term 5 - 15 45 - 135.. is an example of a geometric series with a common ratio of -3.
The common ratio will be;
[tex]\rm r= \frac{-15}{3} \\\\ \rm r= -5[/tex]
The first term is 3
So the sum using summation notation will be;
[tex]S_n = \frac{a(1 - r^n)}{(1 - r)} \\\\ S_n = \frac{3(1 - (-5)^4)}{(1 - (-5))} \\\\ S_n =- 312[/tex]
Hence the sum using summation notation will be - 312.
To learn more about the geometric progression refer to;
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three ratios that are equivalent to 5:2
Answer:
10:4
15:6
20:8
HOPE THIS HELPS!!!
Given:
The ratio of two numbers is 5:2.
To Find:
What are the other ratios which are equivalent to the above ratio?
Solution:
The given problem can be solved using the concepts of ratio and proportions.
1. It is given that the ratio of two numbers is 5:2.
2. Consider two numbers a and b such that the simplest ratio between the two numbers is a:b.
=> Ratio of the numbers a and b = a:b,
=> According to the properties of ratios the operation a:b can also be written as a/b.
=> a/b can also be written as.
=> a/b can also be written as.
=> Similarly a/b can be conclusively written as. (Where n is not equal to 0).
3. The ratio of two numbers will always remain the same even if the numerator and the denominator are multiplied with the same factor. In such cases, the ratio always remains the same.
4. 5:2 = 5/2 can also be written as,
=> ... , . (Where n is not equal to zero).
Therefore the ratios 10:4, 15:6, 20:8, 25:10,.., 5n:2n are equal to the ratio 5:2.
The measure of angle 1 is 102°.
What is the measure of angle 2?
Answer:
Step-by-step explanation:
∠1 & ∠2 are co interior angles. co interior angles are supplementary.
∠1 + ∠2 = 180
102 + ∠2 = 180
∠2 = 180 - 102
∠2 = 78°
There are 3 cards in Box A and 3 cards in Box B.
There is a number on each card.
Box A
3,4,5
Box B
9,2,3
Ryan takes at random a card from Box A and a card from Box B.
He adds together the numbers on the two cards to get a total score.
Work out the probability that the total score is an odd number.
Answer:
4/9Step-by-step explanation:
Possible number of pairs of given cards:
3*3 = 9Number of sums with odd score, two odd numbers added to an even number from each box:
2*1 + 1*2 = 4 (pairs of 3 and 5 with 2 or pairs of 9 and 3 with 4)Required probability:
P(odd) = 4/9Becky had d DVDs. Her mother bought her 22 more DVDs. Write an expression that shows how many DVDs Becky has now.
Answer:
d+22=t
d dvds plus 22 dvds equals t dvds
A human being blinks about 1,500 times in 2 1/2 hours.How many times will he blink in 10 hours?
Answer:an average human blinks a lot
Step-by-step explanation:
they blink a lot for the eyes
Quadrilateral ABCD is a parallelogram. If AB=2x-10 and CD=x+30,then AB=_
Answer: 70
Step-by-step explanation:
Because opposite sides of a parallelogram are equal, AB=CD. So,
2x-10=x+30
x=40
Therefore, AB=2(40)-10=70
what x what = 1600 pls help me
Answer:
80
Step-by-step explanation:
40×40=1600
Go the cal and check it yrself plss
I'm just trying to help
Brainliest plss
If u like to
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6/42 in simplest form
6/42 in simplest form :
Divide both the nominator and the denominator by the HCF (highest common factor) : 6
6/42 = 6:6/42:6 = 1/7
PLLKEEASE HELPPPPPPP ASAPP
Answer:
x = 19
Step-by-step explanation:
(5x + 4)° + (x - 2)° + (3x + 7)° = 180°
(5x + x + 3x)° + (4 - 2 + 7)° = 180°
9x° + 9° = 180° → ÷9
x + 1 = 20
x = 20 - 1
x = 19
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Brad ordered 6 equal-priced items. If the shipping cost was $7 and he paid a total of $37, how much did each item cost? Write and solve an equation to answer the question, and then identify the statement that is not true.
Answer:
B gives you the equation, A is wrong
Step-by-step explanation:
We have this information: 6 items, $37 total, and shipping cost $7.We know that we would have to divide $30 by 6 to get the cost for each item, and add $7 to get $37.Each item would cost $5.With this information, we know that C and D are true.Using the information we have (6 being the divisor and 37 being the total) we know that B is not wrong. B gives us the equation, which you can type in.In conclusion, A is wrong.If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.
Answer:
it a
Step-by-step explanation:
I took the test
Please help me 100 points and brainliest
Which net represents this solid figure?
The one you picked, on the bottom left is correct
The top two both have rectangles and triangles, making them most likely triangular prisms. To the bottom right, the net represents a cube, which is incorrect, because the figure is supposed to be a rectangular prism.
Answer:
The on you picked should be correct
Step-by-step explanation:
The expression x+8x+10 is modeled below
with aigebra Times
What would need to be added to
complete the square ?
Answer:
add 6 unit tiles
Step-by-step explanation:
The square is completed when the algebra tile grid pattern is a square. This one will be a square when 6 more unit tiles are added to fill the empty spaces at the bottom right.
We need to add 6 to complete squares.
What must be added to complete the square?
Here we have the expression:
x^2 + 8x + 10
By looking at the image, we can see that we need to add 6 cubes of the ones with the digit 1.
That is equivalent to adding 6 to our expression (and we also subtract 6 so we don't change it) then we have:
x^2 + 8x + 10 + 6 - 6
(x^2 + 8x + 10 + 6) - 6
(x^2 + 8x + 16) - 6
(x^2 + 2*4*x + 4^2) - 6
(x + 4)^2 - 6
So we completed squares, then we conclude that we need to add 6 to complete squares.
If you want to learn more about completing squares, you can read:
https://brainly.com/question/10449635
Find the measure of the missing ANGLE.
20
700
P
?
Answer:
35°
Step-by-step explanation:
The circumference angle is half of the central angle.
Find the measure of angle A.(First solve for x, then plug it into 9x+4 to get the final answer!)
Answer:
40 degrees
Step-by-step explanation:
Sum of all angles of triangle is 180 degrees.
So, 80+(9x+4)+(16x-4)=180
80+25x=180
25x=100 -> x=4
So angle A = 9(4)+4= 40 degrees
Brian invests £1800 into his bank account. He receives 5% per year simple interest.
How much will Brian have after 6 years? Give your answer to the nearest penny where
appropriate.
Answer
#540
Explanation
5 over 100 to multiply by 1800
and you divide
Lucy’s mom started a savings account for Lucy to go to college when she was 5 years old. She put $1000 into an account that earned 6% interest. Lucy is now 18. How much money does Lucy have?
With the Loan principle at $1000, interest at 6%, with a time of 13 years, The amount of money has Lucy has is mathematically given as
X=$780
What is the amount of money has?Question Parameters:
Lucy went to college when she was 5 years old.
he put $1000 into an account that earned 6% interest
Generally, the equation for the annual interest is mathematically given as
X=1000*0.06
X=60
Since She was 5and now 18
18-5=13
In conclusion, the amount of money has
X=13*60
X=780
Read more about Arithmetic
https://brainly.com/question/22568180
PLS help,269 divided by 4
Answer:
PLS help,269 divided by 4
Step-by-step explanation:
Write and evaluate the expression. Then, select the correct answer. Two less than the quotient of a number and four, increased by ten; evaluate when m = 12 2 4m -10, when m = 11, the value is 40 4m 2 10, when m = 11, the value is 60 2 -StartFraction m Over 4 EndFraction 4m 10, when m = 12, the value is 9 StartFraction m Over 4 EndFraction-2 10, when m = 12, the value is 11.
The expression is 2 - m/4 + 10, when m = 12, the value is 9. Then the correct option is C.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Two less than the quotient of a number and four, increased by ten.
That can be written as in the form of m will be
[tex]\rm 2 - \dfrac{m}{4} + 10[/tex]
If the value of m is 12, then we have
[tex]\rm 2 - \dfrac{m}{4} + 10\\\\\rm 2 - \dfrac{12}{4} + 10\\\\2- 3 + 10\\\\12 - 3 \\\\9[/tex]
Thus, the expression is 2 - m/4 + 10, when m = 12, the value is 9. Then the correct option is C.
More about the Linear system link is given below.
https://brainly.com/question/20379472
Answer:
D
Step-by-step explanation:
Re-write the statement 19 + 7 ÷ 2 × 6 + 1 by including two pairs of brackets
to make the total value equal to 2.
Answer:
(19 + 7) ÷ (2 × 6 + 1)
Step-by-step explanation:
26 ÷ (12 + 1)26 ÷ 132In What temperatura is halfway between -2 and 4??
Answer:
1
Step-by-step explanation:
add then together
-2 + 4 = 2
then divide by the amount of numbers added up (in this case 2)
2/2 = 1
Answer:
I'm gonna say positive 2.
Step-by-step explanation:
Hope this helps!
(GIVING 20 POINTS!!) Find the discriminant for the following equation: 3x^2 + 4x = 2 : 8 -8 40 -40
Step-by-step explanation:
b² - 4ac
= 16 - 4(3)(-2)
= 16 + 24
= 40
joes dad weighs 140 pounds more than joe. their combined is 336 pounds. how much does his dad weigh?
Answer: 238 lbs
Step-by-step explanation:
x = joe's weight
y = joe's dad's weight
x + y = 336
y = x +140
Substitute for y
x + x + 140 = 336
2x + 140 =336
2x = 196
x = 98
Joe weighs 98 lbs
Now, plug that into Joe's dad's weight equation
y = 98 + 140
y = 238
Joe's dad weighs 238 lbs
Write 3 other expressions that are equivalent to 8x-12
To write equivalent expressions, we multiply all the quantites by the same number.
8x - 12 = ( 2 x 8x) - (2 x 12) = 16x - 24
Using the same method, you can write 3 equivalent expressions :
16x - 24 ; 24x - 36 ; 32x - 48
I need help pls it’s pretty hard
Answer:
x 8 -5
9 72 -45
-6 -48 30
Step-by-step explanation:
We have to complete the multiplication grid, where each cell is the result of multiplying the column lable by the row label.
For the blank in the first column, we have to multiply:
8×(-6)=-48
We now have to find the column label for the second column.
If we call this label x, we know that -6 times x is equal to 30.
Then, we can find x as:
(-6)×x=30
[tex]x=\frac{30}{-6}[/tex]
x=-5
Then, we can complete the first row by multiplying -5 times 9:
-5×9=-45
Then, the table becomes:
x 8 -5
9 72 -45
-6 -48 30
Mary has y yards of fabric. She used 2 yards to sew skirt . She used the remaining fabric to make 5 jackets
b. if she has 17 yards of fabric, how much material was used for each jacket?
Answer:
the answer is 3
Step-by-step explanation:
if she had 17 yards of fabric then subtrct two.
17-2=15
she made 5 jackets
15÷5=3
Nathan has some overdue library materials. He has a DVD that occurs a fine of one. $15 per day and a book that occurs $0.35 per day. which equation shows how many days it would take Nathan‘s phone to be $22.50
Answer:
1.15x + 0.35x = 22.50
Step-by-step explanation:
Let x = number of days
If:
DVD incurs an overdue fine of $1.15 per daybook occurs an overdue fine of $0.35 per daytotal fine = $22.501.15x + 0.35x = 22.50
Jacob spent $40 dollars on supplies to make 100 shirts for a baseball team fundraiser. Solve the inequality to help him decide how much to charge for each shirt to make a profit of more than $350
100t - 40 > 350
A) t < 39
B) t < 31
C) t > 39
D) t > 31
Answer:
I do believe the answer is A
Use the graph of the parabola to fill in the table.
(a) Does the parabola open upward or downward?
O upward
o downward
10
10
(b) Find the intercept(s).
For both the x- and y-intercept(s), make sure
to do the following.
• If there is more than one, separate them
with commas.
• If there are none, select "None".
x-intercept(s): 1
y-intercept(s): 1
(C) Find the coordinates of the vertex.
vertex: (D
(d) Find the equation of the axis of symmetry.
equation of axis of symmetry: 1
The graphs of parabolas are used to represent quadratic functions and equations
The direction of the parabolaFrom the graph, we can see that the graph of the parabola opens downward
The interceptsThe graph crosses the x-axis at x = 2, and it crosses the y-axis at y = -4
So, the x-intercept is x = 2, and the y-intercept at y = -4
The vertexThis is the maximum point on the graph.
So, the coordinate of the vertex is (2,0)
The equation of the parabolaA parabola is represented as:
[tex]y = a(x - h)^2 + k[/tex]
The parabola opens downward.
So, we have:
[tex]y = -1(x - h)^2 + k[/tex]
The vertex is (2,0).
So, we have:
[tex]y = -1(x - 2)^2 + 0[/tex]
[tex]y = -(x - 2)^2[/tex]
Hence, the equation of the parabola is [tex]y = -(x - 2)^2[/tex]
Read more about parabolas at:
https://brainly.com/question/15189614
Evaluate when 35/a a=7.
Hello.
All we should do in order to evaluate the given expression is plug in the value of the variable, a, and solve.
[tex]\mathrm{\displaystyle\frac{35}{a} }\\\mathrm{\displaystyle\frac{35}{7} }[/tex]
Now, divide:
[tex]\mathrm{5}[/tex]
Therefore, the final answer is
[tex]\mathrm{5}[/tex]
I hope it helps.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
helpppppppppppppppppp meeeeeeeeeeeeeeeeeeepwesssssssssssssssssssss...
Answer: 6.6, 6.6072, 6.67, 8.526
Step-by-step explanation: Make sure to mark me brainliest I answered u fast thanks <3
By ~"Gamer"~
