Independent Practice
Find the first, fourth, and eighth terms of the sequence.
an=0.5 · 3n−1a subscript n baseline equals 0.5 times 3 superscript n minus 1 baseline
A.
0.667; 4.5; 364.5
B.
3; 0.375; 0.0234375
C.
0.5; 13.5; 1093.5
D.
0.5; 121.5; 280.5
Answers
Answer:
C.
0.5; 13.5; 1093.5
Step-by-step explanation:
Related Questions
Can i please get this answered
Answers
Answer:
0 is the answer . The explanation is in the attachment .
The Vertices of a quadrilateral are A(4,-3),B(7,10),C(-8,2)and D(-1,-5).Find the length of each diagonal.Show me with the steps Please!
Answers
Answer:
13 and 17 units
Step-by-step explanation:
explaination is in pic.
The length of the diagonals of the quadrilateral AC and BD are 13 units and 17 units respectively, as per length between two points.
What is the length between two points in a plane?The length between two given points (x₁, y₁) and (x₂, y₂) will be:
√[(x₂ - x₁)² + (y₂ - y₁)²] units
Given, the vertices of a quadrilateral are A(4,-3),B(7,10),C(-8,2)and D(-1,-5).
Therefore, the diagonals of the quadrilateral will be AC and BD.
The coordinates of the diagonal AC are (4, - 3) and (- 8, 2).
Now, the length of the diagonal AC will be:
= √[(-8 - 4)² + (2 - (- 3))²] units
= √[(- 12)² + (5)²] units
= √[144 + 25] units
= √(169) units
= 13 units (length can't be negative)
Similarly, the coordinates of the diagonal BD are (7, 10) and (- 1, - 5).
Now, the length of the diagonal BD will be:
= √[(-1 - 7)² + (- 5 - 10)²] units
= √[(- 8)² + (- 15)²] units
= √[64 + 225] units
= √(289) units
= 17 units (length can't be negative)
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Write in factored form
m^2 - n^4
Answers
The answer is : [tex]\left(m+n^2\right)\left(m-n^2\right)[/tex]
Here are the steps below to help you! ^^
A scientist started with a sample of 8 cells. The sample increased as shown in the table.
Assume that the pattern in the table continues. Which equation can be solved for t, the time in hours when the number of cells will reach 100,000?
A
8⋅t4=100,000
B
8⋅4t=100,000
C
4⋅t8=100,000
D
4⋅8t=100,000
Answers
Answer:
100000 = 8 (4) ^t
Step-by-step explanation:
We are multiplying by 4 each time
y = a (4)^t
The initial amount is 8
y = 8 (4)^t
We want to get to 100000
100000 = 8 (4) ^t
Answer:
B
8 ⋅ 4^t = 100,000
Step-by-step explanation:
which of the following is equal to square root ^3 square root 2
Answers
Answer:
[tex]2^{\frac{1}{6} }[/tex]
Step-by-step explanation:
(2^1/3)^1/2 = 2^(1/3 x 1/2) =2^1/6
In triangle ABC, AC=13, BC=84, and AB=85. Find the measure of angle C
Answers
Answer:
the answer is the number 6
2x - y - 4 = 0
3x + y - 9 = 0
What is the solution set of the given system?
A. {(6, 5)}
B. {(5, 6)}
C. {(13/5, 6/5)}
D. {(6/5, 13/5)}
Answers
Step-by-step explanation:
+ Both equations
You will get : 5x=13 ; x=13/5
and put x to the first equation
2*13/5-y=4
y=6/5
(13/5;6/5)
Answer is C
upon receiving your first salary, you deposited 3000 taka monthly in a fund for your future for 18 years. the fund earns 6% interest rate compounded monthly. after 18 years, you want it to make payments at the end of every quarter for five year 4.5% compounded quarterly, what is the amount of each annuity payment to you?
Answers
The Annuity payment will be "65,209.35 Taka". A further solution is provided below.
Given:
Monthly payment,
= 3000 Taka
Interest rate,
= 6% (compounded monthly)
Time,
= 18 years
The Future value will be:
→ [tex]FV = PMT\times \frac{((1+r)^{nt}-1)}{r}[/tex]
By putting the values, we get
[tex]=3000\times \frac{((1+\frac{6}{12\times 100} )^{12\times 18}-1)}{\frac{6}{12\times 100} }[/tex]
[tex]=3000\times \frac{((1+\frac{6}{1200} )^{216}-1)}{\frac{6}{1200} }[/tex]
[tex]=1,162,059.58 \ Taka[/tex]
hence,
The Annuity payment will be:
→ [tex]P=\frac{PV(\frac{r}{n\times 100} )}{1-(1+\frac{4.5}{4\times 100} )^{-4\times 5}}[/tex]
[tex]=P=\frac{PV(\frac{r}{n\times 100} )}{1-(1+\frac{4.5}{4\times 100} )^{-20}}[/tex]
By substituting all the values, we get
[tex]=65,209.35 \ Taka[/tex]
Thus the correct answer is "65,209.35 Taka".
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Find the value of a. A. 57 B. 104 C. 26 D. 52
Answers
Answer:
Option D, 52
Answered by GAUTHMATH
ABCD is a rectangle. AB = 3x+5, AC = 7x-9, BC = 2y+5, BD = 2x+62. Solve for x. (Round your answer to one decimal place, if necessary.)
Answers
Answer:
x=14.2
Step-by-step explanation:
AC = BD
The diagonals of a rectangle are equal
7x-9 = 2x+62
Subtract 2x from each side
7x-9-2x = 2x+62-2x
5x-9 = 62
Add 9 to each side
5x-9+9 = 62+9
5x= 71
Divide by 5
5x/5 = 71/5
x=14.2
8a^3-36a^2+54a-27-64p^3
Answers
Answer:
8a^3-64p^3-36a^2+54a-27
Step-by-step explanation:
since it no common variable so it can not be further solved
Five consecutive multiples of 7 have a sum of 350. What is the smallest of these numbers?
A. 70
B. 56
C. 77
D. 84
Answers
Answer:
B. 56
Step-by-step explanation:
x + (x + 7 ) + ( x + 14 ) + ( x + 21 ) + ( x + 28 ) = 350
( x + x + x + x + x ) + ( 7 + 14 + 21 + 28 ) = 350
5x + 70 = 350
- 70 - 70
_____________
5x = 280
x = 56
Hope this helps!
The smallest number is 56, the correct option is B.
What is Sum?The sum is the output of the mathematical operation, Addition.
Let the first number is x, they are multiples of 7,
As they are multiples of 7, the consecutive numbers will be added by 7 for next term.
The 5 consecutive numbers can be written as x, (x+7), (x+14), (x+21), (x+28).
The equation can be formed for the numbers that are given as,
An equation is a mathematical statement that relates an algebraic expression with other expression by an equal sign.
The sum of the multiples is 350
x + (x + 7 ) + ( x + 14 ) + ( x + 21 ) + ( x + 28 ) = 350
Grouping the variables and the constants separately
( x + x + x + x + x ) + ( 7 + 14 + 21 + 28 ) = 350
5x + 70 = 350
Adding (-70) to both sides of the equation
5x = 280
Dividing both sides by 5
x = 56
The value of the first number of the series is obtained.
The first value is the smallest number of the series.
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Simplify
1)a³b⁴/ ab³
2)2 (x³ )²
3)3x*2x³ y²
Answers
Answer:
1) a³b⁴/ ab³ = a²b
2)2 (x³ )² = 2x^6
3)3x*2x³ y² = 6x⁴y²
find the surface area of the cylinder and round to the nearest tenth
Answers
Answer: A = 833.66 in^2
Step-by-step explanation:
Area of the base = (7^2)(pi) = 49 pi = 153.9 in^2
Height of the cylinder = 12 in
Circumference of the base = (2)(pi)(r) = 44in
Surface area = (2)(pi)(7)(12) + (2)(pi)(7) = 833.66 in^2
I don't understand this one
Answers
Answer:
9/8 = n
Step-by-step explanation:
9 = 8n
Divide each side by 8
9/8 = 8n/8
9/8 = n
A furniture store is having a sale on sofas and you're going to buy one. The advertisers know that buyers get to the store and that 1 out of 5 buyers change to a more expensive sofa than the one in the sale advertisement. Let X be the cost of the sofa. What is the average cost of a sofa if the advertised sofa is $250 and the more expensive sofa is $450
Answers
Answer:
$290
Step-by-step explanation:
We are told that 1 out of 5 buyers change to a more expensive sofa than the one in the sale advertisement.
Now we are told that the advertised sofa is $250 and the more expensive sofa is $450.
Thus;
P(x) for expensive sofa = 1/5
P(x) for sofa in sale advertisement = 4/5
Thus, expected value is;
E(X) = (1/5)450 + (4/5)250
E(x) = 90 + 200
E(x) = $290
Answer:
The average cost of a sofa = [tex]\$290[/tex]Step-by-step explanation:
Cost of advertised sofa = [tex]\$250[/tex]
Cost of more expensive sofa = [tex]\$450[/tex]
So, the average cost of sofa,
[tex]E(x) = (450*\frac{1}{5})+ (250*\frac{4}{5})\\\\E(x) = 90 + 200\\\\E(x) = 290[/tex]
Hence,
The average cost of a sofa = [tex]\$290[/tex]
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The Line segments are translated 2 units to the left to form A’B’ and C’D’. Which statement describes A’B’ and C’D’?
Answers
Answer:
Line segments A'B' and C'D' do not intersect and are the same distance apart as AB and CD.
Step-by-step explanation:
Na
C
9
Which rule describes the transformation?
Parallelogram ABCD is rotated to create image
A'B'C'D'.
SEE
0 (x, y) - (y, -x)
O (x, y) + (-y, x)
O (x, y) + (-X, -y)
(x, y) - (x,-y)
5
VX
4
R
D
2
1
C
-5.-5.4.-3.-2.-
23
4
SIB
Х
2
D
A
C
B
no
Answers
Answer:
(x, y) → (y, -x)
Step-by-step explanation:
The coordinates of the vertices of parallelogram ABCD are; A(2, 5), B(5, 4), C(5, 2), and D(2, 3)
The coordinates of the vertices of parallelogram A'B'C'D' are; A'(5, -2), B'(4, -5), C'(2, -5), and D'(3, -2)
The rule that escribes the transformation of the rotation of parallelogram ABCD to create the image A'B'C'D' is presented, by observation, is therefore;
(x, y) → (y, -x)
The resulting transformation used will be (x, y) -> (y, -x)
Transformation of coordinatesTransformation are rules applied to an object to change its orientation
For the given parallelogram, in order to know the rule used, we need the coordinate of the image and preimage
The coordinate of A is (2, 5) while that of A' is (5, -2).
From both coordinates, you can see that the coordinate was switched and the resulting y coordinate negated.
Hence the resulting transformation used will be (x, y) -> (y, -x)
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Please help me I’m confused
Answers
A midpoint is a point that divides a given line into two equal halves.The answers to the questions are:
1. BC = 89
b. AB = 45
c. AC = 44
2. The coordinate of I is 2.5
3. J = 19
4. MQ = 32
5. NO = 13
6. NO = 23
b. MN = 25
A line segment can be divided into different fractions. Where the point that divides the line segment into equal parts is the midpoint. however, number line is a system that shows the location or positions of all directed numbers.
The given questions can be solved as follows:
1. Given that point A is between BC and AB = 4x -3, BC = 7x + 5, AC = 5x - 16
But,
BC = AB + AC
7x + 5 = (4x -3) + (5x - 16)
= 9x - 19
7x + 5 = 9x - 19
19 + 5 = 9x - 7x
24 = 2x
x = [tex]\frac{24}{2}[/tex]
x = 12
So that;
a. BC = 7x + 5
= 7(12) + 5
BC = 89
The value of BC is 89.
b. AB = 4x -3
= 4(12) - 3
AB = 45
Thus AB has a value of 45.
c. AC = 5x - 16
= 5(12) -16
AC = 44
The value of AC is 44.
2. Given that H is the mid point of GI, and G = 8, I = -3.
Then;
I = 2.5
The coordinate of I is 2.5
3. A midpoint is a point that divides a line segment in to two equal halves. Given that J is the midpoint of KL. KL = 38
J = [tex]\frac{KL}{2}[/tex]
= [tex]\frac{38}{2}[/tex]
J = 19
The value of the midpoint J is 19.
4. It can be deduced from the conditions given in the question that:
MQ = MN + NO + OP + PQ
= 8 + 8 + 16 (NB: OP + PQ = 16)
MQ = 32
Thus, value of MQ is 32.
5. Since P is the mid point of NQ, and OP = 11, OQ = 35
Then;
PQ = OQ - OP
= 35 - 11
PQ = 24
Since, PQ = NP =24
Then;
NO = NP - OP
= 24 - 11
NO = 13
NO has a length of 13.
6. NO = 2y + 11, OP = 3y - 2, NP = 6y + 3 and MP = 64.
But,
NO + OP = NP
(2y + 11) + (3y - 2) = 6y + 3
5y + 9 = 6y + 3
9 - 3 = 6y - 5y
y = 6
So that;
a. NO = 2y + 11
= 2(6) + 11
NO = 23
Here, the value of NO is 23.
b. MN = MP - NP
But,
NP = 6y + 3
= 6(6) + 3
NP = 39
Then;
MN = 64 - 39
MN = 25
So that MN has a value of 25.
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At the city museum, child admission is and adult admission is . On Wednesday, three times as many adult tickets as child tickets were sold, for a total sales of . How many child tickets were sold that day
Answers
Complete question :
At the city museum, child admission is $6.30 and adult admission is $9.80. On Wednesday, three times as many adult tickets as child tickets were sold, for a total sales of $ 1178.10 . How many child tickets were sold that day?
Answer:
33 children ticket
Step-by-step explanation:
Let :
Number of Child admission = x
Number of Adult admission = y
On Wednesday ;
y = 3x
9.80y + 6.30x = 1178.10
9.80(3x) + 6.30x = 1178.10
29.40x + 6.30x = 1178.10
35.70x = 1178.10
x = 1178.10 / 35.70
x = 33
hi, please solve these three questions for me, i have to shoe solving steps.
Answers
question 3
Step-by-step explanation:
i only able to show you the step of question 3..so sorry
____×____=126
Fill the blank pls I need it fast
Answers
Answer:
Answer for this is 62 * 2 = 126
Step-by-step explanation:
Answer:
14×9=126
Step-by-step explanation:
how do you explain it lol
find the measure of the indicated angle to the nearest degree
Answers
[tex]\boxed{\sf sin\Theta=\dfrac{P}{H}}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{16}{26}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{8}{13}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=0.5[/tex]
Convert to p/q form[tex]\\ \sf\longmapsto sin\Theta=\dfrac{5}{10}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=sin30[/tex]
[tex]\\ \sf\longmapsto \Theta\approx30°[/tex]
A storeowner orders 25 calculators that cost $38 each. The storeowner can sell each calculator for $42. The storeowner sold 22 calculators to customers. He had to return 3 calculators that were never sold and pay a $2 charge for each returned calculator (although the initial cost is refunded). What is the storeowner's profit?
Answers
Answer:
Step-by-step explanation:
25*-30= -$750
Second: He sells 22 of those calculators for $35 each, so he is making money.
22*35= $770
Third: With the remaining three calculators, he must pay $2 each for returned calculators, so he is losing money again.
3*-2= -6
Add all the costs and sales together, and you get 770-750-6= $14 profit
However, the problem does not say if he gets his money back for the 3 returned calculators. In that case if he did, you would add the cost of each of those calculators to his profit. 30*3= 90
$90+$14= $104 profit
here u go
The sum of two numbers is 83 if one of the number is 7 more than the other find the two numbers?
Answers
Answer:
48.5 and 34.5
Step-by-step explanation:
83 divided by 2 and then subtract 7
Answer:
45 and 38 equal 83 and 45 is 7 more than 38
What is the Answer to: 120 Times 2/3
Answers
Answer:
80
Step-by-step explanation:
You could multiply by 2 and then divide by 3
120*2 = 240
240/3 = 80
Or you could divide by 3 and then multiply by 2
120/3 = 40
40*2 = 80
Answer:
80Step-by-step explanation:
120 × 2/3= 120/1 × 2/3= 240/3= 80[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
what is this please tell answer
Answers
Answer:
x=6, y=4, z=8
(c) 6I hope this is helpful!
of (3, -2) reflected across the line x = 1 is?
Answers
Answer: (-1, -2)
===========================================================
Explanation:
Plot (3,-2) on the xy grid. Then draw a vertical line through 1 on the x axis.
Note that the horizontal distance from the point to the line is exactly 2 units. We move 2 units to the left to go from (3,-2) to (1,-2). Then we move another 2 units to the left to arrive at the final destination of (-1, -2)
In short, (3,-2) reflects over the vertical line x = 1 to get to (-1, -2)
See the diagram below.
Warren is on vacation and needs to arrange transportation. A rental car costs 40 dollars per day plus a one-time cost of 14 dollars for insurance. Construct a function C(x) that gives the total cost of renting a car for x days. C(x)=________.
If Warren has budgeted 254 dollars for the rental, how many days can he afford?
Answers
Answer:
C(x)=40x+14, 6 days
Step-by-step explanation:
C(x)= payment per day*x + initial payment. the payment per day is $40 while the initial payment is $14. so C(x)=40x+14.
C(x)=254=40x+14, 40x=240, x=6
Which table represents a function?
Answers
Answer:
The last one
Step-by-step explanation:
All the other tables have repeating x values
I hope this helps!
pls ❤ and give brainliest pls
