Answer:
[tex]a_7=40960x^{33}[/tex]
Step-by-step explanation:
Geometric sequence has explicit form:
[tex]a_n=a \cdot r^{n-1}[/tex] where [tex]a[/tex] is first term and [tex]r[/tex] is the common ratio.
First term here is [tex]a=10x^3[/tex] and [tex]r[/tex] could be found by doing second term divided by first term, [tex]\frac{40x^8}{10x^3}=4x^5[/tex].
Therefore the [tex]n[/tex]th term is given by
[tex]a_n=10x^3 \cdot (4x^5)^{n-1}[/tex].
So the [tex]7[/tex]th term is given by
[tex]a_7=10x^3 \cdot (4x^5)^{7-1}[/tex].
Let's simplify:
[tex]a_7=10x^3 \cdot (4x^5)^{7-1}[/tex]
[tex]a_7=10x^3 \cdot (4x^5)^{6}[/tex]
[tex]a_7=10x^3 \cdot (4^6(x^5)^6)[/tex]
[tex]a_7=10x^3 \cdot (4096x^30)[/tex]
[tex]a_7=40960x^{33}[/tex]
11. The sum of three consecutive odd integers is
93. Find the integers.
Answer:
29, 31, 33
Step-by-step explanation:
Tom bought $81 worth of milk. The price of a bottle of Brand A milk was $1.50 and of Brand B milk was $2.10. He bought 40 bottles of Brand A milk. How many bottles of Brand B milk did he buy?
Please help simplify with work. Will give brainliest.
Answer:
[tex]162 {x}^{10} {y}^{4} {z}^{12} [/tex]
Step-by-step explanation:
[tex]2 {x}^{4} (9 {x}^{3} y^{2} {z}^{6} {)}^{2} [/tex]
➡️[tex] {9}^{2} \times ( {x}^{3} {)}^{2} \times ( {y}^{2} {)}^{2} \times ( {z}^{6} {)}^{2} [/tex]
➡️ [tex]81 \times ( {x}^{3} {)}^{2} \times ( {y}^{2} {)}^{2} \times ( {z}^{6} {)}^{2} [/tex]➡️ [tex]81 {x}^{6} \times ( {y}^{2} {)}^{2} \times ( {z}^{6} {)}^{2} [/tex]➡️ [tex]81 {x}^{6} {y}^{4} \times ( {z}^{6} {)}^{2} [/tex]➡️ [tex]81 {x}^{6} {y}^{4} {z}^{12} [/tex]➡️ [tex]2 {x}^{4} \times 81 {x}^{6} {y}^{4} {z}^{12} [/tex]➡️[tex]162 {x}^{4} \times {x}^{6} {y}^{4} {z}^{12} [/tex]
➡️[tex]162 {x}^{4 + 6} {y}^{4} {z}^{12} [/tex]
➡️[tex]162 {x}^{10} {y}^{4} {z}^{12} [/tex] ✅
Please help! Please don't answer if you don't know!
Answer:
[-0.25 1.25]
[ ]
[-0.75 2.75]
If not satisfied than..
You can write it in other way as show in step by step
Step-by-step explanation:
Step 1:
First of all find the determinate.
Cross multiply the number 11 ✖ -1
detA = 11 × -1= -11 ---eq1
And now cross multiply the number 3 ✖ - 5
detA = 3 × -5= -15 ---eq2
Now we use eq 1 and 2
detA = (-11)-(-15)
Minus cancels minus
So it becomes
detA = -11 + 15
= 4
Step 2:
We find adjacent of the given.
[11 -5]
adjA= [ ]
[3 -1 ]
We change the places. The number 11 goes to in place of -1. -1 goes in place of 11.
And we change the signs of -5 and 3. -5 becomes 5 and 3 becomes -3.
We get
[-1 5]
adjA = [ ]
[-3 11]
Step 3:
Now we use the following formula
1
A^-1 = -------- adjA
detA
1 [-1 5]
A^-1 = ------- [ ]
4 [-3 11]
And now multiply
1
---- with each number of adjA.
4
And than subtract..
And you will get the inverse matrix
If the answer comes same than that's the answer for inverse matrix
Thank you.
Explain what are all of the properties of real numbers and use an example for each.
Answer:
mark me as a brainlist answer
Step-by-step explanation:
Give examples to explain the properties of real numbers
Property (a, b and c are real numbers, variables or algebraic expressions)Examples8.Additive Inverse Property a + (-a) = 04 + (-4) = 09.Multiplicative Inverse Property10.Zero Property of Multiplication a • 0 = 04 • 0 = 011.Closure Property of Addition a + b is a real number10 + 5 = 15 (a real number)
Simplify: (14^6*15^5)/(35^6*6^5)
Answer:
2/5
Step-by-step explanation:
=(2*7)^6 * (3*5)^5/ (7*5)^6 * (2*3)^5
=(2^6 * 7^6) * ( 3^5 * 5^5) / (7^6 * 5^6) * ( 2^5* 3^5)
=2^5 * 2^1 * 5^5/ 5^5 * 5^1 *2^5
=2/5
The simplified expression of (14^6*15^5)/(35^6*6^5) is 2/5
How to simplify the expression?The expression is given as:
(14^6*15^5)/(35^6*6^5)
Express 14 as 2 * 7, 15 as 3 * 5 and 35 as 5 * 7
[tex]\frac{(2 * 7)^6 * (3 * 5)^5}{(5 * 7)^6 * (2 * 3)^5}[/tex]
Expand the expression
[tex]\frac{2^6 * 7^6 * 3^5 * 5^5}{5^6 * 7^6 * 2^5 * 3^5}[/tex]
Divide the common factors
[tex]\frac{2}{5 }[/tex]
Rewrite as:
2/5
Hence, the simplified expression of (14^6*15^5)/(35^6*6^5) is 2/5
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2. Using what you learned in Question 1, try to write
each of these quadratic expressions as a product of
two linear expressions. That is, try to write each
expression in factored form.
a. x^2 + 5x + 6
b. x^2 + 2x - 15
C. X^2 - 3x + 10
d. x^2 - 9x+8
e. x^2 - 16
f. X^2 - 10x + 6
Answer:
Ans
Step-by-step explanation:
In Q. No. F, 1st page last step there is /2.
OK
Randy and Trey take turns cleaning offices on the weekends. It takes Randy at most 4 hours to clean the offices. It takes Trey at most 6 hours to clean the offices. What is the greatest amount of time it would take them to clean the offices together?
2.4 hours
2.5 hours
3.0 hours
4.0 hours
The answer is supposedly 2.4 hours, but how ?? Please explain. Thanks!
In one hour Randy cleans at least 1/4 of the offices and in one hour Trey cleans at least 1/6 of the offices.
Working together they would clean at least 1/4 + 1/6 = 5/12 of the offices.
Let x be the greatest amount of time it would take them to clean the offices together. Then we can write the following equation:
5x/12=1
Darel went to the mall and spent $41. He bought several t-shirts that ach cost
$12 and he bought 1 pair of socks for $5. How many t-shirts did Darel buy?
Answer:
3
Step-by-step explanation:
12x+5(1)=41
12x=-5+41
12x=36
x=36/12
x=3
12(3)+5(1)=
36+5=41
My victory will be in your hands if you answer this ✌✌✌✌✌
Add dress and shoes together:
30 + 25 = 55
1/5 off means the total after discount would be 4/5 ( 1 - 1/5 = 4/5)
Multiply total price by 4/5:
55 x 4/5 = (55 x4)/5 = 220/5 = 44
Total after discount is 44
Now add shipping:
44 + 8 = 52
Total paid = £52
Answer:
She will pay $52
Step-by-step explanation:
So she buys them both, which equals 55 dollars. But the website has a deal that is if you buy both of them it's 1/5 of the price off. And 1/5 of 55 is $11, so 55-11=44. You might think you're done but your not. At the end it says they add $8 for the shipping/handling, which is 44+8. This equals 52 dollars. By the way substitute this money sign $ for the one on your page
At 4:00 a.m., the temperature was -9°F. At noon, the temperature was 18°F. What
was the change in temperature??
help me pls :\
Translate 13 more than n to an algebraic expression
Answer:
13+n
Step-by-step explanation:
Answer:
13 + n
Step-by-step explanation:
This is because the known number is 13 times more than n so if the value of n is found, _+ 13_ will give you the final answer.
solve for variable (image attached)
Answer:
x = 2
Step-by-step explanation:
Given
[tex]\frac{3(6x+8)}{4}[/tex] = 15 ( multiply both sides by 4 to clear the fraction )
3(6x + 8) = 60 ( divide both sides by 3 )
6x + 8 = 20 ( subtract 8 from both sides )
6x = 12 ( divide both sides by 6 )
x = 2
The value of x in the equation is 2
The equation given :
3(6x + 8) / 4 = 15
Multiply both sides by 4
3(6x + 8) = 15 × 4
3(6x + 8) = 60
Open the bracket
18x + 24 = 60
18x = 60 - 24
18x = 36
x = 36/18
x = 2
The value of x in the equation is 2
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A couple is getting married. The event venue for their reception costs $3000 plus $20 per guest for catering. Decorations will cost $750. If the couple wants to keep the total cost of their reception under $6,000, what is the maximum number of guests that they can invite? Define a variable, write an inequality and solve.
Answer:
112.5 guests
Step-by-step explanation:
3,000 + 750 = 3,750. 6,000 - 3,750 = 2,250. 2,250/20 = 112.5 hope this helps
Point W is on line segment V X. Given VX = 18 and VW = 14 determine the length W X
Answer: WX = 4
Concept:
Here, we need to know the idea of segment addition postulate.
The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
Solve:
Given information
VX = 18
VW = 14
Given expression deducted from the segment addition postulate
WX = VX - VW
Substitute values into the expression
WX = 18 - 14
Simplify by subtraction
WX = 4
Hope this helps!! :)
Please let me know if you have any questions
How many different ways can you use the digits 3 and 5 to write
expressions in exponential form? What are the expressions?
Answer:
Therefore , Total no of ways to fill the 3-digits number is = 3*3*3 =27 . So, we can make 27 different 3-digits number using these numbers 1 ,5 ,7 by arranging them in 27 different waysStep-by-step explanation:
Meena's age is four times her daughter's age. Two years ago she was five times herdaughter's age. Find their present ages. pls explain step by step
Answer:
8 and 32
Step-by-step explanation:
let daughter's age be x then Meena's age is 4x
2 years ago daughter's age was x- 2 and Meena's age was 4x - 2
Meena was 5 times her daughter's age then , so
4x - 2 = 5(x - 2)
4x - 2 = 5x - 10 ( subtract 4x from both sides )
- 2 = x - 10 ( add 10 to both sides )
8 = x
Thus
daughter is 8 years and Meena is 4 × 8 = 32 years
A total of 388 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold?
Answer:
97
Step-by-step explanation:
388 (number of tickets) / 4 (number of groups (adults, and the 3 times as many kids))
If the number of student tickets sold was three times the number of adult tickets sold, 97 adult tickets were sold.
Let's assume the number of adult tickets sold is 'x.'
According to the information given, the number of student tickets sold was three times the number of adult tickets sold. So, the number of student tickets sold is 3x.
The total number of tickets sold is the sum of the adult and student tickets, which is 388:
x + 3x = 388
Now, combine like terms:
4x = 388
To find the value of 'x,' divide both sides of the equation by 4:
x = 388 / 4
x = 97
To verify the result, let's find the number of student tickets:
Number of student tickets = 3 * 97 = 291
Now, let's add the adult and student tickets:
97 (adult) + 291 (student) = 388
The result checks out, and we have 97 adult tickets and 291 student tickets, which together sum up to the total of 388 tickets sold for the school play.
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What are the dimensions of this rectangle?
Answer:
F:53cm by 102cm
Step-by-step explanation:
The perimeter of a rectangle can be seen as 2l + 2w, with the length being l, and the width being d. If the ratio is 3:2, then 3+2= 5 parts would be the sum of the length and the width, This is half of the perimeter 2(l+w), so 510÷2 = 255. One part would be 255÷5=51.
If you put it into the ratio, effectively it is:
Length:Width
3×51:2×51
153 :102
Therefore the dimensions are 153cm by 102cm, which is F.
HELP ME PLEASE! IM IN SEARCH OF ANSWERS AND I DONT GET ANY UNDER MY POST SO IF YOU COULD, PLEASE ANSWER THIS QUESTION AND EXPLAIN IF YOU WANT.
FEEL FREE TO CHECK MY USER FOR QUESTIONS FOR YOU TO ANSWER!!!
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Answer:
3 a) 8x +8 in
3 b) 24 in
3 c) 4x +4 in
3 d) 16x + 16 in
Step-by-step explanation:
3 b) You have to put 2 in place of x and calculate the perimeter:
8•2 +8
16 +8
24 in
Only some of the students in the Level 1 swim lessons move up to Level 2 at the end of the session. The table shows what fraction of each swim instructor's students move up to Level 2. Which list orders the fractions from least to greatest?
Answer:
7/12 ,2/3, 17/24, 3/4
Which theorem can be used to show that AABC = ADEC?
Its line segment please help
Step-by-step explanation:
[tex]here \: c \: is \: the \: mid \: point \\ so \: bc = cd \\ 6x - 16 = 4x + 10 \\ x \: terms \: to \: gather \\ 6x - 4x = 10 + 16 \\ 2x = 26 \\ x = \frac{26}{2} = 13 \\ \\ thank \: you[/tex]
If 2x minus 4 equals negative 18 what is x with shown work
Answer:
-7
Step-by-step explanation:
Equation: 2x - 4 = -18
First, add 4 to both sides:
2x = -14
Finally, divide both sides by 2:
x = -7
Check (optional):
2(-7) - 4 = -18
-14 - 4 = -18
-18 = -18 so this is correct
If you're confused about any of these steps, just let me know and I'll try to clear it up for you! :)
Roland purchased a new pair of shoes online that normally sell for $125.00 but were marked down to $93.75. What is the discount rate Roland received? (1 point)
O 10%
O 13%
O 25%
75%
Answer:
25%
Step-by-step explanation:
125.00x = 93.75
x = 93.75 / 125 = 0.75
meaning that 93.75 is 75% of 125
and, therefore, the item was discounted 100 - 75 % = 25%
I NEEDDD HELPPPP!! Order the numbers from least to greatest. 1=least and 4=greatest
Answer:
✓9/4,5/3,✓5,2.5
Step-by-step explanation:
✓9/4=3/2=1.5
✓5=2.2
5/3=1.6
Need help ASAP pls !!!!
What number doubled and added to 12 gives 20?
Answer:
8
Step-by-step explanation:
4 doubled and added to 12 gives 20.
What is algebraic expression?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3. Word illustration: The product of 8 and 3 is 11
Given
Let number be x
2x + 12 = 20
2x = 20-12 = 8
2x = 8
x = 8/2 = 4
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Need help understanding! please and thank you.
Answer:
I only know 5 and 6. 7 stumped me
5) even
6) odd
Step-by-step explanation:
f(x) 2x+6; vertical shrink by a factor of 1/2