Answer:
x = ± [tex]\sqrt{2}[/tex]
Step-by-step explanation:
given the 3 terms of a geometric sequence
[tex]\sqrt{x-1}[/tex], 1, [tex]\sqrt{x+1}[/tex], then the common ratio r
r = [tex]\frac{\sqrt{(x+1)} }{1}[/tex] = [tex]\frac{1}{\sqrt{(x-1)} }[/tex] ( cross- multiply )
[tex]\sqrt{(x+1)(x-1)}[/tex] = 1 ( square both sides )
(x + 1 )(x - 1 ) = 1 ← expand factors on left side )
x² - 1 = 1 ( add 1 to both sides )
x² = 2 ( take the square root of both sides )
x = ± [tex]\sqrt{2}[/tex]
The value of x is ±[tex]\sqrt{2}[/tex].
What is a Geometric Sequence?It is a sequence, where the ratio of two consecutive terms in a sequence are constant.It is a finite or infinite sequence.Geometric Sequence G is given by: G = a, ar², ar³,..... (a = first term; r = constant ratio)Given:
Geometric Sequence with first three terms.
[tex]\sqrt{x-1},1, \sqrt{x+1[/tex]
We have to find the value of x.
Now, if the given sequence is geometric then we can find the common ratio of the sequence.
The common ratio is given by:
r = [tex]\frac{1}{\sqrt{x-1} }[/tex] and r = [tex]\frac{\sqrt{x+1} }{1}[/tex]
Now, we can equate the both the values of r to solve for the value of x.
[tex]\frac{\sqrt{x+1} }{1} = \frac{1}{\sqrt{x-1} }[/tex]
Now, multiplying the numerator on both sides by [tex]\sqrt{x-1}[/tex], we get:
[tex]\sqrt{x+1} \sqrt{x-1} =1[/tex]
[tex]\sqrt{(x-1)(x+1)}=1[/tex]
[tex]\sqrt{x^2-1} =1[/tex]
Now, squaring on both sides of the equation, we get:
⇒ x² - 1 = 1
⇒ x² = 2
Now, taking square root on both the sides, we get:
⇒ x = ±[tex]\sqrt{2}[/tex]
Therefore, for a given geometric sequence the value of x will be ±[tex]\sqrt{2}[/tex].
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Simplify.
4(x − 5) + 2(y + 6) − 10
A) 4x + 2y − 18
B) 4x + 2y + 18
C) 4x + 2y − 9
D) 6xy − 15
Answer:
2y+4x-18
Step-by-step explanation:
4(x-5) +2(y + 6) -10
4x-20+2y+12-10
4x+2y-18
The expression 4(x-5) + 2(y+6) - 10 simplifies to 4x + 2y - 18 using the distributive property and combining like terms. Answer choice (A) is the correct one.
Explanation:To simplify the expression 4(x - 5) + 2(y + 6) - 10, you need to use the distributive property. This property allows you to multiply a number outside of a bracket with each term inside the bracket.
First, distribute 4 into (x - 5) which gives you 4x - 20. Then distribute 2 into (y + 6) which gives you 2y + 12. Now, you have 4x - 20 + 2y + 12 - 10
Combine like terms by adding or subtracting them. In this case, -20, +12 and -10 are like terms. When you add these together, you get -18. So, the simplified expression becomes 4x + 2y - 18. Therefore, answer choice (A) is correct.
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Does (6 , -3) make the equation y=-2x true ?
Answer:
No
Step-by-step explanation:
Note that:
(x , y) = (6 , -3) ∴ x = 6, y = -3
Plug in 6 for x in the equation, and -3 for y.
y = -2x
(-3) = (-2)(6)
Simplify. Multiply.
(-3) = (-12)
-3 ≠ -12 ∴ (6 , -3) is not a solution for y = -2x
~
Answer:
False
Step-by-step explanation:
(6,-3) means x=6 and y=-3
Substitute into the equation
y= -2x
-3 = -2(6)
-3 = -12
This is false
517x82= what is the anser
Answer:
The answer is 42394
7. Multiply the binomials: (x - 9)(x + 2)
a. x^2 - 7x - 18
b. x^2 - 11x - 18
c. x^2 - 7x + 18
d. x^2 + 7x - 18
Answer:
the answer is a. x^2-7x-18
first you distribute the x in the first equation getting you x^2 +2x, then you distributed the -9 getting -9x-18. you then put those together, x^2+2x-9x-18. Finally you simplify to x^2-7x-18
Find the height of a soup can if the area of the label is 302 square centimeters and the radius of the can is 4 centimeters
[tex]\bf \textit{surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ SA=302\\ r=4 \end{cases}\implies 302=2\pi (4)(h+4) \\\\\\ 302=8\pi (h+4)\implies \cfrac{302}{8\pi }=h+4\implies \cfrac{302}{8\pi }-4=h\implies 8.016\approx h[/tex]
Find the square root of 15129 by division method
[tex]\underline{\ \ \ \ \ \ 123}\\1\ \ \ |15129\\\underline{\ \ \ \ \|1}\\22\ |\ 51\\\underline{\ \ \ \ |\ 44}\\243|\ \ 729\\\underline{\ \ \ \ \ |\ 729}\\.\qquad\ \ \ 0[/tex]
[tex]\sqrt{15129}=123[/tex]
[tex]\begin{array}{c|c}15129&3\\5043&3\\1681&41\\41&41\\1\end{array}15129=3\cdot3\cdot41\cdot41=3^2\cdot41^2\\\\\sqrt{15129}=\sqrt{3^2\cdot41^2}=\sqrt3^2}\cdot\sqrt{41^2}=3\cdot41=123[/tex]
[tex]Used:\\\\\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\\\sqrt{a^2}=a\ for\ a\geq0[/tex]
Each sheet cake requires 3 cups of flour and 2 cups of sugar. If a bakery has 75 cups of flour and 75 cups of sugar, how many sheet cakes can be made?
Answer: 25
Step-by-step explanation: Flour: 75 divided by 3 equals 25. The sugar does not matter in this situation but there will be 25 cups of sugar left if you want to know. Hope this helps!
Answer:
25 sheets
Step-by-step explanation:
Each sheet cake requires 3 cups of flour and 2 cups of sugar.
A bakery has 75 cups of flour and 75 cups of sugar.
Each sheet needs flour = 3 cups
75 cups of flour can make sheet = [tex]\frac{75}{3}[/tex]
= 25 sheets
for 25 sheets we need sugar = 25 × 2 = 50 cups of sugar
There are more amount of sugar than we need.
Therefore, 25 sheets can be made by 75 cups of flour.
you buy 3 pairs of pants for $19 each and 5 shirts for $10 each. which of the following is a good estimation of how much money you spent?
A. 110
B. 150
C. 190
D. 230
E. 270
Answer:
110
Step-by-step explanation:
cause you would have to multiply the you bought to the cost of them and you add those two totals together
Answer:110
Step-by-step explanation:
19times3=575times10=5057+50=107estimation is 110
please help 20 points.
Marco went to the library. He checked out 6 movies. The rest of the items he checked out were books. He checked out a total of 17 items. How many books did he check out?
Use the variable b to represent the number of books Marco checked out.
Which equation represents this situation and its solution?
6b = 17; b = 23
b + 6 = 17; b = 11
b + 23 = 17; b = 6
23b = 17; b = 6
Answer:
the second one is your answer
A volume of the triangular block is 4 cubic inches, what is the approximate length of y? Round to the nearest tenth of an inch
Answer:
2.8 inches will be the approximate length of the y.
Step-by-step explanation:
volume = 1/2 x A x C x H = 4 cubic inches
Because the volume of the triangular block is 4 cubic inches.
Formula:
A x C = Base x Height
Answer:
2.8 in
Step-by-step explanation:
What is the solution to the system of equations Y equals -1/4 X +2 and 3Y equals -3/4 X -6
Answer:
No solutions
Step-by-step explanation:
y = -1/4 x+2
3y = -3/4 x -6
We can use substitution since the first equation is solved for y
Every time there is a y in the second equation, replace it with -1/4 x +2
3 (-1/4 x+2) = -3/4 x -6
Distribute
-3/4 x +6 = -3/4 x-6
Add 3/4 x to each side
-3/4 x + 3/4 x +6 = -3/4 x + 3/4x-6
6 = -6
Since this not a true statement, the system of equations has no solutions
Please help my mother is yelling at me to go to bed
Answer:
a) 26
b) 48
c) 54
d)74
Step-by-step explanation:
and negative divided by a negative is postitive right? yes, then it is just simple division
In the game "let's make a meal," there are 10 covered dishes to choose from: 2broccoli,2cake,2 carrot,1chicken,2fish,and 1 meatloaf
What is the probability of choosing a vegetable
A:4/5
B:1/2
C:1/10
D:2/5
Answer:
D:2/5
Step-by-step explanation:
There are 4 vegetables to choose from; 2 broccoli and 2 carrots.
This is out of 10 covered dishes.
This gives the probability 4/10, which simplifies to 2/5.
Answer : The correct option is, (D) [tex]\frac{2}{5}[/tex]
Step-by-step explanation :
Probability : It is defined as the extent to which an event is likely to occur. That means, it is measured by the ratio of the favorable outcomes to the total number of possible outcomes.
[tex]\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of favorable outcomes}}[/tex]
Total favorable outcomes are, 2 broccoli, 2 cake, 2 carrot, 1 chicken, 2 fish, and 1 meat loaf = 10
Favorable outcomes of choosing a vegetable are, 2 broccoli and 2 carrot
Number of favorable outcomes of choosing a vegetable = 4
Total number of outcomes = 10
[tex]\text{Probability}=\frac{\text{Number of favorable outcomes for a multiple of 3}}{\text{Total number of favorable outcomes}}[/tex]
[tex]\text{Probability}=\frac{4}{10}[/tex]
[tex]\text{Probability}=\frac{2}{5}[/tex]
Therefore, the probability of choosing a vegetable is, [tex]\frac{2}{5}[/tex]
Mark the points (10, 14), (15, 11.11), and (10, 8.22). Enter the coordinates in the input window, if you wish. Then connect the points to form a triangle. Part A Measure the lengths of the sides of the triangle and record them in the table.
Answer:
The points form a equilateral triangle of side 5.78 units.
Step-by-step explanation:
The length of the sides of the triangle is calculated using the distance formula.
The distance between the points (x₁,y₁) and (x₂,y₂) is
[tex]d= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
Now,
AB = [tex]\sqrt{(11.11-14)^{2}+(15-10)^{2}}=\sqrt{8.3521+25} = \sqrt{33.3521}=5.78[/tex]
BC = [tex]\sqrt{(8.22-11.11)^{2}+(10-15)^{2}}=\sqrt{8.3521+25} = \sqrt{33.3521}=5.78[/tex]
CA = [tex]\sqrt{(8.22-14)^{2}+(10-10)^{2}}=5.78[/tex]
The length of the sides of the triangle is 5.78. All the sides are equal in length. It is an equilateral triangle.
Which of the following best describes the relationship between (x + 1) and the polynomial -3x3 - 2x2 + 1?
A.
(x + 1) is a factor.
B.
It is impossible to tell whether (x + 1) is a factor.
C.
(x + 1) is not a factor.
Answer:
(C) (x+1) is not a factor
Step-by-step explanation:
To show that x+1 is not a factor, in other words to show that the polynomial cannot be written as a product
[tex](x+1)\cdot(some\,\,quadratic)=-3x^3-2x^2+1[/tex]
it suffices to test that x=-1 is not a root of the original cubic:
[tex]-3x^3-2x^2+1|_{x=-1}=-3(-1)^3-2(-1)^2+1=2\neq 0[/tex]
which is hereby shown and the option (A) is out.
Option (B) is non-sense.
Option (C) is the correct answer.
After applying the Factor Theorem, we find that substituting -1 into the polynomial [tex]-3x^3 - 2x^2 + 1[/tex] does not yield zero; hence, (x + 1) is not a factor, option C.
The student has asked whether (x + 1) is a factor of the polynomial [tex]-3x^3 - 2x^2 + 1[/tex]. To determine if (x + 1) is indeed a factor, one could perform polynomial division or apply the Factor Theorem. According to the Factor Theorem, (x + 1) is a factor if and only if substituting -1 for x in the polynomial yields zero. Substituting, we get:
[tex]-3(-1)^3 - 2(-1)^2 + 1 = 3 - 2 + 1 = 2[/tex]
Since the result is not zero, (x + 1) is not a factor of the polynomial. So, the correct answer to the student's question is option C: (x + 1) is not a factor.
Wrens did jenni are reading the same book.wren is on page 17 and reads 6pages every night .jeeni is on page 13 and reads 8 pages evernigjt period. After how many nights will they have read the same number of pages, how many pages will that be
Answer:
After 2 nights they would have read the same amount of pages. That is 29 pages.
Step-by-step explanation:
1. 6x+17=13+8x Put the problem in to a equation
2. 6x+17=13+8x Subtract 8x from both sides
-8x -8x
3. -2x+17=13 Subtract 17 from both sides
-17 -17
4. -2x=-4 Divide by -2
-2 -2
5. x=2 x=2
write down an expression for the nth term of the following sequence, 7, 16, 25, 34, 43
Answer:9n-2
Step-by-step explanation:
1st = 9*1-2= 7
2nd = 9*2-2= 16
3rd = 9*3-2= 25
4th = 9*4-2 = 34
...
The nth term of the sequence 7, 16, 25, 34, 43, which is an arithmetic sequence with a common difference of 9, is given by the expression 9n - 2.
The sequence given is 7, 16, 25, 34, 43. To find the nth term expression of this sequence, first, we can observe the pattern that each term increases by 9. Therefore, the sequence is an arithmetic sequence. We can use the formula for the nth term of an arithmetic sequence, which is [tex]a_n = a_1 + (n - 1)d[/tex], where [tex]a_1[/tex] is the first term and d is the common difference.
The first term a1 is 7, and the common difference d is 9. So, the nth term is:
[tex]a_n = 7 + (n - 1) \times9[/tex]
To simplify, it will be:
[tex]a_n = 7 + 9n - 9a_n = 9n - 2[/tex]. This is the expression for the nth term of the given sequence.
Solve the inequality and express your answer in interval notation. x^2+8x+5<0
Answer:
-7.32 < x < -0.68 0r -4-√11 < x < √11 - 4
Step-by-step explanation:
The given inequality is x^2 + 8x + 5 < 0
Here we cannot factorize, so we need to use the quadratic formula to find the solution.
The quadratic formula x = [tex]\frac{-b +/- \sqrt{b^2 - 4ac)} }{2a}[/tex]
Here a = 1 , b = 8 and c = 5
Plug in these values in the formula, we get
x = -8 ± √(8)^2 - 4*1*5) ÷ 2(1)
x = (-8 ±√44)/2
x = (-8 ±2√11)/2
x = -4 ± √11
There are two values for x.
x = -4 + √11 and x = -4-√11
√10 = 3.16
So x = -4 + 3.32 and x = -4 - 3.32
x =-0.68 and x = -7.32
This means
-7.32 < x < -0.68 0r -4-√11 < x < √11 - 4
Thank you.
Answer:
[tex]-4-\sqrt{11} <[/tex] x [tex]-4+\sqrt{11}[/tex]
Step-by-step explanation:
We are given the following quadratic inequality by applying the quadratic formula to solve it (since it can not be factorized) and then express it in an interval notation:
[tex]x^2+8x+5<0[/tex]
We know the quadratic formula:
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
Putting in the values to get:
[tex]x=\frac{-8+-\sqrt{8^2-4(1)(5)} }{2(1)} \\\\x=\frac{-8+-\sqrt{44} }{2}[/tex]
[tex]x=-4-\sqrt{11} , x=-4+\sqrt{11}[/tex]
Therefore, the interval notation for the given quadratic inequality for x will be:
[tex]-4-\sqrt{11} <[/tex] x [tex]-4+\sqrt{11}[/tex].
Find the sum or different 11/18-1/6
Answer:
4/9
Step-by-step explanation:
11/18-1/6
The first step is to get a common denominator, which is 18. We can multiply 1/6 by 3/3 to get the denominator to 18
11/18 - 1/6 *3/3
11/18 - 3/18
8/18
Now we can simplify the fraction by dividing the top and bottom by 2
4/9
Answer:
4/9
Step-by-step explanation:
11/18 - 1/6
1 times by 3
6 times by 3
11/18-3/18
8/18
8 divided by 2
18 divided by 2
4/9
Harper fills pots each with 4 liters of water how many liters of water does he pour into the pots?
Answer:
12 liters of water
Step-by-step explanation:
3 times 4 =12 liters
Answer:
12 liters
Step-by-step explanation:
You have 3 pots and 4 liters in each so you would multiply these two numbers and you will get 12:
3 × 4 = 12
A shop has 15% sale. Originally a computer cost £275. How much does the computer cost in the sale?
Answer:
= 233.75
Step-by-step explanation:
To find the discount, we multiply the original price by the percent off
discount = 275* .15
= 41.25
To get the sale price, take the original price and subtract the discount
sale price = 275-41.25
= 233.75
Kiera used place value and the distributive property to find the product of 12 and 597. Her work is shown below. 12(597) = 12(500 + 90 + 7) = 12(500) + (90)(7) = 6000 + 630 = 6,630 What is Kiera’s error?
Answer:
(90)(7) ⇒ the error was multiplying 90 and 7.
Step-by-step explanation:
12(597) = 12(500 + 90 + 7)
= 12(500) + (90)(7)
= 6000 + 630
= 6,630
The part in bold shows where the error is. It was not correct to multiply 90 and 7.
The process was to proceed as follows:
12(597) = 12(500 + 90 + 7)
= 12(500) + 12(90) + 12(7)
= 6000 + 1080 + 84
= 7,164
Answer: Kirera did not multiply each added by 12.
A mortised traveled 311 miles on 12 gallons of gas to the nearest tenth how many miles can the motorist travel on one gallon of gas
Answer:
25.9 miles
Step-by-step explanation:
To find out how far he can go on one gallon of gas, we divide miles by gallons.
311 miles/ 12 gallons
25.91666666 miles per gallon
So on one gallon of gas, he can go 25.9166666666 miles
Rounding to the nearest tenth.
25.9 miles
PLEASE HELP MEH!
I've literally been stuck on this question for 4 hours, tried to get help from my dad, tried to get help from Khan Academy. NOTHING IS WORKING! IF SOMEONE CAN HELP I WILL MARK BRAINLIEST. I need to solve for x and y which is blank.
Answer: x=72, y=26
Step-by-step explanation:
Since a line is 180°, we can do:
2x+10+y=180
2x+y=170
Since a triangle is 180° also, we can do:
x+y+82=180
x+y=98
If we subtract x+y=98 from 2x+y=170, we get:
2x+y=170
x+y=98
x=72
If we insert x=72 into x+y=98, we get:
72+y=98
y=26
We can check our answer by inserting x=72 and y=26 into x+y+82=180
72+26+82=180
98+82=180
180=180
the temperature drops -9/10 every hour how much will it change in 3/2 hours
Answer:
0.45
Step-by-step explanation:
Ok so you start with -0.9. You need to find how much it will change in an hour and 30 minutes. So you subtract -0.9 from -0.9 and you'd get 0. Now, we have to subtract half of -0.9 (because 30 minutes is half an hour). Half of -0.9 is -0.45. Subtract 0 by -0.45 and you get 0.45.
Answer:
It varies 0,45. For 1,35 - 0,9 = 0,45
Step-by-step explanation:
-9/10 = -0,9
3/2 = 1,5
1h ------- -9/10
1,5h --------- x
x = 1,5 * -0,9
x = -1,35
agent burn transferred classified files from the CIA Mainframe into his flash drive the drive had 36.5 megabytes on it before the transfer and the transfer happened at a constant rate after 125 seconds there were 549 megabytes on the drive the drive had a maximum capacity of 1000 megabytes. What was the speed of the transfer
Answer:
see below PLEASE GIVE BRAINLIEST
Step-by-step explanation:
549 - 36.5 = 512.5mb were trf
512.5/125 = 4.1mb per second
Answer:
Step-by-step explanation:
The speed of the transfer was 4.1 megabytes per second. It took the drive 235 seconds to be completely full.
The team score in a basketball game depends on the number of baskets scored in the game
A. Score(game), or S(g)
B. Score(basketball), or S(b)
C. Game(score), or G(s)
D. Team(score), or T(s)
Answer:
B is the answer, hope this helps.
The subject of this question is Mathematics. The dependent variable in a basketball game is the team score, represented by option D: Team(score), or T(s).
Explanation:The subject of this question is Mathematics. The question is asking about the dependent variable in a basketball game, which is the team score. The team score depends on the number of baskets scored in the game, represented by option D: Team(score), or T(s).
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I need the answer ASAP!!
Answer:
40
Step-by-step explanation:
15 divided by 3 is 5 and since it is 5 per hour 8 times 5 is 40
Answer:
$40
Step-by-step explanation:
So if Logan's rate is $15/3 hours = $5 per hour,
Then $5 × 8 hours = $40 in total.
Hope this helps! Have a nice day!
solution to 3x = 156
Answer:
x=52
Step-by-step explanation:
Answer:
52
Step-by-step explanation:
156 divided by 3= 52
3*52=156
luna ray has 1 orange pick for every 2 green picks. how many green picks does luna have if she has 12 total picks.
Answer:
8 green
Step-by-step explanation:
orange: green
1 :2
1+2 = 3 so she has 3 total picks
12/3 =4
So we need to multiply by 4
1*4 : 2*4 total pick 3*4
4:8 12 total picks
4 orange 8 green 12 total