denote by u¹ the first term
hence u⁹ is the 9th term
[tex]u_{n} = u_{1} + (n - 1)d[/tex]
[tex]u_{2} = 2 \: \: \: \: \: \: u_{6} = - 14 \\ u_{1} + (2 - 1)d = 2 \\ u_{1} + (6 - 1)d = - 14[/tex]
[tex]u_{1} + d = 2 \\ u_{1} + 5d = - 14 \\ \\ \: \: \: (u_{1},d)=(6,-4)[/tex]
[tex]u_{9} = u_{1} + (9 - 1)d \\ u_{9} = u_{1} + 8d \\ u_{9} = 6+ (8)( - 4) \: \\ u_{9} = - 26[/tex]
Answer: a₁=6 a₉=-26
Step-by-step explanation:
a₂=2 a₆=-14 a₁=? a₉=?
a₂=a₁+(2-1)d
a₆=a₁+(6-1)d
a₁+d=2 (1)
a₁+5d=-14 (2)
Subtract equation (1) from equation (2):
4d=-16
Divide both parts of the equation by 4:
d=-4
Hence,
a₁+(-4)=2
a₁-4+4=2+4
a₁=6
a₉=a₁+(9-1)d
a₉=6+8(-4)
a₉=6+(-32)
a₉=6-32
a₉=-26
answer the question in the photo 50 POINTS!!
Answer:
infinitely many solutions
Step-by-step explanation:
a) (+12) ÷ (+4)
c) (-18) ÷ (+9)
e) (+72) ÷ (-8)
g) (-14) ÷ (+1)
i) (-27) + (-3)
b) (-15) ÷ (-3)
d) (+81) ÷ (-9)
f) (-64 : (-8
h) (+54) ÷ (-6)
j (+32) + (+4)
Answer:
Hope this helps :)
a) (+12) ÷ (+4) = 3
c) (-18) ÷ (+9) = - 2
e) (+72) ÷ (-8) = - 9
g) (-14) ÷ (+1) = - 14
i) (-27) + (-3) = - 30
b) (-15) ÷ (-3) = 5
d) (+81) ÷ (-9) = - 9
f) (-64 : (-8) =
If the sign is +, then the answer is - 72.
If the sign is ÷, then the answer is positive 8.
If the sign is x, then the answer is positive 512.
If the sign is - , then the answer is - 56.
h) (+54) ÷ (-6) = - 9
j (+32) + (+4) = 36
Kiara has 6 coins she puts the same number of coins in each of three envelopes how many coins does kiara put in each envelope
The total number of coins Kiara put in each envelope are 2.
According to the given question.
Total number of coins Kiara have = 6
Total number of envelopes Kiara have = 3
Since, we have to find the number of coins Kiara put in each envelope. So, for this we will divide total number of coins by total number of envelopes.
Therefore,
The total number of coins Kiara put in each envelope
= 6/3
= 2
Hence, the total number of coins Kiara put in each envelope are 2.
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What is the frequency of the sound? assume vsoundvsoundv_sound =340 m/s=340 m/s .
According to the given statement the frequency of the sound = 693.87h2b.
What is frequency?The frequency of a repeated event is its number of instances per unit of time. In certain cases, it is also referred to as temporal frequency or ordinary frequency to underline differences with spatial and angular frequencies, respectively. One hertz (Hz) equals one (event) per second, which is how frequencies is expressed. Because it reflects the duration of time for one cycle of a recurring occurrence, the period is the opposite of the frequency. For example, the period, T, of a heart beating at such a frequency of 120 times per minute (2 hertz), is equivalent to 0.5 seconds (60 seconds divided by 120 beats).
According to the given information:let consider Speaker at 2x 1 and the listener at p.
lot wake interfere at pence path difference for interfering phase difference
(2π/λ )Δx₁ = 2πn
When spark move for word, the path difference:
Δx₂ = 0.950
Then phase difference
Δ∅₂ = (2π/1)Δx₂ = 2
Δ∅₂ - Δ∅₁ = (2π/λ)(Δx₂ - Δx₁) = 2π
2π x .49
λ = 0.49
frequency
f λ = Vsound
f = 340/0.49
= 693.87h2b
When separation is Δx₁ = 0.46
Δ∅₁ = 2π/0.49) x 0.46
= 5.993 radian
When separation is w2 = 0.95
it will gives 12.18116 radian.
According to the given statement the frequency of the sound = 693.87h2b.
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how many groups of 9/2 are in 1
Answer:
Step-by-step explanation:
9/2 = 4 1/2
9/2=4.5
So, we divide 1 by 9/2 to find the answer
1/4.5 = 0.2222222222
Hope this helps! ^^
There are 0.22 groups or 2/9 groups of 9/2 in unity.
What are fractions?A common fraction is a numeral which represents a rational number. That same number can also be represented as a decimal, a percent, or with a negative exponent. Example -
2/5, 5/6, 7/9
We have a fraction and a whole number.
Assume that there are [x] groups of 9/2 each. Then, we can write -
9x/2 = 1
x = 2/9
x = 0.22 (rounded of)
Therefore, there are 0.22 groups or 2/9 groups of 9/2 in unity.
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Rocko paid $12.50 for 25 game tickets. Louisa paid $17.50 for 35 game tickets. What is the constant of proportionality? Express your answer in decimal form.
The constant of proportionality is 0.5.
How to compute the value?From the information, Rocko paid $12.50 for 25 game tickets and Louisa paid $17.50 for 35 game tickets.
The constant of proportionality can be illustrated as k.
Therefore, 12.50 = 25 × k
12.50 = 25k
Divide
k = 12.50/25
k = 0.5
The constant of proportionality is 0.5.
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Perimeter < 18.7 feet
4,1 ft
4.9 ft/
6.4 ft
x ft
Inequality:
Solution:
For this question, the inequality is 4.9+4.1+6.4.+x < 18.7 and the solution is x < 3.3 ft.
PerimeterThe perimeter of a geometric figure is the sum of its sides. Thus, for a square, for example, the perimeter is S1+S2+S3+S4, where S represents the dimension of each side.
In this question the sides are: 4.9, 4.1, 6.4 and x. The exercise also informs that the perimeter is less than 18.7 ft.
Thus, you can write
4.9+4.1+6.4.+x < 18.7
x+15.4 < 18.7
x < 18.7 - 15.4
x < 3.3 ft.
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amelia is documenting the height of sunflower plants each week. she has determined the function to be f(x)
According to the given statement the correct option is: D.
Domain, nonnegative values; range, values greater than 3.
How do we define range?The difference between the greatest and lowest values inside one set of integers is known as the range. Subtract the smallest from the greatest value in the set to determine range.
According to the given information:f(x) = 3x + 3
where f(x) is the plant's height and x is the passage of time.
The set of input values is known as the domain and the collection of output values is known as the range.
Because the value of time cannot be negative, the domain has non-negative values.
The lowest possible value of x is 0. Replace x=0 in the provided function.
f(x) = 3x + 3
f(0) = 3(0) + 3
= 3
At x=0, f(x) has a minimum value of 3, or 3. As x increases, function's value rises. Range thus refers to values greater or equal to 3.
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I understand that the question you are looking for is:
Amelia is documenting the height of sunflower plants each week. She has determined the function to be f(x) = 3x + 3, where x represents time and f(x) represents the height of the plant. Which of the following options describes the restrictions to the domain (x) and range f(x) correctly
a. Domain, nonnegative values; range, nonnegative values
b. Domain, nonnegative values; range, values greater than −1
c. Domain, nonnegative values; range, values less than −1
d. Domain, nonnegative values; range, values greater than 3
A girl but a T-shirt for $25 then her friend by the same shirt for 30% off how much did the friend pay for the shirt
Her friend bought the same T - shirt for $ 17.5 after 30 % discount.
We are given that a girl bought a T- shirt for $ 25.
Selling price = $ 25
Now, her friend bought the same T- shirt for 30 % off.
Discount rate = 30 %
Let the discounted price at which her friend bought the t - shirt be x.
So, we get that:
x = $ 25 - 30 % of $ 25
x = $ 25 - 30 / 100 × 25
x = $ 25 - $ 7.5
x = $ 17.5
Therefore, her friend bought the same T - shirt for $ 17.5 after 30 % discount.
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Solve the equation. First estimate using the perfect square closest to 78 . Then use a calculator. Estimate. n2=78 (the 2 is meaning squared)
- - - - - - - - - - - - - - - - - - - - - - - -
Work below!
- - - - - - - - - - - - - - - - - - - - - - - -
My estimate: 8.8 x 8.8 = 77.44
Calculated answer: 8.8 x 8.8 = 77.44
Why are they the same? Because 78 is simply not a perfect square. Therefore 77.44 must be rounded up to 78.
- - - - - - - - - - - - - - - - - - - - - - - -
Good luck! :)
~pinetreee
The manufacturing cost of a cell phone was $146. Sellers first marked up 1
the cost by 20 percent. Sales were poor, so sellers decreased the markup to
15 percent. Calculate the old and new selling prices?.
selling price = original cost + markup
Old Selling Price: $185.80 New Selling Price: $177.90
Old Selling Price: $175.20 New Selling Price: $167.90
Old Selling Price: $235.90 New Selling Price: $189.80
Answer:
Old 175.20, New 167.90
Step-by-step explanation:
Manufacturing cost: $146
Old Price $146 + 20% markup = $175.20
New Price $146 + 15% markup = $167.90
Given the rule what is the new coordinate? Show all of your work.
Rule: (x, y) → (x - 7.5, y + 6.8)
Original coordinate: (5, 3)
Using translation concepts, the new coordinates are given as follows:
(-2.5, 9.8).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.
For this problem, the rule is given as follows:
(x, y) → (x - 7.5, y + 6.8)
This means that the figure is shifted:
7.5 units left.6.8 units up.The original coordinate is given by:
(5,3), meaning that x = 5 and y = 3.
Applying the rule, we have tat:
5 - 7.5 = -2.5.3 + 6.8 = 9.8.Hence the new coordinates are given as follows:
(-2.5, 9.8).
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can someone help me please
{-3 if x ∈ [-2,-5]}, {-2 if x ∈ (-2,3]} and {3 if x ∈ (3,4]} are the required answer for the function f(x).
Interval notation is a method to represent an interval on a number line. In other words, it is a way of writing subsets of the real number line. An interval comprises the numbers lying between two specific given numbers.
Intervals can be classified based on the numbers the set comprises. Some sets include the endpoints specified in the notation, while some might partially or not include the endpoints. In general, there are three types of intervals given as,
open interval shown by round brackets.close interval shown by square brackets.half-open interval shown by mixture of round and square brackets.For the given graph we can conclude the interval one by one.
For the first blank {-3 if x ∈ [-2,-5]}
For the second blank {-2 if x ∈ (-2,3]}
For the third blank {3 if x ∈ (3,4]}
Therefore, {-3 if x ∈ [-2,-5]}, {-2 if x ∈ (-2,3]} and {3 if x ∈ (3,4]} are the required answer for the function f(x).
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what is inverse function of f(x) = sqrt-3x-27
Answer: [tex]f^{-1} (x) = -\frac{x^{2} }{3} -18x -243[/tex]
Step-by-step explanation: that would be the inverse function
in june 2012, a gallup poll asked u.s. adults whether immigration was a good thing or a bad thing for the country. out of 1004 respondents, 663 said it was a good thing.
The 95% confidence interval for the proportion who believe immigration is a good thing is 0.631< p < 0.689.
What is immigration?Immigration is the term used to describe the international movement of individuals to a country of destination where they do not have nationality or ancestry in order to settle as citizens or permanent residents. The definition of immigration or migration excludes commuters, tourists, and other short-term visitors; seasonal labor immigration is occasionally included, though.
Research indicates that migration has favorable economic impacts for both the sending and receiving countries. The majority of the time, according to research, immigration benefits the native people economically. However, there is some debate over whether low-skilled immigration has a negative impact on low-skilled natives.
Given that,
Point estimate = sample proportion = [tex]\hat p = x / n = 663 /1004=0.660[/tex]
1 - [tex]\hat p[/tex] = 1-0.660=0.34
Margin of error = E = [tex]Z\alpha/2 * \sqrt(((\hat p * (1 - \hat p)) / n)[/tex]
= [tex]1.96 (\sqrt((0.66*0.34) /1004 )[/tex]
E = 0.029
A 95% confidence interval it is given as ,
[tex]\hat p - E < p < \hat p + E[/tex]
0.66 - 0.029 < p < 0.66+ 0.029
0.631< p < 0.689
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two complementary angles are in a ratio of $3:2$. what is the measure, in degrees, of the smaller angle?
The measure of the smaller angle of the complementary angles is: 36 degrees.
What are Complementary Angles?If the sum of two angles equals 90 degrees, then they are complementary angles.
Given that the ratio of two complementary angles is 3:2, therefor:
3x + 2x = 90
5x = 90
5x/5 = 90/5
x = 18
The smaller angle = 2x = 2(18) = 36 degrees.
The larger angle = 3x = 3(18) = 54 degrees.
Therefore, the measure of the smaller angle of the complementary angles is: 36 degrees.
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Find the weighted average of the points in the line
The weighted average of the points in the line is 7.5
How to find the weighted average of the points in the line?The points are given as
3 and 12
The weighted average of the points in the line is calculated as
Weighted average = Sum/Count
So, we have:
Weighted average = (3 + 12)/2
Evaluate
Weighted average = 7.5
Hence, the weighted average of the points in the line is 7.5
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slove this 97-29+34-45*3
Answer:
-33
Step-by-step explanation:
(b/a)^3 + a^2 for a= -2 and b =4
Answer: -4
Step-by-step explanation:
a = -2 and b = 4
(b/a)^3 + a^2=
(4/(-2))^3 + (-2)^2=
(-2)^3 + 4=
-8+4=-4
if dr. lintz tried to make inferences about the outcomes of individuals based on her data of state legislatures, what mistake would she be making?
A unit of analysis is merely the entity under investigation. This is generally individuals but in case of Dr. Lintz, it really is state legislatures. The variables record information about the legislative bodies themselves, rather than the individuals who make up those bodies.
What is state legislatures?A state legislature is a broad term that refers to the legislative body in any of the 50 states in the United States. The formal name differs from one state to the next.
Some key features regarding the state legislatures are-
Every state (except Nebraska) has a bicameral legislature, which means the legislature is divided into two separate legislative chambers (or "houses"); Nebraska does have a unicameral, or one-chamber legislature. The smaller chamber is called the "Senate" in all bicameral legislatures and is commonly referred to as the "upper house." The smaller chamber generally, but not always, has the exclusive power to approve appointments made by the governor and to attempt articles of impeachment.To know more about the state legislatures, here
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(8x^2+3x−4)+(−2x^2+8x)
Select the reason why these triangles are
similar. If they are not, select "Not similar."
88°
62°
88°
30° help asap this is my last question
The triangles are similar by AA.
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary.
In similar triangles, corresponding sides are always in the same ratio.
Corresponding angles in similar triangles are always congruent.
Therefore, the angles of the first triangle are 88, 30 and 62 and the angles of the second triangle are 62, 88 and 30 degrees.
If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.
Therefore, the triangles are similar by AA.
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conclusions concerning cause-and-effect relationships are only possible when the method is used. a. survey b. experimental c. correlational d. descriptive
Conclusions concerning cause-and-effect relationships are only possible when the method is used by Experimental.
Cause and effect relationship is the concept that states about happening of a particular event causes another event to take place. Cause is the action that makes occurrence of effect. Cause is the reason because of which a event happens and effect is the result of that.
Conducting an experiment can clarify the concept to make it more understandable as conduction the experiment is the cause and the outcome is the effect caused due to experiment.
Other options are not appropriate as co-relational research measures two factors to understand relation without experimenting. Naturalistic observation is observing the happening of the natural surrounding and survey is recording the happening or event. Thus, the correct option is option(d).
The primary reason descriptive/correlational research cannot determine conclusively that variables have a cause-and-effect relationship is because in conducting researchThe researcher can't control occasions or control factors. A correlational report is a quantitative strategy for the look into in which you have at least 2 quantitative factors from a similar gathering of subjects, and you are attempting to decide whether there is a connection between the 2 factors.
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Find the degree measure of each angle in the triangle
Answer:
gooddddd luuuuuuuccccccckkkkk
Answer:
<K = 55 <L = 55 <M = 70
Step-by-step explanation:
As it is an isosceles triangle, Two sides of the triangle will be equal and their angles will be equal too.
L and K are both = (4x + 3)
All angles in a triangle add up to 180
(4x + 3) + (4x + 3) + (5x + 5) = 180
4x + 3 + 4x + 3 + 5x + 5 = 180
13x + 11 = 180
13x = 180 - 11
13x = 169
x = 169/13
x = 13
<K = 4x + 3 = 4(13) + 3 = 55
<L = 4x + 3 = 4(13) + 3 = 55
<M = 5x + 5 = 5(13) + 5 = 70
What is the greatest commen factor of 338
Answer:
2
Step-by-step explanation:
HELPPPP MATH 20 pointssss
Answer:
first one if I'm not wrong
Evaluate expression if r=3, q=1 , and w=-2 .
r w-6
The result of evaluating the expression r w-6 is equal to -12.
To evaluate an expression is a term used in maths that generally means to come up with a solution to an equation and if it is not possible then reduce it to a smaller equation by exchanging the variables with the given numerical values.
We can evaluate the given expression as follows:
Since r = 3 and w = -2, we can substitute r and w in the expression, r w-6, with 3 and -2 respectively.
r w - 6 = 3 (-2) - 6
3 (-2) - 6 = -6 -6 = -12.
Hence if we evaluate the expression r w-6, the result will be -12.
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What do you notice about the angle measures of complementary angles, supplementary angles, and vertical angles?
Answer:
1. The sum of the measures of complementary angles is 90°.
2. The sum of the measures of supplementary angles is 180°.
3. The measures of vertical angles are equal.
solve the equation 10 = 5x -15
Answer: x = 5 or YOUR DAD
Step-by-step explanation:
1. Add 15 to both:
10 + 15 = 5x - 15 +15
2. Divide by 5 on both sides:
25/5 = 5x/5
3. Simplify:
5 = x
4. Symmetric Property of Equality:
x = 5
Answer:
Question
solve the equation 10 = 5x -15 The answer is X=5
Step-by-step explanation:
10 = 5x -15
Switch sides5x - 15 = 10
Add 15 to both sides5x - 15 +15 = 10+ 15
Simplify5x = 25
Divide both sides by 55x/ 5 = 25/ 5
And then SimplifyU get x = 5
Hope this helps :)
.........................
Answer:
Step-by-step explanation: