Answer: [tex]2\text{x}^4, \ 2\text{x}^7, \ 2\text{x}^{10}, \ 2\text{x}^{13}[/tex]
===========================================================
Explanation:
The first term is [tex]a_1 = 2\text{x}[/tex] and the common ratio is [tex]r = \text{x}^3[/tex]
To get the second term, we multiply the first term by that common ratio
[tex]a_2 = a_1*r = 2\text{x}*\text{x}^3 = 2\text{x}^4[/tex]
Repeat a similar idea for the third term
[tex]a_3 = a_2*r = 2\text{x}^4*\text{x}^3 = 2\text{x}^{4+3} = 2\text{x}^7[/tex]
and the fourth term is
[tex]a_4 = a_3*r = 2\text{x}^7*\text{x}^3 = 2\text{x}^{7+3} = 2\text{x}^{10}[/tex]
The fifth term is
[tex]a_5 = a_4*r = 2\text{x}^{10}*\text{x}^3 = 2\text{x}^{10+3} = 2\text{x}^{13}[/tex]
Something to notice: The exponents of the first five terms are: 1, 4, 7, 10, 13. The sequence of exponents is arithmetic even though the original underlying sequence is geometric.
The reason why the exponent sequence is arithmetic is because we keep multiplying by [tex]\text{x}^3[/tex], and hence we keep adding 3 to each exponent to get the next exponent.
-----------------------------------------
To summarize, the first five terms are:
[tex]2\text{x}, \ 2\text{x}^4, \ 2\text{x}^7, \ 2\text{x}^{10}, \ 2\text{x}^{13}[/tex]
We will ignore the first term 2x since your teacher wanted you to find the next four terms after that first term (i.e. term2 through term5).
What is the probability of guessing all of the correct answers?
P(correct) = _______
Since each response is distinct, the odds of correctly predicting each response is 1/3× 1/3× 1/3, or 1/27.
Probability is the ability to happen. The occurrence of random events is the subject of this branch of mathematics. The value is expressed as a number between 0 and 1.
For instance, when a coin is tossed into the air, a Head or Tail are two possible results.
Hence, the term "probability" is most commonly used to refer to the likelihood that a specific event (or group of events) will occur, either as a linear scale from 0 (impossibility) to 1 (certainty) or as a percentage between 0 and 100%. Statistics is the study of events subject to probability.
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What is the length of the long leg in the right triangle shown below? O A. 6 B. 3 C. 643 D. 6√2 30* N 60°
Answer:
c.) 6√3
Step-by-step explanation:
This can be solved using both sine and cosine rule.
1st method:
[tex]\sf sin(x) = \dfrac{opposite}{hypotenuse}[/tex]
[tex]\sf sin(60) = \dfrac{long \ leg}{12}[/tex]
[tex]\sf long \ leg= 12sin(60)[/tex]
[tex]\sf long \ leg= 6\sqrt{3}[/tex]
2nd method:
[tex]\sf cos(x) = \dfrac{adjacent}{hypotenuse}[/tex]
[tex]\sf cos(30) = \dfrac{long \ leg}{12}[/tex]
[tex]\sf long \ leg= 12cos(30)[/tex]
[tex]\sf long \ leg=6\sqrt{3}[/tex]
Tom rolls 2 fair dice and adds the
results from each.
Work out the probability of getting a
total more than 4
The probability of getting a total of more than 4 is 5/6.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.So, formula: P = favorable events/total events
Total outcomes = 36Favorable outcomes (sum more than 4) = 30(Refer to the image attached below)
Insert values in the formula as:
P = favorable events/total eventsP = 30/36P = 5/6Therefore, the probability of getting a total of more than 4 is 5/6.
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Choose the correct term to complete each sentence.
(Radical functions/Inverse functions) are of the form f(x)=n√x
Radical functions are of the form f(x)=n√x.
If we want to find the inverse of a radical function, we will need to restrict the domain of the answer because the range of the original function is limited. Determine the range of the original function. Replace f(x) with y, then solve for x.
MORE: Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root. Radicand - A number or expression inside the radical symbol. Radical equation - An equation containing radical expressions with variables in the radicands.
To reverse that operation, you can find the square root of that power: In this case, the sign asks you to find which factor can be multiplied by itself twice to equal the expression inside the radical. (The expression inside the radical is also called the radicand.)
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Mr yuan wants to use his credit to pay off the full amount that another customers balance does Mr,Yuan have enough money to pay it off.
If Mr. yuan wants to use his credit to pay off the full amount that another customer's balance, then he can pay off for Wenner.
Customer Balance ($)
Girardi -85.23
Lewis 20.44
Stein 116.33
Yuan 13.50
Wenner -9.85
As he got the balance of -9.85 and Mr. yuan got the balance of 13.50. About the above problem is based on financial literacy which is the ability to understand and make full of our financial skills. Some of the basics of financial literacy which we can have practical applications are such as budgeting, banking, handling credit and debt, and investing. Financial literacy is essential just to avoid higher levels of debt and to have enough income for retirement.
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What is the slope and y-intercept of the line 3x - 2y = 12?
Answer:
Slope: (3/2)
y-intercept: (0, -6)
Step-by-step explanation:
3x - 2y = 12
-3x -3x
-2y = -3x + 12
÷-2 ÷-2 ÷-2
---------------------
y = (3/2)x - 6
Slope: (3/2)
y-intercept: (0, -6)
I hope this helps!
find the value of k so that the point A lies on the line given by the equation.
A(2,1), 3x+ky=8
The value of K is 2 so that the point A lies on the line given by the equation A (2,1), 3x+ky=8.
Given: Equation is 3x+ky=8
Points A (2,1)
We need to determine the value for K
3x+ky=8 — 1 (Take as equation 1)
Substitute the points in equation 1
So, we take x = 2 and y = 1
3(2) +k (1) = 8
6+k = 8
k = 8 - 6
k = 2
When graphing points on a coordinate plane, it is often helpful to find the value of k that makes the point lie on a line. For this problem, k = 2 so that A (2,1), 3x+ky=8.
Hence, the value of K is 2 so that the point A lies on the line given by the
equation A (2,1), 3x+ky=8.
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please help!!!! give 100 points
Answer:
m<1=75 degree m<2=105degree
m<3=75 degree m<4=105 degree
Answer:
m∠1 = 75°
m∠2 = 105°
m∠3 = 75°
m∠4 = 105°
Step-by-step explanation:
Angles on a straight line sum to 180°
⇒ m∠1 + m∠2 = 180°
Given:
m∠2 - m∠1 = 30°⇒ m∠2 - m∠1 + m∠1 = 30° + m∠1
⇒ m∠2 = 30° + m∠1
Substitute the found expression for m∠2 into the first equation and solve for m∠1:
⇒ m∠1 + m∠2 = 180°
⇒ m∠1 + 30° + m∠1 = 180°
⇒ m∠1 + 30° + m∠1 - 30° = 180° - 30°
⇒ m∠1 + m∠1 = 150°
⇒ m∠1 = 150° ÷ 2
⇒ m∠1 = 75°
As angles on a straight line sum to 180°, subtract m∠1 from 180° to find m∠2:
⇒ m∠2 = 180° - m∠1
⇒ m∠2 = 180° - 75°
⇒ m∠2 = 105°
Vertical Angles Theorem: When two straight lines intersect, the opposite vertical angles are the same (congruent).
⇒ m∠3 = m∠1 = 75°
⇒ m∠4 = m∠2 = 105°
Five times the sum of 4 and some number is
15. What is the number?
Answer:
I believe the answer is 5(N+4) /5 = -15/5 . n = -3 - 4 = -7
Step-by-step explanation:
The height h of a balloon, in feet, t seconds after it is released is given by the function
h(t)=2t+6. What is the value of h(20), and what does it mean in the context of the situation?
The value of h(20) is 46 and the meaning in the context of the situation is that the balloon is at 46 feet after 20 seconds
What is the value of h(20), and what does it mean in the context of the situation?The equation of the function is given as
h(t) = 2t + 6
For h(20), it means that t = 20
So, we have
h(20) = 2 * 20 + 6
Evaluate
h(20) = 46
Hence, the value of h(20) is 46 and the meaning in the context of the situation is that the balloon is at 46 feet after 20 seconds
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1,000 times 10 of the power of 3
Answer:
1,000,000
Step-by-step explanation:
10 to the power of 3 is 1,000.
1,000 x 1,000 = 1,000,000
Answer:
1 Million
Step-by-step explanation:
Start with your exponents
[tex]\mathrm 10^3 = 10 \times 10 \times 10\\= 1,000[/tex]
Multiply
[tex]1,000 \times 1,000 = 1,000,000[/tex]
17/60/17/3+(5/2-21/3*5/7)*(13*5/26+1/2)
[tex] \implies - \frac{149}{20} \\ [/tex]
Step-by-step explanation:[tex] \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{5}{2} - \frac{21}{3} \times \frac{5}{7} )( \frac{13 \times 5}{26} + \frac{1}{2} )\\[/tex]
According to the Bodmas rule,
B stands for BracketO stands for orderD stands for DivisionM stands for MultiplicationA stands for AdditionS stands for SubtractionAccording to the question,
[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{5}{2} - \frac{21}{3} \times \frac{5}{7} )( \frac{13 \times 5}{26} + \frac{1}{2} ) \\[/tex]
[tex] \implies \: \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{5}{2} - \frac{21 \times 5}{3 \times 7} )( \frac{65}{26} + \frac{1}{2}) \\ [/tex]
[tex] \implies \: \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{5}{2} - \frac{105}{21} )( \frac{65}{26} + \frac{1}{2}) \\ [/tex]
[tex] \implies \: \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{(21 \times 5 )- (2 \times 105)}{42} )( \frac{(1 \times 65 ) + (13 \times 1)}{26} ) \\ [/tex]
[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( \frac{105 - 210}{42})( \frac{65 + 13}{26} ) \\ [/tex]
[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( - \frac {105}{42})( \frac{78}{26} ) \\ [/tex]
[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( - \frac {105 \times 78}{42 \times 26})\\ [/tex]
[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} + ( - \frac {8190}{1092})\\ [/tex]
[tex] \implies \frac{ \frac{ \frac{17}{60} }{17} }{3} - \frac {8190}{1092}\\ [/tex]
[tex] \implies \frac{17}{60} \times \frac{3}{17} - \frac{8190}{1092} \\ [/tex]
[tex] \implies \frac{17 \times 3}{60 \times 17} - \frac{8190}{1092} \\ [/tex]
[tex] \implies \frac{51}{1020} - \frac{8190}{1092} \\ [/tex]
[tex] \implies \: \frac{(91 \times51) -(85 \times 8190) }{92820} \\ [/tex]
[tex] \implies \: \frac{4641 -696150 }{92820} \\[/tex]
[tex] \implies \: - \frac{691509 }{92820} \\[/tex]
[tex] \implies \: - \frac{691509 \div 4641 }{92820 \div 4641} \\[/tex]
[tex] \implies - \frac{149}{20} \\ [/tex]
This is a course test, due kinda soon. Picture Is Problem
Answer:
4 and 4
Step-by-step explanation:
i could be wrong but same length and size
Solve each equation. Check your answers.
log 6 x-3=-4
log (6x) - 3 = -4 => x = 0.167, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
log (6x) - 3 = -4 => log (6x) = -1
Since the base of the logarithm taken generally is 10, raising both the sides by 10:
[tex]10^{log_{10}(6x)}=10^{-1}[/tex]
=> 6x = [tex]\frac{1}{10}[/tex]
=> x = [tex]\frac{1}{60} = 0.167[/tex] (approx.)
Hence, log (6x) - 3 = -4 => x = 0.167, by properties of logarithm.
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Amanda borrowed $8000 from two sources: her parents and a credit union. Her parents charged 3% simple interest and the credit union charged 6% simple
interest. If after 1 yr, Amanda paid $225 in interest, how much did she borrow from her parents, and how much did she borrow from the credit union?
Using the simple interests, we can say that:
Amanda borrowed $4500 from her parents.Amanda borrowed $500 from the credit union.In the question, we are given that Amanda borrowed $5000 from two sources: her parents and a credit union. Her parents charged 5% simple interest and the credit union charged 6% simple interest.We are asked to calculate how much did she borrow from her parents, and how much did she borrow from the credit union, if after 1 year, she paid $255 in interest.We assume that Amanda borrows $x from her parents.Then we know that she would have borrowed $(5000 - x) from the credit union as the total borrowed amount was $5000.We know that the simple interest (S.I.) on $P, at the rate of r%, for a period of t years, is calculated as S.I. = Prt/100.Thus, for the amount she borrowed from her parents, the simple interest is, S.I. = (x)(5)(1)/100 = x/20.For the amount she borrowed from the credit union, the simple interest is,S.I. = (5000 - x)(6)(1)/100 = (30000 - 6x)/100 = 300 - 3x/50.Thus, the total interest Amanda needs to pay is x/20 + 300 - 3x/50 = 300 - x/100.But, we are given that the total interest Amanda pays is $255.Thus, we can write that 255 = 300 - x/100,or, x/100 = 300 - 255,or, x/100 = 45,or, x = 4500.Thus, the amount Amanda borrows from her parents = $4500.The amount she borrows from the credit union is $(5000 - 4500) = $500.Thus, Using simple interests, we can say that:Amanda borrowed $4500 from her parents.Amanda borrowed $500 from the credit union.
Angle 1 and Angle 2 are a Linear pair.
M angle 1 =x-20 and M angle 2 =x+28
Find the measure of each angle.
Angle 1 = ? Angle 2 = ?
Answer:
Answer: ∠1 = 109° ∠2 = 71°
Step-by-step explanation:
If the two angles form a linear pair, then their sum is 180°
∠1 + ∠2 = 180°
(5x + 9) + (3x + 11) = 180
8x + 20 = 180
8x = 160
x = 20
∠1 = 5x + 9
= 5(20) + 9
= 100 + 9
= 109
∠2 = 3x + 11
= 3(20) + 11
= 60 + 11
= 71
CHECK:
∠1 + ∠2 = 180°
109° + 71° = 180°
180° = 180°
Step-by-step explanation:
hope it helps
What decimal is represented by the point on the number line?
Answer:
9.25
Step-by-step explanation:
numbeer line is split into 4 things so 1/4 those things is 0.25
its .25 since its the first quarter
its adding 0.25 each dash so the next dash up would be 0.5 etc.
Tarini took a math quiz. For each incorrect question, she lost 2 points. If Tarini got 5 questions incorrect, how many points did she lose? Represent your answer as an integer.
Answer: She lost 10 points
Step-by-step explanation:
She loses 2 points per the wrong answer. Therefore, do 2 times 5. That gives you ten.
An integer is just a positive whole number btw!
I hope this helps!
Could you show how you did it
ok
Step-by-step explanation:in
evaluate the expression for the given value of the variable
please show work [tex]|-4b-8|+|-1-b^2|+2b; with b=-3[/tex]
The value of the expression when b = -3 is 24
What are functions?Functions can be defined as expression, rules or law that explains the relationship between two variables:
A dependent variablesAn independent variableIt is also important to note that the absolute value of a number is the distance of the number from zero irrespective of its direction in a number line.
Absolute value of a number must take a positive sign.
It is denoted with the symbol '| | '
Given the expression;
| -4b - 8 | + | -1 - b²| + 2b
Substitute the value of b as -3
We have;
|-4(-3) - 8| + |-1 - (-3)²| + 2(-3)
expand the bracket
|-12-8| + |-1 - 9| - 6
Take the absolute values
20 + 10 - 6
24
Thus, the value of the expression when b = -3 is 24
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I NEEEEED HELPPPP PLEASEEEE
Answer:
D. y = -6x + 12
Step-by-step explanation:
(2, 0), (0, 12)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 12 - 0 12
m = ------------ = ------------ = ------- = -6
x₂ - x₁ 0 - 2 -2
y - y₁ = m(x - x₁)
y - o = -6(x - 2)
y = -6x + 12
I hope this helps!
Point W is located at (7, 3) on a coordinate plane. Point W
is translated 2 units to the left and 3 units up. What will
be the x-coordinate of the image point W' ?
The Image of the point W(7,3) after the translation is W'(5,6),hence the x-coordinate of the translated point is 5
Translation is used in co-ordinate geometry to find the co-ordinates of an image after moving the point from its original position.
A point on the cartesian plane is represented in the form of (x,y). Where x represents the position of the point along the x-axis and y represents the position of the p[point from the y-axis.The distance of the point from the origin is calculated by the distance formula based on Pythagorean theorem.When a points is translated to the left or downwards x and y coordinate values are decreased.When a points is translated to the right or upwards x and y coordinate values are increased.The given point is W(7,3). The point is translated 2 units to the left and 3 units upwards. Hence the new coordinates of the point is given by:
W(7,3)→W'(5,6)
Therefore the x-coordinate of the translated point is 5.
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Mrs. Harkins is going to plant her new garden. She purchases 4 tomato plants for $2.59
each, a package of water melon seeds and plants for her new garden?
The sum total Mrs. Harkins is going to spend is $ 10.36 + $1.87 + $ 3.88 which comes out to be $16.11
With the given information we can easily calculate the following
The cost of 4 tomato plants which can be calculated as mentioned cost of one tomato plant in the question = 4× $2.59 = $10.36
The cost of a package of watermelon seeds as mentioned in the question = $1.87
The cost of jalapeno plant as mentioned in the question = $3.88
The sum total Mrs. Harkins is going to spend the sum total of cost of plant and seeds is $ 10.36 + $1.87 + $ 3.88 which comes out to be $16.11
Correct question is 5. Mrs. Hoskins is going to plant her new garden. She purchases 4 tomato plants for $2.59 each, a package of watermelon seeds for $1.87, and jalapeno plant for $3.88. How much will Mrs. Hoskins spend on seeds and plants for her new garden?
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Slope = -2, y-intercept = -4
Y=
[tex]\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \implies {\LARGE \begin{array}{llll} y = \stackrel{m}{-2} x\underset{b}{-4} \end{array}}[/tex]
6 negative tiles. 1 tile is crossed out.
Negative 6 minus (negative 1)
Negative 6 minus 1
Negative 5 minus (negative 1)
Negative 5 minus 1
The expression that is the representation of the number of available tiles is (a) -6 - (-1)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to interpret the representation of the tiles?The representation of the tiles is given as
6 negative tiles1 tile is crossed out.The above representation of tiles implies that:
Total number of tiles = 6All tiles are negativeOne of these negative tiles is crossed outThe representation of the tiles is
Available tiles = Total number of tiles - (The number of tiles crossed out)
The above equation implies that:
Available tiles = -6 - (-1)
We do not need to evaluate the expression
Hence, the expression that is the representation of the number of available tiles is (a) -6 - (-1)
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983,512 × 1=
A. 983,512
B. 983,513
The value of 983,512 × 1 will be 983,512 by using the multiplicative identity of multiplication.
We are given the expression:
983,512 × 1
We need to find the result after multiplication.
Multiplication is one of the basic operations of mathematics that is used to simplify the expression.
Here, we will use the property of multiplicative identity as the number is multiplied by 1.
By using this, we get that the result will be the same number as anything multiplied by 1 will always give the same number.
So, we get that:
= 983,512
Therefore, we get that, the value of 983,512 × 1 will be 983,512 by using the multiplicative identity of multiplication.
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Let f(x)=2 x²+8 and g(x)=x-3 . What are f+g and f-g ? What are their domains?
Domain of f + g ( x) = R and f - g ( x) = R
Given :
F(x) = 2x^2 + 8 and g(x) = x-3
From this, we get to know that f(x) and g(x) assume real values for all values of x.
Hence, domain (f)= Real(R) and domain (g)= real ( R ) .
Therefore D (f) and D(g) are Real Number
Now,
A > (f + g ) : R ----> R is given by (f + g) (x)
= f(x) + g(x) = 2x^2 + 8 + x- 3
= 2x^2 + x + 5
Hence, domain ( f + g ) = Real ( R )
B > (f – g) : R---> R is given by ( f-g ) (x)
= f(x) – g(x) = 2x^2 + 8 – ( x – 3)
= 2x^2 -x + 11
Hence, domain ( f - g ) = Real ( R ) .
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Which interval for the graphed function contains the local
maximum?
O
O [1, 2]
O[2,3]
O[3, 4]
[-1, 0]
Answer: The answer is C.
Step-by-step explanation:
I need help with this its due today
Two boats, originally 35 km apart, sail toward each other. The
first goes at a speed of 8.5 kph. The second goes at a speed of
5.5 kph. How long until they meet? Hint: your answer will be a
decimal.
The will meet after 2.5 hour.
To solve for distance use the formula for distance d = st, or distance equals speed times time.
distance = speed x time
Rate and speed are similar since they both represent some distance per unit time like miles per hour or kilometers per hour. If rate r is the same as speed s, r = s = d/t. You can use the equivalent formula d = rt which means distance equals rate times time.
distance = rate x time
To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time.
speed = distance/time
To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.
time = distance/speed
let say they will meet after time t.
distance covered by first boat = velocity of boat × time= 8.5t
distance covered by second boat= 5.5t
distance between both boats = 35km.
by equating both the distance
35km = 8.5t+5.5t
35km = 14t
t= 35÷14 =2.5 hour= 9020.618 seconds.
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