After solving, the factors of the equation x²+7x-8=0 are:
(x + 8) and (x - 1)What is an equation?A mathematical statement made up of two representations joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value for the variable x as x = 7 after solving this equation.So,
Given equation: x²+7x-8=0Then,
x²+7x-8 = 0x²+x( - )-8 = 0x²+x( 8 - 1 )-8 = 0x²+8x -x -8x(x + 8) -1( x+8)Factors are: (x + 8) and (x - 1)
Therefore, after solving, the factors of the equation x²+7x-8=0 are:
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The rental costs for a car are shown in the graph. Estimate the rental cost for 6 days
$210
$160
$150
$200
$180
Rental Cost
Time (days)
Answer:
180
Step-by-step explanation:
round 43.093 to the hundredths place
Answer:
43.09
Step-by-step explanation:
All the info you need to answer the questions are in the photo answer A and B. Giving brainliest . Answer asap!!
Answer: Solution is where the x intercepts on the graph
Step-by-step explanation:
Least common dinaminator
sa paanong paraan nagiging instrumento
Answer:
Steps below
Step-by-step explanation:
a/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcda/b+c/d=a/bc+c/bd=abd+c/bcd
17 The table shows the probabilities that a biased dice will land on 2, on 3, on 4, on 5 and on 6
Number on dice
Probability
1
2
0.17
3
4
0.18 0.09
5
0.15
6
0.1
Neymar rolls the biased dice 200 times.
Work out an estimate for the total number of times the dice will land on 1 or on 3
The total number of occasions the dice would land on 1 or 3 is 98.
What are the components of probability?The probability space associated with a randomly chosen experiment is established by three components: the result space, whose element is an experiment outcome, a collection of events F whose elements represent subsets of, and a probability measure IP assigned towards the elements in F.
How do you get good at probability?As a result, for problems like Cards, Coins, and Dices, it is preferable to record the potential scenarios and determine the individual probabilities of each case before ORing/ANDing them in accordance with the problem demand. If done correctly, this will provide a great solution that will never fail you.
According to the given data:All of the probability will add upto 1.
this give us the equation:
P(1)+0.17 + 0.18 + 0.09 + 0.15 + 0.1 = 1
P(1) + 0.69 = 1
P(1) = 1 - 0.69
P(1) = 0.31
We now need to find the probability of 1 or 3
P(1 or 3) = P(1) + P(3)
= 0.31 + 0.18
= 0.49
We now use the predicting outcomes formula.
expected = P(1 or 3) x no. of times.
= 0.49 x 200
= 98
the total number of times the dice will land on 1 or on 3 = 98.
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Last year Keisha paid $765 in taxes while working a part-time job and going to school. Now she's working full-time, she was shocked to find their taxes jumped 612% how much does Keisha pay taxes now
Answer:
Step-by-step explanation:
Formula: Amount of taxes part time x 1+(amount jumped)
Therefore just do : 765 x 7.12 = $5446.80
Determine whether each statement is always, sometimes, or never true.
ln t=log e t
ln (t) = [tex]log_e(t)[/tex] is always true, by the definition 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,
According to the definition of logarithm, we can see that it is the normal logarithm or log function with the value of base being 'e', i.e., [tex]log_e(t)[/tex].The representation of natural logarithm is ln (t).Hence, ln (t) = [tex]log_e(t)[/tex] is always true, by the definition of logarithm.
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Find the inverse of each function. Is the inverse a function?
f(x)= √2 x-1+3
Yes , the given function is an inverse function which is given by [tex]f^{-1}(y)=\frac{y-2}{\sqrt{2} }[/tex] .
An inverse function or anti -function is defined as a function that can be inverted into another function. Simply put, if the function 'f' makes x into y, the inverse of 'f' makes y into x. Where a function is denoted by 'f' or 'F', the inverse is denoted by f-1 or F-1. A function accepts values, performs some operation on those values, and produces an output. The inverse function works in line with the result and returns to the original function. An inverse function returns the original value that the function provided the output for.
We have given a function [tex]f(x)=x\sqrt{2} -1+3[/tex] . ....(1)
On simplifying the equation we, get
[tex]f(x)=x\sqrt{2} +2[/tex]
Let y = f(x)
[tex]y=x\sqrt{2} +2\\\\y-2=x\sqrt{2}\\\\x=\frac{y-2}{\sqrt{2} }[/tex] ......(2)
Swap the values of x and y, then the inverse is then
[tex]x=f^{-1}(y)[/tex] ...(3)
Comparing equation (2) and (3) , we get
[tex]f^{-1}(y)=\frac{y-2}{\sqrt{2} }[/tex]
We can check that this is really an inverse function or not
Putting [tex]x=f^{-1}[/tex] in equation (1) , we get
[tex]f(f^{-1}(y))=\frac{y-2}{\sqrt{2} } \sqrt{2} -1+3\\\\y=y-2+2\\\\y=y[/tex]
As LHS = RHS which means inverse function is correct .
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leora mows lwans in her neighborhood. the graph shows how much she earns
I found the graph, the answer should be 25$
What is the value of (–1.23)(–5.31)?
A: -653.13
B: -6.5313
C: 6.5313
D: 653.13
Thank You
Answer:C
Step-by-step explanation:
its because the formula gives away the answer in a impecable way
On a coordinate plane, a curved line, labeled f of x, with a minimum value of (negative 1.9, negative 5.7) and a maximum value of (0, 2) crosses the x-axis at (negative 2.5, 0), (negative 0.75, 0), and (0.75, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function f(x)?
F(x) < 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
F(x) > 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
F(x) < 0 over the intervals ( –2.5, –0.75) and (–0.75, ∞).
F(x) > 0 over the intervals ( –2.5, –0.75) and (0.75, ∞).
The statement that is true about the graphed function f(x) is that D. F(x) > 0 over the intervals ( –2.5, –0.75) and (0.75, ∞).
What is a coordinate plane?The intersection of the x-axis, the horizontal line, and the y-axis, the vertical line, creates a coordinate plane, which is a two-dimensional plane. The origin is the point at which these parallel lines cross one another.
In this case, the statement that is true about the graphed function f(x) is that F(x) > 0 over the intervals ( –2.5, –0.75) and (0.75, ∞).
The appropriate graph is attached.
In conclusion, the correct option is D.
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Help me pls
I need solution
The expression is simplified to 10x² + 48x + 3 =0
How to determine the valueGiven the expression as;
[tex]5^(^4^x^+^1^)^(^x^+^2^) + 4. 5^x^(^x^+^1^5^) = 5^-^2^x^2+^2^1^x^-^1[/tex]
We take the numerators have the same base, then we have;
(4x+1)(x+2) + 4(x(x+ 15) = -2x² + 21x - 1
expand the bracket
4x² + 8x + x + 2 + 4(x² + 15x) = -2x² + 21x - 1
4x² + 8x + x + 2 + 4x² + 60x = -2x² + 21x - 1
collect like terms
4x² + 4x² + 2x² + 8x + x + 60x - 21x = - 1 - 2
Add or subtract like terms
10x² + 48x = -3
Make into a quadratic equation
10x² + 48x + 3 =0
Thus, the expression is simplified to 10x² + 48x + 3 =0
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Each pair of values is from a direct variation. Find the missing value. (2,5),(4, y)
The missing value of direct variation is 10
What is direct variation ?The direct variation property states that , whenever the division of values of two quantities is a constant value then there is same variation between these two corresponding values. Or we can also say that if the divisible nature of two corresponding values is constant, then one quantity is directly varies with second quantity. That mean if one quantity increase other will also increase and vice versa.
Let say if x and y are two values and k is a constant value, then
According to direct variation
k = y/x or y = k x
In the given question,
Take the order pair (2,5)
As it is an direct variation, we can substitute it
y=k x
5=k (2)
K=2.5
Now find the direct variation equation
y=k x
Also, k=2.5
Solve this equation for the second pair (4,y)
As, y=2.5 x
y= 2.5 (4) = 10
Therefore, missing value is 10
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Fragrance
(mL)
80
120
160
Wax
(L)
2
3
4
Type 3
Fragrance Wax
(mL)
250
500
750
Type 3
OType 4
Mark this and return
(L)
10
20
30
Which type of candle has the greatest ratio of fragrance to wax?
Type 1
OType 2
Save and Exit
Fragrance Wax
(mL)
(L)
150
3
250
300
Types
240
270
Type 4
Fragrance
(mL)
30
NEAL
5
6
Wax
(L)
1
8
9
Multiply. (10+√6)(10-√3)
The answer is 102.93174866
The Karatsuba set of rules becomes the primary multiplication set of rules asymptotically quicker than the quadratic "grade faculty" algorithm. The Toom–cook algorithm (1963) is a faster generalization of Karatsuba's technique, and the Schönhage–Strassen algorithm (1971) is even quicker, for sufficiently big n.
Multiplication is the main device for lots of forms of maths which include algebra, calculus, equations, and greater. The capacity to rehearse and understand multiplications up to and such as 12 by means of the final yr of number one college will permit your toddler to with a bit of luck and skillfully address greater complex mathematical topics.
Familiarity and skillability with the primary timetables are essential building blocks in math. It opens the door to multi-digit multiplication and demystifies tactics like long department and simplifying fractions. It lays the foundation for algebra.
Multiply 10 by
10.100+10(−√3)+√6⋅10+√6(-√3)
Multiply −1 by 10.100-10√3+√6⋅10+√6(−√3)
Move 10 to the left of
√6.100-10√3+10.√6+√6(−√3)
Multiply √6(−√3).
Combine using the product rule for radicals.
100−10[tex]\sqrt{3}[/tex]+10[tex]\sqrt{6}[/tex]−[tex]\sqrt{6.3}[/tex]
Multiply 6 by
3.100−10[tex]\sqrt{3}[/tex]+10[tex]\sqrt{6}[/tex]−[tex]\sqrt{18}[/tex]
Rewrite 18 as 32⋅2.
Factor 9 out of
18.100−10[tex]\sqrt{3}[/tex]+10[tex]\sqrt{6}[/tex]−[tex]\sqrt{9}[/tex](2)
Rewrite 9 as
32.100−10[tex]\sqrt{3}[/tex]+10[tex]\sqrt{6}[/tex]−[tex]\sqrt{32.2}[/tex]
Pull terms out from under the radical.
100−10[tex]\sqrt{3}[/tex]+10[tex]\sqrt{6}[/tex]−(3[tex]\sqrt{2}[/tex])
Multiply 3 by −1.100−10[tex]\sqrt{3}[/tex]10[tex]\sqrt{6\\}[/tex]−3[tex]\sqrt{2}[/tex]
The result can be shown in multiple forms.
Exact Form:
100−10[tex]\sqrt{3}[/tex]+10[tex]\sqrt{6\\}[/tex]−3[tex]\sqrt{2}[/tex]
Decimal Form:
102.93174866
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The fuel tank of a certain airplane can hold up to 300
The Range of the given function weight is; [4,000 , 5,800]
How to find the range of a function?The range of a function is defined as the set of all possible output values of that function.
We are Given:
Function; W = 6F + 4000
Full amount of fuel = 300 gallons
No amount of fuel = 0 gallons
Thus, the set of all possible input values which is the domain is;
Domain : amount of fuel = [0 , 300]
If F = 0, then we have;
W = 6F + 4,000
W = 6(0) + 4,000
W = 4,000
If F = 300, then we have;
W = 6F + 4,000
W = 6(300) + 4,000
W = 5,800
Thus, we conclude that the Range of weight is; [4,000 , 5,800]
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Complete question is;
The fuel tank of a certain airplane can hold up to 300 gallons of fuel. Let Wbe the total weight(in pounds) Let F be the total amount of fuel in this tank ( in gallons) Suppose that W = 6F +4000 gives W as a function of F
solve for x. x - 16 = -20
PLEASE HELPP
Answer:
x = -4
Step-by-step explanation:
x - 16 = -20
16 is being subtracted from x. To get x alone, you need to add 16 to x - 16.
We must do the same to both sides of an equation, so we add 16 to both sides of the equation.
x - 16 + 16 = -20 + 16
x = -4
Graph this function.
f(x) = x - 2
A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A is uniquely associated with an object f(a) in B. A function is therefore a many-to-one (or sometimes one-to-one) relation. The set A of values at which a function is defined is called its domain, while the set f(A) subset B of values that the function can produce is called its range. Here, the set B is called the codomain off.
A function from a set X to a set Y is an assignment of an element of Y to each element of X. The set X is called the domain of the function and the set Y is called the codomain of the function.
A function, its domain, and its co-domain are declared by the notation f: X→Y, and the value of a function f at an element x of X, denoted by f(x), is called the image of x under f, or the value of f applied to the argument x.
Functions are also called maps or mappings, though some authors make some distinction between "maps" and "functions"
f(x) = x - 2
X=0
f(0) = 0-2
f(0) = -2 ...(1)
f(1) = 1-2
f(1) = - 1 .....(2)
f(2) = x-2
f(2)= 2-2
f(2)= 0....(3)
Answer = Straight line figure
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what the base 5 system of 1120 can someone help me
Solution :
base 10
A number base (or base for short) of a numeral system tells us about the unique or different symbols and notations it uses to represent a value. For example, the number base 2 tells us that there are only two unique notations 0 and 1. The most common number base is decimal, also known as base 10.
Step1:
Converting 1120 to base 10.
1*103=1000
1*102=100
2*101=20
0*100=0
Adding all to get Ans=1120 based 10
Step2
Converting 1120 based 10 to 5
The equation calculation formula for 1120 based 10 numbers to 5 is like this below.
5|1120
5|224|0
5|44|4
5|8|4
5|1|3
5|1|1
Ans:13440 based 5
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Hello... HELP PLEASE
worth 20 pts and brainliest :)))
(science)
Answer:
-2
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
For a given atom, net charge can be determined by looking at how many protons the atom has in its nucleus and how many electrons it has surrounding its nucleus.
More specifically, the atom will have
a positive net charge if it has more protons in its nucleus than electrons surrounding its nucleus
a negative net charge if it has more electrons surrounding its nucleus than protons in its nucleus
no net charge if it has equal numbers of protons and electrons
When an atom carries a positive net charge, it forms a cation, or positively charged ion. Likewise, when an atom carries a negative net charge, it forms an anion, or negatively charged ion.
In your case, the atom is said to contain
eight protons
nine neutrons → they do not influence the net charge of the atom
ten electrons
Now, electrons and protons carry opposite charges. A proton is said to carry a 1+ charge, while an electron is said to carry a 1−.
In your case, you have 8 protons and 10 electrons. This means that the atom will carry a total
2×(1−)=2−
net charge.
Therefore, you are dealing with an anion that carries a 2− net charge, i.e. it has two more electrons than it does protons.
A recipe calls for one cup of flour to make four pancakes. How many pancakes can be made with eight cups of flour?
Answer:
32
Step-by-step explanation:
Since 1 cup is equal to 4 pancakes would need to multiply 8 cups by 4 pancakes (how many you make with one cup) Which will give you 32. You can check by dividing 32 by 8 or 4 and you will get one of the numbers.
Hope that helps, please comment if you need anything else :D
Need asap pleaseeeeeeeeeeee
The exponent property that should be applied is the quotient of a power property. Option A
What are index forms?
Index form of a number can be defined as the power or exponent raised to a number or variable.
It is also known as the standard form of a number.
What is the quotient of a power property?The quotient of a power property states that the power of a quotient is equivalent to the quotient that is obtained when the numerator and denominator are each raised to a particular power differently, before the division is carried out.
It is used to simplify the problem of division involving exponents.
Given the expression;
3r³b^5/9b
Take the inverse exponent of the divisor
3r³b^5 × b^-1/ 9
Divide the common factors
r³b^5 × b^-1/3
Add the common exponents
r³b^4/3
Thus, the exponent property that should be applied is the quotient of a power property. Option A
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Write each expression as a single natural logarithm. 2 ln 8-3 ln 4
ln 1 is the converted from the expression 2 ln 8-3 ln 4 to a single natural logarithm.
What is a natural logarithm?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.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
We need to convert 2 ln 8-3 ln 4 as a single natural logarithm
First apply power property
⇒ ln 8² - ln 4³
⇒ ln 64 - ln 64
Now, applying quotient property
⇒ ln [tex]\frac{64}{64}[/tex] = ln 1
Here, we finally converted 2 ln 8-3 ln 4 to a single natural logarithm ln 1
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Write each logarithm as the quotient of two common logarithms. Do not simplify the quotient.
log₄3 x
Each logarithm as the quotient of two common logarithms is :
[tex]\frac{log\\ 3x}{log \\4}[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_ax=N[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms are :
log a × b = log a + log blog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)The given expression is,
log₄3 x
as, [tex]log_bm= \frac{log_cm}{log_cb}[/tex]
therefore ,
log₄3 x = [tex]\frac{log \ 3x}{log \ 4}[/tex]
Hence, logarithm as the quotient of two common logarithms is :
[tex]\frac{log\\ 3x}{log \\4}[/tex]
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Write an equation of the line that passes through each pair of points (9, 4), (−1, −1)
[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{9}}} \implies \cfrac{ -5 }{ -10 }\implies \cfrac{1}{2}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{9}) \\\\\\ y-4=\cfrac{1}{2}x-\cfrac{9}{2}\implies y=\cfrac{1}{2}x-\cfrac{9}{2}+4\implies y=\cfrac{1}{2}x-\cfrac{1}{2}[/tex]
A gift shop is having a sale. You can buy 14 cards for $6. What is the cost of 35 cards during the sale?
Answer:
I think it's $15 I hope this helps
Answer:
$15
Step-by-step explanation:
If 14 cards cost $6, then 7 cards will cost $3
So 35 cards will cost: $3 x 5 = $15
-4x +4 - 12x combining like terms?
Answer:
-16x+4
Step-by-step explanation:
4 is the only constant term there dont have to change
-4x-12x =-16x
so you get -16x+4
Hey there!
-4x + 4 - 12x
COMBINE the LIKE TERMS
= (-4x - 12x) + (4)
= -4x - 12x + 4
= -16x + 4
Therefore, your answer should be:
-16x + 4
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Is the expression 33x33^7 equivalent to (33x33)^7? Explain. srry for the question again
Answer:
C
Step-by-step explanation:
lets start with the first equation
33*33^7
Since they are not in parentheses, the only one going the power of 7 is the second 33. The first 33 will just have n exponent of one, so you add those together and get 33^8
The next equation is explained like this
(33*33)^7
Since this equation is in parentheses, first you will combine the 33:
(33^2)^7
Then, you will follow power to a power rule, and multiply the 2 and 7 to get this answer:
33^14
Then, find the awnser that matches.
2. When new IPhones come out, the price of the previous IPhone
drops. The price of the IPhone 10 has been the following:
2018: $1000
2019: $700
2020: $490
2021: $343
2022: $240
a. What type of sequence do we have?
b. What is the ratio/difference?
c. How much will the IPhone 10 cost in 2025?
a. The type of sequence we have here is a Geometric Progression.
b. The common ratio of the sequence is 7/10.
c. iPhone 10 will cost $83 in 2025.
What is a geometric progression?In a particular kind of progression called a Geometric Progression, each succeeding term has a fixed ratio known as a common ratio.The term "GP" is also frequently used. The general form of the GP is written as a, ar, ar²,..., where a denotes the first term and r denotes the common ratio of the progression.The common ratio can be both positive and negative numbers.Given sequence is:
$1000, $700, $490, $343, $240
a. To determine the type of sequence we find the common ratio between terms:
700/1000 = 7/10
490/700 = 7/10
All terms differ by a common ratio hence it is a geometric progression.
b. From above,
1000 × 7/10 = 700
700 × 7/10 = 490
490 × 7/10 = 343
343 × 7/10 = 240
Hence, the common ratio of G.P is 7/10.
c. The next terms in the given G.P is:
240 × 7/10 = 168
So, iPhone 10 will cost $168 in 2023.
168 × 7/10 = 118
So, iPhone 10 will cost $118 in 2024.
118 × 7/10 = 83
So, iPhone 10 will cost $83 in 2025.
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Find each product or quotient. √x³ / √5 x²
The quotient of √x ³ / √5 x ² is √ ( x / 5 )
To find : the product of √x ³ / √5 x ²
By checking the power of roots for each term
The terms which are given are √x ³ and √5 x ²
Since both the numbers have the same root power they can be combined under the same square root for further operation
Dividing the terms
=> √ ( x ³ / 5 x ² )
=> √ ( x / 5 )
Therefore, we get the quotient of √x ³ / √5 x ² as √ ( x / 5 ).
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