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]
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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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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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
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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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
round 43.093 to the hundredths place
Answer:
43.09
Step-by-step explanation:
Factor each expression.
4 x²-8 x+3
After factorizing the expression we get: (2x ₋ 1) (2x ₋ 3) as factors of the expression.
Given the expression is 4x² ₋ 8x ₊ 3 = 0
factorize the expression.
The word "factor" is used to describe a number as the result of any two other numbers. Any mathematical object, including numbers, polynomials, and algebraic expressions, can have factors by using the factorization method. Finding the factors of a given algebraic expression is referred to as factorization of an algebraic expression.
4x² ₋ 8x ₊ 3 = 0
4x² ₋ 2x ₋ 6x ₊ 3 = 0
2x(2x ₋ 1) ₋ 3(2x ₋ 1) = 0
(2x ₋ 1) (2x ₋ 3)
Hence we get the factors of the expression as (2x ₋ 1) (2x ₋ 3)
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PLEASE HELP!! WILL GIVE BRANLIEST!!
The Smiths and the Martins are going to Brooklyn Pizza for dinner. The Smiths order 3 slices of pizza and 3 sodas and have a bill that totals $15. The Martins order 4 slices of pizza and 3 sodas and have a bill that totals $18. What is the cost of one slice of pizza?
Answer:
2.5
Step-by-step explanation:
15/6 (3p + 3s) = 2.5
18/7 (4p + 3s) = 2.5
Fragrance
(mL)
80
120
160
Wax
(L)
2
3
4
Type 3
Fragrance Wax
(mL)
250
500
750
Type 3
OType 4
Mark this and return
(L)
10
20
30
Which type of candle has the greatest ratio of fragrance to wax?
Type 1
OType 2
Save and Exit
Fragrance Wax
(mL)
(L)
150
3
250
300
Types
240
270
Type 4
Fragrance
(mL)
30
NEAL
5
6
Wax
(L)
1
8
9
Please help me please help me please help me
Answer:
(-2, -2)
Step-by-step explanation:
The point U, when rotated 270 degrees, will end up at the point (-2, -2) on the graph.
leora mows lwans in her neighborhood. the graph shows how much she earns
I found the graph, the answer should be 25$
Divide. Rationalize all denominators. √8/√6
The rationalization of the denominator is 4√3 / 6 .
Rationalization may be a method that finds application in elementary pure mathematics, wherever it's wont to eliminate the real number within the divisor.Rationalization are often thought-about because the method wont to eliminate a radical or AN number from the divisor of AN pure mathematics fraction. That is, take away the radicals during a fraction in order that the divisor solely contains a real.We have given a fraction √8/√6 . ...(1)
The denominator of the fraction is √6.
Multiplying and dividing by √6 in equation (1), we get
√8/√6 = √8 × √6 /√6 × √6
= √48 /6
= 4√3 / 6
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-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:)
The grid above shows the graph of the parent function f (x) = |x| and a translated functions graph.
Write the equation for the translated graph.
The equation of the graph that is obtained by translating the parent function is as follows:
g(x) = |x + 2| + 1
How to write the equation of the translated graph?The parent function is given as
f(x)= |x|
The following is a translation of the parent function f(x), which may be derived from the graph as follows:
2 units left translation
1 unit up translation
The translation of the sequence mentioned above is expressed as
(x, y) = (x + 2, y + 1)
So, we have
g(x) = |x + 2| + 1
Therefore, the equation of the graph that has been translated is g(x) = |x + 2| + 1
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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
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
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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Find the inverse of each function. Is the inverse a function? f(x)=(x-2)³
The inverse function is given by f⁻¹(x)=∛x+2 and the inverse is a function.
The opposite function is referred to as the inverse of a function. To map the dependent variable y based on the independent variable x, we should ideally utilize a function. The relationship that determines the value of x based on a certain value of y is known as an inverse function.
The domain of a function shifts to the range for an inverse function, and vice versa.
For a function that is mathematically denoted by the formula y=g(x), where g(x) is a polynomial of x. We use y to solve the equation for x.
Given function is in the form f(x)=(x-2)³
It can be written as
y=(x-2)³
Then we take the cube root on either sides of the equation.
∛y=x-2
or, x=∛y+2
So the inverse function is:
f⁻¹(x)=∛x+2
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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:
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.
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.
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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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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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
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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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