What is the inverse function of y=2^-x?
Answer:
Step-by-step explanation:
Find the Inverse y=2x. y=2x y = 2 x. Step 1. Interchange the variables. x=2y x = 2 y. Step 2. Solve for y y
Answer: The inverse of the function y = 2x2 + 2 is f-1(x) = √(x - 2) / √2.
write a quadratic function with vertex of (2, -3)
This can be re-inserted into our vertex equation to obtain. y=2(x−2)2+3.
In "standard form," if your instructor desires it, we can expand the right side to get:
Write a quadratic function with a vertex of (2, "-3)" to show results
Find write a quadratic function with vertex of instead (2, -3)
Answer 1
A quadratic's common vertex form is. y=m(x−a)2+b.
In light of the vertex, this becomes (2,3).
So, we do. 11=m(4−2)2+3. f(x) = a(x - h)2 + k, where a, h, and k are constants, is the vertex form of a quadratic function (h, k). If the vertex form of the quadratic parent function f(x) = x2 is used, then y = a(x - h)2 + k, where a = 1, h = 0, and k = 0.
Putting it simply: 8=m(2)2. 8=4m. m=2.
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carnegie vanguard is selling tickets to a theatre performance. on the first day of ticket sales the school sold 3 student tickets and 1 adult ticket for a total of $38. the school took in $52 on the second day by selling 3 student tickets and 2 adult tickets. find the price of an adult ticket and the price of a student ticket
The price of an adult ticket and a student ticket is $14 and $8, respectively.
Using algebraic expression and equation, we can express each statement and determine the price of each ticket.
Let x = the price of an adult ticket
y = the price of a student ticket
If on the first day of ticket sales, the school sold 3 student tickets and 1 adult ticket for a total of $38, then we can express this as:
3y + x = 38 (equation 1)
If the school took in $52 on the second day by selling 3 student tickets and 2 adult tickets, then we can express this as:
3y + 2x = 52 (equation 2)
3y + 2x = 52 (equation 2)
-(3y + x = 38) (equation 1)
x = 14
Substitute the value of x in any of the two equations.
3y + x = 38 (equation 1)
3y + 14 = 38
3y = 38 - 14
3y = 24
y = 8
price of an adult ticket = $14
price of a student ticket = $8
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Analyze each scenario and graph: voice instructor notices that only one out of every ten of her students can sing soprano: store owner notices that in his parking lot; two out of every six vehicies are trucks: 60 70 Total Number of Vchicles Total Number of Students Identify the proportional relationship represented by each line as it relates to the scenario Explain your reasoning_ b. Write an equation that has constant of proportionality between those represented on the graph
Using proportional relationships, we have that:
a) They are defined as follows:
Soprano = 0.1 x Students.Trucks = 1/3 x Vehicles.b) The relation is Out of State Team = 1/5 x Residents.
Proportional relationships and graphsA graph represents a proportional relationship if the output variable y in the y-axis is written as a product of the input variable x in the x-axis and the constant of proportionality k, as follows:
y = kx.
Voice instructor notices that only one out of every ten of her students can sing soprano, hence the constant is:
k = 1/10 = 0.1.
Then the relationship is:
Soprano = 0.1 x Students.
Two out of every six vehicles are trucks, hence the constant is:
k = 2/6 = 1/3.
Hence the relationship is:
Trucks = 1/3 x Vehicles.
Then, in item b, we want to write a relation that has a constant between those represented on the previous relations, that is, between 1/10 and 1/3.
One possible constant is of 1/5. Supposing that one out of five New York City residents root for out of state NFL teams, the relation is:
Out of State Team = 1/5 x Residents.
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Which box-and-whisker plot represents this data: 6, 7, 9, 9, 20, 22, 26, 28, 29, 30?
The Last box-and-whisker plot represents the data 6, 7, 9, 9, 20, 22, 26, 28, 29, 30.
What is the box-and-whisker plot?A box and whisker plot is a visual representation of variance in a set of data. The majority of the time, a histogram analysis gives an adequate display, but a box and whisker plot can add more detail while enabling the display of various sets of data on the same graph.It divides the data into five numerical categories: minimum, first quartile (Q1), median, third quartile (Q3), and "maximum." You can learn more about your outliers' values from it.The box-and-whisker plot and the box-and-whisker diagram are other names for a box plot that also includes lines (referred to as whiskers) extending from the box to indicate variability outside the top and lower quartiles.To learn more about box-and-whisker plot sums, refer
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Round to 2 decimal places
9.725
Answer: 9.73
Step-by-step explanation:
the five at the end indicates rounding up so the answer for the 2 decimal places is 9.73.
Answer:
9.73
Explanation :–Rule #1: If the last digit in 9.725 is less than 5, then remove the last digit.
Rule #2: If the last digit in 9.725 is 5 or more and the second to the last digit in 9.725 is less than 9, then remove the last digit and add 1 to the second to the last digit.
Rule #3: If the last digit in 9.725 is 5 or more and the second to the last digit in 9.725 is 9, and the third to the last digit is less than 9, then remove the last digit, make the second to last digit 0, and add 1 to the number to the third to the last digit.
Rule #4: If the last digit in 9.725 is 5 or more and the second to the last digit is 9, and the third to the last digit is 9, then add 1 to the number on the left side of the decimal point and make the right side of the decimal point 00.
When rounding 9.725 to two decimal places we use Rule #2. Therefore, the answer to "What is 9.725 rounded to 2 decimal places?" is:
9.73 Find the measure of angle b.
A. 38
B. 67
C. 75
D. 105
Answer:
it’s B
Step-by-step explanation:
just took the test
Answer:
D.105
Step-by-step explanation:
sum of measures of the three angles equal 180
therefore measure of angle B equal 180-(52+23)=105 degree
it's page 23.. pls
answer it i rlly need it in monday
ty if u answered this.
Answer:
See picture
Step-by-step explanation:
question content area bottompart 1(a) what minimum percentage of commuters in has a commute time within standard deviations of the mean?enter your response here% (round to one decimal place as needed.)part 2(b) what minimum percentage of commuters in has a commute time within standard deviations of the mean? what are the commute times within standard deviations of the mean?the minimum percentage of commuters in that has a commute time within standard deviations of the mean isenter your response here%.(round to one decimal place as needed.)part 3the commute times within standard deviations of the mean are betweenenter your response here andenter your response here minutes.(type integers or decimals. do not round. use ascending order.)part 4(c) what is the minimum percentage of commuters who have commute times between minutes and minutes?enter your response here% (round to one decimal place as needed.)
The answers to all the subparts are given below:
(A) Minimum percentage of commuters in the city: 0.75(B) Minimum percentage of commuters in the city has a commute time within 1.5 standard deviations of the mean: [16.65, 37.95](C) Minimum percentage of commuters who have commute times between 6 minutes and 48.6 minutes: 89%What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement. By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)×100%.So, (A) Chebyshev's theorem is used:
There can only be 1/k2 values of a distribution.k deviations from the mean are used.Here k = 2So,
1/k² = 1/2² = 1/4 = 0.25Therefore, the minimum proportion of commuters who are within two standard deviations of the mean is:
1 - 0.25 = 0.75 m(B) Minimum percentage of commuters in the city has a commute time within 1.5 standard deviations of the mean:
Here, k = 1.5
1/k² = 1/1.5² = 1/2.25 = 0.444Consequently, the shortest commute within two standard deviations of the mean is:
1 - 0.444 = 0.56 = 56%Within 1.5 standard deviations, commute times:
[27.3 - (1.5 × 7.1), 27.3 + (1.5 * 7.1)[16.65, 37.95](C) Minimum percentage of commuters who have commute times between 6 minutes and 48.6 minutes:
X - m /sdX = 6= (6 - 27.3) / 7.1 = - 3X = 48.6= (48.6 - 27.3) / 7. 1 = 3So,
1/k² = 1 / 3² = 1/91 - 1/9 = 8/9= 0.888 = 0.89 = 89%Therefore, the answer to all the subparts are given below:
(A) Minimum percentage of commuters in the city: 0.75(B) Minimum percentage of commuters in the city has a commute time within 1.5 standard deviations of the mean: [16.65, 37.95](C) Minimum percentage of commuters who have commute times between 6 minutes and 48.6 minutes: 89%Know more about percentages here:
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The correct question is given below:
The mean commute time to work for a resident of a certain city is 27.3 minutes. Assume that the standard deviation of the commute time is 7.1 minutes to complete parts (a) through (c).
(a) What minimum percentage of commuters in the city has a commute time within 2 standard deviations of the mean?
nothing% (Type an integer or a decimal.)
(b) What minimum percentage of commuters in the city has a commute time within 1.5 standard deviations of the mean? What are the commute times within 1.5 standard deviations of the mean?
The minimum percentage of commuters in the city that has a commute time within 1.5 standard deviations of the mean is nothing%. (Round to one decimal place as needed.)
The commute times within 1.5 standard deviations of the mean are between nothing and nothing.
(Type an integer or a decimal. Use ascending order.)
(c) What is the minimum percentage of commuters who have commute times between 6 minutes and 48.6 minutes?
nothing% (Round to one decimal place as needed.)
a 5 pound bag of apples costs $4.50, and an 8 pound bag of the same type of apples costs $7.52. greg found the unit price between the cost and weight for each bag of apples. what is the difference between the unit prices?
Answer:
Step-by-step explanation: $3.02
3 pounds difference
23 squared + x squared = 35 squared solve for X
Answer:
x = 2√174, -2√174
x ≈ 26.38
Step-by-step explanation:
23² + x² = 35²
529 + x² = 1225
-529 -529
----------------------
x² = 696
√x² = √696
x = 2√174, -2√174
----------------------------------------------------------------------------------------------------------
b = √c² - a²
b = √35² - 23²
b ≈ 26.38
I hope this helps!
need help y’all pls ♀️
The parameters are ΔUVW with side UW extended to X then m ∠UVW = (3x + 4)°, m ∠VWX = (8x -12)° and m ∠WUV = (x + 20)° then the value of x = 9°.
How to estimate the value of x?The given parameters exist;
ΔUVW with side UW extended to X
m ∠UVW = (3x + 4)°, m ∠VWX = (8x -12)° and m ∠WUV = (x + 20)°
We have that m ∠UVW + m ∠WUV + m ∠VWU = 180° (Sum of the interior angles of a triangle theorem)
Therefore, m ∠VWU = 180° - (m ∠UVW + m ∠WUV)
Also, we have that m ∠VWX and m ∠VWU exist supplementary angles, (The sum of angles on a straight line)
∴ m ∠VWX + m ∠VWU = 180° (Definition of supplementary angles)
m ∠VWU = 180° - m ∠VWX
∴ m ∠VWX = (m ∠UVW + m ∠WUV)
Substituting the values in the above equation, we get;
(8x -12)° = (3x + 4)° + (x + 20)°
simplifying the above equation, we get
8x - 3x - x = 4 + 20 + 12
4x = 36
x = 36/4 = 9
Therefore, the value of x = 9°.
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What percentage is 55cm of 4 metres?
100 POINTS PLS HELP
Add parenthesis and grouping symbols to each order of operations problem to make the equation true.
1. 4 ✖️ 3 + 7 - 6 ✖️ 1 + 4 = 20
2. 60 - 18 ➗ 2 + 4 + 10 ➗ 2 = 12
3. 80 - 36 ➗ 2 + 6 - 2 ✖️ 5 + 1 = 44
4. 3 ✖️ 5 + 4 - 2 ✖️ 2 + 6 - 4 = 15
The equations with parentheses added to make them true are;
(4 × (3 + 7 - 6) × 1) + 4 = 20(60 - 18) ÷ (2 + 4) + 10÷2 = 1280 - 36 ÷ (2 + 6 - 2) × (5 + 1) = 443 × (5 + 4) - (2 × (2 + 6) - 4) = 15What is the effect of parentheses in a mathematical expression?Parentheses indicate that operations within it should be completed first before those that are outside the parentheses.
The given terms of the equations can be regrouped with parentheses to make the equations true as follows;
1. 4 × 3 + 7 - 6 × 1 + 4 = 20
The above equation gives;
3 + 7 - 6 = 4
Therefore;
4 × 3 + 7 - 6 × 1 + 4 = 4 × (3 + 7 - 6) × 1 + 4
4 × (3 + 7 - 6) × 1 + 4 = (4 × 4) × 1 + 4
(4 × 4) × 1 + 4 = 16 × 1 + 4 = 16 + 4 = 20
Which gives;
(4 × (3 + 7 - 6) × 1) + 4 = 202. 60 - 18 ÷ 2 + 4 + 10 ÷ 2 = 12
60 - 18 = 42
2 + 4 = 6
The first four terms, therefore gives;
(60 - 18) ÷ (2 + 4) = 7
10÷2 = 5
Which gives;
60 - 18 ÷ 2 + 4 + 10 ÷ 2 = (60 - 18) ÷ (2 + 4) + 10÷2
(60 - 18) ÷ (2 + 4) + (10÷2) = 7 + 5 = 12
Which gives;
60 - 18 ÷ 2 + 4 + 10 ÷ 2 = (60 - 18) ÷ (2 + 4) + 10÷2 = 12
The expression is therefore;
(60 - 18) ÷ (2 + 4) + 10÷2 = 123. 80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 44
80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 80 - 36 ÷ (2 + 6 - 2) × (5 + 1)
(2 + 6 - 2) = 6, and (5 + 1) = 6
Therefore;
80 - 36 ÷ 2 + 6 - 2 × 5 + 1 = 80 - ((36 ÷ 6) × 6)
80 - ((36 ÷ 6) × 6) = 80 - ((36 × 6) ÷ 6)
80 - ((36 × 6) ÷ 6) = 80 - (36 × 1) = 44
Therefore;
80 - 36 ÷ (2 + 6 - 2) × (5 + 1) = 444. 3 × 5 + 4 - 2 × 2 + 6 - 4 = 15
3 × 5 + 4 - 2 × 2 + 6 - 4 = 3 × (5 + 4) - (2 × (2 + 6) - 4)
3 × (5 + 4) - (2 × (2 + 6) - 4) = 3 × 9 - (16 - 4)
3 × 9 - (16 - 4) = 27 - 12 = 15
Therefore;
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Dennis runs 3.2 miles every day. His
brother Gary runs 1.7 times as far every day. How fa
does Gary run
Answer:5.44
Step-by-step explanation:
3.2x1.7
given h(x)=4x+4,find h (2)
The output value of h( 2 ) in the function h( x ) = 4x + 4 is 12.
What is the output value of h(2) in the given function?A function is a relationship that maps one input to one output, for a relation to qualify as a function, each of its x-value can only have one y-value.
Given the data in the question;
h( x ) = 4x + 4h( 2 ) = ?To solve for the output value of h( 2 ), replace all the occurrence of x with 2 in the function and simplify.
h( x ) = 4x + 4
h( 2 ) = 4( 2 ) + 4
Multiply 4 and 2
h( 2 ) = 8 + 4
Add 8 and 4
h( 2 ) = 12
Therefore, the output value is 12, this forms an ordered pair of (2,12) on the graph.
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Isaac is going to invest in an account paying an interest rate of 6.3% compounded monthly. How much would Isaac need to invest, to the nearest ten dollars, for the value of the account to reach $57,000 in 7 years?
Isaac need to invest $ 36720.
Given,
Isaac is going to invest in an account paying an interest rate of 6.3% compounded monthly.
and, the value of the account to reach $57,000 in 7 years.
To find the how much would Isaac need to invest.
Now, According to the question:
Let x be the invest in an account.
Based on the given conditions,
formulate:
x . [tex]([/tex]1 + 6.3%/ 12[tex])^7^.^1^2[/tex] = 57000
Solve the equation
x . (1 + 0.063/12[tex])^7^.^1^2[/tex] = 57000
Convert decimals to integers
x . (1 + 63/12000[tex])^7^.^1^2[/tex] = 57000
Reduce the fraction
x . (1 + 21/4000[tex])^7^.^1^2[/tex] = 57000
x . ([tex]\frac{4000+21}{4000})^8^4[/tex] = 57000
Calculate the sum or difference
x . (4021 / 4000[tex])^8^4[/tex] = 57000
x = [tex]\frac{57000}{(\frac{4021}{4000})^8^4 }[/tex]
Simplify using exponent rule with same exponent :
[tex](ab)^n = a^n . b^n[/tex]
x = [tex]\frac{57000 . 4000^8^4}{4021^8^4}[/tex]
Solve the above equation, we get
x = 36720
Hence, Isaac need to invest $ 36720
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please help me.
please
Answer:
77/12
Step-by-step explanation:
3 3/4 + 2 2/3
15/4+8/3
45/12+32/12
77/12
A group of Mathematics faculty at the local college consists of 7 women and 9 men. Four people are to be selected to go to a conference. How many different ways can a group of four people be selected from this group of 16?
In how many ways can four women be chosen from the group of 7 women?
What is the probability that all women will be chosen to attend the conference?
Enter a reduced fraction or decimal.
In 1820 different ways a group of four people can be selected from this group of 16.
In 35 ways four women can be chosen from the group of 7 women.
The probability that all women will be chosen to attend the conference is 1.92%.
What is probability?The proportion of favourable outcomes to all possible outcomes of an event is known as the probability. The number of positive outcomes for an experiment with 'n' possible outcomes can be represented by the symbol x. The probability of an event can be determined using the following formula.
To find how many different ways can a group of four people be selected from this group of 16, we will implement the combination formula.
[tex]^n C_r=\frac{n !}{r ! (n-r) !}[/tex]
Where,
nCr = number of combinations
n = total number of objects in the set
r = number of choosing objects from the set
Here, n = 16 and r = 4, substituting the values we get
[tex]^{16} C_4=\frac{16 !}{4 ! (16-4) !}[/tex]
[tex]^{16} C_4 =[/tex] 1820
Hence, in 1820 different ways a group of four people can be selected from this group of 16.
To find how many ways can four women be chosen from the group of 7 women we will implement the combination formula.
Here, n = 7 women and r = 4 women, substituting the values we get
[tex]^7 C_4=\frac{7 !}{4 ! (7-4) !}[/tex]
[tex]^7 C_4=[/tex] 35
Thus, in 35 ways four women can be chosen from the group of 7 women.
The probability that all women will be chosen to attend the conference is
[tex]\frac{^7 C_4}{^{16}C_4}[/tex] = 35/1820
= 0.01923076
= 1.92%
Thus, the probability that all women will be chosen to attend the conference is 1.92%.
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Hello, can you help me figure out what mistake I have made?
solution
To factorize the Trinomial, we seek two numbers such that the product is -14 and the addition is 5
We have
Pair Product sum
(-2, 7) -14 5
Hence we have
[tex]\begin{gathered} x^2+5x-14=x^2-2x+7x-14 \\ \Rightarrow x(x-2)+7(x-2) \\ \Rightarrow(x-2)(x+7) \end{gathered}[/tex]Hence the correct option is C
Give the digits in the ones place and the hundredths place.
18.09
The digits at ones place are 8 and the hundredth place is 9.
The number which is left to the decimal is considered in one's places as proceeding with the numbers tens places and the hundredth place is obtained. Similarly on the right side moving towards the right gives tenth place and hundredth place.
18.09
(1) - It is in the Tens place
(8) - Ones place
(.) - Decimal point
(0) - Tenth place
(9) Hundredth place
Therefore, The digits at one place are 8 and the hundredth place is 9.
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Let's explore a job or career based on a salary. A high school graduate can make $31,200 per year. Any additional year of training or schooling can
increase the salary by $4,000 per year. Complete the table to show salaries of individuals who have the following years of training or schooling beyond
high school. In the last cell, give a general algebraic expression (using x instead of a number) to represent a job or career salary based on
The complete table will be;
In 2 years, The amount of salary = $35,200
In 5 years, The amount of salary = $31,200 + 5 x $4,000 = $51,200
In 10 years, The amount of salary = $71,200
In x years, The amount of salary = = $31,200 + $4,000x
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A high school graduate can make $31,200 per year.
Any additional year of training or schooling can increase the salary by $4,000 per year.
Now, In one year, Salary = $31,200
So, In 2 years, The amount of salary = $31,200 + $4,000
= $35,200
In 5 years, The amount of salary = $31,200 + 5 x $4,000
= $31,200 + $20,000
= $51,200
In 10 years, The amount of salary = $31,200 + 10 x $4,000
= $31,200 + $40,000
= $71,200
In x years, The amount of salary = $31,200 + x × $4,000
= $31,200 + $4,000x
Thus, The complete table will be;
In 2 years, The amount of salary = $35,200
In 5 years, The amount of salary = $31,200 + 5 x $4,000 = $51,200
In 10 years, The amount of salary = $71,200
In x years, The amount of salary = = $31,200 + $4,000x
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A thief steals an ATM card and must randomly guess the correct four-digit pin code from a 4-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
The number of possible codes is
(Type an integer or fraction. Simplify your answer.)
The probability that the correct code is given on the first try is
(Type an integer or fraction. Simplify your answer.)
Eli can run 12 miles in 72 minutes. How many miles can he run in 60 minutes?
PLEASE HELP\
I WILL GIVE BRAINLIEST
Answer:
g(x) = |x + 3|
g(x) is nonnegative on all real numbers.
g(x) is decreasing on x <= -3 and increasing on x >= -3.
As x tends to negative infinity, g(x) tends to positive infinity.
As x tends to positive infinity, g(x) tends to positive infinity.
Domain: all real numbers
Range: all nonnegative real numbers
You are making extra part kits for a game. The table below lists the number of each part needed per kit, as well as the number of each part that you have available.
Part Number in each kit Number available
People marker 6 287
6-sided die 3 143
Teleporter marker 7 341
You make as many kits as you can. With the parts remaining, you could make 1 more kit if you had:
A.1 more people marker and 1 more die.
B.1 more die and 1 more teleporter marker.
C.1 more teleporter marker and 1 more people marker.
D.2 more people markers.
E.2 more teleporter markers.
Applying mathematical operations with the remaining parts, you could have 1 more kit if you had A.1 more marker and 1 more die.
How is the number determined?Using mathematical operations of divisions, subtractions, and additions, we can determine the number of kits made from the materials and the part required to make one additional kit.
For instance, 287 people marker can make 47 (287/6) kits with 5 remaining, which requires another 1 part to complete another kit.
143 6-sided die can also make 47 kits (143/3) with 2 parts, which require an additional 1 part to make another kit.
The above parts are unlike the teleporter marker, which had already made 48 kits with 5 of its part remaining.
Part Number in each kit Number available # of Kits Made
People marker 6 287 47
6-sided die 3 143 47
Teleporter marker 7 341 48
Thus, using mathematical operations, we can determine that to complete the number of kits to 48, the kit maker requires Option A.
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y < x² - 2x
find the vertex
The vertex of the equation is (1, -1).
The equation of a parabola in vertex form is,
y = a(x-h)² + k
The coordinates of the vertex are (h,k) respectively and a is a constant.
Given:
y = x² - 2x
Rearrange the given equation in the form of the equation of the parabola in vertex form using the method of completing the square.
y = (x² - 2x + 1) - 1
y = (x - 1)² - 1
Therefore, the vertex of the equation is (1, -1).
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Please help Im begging
Answer:
x = 27
Step-by-step explanation:
AOB is a straight angle = 180°
the 3 angles on it therefore sum to 180° , that is
36 + 90 + 2x = 180
126 + 2x = 180 ( subtract 126 from both sides )
2x = 54 ( divide both sides by 2 )
x = 27
v = ___ (look at photo) { will mark brainliest if correct }
Answer: v = 17°
Step-by-step explanation:
All triangles add up to 180°.
[tex]94+35+3v=180[/tex]
[tex]3v=51\\v=17[/tex]
Answer:
Step-by-step explanation:
v=51
What is the value of k when k^3 = 1 /125 ?
Answer:
1/5
Step-by-step explanation:
Finding the unknown value in exponent form:
Prime factorize 125.
125 = 5 * 5 * 5 = 5³
[tex]\sf k^3 = \dfrac{1}{125}\\\\ k^3 = \left(\dfrac{1}{5}\right)^3[/tex]
As exponents are same, compare the bases,
[tex]\sf k = \dfrac{1}{5}[/tex]
Answer:
x=1/5
Step-by-step explanation:
[tex]k^3=1/125\\[/tex]
[tex](k^3)^\frac{1}{3} =(\frac{1}{125} )^\frac{1}{3}[/tex]
[tex]k^3^\frac{1}{3} =\frac{1}{125^\frac{1}{3}}[/tex]
[tex]k=\frac{1}{5}[/tex]
Hope this Helps :)