Answer: 1/3
Step-by-step explanation:
Solve each equation by using the graph of the related function.
9th grade algebra
Answer:
Q14 x = 3
Q15 No unique solution
Step-by-step explanation:
Q14
The value of x where the line crosses the x axis is the solution for x
Here we see the line crosses the x axis at x = 3 so solution is x =3
Mathematically,
2x - 3 = 3
2x = 3 + 3 adding 3 to both sides
2x = 6
x = 6/2 = 3
Q15
This is a horizontal line which crosses the y-axis at y = 1
Since this does not cross the x axis but is parallel to it, there is no unique solution for x
Mathematically,
-4x + 2 = -4x + 1
Adding 4x to both sides we get the absurdity that 2 = 1 and that indicates no unique solution for x. Alternatively we can say that x has an infinite number of solutions
can you solve please
Answer:
y = 10 , ∠ C = 40° , ∠ D = 76°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ DEF is an exterior angle of the triangle , then
∠ C + ∠ D = ∠ DEF , that is
4y + 7y + 6 = 116
11y + 6 = 116 ( subtract 6 from both sides )
11y = 110 ( divide both sides by 11 )
y = 10
Then
∠ C = 4y = 4(10) = 40°
∠ D = 7y + 6 = 7(10) + 6 = 70 + 6 = 76°
Answer:
y = 10
∡C = 40°
∡D = 76°
Step-by-step explanation:
Supplementary angles sum 180°
116° and ∡E are supplementary angles:
116 + E = 180°
E = 180 - 116
E = 64°
∡E = 64°
Internal angles of a triangle sum 180°
∡D + ∡C + ∡E = 180°
7y+6 + 4y + 64 = 180
7y + 4y + 6 + 64 = 180
11y + 70 = 180
11y = 180 - 70
11y = 110
y = 110/11
y = 10
Then:
∡C = 4y = 4*10 = 40°
∡D = 7y + 6 = 7*10 + 6 = 70 + 6 = 76°
Use the marginal tax rate chart to answer the question.
Tax Bracket Marginal Tax Rate
$0–$10,275 10%
$10,276–$41,175 12%
$41,176–$89,075 22%
$89,076–$170,050 24%
$170,051–$215,950 32%
$215,951–$539,900 35%
> $539,901 37%
Part A: Demonstrate how to calculate the amount of taxes owed on a taxable income of $39,000. (4 points)
Part B: The piecewise function represents the amount of taxes owed, f(x), as a function of the taxable income, x. Using the same taxable income from Part A, demonstrate how to calculate the amount of taxes owed using the piecewise function. (4 points)
A piecewise function f of x in seven pieces. The function is defined by part 1, which is 0 point 10 times x for x less than or equal to 10,275; part 2, which is 0 point 12 times x minus 205 point 50 for 10,276 is less than or equal to x which is less than or equal to 41,175; part 3 which is 0 point 22 times x minus 4,323 for 41,176 is less than or equal to x which is less than or equal to 89,075; part 4 which is 0 point 24 times x minus 6,105 point 50 for 89,076 is less than or equal to x which is less than or equal to 170,050; part 5 which is 0 point 32 times x minus 9,070 point 32 for 170,051 is less than or equal to x which is less than or equal to 215,950; part 6 which is 0 point 35 times x minus 26,187 point 50 for 215,951 is less than or equal to x which is less than or equal to 539,900; and part 7 which is 0 point 37 times x minus 36,985 point 67 for x is greater than or equal to 539,901.
Part C: Compare the piecewise function to the marginal tax rate chart. How is the marginal tax rate chart represented in the piecewise function? (2 points)
a) The taxes to be paid for someone with a taxable income of $39,000 are of: $4,680.
b) The piece-wise function is defined as follows:
f(x) = 0.1x, 0 ≤ x ≤ 10275;f(x) = 1027.5 + 0.12(x - 10275), 10276 ≤ x ≤ 41175.f(x) = 4941 + 0.22(x - 41175), 41176 ≤ x ≤ 89075.f(x) = 19596.5 + 0.24(x - 89075), 89076 ≤ x ≤ 170050.f(x) = 40812 + 0.32(x - 170050), 170051 ≤ x ≤ 215950.f(x) = 69104 + 0.35(x - 215950), 215951 ≤ x ≤ 539900.f(x) = 188965 + 0.37(x - 539900), x > 539901.c) The tax rates are used as the slope for each linear definition of the piece-wise functions, while the bounds of the intervals are used to calculate the intercept.
How to obtain the amount of taxes owed and how to define the piece-wise function?The amount of taxes owed is obtained applying the proportion of the tax rate relative to the annual salary.
The tax rate for a taxable income of $39,000 is of 12%, hence the amount is given as follows:
0.12 x 39000 = $4,680.
The piece-wise functions for this problem are all derived considering the intervals with the tax brackets,
For the first tax bracket, the proportion is merely applied, as follows:
0.1x, 0 ≤ x ≤ 10275;
For each bracket, starting on the second, the maximum tax rate of the previous rate is calculated, and added to the excess of the income relative to the maximum of the previous tax bracket multiplied by the proportion.
For the first tax bracket, the maximum income is of:
$10,275.
The maximum tax of the first tax bracket is of:
0.1 x 10275 = 1027.5. -> the maximum value of the nth bracket is the starting value of the nth+1 bracket.
Then the function for the second bracket rate is obtained as follows:
f(x) = 1027.5 + 0.12(x - 10275), 10276 ≤ x ≤ 41175.
The same procedure is applied to any of the remaining brackets, taking the previous bracket to obtain the function.
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Ally got a haircut for $45. She wants to leave a 20% tip. How much money should she give the hair dresser altogether?
Answer:
$51.75
Step-by-step explanation:
Use a tip calculator.
20. A gym membership
is offered in January
for $29.00 per month. If you pay upfront for
the year, you are given a 20% discount on the
monthly cost. How much money do you save
after a year by paying upfront rather than
monthly?
Donna bought 3 bags of dog treats for $6.03. What is the cost per bag of dog treats?
6.3x - 7.015 + 9.9 simplified
Answer: 6.3x + 2.885
Step-by-step explanation:
Since there is only one factor of x, we cannot simplify x.
We can simplify the constants though.
6.3x + (-7.015 + 9.9)
= 6.3x + 2.885
is -10,-7,-4, 1, an arithmetic sequence
Find the equation of the line through point (4,−7) and parallel to y=−23x+32. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12).
(check the image)
The equation of the required line is given as y = -23x - 92.
What is the equation for a straight line?A straight line can be written in the form of equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
The given problem can be solved as follows,
The equation of the line is y = −23x + 32.
Then, its slope is given by -23.
Since the parallel lines have the same slope, the slope of the line parallel to y = −23x + 32 is -23.
Now, the equation of the line passing through (4, -7) and parallel to the given line can be written as,
(y + 7)/(x - 4) = -23
=> y + 7 = -23x - 92
=> y = -23x + -99
=> y = -23x - 92
Hence, the equation of the line passing through (4, -7) and parallel to y = −23x + 32 is y = -23x - 92.
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Let f(x)=6(3)^x. Need help
Answer:
What are Functions ?A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain. For all values of a and b, f = (a,b)|
If every element in set A has exactly one and only one image in set B, then the relation is said to be a function.
A function is a relation from a non-empty set B such that its domain is A and it never has the same first member in two different ordered pairs.
In arithmetic, a function can be represented as:
a set of ordered pairs
an arrow diagram
a table form
a graphical form
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The mean mass of 5 boys is 62kg.When the mass of a boy is excluded,the mean mass of the remaining 4 boys becomes 64kg.Find the mass of the boy that has been excluded
The mass of the boy removed is 54.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
let's take the weight of five boys is x
so,
x/5 = 62
x = 310
and let's take the weight of four boys is y.
so,
y/4 = 64
y = 256
let's take the weight of a boy which is removed from them is z
so,
x - z = y
x - y = z
310 - 256 = z
z = 54
Hence, the mass of the boy removed is 54.
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Find the value of x that will make L||M
L-
2x + 5
M-
x-5
x = [?]
The value of x that will make L || M is x/2
How to form parallel linesAs a parallel line part of the qualities include that the slopes of the lines are equal
The equation of line is L = 2x + 5 and M = x - 5
The slope intercept form of the form as
y = mx + c
where
m = slope
c = intercept
x = input variables
y = output variables
to make line L parallel to line M
2x ⇔ x
hence x in line L will be equal to x/2
L = 2x + 5
L = 2(x/2) + 5
L = x + 5
L = x + 5 is parallel with M = x - 5
L = 2x + 5 is parallel with M = 2x - 5
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Good points please answer
The values of sin2x, cos2x and tan2x is -3/5, -4/5 and 3/4 respectively.
What is sine function?
The ratio of the opposite side's length to the hypotenuse of a right-angled triangle is known as the sine function in trigonometry. A right triangle's unknown sides or angles can be determined using the sine function. The ratio of the side opposite the angle (also known as the perpendicular) and the hypotenuse is known as the sine of an angle in a right-angled triangle.
The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: sin = Perpendicular / Hypotenuse.
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I NEED HELPPPP!!!!!!!!!!!
Answer:
125 in^2
Step-by-step explanation:
Assuming that s is the length of a side in the base.
Surface Area is the area of every shape in the figure added together.In this figure you have 4 triangles and one square as the base.For the base you would find the area of a square (the base is a square) 5 x 5 = 25There are four triangles that you need to find the area of which all have the same surface area.To get the area of a triangle first split the triangle into 2 halves making a right triangle. This will make the dimensions 2.5 for base and 10 for height.Do base x height of the right triangle to get the full triangles area. (2.5 x 10 = 25).You now know the area of one triangle which there are four of in this problem so you can do 4 x 25.The surface area of the triangles is 100.Add the area of the base (25 + 100).The surface area of this figure is 125 in^2if the group consists of five girls and five boys, what is the probability that all the girls end up on the same team?
The likelihood that every girl is on the same team is 1/252.
Describe probability?A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Since the team's student lineup is not crucial, a mixture will be employed.
C(10,5) = 252 is the number of possible methods to choose 5 students from a class of 10.
Rest Team B will consist of 5 students. Consequently, there are 252 items in the sample space.
Let two women join team A. then the number of methods for choosing the final three members from the eight remaining members C(8,3) = 56
Likewise if two girls are in team B then possible number of different groups is 56.
Therefore total number of different groups such that two girls are in one team is 56+56 = 112.
The required probability is
P(two girls are in one team) = 112 / 252
Number of ways of selecting all girls in one team and boys in another team is 1. So required probability is
P( girls in one team) = 1/ 252
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If the area of the smaller circle is half the area of the larger, the ratio of the radius of the smaller circle to that of the larger circle is?
The ratio of the radii of smaller circle to that of larger circle is 1/√2.
Let the Radius of smaller circle is "r".
So the area of the smaller circle will be π(radius)²=πr²
Let the Radius of the larger circle is "R".
So the area of the larger circle will be π(radius)²=πR².
In question it is given that, the area of the smaller circle is half of the area of larger circle.
That means,
area of smaller circle=1/2 area of larger circle
area of smaller circle=1/2 area of larger circleπr²=1/2 πR²
area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²
area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2
area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2r/R=√1/2
area of smaller circle=1/2 area of larger circleπr²=1/2 πR²r²=1/2 R²r²/R²=1/2r/R=√1/2r/R=1/√2
Ratio of smaller circle to that of larger circle is 1/√2 .
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which sampling strategy is most commonly used in ethnography? group of answer choices purposive sampling cluster sampling stratified random sampling derivative sampling
The size of the subculture or group under studied determines the sampling size in ethnography. In this regard, it might not be possible to predetermine the participant count. The complete subculture or group being studied serves as the study sample size in anthropological research.
The non-random sample that best resembles stratified random sampling is quota sampling.
Using the non-probability sampling technique of quota sampling, researchers select a sample of people who are typical of the population. These people are chosen by researchers based on specific traits or qualities. In order to use market research samples for data collecting, they decide on and set sample quotas. These samples accurately reflect the entire population. The interviewer's or researcher's knowledge of the population will be the only factor used to select the final subgroup.
Probability sampling means that every member of the population has a chance of being selected.
There are four main types of probability sample.
Simple random sampling.
Systematic sampling.
Stratified sampling.
Cluster sampling.
For instance, a tobacco company would want to know which age group in a given city loves which brand of smokes. The age groups of 21–30, 31–40, 41–50, and 51+ are subject to survey quotas. Based on these findings, the researcher makes an estimation of the smoking trend in the city's inhabitants.
Therefore,
The size of the subculture or group under studied determines the sampling size in ethnography. In this regard, it might not be possible to predetermine the participant count. The complete subculture or group being studied serves as the study sample size in anthropological research.
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Norma went out to her garden and cut 3 roses from the first rose bush, 5 roses from the second rose bush, 8 roses from the third rose bush, and 13 roses from the fourth rose bush. What kind of sequence is this?
The kind of sequence is a prime number if Norma cuts 3, 5, 8, 13 roses from the four bushes.
What is a prime number?A prime number is a natural number higher than 1 that is not the sum of two lesser natural numbers. A composite number is any natural number that is more than 1 but not a prime. As an illustration, the number 5 is prime since there are no other ways to write it either a product than as 1 5 or 5 1. The basic arithmetic theorem states that every natural number greater than 1 is either a prime itself or can be factored as a product of primes that is unique up to their order, making primes a prominent concept in number theory.
Given,
The number of roses cut by Norma from the first rose bush are 3 roses.
And from the second rose bush are 5 roses and from the third rose bush are 8 roses.
And from the fourth rose bush are 13 roses.
1 2 3 4
3 5 8 13
Here, the roses are 3, 5, 8, 13
Therefore, the kind of sequence is a prime number.
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The least common multiple of two whole numbers is 40. The ratio of the greater number to the lesser number is 5 : 4. What are the 2 numbers?
Answer:
10 and 8
Step-by-step explanation:
must be in the ratio 5:4, 5 x 4 =20, so if you multiply by 2 the ratio is 10:8 (same thing). The least common multiple of 10 and 8 is 40 because you can do 10 x 4 = 40 and 8 x 5 = 40.
The Micro Devices Company earned 4,632,859,678 dollars this year. 1,459,632,852 dollars were earned last year. Which is the best estimate of how many more dollars were earned this year than last year?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
The amount earned by 217% more from last year to this year.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Amount earned last year = 1,459,632,852
Amount earned this year = 4,632,859,678
The best estimate of the amount earned this year than last year.
= [ (4,632,859,678 - 1,459,632,852 ) / 1,459,632,852 ] x 100
= ( 3173226826 /1,459,632,852 ) x 100
= 217 %
Thus,
The amount earned by 217% more from last year to this year.
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Landon is building new bookshelves for his bookstore's new mystery section. Each shelf can hold 35 books. There are 1,190 mystery books. How many shelves will he need to build?
How many shelves will he need to build?
Single bookcase units with two sides, top and bottom should be no wider than 36 inches without a center support.
How wide should shelves be?For most shelves made from 3/4 inch stock, a practical span is 30 to 36 inches. Shelf depth is determined by the size of the items to be stored, generally within the range of 6 to 24 inches. Shelf depth for a general purpose bookshelf is usually 10 to 12 inches. Landon is building new bookshelves for his book store.Plywood for shelves should be 3/4 inch thick or thicker. Standard sheets of plywood come in 1/4-inch, 3/8-inch, 1/2-inch, 5/8-inch, and 3/4-inch thicknesses. Plywood panels over 3/4 inch in thickness are usually special order products.I cut 1 1/2″ strips of plywood and secured three strips to each shelf, including the top and bottom of the bookshelf. The plywood strips are attached on edge, or on their sides, providing the most rigidity.Plywood is the go-to material used for pantry shelves. It's versatile, available in virtually any species of hardwood, and can easily be cut using any table saw. Plywood is ideal for pantry shelves because its edges can be finished with wood trim or iron-on veneer bandingEach shelf can hold 33 books
There are 1221 mystery books
Therefore the number of shelves he will need to build can be calculated as follows
= 1221/33
= 37
Hence Landon will need to build 37 shelves,
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Is Side-Side-Side a postulate or a theorem? Explain
Answer: Postulate
Step-by-step explanation:
Side-Side-Side (SSS) Postulate
If three sides of one triangle are congruent to three sides of another triangle, then the two are congruent.
what is the digital index of 23475
answer:the answer for digital index of 23475 is 3
answer: 3
explanation: the digital index is 3 because 23475 is divisible by 3
Find the median of the test scores: 95 65 90 95 70 65 35 70 60 70 95
What is the 10th term of the geometric sequence 9, -18, 36,
Answer:
Step-by-step explanation:
Answer: -4608
========================================================
Explanation:
a = 9 = first term
r = -2 = common ratio
We multiply each term by -2 to generate the next term
The nth term for this geometric sequence is a*(r)^(n-1) which becomes 9(-2)^(n-1)
If you tried plugging in say n = 2, you should find that,
9(-2)^(n-1)
9(-2)^(2-1)
9(-2)^1
9(-2)
-18
So that confirms the second term. I'll let you try the other values of n to confirm it further.
----------------------
From here, you plug in n = 10 to find the tenth term
9(-2)^(n-1)
9(-2)^(10-1)
9(-2)^9
9(-512)
-4608
Solve the following system of equations by elimination. What is the value of y?
2x5y = 1
-3x+2y=-18
y = 3
y = -3
y = 1.5
y=-1.5
The value of the variable 'y' will be 3. Then the correct option is A.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The system of the linear equation is given below.
2x - 5y = 1 ...1
-3x + 2y = - 18 ...2
Multiply equation 1 by 2 and equation 2 by 5, then we have
4x - 10y = 2
-15x + 10y = - 90
Add both equations, then we have
4x - 15x = 2 - 90
11x = 88
x = 8
Then the value of the variable 'y' is calculated as,
-3 (8) + 2y = - 18
- 24 + 2y = - 18
2y = 24 - 18
2y = 6
y = 3
The worth of the variable 'y' will be 3. Then the right choice is A.
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Match the type of slope to the equation. You may need to solve for slope-intercept form for some equations.
y-12
x--13
-6y--2x+30
3x+5y-15
The required slopes of the line are as follows,
(a) y = 12, the slope is m = 0,
(b) x = -13, the slope is not defined.
(c) -6y = -2x + 30, the slope is positive, m = 1 / 3.
(d) 3x + 5y =15, the slope is negative, m= -3/5.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
here,
(a)
y = 12
Comparing the above expression with the standard equation of line y = mx + c,
From comparison,
mx = 0
m = 0
(b)
x = -13,
x + 13 = 0
Comparing the above expression with the standard equation of line y = mx + c,
From comparison,
mx = 1 / 0 (because the equation does not contain the term y)
m = not defined.
Similarly,
(c) -6y = -2x + 30, the slope is positive, m = 1 / 3.
(d) 3x + 5y =15, the slope is negative, m= -3/5.
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express x² - 8x + 5 in the form {x-a]²-b where a and b are the integers
x² - 8x + 5 can be expressed as (x - 4)² - 11 in the form (x - a)² - b, where a = 4 and b = 11.
Let y = x² - 8x + 5 ..................( 1 )
Expanding (x - a)² - b we get,
x² - 2ax + a² - b ......................( 2 )
Equating ( 1 ) and (2), we get
x² - 8x + 5 = x² - 2ax + a² - b
Comparing the coefficient of x,
- 8 = - 2a
a = 4
Comparing constants,
a² - b = 5
since we know a = 4
4² - b = 5
16 - b = 5
b = 11
Hence x² - 8x + 5 = (x - 4)² - 11
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Please help me. I will give brainliest to the first and correct person who answers. There has to be 2 people tho
Answer: The value of x is 0.625
Step-by-step explanation:
x=5/0.8
since figure A is scaled to 5 by 0.8, we divide 5 by 0.8 to find x.
x=0.625
Solve the ytem of equation by the addition method.
−4x = −4y − 12
−16x 6y = 12
For the above system of equations, 4x-4y=12 and 16x-6y=-12, the values of x and y are 4.5 and -10 respectively.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
4x-4y=12
16x-6y=-12
multiply equation 1 by 4,
16x-16y=48
-16x+6y=12
-10y=60
y=-10
-16x-60=12
-16x=72
x=72/16
x=4.5
The value of x is 4.5 and y is -10 for the given system of equation as 4x-4y=12 and 16x-6y=-12.
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