Answer:
Here is your answer,
Step-by-step explanation:
(c)
x + y = 31 ------ (i)
x - y = 5 ------ (ii)
We have subtract eqn (ii) from eqn (i). Here we get the equation as,
2y = 26
y = 13 ------(iii)
Put eqn (iii) in eqn (i), we get -
=> x + y = 31
=> x = 31 - 13
=> x = 18
Therefore, their present ages of younger brother & older brother is 13 yrs & 18 yrs respectively.
a florist has 25 flower arrangements to sell. the amount of money the florist makes for selling x flower arrangements is represented by a function. f(x)
In linear equation, The domain defines the values of numbers of flower arrangements that
can be expected from the florist.
The practical domain of the function is; All integers from 0 to 25, inclusive.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
The domain of the function = The possible number of flower arrangements
that can be sold
The possible number of flower arrangements that can be sold = Whole
numbers from 0 to 25
Therefore;
The possible number of flower arrangements that can be sold = 0 ≤ x ≤ 25
Where;
x = An integer
Which gives;
The domain of the function, D = {0 ≤ x ≤ 25 | x ∈ Z}
Therefore;
The practical domain of the function if the florist sells 25 flower
arrangements is D = All integers from 0 to 25, inclusive.
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Here are the hottest recorded temperatures (in °F) for eight cities throughout North America.
Complete the grouped frequency distribution for the data.
In the distribution, the frequency of a class is the number of temperatures in that class.
(Note that we are using a class width of 5 .)
The frequency distribution of the data from 103 to 107 is 2, from 108 to 112 is 4 and from 113 to 117 is 2.
What is frequency distribution in a given set of data?Frequency distribution in a data set is the no. of times a certain data of an interval of grouped data occurs.
Temperature(°F) Frequency
103 to 107 2
108 to 112 4
113 to 117 2
The class width of a data set is represented by the two consecutive lower limits.
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On a 60-mile road there are 7 rest stops placed at.
equal intervals, including one at each end of the
road, as shown above. What is the distance, in feet,
between two consecutive rest stops?
(Note: 1 mile = 5,280 feet)
A) 31,680
B) 36,960
C) 45,257
D) 52,800
Answer:
C. 45,257
Step-by-step explanation:
5280 * 60 = 316,800
316,800 ÷ 7 = 45,257
The distance between two consecutive rest stops is 45257 feet.
What is division?Division is the process of dividing a number by a given number.
Given that, the 60-mile road is divided into 7 equal parts.
The length of each part is:
60/7 mile
Given that;
1 mile = 5280 feet
Therefore;
60/7 mile = (60/7)5280 feet
60/7 mile ≈ 45257 feet
Hence, the distance between two consecutive rest stops is 45257 feet.
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pls pls help due tommorw!!! pretty easyyy!
The monomial that we need to add to have a square of a difference is:
-2bc
Which binomial should we introduce?
Remember that the square of a difference is written as:
(a - b)^2 = a^2 - 2ab + b^2
Here we have the two terms:
0.01*b^2 + ... + 100c^2
We can rewrite the known terms as:
0.01*b^2 = (0.1*b)^2
100*c^2 = (10c)^2
Then our expression becomes:
(0.1*b)^2 + ... + (10c)^2
And the missing term must be:
-2*(0.1b)*(10c) = -2bc
Then the complete expression is:
(0.1b)^2 - 2bc + (10c)^2 = (0.1b - 10c)^2
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In ΔPQR, p = 4.7 inches, ∠P=76° and ∠Q=57°. Find the length of q, to the nearest 10th of an inch.
The length of side q to the nearest 10th of an inch is 4.1 inches.
What is the sine rule for a triangle?The sine rule for a triangle ABC is a/sinA = b/sinB = c/sinC.
Given, In ΔPQR, p = 4.7 inches, ∠P=76°, and ∠Q=57°.
∴ the length of q can be obtained by,
p/sinP = 1/sinQ.
4.7/sin76° = q/sin57°.
4.7/0.97 = q/0.84.
q = (4.7×0.84)/0.97.
q = 4.1 inch.
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18 (a) Reflection: in the x-axis (b) Rotation: 180° 19 20 21 22 Triangle DEF with vertices D(-6, -1), E(-3, -2) and F(-5, -7):
(a)Reflection: in the x-axis
(b) Rotation: 180°
The vertices after reflection will be (-6, 1), (-3, 2), (-5, 7) and the vertices after rotation of 180° will be (6, 1), (3, 2), (5, 7).
What is the reflection of points?A form of Euclidean space isometry in geometry is called a point reflection, also known as a point inversion, center inversion, or asymmetry through a point.
An object is said to have point symmetry if it is unchanged under a point reflection, and central symmetry or being centrally symmetric if it is invariant below a point reflective thinking through its center.
As per the given information in the question,
The given vertices of the triangle are:
D(-6, -1), E(-3, -2), F(-5, -7).
a.
The equation towards reflection in the x-axis: (x, -y)
D = (-6, -1)
Reflected vertex = (-6, 1)
E = (-3, -2)
Reflected vertex = (-3, 2)
F = (-5, -7)
Reflected vertex = (-5, 7)
b.
Now let's find out the rotation of 180° of the given points,
As we can see that the vertices are in the third quadrant because both the points of each vertex are negative, so after rotation of 180° it will move to the 1st quadrant where all the points are positive.
So,
D = (-6, -1)
After rotation, D = (6, 1)
E = (-3, -2)
After rotation, E = (3, 2)
F = (-5, -7)
After rotation, F= (5, 7)
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how many. roots
f(x) = 4x5 – 3x
The function f(x) is 4x5 – 3x has exactly 5 roots according to the Fundamental Theorem of Algebra.
How to find number of roots ?According to the Fundamental Theorem of Algebra, a polynomial function of degree n has exactly n roots (also known as zeros).In other words, if f(x) is a polynomial function of degree n, then there exist n values of x, called roots or zeros, that satisfy the equation f(x) = 0.The Fundamental Theorem of Algebra is important because it guarantees the existence of solutions to polynomial equations, which are equations that have the form f(x) = 0, where f(x) is a polynomial function.In this case, the polynomial function is f(x) = 4x^5 - 3x, which is of degree 5. Therefore, the function has exactly 5 roots according to the Fundamental Theorem of Algebra.The correct answer is therefore d) 5 roots.
Complete question :
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?
f(x) = 4x5 – 3x
1 root
2 roots
4 roots
5 roots
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Alexander is in the business of manufacturing phones. He must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. Let C represent the total cost, in dollars, of producing pp phones in a given day. A graph of C is shown below. Write an equation for C then state the y-intercept of the graph and determine its interpretation in the context of the problem.
C = [___________]
The y-intercept of the function is [____] which represents
(A: The number of days to produce all of the phones.)
(B: The fixed cost for all rent and equipment.)
(C: The total cost to produce all of the phones.)
(D: The additional cost to produce each phone.)
(E: The number of phones produced in day.)
The equation of line of c and y intercept are y = 100x +400 and 400 respectively.
Explain equation of lineThe equation, y = mx + b, is in slant capture structure for the situation of a line. At the point when a condition is here, the slant of the line is given by m and the y-capture is situated at b. For instance, a line with the situation y = 2x + 4 has a slant of 2 and a y-catch of 4.
According to question:Let take two random points lying on the line.
(0, 400) and (1, 500)
we know that,
Slope(m) = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = (500-400)/(1-0) = 100
And y-intersect from the graph is c = 400
Then,
Y = mx + c
y = 100x +400
Y-intercept represent the number of phones produce in a day.
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a water tank already contains 2 gallons of water when braxtor begins to fill it. water flows into the tank at a rate of 0.25 gallons per minute. Write an slope on a graph for this and x,y table plus equation
Hence, the slope of equation is [tex]f(x)=-0.25x+2[/tex].
What is the slope of the line?
The slope is always estimated by determining the ratio of the “vertical change” to the “horizontal change” between any two different points on a line.
Suppose that the amount of water in the tank after a certain number of minutes.
Let [tex]x[/tex] be any value. So, after the [tex]x[/tex] minutes the tank has lost [tex]0.25x[/tex] gallons from the original [tex]2[/tex] .
So, the [tex]f(x)=2-0.25x[/tex] where [tex]f(x)[/tex] is the number of gallons remaining after [tex]x[/tex] minutes and here [tex]x[/tex] is the number of minutes.
[tex]f(x)=2-0.25x\\\\f(x)=-0.25x+2[/tex]
Hence, the slope of equation is [tex]f(x)=-0.25x+2[/tex].
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PLEASE HELP ASAP!!!!
Answer:
#1
Step-by-step explanation:
3x4=12 not 7
To qualify for the next marathon, a runner's time must be less than 3 and 1/4 hours. Indicate whether or not each runner will qualify for the next marathon.
Answer:
There was no data provided but due to simple research i have conducted the following data
Qualifiers are in bold, italics and underlined.
Step-by-step explanations:
Chio- 3 1/5
Kevin- 3.2
Ojas- 3 8/30
Sydney- 3 13/60
Qualifiers: Chico, Kevin
let me know if this is incorrect data
Literal Equations
help asap !!
Answer:
Step-by-step explanation:
-6y = -5x + 36
y = 5/6x - 6
a restaurant offers 9 entrees and 11 desserts. in how many ways can a person order a two-course meal?
The number of possible ways a person can order a two-course meal = 99
In this question, we have been given a restaurant offers 9 entrees and 11 desserts.
We need to find the number of possible combinations (ways) a person can order a two-course meal.
Here, the entrees = 9
and the desserts = 11
The entrees can be ordered in 9 ways
The desserts can be ordered in 11 ways.
a two-course meal = entrees * desserts
so, the number of possible ways a person can order a two-course meal would be,
a two-course meal = 11 * 9
a two-course meal = 99
Therefore, in 99 ways a person can order a two-course meal.
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Ordered pairs of -3x + y < 11
The order pair will be greater than (-2,5) because when substituted the value (-2,5) will give 11 that will be false.
What is ordered pair?An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it can be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers. Two variables are frequently represented by ordered pairs. (x, y) = (7, - 2) means that x = 7 and y = -2. The x-coordinate is the number that corresponds to the value of x, and the y-coordinate is the number that corresponds to the value of y.
Here,
The given inequality,
-3x+y<11
at (0,0)
0<11
it is true.
at (1,1)
-3+1<11
-2<11
it is true.
Because 11 will be false when the value (-2,5) is substituted, the order pair will be greater than (-2,5).
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Evaluate f(x)=2x+5 when x=0, x=1, x=5
Th value of the equation f ( x ) is given as
when x = 0 , f ( 0 ) = 5
when x = 1 , f ( 1 ) = 7
when x = 5 , f ( 5 ) = 15
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given as
f ( x ) = 2x + 5
Now , the values of the function f ( x ) can be determined when we substitute for the values for x in the equation
So , in order to find f ( 0 ) , substituting the value for x as x = 0, we will get the value for the function
a)
when x = 0
The equation is f ( x ) = 2x + 5
f ( 0 ) = 2 x 0 + 5
f ( 0 ) = 5
So , the value of f ( 0 ) = 5
b)
when x = 1
The equation is f ( x ) = 2x + 5
f ( 0 ) = 2 x 1 + 5
f ( 0 ) = 7
So , the value of f ( 0 ) = 7
c)
when x = 5
The equation is f ( x ) = 2x + 5
f ( 0 ) = 2 x 5 + 5
f ( 0 ) = 15
So , the value of f ( 0 ) = 15
Therefore , the values of the equations are f ( 0 ) = 5 , f ( 1 ) = 7 , f ( 5 ) = 15
Hence ,
Th value of the equation f ( x ) is given as
when x = 0 , f ( 0 ) = 5
when x = 1 , f ( 1 ) = 7
when x = 5 , f ( 5 ) = 15
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At a local print hop, 16 copie can be made for $8. At thi rate, how much would it cot to make 88 copie?
Rate at which 88 copies will get printed is 44 dollars
What is unitary method ?By using the unitary method to find the value of a single unit, we may use that value to calculate the values of the required number of units.
According to the given information :
Applying the unitary method
we get,
Rate at which 16 copies get printed = 8 dollars
Rate at which one copy gets printed = [tex]\frac{8}{16}[/tex]
Rate at which 88 copies get printed = [tex]\frac{8}{16}[/tex]×88
= 44 dollars
Rate at which 88 copies will get printed is 44 dollars.
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Write a equation for each one please this is urgent!!!
50 points to whoever answers!!!
1. A line with a slope of 0 and a y-intercept of 5.
2. A line with a slope of 2 and a y-intercept of -1.
3. A line with an undefined slope and an x-intercept of -1.
Answer:
1. y = 5
2. y = 2x - 1
3. x = -1
A small pool for children has some water in it. Jabari uses a garden hose to add water to it. The total amount of water in gallons, y, is a function of the time in minutes since Jabari turns on the hose, x.
The graph of the linear function passes through the points (2,44) and (5,80). What is the equation of this function?
y=?x+?
The equation for the given linear function is y = 12m + 20.
What is a linear equation?A linear equation in two variable has the general form as y = ax + by + c, where a, b and c are integers and a, b ≠ 0.
It can be represented as a straight line on a graph.
The given points for the linear function are (2, 44) and (5, 80) respectively.
The slope can be obtained as,
m = (80 - 44)/(5 - 2)
= 36/3
= 12
Substitute the value of m in the general form y = mx + c to obtain,
y = 12x + c
Now, substitute x = 2 and y= 44 in the above expression as,
44 = 12 × 2 + c
=> c = 44 -24
=> c = 20
Thus the linear function can be written in the form of equation as,
y = 12m + 20
Hence, the equation of the function for the given case is y = 12m + 20.
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I really need help with these questions!! Please make it quick!!!
Answer:
The selected answer should be correct!
Step-by-step explanation:
I did the problem step by step and got 1 5/7 which is the simplified version of 1 15/21.
I hope this helped somewhat!!
O A. (2,4) O B. (1,2) O D. (2,2) What is the midpoint of the line segment with endpoints (-1, 7) and (3, -3)?
The midpoint of the line segment is (1, 2). Then the correct option is B.
What is the mid-point of the line segment?Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).
Then the coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
The endpoints of the line segment are (-1, 7) and (3, -3). Then the mid-point of the line segment will be given as,
(x, y) = [(-1 + 3) / 2, (7 - 3) / 2]
(x, y) = (2/2, 4/2)
(x, y) = (1, 2)
The midpoint of the line portion is (1, 2). Then the right choice is B.
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The height of an object that is dropped from the top of a tower is given by the expression −16t2 + 441, where t is the time in seconds.
(a) Factor this expression.
(b) Use a spreadsheet to determine how many seconds it takes the object to fall to a height of 377 feet. (Use 0.5-second intervals for t.)
t = BLANK sec
i need this fast
Hello,
I hope you and your family are doing well!
Part A)
The given expression is in the form y = -16t^2 + 441, which is a quadratic equation. A quadratic equation can be factored into the form (ax + b)(cx + d) = 0, where a, b, c, and d are constants.
To factor in the given expression, we can start by completing the square. To complete the square, we need to add and subtract the square of half of the coefficient of the x^2 term, which is (1/2)(-16) = -8. This gives us:
y = -16t^2 + 441 = (-16t^2 - 8t^2) + 441 = -24t^2 + 441
Now, we can rewrite the expression as follows:
y = -24t^2 + 441 = (-8t^2) + 441
To complete the square, we need to add and subtract (1/2)^2(-8)^2 = 16:
y = (-8t^2 + 16) + 425
This expression can be rewritten as:
y = (-8t^2 + 16) + (20t)^2
So the expression can be factored as:
y = (-8t + 4)(2t - 5) (this is the answer)
Part B)
To find the time it takes the object to fall to a height of 377 feet, we can set y equal to 377 and solve for t. Substituting the factored form of the expression into the equation and solving for t gives us:
377 = (-8t + 4)(2t - 5)
We can then solve this equation by setting each factor equal to 0 and solving for t. This gives us:
-8t + 4 = 0
2t - 5 = 0
Solving these equations separately gives us:
t = 1/2
t = 5/2
The time it takes the object to fall to a height of 377 feet is t = 1/2 seconds. (or 0.5 in decimal form)
Please give this answer 5 stars and brainliest if you find it helpful. Don't hesitate to reach out if you have more questions.
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Tell whether ABC and DCB can be proven congruent.
No, there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.
What is congruent?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Here,
We have to prove whether ΔABC and ΔDCB can be proven congruent.
For this, we examine the given diagram and concluded that there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.
Hence, No, there isn’t enough information because only two pairs of corresponding sides can't be used to prove that two triangles are congruent.
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best answer gets brainliest! please explain
Answer: -8
Step-by-step explanation:
We see on the graph that there are two points located y=4. They are (7,4) ( -8,4).
So the other value other than 7 is -8!
Read the story.
Peace Park sets up an outdoor ice-skating rink each winter. Yesterday afternoon, there
were 5 skaters who brought their own skates for every 3 skaters who rented skates.
Pick the diagram that models the ratio in the story.
If there were 12 more skaters who brought their own skates than skaters who rented skates,
how many skaters were there altogether?
skaters
The diagram 2 represents the model that depicts the ratio given in the story.
What is a ratio?Ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
Given is that Peace Park sets up an outdoor ice-skating rink each winter. Yesterday afternoon, there were 5 skaters who brought their own skates for every 3 skaters who rented skates.
The given ration of 5 skaters for every 3 skaters is shown in the
diagram 2. In the first column, five blocks are colored and in the second
column, three boxes are colored.
Therefore, the diagram 2 correctly represents the model in the story.
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The diagram shows a border that is 4 inches wide surrounding Annie's painting.
Write an expression, in factored form, that represents the area of the border.
__ square inches
since the border is 4 inches wide and there are 2 sides to the border , the expression in factored form that represents the area of border = 8 x (length of border)
What is area of rectangle?The area of a rectangle is the amount of two-dimensional space that the rectangle occupies. It is calculated by multiplying the length of the rectangle by its width.
What is perimeter of rectangle?The perimeter of a rectangle is the distance around the outside of the rectangle.
(4 inches) * (2 sides) * (length of border) = 8 inches * (length of border)
To write this expression in factored form, we can factor out the 8 inches:
8 inches * (length of border) = 8 inches * (length of border)
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Line m passes through point (-2,-1) and is perpendicular to the graph of y= -2/3 x + 6. line n is parallel to line m and passes through point (4,-3). Which is the equation of line n in slope-intercept form
Equation of line in slope-intercept form is 3y-2x= -1.
What is a slope-intercept form?There are four alternative ways to figure out the equation of any straight line, one of which is the slope-intercept form.Typically, straight lines are shown as y = mx+c. The x and y variables are said to have a maximum power of unity by this common straight line equation. As a result, x = x1 and y = y1.Additionally, this demonstrates that only linear equations can be solved using the slope-intercept form. You ought to be able to solve linear equations with two variables. The graph of such equations is a straight line, as you should be aware of.Furthermore, you must be sure that you comprehend how linear equations' y-intercept, x-intercept, and slope properties work.Hence, Equation of line in slope-intercept form is 3y-2x= -1.
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Select the correct answer. Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-13) = 20 B. g(-4) = -11 C. g(7) = -1 D. g(0) = 2
The correct answer is option B: "g(-4) = -11". This statement is consistent with the given information about the domain, range, and specific values of the function g. Since the domain of g is -20 ≤ x ≤ 5, the value x = -4 is within the domain of the function, and therefore we can evaluate g at this value. Similarly, since the range of g is -5 ≤ g(x) ≤ 45, the value g(-4) = -11 is within the range of the function. Furthermore, since g(0) = -2 and g(-9) = 6, we know that g takes on negative values, which is consistent with the fact that g(-4) = -11.
Option A, C, and D are all incorrect because they do not satisfy the conditions of the domain and range of the function g. For example, option A states that g(-13) = 20, but since the domain of g is -20 ≤ x ≤ 5, the value x = -13 is not within the domain of the function, and therefore it is not possible to evaluate g at this value. Similarly, option C states that g(7) = -1, but since the range of g is -5 ≤ g(x) ≤ 45, the value g(7) = -1 is not within the range of the function, and therefore this statement cannot be true for g. Option D states that g(0) = 2, but since we are given that g(0) = -2, this statement is not consistent with the given information about the function g.
Solve for x. 1+|2+x|=9
Answer: 6
Step-by-step explanation:
Remember:
Anything in | | is considered positive.
Simplified:
1+2+x=9
3+x=9
Solve for x:
x=9-3
x=6
David has $90 to spend on sneakers. the sales tax in his state is 6%. vincent has $95 to spend on sneakers. the sales tax in his state is 9%. both boys are interested in a pair of sneakers that costs $86. who will be able to buy the sneakers?
a. david
b. vincent
c. both
d. neither
Option B is correct, Vincent will be able to buy the sneakers, while David will not be able to.
Because the shoe cost after including sales tax is
6% of 86$ is 5.16$
so, 86 + sales tax (which is 5.16) = 91.16$
David only has 90$ so he can't afford the sneakers. They are 1.16$ over his budget.
While for Vincent,
9% of 86$ is 7.74$
so, 86 + sales tax (which in this case is 7.74) = 93.74
Vincent has 95$ to spend so he can afford the shoes.
A sales tax is a tax paid to a governing body for the income of certain items and services. Typically, legal guidelines permit the seller to gather funds for the tax from the customer at the factor of purchase. While a tax on goods or services is paid to a governing body immediately by means of a patron, it also includes called a use tax. frequently legal guidelines offer for the exemption of positive goods or services from income and use tax, which includes food, schooling, and medicines. A fee-introduced tax (VAT) collected on goods and services is associated with a sales tax. See the contrast with income tax for key variations.
Traditional or retail income tax is levied at the sale of an amazing to its very last quit person and is charged whenever that item is sold retail. sales to corporations that later resell the products aren't charged the tax. A patron who isn't always an end-user is generally issued a "resale certificate" by way of the taxing authority and required to provide the certificate (or its identification variety) to a seller on the point of buy, at the side of an assertion that the object is for resale. The tax is otherwise charged on each item sold to clients without any such certificate and who are underneath the jurisdiction of the taxing authority.
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Find the fourth degree polynomial function with zeros 5, -5, 5i, and -5i. Write the function in factored form.
The fourth degree polynomial function with zeros 5, -5, 5i, and -5i. written in factored form is
(x - 5) (x + 5) (x - 5i) (x + 5i)How to find the function with the given zerosThe zeros of a polynomial function is the the value of x when the function is equal to zero
The zero is also called the root of the polynomial
To find the polynomial we equate to the zeros
the first
x = 5
x - 5 = 0
the second
x = -5
x + 5 = 0
the third
x = 5i
x - 5i = 0
the fourth
x = -5i
x + 5i = 0
Bringing the terms together
(x - 5) (x + 5) (x - 5i) (x + 5i)
Therefore the polynomial of zeros 5, -5, 5i, and -5i is gotten in factored form in the form (x - 5) (x + 5) (x - 5i) (x + 5i)
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