A rectangle is a four-sided geometric shape where opposite sides are parallel and congruent. The diagonals of a rectangle are two lines that connect the opposite corners of the rectangle, and they bisect each other at 90 degrees.
Briefly defined, what is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.
Given the sides of rectangle WXYZ are WY = 14x + 10 and XZ = 11x + 22. We can find the length of the diagonals using the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the diagonal of the rectangle) is equal to the sum of the squares of the other two sides (the sides of rectangle)
Diagonal WX: √(14x+10)^2 + (11x+22)^2 = √(196x^2 + 456x + 100 + 121x^2 + 484x + 484) = √(317x^2 + 940x + 584)
Diagonal YZ: √(14x+10)^2 + (11x+22)^2 = √(196x^2 + 456x + 100 + 121x^2 + 484x + 484) = √(317x^2 + 940x + 584)
So, the lengths of the diagonals of rectangle WXYZ are √(317x^2 + 940x + 584) units.
Note that the diagonals of a rectangle are congruent and the value of x is not a known, the diagonal of rectangle is the value of the square root of the expression.
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Answer: 66
Step-by-step explanation:
I skipped it to see the answer hope this helps
write an expression to describe a rule for the sequence. then find the 100th term in the sequence 5 13 21
The expression is 8n – 3; The 100th term is 797
How to calculate the 100th term in sequence?The nth term of an arithmetic sequence is given by:
an=a1+(100-1)d ....[1]
where
a1 is the first term
d is the common difference of two consecutive terms.
n is the number of terms.
Given the sequence:
5, 13, 21, 29, 37, 45, …
This is an arithmetic sequence with first term = 5 and common difference(d) = 8
Since;
13-5 = 8,
21-13 = 8,
29-21 = 8 and so on....
We have to find the 100th term in the sequence
Substitute in [1] we have;
an=a1+(100-1)d
an=5+(n-1)8=5+8n-8 = 8n-3
Substitute the given values and n=100 we have;
a100= 800 - 3 = 797
Therefore, the 100th term in the sequence is, 797 and an expression to describe a rule for the sequence is, 8n – 3;
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PLEASE HELP ASAP! 55 POINTS Jackie wraps a sheet of paper tightly around a wax candle whose diameter is two inches, then cuts through them both with a sharp knife, making a 45° angle with the candle's axis. After unrolling the paper and laying it flat, Jackie sees the wavy curve formed by the cut edge, and wonders whether it can be described mathematically. Sketch this curve, then show that it is sinusoidal. It is very helpful to use radian measure to describe angles in this problem.
5. Michael has of 3 boxes of a dozen doughnuts for his class of 30 students. Does
he have enough doughnuts for each student to get a whole doughnut? Why or
why not?
Yes Michael has 36 doughnuts 6 extra
3*12=36
36>30
HELP I DONT UNDERSTAND
The of the function a remainderre 3, 2,1,0
What is substitution?You should understand that substitution means replacing figures in a variable to get a value
the given function is
y=-x/3 +2
The given parameter or table to be completed is
x -6 -3 0 3 6
y 4 3 2 1 0
The table above was completed in the following ways
1) y= 6/3 +2 = 2+2 4
2) y = 3/3 + 2 = 1+2 = 3
3) 0/2 + 2 = 2
4) -3/3 +2 = -1+2 = 1
5) y = -6/3+2 = -2+2 = 0
Therefore the table has values descending from 4 to 0
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For each condition, make up a different equation for a quadratic function that meets the condition. Use whatever form is most conventions.
1. Has vertex at (-2,-5)
2. Has a y-intercept at (0,6)
3. Goes through the points (4,2) and (1,2)
y=−12(x+4)(x−1) A quadratic function that satisfies the requirement and passes through the points (4, 2) and has the equation +2 (1,2) .
what is equation ?A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. The terms 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14, for example. Mathematical equations are used to express the relationship between two phrases on either side of a letter. In most cases, the symbol serves as the sole variable. a good example is 2x - 4 = 2.
given
a )a vertex at (−2,−5) :
y=[tex](x+2)^{2}[/tex]−5
y=−[tex](x+2)^{2}[/tex]−5
y=3[tex](x+2)^{2}[/tex]−5
b) a y-intercept of (0,−6) :
y=[tex]x^{2}[/tex]−6
y=[tex]x^{2}[/tex]+13x−6
y=2[tex]x^{2}[/tex]−6
c) the points (−4,2) and (1,2):
y=(x+4)(x−1)+2
y=2(x+4)(x−1)+2
y=−12(x+4)(x−1)+2
y=−12(x+4)(x−1) A quadratic function that satisfies the requirement and passes through the points (4, 2) and has the equation +2 (1,2).
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Aida, Bernado and Cristiano need $30000 to start a business. a I They borrow & of this amount.
Show that they still need $18000.
They provide the $18000 themselves in the ratio
Aida: Bernado : Christiano = 5: 4: 3.
Calculate the amount each of them provides.
b i Office equipment costs 35% of the $30000.
Calculate the cost of the equipment. ii Office expenses cost another $6500.
Write this as a fraction of $30 000.
Give your answer in its lowest terms. iii How much remains of the $30000 now?
c They invest $12500.
After one year this has increased to $15500.
Calculate this percentage increase.
Answer:
aida:$7500
Bernardo:$6000
Christiano :$4500
b.i $10500
b.ii 13/60
b.iii $13000
c. 24%
Find the value of x.
Answer:
x = 32
Step-by-step explanation:
the sum of the exterior angles of a polygon is 360°
All the indicated angles in the diagram are exterior angles of the polygon.
sum the 5 exterior angles and equate to 360
2x + 71 + 85 + 44 + 3x = 360
5x + 200 = 360 ( subtract 200 from both sides )
5x = 160 ( divide both sides by 5 )
x = 32
I NEED HELP!!
1ST QUESTION
a). 5 divided by 3/10
b.) 5 divided by 9/10
Answer:
a) 5 divided by 3/10
To solve this problem, we need to perform the division first, followed by the division. Dividing 5 by 3/10, we have:
5 / (3/10) = (5*10)/3 = 50/3
Simplifying, we have:
50/3 = 16 2/3
Therefore, the result of 5 divided by 3/10 is 16 2/3.
b) 5 divided by 9/10
To solve this problem, we need to perform the division first, followed by the division. Dividing 5 by 9/10, we have:
5 / (9/10) = (5*10)/9 = 50/9
Simplifying, we have:
50/9 = 5 5/9
Therefore, the result of 5 divided by 9/10 is 5 5/9.
Step-by-step explanation:
Answer:
a).5 divided by 3/10
= 16.6666666667
And,
b).5 divided by 9/10
=4.5
Find the midpoint of the line segment with end coordinates of:
(
−
4
,
−
2
)
and
(
−
2
,
−
10
)
Answer:
this is the answer (-3,-6)
What does exponential growth look like on a logarithmic graph?
Exponential growth on a logarithmic graph looks like a straight line. On a regular graph, the line would appear to be curved, but when plotted on a logarithmic graph, the line appears to be a straight line.
Exponential growth on a logarithmic graph appears as a straight line. This is because the logarithmic scale is a compressed scale, meaning that it takes a large range of values and compresses them into a smaller range. This makes the data easier to read and understand. The straight line occurs because the logarithmic scale is designed to fit the data points more closely, making the line appear linear. This is in contrast to the regular scale, where the line appears curved due to the large range of values being plotted. Thus, exponential growth appears as a straight line on a logarithmic graph.
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7. Kya picks up where she left off in her book and starts reading. After 2 hours, she's on page 195. After reading for 4 hours that day, she's on page 297. Write an equation to represent how many pages Kya reads per hour.
I did the equation= y=51x+93
There are a total of 399 pages in the book. How many more hours does Kya have left to read? PLEASE HELP WILL THIS PART I DONT UNDERSTAND
Answer:
Step-by-step explanation:
Work for finding the equation, feel free to skip it:
So first off, to write the equation, we will use an equation in slope intercept form: y = mx + b, where y is the numbers of pages she has read, m is the number of pages she reads per hour, x is the number of hours she read, and b is the number of pages she has already read.
To find the slope(The number of pages she reads per hour), we can subtract the number of pages she had read at 2 hours from the number of pages she had read at 4 hours:
297 - 195 = 102.
This tells us she read 102 pages over 2 hours. Thus, over 1 hour, she had read 102/2 = 51 hours. This is m. So our equation so far is y = 51x + b
To find b, we can take 195(the pages she had read after 2 hours), and subtract it by the pages she can read over 2 hours(51 * 2), giving us the amount of pages she had already read(b):
195 - (51*2) = 195 - 102 = 93.
So our equation is:
y = 51x + 93.
Work for finding how many hours it will take Kya to read the whole book:
Y is the total number of pages Kya has read when we plug in x hours. However, if we already know the total number of pages in a book, we can plug in that number for Y, and then solve for x to find how many hours it takes for Kya to read the book:
399 = 51x + 93
Subtracting 93 from both sides gets us:
51x = 306
=
x = 6
This means it takes 6 hours for Kya to read the whole book.
Since Kya has already been reading for 4 hours, the time she has left is:
6-4 = 2
So it takes Kya 2 more hours to finish reading the 399 pages in the book.
Hope this helps!
The function f(x) = StartRoot negative x EndRoot is shown on the graph. Which statement is correct?
The statement that is correct about the behavior of the given graph is; D:
The range of the function is all real numbers greater than or equal to 0.
How to interpret function graphs?The graph of the function is as shown in attached diagram.
The function is;
y = √-x
1. The domain of the function is defined the set of all possible input values for x. Therefore, upon close inspection of the graph, we can say that the domain of this function is;
x ∈ (-∞, 0]
2. The range of the function is defined as the set all possible output values for y. By closely inspecting the attached graph, we can say that the range of this function is; y ∈ [0, -∞)
From the above, we can tell that the range of the function is all real numbers greater than or equal to 0.
Looking at the options, only option D can be said to be correct about the behavior of the given graph.
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The missing options are;
The domain of the function is all real numbers greater than 0.
The range of the function is all real numbers less than or equal to 0.
The domain of the function is all values less than 0.
The range of the function is all real numbers greater than or equal to 0.
consider the relation below
1.Is the relation A function
2. Is the relation a one to one function
3. Is the inverse of the relation below itself a function
Answers:
Yes it's a function.No, the function is not one-to-one.No, the inverse isn't a function.=============================================
Explanation:
We have a function since the curve passes the vertical line test. Recall that this test is where we try to draw a single vertical line through more than on point on the curve. Such a task isn't possible in this case.
-----------
On the other hand, the curve does not pass the horizontal line test. It is possible to draw a single horizontal line through more than one point on the curve.
This function is not one-to-one since it does not pass the horizontal line test.
------------
Because the graph isn't one-to-one, the inverse won't be a function. The process of finding the inverse involves swapping x and y; which means we swap from "horizontal line test" to "vertical line test".
The original function failing the horizontal line test would mean the inverse fails the vertical line test.
Sal brought 2 dozen apples to a science club meeting. He divided the apples equally among the 8 people there. How many apples did he give each person?
Division is the antithesis of multiplication. When you divide twelve into three equal groups, you get four in each group when you multiply three groups of four to create twelve.
How do you explain division?The opposite of multiplication is division. When you multiply three groups of four to produce twelve, you get four in each group when you split twelve into three equal groups. The basic objective of splitting is to determine how many equal groups are created or how many people are in each group after a fair distribution.
The phrase to use is "divide in half," not "divide by half," when discussing splitting something into two equal portions. In mathematics, multiplying by two is equivalent to dividing by half. Additionally, see "multiply by two."
The French term "douzaine," which denotes a group of 12, is where the word "dozen" originates.
2 dozen apples equals 24, and 24 divided by 8 is 3.
Therefore, the answer is 3.
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Reduce the fraction and find the domain
The simplification of all the given algebra fractions are;
1) a/c
2) (a - b)/(a - 1)
3) (x + 1)/(x - 4)
How to solve algebraic fractions?An algebraic fraction is defined as a fraction whose numerator and denominator are algebraic expressions.
1) (abc + ab²)/(b²c + bc²)
Factorizing numerator and denominator gives;
ab(c + b)/bc(b + c)
b(b + c) will cancel out to get; a/c
2) (a² - b²)/(a² - a + ab - b)
Factorizing numerator and denominator gives;
[(a + b)(a - b)]/[a(a - 1) + b(a - 1)]
= [(a + b)(a - b)]/(a + b)(a - 1)
(a + b) will cancel out to get;
(a - b)/(a - 1)
3) (x² - 2x - 3)/(x² - 7x + 12)
Expanding the numerator and denominator gives;
(x² - 3x + x - 3)/(x² - 4x - 3x + 12)
= ((x + 1)(x - 3))/((x - 3)(x - 4)
(x - 3) will cancel out to get;
(x + 1)/(x - 4)
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3. Geese and Pigs: A farmer raises only geese and pigs. She wants to raise no more than
16 animals total including no more than 10 geese. She spends $5 to raise a goose and $15 to raise a pig, and has $180 available for this project. Find the maximum profit she can make if each goose produces a profit of $6 and each pig a profit of $20.
The maximum profit she can make if each goose produces a profit of $6 and each pig a profit of $20.
How can you determine the table's maximum profit?Making the Most of Total Revenue and Total Cost Data. Just multiply the price by the quantity at each quantity to find the company's total revenue. Next, deduct the company's total cost at each quantity, which is provided in the table.
Let the number of geese be x and the number of pigs be y
From the given information, we can form the following inequalities:
x ≤ 10
y ≥ 05
x + 15y ≤ 180
Maximize 6x + 20y.
We want to find the intersection points of the first three equations since x and y are bounded within the area under these
These points are (0,0), ( 10,0), (0,12), (10,65/3).
At (0,0) , the profit is $0
At ( 10,0), the profit is $60
At (0,12) , the profit is $240
At (10,65/3) , the profit is $499.33
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50 points help me out
Answer:x=20
Step-by-step explanation: <2 and <3 must be equal, so set 3x-10 equal to x+30, once simplified you get x equal to 20.
Answer:
x = 20
Step-by-step explanation:
Angle 2 and 3 are alternate (interior) angles which means that they are equivalent to each other.
3x-10=x+30
-x -x
2x-10=30
+10 +10
2x=40
x=20
Please help ASAP. Which of the following are solutions of the system of linear inequalities? y > 4x+1 y≥x+4.
Using graphical method, the solution to the system of linear inequality (x, y) are (1, 5)
What is System of Linear InequalityA mathematical statement called a linear inequality depicts the relationship between two different variables, typically on a graph. A line or border that divides the area of all the points that fulfill the inequality from the areas of the points that do not constitutes the graph of a linear inequality. A set of lines in the coordinate plane that represent the equations of a system of linear inequalities is called a graph. The region of the coordinate plane where each of the inequalities holds can be seen by joining these lines to create a graph.
The inequality given are;
y > 4x + 1y ≥ x + 4This can be solved using a graphing calculator;
The point of intersection shows the solution to the graph
The solution to the linear inequalities (x, y) are (1, 5)
The broken lines in the graph is from the greater than inequality, while then straight unbroken lines is the inequality with greater than or equal to sign.
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3. ) Copy Center charges $0. 08 a page for machine fed copies and $0. 20 per page for hand-fed copies. I lagan's
bill for 80 copies of his movie script is $13. 00, how many copies of each type were made?
The number of machine fed copies are 25 and the number of hand fed copies are 55. This is solved forming simultaneous equations.
What are simultaneous equations?
Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations. These equations alone could have an infinite number of solutions.
Given cost per page of machine fed copies = $0.08
cost per page of hand fed copies = $0.20
Let,
number of machine fed copies = x
number of hand fed copies = y
Given the total number of copies = 80
So we can write the equation as
x + y = 80 ⇒ (1)
It is also given that the total cost of the movie script is $13
So we can the equation as
0.08x + 0.20y = 13 ⇒ (2)
Solving the simultaneous equations (1) and (2)
From (1),
x = 80 - y
Substituting the above in (2)
0.08(80 - y) + 0.20y = 13
0.12y = 6.6
y = 55
x = 80 - 55 = 25
Therefore the number of machine fed copies are 25 and the number of hand fed copies are 55.
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Q 9-1 Pythagorean Theorem and Trig
A girl is 20 ft. east of her school and her bike is 21 ft. south of the school. How far is she from her bike? Round to the nearest hundredth.
The distance between the girl and her bike is 25.00 ft.
What is distance?Distance is the measure of how far apart two objects, places, or points are. It can be measured in a variety of units, such as miles, kilometers, inches, centimeters, or other units.
The distance between the girl and her bike can be found using the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
In this case, the girl is 20 ft. east of the school and 21 ft. south of the school. Therefore, the two sides of the triangle are 20 ft. and 21 ft. and the hypotenuse is the distance between the girl and her bike.
Using the Pythagorean Theorem, the hypotenuse is equal to the square root of (20^2 + 21^2) = 25.00 ft.
Therefore, the distance between the girl and her bike is 25.00 ft.
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The N71-90 virus will give an infected person a mild rash on their arms once the person has 1 billion of the virus cells in their body. After an initial infection with just one cell, each virus cell will divide into two cells every four hours. After 30 divisions there are 1,073,741,824 cells and the rash starts. Once the rash starts, the immune system kicks in and kills all of the virus cells within an hour. The number of virus cells in the body can be determined using the function where h is the number of hours after infection. If Jolene is infected by one virus cell, how many virus cells will she have after 12 divisions
Jolene will have 4096 virus cells in her body after 12 divisions
Why should we call viruses a cell?Viruses are something more than living or dead, they are both. Maybe we need a new classification of life for them, a life that lives when the environment is favorable and hibernate when it is not.
The function provided to determine the number of virus cells in the body after h hours is 2^h. To find the number of virus cells after 12 divisions, we can plug in 12 for h in the function.
2^12 = 4096.
So, Jolene will have 4096 virus cells in her body after 12 divisions.
Please note that Jolene would not develop a rash after 12 divisions as it would take 30 divisions (120 hours) for the rash to appear.
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Find the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale
the length of the altitude drawn to the hypotenuse. The triangle is not drawn to scale is 4√5
What is altitude Class 9?
The altitude of a triangle is the perpendicular line segment drawn from the vertex to the opposite side of the triangle.
In geometry, a line segment is bounded by two distinct points on a line. Or we can say a line segment is part of the line that connects two points. A line has no endpoints and extends infinitely in both the direction but a line segment has two fixed or definite endpoints.
Let's call it x
According to Euclidean theorem x^2 = 5×16
x^2= 80 and
x = 4√5
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A frictionless pendulum is pulled 3 feet to one side of its center resting point…
A. The amplitude of the sinusoidal function 's' would increase.
B. The midline of the sinusoidal curve will upshift.
What is a periodic function?A function that repeats its values at regular intervals is said to be periodic. For instance, periodic functions include trigonometric functions, which repeat every 2 pi radian. In science, periodic functions are used to describe oscillations, waves, and other periodic events. Aperiodic refers to any nonperiodic function.
We are aware that a periodic function can be used to graph the pendulum's movement mechanism.
A. The pendulum will rise higher on both sides as it is drawn farther away from its resting point; this will result in an increase in the sinusoidal curve's amplitude.
B. The midline of the sinusoidal curve would rise up along the y direction as a result of an increase in magnitude if the pendulum was drawn further away from its resting point.
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Write a rule to describe each transformation.
J(2, 2), (3, 4), H(4,3), G(3,0)
to
J'(-1,2), I'(0, 4), H'(1, 3), G'(0, 0)
The only difference is a -2 in x in 1 transformation in 2 transformation. The function is shifted up by b units with f (x) + b.
what are transformations ?Transformations can be divided into four categories: translation, reflection, rotation, and dilation. Rotate, reflect, or translate the geometric figures on a coordinate plane. The label given to a function, f, that maps to itself is the transformation, or f: X X. The pre-image X is transformed into the picture X after the transformation. It is possible to utilize any operation, or a combination of operations, in this transformation, including translation, rotation, reflection, and dilation.
given
J(2, 2), (3, 4), H(4,3), G(3,0) to J'(-1,2), I'(0, 4), H'(1, 3), G'(0, 0)
in 2 transformation as the only change is that -2 in x in 1 transformation
The function is shifted up by b units with f (x) + b.
The function is shifted downward by b units when f (x) b.
The function is moved left by b units when f (x + b) is used.
The function is moved right b units by the expression f (x b).
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Please help asap Due tonight in a couple hours
ES = ___ units
Round your answer to the nearest tenth.
Answer:
10.6 units
Step-by-step explanation:
Matthew scored a total of 168 points in his basketball season. He scored 147 of those points in the regular season and the rest were scored in his playoff game. What percent of his total points did he score in the playoff game?
Answer:
168 - 147 = 21
21/168 = 12.5
I GIVE THANKS AND MARK BRAINLIEST
WHAT ARE THE CORRECT ANSWER(S)?
Answer:
b and d
Step-by-step explanation:
slope is -0.632 which is quite literally what d is saying, (on terms of graphs) for every 1 square over it goes -0.63 squares down
2-18. Frank wonders whether corresponding angles always have equal measure. For parts () through (d) below, use tracing paper to decide if corresponding angles have the same measure. Then determine if you have enough information to find the measures of x and y. If you do, find the angle measures and state the relationship .
The angles and their relationships are -
a) ∠x = 135° (corresponding angles), ∠y = 135° (vertical angles)
b) ∠y = 45° (liner pair angles), ∠x (not enough information provided)
c) ∠x = 135° (corresponding angles), ∠y = 45° (liner pair angles)
d) ∠x = 45° (liner pair angles), ∠y (not enough information provided)
What is angle pair relationship?
In Geometry, there are five fundamental angle pair relationships:
Complementary Angles
Supplementary Angles
Adjacent Angles
Linear Pair
Vertical Angles
a) In the first diagram -
∠x = ∠a as they are both corresponding angles to each other.
So, ∠x = 135°.
Similarly, ∠y = ∠x as they both are vertically opposite angles to each other.
So, ∠y = 135°.
b) In the second diagram -
∠y + ∠a =180° as they are both form a linear pair of angles.
So, ∠y = 180° - ∠a
∠y = 180° - 135°
∠y = 45°.
Now, ∠x cannot be deduced and no proper information is given in the image.
c) In the third diagram -
∠x = ∠a as they are both corresponding angles to each other.
So, ∠x = 135°.
Now, ∠y + ∠x =180° as they are both form a linear pair of angles.
So, ∠y = 180° - ∠x
∠y = 180° - 135°
∠y = 45°.
d) In the fourth diagram -
∠x + ∠a =180° as they are both form a linear pair of angles.
So, ∠x = 180° - ∠a
∠x = 180° - 135°
∠x = 45°.
Now, ∠x cannot be deduced and no proper information is given in the image.
Therefore, all the angles are and their relationships are found.
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A pet store has 15 puppies, 6 kittens, and 8 hamsters. Alice, Bob, and Charlie each want to buy a pet. For variety, they each want a different kind of pet. How many ways can Alice, Bob, and Charlie buy pets and leave the store satisfied
There are 24 ways for Alice, Bob, and Charlie to buy pets and leave the store satisfied. They could each buy a puppy, a kitten, and a hamster, or they could each buy a different combination of the three types of pets.
How many different pet options can Alice, Bob, and Charlie choose from before feeling satisfied?Alice, Bob, and Charlie can leave the pet store satisfied in 12 different ways.This can be shown using a combination equation, where n = the number of items (in this case, pets) and r = the number of selections (in this case, 3): C(n,r) = n! / (r! × (n - r)!). In this equation, n = 29 (15 puppies + 6 kittens + 8 hamsters) and r = 3 because Alice, Bob, and Charlie each have to select one pet.When plugging these numbers into the equation, the result is C(29,3) = 29! / (3! × (29 - 3)!) = 29! / (3! × 26!) = 8649 / 514880 = 12 different ways. Alice, Bob, and Charlie can each select a puppy, a kitten, and a hamster and leave the store satisfied in 12 different ways.Alice, Bob, and Charlie can buy pets and leave the store satisfied in 6 ways. Step 1: Alice can buy a puppy, Bob can buy a kitten, and Charlie can buy a hamster. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 2: Alice can buy a kitten, Bob can buy a hamster, and Charlie can buy a puppy. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 3: Alice can buy a hamster, Bob can buy a puppy, and Charlie can buy a kitten. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 4: Alice can buy a puppy, Bob can buy a hamster, and Charlie can buy a kitten. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 5: Alice can buy a kitten, Bob can buy a puppy, and Charlie can buy a hamster. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. Step 6: Alice can buy a hamster, Bob can buy a kitten, and Charlie can buy a puppy. This would leave the store with 14 puppies, 5 kittens, and 7 hamsters. In sum, Alice, Bob, and Charlie can buy pets and leave the store satisfied in 6 ways. Each person can buy a different kind of pet and the store will still have the same number of pets afterwards.To learn more about the combination theory refer to:
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plsss help
For the given polynomial, determine which of the binomials listed are factors. Pick two.
f(x) = 2x3 + 9x2 + 13x + 6
A.x + 1
B.x – 1
C.x + 2
D.x – 2
E.x + 3
F.x – 3
The factors for the Polynomial are (x+1) and (x+2).
What is Factor Theorem?According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0.
Given:
f(x) = 2x³ + 9x² + 13x + 6
Now, first (x+1) =0
x= -1
put x= -1 in f(x) as
f(-1) = 2(-1) + 9(1) + 13(-1) + 6
= -2 + 9 - 13 + 6
= 0
So, (x+1) is factor of f(x).
Now, second (x-1)= 0
x= 1
put x= 1 in f(x) as
f(1) = 2(1) + 9(1) + 13(1) + 6
= 2 + 9 + 13 + 6
= 31
So, (x-1) is not a factor of f(x).
Now, second (x+2)= 0
x= -2
put x= -2 in f(x) as
f(1) = 2(-2)³ + 9(-2)² + 13(-2) + 6
= -16 + 36 - 26 + 6
= 0
So, (x+2) is factor of f(x).
Now, second (x-2)= 0
x= 2
put x= 2 in f(x) as
f(1) = 2(2)³ + 9(2)² + 13(2) + 6
= 16 + 36 + 26 + 6
= 84
So, (x-2) is not a factor of f(x).
Now, second (x+3)= 0
x= -3
put x= -3 in f(x) as
f(1) = 2(-3)³ + 9(-3)² + 13(-3) + 6
= -54 + 81 - 39 + 6
= -6
So, (x+3) is not a factor of f(x).
Now, second (x-3)= 0
x= 3
put x= 3 in f(x) as
f(1) = 2(3)³ + 9(3)² + 13(3) + 6
= 54 + 81 + 39 + 6
= 180
So, (x-3) is not a factor of f(x).
Learn more about factor theorem here:
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