When a number is multiplied by itself, the result is the perfect square. The same two binomials are multiplied to produce the perfect square trinomial, which is an algebraic expression. This is the first condition to know that a given trinomial is a perfect trinomial.
A binomial expression has two terms, a variable and a constant, which are either separated by the "+" or "-" sign, whereas a trinomial expression has three terms. The "+" or "-" sign is used to denote the separation of terms in trinomials as well. There are typically two forms of a perfect square trinomial. in other words, a2 + 2ab + b2 or a2 - 2ab + b2. Let's now examine the procedures for converting a given binomial into a perfect square trinomial and vice versa. If a trinomial is given, we can determine if it is a perfect square trinomial.To learn more about polynomials here
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(05.05 MC)
Using the two-way table, what percentage of the students that do not like to travel out of state like camping? Round to the nearest whole percent.
Likes Traveling Out of State Does Not Like Traveling Out of State Row totals
Likes Camping 52 38 90
Does Not Like Camping 36 74 110
Column totals 88 112 200
a
32%
b
34%
c
38%
d
42%
AND
(05.05 LC)
Dean collected data on the favorite sports of the students of two grades. The table shows the relative frequencies of rows for the data collected:
Favorite Sport
Swimming Running Volleyball Row totals
Grade 8 0.17 0.24 0.05 0.46
Grade 9 0.14 0.18 0.22 0.54
Column totals 0.31 0.42 0.27 1
Based on the data, which statement is most likely correct?
a
In Grade 8, 17 students liked swimming.
b
In Grade 9, 27% of students liked volleyball.
c
In Grade 9, 14 students liked running.
d
In Grade 9, 18% of students liked running.
The percentage of the students that do not like camping like travelling out of state is 33% and this can be determined by using the given data.
what is meant by camping?
The statement is most likely In Grade 9, 18% of students liked running is a correct answer.Based on the data, in grade9, 27 of student liked volleyball most likelyed.Using the two-way table, what percentage of the students that do not like to travel out of state like camping near whole percent is 42%.Camping is an outdoor activity that involves spending the night somewhere other than your house, either without shelter or with just a tent or other form of portable shelter.Usually, people travel from more urbanized regions to spend time outside in more rural ones in search of enjoyable or educational activities.Camping is distinguished from day trips, picnics, and other equally brief recreational activities by the night (or more) spent outside.To the complete questions is;
Likes Traveling Out of State Does Not Like Traveling Out of State Row totals Likes Camping 52 38 90
Does Not Like Camping 36 74 110
Column totals 88 112 200
a)32% b)34% c)38% d)42%
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What is the nature of roots of the quadratic equation 5x² 2x 3 0?.
The roots are hypothetical, meaning that they have two false roots. As a result, a quadratic equation has real, unequal, and irrational roots.
What is the roots equation's nature?The quadratic equation with roots ax2 + bx + c = 0 has real and unequal roots when a, b, and c are real numbers, a 0, and the discriminant is positive.
5x 2 2x+3=0 a=5, b=2, c=3, D=b 2 4ac D=56 0
What kind of roots are they?The equation's nature of roots indicates whether it contains rational, irrational, or fictitious roots. Imaginary roots and unreal roots are synonyms.
What makes a quadratic equation what it is?A degree two equation of the form ax2+bx+c = 0—where an is not equal to 0—is a quadratic equation. The quadratic equation's roots are the value of x in this equation. The only roots of a quadratic equation are two. These roots can have both real and made-up characteristics.
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Full Question = Write the nature of roots of the quadratic equation 5x2 - 2x + 3 = 0.
12 times 12=144
I think
Answer:yes
Step-by-step explanation:
Answer:
correct
Step-by-step explanation:
1. There are 12 boys and 18 girls in a
Math class. What is the ratio of girls
to total students? (6.RP.1)
*
Answer: 3:5
Step-by-step explanation:
total students: 12+18=30
ratio: 18 girls :30 students total
simplify: 18/6 : 30/6= 3:5
Why are the values for sine and cosine equal at 45?.
Answer: In an equilateral triangle, the hypotenuse and its opposite side are equal
By the way, I am human. There is too many bot answers.
The values for sine and cosine are equal at 45 degrees because they are related to the right triangle formed by the angle.
In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. The cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse.
When the angle is 45 degrees, the triangle formed is a 45-45-90 triangle, this is a special triangle in which all the angles are 45 degrees and all the sides are in the ratio of 1:1:√2.
In this triangle, the hypotenuse is √2 times the length of either leg. So, the sine of 45 degrees is opposite/hypotenuse = (1/√2) and the cosine of 45 degrees is adjacent/hypotenuse = (1/√2). Since the opposite and adjacent sides are of the same length in the 45-45-90 triangle, the sine and cosine of 45 degrees are equal.
So, sine 45 = cosine 45 = 1/√2.
About one through 2% of the population ha red hair. If 800 people were randomly ampled about how many of them would you expect to be redhead?
We would expect about 16 people in a sample of 800 people to be redheads, give or take some random variation.
What is probability ?
Probability is the measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain. Probability can be expressed as a fraction, decimal, or percentage. For example, a probability of 0.5 is the same as a probability of 1/2 or 50%.
The probability of an event can be calculated by counting the number of favorable outcomes and dividing by the total number of possible outcomes.
If 2% of the population has red hair, we can expect 2 out of every 100 people in the population to be redheads. To find out how many redheads we would expect in a sample of 800 people, we can use this proportion and multiply it by the number of people in the sample.
2/100 * 800 = 16
So, we would expect about 16 people in a sample of 800 people to be redheads, give or take some random variation.
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Chance is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes the impossibility of an occurrence and 1 denotes its certainty. It is possible to represent probability as an integer, decimal, or percentage. A probability of 0.5, for instance, is equivalent to a possibility of 1/2 or 50%.
By counting the favorable outcomes and dividing by the total number of potential outcomes, one can determine the probability of an occurrence.
We can anticipate that 2 out of every 100 people in the community will have red hair if red hair makes up 2% of the population. We can calculate the proportion of redheads we would anticipate in an 800-person group by
please help with this coordinates question
Answer:
Coordinates of C are (22, 20)
Step-by-step explanation:
We can see the squares are identical
The x-distance between A and B is 38 - 6 = 32
This covers 4 squares so each square side length = 32/4 = 8
Since point C is two squares away, the x-coordinate of C is 8 x 2 = 16 units away from the A x coordinate
x-coordinate of C = x-coordinate of A + 16 = 6 + 16 = 22
So x-coordinate of C is 22
To find the y-coordinate of C, because it is a square each vertical side of the square is also 8 units
If the third square were aligned with the top right of the second square, the y-coordinate of that square should be :
y-coordinate of A + 2 x 8 = 7 + 16 = 23
In this case, the y-coordinate of B should have been 23 + 2 x 8 = 23 + 16 = 39
However, because of the downward shift of the third square, the y-coordinate of B is only 36
39-36 = 3
So the third square has been shifted down by 3
Therefore y coordinate of C = 23 - 3 = 20
Coordinates of point C: (22, 20) which will result in the figure shown.
Just to verify
Since point B is 16 units to the right of C, its x-coordinate = 22 + 16 = 38
Point B
Point B y-coordinate is 16 units vertically up from y-coordinate of C.
So y-coordinate of B = 20 + 16 = 36
Hence verified
I hope that makes sense.
The attached figure shows exactly the figure in the question but with the coordinates marked. You can independently verify this
The ratio to the total number of tudent in cla i 4 to 7. How many tudent are girl if the cla ha 21 tudent in all
There are total of 12 girls in the class.
what is ratio?A mathematical comparison of two or more values or quantities is called a ratio. It can be used to compare the relative sizes or amounts of various items since it expresses the relationship between the values in terms of a proportion or a fraction.
Let the number of girls in the class be x and the number of boys in the class be y
so total number of students in the class is x+y
ration of number of girls to the total number of students is x/(x+y)
given that total number of student is x+y which is 21
so x/21 = 4/7
=> x= (21*4)/7
=> x= 3*4
=> x=12
so the total number of girls in the class is 12.
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Complete question:
The ratio of girls to the total number of students in class is 4 to 7. How many students are girls if class has 21 students in all?
Identify the type of display that would be most appropriate for the description of the given data set.
The number of pets in each student's household.
A BAR graph would be most suitable for displaying the given data.
What is the purpose of a graph?The visual representation of numerical data is a graph. Graphs offer a visual means of presenting complicated data and demonstrating the link between various variables or data sets. Graphs are a fantastic tool for highlighting patterns and connections in data.
Given data, The number of pets in each student's household.
Stem-and-leaf plot:
A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. As data are gathered, they are organised using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. The term stems from the fact that each number in the data is divided into a stem and a leaf.
Thus it is not suitable for given data.
Line graph:
An individual data point is connected by a line in a line graph, sometimes referred to as a line plot or a line chart. A line graph shows numerical values over a predetermined period of time. Line graphs are frequently used in finance to show the historical price movement of an asset or instrument.
Since, we have similar but Discrete with three variables in our data thus this graph is also not suitable.
Bar graph:
A bar graph (also known as a bar chart or bar diagram) is a visual tool that uses bars to compare data among categories. A bar graph may run horizontally or vertically.
Since we need to compare the data thus, bar graph is most suitable for the giving condition.
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How is the graph of y =- 3?.
Its slope is 0, which indicates that it is a horizontal line, and its
y-intercept is −3.
When an equation of a line has only one variable, the resulting graph is a horizontal or a vertical line.
The graph of the line x=a
, where a is a constant, is a vertical line that passes through the point (a,0) . Every point on this line has the x-coordinate equal to a, regardless of the y-coordinate.
The graph of the line y=b , where b is a constant, is a horizontal line that passes through the point (0,b) . Every point on this line has the y-coordinate equal to b, regardless of the x-coordinate.
We can write
y=−3
as
y=0x−3
So, its slope is 0, which indicates that it is a horizontal line, and its
y-intercept is −3. Hence, its graph looks like
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Please help! Each pair of polygons us similar. Find each missing side measure
Answer:
x = 3
Step-by-step explanation:
18/2 = 27/x
9/1 = 27/x
9x = 27 × 1
x = 3
Answer:
x = 3 because 18 divided by 2 equals nine, also meaning that 2 x 9 = 18. Now since we figured out that 9 is how many times more/less the number is between the polygons. (I'm so sorry if I can't explain clearly) Now we just get 27 and divide it by 9 which leaves us with our answer 3.
What is the area of triangle with base 4. 8 cm and hight 3. 6 cm?.
The area of a triangle with a base of 4.8 cm and height of 3.6 cm is 8.64 cm².
Area of triangle = ½ × base × height
= ½ × 4.8 × 3.6
= 8.64 cm²
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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the table below shows imformation about the distance walked by some hikers work out the minimum number of hikers who could have walked between 8 miles and 19 miles work out the maximum number of hikers who could have walked between 8 and 19 miles
PLEASE HELP!
The minimum number of hikers that could have walked between 8 miles and 19 miles is given as follows:
7.
The maximum number of hikers that could have walked between 8 miles and 19 miles is given as follows:
17.
How to obtain the amounts?The frequency table gives the number of observations on each interval.
Then the minimum number of hikers that could have walked between 8 miles and 19 miles is obtained when:
All the 4 observations in the interval 5 <= x < 10 are less than 8.All the 6 observations in the interval 15 <= x < 20 are more than 19.Hence the minimum amount is of 7.
The maximum number of hikers that could have walked between 8 miles and 19 miles is obtained when:
All the 4 observations in the interval 5 <= x < 10 are more than 8.All the 6 observations in the interval 15 <= x < 20 are less than 19.Hence the maximum amount is of 4 + 7 + 6 = 17.
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If 11/5x5^x-5^x-1=50,then find the value of x
Answer:
1.77865216
Step-by-step explanation:
For what value of k does the system of equations kx 2y 5 and 3x 4y 10 have no solution?.
Hence value of k does the system of equations k x +2y= 5 and 3x - 4y =10 have no solution[tex]\frac{-3}{2}[/tex]
The given system of equations:
k x + 2y = 5
⇒ k x + 2y - 5 = 0 ….( i)
3x - 4y = 10
⇒3x - 4y - 10 = 0 …(ii)
These equations are of the forms:
a1x + b1y + c1 = 0
a2x + b2y + c2 =0
where, a1 = k
b1 = 2
c1 = -5
a2= 3
b2 =-4
c2 = -10
[tex]\frac{a1}{a2} \neq \frac{b1}{b2}[/tex]
[tex]\frac{k}{3} \neq \frac{2}{-4}[/tex]
[tex]k\neq \frac{-3}{2}[/tex]
Thus for all real values of k other than −3/2 ,
the given system of equations will have a unique solution.
(ii) For the given system of equations to have no solutions, we must have:
[tex]\frac{a1}{a2} = \frac{b1}{b2}\neq \frac{c1}{c2} \\\\ \frac{k}{3} = \frac{2}{-4}\neq \frac{-5}{-10} \\ \\ \frac{k}{3} = \frac{2}{-4}\\ \\ \frac{k}{3} \neq \frac{1}{2} \\ \\ \\k \neq \frac{3}{2} \\\\k =\frac{-3}{2} \\[/tex]
Hence value of k does the system of equations k x +2y= 5 and 3x - 4y =10 have no solution[tex]\frac{-3}{2}[/tex]
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A bag contains 6 red marbles, 5 blue marbles and 4 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be blue?
The exact probability that would make the three marbles to be blue is 6/273,
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability that exactly three marbles drawn would be blue = (number of blue marbles / total number of marbles) x [(number of blue marbles / total number of marbles) - 1] x [((number of blue marbles / total number of marbles) - 1]
Total number of marbles = 6 + 5 + 4 = 15
= (5/15) x (4/14) x (3/13) = 6/273
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What is vertex form of a quadratic equation?.
The vertex form of a quadratic equation is written as y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola and a is the leading coefficient.
The vertex form can be converted from the standard form (y = ax^2 + bx + c) by completing the square and shifting the parabola horizontally and vertically.
The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola, which is the lowest point for a parabola that opens upwards, and highest point for a parabola that opens downwards. The "a" coefficient is the leading coefficient which represents the direction of the parabola, whether it opens upwards or downwards. The vertex form is useful in identifying the vertex of the parabola and its symmetry axis, as well as its direction.
So, the vertex form of a quadratic equation is written as y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola and a is the leading coefficient.
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How do you find the standard deviation of a sample mean and n value?.
Divide the population standard deviation () by the square root of the sample size (n) to obtain the standard deviation of the sample mean (X).
How can the distribution of sample means' mean and standard deviation be determined?The sample mean is normally distributed, with mean X= and standard deviation X=/n, where n is the sample size, for samples of any size taken from a population that is normally distributed.
How is the sampling distribution's SD determined?The standard deviation of the population divided by the square root of the sample size is equal to the standard deviation of the sampling distribution of means.
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There are 5280 feet in a mile and about 3.28 feet in a meter. Given that sound travels about 343 meters per second what’s is the distance in miles from alyssa to the lighting bolt
Answer: We know that sound travels about 343 meters per second. To convert the distance in meters to miles, we need to use the conversion factor that there are 3.28 feet in a meter and 5280 feet in a mile.
1 mile = 5280 feet = 5280/3.28 meters = 1600 meters
Therefore, the distance in miles from Alyssa to the lightning bolt can be calculated by dividing the distance in meters by the number of meters per mile:
distance in miles = distance in meters/1600
So, the distance in miles from Alyssa to the lightning bolt is 343 meters/1600 miles = 0.215 miles (approx)
Note that this calculation is based on the assumption that sound travels 343 meters per second and it's an approximation.
Step-by-step explanation:
What is the definition of the sine ratio in a right triangle?.
The trigonometric ratio sine compares the lengths of the right triangle's two sides. Sin, though commonly abbreviated to sin, is actually pronounced sine.
If you know at least one side of the triangle and one of the acute angles, you can use this function to calculate the length of the side.The trigonometric ratio sine compares the lengths of the right triangle's two sides. Sin, though commonly abbreviated to sin, is actually pronounced sine. If you know at least one side of the triangle and one of the acute angles, you can use this function to calculate the length of the side. In a nutshell, the sine, cosine, and tangent ratios are the three basic trig ratios.To learn more about the sine triangle here
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What is the slope of the line that contains
the points (13, -2) and (3,-2)?
-2/5
O o
O-5/2
indefined
Slope of the line that contains the points (13, -2) and (3,-2) is 0.
What is Slope of line?
The increase divided by the run is the slope. By examining the rise and run, you can infer the slope of a line from its graph. A line has the property that its slope remains constant throughout. Therefore, you may determine the slope by selecting any two points along the line's graph.
By definition, the slope or gradient of a line describes its steepness, incline, or grade.
m = y2 - y1/x2 - x1
Given ;
x1 =13, x2 = 3, y1 = -2, y2 = -2
ΔX = x2-x1
ΔX = 3 - 13
ΔX = -10
Now, calculating ΔY ;
ΔY = y2 - y1
ΔY =-2 - (-2)
ΔY = 0
Hence, Slope of the line is ;
Slope(m) = ΔY/ΔX
Slope(m)= 0/-10
Slope (m) = 0
Therefore , Slope of the line that contains the points (13, -2) and (3,-2) is 0.
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Can someone help me on this and show me how to do it like show the work
Answer:
381 feet
Step-by-step explanation:
You are 220 ft from a tree whose top you see at a 60° angle of elevation. You want to know the height of the tree.
TangentThe tangent relation between sides of a right triangle is ...
Tan = Opposite/Adjacent
where "opposite" and "adjacent" refer to the sides opposite and adjacent to the acute angle of interest.
ApplicationHere, the 60° angle of elevation is adjacent to the 220 ft distance from the tree, and opposite the height of the tree. This means ...
tan(60°) = height/(220 ft)
Multiplying by 220 ft, we find the height to be ...
height = (220 ft)tan(60°) = 220√3 ft ≈ 381 ft
The tree is 381 feet tall.
__
Additional comment
The triangle that models this geometry is a 30°-60°-90° right triangle, one of the "special" right triangles that often shows up in geometry and trigonometry problems. Its side lengths have the ratio 1 : √3 : 2. Knowing this, you know the tree height is √3 times the distance from the tree:
220√3 ft
Your calculator can tell you this is about 381 feet.
To find the height of the tree, we can use the tangent function, which relates the opposite side (the height of the tree) to the adjacent side (the distance from the tree) and the angle. The formula is:
Why is it referred to as a tangent function?
Tangent is derived from the Latin verb tangere, which means "to touch." A circle has one point where a line that is tangent to it intersects.
tangent(angle) = opposite / adjacent
In this case, the angle is 60 degrees, the opposite side is the height of the tree, and the adjacent side is the distance from the tree, which is 220 feet. So we can write:
tan(60) = height / 220
To find the height, we can divide both sides by the tangent of 60 degrees:
height = 220 * tan(60)
The exact value of the height of the tree is not possible to be obtained with the given information, the height of the tree is a number in the infinite set of real numbers.
We can use a calculator or a table of tangents to find an approximate value of the height.
It could be around 379.3 ft.
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two radios were bought at the same cost one was sold at a profit of 12% and the other at the profit of 17% if the difference in the selling price of the two radios was 125 what was the cost of each radio
HELPP PLEASE ITS URGENT!!!!!!
Answer:
ans is= Rs.2925. . . . . . .
helphelp plsssssssss
-8 hshdjdbdkdndidjdndjdodjfodjdjd
Step-by-step explanation:
2*(-2)-4=
-4-4=
-8
find the logarithmic function [tex]f(x)=\log _(_a_)(x-h)[/tex] that describes each graph.
The form of function is a logarithmic function. either "y equals the log of x, base b" or "y equals the log, base b, of x."
What is logarithmic function?
An exponential function's inverse is a logarithmic function. An exponential function's basis is the same as that of a log function. Exponents include logarithms. f(x) = bx is the formula for the exponential function. f(x) = log base b of x is how the logarithmic function is expressed.
The expression "y equals the log of x, base b" or "y equals the log, base b, of x" is the definition of a logarithmic function. In both cases, b > 0, b 1, and x > 0. There are no limitations on y. logarithm, the exponent or power that a base must be increased to in order to get a specific number. If bx = n, then mathematically, x is the base-b logarithm of n.
Determine the logarithmic function of the provided graph by using the provided points in the following manner:
[tex]f(x) = log_a(x-h)[/tex]
Create two equations by substituting the provided points (3/2, 1) and (3, -1) into the formula:
[tex]log_a(\frac{3}{2}-h) = 1[/tex]
[tex]log_a({3}-h) = -1[/tex]
To isolate a, use the log law and rearrange each equation:
[tex]log_a(\frac{3}{2}-h) = 1[/tex]
⇒ [tex]a^1 = (\frac{3}{2}-h)[/tex]
⇒1/a = 3 - h
⇒ a = 1/ [tex]\frac{3}{2}[/tex] - h ....................................(1)
[tex]log_a({3}-h) = -1[/tex]
⇒[tex]a^{-1} = ({3}-h)[/tex]
⇒ 1/a = 3-h
⇒ a = 1/3-h ..............................................(2)
Solve for h:
⇒ 3/2 - h = 1/3-h
⇒ 3-2h/2 = 1/3-h
⇒ 9 - 9h + 2h^2 = 2
⇒(2h-7)(h-1) = 0
⇒ h = 7/2, 1
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Spin a spinner with three equal sections colored red, white, and blue. what is p(yellow)? a. 33%b. 0% c. 100% d. 66%
Spinning a spinner with three equal sections colored white, red, and blue yield the probability of having yellow color is B: '0%', i.e p (yellow) = 0%.
As in the given scenario where a spinner with white, red, and blue colors is rolled and is asked about determining the p(yellow). That is the probability of getting yellow at which the spinner stops. It is clearly written that the spinner has three sections of equal colors which are red, blue and white. And there is no section on the spinner with yellow color, so it is not possible to get yellow color over rolling of the spinner.
It means that 0% probability exists for yellow color.
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Complete each congruency statement, and name the rule used.
If you cannot show the triangles are congruent from the given information, leave
the triangle's name blank and write CNBD for "CanNot Be Determined" in place
of the rule.
Answer: [tex]\triangle LAW \cong \triangle WKL[/tex] by ASA
Step-by-step explanation:
[tex]\angle AWL \cong \angle WLK[/tex] (right angles)[tex]\angle ALW \cong \angle LWK[/tex] (given)[tex]\overline{WL} \cong \overline{WL}[/tex] (reflexive)Therefore, [tex]\triangle LAW \cong \triangle WKL[/tex] by ASA.
Re-write the quadratic function below in Standard Form
y= 4(x-7)(x-1)
Standard form of the quadratic function is,
⇒ y = 4x² - 32x + 28
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The quadratic equation is,
⇒ y = 4 (x - 7) (x - 1)
Now, We can simplify the equation in standard from as;
⇒ y = 4 (x - 7) (x - 1)
⇒ y = 4 (x² - x - 7x + 7)
⇒ y = 4 (x² - 8x + 7)
⇒ y = 4x² - 32x + 28
Thus, The standard form is,
⇒ y = 4x² - 32x + 28
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Find the size of the angle marked y, correct to three significant figures
The size of the angle marked y correct to three significant figures is 26.6°.
What is Right Angled Triangle?Right angled triangle are those triangle for which one of the angle is 90 degrees.
Given is a right angled triangle.
By the definition of trigonometric functions,
Sin y = Opposite side / Hypotenuse
sin y = 31.4 / 70.2
sin y = 0.447
y = 26.57
= 26.6
Hence the value of y is 26.6.
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Cahew and peanut are combined to make a nut mixture. At leat 1/4 of the mixture, by weight, i cahew, and the total weight of the mixture cannot exceed 48 ounce. Which ytem of inequalitie model thi ituation
The weight of the cashews plus the weight of the peanuts cannot be more than 192 ounces and the weight of the cashews must be at least one-fourth of the total weight of the mixture.
Step 1: Let c = weight of cashews
Step 2: Let p = weight of peanuts
Step 3: 0.25c + p ≤ 48
Step 4: Multiply both sides by 4
Step 5: 4(0.25c + p) ≤ 4(48)
Step 6: c + p ≤ 192
This system of inequalities models the situation of combining cashews and peanuts to make a nut mixture. The first inequality states that the weight of the cashews plus the weight of the peanuts cannot exceed 48 ounces, and the second inequality states that the weight of the cashews must be at least one-fourth of the total weight of the mixture. To model this situation, we let c equal the weight of the cashews and p equal the weight of the peanuts. We then multiplied both sides of the first inequality by four to get the second inequality, which states that the weight of the cashews plus the weight of the peanuts cannot exceed 192 ounces. This system of inequalities accurately models the situation of combining cashews and peanuts to make a nut mixture, and it ensures that the weight of the cashews is at least one-fourth of the total weight of the mixture.
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