An example of perpendicular equations are:
f(x)=2x+4
g(x)=[tex]\frac{-1}{2}\\[/tex]x+2
A straight line passing through a point is called a perpendicular line. It forms a 90-degree angle with a specific place where the line passes. The need for determining the perpendicular line is coordinates and a line equation.
Think about a line with the equation ax + by + c = 0 and the coordinates (x1, y1). The slope should be a/b. Let m1 and m2 represent the slopes of two lines; their product will be -1 if the lines are perpendicular to one another.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
m = Δy/Δx = dy/dx = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
A line's slope often indicates the steepness and direction of the line.
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Think about a line with the equation ax + by + c = 0 and the coordinates (x1, y1). The slope should be a/b. Let m1 and m2 represent the slopes of two lines; their product will be -1 if the lines are perpendicular to one another.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
m = Δy/Δx = dy/dx = change in y/change in x
where "m" represents a line's slope.
Graphing root functions
Really need help with the 4 questions
what is the slope between (7,-4) and (2,-4)
Answer:
0
Step-by-step explanation:
Rise over run.
Difference between y is 0.
Difference between x is 5.
0/5 = 0.
Answer:
m = 0
Step-by-step explanation:
Slope is rise/run or (y2 - y1) / (x2 - x1)
We see the y stay the same, and the x decrease by 5, so the slope is
m = 0/5
How do I calculate how much paint I need?
According to good rule of thumb is 250 to 400 square feet per gallon for each coat, and 170 to 200 square feet per gallon for two coats.
It might be challenging to calculate or estimate the precise amount of paint that you will need when painting your home.
Every paint has a spread rate that controls how many square feet may be covered each gallon. A good rule of thumb is 250 to 400 square feet per gallon for each coat, and 170 to 200 square feet per gallon for two coats. Choosing the proper quantity of paint for steel is a tough matter because high-quality paint is expensive and you don't want to overbuy. To avoid overbuying paint, we advise simply purchasing 80% of the projected amount at first and the remaining 20% after you are nearly completed.
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what’s the equation when the points are (3,-6) and (5,-5)
Answer:0.5x - y -7.5 = 0
Step-by-step explanation:
What degree is a 3 to 1 slope?
Answer:
Slope
Angle (degrees) Gradient Grade (%)
2 to 1 = 3.493 to 1 = 5.244 to 1 = 6.99Therefore, the correct answer is 5.24
Alyssa is 1.65 meters tall. At 11 a.m., she measures the length of a tree's shadow to be 27.75 meters. She stands 23.5 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answer:
The tree is 10.77 meters tall.
Step-by-step explanation:
The given diagram is an example of similar triangles. Look at the image I attached to my response to see this problem in terms of triangles.
The triangle that is formed by Alyssa and her shadow and the triangle that is formed by the tree and its shadow is an example of similar triangles because they both share an internal angle.
As per the similar triangles theorem, the ratios of the corresponding sides of both sides are proportional.
Thus, we have to make a proportion of the corresponding sides of both triangles to solve for the height of the tree. Let x = the height of the tree.
Proportion: [tex]\frac{BE}{BC} = \frac{DE}{AC}\\[/tex]
BE = 4.25 meters
BC = 27.75 meters
DE = 1.65 meters
AC = x meters
[tex]\frac{4.25}{27.75} = \frac{1.65}{x}[/tex]
Now, cross multiply to solve for x.
[tex]4.25x = 1.65(27.75)\\4.25x = 45.7875\\x = 10.77[/tex]
∴ The tree is 10.77 meters tall!
The height of the tree to the nearest hundredth of a meter is,
⇒ 10.77 meters
We have to given that;
Alyssa is 1.65 meters tall. At 11 a.m., she measures the length of a tree's shadow to be 27.75 meters. She stands 23.5 meters away from the tree.
Now, we can make a proportion of the corresponding sides of both triangles to solve for the height of the tree.
And, Let us assume that,
x = the height of the tree
Hence, We get;
⇒ (27.75 - 23.5) / 27.75 = 1.65 / x
Solve for x;
⇒ 4.25 / 27.75 = 1.65 / x
Cross multiply we get;
⇒ 4.25x = 1.65 x 27.75
⇒ 4.25x = 45.78
⇒ x = 10.77 meters
Thus, The height of the tree to the nearest hundredth of a meter is,
⇒ 10.77 meters
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Is equidistant from all points on the circle?
The point from which all the points on a circle are equidistant is called the center of the circle, and the distance from that point to the circle is called the radius of the circle. A circle is named with a single letter, its center.
Every point in a circle is equally distance from the center. Similar to a sphere, every point on a sphere is equally distance from the center.
Two equal chords on a circle indicate that they are equally spaced from the circle's center.
The incenter of a triangle is the point that is equally far from each of its sides. A median is a line segment that has one of its endpoints in the vertex of a triangle and the other endpoint in the midpoint of the side opposite the vertex. The three medians of a triangle meet in the centroid.
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find the x number i will gave 10 points
Answer:
x is 5 cm
Step-by-step explanation:
x is half of the diagonal and we can see that the diagonal is 10 cm
and half of 10 is
The square root of a negative number is supposed to not exist/be an imaginary number.
Am I right? Is this operation right?
Answer: You are correct, because negative number don't have real square roots
Step-by-step explanation:
Can a 2 year old count?
Therefore , the 2 year old children can able to count to 1 to 100 counting by making them learn.
By counting, what do you mean?The counting-on method can be used by mathematicians to add numbers. With this approach, a student first adds the larger number,
variable then "counts on" with the other addends to arrive at the sum. If the number sentence is 4 + 3, the student will understand that 4 is the greater number and will add three additional numbers, such as the integers "4... 5, 6, 7."
Here,
Every child is different in how they grow and learn, yet many
Children as young as two years old may count past ten and learn their numbers from 1 to 100.
They could be ready to try numbering in fives or using other skip counting strategies (5, 10, 15, 20, and so on).
As soon as you can, begin teaching your child how to recognise
numbers.
As a result, by making the toddlers study, two-year-olds can count to one hundred.
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What are the roots of the quadratic equation 4x 2 − 7x 2 0?
The roots of the quadratic equation 4x2 − 7x + 0 are -7/4 and 0.
What is quadrtic ic equation?A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. Quadratic equations are used to solve problems involving areas, lengths, and other geometric figures, as well as to find unknown values. Such equations are often used in calculus and physics.
To find the roots, you can use the quadratic formula, which is x = -b ± √b2 - 4ac/2a. In this case, a = 4, b = -7, and c = 0, so the roots are -7/4 and 0.
Another way to find the roots is to use the factoring method. To factor 4x2 − 7x + 0, you can factor out 4x and then group the terms to get 4x(x − 7) + 0. Then you can set each factor equal to zero to get x = 0 and x = 7. Therefore, the roots of the equation 4x2 − 7x + 0 are -7/4 and 0.
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There are 6 seniors on student council. Two of them will be chosen to go to
an all-district meeting. How
many ways are there to choose the students who
will go to the meeting?
Decide if this is a permutation or a combination, and then find the number of
ways to choose the students who go.
By using the property of combination, it can be calculated that -
This is a problem of combination.
There are 15 ways to choose the students who will go to the meeting
What is combination?
Combination is the process of selection some objects from a group of items where the order of the selection do not matter
This is a problem of combination
Number of seniors = 6
Number of students will go to the all district meeting = 2
Number of ways to choose the students who will go to the meeting =
[tex]{6 \choose 2}[/tex]
= [tex]\frac{6!}{(6 - 2)! \times 2!}[/tex]
= 15
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Six lines are drawn, no two of which are parallel. If no more than two of the lines pass through any one point, what is the number of triangles formed?
Answer: I believe 20.
Take one pair of lines. They will intersect at a point (no lines parallel). The other four lines will intersect at different points (no more than two lines through one point) giving four triangles. There are 6C2 = 15 different pairs of lines so 15*4 = 60 triangles. However, each triangle will come from three different points so we need 60/3 = 20 distinct triangles.
EDIT: Now that I’m more awake, it occurs to me there is a much easier answer. Since no two lines are parallel and no three lines are coincident, every combination of three lines must form a triangle. There are 6C3 = 20 triangles.
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
combinations
C(n,r)= n! / (r! * (n−r)!)
n = 6 : total number of lines
r = 3 : because its 3 lines to make a triangle
6 lines
6C3 = 20 triangles
quora glenn clemens
mathplanet
Bisecting Bakery sells cylindrical round cakes. The most popular cake at the bakery is the red velvet cake. It has a radius of 15 centimeters and a height of 12 centimeters.
If everything but the circular bottom of the cake was iced, how many square centimeters of icing is needed for one cake? Use 3.14 for π and round to the nearest square centimeter.
The Answer Is 1,837 cm
Given an angle t that corresponds to the point (- 3 squared/2, 1/2) on the unit circle show
below, find cos(t) and sin(t).
Answer:
Step-by-step explanation:
Your question asks what is -[tex]3^{2}[/tex] / 2 but, since it's on the Unit circle, I know you meant - [tex]\sqrt{3}[/tex] /2 Also, it's one of those known angles on the unit circle.
note that the angles can all be put in the form of [tex]\sqrt{x}[/tex] / 2 , where x = 0,1,2,3,4 , for the five special points on the unit circle.
as the attached pic shows, Cos(t) for the given point would be 180-150°= 30 and sin(t) would be 90 - 30 = 60 °
it's not easy to understand how I got those angles, just ask if you don't get it. :)
4. Volume of a cone is (1/3)3.14r²h. Solve for h.
The required solution would be h = 3Vr²/3.14 for h, where V is the volume of a cone.
What is the volume of a cone?The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.
The volume of the cone (V ) = 1/3πhr²
We have been given that the volume of a cone is (1/3)3.14r²h
We have to determine the solution for h
As per the given question, we have
⇒ V = (1/3)3.14r²h
Multiply by 3 into the above equation,
⇒ 3V = 3.14r²h
Divided by 3.14 into both sides
⇒ 3V/3.14 = r²h
⇒ h = 3Vr²/3.14
Therefore, the required solution would be h = 3Vr²/3.14.
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The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots. How many two-point and three-point shots did the Cruisers score?
The number of two-points and three points shot The Cruisers scored are 24 and 19 points respectively.
How to find the number of two and three points made?The Cruisers scored a total of 105 points in a basketball game. They also had a total of 43 baskets, of which some were two-point shots and some of were three-point shots.
Therefore, the number of two-points and three-points the cruiser scored is as follows:
x = number of two-points
y = number of three-points
So;
x + y = 43 -------1
Also;
2x + 3y = 105 -----2
Multiplying equation(1) by 2
2x + 2y = 86
2x + 3y = 105
Subtract equation(i) from equation(ii)
y = 19
To find x:
x = 43 - 19
x = 24
Therefore,
number of two-points = 24
number of three-points = 19
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How do you make 5 with 4 2s?
The equation to form 5 with 4 2s is 2 + 2+ (2/2).
Explain the method of BODMAS?Children can use the acronym BODMAS to help them remember the right order to carry out mathematical operations while solving problems.
B-Brackets, O-Orders (powers/exponents as well as roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction are all abbreviated as BODMAS.The acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction, is also known as BODMAS in some areas.Brackets, then order (or "of" in some curricula), next multiplication and division, finally addition and subtraction is an acronym for the order of operations in mathematics, with B coming first and AS coming last.The formation of 5 with 4 2s is -
= 2 + 2+ (2/2)
= 2 + 2 + 1
= 5
Thus, the expression to form 5 with 4 2s is 2 + 2+ (2/2).
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If your starting balance is $250, what is your new balance after a withdrawal of $56.50 and a deposit of $25.00?
Answer:
$218.5
Step-by-step explanation:
its $218.5 because 250 - 56.50 = 193.5 and 193.5 + 25.00 + 218.5
Which equation is the inverse of 2 x 2 )= 8 7 y?
[tex]y=2[/tex] ± [tex]\sqrt{28+4x}[/tex] is the equation that equals 2(x - 2)2 = 8(7 + y).
Addition and subtraction, multiplication, and division are examples of inverse operations, which are pairs of mathematical operations where one operation reverses the effects of the other. In most cases, a number's inverse refers to its reciprocal, or x - 1 = 1 / x. When a number is combined with its reciprocal, or inverse, the result is 1, or 1.
Considering the equation:
[tex]2(x-2)^2=8(7+y)[/tex]
Change the x and y variables.
[tex]2(y-2)^2=8(7+x)[/tex]
In terms of x, solve for y.
We have two sides, therefore divide them by two.
[tex](y-2)^2=4(7+x)[/tex]
Using the distribution property, [tex]a.(b+c)=a.b+a.c[/tex]
[tex](y-2)^2=28+4x[/tex]
Square-rooting both sides yields:
[tex]y-2=[/tex]±[tex]\sqrt{28+4x}[/tex]
our two sides plus two;
[tex]y=2[/tex]±[tex]\sqrt{28+4x}[/tex]
As a result, equation [tex]y=2[/tex]±[tex]\sqrt{28+4x}[/tex] is the opposite of [tex]2(x-2)^2=8(7+y)[/tex]
The complete question is:-
Which equation is the inverse of 2(x – 2)2 = 8(7 + y)?
Options:
–2(x – 2)^2 = –8(7 + y)
y= 1/4 x^2 -x -6
y= -2 +/- sqrt of 28+4x
y= 2 +/- sqrt of 28+4x
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What is the relationship between numerator and denominator?
The denominator of a fraction represents the number of equal parts in a whole, while the numerator represents the number of parts considered.
What is a fraction?A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator.In a simple fraction, they are both integers. A complex fraction has a fraction in either the denominator or the numerator. The denominator of a proper fraction is less than the numerator. A numerator is the total number of parts.A denominator is the lowest number in a fraction that represents the number of equal parts into which an item is divided. It is the fraction divisor.A fraction as p/q can be thought of as p parts, which is the numerator of a whole object, divided into q equal parts which is denominator.To learn more about fraction refer to :
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suppose the length of time (in minutes) going through customs at u.s. airports with global entry (goes) is normally distributed with a population mean of 40 minutes and a population standard deviation of 12 minutes. what is the approximate wait time for the fastest 4% of passengers?
The approximate wait time for the fastest 4% of passengers is approximately 29.29 minutes.
What is Standard Deviation?
It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
To find the approximate wait time for the fastest 4% of passengers, we need to use the normal distribution and the inverse normal distribution function.
The normal distribution is a continuous probability distribution that is symmetrical around the mean, and is defined by the mean and standard deviation. In this case, the mean wait time for passengers with global entry is 40 minutes and the standard deviation is 12 minutes.
The inverse normal distribution function is a mathematical function that takes a probability as input and returns the corresponding value from the normal distribution. In other words, it allows us to find the value that corresponds to a given percentile of the normal distribution.
To find the wait time for the fastest 4% of passengers, we need to find the value that corresponds to the 4th percentile of the normal distribution. To do this, we can use an inverse normal distribution calculator or a normal distribution table.
Plugging in the mean and standard deviation of the wait time and the percentile of 4, we get a value of approximately 29.29 minutes. This is the wait time for the fastest 4% of passengers.
So, The approximate wait time for the fastest 4% of passengers is approximately 29.29 minutes.
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solve this equation using zero product property and show the work
(x-5)(x+7)=0
According to question,
Given data,
We know that;
Zero product property,
ab =0
either a or b or both must be zero.
(x-5) (x+7) = 0
Where a=(x-5)
b= (x+7)
then,
x-5=0(both side equation adding +5)
+5=+5
So,
x = 5
therefore,
x+7=0(both side equation substrate -7)
-7=-7
So,
x=7
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Matt shot an 86 on the golf course on Monday then on Friday he shot a 95 what is the percentage of change rounded to the nearest 10th of a percent?
Answer:
increase 10.5 percent
Step-by-step explanation:
..
If the interior angle of triangle are 3x,4x,and5x find the ize of angle of the traingle. Alo fing the difference between larget and malleat angle
Answer:
45, 60, 75
Difference between the largest and smallest angles
75 - 40 = 35
Step-by-step explanation:
First solve for x. The sum of the interior angles of a triangle is 180
3x + 4x + 5x =180 Combine like terms
12x + 180 Divide both sides by 12
[tex]\frac{12x}{12}[/tex] = [tex]\frac{180}{12}[/tex]
x = 15
3x = 3(15) = 45
4x = 4(14) = 60
5x = 5(15) = 75
Step-by-step explanation:
please, burn this into your brain for life :
the sum of all angles in a triangle is always (yes, no exceptions) 180°.
so,
3x + 4x + 5x = 180
12x = 180
x = 180/12 = 15
3x = 3×15 = 45°
4x = 4×15 = 60°
5x = 5×15 = 75°
the difference between largest and smallest angle is therefore
75 - 45 = 30°
What is the median of 8 5 7 9 11 6?
For the given observation 5,6,7,8,9,11 the Median is 7.5
The median is one of the metrics of central tendency. The middle value in a group of numbers is known as the median. It divides a given data sample into the higher half and the lower half. At least half of the observations fall below the median and at least half of the observations fall above the median.
If a data collection contains an even number of observations, the median can be determined as follows:
Sort the information either by ascending or by descending.
Identify the (n/2)nd and [(n/2) + 1] th observations if there are an even number of observations (let's say n).
The median of the provided data is equal to the average of the top two observations (as determined in step 2).
Here n = 6, So [6/2 + (6/2)+1}/2
=> Median = 7.5.
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Can anyone help me answer this question?
Let A, B, C e sets. Which of the following properties is the cumulative law?
a. A ∪ B = B ∪ A
b. A ∩ B = B ∩ A
c. A ∩ B = B ∪ A
d. (A ∪ B) ∪ C = A ∪ (B ∪ C)
The property that represents the commutative law of sets is given as follows:
d. (A ∪ B) ∪ C = A ∪ (B ∪ C)
What is the commutative law of sets?The cumulative law of sets states that the order in which the union operation is made does not change the resulting set of these multiple union operations.
The symbol that represents the union operation is given as follows:
∪.
Hence statement d is the correct statement of the commutative law of sets, as:
In (A ∪ B) ∪ C, the union of A and B is first obtained, and then united with set C.In A ∪ (B ∪ C), the union of B and C is first obtained, and then united with set A.For both cases, the resulting set is the same.
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. a pole is carried down a hallway 9 ft wide. at the end of the hall, there is a right-angled turn into a narrower hallway 6 ft wide. what is the length of the longest pole that can be carried horizontally around the corner?
Using the geometry of the right angle triangle. Since, The narrower hallway is 6ft. The answer is 6ft.
What do you mean by geometry?A subfield of mathematics called geometry examines the dimensions, placements, angles, and sizes of objects.
What is a right angle triangle?A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.
Larger hallway= 9 ft
narrower hallway=6 ft
Since, After turning in the corner, The pole should be carried through the 6ft wide hall. The maximum length of the pole is 6ft.
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IQ scores are collected from a sample of 36 students
at a large university. The scores are summarized in
the histogram below.
Which of the following statements is true of the mean
and median?
O The mean is equal to the median IQ.
O The mean is less than the median IQ
O The mean is greater than the median IQ.
O It cannot be determined because we cannot tell the
exact values of the IQ scores in the sample.
Answer: The mean is less than the median IQ
Step-by-step explanation:
When a distribution is skewed left (there is an obvious tail going in the left direction, which is true in this case), then the mean is drawn down because it is not resistant to any outliers, or unusual data points.
The median, however, is resistant to outliers and will not move as much.
Therefore, the mean will be less than the median.
The relationship between the mean and median of a data set is determined by whether the data is symmetrically distributed, positively skewed, or negatively skewed. However, without a visual representation or specific values, we cannot definitively compare the mean and median of the IQ scores.
Explanation:In order to determine the relationship between the mean and the median of a data set, we need to know the nature of its distribution. If the data is symmetrically distributed, the mean and the median will be equal. If the data is positively skewed (has a long right tail), the mean will be larger than the median. If the data is negatively skewed (has a long left tail), the mean will be less than the median.
However, in the absence of the actual histogram in your question, the correct answer would be 'It cannot be determined because we cannot tell the exact values of the IQ scores in the sample.' This is because without a visual representation or specific values, we cannot determine the distribution's skewness, and by extension, cannot compare the mean and median.
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select the statement regarding the correlation coefficient (r) that is true. a.) a correlation coefficient of 1 implies a weak correlation between two variables. b.) the correlation coefficient describes the direction of the association between two variables. c.) the sign of the correlation coefficient might change when we combine two subgroups of data. d.) correlation coefficient cannot be calculated for all scatterplots.
The statement regarding the correlation coefficient (r) that is true is b) "the correlation coefficient describes the direction of the association between two variables."
The correlation coefficient is a measure of the strength and direction of the relationship between two variables. A correlation coefficient of 1 implies a strong positive correlation between the variables, meaning that as one variable increases, the other variable also tends to increase.
A correlation coefficient of -1 implies a strong negative correlation between the variables, meaning that as one variable increases, the other variable tends to decrease. A correlation coefficient of 0 implies no correlation between the variables. The sign of the correlation coefficient (positive or negative) indicates the direction of the association between the variables, while the magnitude of the coefficient (closer to 1 or -1) indicates the strength of the association.
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