keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the line above
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{4}}} \implies \cfrac{3 +2}{-1 -4}\implies \cfrac{5}{-5}\implies \cfrac{1}{-1}\implies -1 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{-1}} ~\hfill \stackrel{reciprocal}{\cfrac{-1}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{-1}{1}\implies 1}}[/tex]
8(x-10)=-88
Show work
Check
Answer:
x = - 1
Step-by-step explanation:
Given:
8(x-10)=-88
Solve:
8(x-10)=-88
Using the distributive property.
How to use distributive property:
Multiply the outside number by the inside parenthesis numbers.
Like this;
8x - 80 = -88
Now add 80 to both sides:
8x - 80+80 = -88+80
8x = -8
Divide both sides by 8:
x = -1
Check:
We can substitute x which is -1 into the equation;
8(-1-10)
8*((-1)-10)
= -88
Hence, x = -1
RevyBreeze
What are the 3 types of 3 dimensional coordinate system?
The 3 types of 3-dimensional coordinate systems are the x-axis, the y-axis, and the z-axis.
The Cartesian coordinates of a point in three dimensions are a triplet of numbers (x,y,z). The three numbers, or coordinates, specify the signed distance from the origin along the x,y, and z-axes, respectively.
The three axes intersect at the point called the origin. The x-axis is the horizontal line along which the wall to your left and the floor intersect.
The y-axis is the horizontal line along which the wall to your right and the floor intersect. The z-axis is the vertical line along which the walls intersect.
To locate the point (a, b, c), we can start at the origin O and move units along the x-axis, then b units parallel to the y-axis, and then c units parallel to the z-axis.
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How do you find the center of dilation of two lines?
Finding the center of dilation of two lines involves determining the point that is equidistant from the two lines.
A dilation is a transformation that changes the size of an object, but not its shape, and the center of dilation is the point from which the object is scaled.
The center of dilation of two lines can be found by constructing a line perpendicular to both lines that bisects the angle between them. The point of intersection of this line with the segment connecting the two closest points on the two lines is the center of dilation.
To find the center of dilation, we can use the following steps:
1. Draw the two lines and find the angle between them.
2. Draw a line perpendicular to both lines and bisecting the angle between them.
3. Draw the segment that connects the two closest points on the two lines.
4. The intersection of the line from step 2 with the segment from step 3 is the center of dilation.
It's also possible to use vector and linear algebra to find the center of dilation for two lines. By finding the slope of each line and their intersection point, the center of dilation can be found as the midpoint of the intersection point of the two lines.
In conclusion, finding the center of dilation of two lines requires determining the point that is equidistant from the two lines.
It can be done by drawing a line perpendicular to both lines that bisects the angle between them, or by using vector and linear algebra to find the intersection point of the two lines and finding the midpoint of that point.
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ASAP please help right now
Answer:
1
Step-by-step explanation:
Because the shape divided has to create another shape and for 1 it's an oval at the beginning and then after the lines of symmetry go through its seen as 8 triangles.
The difference of the two numbers is 2 The sum of the same two numbers is 6. Write the numbers from least to greatest.
Answer:
2 and 4
Step-by-step explanation:
The difference of 4 and 2 is 2 because 4-2=2, and this matches the first part of the question. 4+2=6, and this is true because it matches the second part of the question. Hope this helps and please mark brainliest! :D
Mancini' Pizzeria ell four type of pizza crut. Lat week, the owner tracked the number old of each type, and thi i what he found. Type of Crut Number Sold
Thin crut 306
Thick crut 212
Stuffed crut 178
Pan tyle 191
Baed on thi information, of the next 3500 pizza he ell, how many hould he expect to be pan tyle? Round your anwer to the nearet whole number. Do not round any intermediate calculation
Now we have a new proportion that out of 3500 pizzas there are a total of 692 thick crust pizzas
Mancini's sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found.
Type of Crust Number Sold
Thin crust 306
Thick crust 212
Stuffed crust 178
Pan style 191
Based on this information, of the next 3500 pizzas he sells, how many should he expect to be thick crust? Round your answer to the nearest whole number. Do not round any intermediate calculations.
692 thick crust pizzas
With the data given in the exercise, we must first find the total number of pizzas, then we must find the proportion between the thick crust pizzas and the total number of pizzas, finally we must propose a rule of three to find the new proportion of crust pizzas thick on a total of 3500 pizzas.
Type of Crust Number Sold
Thin crust 306
Thick crust 212
Stuffed crust 178
Pan style 191
total pizzas : 1040
Now we must calculate for 3500 pizzas how much would be the total of thick crust pizzas. For that we must use the relationship found, that is, in 1040 pizzas there are 240 thick crust pizzas
x = 692
Now we have a new proportion that out of 3500 pizzas there are a total of 692 thick crust pizzas
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Write an equation in slope form of the line that passes through the given point and is parallel to the graph of the given equation
(-6,-8);y=-4x+2
An equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation is y = -4x - 32.
What is the point-slope form?Mathematically, the point-slope form of a line is given by this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.From the given linear equation y = -4x + 2, the slope is given by:
y = -4x + 2
m₁ = -4
In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ (m represents the slope.)
At point (-6, -8), an equation of this line can be calculated in slope-intercept form as follows:
y - y₁ = m(x - x₁)
y - (-8) = -4(x - (-6))
y + 8 = -4(x + 6)
y + 8 = -4x - 24
y = -4x - 24 - 8
y = -4x - 32
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Triangle BCD has coordinates B(-8,-6), C(-5,2) and D(-2,7). What are the coordinates of D' after a translation of (x,y) -› (x+10, y+1)
Answer:
Step-by-step explanation:
x'=x+10,y'=y+1
so,the x' in D' is -2+10 = 8, y' in D' is 7+1=8
then, the D' is (8, 8)
What are the 3 types of coordinate input AutoCAD?
The three types of coordinate input in AutoCAD are absolute coordinates, relative coordinates, and polar coordinates
Absolute coordinates are based on the origin of the drawing, which is the point 0,0. To specify an absolute coordinate, you enter the X and Y coordinates of the desired point. For example, if you want to specify a point at X=4 and Y=6, you would enter ‘4,6’.
Relative coordinates are based on a point relative to the last point specified. To specify a relative coordinate, you enter the distance in the X and Y directions from the last point specified. For example, if you want to specify a point that is 4 units to the right and 6 units up from the last point, you would enter ‘4,6’.
Polar coordinates are based on a distance and an angle from the last specified point. To specify a polar coordinate, you enter the distance and angle from the last point. For example, if you want to specify a point that is 8 units away at an angle of 90 degrees, you would enter ‘8<90’.
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9,365,000 rounded to the nearest million place
Find the polynomial function in standard form that has the zeros listed. 2 (multiplicity 2), 3+i (multiplicity 1)
A. f(x) = x4 - 10x³ + 36x² - 56x +32
B. f(x) = x4 – 10x³ + 38x² - 64x + 40
C. f(x) = x³8x² +22x - 20
D. f(x) = x4 – 10x³ + 37x² − 60x + 36
The polynomial function in standard form that has the zeros - 2 (multiplicity 2), and 3+i (multiplicity 1) is option b: f(x) = x^4-10x^3+38x^2-64x+40.
What is a polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
The zeros of the polynomial function are -
2 (multiplicity 2), and 3+i (multiplicity 1)
If the zero is 2, the factor is (x-2).
A multiplicity of 2 implies there are 2 factors -
(x-2) or (x-2)(x-2) = (x-2)^2
= (x^2-4x+4)
For the complex zero (3+i), there will also be a zero at the complex conjugate (3-i).
The factors are -
= [x-(3+i)] and [x-(3-i)] or
= (x-3-i)(x-3+i)
= x^2-3x+ix-3x+9-3i-ix-+3i-i^2
= x^2-6x+9-i
= x^2-6x+9-(-1)
= x^2-6x+10
Multiply all factors to find the polynomial in standard form -
f(x) = (x^2-4x+4)(x^2-6x+10)
= x^4-6x^3+10x^2-4x^3+24x^2-40x+4x^2-24x+40
= x^4-10x^3+38x^2-64x+40
Therefore, the polynomial function in standard form is x^4-10x^3+38x^2-64x+40.
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I need help im stuck
The height of the cylinder is 22 inches.
What is height ?
Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base and something above it. Height is used to describe everything that may be measured vertically, high or low.
Height is a measurement of vertical distance, or how high something or someone is (how tall they are) (how "high" a point is). For instance, "That building is 50 meters high," or "An airplane flies around 10,000 meters high."
Height is a basic physical characteristic that is commonly expressed in feet (ft) plus inches (in) in the United States and centimeters (cm) in other countries. The SI unit would be meters since these are length measurements. Remember that x feet plus y inches is typically written as x' y.
Seeing the figure we get to know the measures of cylinder
radius = 8 inches
height = 22 inches
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Find k so that 4x + 3 is a factor of 20x³ + 23 x² - 10x + k.
Answer:
k= 28.875
Step-by-step explanation:
4x+3= 0
4x= -3
X = -3/4
f(X)= 20x³+23x²-10x+k
0= 20(-3/4)³ + 23 (-3/4)² -10(-3/4)+k
20(-27/64)+23(9/16) +30/4+k
-540/64+207/16+7.5+k
-8.4375+12.9375+7.5+k. 0=-28.875+k
k=28.875
What is the factor theorem simple?
In mathematics, the factor theorem mostly used when factoring the polynomials totally. factorial theorem is that links factors and zeros of the polynomial.
By 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.
including, we can say, if (x-a) is a factor of polynomial f(x), then f(a) = 0. This also proves that the converse of the theorem. Let us see the proof and example.
Factor theorem is mostly used for factoring a polynomial and searching the roots of the polynomial. It is an important case of a polynomial remainder theorem.
As examined in the introduction, a polynomial f(x) has a factor (x-a), if and only if, f(a) = 0. It is one of the processes to do the factorization of a polynomial.
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A person hang gliding at an altitude of 300 feet is over a spot 2,250 feet from an
area of soft grass where he would like to land. At what angle of depression should
he see the grass?
Answer:
Below
Step-by-step explanation:
This is a right traingle with legs 300 and 2250
Tangent = opp leg / adjacent leg
Arc tan (opp / adj) = arctan (300/2250) = 7.6°
Using the diagram below, find the measure of angle A.
A
101°
92°
B
68°
C
Answer: the missing angle is going to be 99 because the shape that is being formed it going to be a quaderdiral because that is the next number up.
Step-by-step explanation: add the degress together and then see what number is the closest
The table gives the annual global plastic production over time, in years, since 1960.
Fit an exponential model to this data.
The exponential model indicates that plastic production has (1) _____ per year. The model predicts that plastic production 15 years after 1960 was closest to (2) _____ million metric tons. Because the correlation coefficient indicates (3) _____
correlation between the model and the data, this prediction (4) _____.
Answer options:
1-
increased by 4.9 metric tons
decreased by 4.9 metric tons
increased by 4.9%
decreased by 4.9%
2-
40
60
70
3-
moderate
strong
weak
4-
is unreliable
can be accepted with confidence
The exponential model indicates that plastic production has increased by 4.9% per year.
Fit an exponential model to this dataThe exponential model indicates that plastic production has increased by 4.9% per year.The model predicts that plastic production 15 years after 1960 was closest to 70 million metric tons.Because the correlation coefficient indicates strong correlation between the model and the data,this prediction can be accepted with confidence.The exponential model is a powerful tool for predicting future trends in plastic production, and it indicates that plastic production has been increasing at an annual rate of 4.9%.This is an important insight, as it can help us to anticipate the future of the industry.With this information, we can estimate that plastic production 15 years after 1960 was likely to be around 70 million metric tons.The strength of this prediction is supported by the correlation coefficient, which suggests a strong correlation between the model and the data.This suggests that the model is a good predictor of future plastic production, and that the prediction of 70 million metric tons is reliable.To learn more about the annual global plastic production over time refer to:
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Given h(2) -I + 4, solve for a when h(2) = 4.
At h(2) = 4 the value of 'I' will be equal to 0.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the function is h(2) = I + 4. The value of I at h(2) = 4 will be calculated as,
h(2) = I + 4.
4 = I + 4
I = 4 - 4
I = 0
Hence, the required value of 'I" at h(2) = 2 will be 0.
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The drama club members at millie’s middle school are selling tickets to the school play. millie wants to determine the average number of tickets sold. first, she surveyed the club members in her homeroom, and then she surveyed every third member of the club in her physical education class. which sampling technique should produce a more representative sample? a. the first sampling method, surveying drama club members in her homeroom, is the most representative. b. the second sampling method, surveying drama club members in her physical education class, is the most representative.c. both samples should be exactly the same. d. neither sample will be representative.
The exact representation of surveying drama club is by second sampling method.
Thus correct option is B .
Given, Selling tickets to the school play .
Systematic random sampling is known to be a type of random sampling technique that needs the selection of samples using a system of intervals in a specific population.
In Systematic Sampling second sampling method is used. Grounded on the fact that the system of sampling is one that's drawn from the population, it's said to be an effective system of sampling.
Hence option B is correct .
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Is the triangle with sides 25cm 5 cm and 24 cm a right triangle give reasons for your answers?
No, a triangle with sides 25 cm, 5 cm and 24 cm does not make a right triangle as these lengths does not adhere to the Pythagorean theorem.
A right triangle has one angle that measures exactly 90 degrees. In a triangle, the longest side (the hypotenuse) is opposite the right angle.
The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the hypotenuse.
In this case, the side lengths do not satisfy the Pythagorean theorem, as (24^2 + 5^2 = 601) ≠ (25^2 = 625)
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What is final value theorem Mcq?
The steady state value of the system is determined using the final value theorem.
The main characteristics of the Laplace transform are the initial and final value theorems. Pierre Simon Marquis De Laplace, a French mathematician and scientist, presented these theorems. Limiting theorems refer to both the initial and final value theorems.
The final value theorem asserts that one can compute a system's ultimate value using. The function's Laplace transform is
[tex]\lim_{t\rightarrow\infty}f(t) = \lim_{s\rightarrow0}sF(s)[/tex]
(1) Final value theorem prerequisites are the functions f(t) and f(t)' should be Laplace transformable.
(2) sF(s), where F(s) is the Laplace transform of f(t), has no pole on the j-w axis and right half plane.
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Solve the inequality for u.
10<-2u
Simplify your answer as much as possible.
Answer:
u < -5
Step-by-step explanation:
-2u > 10 (Divide both sides by -2)
u > -5 (Change the greater than sign to a less than sign since we divided by a negative number)
Final Answer: u < -5
How to tell if a system of equations has no solution or infinitely many matrix?
Checking nonzero rows in the matrix is the first step in determining whether a matrix has an infinite solution. The matrix has an infinite solution if the number of variables is more than nonzero rows, according to this statement.
What does matrix mean?
A matrix is a collection of numbers that have been put in rows and columns to make a rectangular array. The elements, or entries, of the matrix are the integers.
In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics.
What are types and a matrix?
The dimensions or size of a matrix are determined by these rows and columns. There are several different kinds of matrices, including row matrices, column matrices, null matrices, square matrices, diagonal matrices, and upper and lower triangular matrices.
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Answer:
First, you have to check the nonzero rows in the matrix to determine whether a matrix has an infinite solution. The matrix has an infinite solution if the number of variables is more than nonzero rows, according to this statement.
Step-by-step explanation:
What is a matrix?
A matrix is a collection of numbers that are arranged in a row and column format in a rectangular or square form depending on the size of their rows and columns.
Operation on matrices:1. Addition: Any numbers of the same index can be added.
2. Subtraction: Any numbers of the same index can be subtracted.
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100 points
solve each system by graphing
x=-3
x-y=-2
Answer:
(-3, - 1)--------------------------
Graph each line:
x = - 3, this is a vertical line passing through x = - 3,x - y = - 2 is y = x + 2, which is the line y = x, translated 2 units up.The intersection of the lines is the solution:
(-3, - 1)Write the equation of a line in point-slope form that goes through the point (6,-1) and m=2:
Step-by-step explanation:
the point-slope form is
y - y1 = m(x - x1)
m is the slope, (x1, y1) is the given point.
so,
y - -1 = 2(x - 6)
y + 1 = 2(x - 6)
lcm(x-3)^2(x+4);(x-3)(x+4)^2
Answer:
[tex](x - {3})^{2} x(x + {4})^{2} [/tex]
if each quadrilateral below is a trapezoid, find the missing measures
If each of the quadrilateral is a trapezoid, then the measure of ∠Q = 89 and ∠S = 153.
What is a trapezoid?A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.
Given that in a trapezoid, the angle T is 91 and the angle R is 27.
For a trapezoid the measure of angle are as follows:
∠T + ∠Q = 180
∠R + ∠S = 180
Substituting the measures of ∠T and ∠R in the above equations we have:
91 + ∠Q = 180
∠Q = 89
27 + ∠S = 180
∠S = 153
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What is the 3D distance formula?
The 3D distance formula is represented as √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)
The 3D distance formula, also known as the Euclidean distance formula, is used to calculate the distance between two distinct points in three-dimensional space. The formula is the square root of the sum of the squares of the differences in the x, y, and z coordinates of the two points. Mathematically it can be represented as:
Distance = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)
Where (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two points.
It's used to measure the distance between two points in 3-D space. It's the straight-line distance between two points. This formula can be applied in various fields such as physics, computer graphics, and robotics.
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Jon left Rick's house and travelled 7 miles
East, 5 miles North, and 5 miles East. How far away is John's house from Rick's house?
John's house is 7 + 5 = 12 miles away from Rick's house in the east-north direction. John's house is 13 miles from Rick's house.
To solve this problem use Pythagoras theorem. Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.
a² + b² = c²
c is the shortest distance or hypotenuse.
Distance of John's house from Rick's house
= [tex]\sqrt{(7+5)^2+5&^2}[/tex]
= [tex]\sqrt{12^2+5^2}[/tex]
= [tex]\sqrt{144+25}[/tex]
= [tex]\sqrt{169}[/tex]
= 13 miles
So, John's house is 13 miles from Rick's house.
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Use a trigonometric ratio to solve for z. Round to two decimal places as necessary!!
HELP, and can someone explain how to get the answer?
On solving the provided question, we can say that by trigonometry so sin 90 = p/h => z = 11
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
here,
it is a right angled triangle
by trigonometry
so sin 90 = p/h
1 = 11/z
z = 11
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