The volume of the solid under the cone z = x2y2 and above the disk x2y2 ≤ 36 is 7056π. This was found by using polar coordinates and integrating the equation V = ∫∫∫r2sin(θ)dzdθdr with the limits of integration r = 0 to 6, θ = 0 to 2π, and z = 0 to x2y2.
The volume of the solid can be found by integrating the equation:
V = ∫∫∫r2sin(θ)dzdθdr
where r is the radius and θ is the angle of the polar coordinates.
The limits of integration are as follows:
r = 0 to 6
θ = 0 to 2π
z = 0 to x2y2
The integral is then:
V = ∫0 to 2π∫0 to 6∫0 to r2sin(θ)dr dθ
V = ∫0 to 2π∫0 to 6 r3sin(θ)θdr
V = ∫0 to 2π [r4sin(θ)]0 to 6 dθ
V = ∫0 to 2π 644sin(θ)dθ
V = 7056π
The volume of the solid under the cone z = x2y2 and above the disk x2y2 ≤ 36 is 7056π. This was found by using polar coordinates and integrating the equation V = ∫∫∫r2sin(θ)dzdθdr with the limits of integration r = 0 to 6, θ = 0 to 2π, and z = 0 to x2y2.
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does anyone know the answer to
– 2p ≤ – 8
Answer:
The answer to the inequality is [tex]p\geq 4[/tex].
Step-by-step explanation:
Lets solve the inequality.
[tex]-2p\leq -8[/tex]
Divide both sides of the equation by -2.
There is an inequality rule that says when multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
First lets divide both sides by -2.
[tex]\frac{-2p}{2} \leq \frac{-8}{2}[/tex]
Simplify the left side by cancelling the common factor of −2.
[tex]p\leq \frac{-8}{2}[/tex]
Simplify the right side by dividing -8 by 2.
[tex]p\leq 4[/tex]
We need to flip the direction of the inequality sign.
[tex]p\geq 4[/tex]
someone help pls ….
“write a cubic function whose graph passes through the given points”
The cubic polynomial with the given points is:
y = (1/4)*(x + 4)*(x - 2)*(x - 5)
How to write the cubic equation?Any polynomial of degree N with the zeros {a,b, c...} and a leading coefficient K can be written as:
y = k*(x - a)*(x - b)*...
Here we have the zeros: -4, 2, and 5, then we can write:
y = k*(x + 4)*(x - 2)*(x - 5)
And it also passes throuh the point (0, 10), then:
10 = k*(0 + 4)*(0 - 2)*(0 - 5)
10 = k*40
10/40 = k
1/4 = k
The polynomial is:
y = (1/4)*(x + 4)*(x - 2)*(x - 5)
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a bacteria culture doubles in size every 8 hours. the culture starts with 150 cells. what function models this situation?
The function model for a bacteria culture that doubles in size every 8 hours is A(t) = 150*2^(t/8)
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
Information about the problem:
A(0) = 150 cellsDoubles in size = 2Hours = 8The function that models the situation is the following:
A(t) = A(0)*2^(t/8)
A(t) = 150*2^(t/8)
Where A(0) is the culture start and t is the time passed.
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HELP ASAP PLSSSS
Compare the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
(graph and chart is attatched)
The slope of f(x) is greater than the slope of g(x).
The slope of f(x) is less than the slope of g(x).
The slope of f(x) is equal to the slope of g(x).
The slope of g(x) is undefined.
a newspaper carrier has $6.85 in change. he has eight more quarters than dimes but two times as many nickels as quarters. how many coins of each type does he have?
The coins of each type are 346 nickels, 165 dimes and 173 quarters. when a newspaper carrier has $6.85 charge by substitution method.
Let x = number of quarters
Then, x-4 = number of dimes and 5x = number of nickels
So, 0.05(5x) + 0.10(x-4) + 0.25x = 6.85
0.6x - 0.4 = 6.85
0.6x = 7.25
x = 12
There are 12 quarters, 8 dimes, and 60 nickels (or)
x = 8 + D(dimes)
D = Q -8
N(nickels) = 2Q
N + D + Q = 685
2Q + Q-8 + Q = 685
4Q = 685+ 8 = 693
Q = 693/4 = over 173
D= over 165
N= over 346
174+ 165 + 346 = 685
the answer is 346 nickels, 165 dimes and 174 quarters.
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write down a closed form for the matrix l−1. multiplying with l−1 from the left also corresponds to an elementary transformation of type 1, what is this transformation?
The closed form for the matrix l−1 is the inverse matrix of l, which corresponds to an elementary transformation of type 1, which is a row transformation.
A closed form for the matrix L-1 is given by the following formula:
L-1 = (1/det(L)) * adj(L)
Where "det(L)" represents the determinant of the matrix L, and "adj(L)" is the adjugate matrix of L. The adjugate matrix of a matrix A is the transpose of its cofactor matrix, and is denoted as adj(A). The cofactor matrix of a matrix is the matrix of determinants of the minors of the matrix multiplied by alternating signs.
The elementary transformation of type 1 is row interchange. This means that two rows of the matrix are interchanged with each other. This transformation has the same effect when applied from the left as from the right, so when multiplying with L-1 from the left, it corresponds to a row interchange.
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a restaurant asks their customers to fill out a questionnaire indicating whether their service was excellent, very good, good, or poor. the rating scale used is an example of the scale. a. binary/dummy b. unordered categorical c. ordered categorical d. continuous
The rating scale used by the restaurant is an example of an ordered categorical scale (c)
An ordered categorical scale is a type of categorical scale where the categories have a specific order or ranking. In this case, the categories "excellent," "very good," "good," and "poor" have a clear order from highest to lowest, indicating the level of customer satisfaction.
A binary/dummy scale, on the other hand, only has two categories, such as "yes" or "no."
An unordered categorical scale does not have a specific order or ranking, such as gender (male or female) or hair color (brown, black, blond, etc.).
A continuous scale, such as height or weight, has an infinite number of possible values and can be measured to any degree of precision.
So, the restaurant's questionnaire uses an ordered categorical scale to measure customer satisfaction.
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By drawing a suitable straight line, solve the equation 1.5^x -x-2=0. Find x= ? Or x=?
The equation 1.[tex]5^x[/tex] - x - 2 = 0 then the value of x be -1.44292524676275.
What is meant by straight line?A line is an endlessly long object without breadth, depth, or curvature in geometry. Thus, despite the fact that they can exist in two, three, or higher dimensional environments, lines are one-dimensional things. The term "line" can also refer to a line segment that has two locations that serve as its ends in daily life.
A line is a straight, one-dimensional figure in geometry that is infinitely long in both directions and has no thickness.
Let the equation [tex]$1.5^x-x-2=0$[/tex]
Lambert form: [tex]$1=-e^{-\ln (1.5) x}(-x-2)$[/tex]
The equation with [tex]$(-x-2) \ln (1.5)=u$[/tex] and [tex]$x=-\frac{u+2 \ln (1.5)}{\ln (1.5)}$[/tex][tex]$1=-e^{-\ln (1.5)\left(-\frac{u+2 \ln (1.5)}{\ln (1.5)}\right)}\left(-\left(-\frac{u+2 \ln (1.5)}{\ln (1.5)}\right)-2\right)$$[/tex]
Simplifying the above equation, we get
[tex]$1=-e^{u+2 \ln (1.5)}\left(\frac{u+2 \ln (1.5)}{\ln (1.5)}-2\right)$$[/tex]
[tex]$1=-e^{u+2 \ln (1.5)}\left(\frac{u+2 \ln (1.5)}{\ln (1.5)}-2\right)$[/tex] in Lambert form: [tex]$e^u u=-\frac{\ln (1.5)}{2.25}$[/tex]
Solve [tex]$e^u u=-\frac{\ln (1.5)}{2.25}: \quad u=\mathrm{W}_{-1}\left(-\frac{\ln (1.5)}{2.25}\right), u=\mathrm{W}_0\left(-\frac{\ln (1.5)}{2.25}\right)$[/tex]
[tex]$$u=\mathrm{W}_{-1}\left(-\frac{\ln (1.5)}{2.25}\right), u=\mathrm{W}_0\left(-\frac{\ln (1.5)}{2.25}\right)$$[/tex]
Substitute back [tex]$u=(-x-2) \ln (1.5)$[/tex], solve for x[tex]$(-x-2) \ln (1.5)=W_{-1}\left(-\frac{\ln (1.5)}{2.25}\right): \quad x=-\frac{W_{-1}\left(-\frac{\ln (1.5)}{2.25}\right)+2 \ln (1.5)}{\ln (1.5)}$[/tex]
Therefore, the simplifying x, we get
[tex]$x=-\frac{W_{-1}\left(-\frac{\ln (1.5)}{2.25}\right)+2 \ln (1.5)}{\ln (1.5)}, x=-\frac{W_0\left(-\frac{\ln (1.5)}{2.25}\right)+2 \ln (1.5)}{\ln (1.5)}$[/tex]
Therefore, the value of x be x = -1.44292524676275.
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A riverboat travelling with the current can go 80 km in 4 hours, on the return trip against the current it took 5 hours to travel the 80 km. Which of the following would represent a linear system that could be used to determine the speed of the riverboat and the current where x is the speed of the riverboat and y is the speed of the current?
Answer:
The following linear equation represents the system:
x + y = 20 (speed of the riverboat and current in km/hr in the same direction)
x - y = 16 (speed of the riverboat relative to the current in km/hr in opposite directions)
Solving for x and y gives us:
x = 18 and y = 2 (speed of the riverboat and current in km/hr).
Step-by-step explanation:
a hypothesis test is: group of answer choices an inferential technique that uses tha data from a sample to draw inferences about a population a descriptive technique that allows researchers to describe a sample an inferential technique that uses information about a population to draw inferences about a sample a descriptive technique that allows researchers to describe a sample
It is an inferential technique that uses the data from a sample to draw inferences about a population.
Hypothesis testing is a type of statistical hypothesis that uses data from a sample to draw judgments about a population parameter or a population probability distribution.
First, an uncertain hypothesis is made about the parameter or distribution. This is named the null hypothesis and is denoted by [tex]H_{O}[/tex]. An alternative hypothesis (denoted [tex]H_{a}[/tex]), which is the opposite of the null hypothesis, is then described.
The hypothesis-testing process involves using sample data to decide whether or not [tex]H_{0}[/tex] can be rejected. If [tex]H_{O}[/tex] is rejected, the statistical determination is that the alternative hypothesis [tex]H_{a[/tex] is true.
Hence, the correct answer is c.
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--The given question is incorrect; the correct question is
"A hypothesis test is
a. a descriptive technique that allows researchers to describe a sample
b. a descriptive technique that allows researchers to describe a population
c. an inferential technique that uses the data from a sample to draw inferences about a population
d. an inferential technique that uses information about the population to make predictions about a sample"--
the surface area of an egg shell scales as the mass of the egg shell raised to what power?
The surface area of an egg shell scales as the mass of the egg shell raised to 1.82694
The term surface area in math is defined as the area occupied by a three-dimensional object by its outer surface
Here we know that the area of a cube with edged is proportional to the second power d² while its volume is proportional to the third power d³.
Here we know that for any bounded solid object, here we have which encloses a region with some volume V and its enclosing surface has area A, where as the same kind of proportions can be derived in terms of a linear dimension d of the object, here for example the diameter of the object.
AS we all know that the surface area is directly proportional to the 3rd power of the mass of the egg, here we have A = km³ where A is the surface area, k a constant of proportionality, and m the mass.
For a chicken egg we have 28 = k(60)⁰°⁶⁷
Here by solving for k we get:
=> k = 28/60⁰°⁶⁷ ≈ 1.82694
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which point is a solution to the system of inequalities a.(2,0) b.(0,2) c.(-2,-2) d.(0,-2)
Answer:It depends on the specific system of inequalities being considered. To determine if a point is a solution to a system of inequalities, you need to substitute the x and y coordinates of the point into each inequality and see if it is true for all of them. If it is true for all of the inequalities, then the point is a solution to the system.
give me a thanks and a 5 star pls!
Step-by-step explanation:
It depends on the specific system of inequalities being considered. To determine if a point is a solution to a system of inequalities, you need to substitute the x and y coordinates of the point into each inequality and see if it is true for all of them. If it is true for all of the inequalities, then the point is a solution to the system.
Does anyone know how to do this. I really need help.
The value of P (factor of 10) is, 1/4.
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We have to given that;
There ae 4 cards to select.
Now, In all 4 cards the factor of 10 is, 2
Hence, The probability to be the factor of 10 is,
⇒ 1 / 4
Thus, The value of P (factor of 10) is, 1/4.
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Describe the transformation of the graph of f (x)=eˣ represented by the graph of g(x)=eˣ⁻⁹+4.
The chester company will increase its automation for the cell product by 2.0. assuming no further change in capacity, how much will this investment in automation cost?
a. $10,000,000
b. $20,000,000
c. $8,750,000
d. $17,500,000
Investment in automation cost = $8,750,000 when there
no further change in capacity.
Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
Following are the informations of Cent:
Current automation = 7%
Capacity of next round = 1,100
New automation = 7 + 2 = 9
Investment in automation cost = Capacity * (4 * (New automation - previous automation)) * 1000
= 1,100 * (4 * (9 - 7)) * 1,000
= 1,100 * (4 * 2) * 1000
= 1,100 * 8 * 1,000
= $8,800,000.
Investment in automation cost = $8,800,000.
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Write an equation to represent the linear function comparing the number of months after the first month (x) to the number of total customers served (y)
Part 1: A small local coffee shop opened in January 2012. In the first month, the coffee shop served 400 customers. After that, the coffee shop served 70 customers each month.
Part 2:How many customers were served after 12 TOTAL months of being in business? HINT: Remember what the variable x represents
An equation to represent the linear function comparing the number of months after the first month (x) to the number of total customers served (y), 400 + 70x
The number of customers served after 12 months, 1240
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
In the first month, the coffee shop served 400 customers
After that, the coffee shop served 70 customers each month
Suppose, coffee shop served x number of months after first month,
Total people served = 400 + 70x
The number of customers served after 12 months,
Total people served = 400 + 70x12
= 400 + 840
= 1240
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How many square feet means 1 acre?
The value of square feet means 1 acre be 43,560 square feet.
What is the difference between square feet and acre?The US measurement system uses the acre as the unit of land area measurement. Every real estate transaction and listing worldwide has a connection to Square Feet.
The length and width of the land—which are often stated in feet—are multiplied to determine the acreage before converting the result to square feet. Following that, the square footage is converted to acres using a conversion ratio of 43560.
For standing or stored water, an acre-foot is the accepted unit of measurement. It is the volume of water necessary to cover an acre of ground that is 43,560 square feet in size and one foot deep. 325,851 gallons make up an acre-foot.
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Given the function y = √√x - 5 Type in the ordered pair to show the x-intercept of
the function. Type it in using the (x,y) format. Hint: Replace y with 0
Need #15
The x-intercept of the function as an ordered pair is equal to (5, 0).
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
In this context, we would replace the y-value with zero (0) by substituting it into the given equation y = ∛x - 5 as follows;
y = ∛x - 5
0 = ∛x - 5
Taking the cube root of both sides of the function, we have the following:
0 = x - 5
x = 5
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Solve the system of equations by the substitution method. 1/3x-y=2 x - 3y = 6
Answer:
No solution
Step-by-step explanation:
1/3x-y=2
x - 3y = 6
Times the first equation by -3
-x + 3y = -6
x - 3y = 6
0 = 0
So, there is no solution.
A "Pick 4" lottery game involves drawing
4
44 numbered balls from separate bins each containing balls labeled from
0
00 to
9
99. So there are
10
,
000
10,00010, comma, 000 possible selections in total:
0000
00000000,
0001
00010001,
0002
00020002,
…
…dots,
9998
99989998,
9999
99999999.
Players can choose to play a "straight" bet, where the player wins if they choose all
4ndigits in the correct order. Since there are
10,000possible selections, the probability a player wins a straight bet is
1/10,000. The lottery pays $9,000
on a successful $2 straight bet, so a player's net gain if they win this bet is $8,998
The expected Net gain is -0.1001.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total possible selection = 10000
Net Gain Probability
Win 8998 1/ 10000
Lose 2 9999/10000
So, E(x) = 8998 x 1/10000 - 9999/10000
= -1001 / 10000
so, the expected Net gain = -0.1001
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Juanita wants to buy a car. The car costs $15,000 and requires a 10% down payment. The dealership offers 5-year financing at 4% APR compounded monthly.
What's the monthly loan payment for this offer? Please enter your answer then show the steps.
A. 248.62
B. 276.25
C. $450.00
D. 523.15
The monthly loan payment for the offer made by Juanita, given the cost of the car and the dealership, is A. 248.62
How to find the monthly loan payment ?First, find the amount taken on loan :
= 15, 000 x ( 1 - 10 % down payment )
= $ 13, 500
The periodic rate is:
= 4 % / 12
= 1 / 3 %
The number of periods :
= 5 years x 12 months a year
= 60 months
The monthly payment is:
Present value of loan = Monthly Payment x Present value interest factor of annuity, 1 / 3 %, 60 months
13, 500 = 54.299068906557 x Monthly payment
Monthly payment = 13, 500 / 54.299068906557
= 248. 62
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What number make the equation true? Enter the anwer in the
What number make the equation true? Enter the anwer in the
If the value of a is 4 the equation will become true.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let the number be a.
2× a = 8 ...(1)
We need to find the value of a such that the above equation is true.
Divide both sides of equation (1) by 2 .
a = 8/2
a = 4
Hence, if the value of a is 4 the equation will become true.
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The Space Needle is 605 feet tall. A model of the building is 15 inches tall. What is the ratio of the height of the model to the height of the actual Space Needle?
A. 12:484
B. 1:484
C. 484:12
D. 484:1
And can u please show how to solve it? :)
Answer:
B. 1:484
Step-by-step explanation:
You want the scale of a 15-inch model that represents a 605-foot building.
ScaleThe scale is the ratio of the model distance to the corresponding real-world distance. To express the scale as a ratio or fraction without units, the measures being compared must have the same units.
scale = 15 in : 605 ft = 15 in : (605 ft · 12 in/ft) = 15 : 7260
scale = 1 : 484
The ratio of heights is ...
B. 1:484
<95141404393>
helppppppppppp00000000
Answer:
21[tex]e^{6}[/tex] and 30[tex]t^{6}[/tex][tex]v^{10}[/tex]
Step-by-step explanation:
using the rule of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
given
3e³ × 7e³
= 3 × 7 × e³ × e³
= 21 × [tex]e^{(3+3)}[/tex]
= 21[tex]e^{6}[/tex]
-------------------------------
(10[tex]t^{4}[/tex][tex]v^{5}[/tex] )(3t²[tex]v^{5}[/tex] )
= 10 × 3 × [tex]t^{4}[/tex] × t² × [tex]v^{5}[/tex] × [tex]v^{5}[/tex]
= 30 × [tex]t^{(4+2)}[/tex] × [tex]v^{(5+5)}[/tex]
= 30[tex]t^{6}[/tex][tex]v^{10}[/tex]
suppose the data on quiz scores will be grouped into five classes. the width of the classes for a frequency distribution or histogram is the closest to .
Answer is Taking data:
28 78 74 89 72
50 55 66 26 84
59 64 88 23 27
70 63 42 37 29
How to defined it?The answer is width of class =13
As the data is not given in the question I'm guessing the data from the question I solved before
28 78 74 89 72
50 55 66 26 84
59 64 88 23 27
70 63 42 37 29
as taking the above data,
maximum value=89
minimum value=23
no : of classes scores are divided into=5 classes
As we know for finding the width of class:
width of class = (maximum value-minimum value)/ no ; of classes
width = (89-23)/5=66/5
width=13.2=13
Note : By using the above given formula you can calculate the width of any data just by taking the maximum and minimum values of data and the number of classes the data is divided into.
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what is the mode frequency of the age variable?
The mode frequency can be a useful tool for understanding the distribution of the data and identifying any outliers or anomalies in the data set.
The mode frequency of the age variable refers to the most frequently occurring age in a given set of data. This measure of central tendency is particularly useful when working with categorical data, such as age ranges.
To calculate the mode frequency, one must first organize the data into a frequency distribution table, which lists all the different ages and the number of times each occurs. The age with the highest frequency is then considered the mode frequency.
For example, if there are 100 individuals in a data set and the ages range from 20 to 60, we would organize the data into age ranges, such as 20-29, 30-39, etc. Then we would count how many individuals fall into each age range and record this information in the frequency distribution table.
If the age range with the highest frequency occurs more than once, we have a multi-modal data set. On the other hand, if there is only one mode frequency, the data set is considered unimodal.
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Linear Equations Digital Escape!
number 4 and 5
The system of equation (4) and (5) have no solution
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
7(5x + 2) = 5x + 2
Divide both sides by 5x + 2
7 = 1
This equation is false, meaning there is no solution for y that satisfies both equations.
How to determine the solution to the systemHere, we have
2y = 6
y = -15
Since these are two different equations with the same variable, y, we can use substitution to find a solution.
Starting with the second equation, y = -15, we can substitute this value into the first equation:
2y = 6
2(-15) = 6
-30 = 6
This equation is false, meaning there is no solution for y that satisfies both equations.
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Complete question
4. How many solutions will this equation have? 7(5x + 2) = 5x + 2
5. Solve the given system of equations 2y = 6 and y = -15
Find the value of x in the rhombus.
(2x^2-25x)
(3x^2+60)
The value of x in the rhombus is -1
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
The shape = rhombus
The diagonals of rhombus bisect each other at 90 degrees
So, we have
2x^2 - 25x + 3x^2 + 60 = 90
Evaluate the like terms
5x^2 - 25x - 30 = 0
Divide through by 5
x^2 - 5x - 6 = 0
So, we have
x^2 + x - 6x - 6 = 0
Factorize
(x + 1)(x - 6) = 0
This gives
x = -1 and x = 6
When x = 6, 2x^2 - 25x is negative
Hence, the value of x is -1
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please help me with my questions
Answer:
m= -3/2
Step-by-step explanation:
To find slope
[tex]m \: = \frac{y2 - y1}{x2 - x1} [/tex]
We have our x1 and y1 of (2,5)
We have our x2 and y2 of (8,-4)
Now we plug in
= (-4-5)/(8-2)
= (-9)/(6)
Simplifying it would be
[tex]m = - \frac{3}{2} [/tex]
Answer: slope 'm' = -3 / 2
Step-by-step explanation: Using the formula m=(y2-y1)/(x2-x1), where 'm' is the slope of the line connecting the two points, we can plug in our x and y values:
x1 = 2
x2 = 8
y1 = 5
y2 = -4
Once we plug in our x and y values, we get the equation
m = (-4 - 5) / (8 - 2)
--> -9 / 6 (We can simplify this fraction to get or answer of -3 / 2)
thanks if you help me
Answer:
B; -2.5
Step-by-step explanation:
A is between the value -2 and -3. If we look at the options, there is only one value between -2 and -3, -2.5. So, A must represent -2.5, meaning that our answer is B.
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