Answer:3
Step-by-step explanation:
It 3 HURRY
Answer:
3rd one
Step-by-step explanation:
it's the only one that makes sense
Hope this helps!
What value of m would make parallelogram wxyz a square.
To make parallelogram WXYZ a square, the following conditions must be met:
1. All four sides of the parallelogram must have equal length.
2. The angles between adjacent sides must be 90 degrees.
Since a square is a special type of parallelogram with all sides equal and all angles equal to 90 degrees, we can determine the value of m that would make WXYZ a square by ensuring that these conditions are met. To find the value of m, we need more information about the dimensions or properties of the parallelogram WXYZ. Please provide additional details or measurements related to the parallelogram. The diagonals of a square are equal in length and bisect each other at 90-degree angles. The perimeter of a square is the sum of all four sides, and the area of a square is calculated by squaring the length of one side.In order for parallelogram WXYZ to be a square, it must have congruent sides and right angles at each vertex.
Since opposite sides of a parallelogram are congruent, we can equate the lengths of adjacent sides to find the value of m that would make it a square.
Let's assume that WX and XY are adjacent sides of the parallelogram.
If WX = XY, then the parallelogram would have congruent sides.
Let's say WX = m and XY = m.
To form a square, the angles at each vertex must be right angles. This means that WX and XY must be perpendicular to each other.
In a square, opposite sides are parallel, so the slopes of WX and XY must be negative reciprocals of each other.
The slope of WX can be represented as (change in y) / (change in x). Since it is perpendicular to XY, its slope will be the negative reciprocal of the slope of XY.
Let's assume the slope of XY is denoted as a. Then the slope of WX would be -1/a.
We can now equate the slopes of WX and XY:
-1/a = (change in y) / (change in x)
Simplifying this equation, we get:
a = -1
Therefore, the slope of XY is -1.
Now, we can equate the lengths of WX and XY:
m = m
Since WX = XY and both sides have length m, we can say that m = m.
So, any value of m would make parallelogram WXYZ a square as long as the sides WX and XY are congruent and perpendicular to each other, with a slope of -1.
hence, the value of m = -1.
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Can someone help me with #19
Answer:
XZ,X(-10,9)
Y(-4,8)
is
X2,YZ(14-1)=12
Write and equation given slope and a point.
M= -1 and (-2,3)
Answer:
y - 3 = - (x + 2)Step-by-step explanation:
y - y₀ = m(x - x₀) - point-slope form where m is the slope and the point is (x₀,y₀)
m = -1
(-2, 3) ⇒ x₀ = -2, y₀ = 3
y - 3 = -1(x - (- 2))
y - 3 = - (x + 2)
one of the biggest ethical issues many marketers face today relates to _____________.
One of the biggest ethical issues many marketers face today relates to consumer privacy and data protection.
In today's digital age, marketers have access to vast amounts of consumer data, including personal information and online behavior. The ethical issue arises when marketers collect, use, and share this data without adequate transparency, consent, or protection of consumer privacy. It raises concerns about invasion of privacy, unauthorized data sharing, and potential misuse of personal information for targeted advertising or other purposes.
Marketers are increasingly under scrutiny to ensure ethical practices in data collection, storage, and usage, balancing the need for effective marketing strategies with respect for individual privacy rights. Failure to address these ethical concerns can lead to loss of trust, reputational damage, and legal consequences for companies. Therefore, marketers must navigate these ethical challenges by adopting transparent and responsible data practices, respecting consumer choices, and implementing robust privacy and security measures.
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Scott likes to run long distances. He can run 20 km, end text in 85 minutes. He wants to know how many minutes (m) it will take him to run 52 km, How long will it take Scott to run 52 km?
Answer:221 min
Step-by-step explanation:
Given
Scott run 20 km in 85 minutes
Speed is given by
\(\Rightarrow \text{speed}=\dfrac{\text{distance}}{\text{time}}\)
Speed of Scott
\(\Rightarrow v=\dfrac{20}{\frac{85}{60}}=\dfrac{20\times 60}{85}=14.117\ km/hr\)
For 52 km, time taken is
\(\Rightarrow \text{time t}=\frac{52}{14.117}=3.683\ hr\ or\\\Rightarrow t=221\ min\)
ANSWER FAST PLS (the second pic is the graph you need)
Answer:
Ann is 0 miles away from home at the point (0,0) This took place before Ann started to walk.
Step-by-step explanation:
The point (0,0) on a number line, also called the axis, means that Ann is 0 miles away from home. This is because, the point is at the start of the graph, and the only numbers in this point is 0. This means, that when at this point, Ann was 0 miles away from home.
Hope this helps! :D
Which of the following best compares the slopes and y-intercepts of the two functions? (1 point)
The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).
The slope of f(x) is equal to the slope of g(x). The y-intercept of f(x) is less than the y-intercept of g(x).
The slope of f(x) is equal to the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).
PLS HELP
Answer:
The slope of f(x) is equal to the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).
Step-by-step explanation:
F(x) is already given to you on the graph. You need to plot the x and g(x) graph. (remember g(x) is just a fancy way of saying y)
Once this line is plotted, you will see that f(x) and g(x) are parallel to one another. G(x) is below f(x), so its y-intercept is lower.
A 40-foot ladder is leaning against a building and forms a 29.32° angle with the ground. how far away from the building is the base of the ladder? round your answer to the nearest hundredth.
The distance between the building and the ladder is 34.876 foot.
What is a Right Triangle?A triangle in which one of the angle measure is equal to 90 degree is called a right triangle.
The ladder forms a right triangle with the building and the ground,
The length of the triangle is 40 foot
The angle made by the ladder is 29.32 degree
By using Trigonometric Ratios
cos 29.32 = Base / Hypotenuse
cos 29.32 = Base / 40
0.8718 × 40 = Base
Base = 34.876 foot
Base is the distance between the building and the ladder.
Base of the ladder = 34.876 foot
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The random variable x represents the number of cars per household in a town of 1000 households. Find the probability of randomly selecting a household that has less than two cars.
Car Households
0 125
1 428
2 256
3 108
4 83
a. 0.809
b. 0.553
c. 0.428
d. 0.125
The probability of selecting randomly household having less than two cars is given by option b. 0.553.
To find the probability of randomly selecting a household that has less than two cars,
Calculate the probability for the values of the random variable x that are 0 or 1.
The total number of households in the town is given as 1000.
The number of households with 0 or 1 car is the sum of the frequencies for x = 0 and x = 1,
Number of households with 0 or 1 car
= 125 + 428
= 553
To find the probability, we divide the number of households with 0 or 1 car by the total number of households,
Probability of randomly selecting a household with less than two cars
= Number of households with 0 or 1 car / Total number of households
= 553 / 1000
= 0.553
Therefore, the probability of household having less than two cars is option b. 0.553.
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write a statement that creates a list called my_nums, containing the elements 5, 10, and 20.
A statement that creates a list is my_nums= [5,10,15]. This is also known as array.
What is an array?An array is a grouping of identically typed elements that are stored in adjacent memory locations and may each be separately referred to using an index to a special identifier. There is no need to declare five distinct variables when declaring an array of five integer values (each with its own identifier).
What are three types of arrays?The three types of arrays are index, multidimensional and associative array.
my_nums= [5,10,15] is an array that stores multiples of 5.
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A statement that creates a list is my_nums= [5,10,15]. This is also known as array.
What is an array?
An array is a data structure consisting of a collection of elements (values or variables), each identified by at least one array index or key. An array is a combination of a set of elements which are all of the same data type, organized in a particular way. Arrays are used to store multiple values in a single variable, structure data, and access data more efficiently. Arrays are generally used to represent data in a structured way, and they can be used to perform various mathematical operations and other calculations. Arrays are also useful for sorting and searching data in a predetermined order.
What are three types of array?
The three types of array are index, multidimensional and associative array.
my_nums= [5,10,15] is an array that stores multiples of 5.
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Work out the equation of the line which has a gradient of -2 and
passes through the point (1, 7)
Answer:
y = -2x + 9
Step-by-step explanation:
1) Use the equation y = mx + c (m being gradient and c being y-intercept)
2) Substitute all the values to get 7 = -2(1) + c
3) Solve to get c:
7 = -2 + c9 = c4) Final answer: y = -2x + 9
In 15 words or fewer, will dividing the two polynomials in the table produce another polynomial? Why or why not?
Dividing two polynomials may produce another polynomial only when the divisor has a lower degree than the dividend. Otherwise, it will generally result in a rational function.
No, dividing two polynomials may not result in another polynomial. It can produce a rational function.
A polynomial is an algebraic expression consisting of terms with non-negative integer exponents. When two polynomials are divided, the result is not always a polynomial.
If the degree of the polynomial being divided (dividend) is higher than the degree of the polynomial dividing (divisor), then the result can be a polynomial with a lower degree. However, if the degree of the divisor is equal to or greater than the degree of the dividend, the result will generally be a rational function, which is a ratio of two polynomials.
A rational function has the form P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) is not equal to zero. The division can introduce terms with negative or fractional exponents, making the result a rational function rather than a polynomial.
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Last year there were 24,584 age-discrimination claims filed with the Equal Employment Opportunity Commission. Assume there were 260 working days in the fiscal year for which a worker could file a claim. A. Calculate the average number of claims filed on a working day. (Round your answer to 4 decimal places. ) Average number of claims b. What is the probability that exactly 100 claims were filed on a working day? (Do not round intermediate calculations. Round your final answer to 4 decimal places. ) Probability c. What is the probability that no more than 100 claims were filed on a working day? (Do not round intermediate calculations. Round your final answer to 4 decimal places. ) Probability
A. The average number of claims filed on a working day is 94.5538.
B. The probability that exactly 100 claims were filed on a working day is 0.0361.
C. The probability that no more than 100 claims were filed on a working day is 0.9583.
A. The average number of claims filed on a working day can be calculated by dividing the total number of claims by the number of working days. In this case, the average would be 24,584 / 260 = 94.55384615.
Therefore, the average number of claims filed on a working day is 94.5538.
B. The probability of exactly 100 claims being filed on a working day can be calculated using the Poisson distribution formula:
P(X = x) = (λˣ)(e^-λ) / x!
Where λ is the mean (or average) number of claims filed on a working day, x is the number of claims we are interested in (100), and e is the base of the natural logarithm (approximately 2.71828).
Plugging in the values, we get:
P(X = 100) = (94.55384615¹⁰⁰)(e^-94.55384615) / 100! = 0.0361
Therefore, the probability of exactly 100 claims being filed on a working day is 0.0361.
C. The probability of no more than 100 claims being filed on a working day can be calculated by summing the probabilities of 0 to 100 claims being filed. This can be done using the Poisson distribution formula:
P(X ≤ 100) = Σ P(X = x) for x = 0 to 100
= P(X = 0) + P(X = 1) + ... + P(X = 100)
= (94.5546^0)(e^-94.5546) / 0! + (94.5546^1)(e^-94.5546) / 1! + ... + (94.5546^100)(e^-94.5546) / 100!
= 0.9583
Therefore, the probability of no more than 100 claims being filed on a working day is 0.9583.
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Drag and drop the constant of proportionality into the box to match the table. If the table is not proportional drag-and-drop not proportional into the box.
Answer:
Proportionality constant = \(\frac{3}{2}\)
Step-by-step explanation:
Let y ∝ x
y = kx
Here, k = proportionality constant
From the table attached,
If x = 2 and y = 3,
3 = 2k
k = \(\frac{3}{2}\)
If x = 4 and y = 6,
6 = 4k
k = \(\frac{6}{4}\)
k = \(\frac{3}{2}\)
Since, k = \(\frac{3}{2}\) is constant in every condition, table represents the proportional relation with proportionality constant \(\frac{3}{2}\).
Using the data in the table, on which interval is the function
increasing?
A)2
B) 0
C) -1 < x < 0
D) -3 < x < -1
Answer:
B
yuueg7wggssee drduuygeddy jrjwd ff
The lengths of the sides of the triangles are 13cm, 14cm, and 15cm. Is the triangle a right triangle?
Answer:
no i don't think
Step-by-step explanation:
it is not be a right angle is 90 and when u add it it doesn't match
When comparing three or more populations means within a set of quantitative data that is categorized according to one factor/treatment, a one-way ANOVA is appropriate.a. It is also appropriate in this situation, however, to compare two means at a time using multiple independent two sample t-tests. b. It is appropriate to compare two means at a time with independent two sample t-tests but it might be time-consuming.c. It is not appropriate to compare two means at a time in the way described. This would inflate the overall Type I Error and is a 'Multiple Testing' problem. The one-way ANOVA controls for the Type I Error and should be used instead.
According one-way ANOVA, the test is false.
We learn about one-way ANOVA
"One-Way ANOVA, also known as "analysis of variance," examines the refers to two or more independent groups to see if there is statistical support for the notion that the related population means are statistically substantially different."
According to the given information, it is inappropriate to compare two means at a time using multiple independent two sample t-tests. It will create multiple testing problem and error.
So using one way ANOVA test when comparing three or more populations refers to within a set of quantitative data that is categorized according to one factor/treatment and compare two means at a time using multiple independent two sample t-tests is false.
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consider three data sets (also, in data set symmetry). 242 probability and statistics for computer scientists (1) 19, 24, 12, 19, 18, 24, 8, 5, 9, 20, 13, 11, 1, 12, 11, 10, 22, 21, 7, 16, 15, 15, 26, 16, 1, 13, 21, 21, 20, 19 (2) 17, 24, 21, 22, 26, 22, 19, 21, 23, 11, 19, 14, 23, 25, 26, 15, 17, 26, 21, 18, 19, 21, 24, 18, 16, 20, 21, 20, 23, 33 (3) 56, 52, 13, 34, 33, 18, 44, 41, 48, 75, 24, 19, 35, 27, 46, 62, 71, 24, 66, 94, 40, 18, 15, 39, 53, 23, 41, 78, 15, 35 (a) for each data set, draw a histogram and determine whether the distribution is rightskewed, left-skewed, or symmetric. (b) compute sample means and sample medians. do they support your findings about skewness and symmetry? how?
a) Histogram for first , second and third data set is present in first, second and third above figure and it shows data is
left-skewed, symmetric and right-skewed.
b) Sample means for first, second and third data set are 14.96667, 20.83, 41.3 respectively. Sample medians for first, second and third data set are 15.5, 21, 39.5 respectively. Yes, they support our findings about skewness and symmetry.
We have three data sets of probability and statistics for computer scientists are present below, (1) 19, 24, 12, 19, 18, 24, 8, 5, 9, 20, 13, 11, 1, 12, 11, 10, 22, 21, 7, 16, 15, 15, 26, 16, 1, 13, 21, 21, 20, 19
(2) 17, 24, 21, 22, 26, 22, 19, 21, 23, 11, 19, 14, 23, 25, 26, 15, 17, 26, 21, 18, 19, 21, 24,
18, 16, 20, 21, 20, 23, 33
(3) 56, 52, 13, 34, 33, 18, 44, 41, 48, 75, 24, 19, 35, 27, 46, 62, 71, 24, 66, 94, 40, 18, 15, 39, 53, 23, 41, 78, 15, 35
a) Histogram is defined as a bar graph like representation of data that buckets a range of classes into columns along the horizontal x-axis.
Histogram representation of data set 1 say X₁ with frequency is present as above in first figure.From the above histogram, the data looks left-skewed.
Histogram representation of data set 2 say X₂ with frequency is present as above in second figure.From the above histogram, data looks like almost symmetric.
Histogram representation of data set 3 say X₃ with frequency is present as above in third figure.From the above histogram, the data looks right-skewed.
b) Sample mean and median :
The mean is the Arithmetic average of a data set. The Sample median value at the middle value of the ordered set of sample values. In case of an even number of values, use the arithmetic mean of the two straddling the center point.As we see here data values are larges in count. So, for making the process easy we can use Excel command.
Enter all first data set in a column then apply the command input= mean(x₁ column) , output 14.96667
= median(x₁column) = 15.5
Now, Mean < Median => Data is left - skewed. Similarly, mean(x₂ column ) = 20.83333 and median(x₂ column) = 21
Mean = 20.83
Median = 21
Mean ≈ Median => Data is symmetric. input : = mean(x₃) ; output : 41.3
input : = median(x₃) ; output: 39.5
Mean = 41.3
Median = 39.5
Mean > Median => Data is right - skewed.
Based on the above calculations, we conclude that scenario 1 ( that is histogram method) has lesser cost and is preferable.
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Determine the equation of the polynomial, f(x), of minimum degree whose graph is shown above. Write your answer in factored form.
f(x)=____
Answer:
\(f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)\)
Step-by-step explanation:
The root -2 has a multiplicity of 2, and corresponds to a factor of \((x+2)^2\).
The root 1 has a multiplicity of 1, and corresponds to a factor of \((x-1)\).
The root 3 has a multiplicity of 1, and corresponds to a factor of \((x-3)\).
So, \(f(x)=a(x+2)^2(x-1)(x-3)\).
Since \(f(0)=10\),
\(10=a(0+2)^2(0-1)(0-3) \\ \\ 10=12a \\ \\ a=\frac{5}{6} \\ \\ \therefore f(x)=\frac{5}{6}(x+2)^2(x-1)(x-3)\)
How does the mean compare to the median? How do the values of 7 and 9 affect these measures of center?
Sorry I suck at taking pictures, and math apparently.
Answer:Bueno, normalmente en los artículos semanales intento transmitir dudas o cuestiones que están en el campo, los trending topics del sector porcino, y está claro que la estadística no es uno de ellos, pero precisamente ayer se dio una situación que me llevó a escribir ésta entrada.
Todos los que trabajamos en el sector porcino estamos acostumbrados a manejar y calcular un montón de datos que nos proporciona el programa de gestión, y en muchas ocasiones realizamos pequeñas (o grandes) pruebas, donde manejamos infinidad de números (pesos, GMD, IC etc…)
Lo que sí es cierto, es que la mayoría de nosotros usamos siempre la media como herramienta fundamental. Media de Nacidos vivos, Media de destetados, Media de peso al nacer, media de peso al destete…..media, media, media…y ¿qué tal si usáramos la Mediana?
Éste fue el debate que tuve ayer con un ingeniero agrónomo (si, si, y yo Veterinaria, diversión asegurada), y el que me ha inspirados para hoy.
Para el que, en estos momentos, esté rebuscando en los archivos de su cerebro, “yo esto lo sabía”, un pequeño recordatorio:
La media o promedio, Se interpreta como “punto de equilibrio” o “centro de masas del conjunto de datos. Es un cálculo muy sencillo en el que intervienen todos los datos. Consiste en el sumatorio de todos los datos dividido por el número de valoresLa mediana, en cambio, es un valor de la variable que deja por debajo de sí a la mitad de los datos, y por encima, la otra mitad.( una vez que estos están ordenados de menor a mayor). Se sitúa, por lo tanto, en la mitad real de los datos.
Es mucho más difícil de calcular:
Con un ejemplo se entiende muchísimo mejor.
Imaginaos una empresa en la que la mayoría de los trabajadores tienen un sueldo de 1000 euros, excepto 2 encargados que cobran 2000 y el jefe que cobra 6000 euros mensuales.
¿Cuál es el salario medio de la empresa?
Si vemos la media sale casi 2000 euros, si miramos la mediana, nos da 1000.
¿Cuál se aproxima más a la realidad?
Cuando los datos son muy homogéneos la media nos da un valor representativo de la realidad, pero cuando los datos son muy heterogéneos no.
Un ejemplo más cercano a nosotros
Queremos saber el peso de los lechones a destete. Imaginemos que la camada A tiene los siguientes pesos: (4-3-5-4.5-6.1-5-3-5.1-6.4-6-6.5-5.5-4.9).
Step-by-step explanatio
The ____ statement is useful when you need to test a single variable against a series of exact integer, character, or string values.
The "switch" statement is useful when you need to test a single variable against a series of exact integer, character, or string values.
The switch statement is a control structure found in many programming languages, including C++, Java, and JavaScript. It allows you to evaluate a variable or expression and compare it against multiple cases.
Each case represents a specific value that the variable or expression is tested against. When a match is found, the corresponding block of code associated with that case is executed.
The switch statement is particularly useful when you have a variable that can take on different values and you want to perform different actions based on those values. Instead of writing multiple if-else statements, the switch statement provides a more concise and efficient way to handle such scenarios.
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x(t)=e j(2t+ 8 π ) [u(t−5)−u(t−10)] y(t)=e 0.5t u(−t+3) 10. What is the period of x(t)+y(t) ? (A) 2 (B) π (C) π/8 (D) 16 (E) 0.5 (F) 4π (G) x(t)+y(t) is aperiodic
Neither x(t) nor y(t) is periodic, their sum x(t)+y(t) is also aperiodic. Therefore, the correct answer is (G) x(t)+y(t) is aperiodic.
To find the period of the sum of two signals x(t) and y(t), we need to determine if either of the signals is periodic and, if so, find the period.
Let's analyze each signal separately:
x(t) = e^(j(2t+8π))[u(t−5)−u(t−10)]:
The exponential term e^(j(2t+8π)) is periodic with a period of 2π/2 = π. However, the presence of the step function u(t−5)−u(t−10) restricts the signal to the interval [5, 10]. Since this interval is shorter than π, x(t) is not periodic.
y(t) = e^(0.5t)u(−t+3)10:
The exponential term e^(0.5t) is not periodic, as it grows exponentially with time. The step function u(−t+3) restricts the signal to the interval [−∞, 3]. Since this interval is infinite, y(t) is also not periodic.
Since neither x(t) nor y(t) is periodic, their sum x(t)+y(t) is also aperiodic. Therefore, the correct answer is (G) x(t)+y(t) is aperiodic.
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Find the slope of a line perpendicular to the line whose equation is
x−y=3. Fully simplify your answer
The slope of a line perpendicular to the line whose equation is x−y=3 is -1.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Since the equation of this line is perpendicular to the line x - y = 3, the slope is given by;
x - y = 3
y = x - 3
Slope, m₁ = 1
m₁ × m₂ = -1
1 × m₂ = -1
m₂ = -1/1
Slope, m₂ = -1
At data point (2, 4) and a slope of -1, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 4 = -1(x - 2)
y = -x + 2 + 4
y = -x + 6
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How many terms are in the expression 3x+y−23−5
Answer:
There are 4 terms
Step-by-step explanation:
“Terms are single numbers, variables, or the product of a number and variables. Examples of terms: 9 a 9a 9a. y y y.”
Nalani says the expression 9+7r cannot be factored using the GCF. Is she correct? Explain why or why not
Answer:
Nalani is correct.
Step-by-step explanation:
Given - Nalani says the expression 9+7r cannot be factored using the GCF.
To find - Is she correct? Explain why or why not.
Proof -
GCF - Greater Common factor
Given that, the expression is - 9 + 7r
As
HCF(9, 7) = 1
So , we can not factor the expression.
i.e. there does not exist any number who is a multiple of 9 and 7 both.
So,
Nalani is correct.
Example -
Let the expression be 24 + 18x
HCF(24, 18) = 6
So,
24 + 18x = 6(4 + 3x)
a particle travels 24.6km in 30 minutes. find the speed of the particle in km/h
Answer:
49.2 km/h
Step-by-step explanation:
30 min times two equal an hour
24.6km times two equal 49.2 km/h
Hope this helps.
Find the length of diagonal AC in the rectangle
at the right
show you’re work plss
Answer:
26
Step-by-step explanation:
Let 10 be a, and 24 be b, and the undefined hypotenuse be c.
\(a^2 + b^2 = c^2\)
\(10^2 + 24^2 = c^2\)
100 + 576 = c
c = 676
\(\sqrt{100} + \sqrt{576} = \sqrt{676}\)
\(10^2 + 24^2 = 26^2\)
c = 26
The value of the undefined line is 26.
5. The volume of a sphere is 3053.628 ft³. Find its surface area.
Answer:
Solution is in attached photo.
Step-by-step explanation:
Use table to find each product
According to the problem the product of (X —6)(3X + 4) is 3X² - 18X - 24.
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The product of (X —6)(3X + 4) can be found by using the distributive property and multiplying each term of the first binomial (X —6) by each term of the second binomial (3X + 4). This can be done by creating a table with the two binomials written out in two columns.
| X | -6 |
| 3X | 4 |
Then, multiply each term in the first column by each term in the second column and add the products together.
X*3X = 3X²
X*4 = 4X
-6*3X = -18X
-6*4 = -24
Therefore, the product of (X —6)(3X + 4) is 3X² - 18X - 24.
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Y = at² - 2at
x = 2a√t
express y in terms of x and a
The expression for y in terms of x and a is y = a(x - √(x² + 2a√t))².
To obtain the expression for y in terms of x and a, we need to simplify the given equation.
Given equation: Y = at² - 2atx = 2a√t
First, let's isolate t in terms of x:
2a√t = at² - 2atx
2√t = t² - 2tx
t² - 2tx - 2√t = 0
Now, we can solve this quadratic equation for t using the quadratic formula:
t = (2x ± √((2x)² - 4(-2√t))) / 2
t = x ± √(x² + 4√t)
Substituting the value of t back into the original equation:
y = a(x - √t)²
y = a(x - √(x² + 4√t))²
y = a(x - √(x² + 4√(a√t)))²
y = a(x - √(x² + 2√(4at)))²
y = a(x - √(x² + 2√(4a)√t))²
y = a(x - √(x² + 2√4a√t))²
y = a(x - √(x² + 2(2√a)√t))²
y = a(x - √(x² + 4√a√t))²
y = a(x - √(x² + 2√a√t)²)
y = a(x - (√(x² + 2√a√t)))²
y = a(x - √(x² + 2a√t))
Therefore, the expression for y in terms of x and a is y = a(x - √(x² + 2a√t))².
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