Using the definition of slope, the points (3 , -5), (-3 , 3), and (0 , 2) are not collinear.
Three or more points are said to be collinear if they lie on a single straight line.
To determine whether the given points are collinear, use the definition of slope. The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.
m = (y2 - y1)/(x2 - x1)
Getting the slope of each pair of points:
(3 , -5) and (-3 , 3)
m = (y2 - y1)/(x2 - x1)
m = (3 - -5)/(-3 - 3)
m = 8/-6
m = -4/3
(-3 , 3) and (0 , 2)
m = (y2 - y1)/(x2 - x1)
m = (2 - 3)/(0 - -3)
m = -1/3
(3 , -5) and (0 , 2)
m = (y2 - y1)/(x2 - x1)
m = (2 - -5)/(0 - 3)
m = 7/-3
m = -7/3
Since collinear points lies on the same line, the slope of any pair of points should be the same. Since the slopes of each pair of points is not equal with each other, then they are not collinear.
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The area of a rectangular garden is 24x^2 - 64x. The width is 8x. Find the length in terms of X.
The length of the garden will be - L = 3x - 8.
We have a rectangular garden.
We have to determine its length.
What is the Area of Rectangle?The area of rectangle is -
A = L x B
According to the question -
Area = [tex]24x^{2} -64x[/tex]
Width = [tex]8x[/tex]
Therefore -
Area = Length x Width
Length = Area / width
Length = [tex]$\frac{24x^{2} -64x}{8x} = 3x -8[/tex]
Hence, the length of the garden will be - L = 3x - 8.
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Choose the vocabulary term that correctly completes each sentence.
If an infinite geometric series ______ then it must have a sum.
If an infinite geometric series is a convergent series then it must have a sum.
What is a convergent series?
If a series' partial sum sequence tends to a limit, it is said to be convergent (or to be convergent)This indicates that as partial sums are added in the order indicated by the indices, they approach closer and closer to a certain number. When a series becomes closer to a particular value as it gets closer to infinity, it is said to be convergent. A series in mathematics is the total of all the terms in an infinite series of numbers.Two forces must be moving in concert for there to be convergence. If a finite real number L serves as the limit of a sequence of real numbers, the sequence is said to be convergent.To learn more about convergent series, refer:
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Use the given information to determine whether LM is a perpendicular bisector, median, and/or an altitude of Δ J K L .
LM ⊥ JK
Since LM ⊥ JK, LM is an altitude by the definition of altitude. We don't know if it is a perpendicular bisector because it is not evident that M is the midpoint of JK.
What is meant by the altitude of a triangle?An altitude of a triangle is a line segment through a vertex that is perpendicular to a line containing the base in geometry. The extended base of the altitude is the line that contains the opposite side. The intersection of the extended base and the altitude is known as the altitude's foot.
A triangle's altitude is the perpendicular drawn from the triangle's vertex to the opposite side. The altitude, also known as the triangle's height, forms a right-angle triangle with the base.
Since LM ⊥ JK, LM is an altitude by the definition of altitude. We don't know if it is a perpendicular bisector because it is not evident that M is the midpoint of JK.
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In this problem, you will investigate expected value.
b. Use the random number generator on a calculator to generate, 20 pairs of integers between 1 and 6 . Record the sum of each pair.
The 20 randomly generated pairs for the numbers 1 to 6 is (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2,3), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,4), (4,5), (4,6), (5,5), (5,6) and the sum of each pair is 2, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 6, 7, 8, 9, 8, 9, 10, 10, 11.
Sum of the number:
When we add two or more numbers, the result or the answer we get can be defined as the SUM. The numbers that are added are called addends.
For example if we add the numbers 2 and 7 then we get the um as 9.
Given,
Here we need to generate the 20 pairs of integers between 1 and 6 . And also we have to record the sum of each pair.
The 20 pairs by using the number 1 to 6 are,
Listed as,
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2,3), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,4), (4,5), (4,6), (5,5), (5,6).
Now the sum of these 20 pairs are,
(1,1) = 1 + 1 = 2
(1,2) = 1 + 2 = 3
(1,3) = 1 + 3 = 4
(1,4) = 1 + 4 = 5
(1,5) = 1 + 5 = 6
(1,6) = 1 + 6 = 7
(2,2) = 2 + 2 = 4
(2,3) = 2 + 3 = 5
(2,4) = 2 + 4 = 6
(2,5) = 2 + 5 = 7
(2,6) = 2 + 6 = 8
(3,3) = 3 + 3 = 6
(3,4) = 3 + 4 = 7
(3,5) = 3 + 5 = 8
(3,6) = 3 + 6 = 9
(4,4) = 4 + 4 = 8
(4,5) = 4 + 5 = 9
(4,6) = 4 + 6 = 10
(5,5) = 5 + 5 = 10
(5,6) = 5 + 6 = 11
Therefore, the sum of each pair is 2, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 6, 7, 8, 9, 8, 9, 10, 10, 11.
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Find the 13th term of the geometric sequence 7, 21, 63
Answer: 3720087
Step-by-step explanation:
n=term number
an=term value
terms: 7, 21, 63...
term number: 1, 2, 3, ...
7 is 1st term. 21 is 2nd term. 63 is 3rd term.
21/7=3
63/21=3
Common change in each term is multiplication by 3
Hence, the formula can be expressed in exponents.
an=3^(n-1) * 7 where n is the term number, an is the term value, and 7 is the 1st term in the sequence.
an=3^(13-1) * 7
an=3^12 * 7
an=531441 * 7
an=3720087
he graph of the function f(x) = (x − 3)(x + 1) is shown. On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1, negative 4), and goes through (3, 0). Which describes all of the values for which the graph is positive and decreasing? all real values of x where x < −1 all real values of x where x < 1 all real values of x where 1 < x < 3 all real values of x where x > 3
Answer:
real x values is x < -1
Step-by-step explanation:
Julia is the oldest of three siblings whose ages are consecutive integers. If the sum of their ages is 42, find Julia's age.
Answer:
Her age is 15.
Step-by-step explanation:
13 + 14 + 15 = 42
Julia is the oldest and 15 is the greatest of the 3 numbers
therefore Julia is 15
The table shows the results of an experiment in which a spinner numbered 1-4 was spun.
What is the experimental probability that the spinner will land on a 4?
Answer:
1/4 or 25% or 0.25
Step-by-step explanation:
Help me pls
thanks
please show work!
Answer:
7. ) 3 3/4 9.) 3 1/8 11.) 7/16 13.) 5 13/15 15.) 7 1/2
Step-by-step explanation:
Number 7, first make 4 1/6 into an improper fraction.
6x4+1= 25/6
25/6x9/10
225/60
Simplified- 3 3/4
Number 9, make 4 3/8 into an improper fraction.
4x8+3= 35/8
35/8x5/7
175/56
Simplified- 3 1/8
Number 11, make 2 5/8 into an improper fraction.
2x8+5= 21/8
21/8x1/6
21/48
Simplified- 7/16
Number 13, make 1 3/5 and 3 2/3 into an improper fraction.
1x5+3= 8/5, 3x3+2=11/3
8/5x11/3
88/15
Simplified- 5 13/15
Number 15, make 3 1/3 and 2 1/4 into an improper fraction.
3x3+1= 10/3, 2x4+1=9/4
10/3x9/4
90/12
Simplified- 7 1/2
Hope that helped! :D
What are the domain and range of the function represented by the set of
ordered pairs?
{(-13, 9), (-7,-5), (5, 14), (11,-10)}
The function's domain and range as represented either by set of ordered pairs:
Domain = (-13 , -7 , 5 , 11)
Range = (9 , -5 , 14 , 11)
What is function's domain and range?Range and domain The domain of something like a function is the set of values that can be plugged into it. This set contains the x values in a function like f. (x). A function's range is the collection of values that the function can take. This is the set of values that the function returns after we enter an x value.
According to the data:The set of ordered pairs = {(-13, 9), (-7,-5), (5, 14), (11,-10)}.
(x,y)
x=input
y=output
As a result, the domain consists only of the first numbers.
range refers to all of the second numbers.
x=domain
y=range
So,
Domain = (-13 , -7 , 5 , 11)
Range = (9 , -5 , 14 , 11)
The function's domain and range as represented either by set of ordered pairs:
Domain = (-13 , -7 , 5 , 11)
Range = (9 , -5 , 14 , 11)
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We have 6 books on mathematics, 3 on physics, and 1 on chemistry, and you must choose 1 book. in how many ways can you do that? (also think why the an
The number of ways that a book can be chosen from all the books can be determined by using combination.
Combination is a method of choosing items from a set in a way that order of selection does not matter. It refers to the combination of n items taken k at a time without repetition. From example, selection of food, menu, subjects, etc.
A combination is the selection of r items from a set of n items without replacement and where order is unimportant.
nCr=n!/r!(n-r)!
Where n! = 1*2*3*….*n
In the given situation, r = 1(number of books to be chosen) and n=10(total number of books)
10C1=10!/1!(10-1)!
10C1=10!/1!(9)!
10C1=(10*9!)/1!(9)!
10C1=10
The number of ways to choose a book from the ten books is 10.
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Expand, x³(3x - 5).
3x^4-5x³
Step-by-step explanation:
Find the slope of the line that contains the points (4,3) and (-2,-5).
The slope of the line that contains the points (4,3) and (-2,-5) is 4/3
In this question,
we need to find the slope of the line that contains the points (4,3) and (-2,-5).
We know that the slope of the line passing though points (x1, y1), (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Let (x1, y1) = (4, 3),
(x2, y2) = (-2, -5)
Using the formula of the slope,
m = (y2 - y1) / (x2 - x1)
m = (-5 - 3) / (-2 - 4)
m = -8 / (-6)
m = 4/3
Therefore, the slope of the line that contains the points (4,3) and (-2,-5) is 4/3
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What are the next three terms in the sequence, 500, 100, 20?
Answer: –1, 9, 19, 29, … (1 point)
38, 37, 32
40, 51, 62
39, 49, 59
38, 47, 56.
Step-by-step explanation: tried
A boat is cruising at a speed of 24 miles per hour. The captain plans to cruise at this speed for the next 9 miles, plus or minus 3 miles. What is the minimum number of hours the boat will cruise at? Maximum number of hours?
Answer:
Minimum 1/4 Hour Maximum 1/2 Hour
Speed is the ratio of distance and time.
The maximum number of hours the boat will cruise is 1/2 hours.
The minimum number of hours the boat will cruise is 1/4 hour.
What is speed?Speed is the ratio of distance and time.
It tells us how fast a body is moving.
We have,
Boat speed = 24 miles per hour.
Speed = distance / time
Distance = 9 miles
Time = distance / speed
Minimum number of hours:
Distance = 9 - 3 = 6 miles
Time = Distance / Speed = 6 / 24 = 1/4 hours
Maximum number of hours:
Distance = 9 + 3
Time = Distance / Speed = 12 / 24 = 1 / 2 hours
Thus,
The maximum number of hours the boat will cruise is 1/2 hours.
The minimum number of hours the boat will cruise is 1/4 hour.
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points A(-1.5) and b(6) are marked on a number line. find the coordinate of point m if it is know that AM:md = 1:2
The coordinates of point m if it is known that am : md = 1 : 2 is (4/3, 5)
How to find the coordinates of point m?The given parameters are
A = (-1, 5)
B = (6, 5)
Ratio, m : n = 1 : 2
The coordinates of point m are calculated using
M = 1/(m + n) * (mx2 + nx1, my2 + ny1)
So, we have
M = 1/(1 + 2) * (1 * 6 + 2 * -1, 1 * 5 + 2 * 5)
Evaluate the sum of products
So, we have
M = 1/3 * (4, 15)
Evaluate the product
M = (4/3, 5)
Hence, the coordinates of point m if it is known that am : md = 1 : 2 is (4/3, 5)
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Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. y=x-2(x+5)
The given function y = x- 2(x+5), is a linear function.
It has no quadratic termIts linear term is -xIts constant term is -10What is a function?A function is a mathematical expression or equation that allows us to visualize graphically the behavior of a function. A function is not real when it cuts the vertical axis at the same point of x.
A function can be linear or quadratic, this is evidenced by the higher exponential degree.
We rewrite the function and reduce it to its minimum expression:
y = x- 2(x+5)
y = x + (-2x - 10)
y = x - 2x - 10
y = -x - 10 , linear function.
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Find the value of x2 for 8 degrees of freedom and an area of .05 in the left tail of the chi-square distribution.
The value of x² for 8 degrees of freedom and an area of .05 in the left tail of the chi-square distribution is 1.344
Chi-square Distribution:
The chi-square distribution is a continuous probability distribution. It is skewed to the right or positively skewed for low degrees of freedom but shifts towards the symmetric distribution as the degrees of freedom are increased.
Given,
Degree of freedom = 8
Area of the left = 0.05
Here we need to find the value X² of the chi-square distribution.
The value of X² of the chi-square distribution is calculated through the formula,
X² = X²₍₁ ₋ₓ₎,y
Where
x represents the area of the given tails
y represents the degree of freedom
Apply the values on the formula,
=> X² = X²₍₁ ₋₀.₀₅₎,8
=> X² = X²₍₀.₉₉₅₎,8
Now, based on the Chi square distribution table,
The value of
=> X² = 1.344
Therefore, the value of x² for 8 degrees of freedom and an area of .05 in the left tail of the chi-square distribution is 1.344
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What is 0.5 written as a fraction?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]0.5*\frac{10}{10} = \frac{5}{10} = \frac{1}{2}[/tex]
O
O
-100
What is the probability of flipping tails on the coin and spinning a 2 on the spinner?
8
Tails
414
4
3
(T.1)
(T.2)
(T.3)
(T.4)
Answer:
a 50% chance of getting tails
but about the spinner It depends on what kind of spinner it is and how many sides/numbers/etc
does it have
Use completing the square to solve for x in the equation (x minus 12) (x + 4) = 9.
The solution fo the equation by completing the square is x = 12.544 or -4.544
What is completing the square method?Completing the square method is a method of solving quadratic equations in which the equation is converted into a perfect square binomial.
How to use completing the square to solve the equation?Given (x - 12)(x + 4) = 9
Expanding the brackets, we have
x² - 12x + 4x - 48 = 9
x² - 8x - 48 = 9
x² - 8x - 48 - 9 = 0
x² - 8x - 57 = 0
To complete the square, we add half the square of the coefficient of x to both sides. so,
x² - 8x - 57 = 0
x² - 8x - 57 + (-8/2)² = 0 + (-8/2)²
x² - 8x - 57 + (-4)² = 0 + (-4)²
x² - 8x + (-4)² - 57 = 0 + (-4)²
(x - 4)² - 57 = 16
(x - 4)² = 16 + 57
(x - 4)² = 73
Taking square roots, we have
x - 4 = ±√73
x - 4 = ±8.544
x = 4 ± 8.544
x = 4 + 8.544 or x = 4 - 8.544
x = 12.544 or -4.544
So, the solution fo the quadratic equation by completing the square is x = 12.544 or -4.544
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Answer:
Step-by-step explanation:
x=+/-square root 73
Michele bought a chocolate cake for $12.75 plus 9 cupcakes to bring to a party. Myka bought 24 cupcakes at the same bakery. If Myka and Michele spent the same amount, how much did each cupcake, x, cost?
Considering the definition of an equation and the way to solve it, each cupcake cost $0.85.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The solution of a equation means determining the value that satisfies it and the equality is true. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Cost of the cupcakeBeing "x" thecost of the cupcake, and knowing that:
Michele bought a chocolate cake for $12.75 plus 9 cupcakes to bring to a party. → Amount spent by Michele=12.75 + 9xMyka bought 24 cupcakes at the same bakery. → Amount spent by Myka= 24xMyka and Michele spent the same amount.the equation in this case is:
Amount spent by Michele= Amount spent by Myka
12.75 + 9x= 24x
Solving:
12.75= 24x - 9x
12.75= 15x
12.75÷ 15= x
0.85=x
Finally, each cupcake cost $0.85.
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For whole number n, n3 will be odd if n is odd and even if n is even
Laci and Leon are saving money to go to an amusement park. Laci has $1 more than 4 times the amount of money Leon has. Together, they have $76. Write an equation to determine how much money they have together
Answer:
Step-by-step explanation:
x+4x+1=76 is the answer
The total cost to buy gloves for the football team can be found using the function \(p=24.99g+5.69\), where \(g)\ is the number of gloves bought. If there are at least \(7\) players but no more than \(14\) players on the football team, what is the domain of the function for this situation
The domain of the given function is a 180.62 to 355.55.
According to the statement
We have to find that the linear equation domain.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
The total cost to buy gloves for the football team can be found using the function \(p=24.99g+5.69\), where \(g)\ is the number of gloves bought. If there are at least \(7\) players but no more than \(14\) players on the football team
Then
p=24.99g+5.69
Now find the value of the g is
p=24.99g+5.69
Here the domain of the g]function is a From 1 to 14.
Then
For 7
p=24.99(7)+5.69
p=174.93+5.69
p = 180.62.
And for 14
p=24.99(14)+5.69
p=349.86+5.69
p = 355.55.
So, The domain of the given function is a 180.62 to 355.55.
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Select the reason that best supports Statement 6 in the given proof.
URGENTTTT!!!
Answer:
B) distributive propertyStep-by-step explanation:
The statements 6 covers the operation:
3(x + 7) = 3x + 21This is the reflection of the distributive property of multiplication.
The matching answer choice is B.
Which expression shows a way to factor 36+48
The expression for 36+48 is 12(3 + 4).
What is factor?A number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.
Given:
36+48
Now, factorise 36 and 48
36=2*2*3*3
48=2*2*2*2*3
So, the common factor is 12.
Hence, the for the factor is 12(3 + 4)
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what is the inverse of h(x)=7x^2+8 with the domain restriction x greater than or equal to 0
The inverse of the function is f-1(x) = √1/7(x - 8)
How to determine the inverse of the function?The function is given as
h(x) = 7x^2 + 8
Express h(x) as y
So, we have
y = 7x^2 + 8
Swap the positions of x and y
So, we have
x = 7y^2 + 8
Rewrite as
7y^2 = x - 8
Divide by 7
y^2 = 1/7(x - 8)
Take the square roots
y = √1/7(x - 8)
Hence, the inverse of the function is f-1(x) = √1/7(x - 8)
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The least preferable and reliable method of selecting people to participate in a research study is:_____.
The least preferable and reliable method of selecting people to participate in a research study is convenience sampling.
Convenience sampling is a type of sampling in which you include people who are easy to reach. Convenience sampling is included in non-probability sampling because it doesn't include a random selection of the participants. Convenience sampling can be used when you need to conduct a study quickly or when you are on a shoestring budget as it is inexpensive compared to other methods of sampling.
It is the least preferable method because of the inability to generalize the result of the survey to the population as a whole. In addition to this, there is a possibility of under or over-representation of the population as a whole. The biggest problem with convenience sampling is dependence as the sample items are connected to each another in some way. This dependency interferes with statistical analysis.
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a. A line passes through (-5,0) and (0,7) . What is an equation of the line in point-slope form?
7 - 0 = 7/5(0 - (-5)) is the equation in slope intercept form for the line passes through points (-5,0) and (0,7).
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope.
We have been asked to write an equation of the line in point-slope form
of a line which passes through (-5,0) and (0,7)
We know that point-slope form = y₂ - y₁ = m(x₂ - x₁)
But first we will find slope(m)
We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
For the pairs of points (-5,0) and (0,7)
⇒ m = [tex]\frac{7- 0}{0 - (-5)}[/tex]
⇒ m = [tex]\frac{7}{5}[/tex]
⇒ m = 7/5
After we substitute the given information we get
7 - 0 = 7/5(0 - (-5))
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