In the set {(3,4), (4,4), (8,-1)} what is this not? *
A-a function
B-a relation
C-a set of real numbers
D-a one to one function
Answers
Given:
The set is
\(\{(3,4),(4,4),(8,-1)\}\)
To find:
The correct option for the given set which represents the quality that is not in the given set.
Solution:
We have,
\(\{(3,4),(4,4),(8,-1)\}\)
It is the set of ordered pairs. So, it is a relation.
For each x-value there is a unique y-value value. So, it is a function.
All elements are real numbers but they not distinct and they are in ordered pairs. So, the given set is not a set of real numbers.
In one to one functions each image has exactly one preimage and each preimage has exactly one image.
In the given set 4 has two preimages 3 and 4. So, the given set is not a one to one function.
Therefore, the correct options are C and D.
Related Questions
The manager of a garden supply company claims that a new organic fertilizer, in comparison with the leading brand, increases the yield and size of tomatoes. To test this claim, 100 gardeners select whether they want to utilize the new organic fertilizer or stick with the leading brand fertilizer for the upcoming gardening season. At harvest time, the size and weight of each tomato are measured, along with the total yield per plant. The data collected is then used to compare the two fertilizers. The variable weight of the tomato in this study is what type of variable?
Answers
The variable "weight of the tomato" on this have a look at is a continuous quantitative variable. It is continuous due to the fact it is able to take on any price inside a certain variety, including grams or ounces, and isn't always restricted to precise discrete values.
The weight of every tomato is measured by the use of a scale or instrument that provides particular numerical values. This non-stop nature of the variable permits for comparisons and calculations the use of mathematics operations, including calculating manner, widespread deviations, or carrying out statistical exams.
The weight of the tomato can vary from very mild to very heavy, and the measurements can capture subtle differences in the tomatoes' sizes and weights.
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1. The price of the video game was $60.00. Thelprice was reduced by 25%. What was the sale price of the video game? A $15.00 B. $25.00 C. $45.00 D. $75.00
Answers
Answer:
The answer is A. $15.00
Step-by-step explanation:
Take 25% of 60 and that is 15. Please give me brainliest
Answer:
$45.00
Step-by-step explanation:
To find percentage, most start out by dividing the percent by 100:
25 ÷ 100 = 0.25
Then, to find the percentage of 60, we multiply them.
$60 x 0.25 = $15
15 is 25% of 60. However, we're asking the sale price of the video game, not the amount it was reduced. To find this out we subtract the reduced amount from the original number:
$60 - $15 = $45
≧◡≦
Mocha here! If this answer helped you, please consider giving it brainliest because I would appreciate it greatly. Have a wonderful day!
6²
Which theorem is shown by the diagram above?
a + b = c
C
D
a - b = c
a² + b² = c²
a²-b² = c²
Answers
The theorem is shown in a pythagoras theorem is c² = a² + b²
Which theorem is shown in a pythagoras theoremThe theorem shown in the Pythagorean theorem is "a² + b² = c²". This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with discovering it.
The Pythagorean theorem applies to right-angled triangles and states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Mathematically, we can express this as:
c² = a² + b²
Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides (called the legs) of the right-angled triangle.
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Aaron's mom had a long day at work. "I feel like I drank 3 gallons of coffee today!" she joked. If she really drank that much coffee, how many times would she have filled her 12-fluid-ounce mug?
Answers
The number of times that she has filled her 12-fluid-ounce will be 33.307.
What is conversion?Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
We know that in 1 gallon, there are 133.228 fluid ounces.
The amount of coffee in 3 gallons will be given as,
3 gallons = 3 x 133.228
3 gallons = 399.684 fluid ounces
The number of times that she has filled her 12-fluid-ounce will be given as,
⇒ 399.684 / 12
⇒ 33.307
The number of times that she has filled her 12-fluid-ounce will be 33.307.
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Let f(x) = sin x and g(x) = x² + 1. Find the following derivatives. d (a) (f(g(x))) (b) = (g(f(x))) dx dx d sin (x²+1) • sin(x²)+1 dx dx = cos(x²+1)(2x)
Answers
To find the derivatives of the given expressions, we can apply the chain rule, which states that the derivative of a composition of functions is equal to the derivative of the outer function multiplied by the derivative of the inner function.
(a) To find the derivative of f(g(x)), we start by differentiating the outer function f with respect to the inner function g(x), and then multiply it by the derivative of the inner function g(x) with respect to x.
df/dx = df/dg * dg/dx
df/dx = cos(g(x)) * (2x)
(b) To find the derivative of g(f(x)), we differentiate the outer function g with respect to the inner function f(x), and then multiply it by the derivative of the inner function f(x) with respect to x.
dg/dx = dg/df * df/dx
dg/dx = 2f(x) * cos(x)
Hence, the derivatives are:
(a) d/dx(f(g(x))) = cos(g(x)) * (2x)
(b) d/dx(g(f(x))) = 2f(x) * cos(x)
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Please Helpppppppppppppppppppp
Answers
Answer:
See below
Step-by-step explanation:
\((f+g)(2)=f(2)+g(2)=7+3=10\)
\((f-g)(4)=f(4)-g(4)=11-15=-4\)
\((f \div g)(2)=7 \div 3 = \frac{7}{3}\)
\((f \times g)(1)=f(1)\timesg(1)=5\times 0=0\)
What shape has 69 sides?
Answers
The polygonal shape of the hexacontakaienneagon has 69 sides.
A polygon is a two-dimensional, closed form that is flat or planar and is limited by straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge. Polygons include shapes like triangles, hexagons, pentagons, and quadrilaterals.
The hexacontakaienneagon shape's number of sides is indicated by the name. For instance, a triangle has three sides, whereas a quadrilateral has four. A two-dimensional closed figure with three or more straight sides is called a polygon. A polygon is any shape with straight edges, such as a triangle or rectangle. Figures with open sides or any curved sides are not considered to be polygons.
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what is the equation of the line that passes through the point (-2,0) and has a slople of -2
Answers
Answer:
y= -2x-4
Step-by-step explanation:
\( (-2,0) = (x_1,y_1) \\ m = - 2\)
Substitute values into point slope form
\(y - y_1 = m(x - x_1) \\ y - 0 = - 2(x - ( - 2)) \\ y - 0 = - 2(x + 2) \\ y - 0 = - 2x - 4\)
\(y = - 2x - 4 + 0 \\ y= - 2x - 4\)
Can someone help me please???
Answers
Answer:
C
Step-by-step explanation:
The sequence is adding +5 every time, and there are all positive numbers in the sequence so it is C.
Find the area of the polygon in square units.
Answers
The area of the polygon is 7.5 square units
How to determine the area of the polygonNote that the polygon given in the diagram takes the shape of a kite.
The properties of a kite are given as;
It two pairs of adjacent equal sidesIt has one pair of opposite angles that are equalThe diagonals are equalThe shorter diagonal forms two isosceles trianglesThe longer diagonal forms two equal trianglesThe diagonals are perpendicular to each otherThe formula for area of a kite is;
Area = pq/2
Area = 3(5)/2
Area = 15/2
Divide the values
Area = 7.5 square units.
Thus, the value is 7.5 square units
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Which ordered pair is a solution to the system of equations?
3x-3y=-9
2x+y=-3
A) (1,2)
B) (-2,1)
C) (0,-3)
D) (0,3)
(I'll give brainliest to the best answer)
Answers
Answer:
B) (-2,1)
Step-by-step explanation:
In order to find a solution to a system of equations, substitute the point's x and y values into both of the equations, solve, and see if it makes the equation true.
1) Let's try the point (-2,1). First, substitute its x and y values into the first equation, 3x - 3y = -9. Thus, substitute -2 for x and 1 for y in the equation and solve:
\(3x-3y = -9\\3(-2)-3(1) = -9\\-6 - 3 = -9 \\- 9 = -9\)
-9 does equal -9, thus (-2, 1) makes the first equation true.
2) Now, do the same thing but with the second equation, 2x + y = -3. Again, substitute -2 for x and 1 for y and solve:
\(2x + y = -3\\2(-2) + (1) = -3\\-4 + 1 = -3\\-3 = -3\)
-3 does equal -3, thus (-2, 1) makes the second equation true.
By substituting its values into both equations, we saw that it made both equations true. Thus, (-2,1) is the answer.
write the rule for the nth term and the 7th term of the sequence 6 24 96 384 1536
Answers
Given
The sequence,
6, 24, 96, 384.
To find the nth term of the sequence.
Explanation:
It is given that,
The sequence is,
6, 24, 96, 384.
That implies,
\(\frac{24}{6}=\frac{96}{24}=\frac{384}{96}=4\)Then, the given sequence is a GP.
Therefore,
The nth term of the given sequence is,
\(\begin{gathered} a_n=ar^{n-1} \\ =6(4)^{n-1} \end{gathered}\)That implies,
\(\begin{gathered} a_7=ar^{7-1} \\ =6(4)^6 \\ =6\times4096 \\ =24576 \end{gathered}\)Hence, the seventh term of the sequence is 24576.
Consider the logistic differential equation:
dy/dx = y/8(6 - y)
Let f(t) be the particular solution to the differential equationwith f(0) = 8
a. What is the limiting factor?
b. Use Euler's method, starting at t=0 with two steps of equalsize, to appropriate F(1).
c. What is the range of f for t > 0
Answers
The approximate value of f(1) using Euler's method with two steps of equal size is 6.636. The range of f for t > 0 is 0 < f(t) < 6.
a. The limiting factor in this logistic differential equation is the carrying capacity, which is 6 in this case. As y approaches 6, the growth rate of y slows down, until it eventually levels off at the carrying capacity.
b. To use Euler's method, we first need to calculate the slope of the solution at t=0. Using the given differential equation, we can find that the slope at t=0 is y(0)/8(6-y(0)) = 8/8(6-8) = -1/6.
Using Euler's method with two steps of equal size, we can approximate f(1) as follows:
f(0.5) = f(0) + (1/2)dy/dx|t=0
= 8 - (1/2)(1/6)*8
= 7.333...
f(1) = f(0.5) + (1/2)dy/dx|t=0.5
= 7.333... - (1/2)(7.333.../8)*(6-7.333...)
= 6.636...
Therefore, the approximate value of f(1) using Euler's method with two steps of equal size is 6.636.
c. The range of f for t > 0 is 0 < f(t) < 6, since the carrying capacity of the logistic equation is 6. As t approaches infinity, f(t) will approach 6, but never exceed it. Additionally, f(t) will never be negative, since it represents a population size. Therefore, the range of f for t > 0 is 0 < f(t) < 6.
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If a, b, and c are solutions to the
equation 3x3 – 25x2 - 50x = 0 and
a < b < c, evaluate 10c – 6a.
Answers
Answer:
\(\displaystyle 10c - 6a = 110\)
Step-by-step explanation:
We are given the equation:
\(\displaystyle 3x^3 - 25x^2 -50x = 0\)
Where a, b, and c are solutions to the equation and where a < b < c, we want to determine the value of 10c - 6a.
To find the solutions of the equation, we can factor:
\(\displaystyle \begin{aligned} 3x^3 - 25x^2 -50x & = 0 \\ \\ x(3x^2 - 25x -50) & = 0 \\ \\ x(3x+5)(x-10) & = 0 \end{aligned}\)
From the Zero Product Property:
\(\displaystyle x = 0 \text{ or } 3x + 5 = 0 \text{ or } x - 10 = 0\)
Solve for each case:
\(\displaystyle x = 0 \text{ or } x = -\frac{5}{3} \text{ or } x = 10\)
We can see that -5/3 < 0 < 10. Thus, a = -5/3, b = 0, and c = 10.
Therefore:
\(\displaystyle \begin{aligned} 10c - 6a & = 10(10) - 6\left(-\frac{5}{3}\right) \\ \\ &= 100 + 10 \\ \\ & = 110 \end{aligned}\)
what are the gametes that can be produced by the following individuals? a. bgbg(1 point) b. bbgg x bbgg (1 point)
Answers
The gametes that can be produced by individual bgbg are B, and G, and the gametes that the offspring can produce are BB, BG, BG, BG, BG, BG, BG, and GG.
a. bgbg
The individual bgbg can produce gametes that are either B or G, as they carry one allele of each. Therefore, the gametes that can be produced by this individual are:
B, G
b. bbgg x bbgg
The individuals bbgg x bbgg are heterozygous for two different traits (B and G). In this cross, each parent can contribute either a B or a G allele to the offspring.
There are four possible combinations of gametes for each parent, for a total of 16 possible offspring combinations:
BB x BB = B offspring: BB, BG, BG, BB
BB x BG = B offspring: BB, BG, BG, BG
BB x GG = B offspring: BG, BG, BG, BG
BG x BG = B offspring: BG, BG, BG, BG
BG x GG = G offspring: BG, BG, BG, GG
GG x GG = G offspring: GG, GG, GG, GG
So, the gametes that can be produced by the offspring are:
BB, BG, BG, BG, BG, BG, BG, and GG
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What is the vertex of the quadratic function f(x) = (x-8)(x - 2)?
Answers
Answer:
The vertex is at (5, -9)
Step-by-step explanation:
The vertex is halfway between the zeros
f(x) = (x-8)(x - 2)
0 = (x-8)(x - 2)
x=8 and x=2 are the two zeros
(8+2)/2 = 10/2 = 5
The x coordinate is at 5
The y coordinate is found by substituting the x coordinate into the function
f(5) = (5-8)(5 - 2) = -3 (3) = -9
The vertex is at (5, -9)
PLEASE HELP its A Math Problem ! Is the following equation linear, quadratic, exponential or none of these? f(x)=3^x+2
None of these
Linear
Exponential
Quadratic
Answers
Answer:
Exponential
Step-by-step explanation:
As the equation involves raising a term to variable power, this equation can be considered exponentialLinear
Ex : x + 2, x + 3, 3x + 4Quadratic
Ex : (x + 4)², 5x² + 7x + 3, 3x² + 2Answer:
(c) Exponential
Step-by-step explanation:
The independent variable in the equation is in the exponent, so this is an exponential equation.
__
Additional comment
Linear and quadratic equations are specific cases of polynomial equations, which involve sums of powers of the variables. The highest power involved is the degree of the equation: 1 for linear, 2 for quadratic.
f(x) = x +2 . . . . has x to degree 1, so is a linear equation
f(x) = 3x^2 -5 . . . . has x to degree 2, so is a quadratic equation
f(x) = √(x -6) . . . . is "none of these"
(This is another vocabulary question. Linear, quadratic, exponential, degree, term, polynomial, ... are all words with specific definitions related to algebraic functions.)
Evaluate:
-1.6 + (-3.8)
Answers
Answer:
-5.4
Step-by-step explanation:
3 tennis balls cost £9. How much does 1 tennis ball cost?
Give your answer to a whole number of pounds.
Answers
Answer:
1 tennis ball would cost £3
Answer:
3
Step-by-step explanation:
(I used the table method and ratio method)
3x3 is 9
3x2 is 6
3x1 is 3
9 divided by 3 is 3
-1/2w - 3/5 = 1/5w
what is w
Answers
Answer:
w= −6/7
Step-by-step explanation:
Find The largest integer which is a factor of both 308 and 952.
Find the smallest integer value of people such that 308p is a multiple of 952.
Answers
The largest factor of 308 and 952 is 28.
What is factor?A number or algebraic expression that divides another number or expression evenly.
The factors of 308 are: 1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308
The factors of 952 are: 1, 2, 4, 7, 8, 14, 17, 28, 34, 56, 68, 119, 136, 238, 476, 952
As, seen from above 28 is the largest number which is common to both.
Now, LCM of 308 and 952 is 10472
Now, 10472/308 = 34
Hence, smallest integer value of people such that 308p is a multiple of 952 is 34.
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Solve for s. You must write your answer in fully simplified form.
-5s = -13
Answers
Hey there!
-5s = -13
DIVIDE -5 to BOTH SIDES
-5s/-5 = -13/-5
CANCEL out: -5/-5 because it give you 1
KEEP: -13/-5 because it help solve for the s-value
NEW EQUATION: s = -13/-5
SIMPLIFY IT!
s = 13/5
Therefore, your answer is: s = 13/5
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
\(\boxed{\sf{s=\dfrac{13}{5} }}\)Step-by-step explanation:
Isolate the term of s from one side of the equation.
-5s=-13First, you have to divide by -5 from both sides.
→ -5s/-5=-13/-5
Solve.
Divide the numbers from left to right.
→ -13/-5=13/5
\(\Longrightarrow: \boxed{\sf{s=\dfrac{13}{5} }}\)
Therefore, the correct answer is s=13/5.I hope this helps! Let me know if you have any questions.
What is the value of x?
Answers
Answer:
C
Step-by-step explanation:
the sum of the exterior angles of a polygon = 360°
the exterior angle to 93° = 180° - 93° = 87°
summing the exterior angles and equating to 360
x + 52 + 87 + x + 3 + 78 = 360 , that is
2x + 220 = 360 ( subtract 220 from both sides )
2x = 140 ( divide both sides by 2 )
x = 70
Answer:
C. 70°
Step-by-step explanation:
93 is as internal angle the supplementary angle to the external angle at that point (together they are 180°).
the sum of the exterior angles of a polygon is 360°.
we have here
52°
180-93 = 87°
x+3
78
x
so,
52 + 87 + 78 + x + 3 + x = 360
220 + 2x = 360
2x = 140
x = 70°
An irrigation system (sprinkler) has a parabolic pattern. Theheight, in feet, of the spray of water is given by the equationh(x) = -z + 10x + 9.5, where T is the number of feetaway from the sprinkler head (along the ground) the sprayis.The irrigation system is positionedfeet abovethe ground to start.The spray reaches aheight offeet at horizontal distance offeet away from thesprinkler head.The spray reaches all the way to the ground at aboutfeet away.
Answers
Given
height of the spray of water is given by
\(h\mleft(x\mright)=-x^2+10x+9.5\)where , x is the number of feet away from the sprinkler head the spray is
Find
The irrigation system is positioned ----- feet above the ground to start.
The spray reaches a height of------- feet at horizontal distance of
feet away from the sprinkler head.
The spray reaches all the way to the ground at about ------ feet away.
Explanation
to find the height above the ground to start,
we have to put x = 0
so , h(x) = 9.5
hence , the irrigation system is positioned 9.5 feet above the ground to start.
the axis of symmetry of quadratic is x = -b/2a
so ,for given quadratic ,
\(x=-\frac{10}{(-2)}=5\)so , the maximum height is
\(\begin{gathered} h(5)=-(5)^2+10(5)+9.5 \\ h(5)=-25+50+9.5 \\ h(5)=34.5 \end{gathered}\)hence , the spray reaches a height of 34.5 feet at horizontal distance of feet away from the sprinkler head.
the maximum distance will be
\(\begin{gathered} \sqrt{34.5}+5 \\ 5.87367006224+5 \\ 10.8736700622\approx10.9 \end{gathered}\)hence , the spray reaches all the way to the ground at about 10.9
feet away.
Final Answer
Hence , The irrigation system is positioned 9.5 feet above the ground to start.
The spray reaches a height of 34.5 feet at horizontal distance of
feet away from the sprinkler head.
The spray reaches all the way to the ground at about 10.9 feet away.
A man bought some story books for 5 Ghana Cedis each from a bookshop
15 of the books got missing. He then sold the rest at 8 Ghana cedis each and made a profit of 90 Ghana cedis. How many books did he buy?
Answers
Answer:
70
Step-by-step explanation:
Let the no of books bought be x
The cost price of 1 book is 5x
No of the missing book is 15
The remaining book is x-15
The selling price of 1 book is 87
Selling price of (x-15) book is 87
Hence the number of books can be calculated as follows
8(x-15)-5x= 90
8x-120-5x= 90
8x-5x= 90+120
3x= 210
x= 210/3
= 70
Hence the number of books bought is 70
I’m looking for x can someone help me
Answers
Answer:
x = 30°
Step-by-step explanation:
Since m and n are perpendicular, then
y + 70° = 90° ( subtract 70° from both sides )
y = 20°
thus 40 + y = 40° + 20° = 60°
Then
x + 60° = 90° ( subtract 60° from both sides )
x = 30°
Let A and B be arbitrary matrices for which the indicated sum is defined. Determine whether the statement below is true or false. Justify the answer. A ⊤
+B ⊤
=(A+B) ⊤
Choose the correct answer below. A. The statement is true. The transpose property states that (A+B) ⊤
=A ⊤
+B ⊤
. B. The statement is false. The transpose property states that (A+B) ⊤
=A ⊤
B ⊤
. C. The statement is true. The transpose property for matrices is the same as for algebraic exponents of real numbers. D. The statement is false. The transpose property is inapplicable here.
Answers
The correct answer is A. The statement is true. The transpose property states that (A+B)⊤ = A⊤ + B⊤.
The transpose of a matrix is obtained by interchanging its rows with columns. When adding two matrices, the sum is computed by adding the corresponding elements of the matrices.
Let's consider the transpose of (A+B). By definition, the (i, j)-th entry of (A+B)⊤ is equal to the (j, i)-th entry of (A+B). This means that the entry in the i-th row and j-th column of (A+B)⊤ corresponds to the entry in the j-th row and i-th column of (A+B).
Now, let's consider the matrices A⊤ and B⊤. The (i, j)-th entry of A⊤ + B⊤ is obtained by adding the (i, j)-th entries of A⊤ and B⊤. Since A⊤ has its rows and columns interchanged from A, the entry in the i-th row and j-th column of A⊤ corresponds to the entry in the j-th row and i-th column of A. Similarly, the entry in the i-th row and j-th column of B⊤ corresponds to the entry in the j-th row and i-th column of B.
Since the sum of the entries in the i-th row and j-th column of (A+B)⊤ and A⊤ + B⊤ are the same, we can conclude that (A+B)⊤ = A⊤ + B⊤.
Therefore, the statement A⊤ + B⊤ = (A+B)⊤ is true, and the transpose property holds for matrix addition.
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2x^3y + 18xy - 10x^2y - 90y
Part A: rewrite the expression so that the GCF is factored completely
Part B: rewrite the expression completely factored. Show the steps of your work
___________________________
Part A: the area of a square is (9x^2 + 24x + 16) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work.
Part B: the area of a rectangle is (16x^2 - 25y^2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work.
___________________________
f(x) = 2x^2 - 5x + 3
Part A: what are the x-intercepts of the graph of f(x)? Show your work
Part B: is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answer and show your work.
Part C: what are the steps you would use to graph f(x)? Justify that you can use the answer in part A and part B to draw the graph.
Answers
The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)
The expression completely factored in is
\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)
Please refer below for the remaining answers.
We have,
Part A:
To rewrite the expression 2x³y + 18xy - 10x²y - 90y so that the greatest common factor (GCF) is factored completely, we can factor out the common terms.
GCF: 2y
\(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)
Part B:
To completely factor the expression, we can further factor the quadratic term.
\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)
Now,
Part A:
To determine the length of each side of the square given the area expression (9x² + 24x + 16), we need to factor it completely.
The area expression (9x² + 24x + 16) can be factored as (3x + 4)(3x + 4) or (3x + 4)².
Therefore, the length of each side of the square is 3x + 4.
Part B:
To determine the dimensions of the rectangle given the area expression (16x² - 25y²), we need to factor it completely.
The area expression (16x² - 25y²) is a difference of squares and can be factored as (4x - 5y)(4x + 5y).
Therefore, the dimensions of the rectangle are (4x - 5y) and (4x + 5y).
Now,
f(x) = 2x² - 5x + 3
Part A:
To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.
2x² - 5x + 3 = 0
The quadratic equation can be factored as (2x - 1)(x - 3) = 0.
Setting each factor equal to zero:
2x - 1 = 0 --> x = 1/2
x - 3 = 0 --> x = 3
Therefore, the x-intercepts of the graph of f(x) are x = 1/2 and x = 3.
Part B:
To determine if the vertex of the graph of f(x) is maximum or minimum, we can examine the coefficient of the x^2 term.
The coefficient of the x² term in f(x) is positive (2x²), indicating that the parabola opens upward and the vertex is a minimum.
To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.
For f(x),
a = 2 and b = -5.
x = -(-5) / (2 x 2) = 5/4
To find the corresponding y-coordinate, we substitute this x-value back into the equation f(x):
f(5/4) = 25/8 - 25/4 + 3 = 25/8 - 50/8 + 24/8 = -1/8
Therefore, the vertex of the graph of f(x) is at the coordinates (5/4, -1/8), and it is a minimum point.
Part C:
To graph f(x), we can start by plotting the x-intercepts, which we found to be x = 1/2 and x = 3.
These points represent where the graph intersects the x-axis.
Next,
We can plot the vertex at (5/4, -1/8), which represents the minimum point of the graph.
Since the coefficient of the x² term is positive, the parabola opens upward.
We can use the vertex and the symmetry of the parabola to draw the rest of the graph.
The parabola will be symmetric with respect to the line x = 5/4.
We can also plot additional points by substituting other x-values into the equation f(x) = 2x² - 5x + 3.
By connecting the plotted points, we can draw the graph of f(x).
The steps to graph f(x) involve plotting the x-intercepts, the vertex, and additional points, and then connecting them to form the parabolic curve.
The answer in part A (x-intercepts) and part B (vertex) are crucial in determining these key points on the graph.
Thus,
The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)
The expression completely factored in is
\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)
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-3=n/2-6 help pleaseeee!!!!
Answers
Answer:
6 = n
Step-by-step explanation:
-3=n/2-6
Add 6 to each side
-3+6 = n/2 -6+6
3 = n/2
Multiply each side by 2
3*2 = n/2 *2
6 = n
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▹ Answer
n = 6
▹ Step-by-Step Explanation
-3 = n/2 - 6
Multiply both sides by 2:
-6 = n - 12
Rearrange the terms:
-n -6 = -12
Calculate:
-n = -6
Change the signs:
n = 6
Hope this helps!
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The specifications for a manifold gasket that installs between two engine parts calls for a thickness of 2.500 mm + 020 mm. The standard deviation of the process is estimated to be 0.004 mm. The process is currently operating at a mean thickness of 2.50 mm. (a) What are the upper and lower specification limits for this product? (b) What is the Cp for this process? (c) The purchaser of these parts requires a capability index of 1.50. Is this process capable? Is this process good enough for the supplier? (d) If the process mean were to drift from its setting of 2.500 mm to a new mean of 2.497, would the process still be good enough for the supplier's needs? R
Answers
The upper specification limit is 2.520 mm, and the lower specification limit is 2.480 mm. The process is not capable according to the purchaser's requirement of a capability index of 1.50.
(a) The upper specification limit (USL) is calculated by adding the process mean (2.500 mm) to the upper tolerance (0.020 mm), resulting in 2.520 mm. The lower specification limit (LSL) is calculated by subtracting the lower tolerance (0.020 mm) from the process mean, resulting in 2.480 mm.
(b) The process capability index (Cp) is calculated by dividing the tolerance width (USL - LSL) by six times the standard deviation. In this case, the tolerance width is 0.040 mm (2.520 mm - 2.480 mm) and the standard deviation is 0.004 mm. Therefore, Cp = 0.040 mm / (6 * 0.004 mm) = 1.25.
(c) The purchaser requires a capability index (Cpk) of 1.50, which measures how well the process meets the specification limits. Since Cp (1.25) is less than the desired Cpk (1.50), the process is not capable according to the purchaser's requirement. It is not good enough for the supplier either, as the Cp is less than the desired level.
(d) If the process mean were to drift to 2.497 mm, the Cp value would remain the same at 1.25. Since the Cp value is still less than the desired Cpk of 1.50, the process would still not be good enough for the supplier's needs, even with the changed process mean.
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