The expression that represents the output value when the input is n is -4 - 2n
How to determine the output value for the input n?From the question, the input parameters are given as
Input 1,2,3,4,n
Similarly, the output parameters are given as
output: -6,-8,-10,-12
So, we have the following table of values
1,2,3,4,n
-6,-8,-10,-12
From the above table of values, we have the following parameters
Sequence type = arithmetic sequenceFirst term, a = -6Common difference, d = -2The output value for the input n is then calculated as
Tn = a + (n - 1) * d
So, we have
Tn = -6 + (n - 1) * -2
Open brackets
Tn = -6 - 2n + 2
Evaluate the like terms
Tn = -4 - 2n
Hence, the output value for the input n is -4 - 2n
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What kinds of quadrilateral is the shape shown? The matching arrow labels indicate that two opposite sides are parallel. (Remind me about the shapes 5 5
The quadrilateral in the picture is a square since all four sides are equal.
The angles are all equal and all are right angles.
Clearly, the quadrilateral is a square.
Beth and 8 of her friends are going bowling Saturday. Each game cost $x plus an additional $3.25 to rent shoes. Write an expression to represent the total cost of an afternoon of bowling if four friends bring their own shoes.
Answer:
9*X+5*3.25
Step-by-step explanation:
So, total 9 person; 4 person have their own shoe.
Cost for game = 9*X;
Cost for shoe = 5*3.25;
So the total cost = 9*X+5*3.25
If there are 20 cookies and 40 carrot each number are the same number of one whole cookies how many cost members might have been at the party,explain
2, 4, 5, 10 and 20 cast members were possible attendees at the celebration.
The acting teacher provided 20 biscuits and 40 carrot sticks as refreshments in light of this.
What are the factors?
A factor in mathematics is an integer that evenly divides another number by itself, leaving no residue.
2, 4, 5, 10, and 20 make up the factors of 20 and 40.
Additionally, the number of cast members must be greater than one and a divisor of 20 and 40.
Therefore, there could be 2, 4, 5, 10, or 20 cast members.
Therefore, 2, 4, 5, 10 and 20 cast members may have attended the celebration.
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Which graph shows y=3⌊x⌋−4? Responses Graph of the function f open argument x close argument equals greatest integer on a coordinate plane. The horizontal x axis ranges from negative 10 to 10. The vertical f of x axis ranges from negative 10 to 10. The graph is a step function with 7 vertical line segments. Each line segment is one unit long, with a closed point on the left side and an open point on the right side. Moving left to right, each line segment is shifted to the right one unit and up one unit, compared to the line segment before it. The endpoints of the first three line segments are as follows. Segment one. Begin ordered pair negative 2 comma negative 10 end ordered pair and begin ordered pair negative 1 comma negative 10. Segment two. Begin ordered pair negative 1 comma negative 7 end ordered pair and begin ordered pair 0 comma negative 7 end ordered pair. Segment three. Begin ordered pair 0 comma negative 4 end ordered and 1 comma negative 4 end ordered pair. The pattern continues with the last line segment at an endpoint. Image with alt text: Graph of the function f open argument x close argument equals greatest integer on a coordinate plane. The horizontal x axis ranges from negative 10 to 10. The vertical f of x axis ranges from negative 10 to 10. The graph is a step function with 7 vertical line segments. Each line segment is one unit long, with a closed point on the left side and an open point on the right side. Moving left to right, each line segment is shifted to the right one unit and up one unit, compared to the line segment before it. The endpoints of the first three line segments are as follows. Segment one. Begin ordered pair negative 2 comma negative 10 end ordered pair and begin ordered pair negative 1 comma negative 10. Segment two. Begin ordered pair negative 1 comma negative 7 end ordered pair and begin ordered pair 0 comma negative 7 end ordered pair. Segment three. Begin ordered pair 0 comma negative 4 end ordered and 1 comma negative 4 end ordered pair.
The graph for the given equation is plotted below.
The given equation is y=3x-4.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
Put x=0, 1, 2, 3, 4,....in the given equation and solve for y
When x=0, y=-4
When x=1, y=-1
When x=2, y=2
When x=3, y=5
Plot the coordinates (0, -4), (1, -1), (2, 2) and (3, 5) on the graph.
Therefore, the graph for the given equation is plotted below.
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Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a
graphing utility, use it to graph the function and verify the real zeros and the given function value.
n= 3:
4 and 4 i are zeros;
f (- 1)= - 255
The polynomial is f(x) = x³ - 12x² + 64x + 128
Given,
The polynomial has 4, 4-4i, and 4+4i as its roots.
f(-1) equals -255
We have to find a polynomial of degree 3.
If x = 4 is a root, then:
(x - 4) is a factor of the polynomial.
If x = 4 - 4i is a root,
Then,
(x - 4 + 4i) is a factor of the polynomial.
If x = 4+4i is a root.
Now,
(x - 4 - 4i) is a factor of the polynomial.
All the three roots are of the same polynomial.
So,
The polynomial is the product of these factors.
f(x) = k(x - 4) (x-4+4i) (x-4-4i)
f(x) = k(x - 4) [(x-4)² - (4i)²]
f(x) = k(x- 4) [x² + 16 - 8x + 16]
f(x) = k(x - 4) [x² - 8x + 32]
f(x) = k[x³ - 8x² + 32x - 4x² + 32x - 128]
f(x) = k[x³ - 12x² + 64x + 128]
Now find "k", we know that f(-1) = -255.
f(-1) = k[(-1)³ - 12(-1)² + 64(-1) + 128]
-255 = k[-1 - 12 - 64 + 128]
-255 = k × -255
k = 1
That is, the polynomial is f(x) = x³ - 12x² + 64x + 128
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Scale factor=.9 is enlarge , reduce , or preserve ?
The scale factor K = 0.9 is smaller than 1, so this is a reduction.
What type of dilation do we have?If we have a dimension L, a change of scale of scale factor K gives the new length: K*L
Then:
if K > 1, we have an enlargement.
if K = 1, we have a preservation (nothing changes)
if 0 < K < 1, we have a reduction.
In this case, we have K = 0.9, this is smaller than 1, so we have a reduction.
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given the figure, find the value of y for which the quadrilateral must be a parallelogram
For the figure to be a parallelogram, then y must be equal to 12
Here, we want to get the value of y for which the the quadilateral must be a parallelogarm
Mathematically, the diagonals of a parallelogarm bisects each other
That means the lengths on either sides are equal
Mathematically, we can get two equations as follows;
[tex]\begin{gathered} 3x\text{ = y} \\ 2x\text{ + 2y = 32} \\ \text{From the second equation;} \\ 2(x+y)\text{ = 2(16)} \\ x\text{ + y = 16} \\ \text{From this, we have that;} \\ x\text{ = 16-y} \\ we\text{ can put this in the first equation;} \\ 3(16-y)\text{ = y} \\ 48\text{ - 3y = y} \\ y\text{ + 3y = 48} \\ 4y\text{ = 48} \\ y\text{ = }\frac{48}{4} \\ y\text{ = 12} \end{gathered}[/tex]Marshall is going to make an apple pie. He buys x pounds of apples and a pie crust that costs $4.50. The total cost in dollars. y. can be found using the equation below. y = 2.57x +4.5 What is the cost per pound of the apples
1) Considering that x is for pounds of apples and y is a total cost of an apple let's find the cost per pound of the apples, given that the y=2.57x +4.5
Let's turn that function into an equation
0=2.57x +4.5 Subtract 2.57x from both sides
-2.57x=4.5 Divide both sides by -2.57
x=-1.75
2) So if no one pie crust is sold, there is going to be a loss of $-1.75, according to that equation.
Therefore, we can infer that the cost per pound of the apples is $1.75
Last month, Sally and Roger sold candy to raise money for their debate team. Roger sold 1/3 as much candy as Sally did. If Sally sold 2 9/10 boxes of candy, how many boxes of candy did Roger sell?
The boxes of candy sold by Roger are 29/30.
According to the question,
We have the following information:
Roger sold 1/3 as much candy as Sally sold.
Sally sold [tex]2\frac{9}{10}[/tex] boxes of candy.
Now, first we will convert the boxes of candy sold by Sally from the mixed fraction.
(More to know: there are three kinds of fraction: mixed fraction, proper fraction and improper fraction. We need to change mixed fraction in most of the cases to solve the questions further.)
We have:
29/10
Now, we know that the boxes of candy sold by Roger is 1/3 of 29/10.
So, we have the following expression:
[tex]\frac{1}{3}* \frac{29}{10}[/tex]
29/30
Hence, the boxes of candy sold by Roger is 29/30.
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Points 1 to 6To present y=-x^3+3x^2, 9 points must be selected, point 1: Domain, 2: zeros of the function, 3: period and symmetry, 4: sign of the function, 5: going to the edge of the function, 6: asymptotes, 7: monotony and extreme values, 8: concavity and convexity, 9: to present the function graphically.
ANSWERS
1. Domain: all real values
2. Zeros: 0 (with multiplicity 2) and 3
3. Not periodic. Symmetric about the point (1, 2)
4. Positive for x < 3; negative for x > 3
5. f → ∞ as x → -∞; f → -∞ as x → ∞
6. none
EXPLANATION
1. The domain of a function is the set of all the x-values for which the function exists. In this case, we have a polynomial function and, therefore, the domain is all real values.
2. To find the zeros of the function, we have to solve,
[tex]-x^3+3x^2=0[/tex]First, factor x² and -1 out. To do so, we have to divide each term by x² and by -1 - or, in other words, divide by -x²,
[tex]\begin{gathered} -x^2\left(\frac{-x^3}{-x^2}+\frac{3x^2}{-x^2}\right)=0 \\ \\ -x^2(x^{3-2}-3x^{2-2})=0 \end{gathered}[/tex]So, we have,
[tex]-x^2(x-3)=0[/tex]In this equation, we can see that if x = 0, then the equation is true. Also, if x = 3 the equation is true. So, these are the two zeros, with the particularity that x = 0 has multiplicity 2. This is because the factor related to that zero is x squared.
Hence, the zeros are 0 and 3. 0 has multiplicity 2.
3. As mentioned before, this is a polynomial function, which means that it is not a periodic function. A cubic function is an odd function, and it is symmetric about the origin. However, this function is not the parent function, x³, but it is symmetric about the point (1, 2).
4. We know that the function is zero at x = 0 and at x = 3. For x < 0, the function is positive,
[tex]with\text{ }x=-1:\text{ }y=-(-1)^3+3(-1)^2=-(-1)+3\cdot1=1+3=4[/tex]For 0 < x < 3, the function is also positive. This is because x = 0 with multiplicity 2.
Then, since the function crosses the x-axis at x = 3 and that zero has multiplicity 1, we can conclude that the function is negative for x > 3.
Hence, is the function is positive for x < 3 and negative for x > 3.
5. As mentioned in part 4, the function is positive for all values of x less than 3, which means that the function goes to infinity as x goes to negative infinity.
Since for x > 3 the function is always negative, it goes to negative infinity as x goes to infinity.
6. A polynomial function has no restrictions in the domain and, therefore, has no asymptotes.
How to find x and y of these figures?
Image is attached
The value of x is 40 and the value of y is 25.
What is consecutive interior angles?
Pairs of angles that are between two lines and on the same side of the line that cuts through the two lines are referred to as consecutive internal angles. According to the theorem, if two lines are parallel, then successive interior angles are supplementary to one another.
Angles that add up to 180 degrees are referred to as supplementary angles.
As we know that the sum of three angles of triangle is 180 degrees.
So from the first figure we get,
2x + x + y + y + 10 = 180
3x + 2y = 170 ...(1)
From the second figure we get,
4x - y + x + 5 = 180 (Since they are consecutive interior angles)
5x - y = 175 ...(2)
After solving equation (1) and (2), we get
x = 40 and y = 25
There the value of x is 40 and the value of y is 25.
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For the function f(x)= x^2+4x-1, what is the range of f (x) for the domain {-2,0,1}?
The range of the given function is {-5,-1,4} which is the B option.
Given function:-
[tex]f(x) = x^2+4x-1[/tex]
Domain = {-2,0,1}
We have to find the range of the given function for the given domain.
Putting x = -2 in the given function, we get,
[tex]f(-2) = (-2)^2+4(-2)-1[/tex]
f(-2) = 4 - 8 - 1 = -5
Putting x = 0 in the given function, we get,
[tex]f(0) = (0)^2+4(0)-1[/tex]
f(0) = 0 + 0 -1 = -1
Putting x = 1 in the given function, we get,
[tex]f(1) = (1)^2+4(1)-1[/tex]
f(1) = 1 + 4 - 1 = 4
Hence, the range of the given function is {-5,-1,4}.
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Given vectors a=(-2, 1) and b = (5, 4), find 5a - 3b.Write your answer in component form.5a - 3b = (0)X 5? ?
In order to find 5a-3b, lets find 5a. This is given by
[tex]\begin{gathered} 5a=5(-2,1) \\ 5a=(-10,5) \end{gathered}[/tex]Similarly, -3b is given by
[tex]\begin{gathered} -3b=-3(5,4) \\ -3b=(-15,-12) \end{gathered}[/tex]Then, by substituting our results into the expression 5a-3b, we get
[tex]5a-3b=(-10,5)+(-15,-12)[/tex]This can can be done by adding entry by entry, that is
[tex]5a-3b=(-10-15,\text{ 5-12)}[/tex]Therefore, the answer is
[tex]5a-3b=(-25,-7)[/tex]a company wants to study the effectiveness of a new pain relief medicine. they recruit 100100100 volunteers who suffer chronic pain. they assign each subject a number from 111 to 100100100 and use a random number generator to assign the first 505050 subjects selected to the treatment group. the remaining 505050 subjects are assigned to the control group. what type of experiment design is this?
The experimental design which is used in the study is Completely randomized design.
Completely Randomized design may be defined as a technique in which all the solutions are assigned at random so that each questions receive all the possible solutions. According to the question we know that the sample size is 100 volunteers who are suffering from chronic pain. Now, out of the 100 volunteers, 50 males and 50 females are chosen. Further out of the 50 males, 25 males are randomly assigned to the treatment group while the other 25 males are assigned to a control group. Since, the treatments are randomly assigned completely, each of the volunteers have an equal chance of receiving the treatments.
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An oatmeal cookie calls for 1/2 cup of butter to make 6 dozen cookies. Hilda needs to make 15 dozen cookies for the bake sale. How many cups of butter will she need
1) Given that an oatmeal cookie has these proportions, let's set a pair of ratios to get that:
[tex]undefined[/tex]Plssss help due tomorrow!!
Answer:
y = -1/3x +1
Step-by-step explanation:
You want the slope-intercept form equation of the line through the points (-3, 2) and (-9, 4).
SlopeThe slope is given by the formula ...
m = (y2 -y1)/(x2 -x)
m = (4 -2)/(-9 -(-3)) = 2/-6 = -1/3
Y-interceptThe y-intercept is given by the formula ...
b = y1 -m(x1)
b = 2 - (-1/3)(-3) = 1
Slope-intercept equationThe slope-intercept equation of the line is ...
y = mx +b
y = -1/3x +1
Solve the unequality
10 is greater than X over six
Answer:
x25 - 24.1x square would be your answer
Step-by-step explanation:
bricklayer brenda would take nine hours to build a chimney alone, and bricklayer brandon would take 1010 hours to build it alone. when they work together, they talk a lot, and their combined output decreases by 1010 bricks per hour. working together, they build the chimney in 55 hours. how many bricks are in the chimney?
When seen as a function, a relationship exists between a set of inputs and outputs.
The number of bricks in the chimney exists 900.
What is meant by functions?A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Simply described, a function is an input-output connection where each input is coupled to exactly one output range, codomain, and domain are included in each function. A function exists generally denoted by f(x) where x exists the input.
Let x be the number of bricks in the chimney. The work done exists the rate multiplied by the time.
Using w = rt, we get
[tex]$x=\left(\frac{x}{9}+\frac{x}{10}-10\right) \cdot 5[/tex]
Expanding the above equation, we get
[tex]$\left(\frac{x}{9}+\frac{x}{10}-10\right) \cdot 5: \quad \frac{19 x}{18}-50$[/tex]
x = (19x / 18) - 50
Multiply both sides by 18
[tex]$x \cdot 18=\frac{19 x}{18} \cdot 18-50 \cdot 18[/tex]
Simplifying the above equation,
x × 18 = 19x - 900
Subtract 19x from both sides
x × 18 - 19x = 19x - 900 - 19x
Simplifying the above equation, we get
-x = -900
Divide both sides by -1
[tex]$\frac{-x}{-1}=\frac{-900}{-1}[/tex]
x = 900
Therefore, the value of x exists 900.
The complete question is:
Bricklayer Brenda would take nine hours to build a chimney alone, and bricklayer Brandon would take hours to build it alone. When they work together, they talk a lot, and their combined output decreases by bricks per hour. Working together, they build the chimney in hours. How many bricks are in the chimney?
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2. Write y=8x+2 in function notation.
Answer:
f(x) = 8x + 2Step-by-step explanation:
GivenEquation y = 8x + 2What is a function notation?It is a representation of the functional relation with dependent and independent variables, normally, x- independent and f(x) - dependent variable.
We can write the given function as:
f(x) = 8x + 2Solve: -3+12x=-3x+27
Answer:
the answer is 2 and one fourth
Step-by-step explanation:
because the 3s cancel out
six children are each offered a single scoop of any of 3 flavors of ice cream from the combinatorial creamery. in how many ways can each child choose a flavor for their scoop of ice cream so that each flavor of ice cream is selected by at least one child?
Answer: 18 combinations
Step-by-step explanation: you want to multiply the amount of ice cream flavors by the amount of children to be able to find the amount of possible combinations. so, 6 children x 3 flavors of ice cream = 18 different combinations. 6 x 3 = 18
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet and the volume of each large box is 15 cubic feet. There were 2 more small boxes shipped than large boxes and the total volume of all boxes was 243 cubic feet. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
The Number of small and large boxes shipped are 10 and 5 respectively.
Large boxes :
Volume = 18 cubic feets
Let number of large boxes = b
Small boxes :
Volume = 10 cubic feets
Number of small boxes = 2b
Total volume shipped = 190 cubic feet
To obtain total volume shipped :
(Number of small boxes × volume of small boxes) + (Number of large boxes × volume of large boxes
Writing as a system of equation :
(10 × 2b) + (18 × b)
20b + 18b = 190 cubic feets
38b = 190
b = 190 ÷ 38
b = 5
Hence,
Number of large boxes = 5
Number of small boxes = 2(5) = 10
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1 - -8= i am having trouble answering it
Answer:
Step-by-step explanation:
2 subtraction symbols equals a plus
so the answer is 9
Write the system of linear equations represented by the augmented matrix to the right use WXY and Z for the variables Write the equation for all the rows
Question: Write the system of linear equations represented by the augmented matrix to the right use W, X, Y and Z for the variables :
Solution:
An augmented matrix is equivalent to a system of linear equations. In this case, the given matrix is represented by the following system of linear equations:
-1 w - 3x +5y +2z = 13
0w + 1x + 3y + 0z = 10
0w + 0x +y - 1z = 3
1w - 3x + 0y + 0z = -2
this is equivalent to:
w - 3x +5y +2z = 13
x + 3y = 10
y - z = 3
1w - 3x = -2
So that, the correct answer is:
w - 3x +5y +2z = 13
x + 3y = 10
y - z = 3
1w - 3x = -2
Can someone please help! And thank you!
Answer:
x = 20
Step-by-step explanation:
X = 20 Because the values are Corresponding Angles This means that they are congruent
PLEASE HELP, thank u
The Nya will pay $46.42 for the sweater. The decimal equivalent of a 20 percent discount is 0.20. To calculate the savings in dollars, multiply the decimal discount by the item's price. For instance, if the item's original price is $24, you would multiply 0.2 by that amount to get $4.80.
Calculation of amount paid to sweater?We have been given that Nya wants to buy a sweater that had an original price of $55. The sweater is now discounted 20%.
the price of sweater after20% discount is 55-20% of 55
The price of the sweater after discount =55-(20/100*55)
The price of the sweater after discount=55-(0.20*55)
The price of the sweater after discount=55-11
The price of the sweater after discount=44
SO The price of the sweater after discount is $44
Now let us find the price of sweater after adding 5.5% sales tax
The price of sweater after sales tax =44+(5.5/100*44)
The price of sweater after sales tax=44+(0.055*44)
The price of sweater after sales tax=44+2.42
The price of sweater after sales tax=46.42
$46.42 is paid for sweater after sales tax
Hence, The Nya will pay $46.42 for the sweater.
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Each exterior angle measure is one eighth the measure of each interior angle??
Answer:
Exterior angle = 20 degrees
Interior angle = 160 degrees
================================================
Explanation:
The phrasing "Each exterior angle measure is one eighth the measure of each interior angle" means,
exterior = (1/8)*(interior)
That rearranges to
interior = 8*(exterior)
Let's say x is the measure of the unknown exterior angle. That makes 8x the measure of the interior angle
The two must add to 180 to form a straight line.
interior + exterior = 180
8x + x = 180
9x = 180
x = 180/9
x = 20 is the measure of the exterior angle
8x = 8*20 = 160 is the measure of the interior angle
Note how 160+20 = 180 to verify our answers.
determine if two triangles are necessarily congruent. if so in a flowchart proof to prove the they are.
Yes the two triangles are necessarily congruent as they are right angled so both the angles are equal and having two sides equal by using SAS rule that is Side, Angle, Side rule by the property of congruency.
What is Congruency?Two figures are considered to be "congruent" if they can be positioned precisely over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
What are the rules of congruency?If two triangles meet all 5 requirements for congruence, then they are congruent. They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SAS) (RHS).
Here the ΔCED and ΔPOR,
∠CED=∠POR
Side PR=CD
Side ED=PO
by using SAS rule,
ΔCED≅ΔPOR
Yes, the two triangles are inherently congruent because they have right angles, which means that both of their angles are equal, and because their sides are equal according to the SAS rule, which stands for Side, Angle, Side.
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− 5/7 . (−3) can someone write this in the simplest form
the average depth of the arctic ocean is 3.953x10^3 feet while the average depth of the atlantic ocean is 1.2851x10^4 feet. approximately how many times deeper is the atlantic ocean than the arctic ocean
By taking the quotient between the average depth of the oceans, we conclude that the atlantic ocean is 3.251 times deeper.
How many times deeper is the Atlantic Ocean?We know that the average depth of the arctic ocean is 3.953x10^3 feet and the average depth of the atlantic ocean is 1.2851x10^4 feet
Notice that both of these are in scientific notation.
To see how many times deeper is the atlantic ocean than the artic ocean we need to take the quotient between the average depth of the atlantic ocean and the average depth of the arctic ocean, this gives:
(1.2851x10^4)/(3.953x10^3) = (1.2851/3.953)*(10^4/10^3)
= 0.3251*(10^1) = 3.251
The atlantic ocean is 3.251 times deeper than the artic.
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