There are no positive or negative zeros, and the number of complex zeros cannot be determined without further information.
To determine the number of positive, negative, and complex zeros of the given polynomial [tex]6 + 9x^2 + 3x^3 + 2x^4 - 12x,[/tex] we need to analyze its behavior and apply the properties of polynomial functions.
Positive Zeros:
Positive zeros are the values of x for which the polynomial evaluates to zero.
To find positive zeros, we set the polynomial equal to zero and solve for x.
However, in this case, we can see that all the coefficients of the terms in the polynomial are positive.
Therefore, there are no positive zeros.
Negative Zeros:
Negative zeros are the values of x for which the polynomial evaluates to zero.
Similar to positive zeros, we set the polynomial equal to zero and solve for x.
However, in this case, we can see that all the coefficients of the terms in the polynomial are positive.
Therefore, there are no negative zeros.
Complex Zeros:
Complex zeros occur when the polynomial has complex roots. Since the given polynomial has only real coefficients, complex zeros will occur in conjugate pairs.
To determine the number of complex zeros, we need to examine the degree of the polynomial.
In this case, the highest power of x is [tex]4 (x^4),[/tex] indicating a fourth-degree polynomial.
A fourth-degree polynomial can have at most four complex zeros. However, we cannot determine the exact number of complex zeros without further information or solving the polynomial explicitly.
In conclusion, the given polynomial has no positive or negative zeros due to all coefficients being positive.
The number of complex zeros cannot be determined without additional information.
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Does the mapping diagram represent a function? Why or why not?
-5
8
9
y
-8
A. Yes; each input pairs with only one output.
B. No; the input value x = -5 pairs with two output values.
C. No; each input pairs with only one output.
D. No; each output value pairs with two input values.
The correct answer is: A. Yes; each input pairs with only one output.
To determine whether the given mapping diagram represents a function, we need to analyze the relationship between the input values (x) and the corresponding output values (y).
Looking at the mapping diagram, we can see that the input value -5 is paired with the output value 8. This implies that when x = -5, the corresponding y value is 8. Similarly, when x = 9, the corresponding y value is -8.
Since each input value has a unique and specific output value, we can conclude that the mapping diagram represents a function. In other words, for every input value, there is only one output value associated with it.
This is consistent with the definition of a function, where each input has a single and distinct output. Therefore, the mapping diagram satisfies the criteria for a function, and the correct answer is:
A. Yes; each input pairs with only one output.
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The mapping diagram does not represent a function that reflects this is: No; each output value pairs with two input values. D.
To determine whether the mapping diagram represents a function, we need to assess whether each input value pairs with only one output value.
Looking at the given mapping diagram:
-5 -> 8
9 -> y
-8 -> y
We can see that the input value -5 maps to the output value 8.
There are two different input values, 9 and -8, that map to the same output value, y.
In a function, each input should correspond to exactly one output, but in this case, the output value y is associated with two different input values.
In this case, y, the output value, pairs with both 9 and -8, indicating that the diagram does not meet the criteria for a function.
We must examine if each input value couples with only one output value in order to evaluate whether the mapping diagram reflects a function.
Observing the provided mapping diagram:
-5 -> 8 9 -> y -8 -> y
As can be seen, the input value of -5 corresponds to the output value of 8.
The identical output value, y, is mapped to two distinct input values, 9 and -8.
A function should have only one output for each input, however in this situation, the output value y is connected to two separate input values.
This figure does not fit the definition of a function because the output value, y, couples with both 9 and -8.
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Find the local and absolute maximum and minimum points in (x, y) format for the
function f(x) = 3/5x^5 - 9x^3 + 2 on the closed interval [-4,5]. Answer the following
questions.
a) Find all critical numbers (x- coordinates only)
b) Find the intervals on which the graph is increasing Mark critical numbers
Pls help I am stuck Tysm
The perimeter of the figure is 30 cm.
How to find the perimeter of a figure?The perimeter of the figure is the sum of the whole sides of the figure. Therefore, the perimeter of the figure can be found as follows:
perimeter of the figure = sum of the whole sides
Therefore,
perimeter of the figure = 6 cm + 9 cm + 2 cm + 3cm + 2cm + 3cm + 2cm + 3cm
Hence,
perimeter of the figure = 15 cm + 5 cm + 5cm + 5 cm
perimeter of the figure = 30 cm
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Show 2x -6 in a line graph
The resulting line graph will be a straight line that starts below the y-axis, crosses it at the point (0, -6), and continues upwards as the x-values increase.
To plot the line graph of the equation 2x - 6, we need to assign values to the variable x and calculate the corresponding values of y.
Let's choose a range of x-values and calculate the corresponding y-values:
For example, let's choose x = -3, -2, -1, 0, 1, 2, and 3.
Substituting these values into the equation 2x - 6, we get:
For x = -3: y = 2(-3) - 6 = -12
For x = -2: y = 2(-2) - 6 = -10
For x = -1: y = 2(-1) - 6 = -8
For x = 0: y = 2(0) - 6 = -6
For x = 1: y = 2(1) - 6 = -4
For x = 2: y = 2(2) - 6 = -2
For x = 3: y = 2(3) - 6 = 0
Now, we can plot these points on a graph with x as the horizontal axis and y as the vertical axis:
(-3, -12), (-2, -10), (-1, -8), (0, -6), (1, -4), (2, -2), (3, 0)
We can then connect these points with a straight line. Since the equation is in the form y = 2x - 6, the line will have a slope of 2 and a y-intercept of -6. The line will have a positive slope, meaning it will slant upwards from left to right.
The resulting line graph will be a straight line that starts below the y-axis, crosses it at the point (0, -6), and continues upwards as the x-values increase.
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two points A and B, due to two spheres X and Y 4.0m apart, that are carrying charges of 72mC and -72mC respectively. Assume constant of proportionality as 9×10^9Nm²/C². Find the electric field strength at points A and B due to each spheres presence
Due to the presence of spheres X and Y, the electric field strength at point B is [tex]1.01 * 10^6 N/C[/tex] and [tex]-4.05 * 10^6 N/C[/tex], respectively.
Given that two spheres X and Y are carrying charges of 72mC and -72mC respectively, and they are located 4.0 m apart from each other. The electric field strength at points A and B due to the presence of each sphere is to be determined.
Let's begin by calculating the electric field strength at point A due to sphere X. Electric field strength is given by E=kq/r², where k is Coulomb's constant, q is the charge and r is the distance between the two charges. The electric field strength at point A due to sphere X, E₁=kq₁/r₁² [tex]= (9*10^9Nm^2/C^2) * (72mC) / (4.0m)^2 = 4.05 * 10^6 N/C[/tex] (approx.)
Similarly, the electric field strength at point A due to sphere Y can be calculated as follows, E₂=kq₂/r₂² [tex]= (9*10^9Nm^2/C^2) * (72mC) / (4.0m)^2 = 4.05 * 10^6 N/C[/tex] (approx.). Here, the negative sign indicates that the electric field due to sphere Y is in the opposite direction to the electric field due to sphere X. Now, let's calculate the electric field strength at point B. The electric field strength at point B due to sphere X, E₁=kq₁/r₁² [tex]= (9*10^9Nm^2/C^2) * (72mC) / (8.0m)^2 = 1.01 * 10^6 N/C[/tex] (approx.)
Similarly, the electric field strength at point B due to sphere Y can be calculated as follows, E₂=kq₂/r₂² [tex]= (9*10^9Nm^2/C^2) * (-72mC) / (4.0m)^2 = -4.05 * 10^6 N/C[/tex] (approx.). Therefore, the electric field strength at point A due to the presence of sphere X is [tex]4.05 * 10^6 N/C[/tex] and due to the presence of sphere Y is [tex]-4.05 * 10^6 N/C[/tex]. The electric field strength at point B due to the presence of sphere X is [tex]1.01 * 10^6 N/C[/tex] and due to the presence of sphere Y is [tex]-4.05 * 10^6 N/C[/tex].
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What is the graph of f(x) = 0.5(4)x (x is an exponent)
It should be a positive graph .
En la tabla se muestra la cantidad de zapatos vendidos en 1 almacén durante una semana, calcula las medidas de tendencia central y realiza el análisis correspondiente
Based on the information, we can infer that the mean is 14.28, the median is 15, and there is no unique mode (several repeated values).
How to calculate measures of central tendency?To calculate the measures of central tendency, we will use the data provided in the table. The pairs of shoes sold on each day are as follows: 10, 14, 15, 12, 16, 18, 16.
Mean:
The mean is calculated by adding all the values and dividing by the total number of items.
Mean = (10 + 14 + 15 + 12 + 16 + 18 + 16) / 7 = 101 / 7 = 14.28
Median:
The median is the value in the middle of an ordered data set. To calculate it, we first order the values from smallest to largest.
10, 12, 14, 15, 16, 16, 18
Since there are an odd number of values, the median is the value in the middle position, which in this case is 15. Therefore, the median is 15.
Mode:
The mode is the value that occurs most frequently in a data set. In this case, there is no value that is repeated more times than the others. The values 16 and 12 are repeated twice each, but there is no single mode. Therefore, there is no single mode in this data set.
Note: Here is the question in English:
The table shows the number of shoes sold in 1 store during a week, calculates the measures of central tendency, and perform the corresponding analysis.
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Question #5
Find the measure of the indicated arc.
OOOO
90°
80°
100°
70°
G
H
40°
F
The value of the required arc in the figure is solved to be
80°How to find the value of the arcThe inscribed angle is given in the problem as 40 degrees. This is the angle formed at the circumference of the circle
The relationship between inscribed angle and the intercepted arc is
intercepted arc = 2 * inscribed angle
in the problem, we have that
intercepted arc = ?
inscribed angle = 40
plugging in the values
intercepted arc = 2 * 40
intercepted arc = 80 degrees
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Statement: Reasons:
DF=EG.
DE
Prove: DE=FG
Statements
DF=EG
DF=DE+EF.
EG=EF+FG
DE+EF=EF+ FG
FL
G
Answer:
az
Step-by-step explanation:
A sixth-grade class recorded the number of letters in each student's first name.
The results are shown in the dot plot.
A dot plot titled lengths of student names show the number of students with a certain number of letters in their name. The data is as follows. 1 dot above 3, 2 dots above 4, 4 dots above 5, 7 dots above 6 and 7, 3 dots above 8, 1 dot above 9, 2 dots above 10, and 3 dots above 11.
Which is the best representation of the center of this data set?
A. 8
B. 5
C. 7
D. 6
What are the coordinates of the midpoint of the line segment whose end points are (2, 6) and (10, 4)?
The midpoint of the line segment with endpoints (2, 6) and (10, 4) is (6, 5).
To find the midpoint of a line segment, we can use the midpoint formula, which states that the coordinates of the midpoint are the average of the coordinates of the endpoints.
Let's denote the coordinates of the first endpoint as (x1, y1) and the coordinates of the second endpoint as (x2, y2).
In this case, the first endpoint is (2, 6) with coordinates (x1, y1) = (2, 6), and the second endpoint is (10, 4) with coordinates (x2, y2) = (10, 4).
To find the midpoint, we use the midpoint formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Plugging in the values, we have:
Midpoint = ((2 + 10) / 2, (6 + 4) / 2)
= (12 / 2, 10 / 2)
= (6, 5)
As a result, (6, 5) is the point on the line segment where the endpoints are (2, 6) and (10, 4) respectively.
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PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS CORRECT (NO LINKS )
Find the measure of arc GW.
Answer:c
Step-by-step explanation:
A national dog show had two types of poodles. This table
shows height data, in inches, for the two types of poodles.
Heights of Poodles
Type of Poodle
Miniature
Standard
Number of Dogs
18
24
Mean Height Variation in Height
(inches)
(inches)
13
23
2
2
What number completes the sentence?
The difference in inches, between the mean height for the two
types of poodles is
times the variation for
either type.
Enter your answer in the space provided.
6. For each final matrix, state the solution.
Please answer this picture
The solutions associated with the final matrices representing a system of linear equations are listed below:
First case: x = 3, y = 1, z = 8
Second case: No solution
Third case: No solution
What are the solutions contained in each final matrix?
In this problem we find three of final matrices, each of them representing a system of linear equations. There are two rules to be considered:
A system has no solution if there is a row with only zeroes in the dependent coefficients matrix.A system has a solution if there is a singular matrix, there is, the dependent coefficients matrix has only ones in the main diagonal and the rest of elements are zeroes.Now we proceed to determine the solution associated with each matrix:
First matrix:
x = 3, y = 1, z = 8
Second matrix:
No solution
Third matrix:
No solution
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Step-by-step explanation:
For the left matrix, since the matrix is already in reduced row form,
The solutions to the matrix is (3,-1,8)
For the middle matrix, we need to convert the -6 to a zero,
notice how in the third row, every entry except the last one is 0, this implies that
0=-2, which is not the case thus the middle matrix has no solution.
For the last one, notice that we have 3 colums but only two non zero rows, this means that this matrix has infinite solutions.
6/7 .r = 3/4 write it as a fraction or as a whole or a mixed number
The solution for "r" is 21/24, which can be simplified to 7/8. The answer can be written as a fraction of 7/8.
To solve for "r" in the given equation, we can use algebraic manipulation.
First, we can multiply both sides of the equation by the reciprocal of 6/7, which is:
7/6: 6/7 · r = 3/4
7/6 · 6/7 · r = 7/6 · 3/4
r = 21/24.
Thus, the solution for "r" is 21/24, which can be simplified to 7/8.
Therefore, the answer can be written as a fraction of 7/8.
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You just inherited a sum of money from a distant uncle. The only stipulation is that you need to save it for 10 years and then you can do whatever you want with it. The amount of the inheritance is $25,000.
Option one: You can put it into a saving account that earns 6% compounded quarterly.
Option two: You can put it into a checking account that earns 4% compounded monthly.
Option three: You can place it into a money market account that earns 3% compounded daily.
Which option is best for you? Why?
Submit a report detailing the reasons you have for the decision you make.
This flexibility of a money market account makes it an ideal option for people who need to save money without risking their inheritance.
After inheriting $25,000 from a distant uncle, you would like to save it for ten years before doing anything with it. Since you want to save the money, there are several options for keeping it safe and earning interest, including a savings account, a certificate of deposit (CD), and a money market account.
Money market accounts, in my opinion, would be the best place to keep the inheritance. The money market account is a low-risk account with high-interest rates, making it an attractive option for someone who wants to save their money. As a result, it would be reasonable to place the inheritance into a money market account that pays a daily compounded rate of 3%.There are several reasons for choosing this option.
Firstly, the daily compounded interest will generate a higher return over the ten-year period than the simple interest or monthly compounded interest offered by other accounts. Second, the account is FDIC-insured, which means that the account holder is guaranteed to receive their money in the event of a bank failure.
Furthermore, the money market account provides easy access to the account holder's money while still earning interest. Most money market accounts have a limit on the number of withdrawals a person can make per month. Still, the account holder can easily transfer funds into a checking account or withdraw money from an ATM if needed.
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which of the following will form the composite function G(F(x)) shown below G(F(x)) = 4√x
NO LINKS!! URGENT HELP PLEASE!!
Please help me with #11. I plotted the points, the rest of the questions I need help with
Answer:
Not parallelogram
Step-by-step explanation:
points A(-4, 1), B(1,3), C(8, -1) and D(4, -3).
The slope of a line can be found using the following formula:
Slope [tex]m= = \frac{(y_2 - y_1) }{(x_2 - x_1)}[/tex]
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Using the formula above,
Side AB: Slope =[tex]\frac{3-1}{1-(-4)}=\frac{2}{5}[/tex]
Side BC: Slope =[tex]\frac{-1-3}{8-1}=\frac{-4}{7}[/tex]
Side CD: Slope =[tex]\frac{-3 - (-1)}{4 - 8}= \frac{1}{2}[/tex]
Side DA: Slope =[tex]\frac{-3 - 1}{4 - (-4)}= \frac{-1}{4}[/tex]
Since The slopes of opposite sides are equal,
Therefore ABCD is not Parallelogram:
HELP ME PLS I'LL MARK BRAINLIEST AND GIVE U 13 POINTS
Answer:
The answer is number 3
Y =-3/7X + 3
Step-by-step explanation:
Substitue with the value of the two points in all answers
The value of the left side must equal the value or the right side
For instance,
The two points are (0,3) & (7,0)
Substitue in the first answer with the point (0,3)
3 = - 3 (rejected)
Second answer
3 = 3 works for the point (0,3) then also Substitue with the other point (7,0)
0 = 6 (rejected)
The third answersub. With point (0,3).
3 = 3 it worksSub. With point (7,0)
0= - 3+3 0=0 it worksThen that's the right one
Circle 1 is centered at (−4,−2) and has a radius of 3 centimeters. Circle 2 is centered at (5,3) and has a radius of 6 centimeters.
What transformations can be applied to Circle 1 to prove that the circles are similar?
Enter your answers in the boxes.
The circles are similar because you can translate Circle 1 using the transformation rule ( , ) and then dilate it using a scale factor of .
The circles are similar because you can translate Circle 1 using the transformation rule (9, 5) and then dilate it using a scale factor of 2.
To prove that Circle 1 and Circle 2 are similar, we need to identify the transformations that can be applied to Circle 1 to obtain Circle 2.
First, let's consider the translation of Circle 1. The translation rule is given by (a, b), where a represents the horizontal shift and b represents the vertical shift.
In this case, to translate Circle 1 to align with Circle 2, we need to shift it 9 units to the right and 5 units up. Therefore, the translation rule for Circle 1 is (9, 5).
Next, let's consider the dilation. A dilation is a transformation that changes the size of the figure but preserves its shape. The scale factor, denoted by k, determines the amount of scaling. In this case, Circle 1 needs to be dilated to match the size of Circle 2.
The scale factor can be determined by comparing the radii of the two circles. The radius of Circle 1 is 3 centimeters, while the radius of Circle 2 is 6 centimeters. The scale factor is obtained by dividing the radius of Circle 2 by the radius of Circle 1: 6/3 = 2.
Therefore, the transformation applied to Circle 1 to prove that the circles are similar is a translation by (9, 5) followed by a dilation with a scale factor of 2.
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10. Consider the quadratic function f(x)=x² +6x. Solve the inequality for f(x) > -5.
Answer: x<-5
x>-1
The solution to the inequality f(x) > -5 is x < -5 or x > -1.
To solve the inequality f(x) > -5 for the quadratic function f(x) = x^2 + 6x, we need to find the values of x that satisfy the inequality.
First, set up the inequality:
x^2 + 6x > -5
Next, move all terms to one side of the inequality to get a quadratic expression:
x^2 + 6x + 5 > 0
To solve this quadratic inequality, we can factor it:
(x + 5)(x + 1) > 0
Now, we need to determine the sign of the expression for different intervals on the x-axis.
a) When x < -5:
If x is less than -5, both (x + 5) and (x + 1) are negative, so their product is positive.
Thus, the inequality is satisfied for x < -5.
b) When -5 < x < -1:
If x is between -5 and -1, (x + 5) is positive, but (x + 1) is negative. The product of a positive and a negative number is negative.
Thus, the inequality is not satisfied for -5 < x < -1.
c) When x > -1:
If x is greater than -1, both (x + 5) and (x + 1) are positive, so their product is positive.
Thus, the inequality is satisfied for x > -1.
Therefore, x -5 or x > -1 is the answer to the inequality f(x) > -5.
In summary:
x < -5 or x > -1.
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Jenny is watching her favorite soccer team playing a match. The odds against her favorite team winning are 7/10. What is the probability of her favorite team winning?
Answer:
70%
Step-by-step explanation:
NO LINKS!! URGENT HELP PLEASE!!
Use the parallelogram ABCD to find the following.
8. part 2
b. AE=
d. m<DCB=
f. m<ADC=
Answer:
b. 7
d. 120°
f. 60°
Step-by-step explanation:
The properties of a parallelogram are:
Opposite sides are parallel and congruent.Opposite angles are equal.Adjacent angles are supplementary.The diagonals bisect each other.The sum of the interior angles is 360 degrees.For Question:
b.
AE=CE=7 since diagonals of parallelogram bisect each other
d.
m ∡ DCB= m ∡DAB=120° Opposite angle in a parallelogram is congruent or equal.
f.
m ∡ ADC=?
Here
m ∡ADC+ m ∡DAB=180° being co interior angle
m ∡ADC+120°=180°
m ∡ADC=180°-120°=60°
m ∡ADC=60°
Answer:
b) AE = 7
d) m∠DCB = 120°
f) m∠ADC = 60°
Step-by-step explanation:
Part bThe diagonals of a parallelogram always bisect each other.
Therefore, point E (the point of intersection of the two diagonals) is the midpoint of diagonal AC. So AE = EC.
As EC = 7, then AE = 7.
[tex]\hrulefill[/tex]
Part dAs the measure of the opposite angles of a parallelogram are equal, then m∠DCB is equal to m∠DAB. From inspection of the given parallelogram, we can see that m∠DAB = 120°. Therefore:
m∠DCB = 120°
[tex]\hrulefill[/tex]
Part fAdjacent angles of a parallelogram are supplementary (sum to 180°).
Angle DAB and angle ADC are adjacent angles, so their sum is 180°.
Therefore:
⇒ m∠ADC + m∠DAB = 180°
⇒ m∠ADC + 120° = 180°
⇒ m∠ADC + 120° - 120° = 180° - 120°
⇒ m∠ADC = 60°
6. Juan y Roberto son dos hermanos que juegan Piedra, Papel y Tijera para determinar quien hace el aseo de su cuarto. ¿Cuántos serán los posibles resultados que podemos tener?, ¿Cuál es la probabilidad de que Juan no haga el aseo? *
Given, Juan y Roberto is two brothers who play Rock, Paper, and Scissors to determine who does the cleaning in their room. The total number of possible outcomes is 3. The possible outcomes are rock, paper, and scissors. So, the probability of Juan not doing the cleaning is 1/2 or 50 percent.
The probability that Juan will not do the cleaning is 1/2 or 50 percent. The possible outcomes for playing the game Rock, paper, and Scissors are given as follows. Rock can break scissors, Paper can cover rock, and Scissors can cut paper. Therefore, there are three possible outcomes in this game. The possible outcomes are rock, paper, and scissors.
The probability that Juan will not do the cleaning is 1/2 or 50 percent since there are two possible outcomes where Juan does not do the cleaning. The two possible outcomes are paper and scissors. Juan can pick the paper or scissors to win. Therefore, the probability of Juan not doing the cleaning is 1/2 or 50 percent.
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What is the volume of the following triangular prism?
A. 380 m³
B. 398 m³
C. 351 m³
D. 327 m³
Answer:
C-351
Step-by-step explanation:
Given the piecewise functions shown below, select all of the statements that are true.
The true statements are:
a. f(-1) = 2
c. f(1) = 0
Let's evaluate each statement using the given piecewise function f(x):
a. f(-1) = -(-1) + 1 = 2
b. f(-2) = -(-2) + 1 = 3 (Not 0, so this statement is false)
c. f(1) = (1)^2 - 1 = 0
d. f(4) = (4)^2 - 1 = 16 - 1 = 15 (Not 7, so this statement is false)
Therefore, the correct statements are:
a. f(-1) = 2
c. f(1) = 0
Statement a is true because when x = -1, we use the first piece of the piecewise function, which gives us -(-1) + 1 = 2.
Statement c is true because when x = 1, we use the third piece of the piecewise function, which gives us (1)^2 - 1 = 0.
Statements b and d are false because they do not match the corresponding values obtained from evaluating the piecewise function at the given inputs.
Therefore, the true statements are:
a. f(-1) = 2
c. f(1) = 0
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Which equation best shows that 45 is a multiple of 15?
Choose 1 answer:
A45-15 = 30
B
45 x 3 = 15
48= 45 +3
45÷3= 15
The correct Option is D. 45÷3= 15 . The equation that best shows that 45 is a multiple of 15 is 45 ÷ 3 = 15.
A multiple is a product that results from multiplying two or more numbers.
A common multiple is a multiple that is common to two or more numbers.
A multiple of a number can be expressed as an integer multiple of the number.
If the result is a whole number, the first number is a multiple of the second.
An equation that shows 45 is a multiple of 15 is as follows: 45 ÷ 3 = 15.
A multiple is a number that can be divided by another number without leaving a remainder.
As a result, we divide 45 by 3 to find out whether 45 is a multiple of 15.
If the result is a whole number, 45 is a multiple of 15.
Here is the equation that shows this: 45 ÷ 3 = 15
Thus, we can conclude that the equation that best shows that 45 is a multiple of 15 is 45 ÷ 3 = 15.
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Jalen bought a new iPad. The screen has a perimeter of inches 36 inches and an area of 80 square inches. What are the dimensions of the iPad’s screen?
Let's assume the dimensions of the iPad's screen are represented by length (L) and width (W). We can use the given information to set up two equations.
Perimeter equation:
The perimeter of a rectangle is given by the formula: 2(L + W). In this case, the perimeter is given as 36 inches.
So, 2(L + W) = 36.
Area equation:
The area of a rectangle is given by the formula: L * W. In this case, the area is given as 80 square inches.
So, L * W = 80.
We now have a system of two equations:
2(L + W) = 36
L * W = 80
From equation 1, we can simplify it to L + W = 18 and rewrite it as L = 18 - W.
Now substitute this value of L into equation 2:
(18 - W) * W = 80
Expanding the equation:
18W - W^2 = 80
Rearranging the equation to quadratic form:
W^2 - 18W + 80 = 0
Factoring or using the quadratic formula, we find the two possible values for W.
The solutions are W = 8 and W = 10.
Now we can substitute these values back into the equation L = 18 - W to find the corresponding values of L.
For W = 8:
L = 18 - 8 = 10
For W = 10:
L = 18 - 10 = 8
Therefore, the dimensions of the iPad's screen can be either 8 inches by 10 inches or 10 inches by 8 inches.
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NO LINKS!! URGENT HELP PLEASE!!
Please help with 23a and 24a
Answer:
perimeter = 75 cm , area ≈ 28.3 in²
Step-by-step explanation:
23 (a)
since the figure is being enlarged by a scale factor of 5
then the perimeter is increased by a factor of 5.
perimeter of larger shape = 5 × 15 = 75 cm
24
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{90}{360}[/tex]
= π × 6² × [tex]\frac{1}{4}[/tex]
= 36π × [tex]\frac{1}{4}[/tex]
= 9π
≈ 28.3 in² ( to 1 decimal place )
What is the sum of the series?
∑k=36(−2k+5)
Enter your answer in the box.
Hello !
Answer:
[tex]\large \boxed{\sf \sum\limits^6_{k=3}(-2k+5)=-16}[/tex]
Step-by-step explanation:
We want to calculate the following sum :
[tex]\sf \sum\limits^6_{k=3}(-2k+5)[/tex]
Let's remember the following property :
[tex]\fbox{\begin{tabular}{1\textwidth}\star\ \underline{\sf Linearity:}\\ \sf \sum\limits^n_{k=n_0}(\alpha a_k+\beta b_k)=\alpha\sum\limits^n_{k=n_0} a_k+\beta \sum \limits^n_{k=n_0}b_k\end{tabular}}[/tex]
Now we can apply this property to our formula :
[tex]\sf \sum\limits^6_{k=3}(-2k+5)\\=-2\sf \sum\limits^6_{k=3}(k)+\sum\limits^6_{k=3}5[/tex]
Now we can calculate :
[tex]\sf \sum\limits^6_{k=3}(-2k+5)\\=-2(3+4+5+6)+(6-3+1)5\\=-2\times18+4\times 5\\=-36+20\\\boxed{\sf \sum\limits^6_{k=3}(-2k+5)=-16}[/tex]
Have a nice day ;)