The correct answer is: c. 4. In some cases, a fourth-degree polynomial with five terms could have at most 4 different linear factors.
To understand how many different linear factors a fourth-degree polynomial with five terms could have at most, let's consider the Fundamental Theorem of Algebra, which states that a polynomial of degree (n) has exactly (n) complex roots, counting multiplicity. For a fourth-degree polynomial, this means it can have at most 4 linear factors, as each linear factor corresponds to a root.
However, the polynomial could have repeated roots, reducing the number of distinct linear factors. If all four roots are distinct, then there will be 4 different linear factors. But if one or more roots are repeated, the number of different linear factors will decrease. The polynomial could have fewer than 4 distinct linear factors if it has repeated roots.
Complete Question:
A fourth degree polynomial with five terms could have, at most, how many different linear factors?
a. 3
b. 2
c. 4
d. 5
which number belongs to the solution set of the equation below? 9x=114
A.14
B.16
C.12
D.18
Need help please help
The length of a rectangle is twice its width. if the perimeter of the rectangle is 54 ft , find its length and width.
Write each number as the product of its prime factors
1.) 76
2.) 35
3.)36
4.) 150
5.)180
6.) 520
please help i have 30 mins to get these answered!! :(
I need help with the following problem
I need hellllllllllllllllllllppppp for this trigonometry question
see attached picture:
the vertical change is the Y calculation
Fill in 2 to 10 so every row and column adds up to 18
Find the coordinates of the midpoint of ab with endpoints a(-10,3) and b(2,-2) worksheet answers
Jo is flipping a fair coin. If the coin is truly fair, how many times should it land on heads if he flips the coin 200 times
a coin has a 1/2 probability of landing on heads
so it should land on heads 1/2 of the time
1/2 of 200 = 100
Final answer:
With a fair coin, theoretical probability suggests that Jo should expect to land on heads roughly 100 times out of 200 flips. Actual results may vary slightly due to random chance, but should approximate 50 percent heads over a large number of trials.
Explanation:
If Jo is flipping a fair coin, on average, we would expect the coin to land on heads 100 times out of 200 flips. This expectation is based on the theoretical probability of getting heads, which is 0.5 or 50% for a fair coin. Therefore, if Jo flips the coin 200 times, the expected number of heads is calculated by multiplying the total number of flips by the probability of getting heads (0.5), which is 200 * 0.5 = 100.
However, it's important to note that while the theoretical probability suggests that Jo should get heads approximately 100 times, the actual result might be slightly more or slightly less due to random chance. The larger the number of flips, the closer the actual results are likely to get to the expected 50 percent heads, as demonstrated by the law of large numbers. But for any finite number of flips, there is always potential for some variation from the expected value.
What is the area of a triangle whose vertices are
R(−4, 2),S(1, 2), and T(−5, −4)?
Enter your answer in the box
Marks canoes rents for $20 plus $35 per hour you do not want to spend more than $1.50.for how many hours can you afford to rent the canoe
while on vacation, your family budgeted $550 for food. Your family went to the grocery store for drinks and snacks and spent $67.19 Each meal you are going to eat out had a budget of $55
Which expression describes the amount of money left in your after you consume your meals ?
A. 550 - (67.19 + 55x)
B.550- x(67.19 -55)
C.550-x(67.19+55)
D.550-(67.19-55x)
Final answer:
The correct expression to calculate the remaining budget for food after spending on groceries and meals out is 550 - (67.19 + 55x), which is option A.
Explanation:
The question asks us to determine which expression correctly represents the amount of money left in the budget for food after the family has spent money on groceries and consumed their meals. The original budget for food is $550, and the family spent $67.19 on drinks and snacks. Each meal they plan to eat out is budgeted at $55. Let's denote the number of meals the family will eat out as 'x'.
To calculate the remaining budget after these expenses, we subtract the cost of groceries and the total cost of eating out (which is $55 times the number of meals 'x'), from the original budget for food. The correct mathematical expression for the remaining budget is:
550 - (67.19 + 55x)
This expression is represented by option A. This correctly factors in the initial expenditure on groceries of $67.19 and then subtracts $55 for each meal 'x' from the remaining budget.
how do you solve this absolute value equation? ∣x−2∣=∣4+x∣
Kristen bought 2 candy bars for $1.29 each and a soda for$1.99. She had to pay $0.38 in tax. How much was her bill?
Answer:
$4.95
Step-by-step explanation:
1.29 * 2 = 2.58 + 1.99 = 4.57
4.57 + .38 = 4.95
If a number is rational then it must be a whole number true or false
There are five position players on a starting basketball team: 2 guards, 2 forwards, 1 canter. Write a ratio in simplest from to express each relationship
Final answer:
The ratios for the basketball positions in simplest form are guards as 2:5, forwards as 2:5, and the center as 1:5.
Explanation:
The question asks to write ratios for the positions on a basketball team and then to express those ratios in simplest form. There are 5 position players on a starting basketball team, consisting of 2 guards, 2 forwards, and 1 center. To express the relationships between each position, we can write the ratios of guards to the total number of players, forwards to the total number of players, and the center to the total number of players.
The ratio of guards to the total number of players is 2 guards to 5 total players, which simplifies to 2:5.
The ratio of forwards to the total number of players is 2 forwards to 5 total players, simplifying to 2:5.
Lastly, the ratio of the center to the total number of players is 1 center to 5 total players, simplified as 1:5.
If f(x)=x^2-3x,find f(-1.8). Show all work
The value of f(x) = x²-3x at x = -1.8 is -2.16.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
We have the quadratic function:
f(x) = x²-3x
So, to find the value at x = -1.8:
Substitute the value to the function.
f(-1.8) = (-1.8)²-3(-1.8)
f(-1.8) = 3.24 - 5.4
f(-1.8) = -2.16
Therefore, the value is -2.16.
To learn more about the quadratic function;
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How to find slope and y intercept 6x-5y=15?
What is the multiplicative rate of change of the exponential function shown on the graph?
A) 2/9
B) 1
C) 4
D) 9/2
Answer:
Option: D is correct.
9/2
Step-by-step explanation:
We have to find the multiplicative rate of change of the exponential function shown on the graph.
We know that a general exponential function is given as:
[tex]y=ab^x[/tex]
where b is the multiplicative rate of change.
Now when x=0 we have y=1.
i.e. 1=a
Hence, a=1
and y=b^x
Also,
the graph passes through (1,9/2)
Now when x=1 we have y=9/2
i.e.
9/2=b
Hence, the multiplicative rate of change is:
9/2
The correct answer is A) 2/9. The multiplicative rate of change of the exponential function shown on the graph is A) 2/9.
To determine the multiplicative rate of change of an exponential function from its graph, we need to identify two points on the graph that are one unit apart horizontally (i.e., one unit apart in the x-direction). The multiplicative rate of change is the ratio of the function values (y-values) of these two points.
Let's assume we have two points, (x, y) and (x+1, y'), where y and y' are the corresponding y-values of the exponential function at these x-values. The multiplicative rate of change, r, is given by:
[tex]\[ r = \frac{y'}{y} \][/tex]
From the graph, we can identify two such points. For example, if the function passes through the y-axis at (0, 1) and then at (1, 2/9), we can calculate the multiplicative rate of change as follows:
[tex]\[ r = \frac{2/9}{1} = \frac{2}{9} \][/tex]
This is the multiplicative rate of change of the exponential function. It indicates that for every unit increase in x, the y-value is multiplied by 2/9.
Therefore, the multiplicative rate of change of the exponential function shown on the graph is A) 2/9.
what is the measure of <DCF
Answer:
The measure of angle DCF is 129 degrees.
Step-by-step explanation:
Angle DCF is the sum of angle DCE plus angle ECF.
This is because, DCF is the main angle and DCE and ECF are its two parts.
Hence, the measure of angle DCF will be = [tex]75+54=129[/tex] degrees.
The answer is :
The measure of angle DCF is 129 degrees.
How to write an equation with an undefined slope?
A boy throws a baseball across a field. The ball reaches its maximum height, 18 meters, after 1 second. After approximately 2.3 seconds, the ball lands on the ground. The ball’s motion can be modeled using the function f(x) = –10x2 + 20x + 8. What is the height of the ball 1.5 seconds after it is thrown?
Answer:
Step-by-step explanation:
Alright, lets get started.
The function that models the height of the ball is given by :
[tex]f(x)=-10x^2+20x+8[/tex]
When we plug x as 1.5 , we could get the height f(1.5) as :
[tex]f(1.5)=-10(1.5)^2 +20*1.5 +8[/tex]
[tex]f(1.5)=-22.5+30+8[/tex]
[tex]f(1.5)=15.5[/tex]
So the height of the ball after 1.5 second is 15.5 meters. : Answer
Hope it will help :)
Answer:
It is c on edge just took the test
Step-by-step explanation:
Find an equation of the line with the given slope and containing the given point. express your answer in slope-intercept form.
a customer brings in a item for refund.The price on the item is $4.80 and the tax is 5%.How much including tax should the cashier refund back to the customer
Answer:
The cashier should refund back to the customer $5,04
Step-by-step explanation:
The cashier has to refund the amount the customer paid, which was the price plus the proportional tax.
Refund=price+tax
Price=$4.80
Tax=$4.80 * 0,05= $0,24
Refund=$4.80 +$0,24=$5,04
if a quadrilaterals diagonals bisect its vertices, what kind of quadrilateral must it be?
A - Rhombus
B - trapezoid
C - rectangle
D - parallelogram
What are the solutions to x2 8x 7 = 0? x = –8 and x = –7 x = –7 and x = –1 x = 1 and x = 7 x = 7 and x = 8?
The correct solutions to the given equation are x = 1 and x = 7.
The solutions to the equation x² - 8x + 7 = 0 are x = 1 and x = 7.
To find these solutions, we can factor the quadratic equation by finding two numbers that multiply to 7 (the constant term) and add up to -8 (the coefficient of the x term).
Therefore, the correct solutions to the given equation are x = 1 and x = 7.
The number of hours per week that the television is turned on is determined for each family in a sample. the mean of the data is 3030 hours and the median is 26.226.2 hours. twenty-four of the families in the sample turned on the television for 1515 hours or less for the week. the 11th11th percentile of the data is 1515 hours. step 2 of 5 : approximately how many families are in the sample? round your answer to the nearest integer.
A horizontal line passes through the point (5, –1). Which point is also on this line?
A.(0, 0)
B.(–1, 5)
C.(5, –4)
D.(–2, –1)
Answer: -2,-1
Step-by-step explanation
If a horizontal line passes through the point (5;-1) then the equation if this line: y=-1
Each point (x;-1) is also on this line.
what is the value of x
6^2 + 8^2 = x^2
36 + 64 = 100
sqrt(100) = 10
x = 10
Determine whether the quantitative variable is discrete or continuous. number of lightning strikes in a city in one year'