Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5.
Answer:
sample response: None of the roots can have multiplicity because the polynomial is cubic and 3 roots are given. Write each root as a linear factor, then multiply the three factors to get the expression for the function.
Step-by-step explanation:
What is the sum of the first 7 terms of the series −4+8−16+32−... ?
is the statement [x]=[x+1] true for all real numbers? explain
Answer:
The Edg answer is as follows -
The statement is not true for all real numbers. It is only true for decimal or fractional values of x .
If x is an integer, then the ceiling function returns x when the input is x . But, the flooring function returns x + 1 when the input is x + 1.
Since x does not equal x + 1 when x is an integer, the expressions are not equal when x is an integer.
Step-by-step explanation:
Real numbers are set of numbers that include rational and irrational numbers.
[x]=[x+1] is not true for all real numbers
Assume that: x is an integer
And x = 5
So, the equation becomes
[tex]5 = 5 + 1[/tex]
[tex]5 = 6[/tex]
The above equation is not true, because:
[tex]5 \ne 6[/tex]
Hence, [x]=[x+1] is not true for all real numbers
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For a large sporting event the broadcasters sold 6969 ad slots for a total revenue of $131131 million. what was the mean price per ad slot?
I really neeed help!! 20 points!!,
the midpoint of PQ is R. R has coordinates (-3,2,-1) and P has coordinates (4,-6,-6). What are coordinates of Q?
The coordinates of point Q are (-10, 10, 4).
Explanation:To find the coordinates of point Q, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points P(x1, y1, z1) and Q(x2, y2, z2) are given by the average of the coordinates:
R = ((x1 + x2) / 2, (y1 + y2) / 2, (z1 + z2) / 2)
In this case, we are given that the midpoint R has coordinates (-3, 2, -1) and one of the points P has coordinates (4, -6, -6). Plugging in these values into the midpoint formula, we can solve for the coordinates of point Q:
Q = (2 * R - P)
Q = (2 * (-3, 2, -1) - (4, -6, -6))
Q = (-6, 4, -2) - (4, -6, -6)
Q = (-10, 10, 4)
a gardener makes a new circular flower bed. the bed is fourteen feet in diameter. Calculate the circumference and the area of the circular flower bed.
The circumference and the area of the circular bed are 14π feet = 43.9823 feet and 49π feet² = 153.9380 feet² respectively.
How is the circumference of a circle calculated?The circumference is the total length covered by the boundary of an object.
To calculate the circumference of a circle with radius r units, we use the formula: Circumference = 2πr units.
How is the area of a circle calculated?The area of an object is the space its planar face or two-dimensional face covers.
To calculate the area of a circle of radius r units, we use the formula: Area = πr² sq. units.
How to solve the question?In the question, we are asked to find the circumference and the area of the circular flower bed that a gardener makes, having a diameter of fourteen feet.
We know that radius = diameter/2 = 14/2 = 7 feet.
To calculate the circumference of the circular bed, we will use the formula 2πr, where r is the radius.
Substituting the radius, r = 7 feet in the above formula, we get:
Circumference = 2(π)(7) feet = 14π feet = 43.9823 feet.
To calculate the area of the circular bed, we will use the formula πr², where r is the radius.
Substituting the radius, r = 7 feet in the above formula, we get:
Area = (π)(7)² feet² = 49π feet² = 153.9380 feet².
Thus, the circumference and the area of the circular bed are 14π feet = 43.9823 feet and 49π feet² = 153.9380 feet² respectively.
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What is 0.3 percent as a fraction
At Brown Elementary School, 80% of all fifth graders ride the bus to school. If 124 fifth graders ride the bus to school, how many fifth graders are there at the school?
Answer: The total number of fifth graders in the school is 155.
Step-by-step explanation: Given that at Brown Elementary School, 80% of all fifth graders ride the bus to school.
If 124 fifth graders ride the bus to school, we are to find the number of fifth graders in the the school.
Let, 'n' be the total number of fifth graders in the school.
Then, according to the given information, we have
[tex]80\%\times n=124\\\\\\\Rightarrow \dfrac{80}{100}\times n=124\\\\\\\Rightarrow \dfrac{4}{5}n=124\\\\\\\Rightarrow n=\dfrac{124\times 5}{4}\\\\\\\Rightarrow n=31\times5\\\\\Rightarrow n=155.[/tex]
Thus, the total number of fifth graders in the school is 155.
If two events a and b are independent and you know that p(a) = 0.75, what is the value of p(a | b)?
a test is worth 90 points and contains 25 questions. multiple-choice questions are worth 3 points each and word problems are worth 4 points. How many of each type of question are there?
If A ⊂ B, then A ∩ B = A ∪ B.
The statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not always true; it holds only if A = B.
The statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not always true.
If [tex]\( A \subset B \)[/tex], it means that every element in set A is also in set B.
Now, consider the intersection of A and B [tex](\( A \cap B \))[/tex]. This intersection contains all elements that are common to both sets A and B.
On the other hand, the union of A and B [tex](\( A \cup B \))[/tex] contains all elements that are in either set A or set B, or both.
Since A is a subset of B, all elements in A are already in B, which means [tex]\( A \cap B = A \)[/tex]. However, [tex]\( A \cup B \)[/tex] would just be B, because all elements in A are also in B, so [tex]\( A \cup B \)[/tex] is simply B.
Therefore, the statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not true in general; it is true only if A = B .
write 2/5 and 1/3 as equivalent fractions using a common denominator
The equivalent fractions with the same denominator are 6/ 15 and 5 /15.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the two fractions are 2/5 and 1/3. The two equivalent expressions with the common base will be written as:-
2/5 = ( 2 x 3 ) / ( 5 x 3 )
2//5 = 6 / 15
1/3 = ( 1 x 5 ) / ( 3 x 5 )
1 / 3 = 5 / 15
Therefore, the two fractions are 6/ 15 and 5 /15.
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The distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations below: Car A: y = 44x + 26 Car B: y = 36x + 66 After how many hours will the two cars be at the same distance from their starting point and what will that distance be?
5 hours, 346 miles 5 hours, 246 miles 3 hours, 246 miles 3 hours, 346 miles
The answer is:
5 hours, 246 miles.
Why?Since we know the equations that represent the distances of both cars at certain times (function of time), we can calculate the time that they will be at the same distance by making their equation equal.
So, we are given the equations:
A-
[tex]y=44x+26[/tex]
B -
[tex]y=36x+66[/tex]
Now, by making both equation equal, we can calculate the time that they will have the same distance, so, we have:
[tex]44x+26=36x+66[/tex]
[tex]44x-36x=66-26[/tex]
[tex]8x=40[/tex]
[tex]x=\frac{40}{8}=5[/tex]
Hence, we have that they will have the same position after 5 hours.
Then, to calculate the distance, we need to substitute the obtained time in any of the given equations, so, substituting into A, we have:
[tex]y=44x+26[/tex]
[tex]y=44*5+26=220+26=246[/tex]
We have that the distance will be 246 miles.
Hence, we have that the answer is:
5 hours, 246 miles.
Have a nice day!
a right rectangular prism is 6cm by 14cm by 5cm. what is the surface area of the right prism?
Final answer:
The surface area of a right rectangular prism with dimensions of 6cm by 14cm by 5cm is calculated by summing up the areas of all faces, resulting in a total surface area of 368cm².
Explanation:
To calculate the surface area of a right rectangular prism, we need to find the area of all the faces and add them together. For a prism with dimensions of 6cm by 14cm by 5cm, it has three pairs of identical faces: two faces that are 6cm by 14cm, two faces that are 6cm by 5cm, and two faces that are 14cm by 5cm.
Using the area formula for rectangles (Area = length × width), we find the areas of these faces:
For the 6cm by 14cm faces: Area = 6cm × 14cm = 84cm². Since there are two such faces, their combined area is 2 × 84cm² = 168cm².
For the 6cm by 5cm faces: Area = 6cm × 5cm = 30cm². Since there are two such faces, their combined area is 2 × 30cm² = 60cm².
For the 14cm by 5cm faces: Area = 14cm × 5cm = 70cm². Since there are two such faces, their combined area is 2 × 70cm² = 140cm².
Adding up all these areas gives us the total surface area of the prism:
Total Surface Area = 168cm² + 60cm² + 140cm² = 368cm²
Therefore, the surface area of the right rectangular prism is 368cm².
Marcia bake 2 pans of brownies. Her family ate 1 1/5 pans. what fraction of a pan of brownies was left?
we know that
To find out the fraction of a pan of brownies that was left subtract [tex]1\frac{1}{5}[/tex] from [tex]2[/tex]
remember that
[tex]1\frac{1}{5}=(1*5+1)/5=\frac{6}{5}[/tex]
so
[tex]2-\frac{6}{5} =(2*5-6)/5=\frac{4}{5}[/tex]
therefore
the answer is
the fraction of a pan of brownies that was left is [tex]\frac{4}{5}[/tex]
The height of a statue is 276 inches. What is the hieght of the statue in meters? Round your answer to the nearest hundredth.
We can convert inches to meters with the following conversion formula:
1 inch = 0.0254 meters
Now we have to find how many meters are there in 276 inches.
So multiplying 0.0254 with 276 would give us the answer.
276 inches = 0.0254 *276 = 7.0104 meters.
Answer : There are 7.0104 meters in 276 inches.
The arena would like to estimate its annual running costs for the next twelve months. Use the following first 4 months' figures to estimate the running costs for 12 months. Month Costs January £14,889.51 February £22,936 March £9,856.88 April £6,777.77 The estimated running costs for 12 months is
Answer:
163,380.48
Step-by-step explanation:
First find the average of the first 4 months' figures.
To do this, find the sum of the first 4 values and then divide by 4, the number of data points:
(14889.51+22936+9856.88+6777.77)/4 = 54460.16/4 = 13615.04
It costs on average £13615.04 per month to run the arena.
This means the estimated running costs for 12 months will be
13615.04(4) = £163,380.48
The formula to convert Celsius to Fahrenheit is F=9/5+32 convert 87 F to Celsius
A) 16c
B) 55c
C)31c
D)99c
Determine whether the sequence is arithmetic, geometric, both or neither.
16, 8, 4, 2
A. arithmetic
B. Goemetric
C. Neither
D. Both
I think its both because An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. Consecutive means one after the other. The constant value is called the common difference. Another way to think about an arithmetic sequence is that each term in the sequence is equal to the previous term plus the common difference and also A geometric sequence is a sequence in which the ratio of any two consecutive terms is constant. This constant value is called the common ratio. Another way to think about a geometric sequence is that each term is equal to the previous term times the common ratio. So when u look at it check out if the 16, 8, 4, and 2 see if they fit these terms
The ratios are constant (0.5), so the sequence is geometric.
Since the sequence is not arithmetic but is geometric, the correct answer is: B. Geometric
To determine whether the sequence 16, 8, 4, 2 is arithmetic, geometric, both, or neither, let's analyze the differences between consecutive terms and the ratios between consecutive terms.
Arithmetic Sequence:
An arithmetic sequence is a sequence in which the difference between consecutive terms is constant.
Calculating the differences:
8 - 16 = -8
4 - 8 = -4
2 - 4 = -2
The differences are not constant, so the sequence is not arithmetic.
Geometric Sequence:
A geometric sequence is a sequence in which the ratio between consecutive terms is constant.
Calculating the ratios:
8 / 16 = 0.5
4 / 8 = 0.5
2 / 4 = 0.5
The ratios are constant (0.5), so the sequence is geometric.
Since the sequence is not arithmetic but is geometric, the correct answer is:
B. Geometric
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Jensen stopped at rest area A along the side of the highway. His map shown below has a scale of 1 inch to 35 miles. Jensen planned to stop at rest stop B next.what is the actual distance in miles between the two rest areas
Jensen stopped at A and planned to stop at B next. He has a map with a scale of 1 inch to 35 miles.
It is clear that 1 inch on map corresponds to 35 miles in actual.
From the map he has, we can see that both places A and B are 2.5 inches apart on map.
Let's assume those are "X" miles away in actual. Then we can use proportions to solve this problem.
1 inch to 35 miles would be same as 2.5 inches to X miles. Mathematically, we can write it as follows :-
[tex] \frac{1 \;inch}{35 \;miles} =\frac{2.5 \;inches}{X \;miles} \\\\
\frac{X \;miles}{35 \;miles} =\frac{2.5 \;inches}{1 \; inch} \\\\
\frac{X}{35} =\frac{2.5}{1} \\\\
Cross \;\;multiplying \\\\
X = 35*2.5=87.5 \;miles [/tex]
Hence, actual distance between A and B is 87.5 miles.
Rewrite the equation below in standard form.
-3x+6y=12
A. 3x-6y=12
B. 3x-6y=-12
C. -x+2y=4
D. x-2y=-4
a rotation of a figure can be achieved by consecutive ___ of the figure over given lines
Polygon B is a scaled copy of Polygon A using a scale factor of 5. How many times larger is the area of Polygon B than the area of Polygon A?
How can I solve the following equation x3+x2+x+1=0?
Choose yes or no to tell if the fraction 3/8 will make each equation true
It says to check if [tex] \frac{3}{8} [/tex] satisfy each equation or not.
Checking first equation :-
96 x [tex] \frac{3}{8} [/tex]
⇒ [tex] \frac{96 * 3}{8} [/tex]
⇒ [tex] \frac{288}{8} [/tex] = 36
⇒ 36 = 36. First equation is "YES".
Checking second equation :-
38 x [tex] \frac{3}{8} [/tex]
⇒ [tex] \frac{38 * 3}{8} [/tex]
⇒ [tex] \frac{114}{8} [/tex] = [tex] \frac{57}{4} [/tex]
⇒ [tex] \frac{57}{4} [/tex] ≠ 14. Second equation is "NO".
Checking third equation :-
16 x [tex] \frac{3}{8} [/tex]
⇒ [tex] \frac{16 * 3}{8} [/tex]
⇒ [tex] \frac{48}{8} [/tex] = 6
⇒ 6 = 6. Third equation is "YES".
Checking fourth equation :-
56 x [tex] \frac{3}{8} [/tex]
⇒ [tex] \frac{56 * 3}{8} [/tex]
⇒ [tex] \frac{168}{8} [/tex] = 21
⇒ 21 = 21. Fourth equation is "YES".
find the measure of DBE if abc is 145
answers
30
60
90
145
Which equation illustrates the identity property of multiplication ? (X+yi)×z=(xz+yzi) (x+yi)×0=0 (x+yi)×(z+wi)=(z+wi)×(x+yi) (x+yi)×1=(x+yi)
The expression that shows identity property of multiplication is (x+yi)×1=(x+yi), the correct option is D.
What is the identity property of multiplication?According to the identity property of multiplication, the product of 1 and a number is the number itself.
The expressions in the question are
(X+yi)×z=(xz+yzi)
(x+yi)×0=0
(x+yi)×(z+wi)=(z+wi)×(x+yi)
(x+yi)×1=(x+yi)
The only expression that shows this property is (x+yi)×1=(x+yi).
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At a school carnival the diameter of the mat of a trampoline is 12 ft and the diameter of its metal frame is 14 ft what is the length in feet of the metal frame that surrounds the trampoline use 3.14 for pie and round your answer to the nearest tenth
The length in feet of the metal frame that surrounds the trampoline is 44 ft.
What is the circumference of a circle?The circumference of a circle is the distance round the circle.
The circumference of a circle = πD
3.14 x 14 = 44 ft
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PLEASE HELP!! 30 POINTS
Match the graph with the correct equation.
A) y + 3 = –(x + 5)
B) y – 3 = –(x + 5)
C) y – 3 = (x + 5)
D) y – 5= –(x + 3)