The equation of a polynomial that has zeros at x = 2i and x = 3 is given as follows:
x³ - 3x² + 4x - 12.
How to obtain the cubic polynomial?We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.
The zeros are given as follows:
x = 2i.x = -2i, as if a complex number is a root, then it's conjugate also is.x = 3.Then the polynomial is obtained as the product of it's linear factors, due to the Factor Theorem, as follows:
(x - 2i)(x + 2i)(x - 3)
(x² + 4)(x - 3)
x³ - 3x² + 4x - 12.
(as the base complex number relation is i² = -1).
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Brianna got $50.00 for her birthday. Her neighbor paid her $10 for walking his dog. Brianna paid back her sister $7.50 she owed her. Then Brianna went to the store to buy a shirt she wanted that cost $18. How much does Brianna have left?
34.50
14.50
35.50
49.5
Answer: 34.5
Step-by-step explanation:
50 + 10 = 60 (birthday and dog walking)
60 - 7.50 = 53.5 (paid what she owed)
52.5 - 18 = 34.5 (bought a shirt)
A small cargo plane currently has 150 pounds of cargo aboard. In addition, n boxes weighing 30 pounds each will be brought aboard.
Suppose that the total weight of the cargo on board must be at most p pounds. Using the values and variables given, write an inequality describing this.
Answer: 150+30n ≤ p
Step-by-step explanation:
150 is your starting amount, and you add 30 lbs of how many ever boxes (n) onto your plane. So far, you have 150 + 30n. Because there is a limit of p amount that you can't exceed, you need a less than or equal to sign because it can be p amount but not over p amount. So your answer is 150 +30n ≤ p
Joe has a 300 foot fence around his rectangular yard. The length is 10 feet more than the width. Which equation can you use to determine the dimensions?
The equation that used to determine the dimension is 2(2x+10) = 300 and the dimensions of the rectangular yard is 80 foot and 70 foot
Total length of the fence = 300 foot
Consider the width of the rectangular yard = x
The length of the rectangular yard = x + 10
The perimeter of the rectangle = 2(l + w)
Where l is the length and w is the width
Substitute the values in the equation
300 = 2(x+10 + x)
300 = 2(2x + 10)
4x + 20 = 300
4x = 300 - 20
4x = 280
x = 280/4
x = 70 foot
The length = x + 10
= 70 + 10
= 80 foot
Therefore, the equation is 2(2x+10) = 300 and dimensions are 80 foot and 70 foot
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x-1/x+1=3/2x+2
Responses
x = − 1 , or , x = 5/2
no solution
x = − 1
x=5/2
The required number solutions of given quadratic equation is -1 or 5/2.
Explain quadratic equation?A quadratic equation in math is a second-degree condition of the structure ax^2 + bx + c = 0. Here a, b, are the coefficients, c is the steady term, and x is the variable. Since the variable x is of the subsequent degree, there are two roots or deals with this quadratic condition.
According to question:We have,
x-1/x+1=3/2x+2
(x - 1)(2x + 2) = 3(x + 1)
2x^2+2x-2x-2 = 3x+3
2x^2-3x-5 = 0
2x^2-5x+2x-5 = 0
x(2x-5)+(2x-5)
(x+1)(2x-5) = 0
x = -1 or x = 5/2
Thus, solution of equation is -1 or 5/2.
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10) In a study of the relationship between the amount of violence a person watches on TV and the viewer's age, 81 regular TV watchers were randomly selected and classified according to their age group and whether they were a "low-violence" or "high-violence" viewer. Below is a segmented bar graph. For this sample, can we conclude there is an association between age group of the viewer and amount of violence watched? If so,what is the relationship?
We can conclude there is an association between age group of the viewer and amount of violence watched and its 55+ year-olds are likely to be categorized as low-violence.
What is segmented bar graph?
In a stacked (or segmented) bar graph:
The horizontal axis still represents one variable, with every bar representing one in every of the catgories of the variable.
Each bar is segmented in step with the classes of the second variable. or else, every bar will be seen as being created from smaller bars stacked on high of every different.
Main body:
We can know from the graph The older the age, the more the Tow-violence, 55+ year-olds are likely to be categorized as low-violence"
so there is an association Choose D
Hence , we can conclude there is an association between age group of the viewer and amount of violence watched and its 55+ year-olds are likely to be categorized as low-violence.
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Please help with the question below
The graph has 2 x-intercepts.
What is the quadratic function?
In mathematics, a polynomial of degree two in one or more variables is referred to as a quadratic polynomial. A quadratic polynomial defines the polynomial function known as a quadratic function.
We have,
f(x) = -3(x-3)² + 1
by simplifying the equation above
-3(x² -6x + 9) + 1 = 0
-3x² + 18x - 27 + 1 = 0
-3x² + 18x - 26 = 0
By calculating the quadratic equation we get
[tex]x=\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
[tex]x=\frac{ -18 \pm \sqrt{18^2 - 4(-3)(-26)} }{2(-3)}[/tex]
[tex]x= 3 \pm \frac{\sqrt{3} }{3}[/tex]
x = 2.42265, x = 3.57735
so the points are (0, 0) and (2.4, 3.6)
The graph crosses the x-axis at (2.4, 3.6)
Hence, the graph has 2 x-intercepts.
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Akbar i 9 year older than yair and hamid i 2 year younger than yair find the expreion for their um of age
When Akbar is 9 years older than Yasir and Hamid is 2 years younger than Yasir then, the expression for their sum of ages is 3x+7
What are linear equations?A linear equation is a mathematical equation that describes a straight line. It is a first-degree polynomial equation, which means that the largest exponent of the variables is 1. Since a and b are constants and x and y are variables, linear equations have the general form ax+by=c. A straight line forms on a coordinate plane when the values of x and y fulfil the expression. The connection between two variables or the price of a product are two examples of real-world events that are frequently modelled using linear equations. Solving a linear equation entails determining the values of the variables that make the equation true. Different techniques, such graphing, substitution, or elimination, can be used to accomplish this.
How to solve?
Let x be Yasir's age
Akbar is x+9
Hamid is x-2
The sum of their ages is x+(x+9)+(x-2)
=3x+7
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Find x and y.
If you could explain how you got the answers, that would be really helpful as i'm really stuck.
From the given picture of a triangle, we have come to find that variable x = 7 and y = 4
What is an isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.
3x - 5 = y + 12 (if two angles of a triangle are equal, the sides opposite
them are also equal) ------------(1)
Also, 3x - 5 = 5y - 4 (sides of a equilateral triangle are equal)
So, 5y - 4 = y + 12
5y - y = 12 + 4
4y = 16
y = 4
Now,
Put value of y in equation (1)
3x - 5 = y + 12
3x = 4 +12 + 5
3x = 21
x = 7
Hence, x = 7 and y = 4
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Determine the value for j in the equation 17 over 20 equals j plus 11 over 20. 3 over 20 6 over 20 6 over 40 28 over 40
FLVS MATH MIDDLE
On solving the provided question, we get the following linear equation as the , that is j = 6/20.
What is a linear equation?A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
How do you identify a linear equation?A mathematical equation is said to be linear if it has the formula y=mx+b, where m denotes the slope and b the y-intercept.
Why is it called linear equation?An algebraic equation is said to be linear if each term has an exponent of 1, and if the equation is graphed, it always produces a straight line. This is the basis for its designation as a "linear equation."
the linear equation:
[tex]17/20 = j + 11/20\\ 17/20 - 11/20 = j + 11/20 - 11/20\\ (17 - 11)/20 = j\\ 6/20 = j[/tex]
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Your checking account balance on May 15 is $124.25. You deposit $223.56 on May 20, write a check for $89.56, and withdraw $80.00 from an ATM on May 25. What is your current balance?
Answer: 178.25
Step-by-step explanation:
124.25 + 223.56 - 89.56 - 80.00
Answer: $178.25
Step-by-step explanation: Your balance on May 15 is $124.25. On May 20, you deposit $223.56, which increases your balance to $124.25 + $223.56 = $347.81. You then write a check for $89.56, which decreases your balance to $347.81 - $89.56 = $258.25. Finally, you withdraw $80.00 from an ATM on May 25, which decreases your balance to $258.25 - $80.00 = $178.25. Therefore, your current balance is $178.25.
please help me thank you
Answer:
135
Step-by-step explanation:
Claire saved 205 coins that are only nickels and quarters. If her
total is $31.85 and she has $27 worth of quarters, how many
nickels does she have?
Answer: 56
Step-by-step explanation: 23+5=56
State the theorem that proves the triangles are congruent. Then write a congruence statement.
Answer:
i think it is the bottom one
Step-by-step explanation:
out of all these numbers -45 -21 -16 12 33 40 which has a difference of 29
Answer:
-45 and - 16 has a difference of 29 b/c -16-(-45)= -16 +45 = 29
What is the slope of 3x + 4y = 12?
O 3/4
O 3
O 4
O -3/4
There are 35 questions total that will be posted in mathematics as this is Algebra I!
Whoever answers correctly and with an explanation will receive Brainliest when the option shows up on my end!
PLEASE ANSWER ASAP!!
Please help asap What is the solution to this system of equations?
A.no solution
B. (2,-2)
C. (-1,1)
D. (-2,1)
The solution to the system of equations is (d) (-2, 1)
How to determine the solution to the systems?From the question, we have the following parameters that can be used in our computation:
y = 2x + 5
y = -1/4x + 0.5
Substitute y = 2x + 5 in the equation y = -1/4x + 0.5
So, we have the following representation
-1/4x + 0.5 = 2x + 5
Collect the like terms
So, the equation becomes
2x + 1/4x = 0.5- 5
So, we have
2.25x = -4.5
Divide by 2.25
x = -2
Substitute x = -2 in y = 2x + 5
y = 2 x -2 + 5
y = 1
Hence, the solution is (d) (-2, 1)
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Janelle set a goal to walk 60 miles this month. She walks at a consistent rate of 4 miles per hour.
Write an equation that shows how the number of miles Janelle has left to walk, y, depends on the number of hours she has already walked, x.
Answer:
[tex]60=4x\\\\15=x[/tex]
I hope this helped.
Answer: y = -4x+60
y is -4 times x plus 60
A mall airplane flew 104 mile in 50 minute. How many mile can it fly in one hour
A small airplane can fly about 124.8 miles in one hour.
In this question, we have been given a small airplane flew 104 miles in 50 minutes.
We need to find the distance the airplane would cover in an hour.
Let a small airplane can fly 'x' miles in one hour.
We know that 1 hour = 60 minutes
Using proportionality we get an equation,
x/104 = 60/50
We solve above equation.
50x = 60 * 104
x = 6240/50
x = 124.8
So, the distance would be 124.8 miles
Therefore, an airplane can fly 124.8 miles in an hour.
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which of the topics are connected together? (at least one connection)
• Absolute Value Inequalities • Linear Function • Quadratic Function • Graph Transformations • Polynomial • End Behavior • Multiplicity of a Zero • Horizontal Asymptote • Limit Notation • System of Equations • Vertical Asymptote • Rational Function • Rational Equation • Radical Function • Radical Equation • Inverse Function • Exponential Function • Logarithmic Function • Conic Sections
Answer:
Function • Quadratic Function •
Absolute Value Inequalities • Linear Function
Please please please help!
For AABC, AB = 6 and BC = 17. Which of the following is a possible length for AC?
Possible length of the third side of the Triangle must be between 11 and 23.
What is the Range of third side of Triangle ?As the third side of the triangle is between the sum of the sides and difference of the sides excluding both the numbers.
As triangle consist of three sides and it should must be in between two extreme values.
As by the property of Triangle
Third side should be less than sum of the sides and,
it should be greater than difference of the sides.
Sum of the sides = AB + BC = 6 + 17 = 23
Difference of the sides = 17 - 6 = 11
Then the third side will be between 11 and 23 excluding 11 and 23.
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suppose that for a science project you wanted to find exactly how much the length of a shadow changes during the day. how would you make this observation?
You should cast a shadow for a person or item at least three times and measure it each time to determine how the length of the shadow varies during the day.
The shape of an object always dictates the shape of its shadow. A shadow's size and shape can alter, though.
For instance, the location of the light source can induce these variations. The length of the shadow is influenced by the sun's position in the sky on a sunny day.
We can achieve the same effect indoors by adjusting the position of a flashlight reflecting on an object.
When the sun is low on the horizon, the shadows are lengthy, and when the sun is high, the shadows are considerably shorter.
So, To determine the change of length of object during the day, one should cast a shadow at least three separate times for a person or object and measure it each time
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1+3+5+8+7+7+8=937392920x
Answer:
Is the question written correctly? As written, the answer is 4.16 x [tex]10^{-8}[/tex].
Step-by-step explanation:
1+3+5+8+7+7+8= 39
39 = 937392920x
x = 39/(937392920)
x = 4.16 x [tex]10^{-8}[/tex]
The perimeter is less than 20 meters Please help I'm desperate
Answer:
Inequality is: x + 16 < 20Solution is: x < 4----------------------------------------
The perimeter is:
P = 4 + 9 + x + 3P = x + 16If the perimeter is less than 20, then the inequality is:
P < 20x + 16 < 20x < 20 - 16x < 4Answer:
x < 4
Step-by-step explanation:
The perimeter of a two-dimensional shape is the distance all the way around the outside.
Therefore, from inspection of the triangle:
⇒ Perimeter = 4 + 9 + x + 3
⇒ Perimeter = x + 16
If the perimeter is less than 20 meters then:
⇒ x + 16 < 20
Solve the inequality:
⇒ x + 16 - 16 < 20 - 16
⇒ x < 4
a cricket with 12 inch diameter is folded in half and folded again what is the area of the resulting shape
The area of the resulting shape if a circle with a 12-inch diameter is folded in half and then folded in half again is 28.26 square inches
What is the area of the resulting shape?Diameter of the cricket = 12 inchArea of a circle = πr²π = 3.14If a circle with a 12-inch diameter is folded into half and then folded into half again the circle will become a quadrant.
So,
The area of a quadrant is area of a circle divided by 4
Area of a quadrant = πr² / 4
Diameter of a circle = 2r
12 = 2r
divide both sides by 2
r = 6 inch
Area of the quadrant = 3.14 × (6)²/4
Area of the quadrant = (3.14 × 36) /4
Area of the quadrant = 113.04 / 4
Area of the quadrant = 28.26 square inches
In conclusion, the area of the quadrant is 28.26 square inches
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Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
There are 723 fifth grade tudent and 685 ixth grade tudent going on a field trip each bu hold 58 tudent how
Students will board the bus at 1350 even though it is not totally full.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few cmmon units for measuring area
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
723+685
1408-58
1350
Hence, Students will board the bus at 1350 even though it is not totally full.
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Jordan is baking pumpkin cupcakes for her
family. She needs 3 4 cup of unsalted butter
and 2 3 cup of brown sugar. Will she use more
butter or brown sugar?
Answer:
3/4>2/3
Explanation:
3/4 is the same as 3*3/4*3, which equals 9/12.
2/3 is the same as 2*4/3*4, which equals 8/12.
Thus, 3/4=9/12 and 2/3=8/12.
9/12 > 8/12, and since 3/4=9/12 and 2/3=8/12, 3/4>2/3.
Hope this helps.
The radius of a circle is 19.5 cm. Find the circumference to the nearest tenth
Answer:
[tex]122.5[/tex]
Step-by-step explanation:
[tex]circumference \: = 2\pi \:r[/tex]
[tex]\pi = 3.14[/tex]
[tex]r = 19.5[/tex]
Replacing:
[tex]2 \times 3.14 \times 19.5 = 122.46[/tex]
Therefore, final answer[tex] = 122.5[/tex](to the nearest tenth)
The answer is 122.5
In the given question, we have given the radius of the circle and we need to find the circumference of the same.
To need to find the circumference, we must recall this formula
Circumference of circle = [tex]2\pi r[/tex]
Now, according to the question
Radius = 19.5 cm
Circumference = 2 * [tex]\pi[/tex] * 19.5
= 2 * 3.14 * 19.5 (Taking [tex]\pi[/tex] = 3.14)
= 122.5 cm
Therefore, the circumference of a circle with radius 19.5 cm is 122.5 cm
On rounding off the answer to the nearest tenth, it remains the same.
Hence, the final answer to the question is 122.5 cm.
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solve the inequality
solve for q
–2.01–q>4.86
Answer:q<-6.87
Step-by-step explanation:
isolate q by adding 2.01 to both sides
-q>6.87
divide by side by -1, and since it is negative flip the sign
q<-6.87
At Jefferon High School, there are 250250 tudent who drive to chool and 375375 tudent who ride the bu to chool
The number of students who drive to school is 125.
What is number ?
A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of expressing numbers that uses digits or symbols to represent them.
At Jefferson High School, there are 250 students who drive to school and 375 students who ride the bus to school. The number of students who drive to school is
=375-250
=125
Hence, the number of students who drive to school is 125.
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