The polynomial having the above quantities is expressed as x³ - 2x² - 5x + 10 = 0
The above situations will form a Cubic polynomial. A Cubic polynomial function may be defined as an expression which can be written in the form of ax³ + bx² + cx + d = 0 where a, b, c and d are coefficients and x is the independent variable. Since, the polynomial should have real coefficients so its multiplicity will be equal to 1. Now, the roots of the polynomial are given as 2 and √5. Since, square roots always occur in pair so the polynomial will have -√5 as its root. Now, the polynomial formed will be
(x - 2) (x - √5) (x + √5) = 0
(x - 2) (x² - 5) = 0
x³ - 5x - 2x² + 10 = 0
=> x³ - 2x² - 5x + 10 = 0 which is the required polynomial.
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Can a table with the same Input and output be a function ?
In this relation table value of x = ( 2,5,7,-4) are following same pattern .
but x = 5 is not input and output of a function.
What is input and output of a function in math?
A function can be represented as an input-output table, such as the one below. According to the same function rule, every pair of integers in the table is connected.The input and output of a function are, respectively, what goes into it and what it produces. Also known as the domain and range, respectively, are the input variable and output variable. The collection of all values that the function will accept as inputs, or its domain, is what makes up the function.x = 2 * 1 = 2 , y = 2
x = 5 * 1 = 5 , y = 5
x = 7 * 1 = 7 , y = 7
x = -4 * 1 = -4 , y = -4
x = 5 * 2 + 1 = 11 , y = 11
In this relation table value of x = ( 2,5,7,-4) are following same pattern .
but x = 5 is not .
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please help me solve now
Answer:
(3000/(5-3))(3+5)
= (3000/2) 8
= 12000
Step-by-step explanation:
Peter hired two combine operators to harvest his 260 acres of wheat. He expected a yield of 50 bushels per acre. The first operator had a 3% grain loss, and the second operator had 5% grain loss. Each operator harvested the same number of acres in the same time. How much was saved by the first operator if wheat sold for $11.97 perbushel?
Answer:
The amount in dollars of wheat saved by the first operator is;
[tex]\text{ \$1,556.10}[/tex]Explanation:
Given that Peter hired two combine operators to harvest his 260 acres of wheat.
And it yeilds 50 bushels per acre.
The total amount of bushels of wheat on the field is;
[tex]\begin{gathered} T=260\times50 \\ T=13,000\text{ bushels} \end{gathered}[/tex]Since each operator harvest the same amount;
[tex]\text{opertor 1= Operator 2 = }\frac{13000}{2}=6500\text{ bushels each}[/tex]If operator 1 loss 3%, the remaining amount is;
[tex]\begin{gathered} A_1=6500-3\text{ \% of 6500} \\ A_1=6500-(0.03)6500 \\ A_1=6305\text{ bushels} \end{gathered}[/tex]Operator 2 loss 5%, the remaining amount is;
[tex]\begin{gathered} A_2=6500-0.05(6500) \\ A_2=6175\text{ bushels} \end{gathered}[/tex]The amount of bushels save by the first operator compared to the second operator is;
[tex]\Delta A=A_1-A_2=6305-6175=130\text{ bushels}[/tex]if wheat is sold for $11.97 per bushel, the amount in dollars of wheat saved by the first operator is;
[tex]\begin{gathered} C=130\text{ bushels }\times\text{ \$11.97 per bushel} \\ C=\text{ \$1,556.10} \end{gathered}[/tex]The amount in dollars of wheat saved by the first operator is;
[tex]\text{ \$1,556.10}[/tex]The parent function f(x)=x2 has been transformed to make the function g(x) by reflection f(x) over the x-axis , vertically shrinking by a factor of 1/2 and translating 2 units up. The equation for g(x) is expressed in which of the functions below
Given:
There are given that the parent function:
[tex]f(x)=x^2[/tex]Explanation:
According to the concept:
The function reflected over the x-axis means, we need to multiply with a negative sign.
That means:
[tex]g(x)=-x^2[/tex]And,
Vertically shrinking by a factor of 1/2 means, multiply by 1/2 in the entire function:
So,
[tex]g(x)=-\frac{1}{2}x^2[/tex]Then,
Translating 2 units up means, adding 2 in the entire function:
So,
[tex]g(x)=-\frac{1}{2}x^2+2[/tex]Final answer:
Hence, the correct option is C.
can you help me with this place
The diameter of Keisha's favorite marble is 2.5cm
The radius of the sphere is the half of the diameter : Radius = Diameter/2
Given diameter of marble = 2.5 cm
So, radius = diameter/2
Radius of the marble = 2.5/2
Radius of the marble = 1.25 cm
The general expression for the volume of sphere with radius 'r' is :
[tex]\text{ Volume of Sphere =}\frac{4}{3}\Pi\times radius^3[/tex]So, the volume of one sphere is :
Substitute the value of r = 1.25 cm
[tex]\begin{gathered} \text{ Volume of Sphere =}\frac{4}{3}\Pi\times radius^3 \\ \text{ Volume of Sphere =}\frac{4}{3}\times3.14\times1.25^3 \\ \text{ Volume of Sphere = 8.18 cm}^3 \end{gathered}[/tex]As, Keisha take 6 marbles
So, the volume of 6 marbles = 8.18 x 6
Volume of 6 marbles = 49.08 cm³
It is given that : 1 cubic centimeter has the massof 2.6 grams
1 cm³ = 2.6 gm
As the volume of 6 marbles is 49.08cm³
So, The mass of 49.08cm³ = 49.08 x 2.6
The mass of 6 marbles = 127.608 gm
127.608 to the nearest whole number is 128
Mass of the 6 marbles is 128 gm
Answer : 128 gm
Elsa is saving money to buy a game. So far she saved $24, which is two-thirds of the total cost of the game. How much does the game cost?
Elsa is saving money to buy a game.
So far she saved $24, which is two-thirds of the total cost of the game.
let the cost of the game is $x
Then, two -third of the total cost = 2/3 x
Since, it is given that 24 is the two-thirds of the total cost of the game.
i.e.
[tex]\frac{2}{3}x=24[/tex]Simplify the expression for x;
[tex]\begin{gathered} \frac{2}{3}x=24 \\ \text{ Apply cross multiplication;} \\ 2x=24\times3 \\ x=\frac{24\times3}{2} \\ x=12\times3 \\ x=36 \end{gathered}[/tex]x = 36
Total cost of the game is $36
....
Tracey paid $180 for an item that was originally priced at $560. What percent of the original price did Tracey pay?
To find the percentage that Tracey paid, we can use the rule of three:
Now, the original price $560 represent the 100%.
If $560 ----------- 100%
then $180----------- x
where x =($180*100)/$560
x = 32.14
Therefore, the percent that Tracey paid was 32.14%
The answer is rounded to the nearest hundredth.
The following table represents the highest educational attainment of all adult residents in a certain town. If a resident who is aged 0 - 39 is chosen at random, what is the probability that they bave completed a bachelor's degree and no more? Round your answer to the nearest thousandth .
ANSWER:
The probability is 0.107 or 10.7%
STEP-BY-STEP EXPLANATION:
The probability is calculated with the number of people who are in that age range and meet the study conditions and the total number of people.
We can determine both data in the table, therefore
[tex]p=\frac{1707}{15921}=0.107\cong10.72\text{\%}[/tex]Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Because angle 5 and 6 are supplementary, the only true statement is:
m∠5 + m∠6 =180°
Which statement is always true?By using the diagram we can see that:
Angles ∠1 and ∠2 are supplementary.Angles ∠3 and ∠4 are supplementary.Angles ∠5 and ∠6 are supplementary.Where two angles are supplementary if their measures add up to 180°, then:
∠1 + ∠2 = 180°∠3 + ∠4 = 180°∠5 + ∠6 = 180°Then the statements that are true are:
m∠5 + m∠6 =180°
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A recipe for trail mix requires 5/6 cup of raisins for 1 batch. Alaina 1 2/3 cups of rasisins to make trial mic Enter tje number of batches of trial mix Alaina makes.
SOLUTION :
Step 1 :
In this question, we have that the recipe for trail mix requires
5/6 cup of raisins for 1 batch.
Then, Alaina uses
[tex]1\text{ }\frac{2}{3}\text{ cups of raisins to make trial mix.}[/tex]Step 2 :
To get the number of batches of trial mix Alaina makes, we have that :
[tex]\begin{gathered} 1\text{ }\frac{2}{3\text{ }}\text{ divided by }\frac{\text{ 5}}{6} \\ \frac{5}{3}\text{ x }\frac{6}{5}\text{ = }\frac{30}{15}\text{ = 2 batches} \end{gathered}[/tex]CONCLUSION :
There would be 2 batches .
find the reciprocal -16/5
Remember that the reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number).
Thereby, the reciprocal of
[tex]-\frac{16}{5}[/tex]is
[tex]-\frac{5}{16}[/tex]Solve for n if 7056n - 4577n = 2257n
Answer:
n=0
Step-by-step explanation:
If five boys can eat 16 slices of pizza, then how many slices can 20 boys eat?
Please help me complete this table
The radius of a circle is 6 centimeters. What is the area of a sector bounded by a 150 degree arc?Give the exact answer in simplest form._____ square centimeters
Concept
[tex]\text{Area of a sector = }\frac{\theta}{360}\text{ }\times\text{ }\pi r^2[/tex][tex]\begin{gathered} \theta\text{ is the angle subtend at the center} \\ r\text{ is the radius} \end{gathered}[/tex]Step 1: List the given data
[tex]\begin{gathered} \theta=150^o \\ r\text{ = 6cm} \\ \pi\text{ = }\frac{22}{7} \end{gathered}[/tex]Step 2: Substitute the values to find the area of the sector.
[tex]\begin{gathered} \text{Area of the sector = }\frac{150}{360}\text{ }\pi\text{ }\times6^2 \\ =\text{ }\frac{150\text{ }\pi\text{x 36}}{360\text{ }} \\ =15cm^2 \end{gathered}[/tex]Ok
Given that events A and B are independent with P(A)=0.85 and P(B) = 0.3,determine the value of P(A|B), rounding to the nearest thousandth, if necessary.
The Solution.
Given that
[tex]\begin{gathered} P(A)=0.85 \\ P(B)=0.3 \end{gathered}[/tex]The conditional probability P(A/B) is given as
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]But for independent events, we have that
[tex]P(A\cap B)=P(A)\times P(B)[/tex]Hence, it follows that
[tex]\begin{gathered} P(A|B)=\frac{P(A)\times P(B)}{P(B)}=P(A)=0.85\approx0.850 \\ \text{though the nearest thousandth is not necessary.} \end{gathered}[/tex]Therefore, the correct answer is 0.85 ( 0.850 if you consider it necessary)
The Product of twice a number and six is the Same as the difference of eleven times the number and 5/7. Find the number
The number x = - 5/7 .
How do you frame an equation?The following steps are necessary to construct a linear equation in one variable from the provided word problem:
Step I: Read the problem attentively and make separate notes for the provided and necessary quantities.
Step II: Use 'x', 'y', 'z', etc. to represent the unknowable quantities.
Step III: Next, convert the issue into a mathematical formulation or statement.
Step IV : Utilizing the conditions provided in the problem, form a linear equation in one variable in
Step V: Verify the equation for the unknown quantity
Let the number be x
Thus according to the question :
( twice a number) × 6 = 11 (number) - 5/7
(2x)6 = 11 x - 5/7
12x = 11 x- 5/7
x= - 5/7
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Is the sequence an arithmetic sequence? 2. -12,4,0, 2....... Yes or No 3. -6,0, 6, 12 ..... Yes or No
For a sequence to be an arithmetic sequence the terms have to have a constant difference between them
2) We have the sequence: -12, 4, 0, 2...
The difference between the terms is not constant, so this is not a arithmetic sequence.
For example, from 4 to 0, there is -4 and from 0 to 2, is 2.
3) The sequence -6,0, 6, 12,... is an arithmetic sequence, because it has a constant difference between the terms (it always add 6 in each step).
Answer:
2. -12,4,0, 2....... No
3. -6,0, 6, 12 ..... Yes
Erin spent $6.75 on art supplies and made cards to sell. On Monday she sold $3.50 worth of cards and on Tuesday she sold $5.25 worth of cards. What was Enn's overall profit or loss? o $1.75 loss o $2.00 profit 0 $8.75 loss O $15.50 profit
He spent $6.75 on art supplies and made the cards .
she sold the made cards on monday and tuesday.
Monday sales = $3.50
Tuesday sales = $5.25
Total sales = 3.50 + 5.25 = $8.75
profit = sales - cost
profit = 8.75 - 6.75 = $2.00
Please see image attached on using the diagram to name the ray
Given:
Find - Name of rays
Sol:
Ray:- In geometry, a ray can be defined as a part of a line that has a fixed starting point but no endpoint can extend infinitely in one direction. On its way to infinity, a ray may pass through more than one point.
So rays is
[tex]=\vec{AE}[/tex]Use the angle relationships present to find angle P
Answer:
65 degress
Step-by-step explanation:
I did a problem like this before
Hello! I need some assistance with this homework question, pleaseQ16
we have the function
[tex]y=\sqrt[]{x}[/tex]shifted down 10 units, is the same that apply the rule
(x,y) -----> (x,y-10)
therefore
the new function is
[tex]y=\sqrt[]{x}-10[/tex]The answer is the first optionwhat is the solution to the equation 5x-1+7x=11
the expression is
5x - 1 + 7x = 11
5x + 7x = 11 + 1
12x = 12
x = 12/12
x = 1
so the answer is x = 1
The pie chart below shows how the annual budget for a certain company is divided by department. If the amount budgeted for sales and research combined is 75,000,000. What is the total annual budget?
$150,000
1) In that pie chart, we can tell that the Sales and Research department combined responds to 50% (35%+15% =50%)
2) Thus, we can tell that:
[tex]\begin{gathered} 0.35x+0.15x=75000 \\ 0.5x=75000 \\ x=\frac{75000}{0.5} \\ x=150,000 \end{gathered}[/tex]So, since 50% of that budget corresponds to $75,000 we can tell that 100% (the total budget) corresponds to twice that figure, which yields 150,000
Find the equation (in terms of x) of the line through the points (-3,-3) and (4,-2) II
Given:
The coordinates of the points through which the line passes,
(x1, y1)=(-3, -3).
(x2, y2)=(4, -2).
The two point form of the equation of a line can be expressed as,
[tex]y-y1=\frac{y2-y1}{x2-x1}(x-x1)[/tex]Substitute the known values in the above equation.
[tex]\begin{gathered} y-(-3)=\frac{-2-(-3)}{4-(-3)}(x-(-3)) \\ y+3=\frac{-2+3}{4+3}(x+3) \\ y+3=\frac{1}{7}(x+3) \\ 7(y+3)=x+3 \\ 7y+7\times3=x+3 \\ 7y+21=x+3 \\ 7y=x+3-21 \\ 7y=x-18 \\ y=\frac{1}{7}x-\frac{18}{7} \end{gathered}[/tex]Therefore, the equation of the line is,
[tex]y=\frac{1}{7}x-\frac{18}{7}[/tex]8x – 12y = – 24 a. x-intercept: b. y-intercept: 10+ C. graph 9 8 7 6 5 4 13 2 -10 -9 -8 -7 -6 -5 -4 -B-2 -1 2 15 4 SI 6 8 9 10 -2 3 -6 -7 -8 9 10 Clear All Draw:
To determine the x- and y-intercepts is best to write the equation in slope-intercept form.
Given
[tex]8x-12y=-24[/tex]-Pass the x-term to the right side of the equation by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 8x-8x-12y=-8x-24 \\ -12y=-8x-24 \end{gathered}[/tex]-Divide both sides of the equal sign by -12
[tex]\begin{gathered} \frac{-12y}{-12}=\frac{-8x}{-12}-\frac{24}{-12} \\ y=\frac{2}{3}x+2 \end{gathered}[/tex]So the equation in slope-intercept form is:
[tex]y=\frac{2}{3}x+2[/tex]a) The x-intercept is the point where the line crosses the x-axis, at this point, the y-coordinate is equal to zero. To determine the x-coordinate of the intercept, you have to equal the equation to zero and calculate the corresponding value of x:
[tex]0=\frac{2}{3}x+2[/tex]-Subtract 2 to both sides of the equal sign
[tex]\begin{gathered} 0-2=\frac{2}{3}x+2-2 \\ -2=\frac{2}{3}x \end{gathered}[/tex]-Multiply both sides of the expression with the reciprocal fraction of 2/3
[tex]\begin{gathered} (-2)\frac{3}{2}=(\frac{2}{3}\cdot\frac{3}{2})x \\ -3=x \end{gathered}[/tex]The x-intercept is (-3,0)
b) The y-intercept is the point where the line crosses the y-axis, at this point, the x-coordinate is equal to zero. To determine the y-intercept, replace the equation with x=0 and calculate the corresponding value of y:
[tex]\begin{gathered} y=\frac{2}{3}x+2 \\ y=\frac{2}{3}\cdot0+2 \\ y=2 \end{gathered}[/tex]The y-intercept is (0,2)
c) To graph the line, plot both intercepts on the coordinate system and then link both points with a line:
A 12-quart cooling system is tested and found filled with a 60% antifreeze solution. The ideal mixture should be a 50% antifreeze solution. How many quarts of solution need to be drained and replaced with pure water to reach the ideal mixture?
Answer:
2 quarts
Explanation:
Let the number of quarts to be drained and replaced = x
From the given problem:
60% of (12-x)=50% of 12
[tex]\begin{gathered} 0.6(12-x)=0.5\times12 \\ 0.6(12-x)=6 \\ 12-x=\frac{6}{0.6} \\ 12-x=10 \\ x=12-10 \\ x=2 \end{gathered}[/tex]2 quarts of the solution needs to be drained and replaced with pure water to reach the ideal mixture.
Select the names of the sides of the triangle. The 2 answer options are leg and hypotenuse.
Given:
[tex]\text{side(c)}=\text{Hypotenus}[/tex][tex]\text{side(a)}=\text{lag}[/tex][tex]\text{side(b)}=\text{lag}[/tex]Question 2a)Tell is this relationship is a direct variation.The equations -15x + 4y = 0 relates the length of a videotape in inches x to its approximate playing time in seconds y.Please enter yes, or nob)Question 3Using the previous function from question 2 , could you please find the playing time of a videotape 1 foot long? seconds
If two variables x and y are proportional (direct variation), one can be written in terms of the another using a constant of proportionality, which is often represented using a letter k:
[tex]y=kx[/tex]Isolate y from the given relationship:
[tex]\begin{gathered} -15x+4y=0 \\ \Rightarrow4y=15x \\ \Rightarrow y=\frac{15}{4}x \end{gathered}[/tex]As we can see, the variable y can be written in terms of x through a constant of proportionality equal to 15/4. Then, the relationship is a direct variation. The answer to Question 2 is: yes.
To find the playing time, replace the value of x. Since 1 foot is equal to 12 inches and the equation y=15/4 x works when x is in inches and y is in seconds, replace x=12 to find the playing time in seconds:
[tex]\begin{gathered} y=\frac{15}{4}\times12 \\ =45 \end{gathered}[/tex]Then, the playing time for a tape 1 foot long is 45 seconds. The answer to Question 3 is: 45.
Jasmine is helping her father plant trees to create a border around the back yard. Jasmine plants a tree every 25 minutes, and her father plants a tree every 15 minutes. If they started together, how long before they would finish planting a tree at the same time?
4. What is the value of x such that 5x + 2a > 2x-a?
a. x < -a
b. x > -a
C. x < a
d. x > a
Answer:
D: x > a
Step-by-step explanation:
We have 5x - 2a > 2x-a
We can rewrite this equation by subtracting 2x on both sides, which gives:
5x - 2x -2a > 2x - 2x - a,
so 3x - 2a > a
We now add 2a on both sides, which gives:
3x -2a + 2a > a + 2a, so 3x > 3a
We nog divide both sides by 3, which gives:
3x/3 > 3a/3, so x>a
The correct answer is D