Answer:c
Step-by-step explanation:
Answer:
Step-by-step explanation:
C
What is a cubic polynomial function in standard form with zeros 1,1,and -3?
Answer:
f(x) = x³ + x² - 5x + 3
Step-by-step explanation:
The cubic polynomial has zeros at 1, 1, - 3.
Therefore, x = 1, 1, - 3 are the roots of the polynomial and hence, (x - 1), (x - 1) and (x + 3) will be factors of the cubic polynomial.
Hence, we can write the polynomial as a function of x as
f(x) = (x - 1)(x - 1)(x + 3)
⇒ f(x) = (x² - 2x + 1)(x + 3)
⇒ f(x) = x³ - 2x² + 3x² + x - 6x + 3
⇒ f(x) = x³ + x² - 5x + 3
So, this is the cubic polynomial function in standard form. (Answer)
- 2 + (-9)
А -11
b -7
c 7
d 11
Answer:
-11
Step-by-step explanation:
Because -2+(-9)=-2-9=-11.
PLZ help me fast 2 mins left
Answer:
[tex]\sqrt{-5}=i\sqrt{5}[/tex]
[tex]\sqrt{-25}=5i[/tex]
Step-by-step explanation:
i is an imaginary unit, this means
[tex]i^2=-1[/tex]
Rewrite -5 as [tex]5\cdot (-1)=5\cdot i^2,[/tex]
then
[tex]\sqrt{-5}=\sqrt{5i^2}=\sqrt{5}\cdot \sqrt{i^2}=\sqrt{5}\cdot i=i\sqrt{5}[/tex]
Rewrite -25 as [tex]-25=25\cdot (-1)=25\cdot i^2,[/tex]
then
[tex]\sqrt{-25}=\sqrt{25\cdot i^2}=\sqrt{25}\cdot \sqrt{i^2}=5\cdot i=5i[/tex]
How can u add 3/10 and 2/5
Answer:
7/10
Step-by-step explanation:
3/10+2/5=3/10+4/10=7/10
Step-by-step explanation:
You first find the LCM and multiply both fractions by it. Over here the LCM is 10.
(10 (3/10) + 10 (2/5))/10
(3+4)/10
7/10
Why is implicit differentiation necessary in order to find derivatives of curves which do not represent functions?
Come up with your own implicitly defined function. What is its first, second, and third derivative?
The answer is implicit
Answer:
Implicit Differentiation is necessary in order to find derivatives of curves that do not represent a function because the functions cannot be simplified to a simple function. Using dy/dx and implicit differentiation can be used to find the derivative with respect to one variable and determine the affect each variable has on one another and calculate the rate of change of the variables over time. Differentiating both x and y in Implicit Differentiation makes it so that complex functions are much easier and instead of solving for one variable, differentiating one variable to the other is an easier method. My implicit function is 2y^2-x^2+x^3y=2. First Derivative= -3yx^2+2x/4y+x^3 Second Derivative= 3yx^4-4y^3-24y^2x+8y/(4y+x^3)^2 Third Derivative = 6y(-x^6+28yx^3+4y^2x^2-8x^2-16y)/(4y+x^3)^3
Jewel wanted to know if there was a correlation between the weight of a dog and its age. She collected data and created the scatterplot shown:
scatter plot with points distributed all over quadrant 1
Determine the closest correlation coefficient (r value) for these data.
0
1
−1
5
Answer:
A. 0
Step-by-step explanation:
Because there is no correlation between any of the points.
Write a subtraction equation that has 2 three digit numbers with different hundreds digits and a difference of less than 100
Answer:
801-792
Step-by-step explanation:
I got my answer by picking out a big number first (801) and subtracting it by another big number (701) to get an answer less than 100.
To form a subtraction equation with two three-digit numbers having different hundreds digits and a difference of less than 100, choose numbers where the hundreds digits are one number apart and the tens and ones digits are close, such as 756 - 657 = 99.
Explanation:To write a subtraction equation that involves two three-digit numbers with different hundreds digits and a difference of less than 100, we need to select numbers where the hundreds digit is only 1 apart and the tens and ones digits are close. For example, the numbers 654 and 756. Subtracting these gives us:
756 - 654 = 102
We notice the result is slightly over 100. Therefore, we can adjust the tens or ones digits to reduce the difference. If we change 654 to 657, then:
756 - 657 = 99
In this case, we achieved a result that is less than 100. It's important to note that, in subtraction, we change the sign of the subtracted number before operating the addition as per standard arithmetic rules.
What is the area of a trapezoid with height 14xy^2 cm, a base with length 3x^2 cm, and another base length 7x^2 cm?
Answer:
[tex]\therefore \textrm{Area of Trapezoid }= 70x^{3}y^{2}\ cm^{2}[/tex]
Step-by-step explanation:
Given:
Shape is of Trapezoid
Height = 14xy² cm
Length 1 = 3x² cm ( one Parallel side)
Length 2 = 7x² cm ( other Parallel side)
To Find:
Area of Trapezoid = ?
Solution:
We know that
[tex]\textrm{Area of Trapezoid }= 0.5(length\ 1+length\ 2)Height[/tex]
substituting the given values we get
[tex]\textrm{Area of Trapezoid }= 0.5\times(3x^{2}+7x^{2})\times 14xy^{2}[/tex]
[tex]\textrm{Area of Trapezoid }= (10x^{2})7xy^{2}[/tex]..((x^{a}x^{b}=x^{(a+b)})
[tex]\therefore \textrm{Area of Trapezoid }= 70x^{3}y^{2}\ cm^{2}[/tex]
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 50 pounds and each large box of paper weighs 80 pounds. There were 4 more large boxes shipped than small boxes and the total weight of all boxes was 1750 pounds. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped where x represent the number of small boxes of paper and y represent the number of large boxes of paper.
Step-by-step explanation:
Given,
Weight of small box of paper = 50 pounds
Weight of large box of paper = 80 pounds
Total weight of boxes = 1750 pounds
Let,
x represent the number of small boxes of papers.
y represent the number of large boxes of papers.
According to given statement;
50x+80y=1750
y = x+4
50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped where x represent the number of small boxes of paper and y represent the number of large boxes of paper.
Keywords: linear equation, addition
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The system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped are:
50x+80y=1750
y = x+4 ,
where x represent the number of small boxes of paper and y represent the number of large boxes of paper.
We have:
Weight of small box of paper = 50 pounds
Weight of large box of paper = 80 pounds
Total weight of boxes = 1750 pounds
Let us consider that the number of small boxes of papers be x.
The number of large boxes of papers be y.
Then, according to question
50x+80y=1750
y = x+4
Therefore, the equations 50x+80y=1750 and y = x+4 can be used to determine the number of small boxes and large boxes of paper shipped.
where, x represent the number of small boxes of paper and y represent the number of large boxes of paper.
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What is the solution to the equation 7(a - 10) = 13 - 202a + 3)?
Answer:
a=0.41
Step-by-step explanation:
7(a-10)=13-202a+3
7a-70=13+3-202a
7a-(-202a)-70=16
7a+202a=16+70
209a=86
a=86/209
a=0.41
To solve the equation 7(a - 10) = 13 - 202a + 3, begin by simplifying both sides of the equation and combining like terms. Then isolate the variable 'a' to one side and the constant terms to the other. Finally, divide both sides by the coefficient of 'a' to solve for 'a'.
Explanation:To solve the equation 7(a - 10) = 13 - 202a + 3, you can start by simplifying both sides of the equation. Expand the terms on the left side by distributing the 7 to the terms inside the parentheses. Combine like terms on both sides of the equation. Then, isolate the variable by moving all the terms with 'a' to one side of the equation and all the constant terms to the other side. Finally, divide both sides of the equation by the coefficient of 'a' to solve for 'a'.
Step-by-step solution:
Distribute 7 to the terms inside the parentheses:https://brainly.com/question/14410653
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Can someone help me please!
Answer:
see explanation
Step-by-step explanation:
Since the lines are parallel then
∠x = 70° ( alternate angles are congruent )
Since the triangle is isosceles then the base angles are congruent, thus
∠y = ∠x = 70°
The sum of the angles in a triangle = 180°
Subtract the sum of x and y from 180 for z
∠z = 180° - (70 + 70)° = 180° - 140° = 40°
Hence ∠x = ∠y = 70° and ∠z = 40°
Write an equation of the line containing the given point and perpendicular to the given line:
(4, - 7); 9x+5y=3
Answer:
[tex]y=\frac{5}{9}x+\frac{-83}{9}[/tex]
Step-by-step explanation:
Given equation of line:
[tex]9x+5y=3[/tex]
To find the equation of line perpendicular to the line of the given equation and passes through point (4,-7).
Writing the given equation of line in standard form.
Subtracting both sides by [tex]9x[/tex]
[tex]9x-9x+5y=3-9x[/tex]
[tex]5y=3-9x[/tex]
Dividing both sides by 5.
[tex]\frac{5y}{5}=\frac{3}{5}-\frac{9x}{5}[/tex]
[tex]y=\frac{3}{5}-\frac{9x}{5}[/tex]
Rearranging the equation in standard form [tex]y=mx+b[/tex]
[tex]y=-\frac{9x}{5}+\frac{3}{5}[/tex]
Applying slope relationship between perpendicular lines.
[tex]m_1=-\frac{1}{m_2}[/tex]
where [tex]m_1[/tex] and [tex]m_2[/tex] are slopes of perpendicular lines.
For the given equation in the form [tex]y=mx+b[/tex] the slope [tex]m_2[/tex]can be found by comparing [tex]y=-\frac{9x}{5}+\frac{3}{5}[/tex] with standard form.
∴ [tex]m_2=-\frac{9}{5}[/tex]
Thus slope of line perpendicular to this line [tex]m_1[/tex] would be given as:
[tex]m_1=-\frac{1}{-\frac{9}{5}}[/tex]
∴ [tex]m_1=\frac{5}{9}[/tex]
The line passes through point (4,-7)
Using point slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where [tex](x_1,y_1)\rightarrow (4,-7)[/tex] and [tex]m=m_1=\frac{5}{9}[/tex]
So,
[tex]y-(-7)=\frac{5}{9}(x-4)[/tex]
Using distribution.
[tex]y+7=(\frac{5}{9}x)-(\frac{5}{9}\times 4)[/tex]
[tex]y+7=\frac{5}{9}x-\frac{20}{9}[/tex]
Subtracting 7 to both sides.
[tex]y+7-7=\frac{5}{9}x-\frac{20}{9}-7[/tex]
Taking LCD to subtract fractions
[tex]y=\frac{5}{9}x-\frac{20}{9}-\frac{63}{9}[/tex]
[tex]y=\frac{5}{9}x+\frac{(-20-63)}{9}[/tex]
[tex]y=\frac{5}{9}x+\frac{-83}{9}[/tex]
[tex]y=\frac{5}{9}x-\frac{83}{9}[/tex]
Thus, the equation of line in standard form is given by:
[tex]y=\frac{5}{9}x-\frac{83}{9}[/tex]
$100 at 9% APR compounded
semiannually for 1 year
The amount at end of 1 year is $ 109.2025
Solution:
Given that,
Principal = $ 100
Rate of interest = 9 % compounded semiannually
Number of years = 1
The formula for total amount using compounded semiannually is:
[tex]A=p\left(1+\frac{r}{n}\right)^{n t}[/tex]
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested or borrowed for
Here, [tex]r = 9 \% = \frac{9}{100} = 0.09[/tex]
Here, n = 2 since interest is compounded semiannually
Substituting the values in formula,
[tex]A=100\left(1+\frac{0.09}{2}\right)^{2 \times 1}[/tex]
[tex]\begin{aligned}&A=100(1+0.045)^{2}\\\\&A=100(1.045)^{2}\\\\&A=100 \times 1.092025=109.2025\end{aligned}[/tex]
Thus the amount at end of 1 year is $ 109.2025
Which expression correctly represents eight times the difference of 4 and a number
The correct mathematical expression for eight times the difference of 4 and a number is 8(4 - n), where 'n' is the variable representing the number.
Explanation:The expression that represents eight times the difference of 4 and a number can be written as 8(4 - n), where 'n' represents the number in question. In this expression, '4 - n' is the difference between 4 and the number, and by multiplying this difference by eight, we are following the order of operations where the subtraction within the parentheses is performed first before the multiplication.
Lisa reads 48 pages in 8 minutes. How many minutes would it take her to read 1 pages?
Answer:
1/6 of one minute, 10 seconds.
Step-by-step explanation:
8/48=1/6
Answer question (picture below) and show work please
Answer:
[tex]A(x)=7x^2-2x+10[/tex]
Step-by-step explanation:
Long Division
The polynomial long division implies the sequential division of each term of the dividend polynomial by the terms of the divisor polynomial. The procedure is a well-know sequence of steps from which there are two outputs: the quotient and the remainder.
We have two mathematical models, one for the total number of visitors who went to a theme park:
[tex]F(x)=126x^3+279x^2+90x+450[/tex]
The other for the number of shows played at the theme park in the same period
[tex]G(x)=18x+45[/tex]
Where x is the number of days since October 1. We are required to find the expression for the average number of visitors per show. It comes by dividing F(x) by G(x). We must perform a long division as shown below.
The average number of visitors per show is
[tex]A(x)=7x^2-2x+10[/tex]
For example, day 5
[tex]A(5)=7\ 5^2-2(5)+10=175[/tex]
There were 175 visitors per show (on average)
Please help, is this the correct answer?
Answer:
B.
Step-by-step explanation:
'At least 35 years old' can be written as ≥ 35 ( greater than or equal to 35) so its graph B.
Note there is a filled circle on the 35 meaning the 35 years is included in the range.
hey i'm dumb and geometry is hard pls help! i will give you branliest!
Answer:
2
Step-by-step explanation:
how many solutions does this equation have -2x+9-3x=-5x+3
Answer:
There is No Solution for the equation.
Step-by-step explanation:
Given:
[tex]-2x+9-3x=-5x+3[/tex]
We need to find number of solutions for above equation.
Now Solving the equation we get;
[tex]-5x+9=-5x+3[/tex]
Now adding both side by 5x we get;
[tex]-5x+9+5x=-5x+3+5x\\\\9=3[/tex]
Which can't be true.
Hence There is No Solution for the equation.
A box is x to inches high,(2x+3)inches wide, and (2x+5) of inches long. In terms of x, what is the volume (v) of the box?
Answer:
The volume of the box is [tex]V=(4x^3+16x^2+15x)\ in^3[/tex]
Step-by-step explanation:
we know that
The volume of the box is equal to
[tex]V=LWH[/tex]
where
L is the length of the box in inches
W is the width of the box in inches
H is the height of the box in inches
we have
[tex]L=(2x+5)\ in\\W=(2x+3)\ in\\H=x\ in[/tex]
substitute in the formula
[tex]V=(2x+5)(2x+3)x[/tex]
[tex]V=(4x^2+6x+10x+15)(x)[/tex]
[tex]V=(4x^2+16x+15)(x)[/tex]
[tex]V=(4x^3+16x^2+15x)\ in^3[/tex]
The value of x that satisfies the equation 4/3=x+10/15
For this case we must find the value of "x" that meets the following equation:
[tex]\frac {4} {3} = x + \frac {10} {15}[/tex]
We subtract [tex]\frac {10} {15}[/tex] on both sides of the equation:
[tex]\frac {4} {3} - \frac {10} {15} = x\\\frac {15 * 4-3 * 10} {3 * 15} = x\\\frac {60-30} {45} = x\\- \frac {30} {45} = x[/tex]
We simplify:
[tex]x =\frac {6} {9}=\frac{2}{3}[/tex]
Finally, [tex]x =\frac {2} {3}[/tex]
Answer:
[tex]x =\frac {2} {3}[/tex]
What is the opposite of the number 5 1/2
Answer: -5 1/2
Step-by-step explanation:
Choose the word or group of words that belong in the underline space
After this summer we __ for nine years straights
A. Will have gone
B. Went
C. Have gone
Answer:
Step-by-step explanation: the answer is A beacause the sentence is in the past tense and answer A is the only one that would be gramatically correct
Final answer:
The correct phrase to complete the sentence is 'A. Will have gone' since it requires the future perfect tense to indicate that nine years will have passed after the upcoming summer.
Explanation:
The correct phrase to complete the sentence "After this summer we __ for nine years straight." is A. Will have gone. This is because the sentence is referring to a future event where the duration of nine years will have been completed after this coming summer, which requires the future perfect tense. The future perfect tense is formed with 'will have' followed by the past participle of the verb, which in the case of 'go' is 'gone'.
Now, let's solve some practice questions:
Under the table _______________.The choir usually _______________.Some of the actors _______________.Some of this song _______________.Either my brother or my sisters _______________._______________.For each blank, you would choose the correct verb tense depending on the context of the sentence provided.
Henry and Gavin are marking exam papers. Each set takes Henry 36 minutes and Gavin 1 hour. Express the times Henry and Gavin take as a ratio.
Give your answer in its simplest form.
The ratio of time taken by Henry to time taken by Gavin is 3:5
Step-by-step explanation:
Time taken by Henry for each set = 36 minutes
Time taken by Gavin for each set = 1 hour
We will convert Gavin's time into minutes.
Time taken by Gavin for each set = 60 minutes
Ratio;
Time taken by Henry : Time taken by Gavin
[tex]36:60[/tex]
Dividing by 6
[tex]\frac{36}{6}:\frac{60}{6}\\6:10[/tex]
Dividing by 2
[tex]\frac{6}{2}:\frac{10}{2}\\3:5[/tex]
The ratio of time taken by Henry to time taken by Gavin is 3:5
Keywords: ratio, division
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Solve the following: 63.9 ÷ 10 = _____
Answer:
6.39
Step-by-step explanation:
6.39
Answer:
6.39
Step-by-step explanation:
When dividing by 10 you can always just move the decimal place once to the left.
Glad I was able to help!!
what is 5 more than the sum
Answer:
5 more of the sum would be + 5 to the final answer you are adding
Step-by-step explanation:
Solve the equation:
bx-c=ax+d
b≠a
Answer:
[tex]x=\frac{d+c}{b-a}[/tex]
Step-by-step explanation:
The question is
Solve for x
we have
[tex]bx-c=ax+d[/tex]
Solve for x
That means ----> isolate the variable x
Group terms
[tex]bx-ax=d+c[/tex]
Factor x left side
[tex]x(b-a)=d+c[/tex]
Divide by (b-a) both sides
[tex]x=\frac{d+c}{b-a}[/tex]
through(-4,3), slope=-2/3
Answer:
y = -2/3 x + 1/3
Step-by-step explanation:
Use the slope-intercept linear formula: y = mx + b
x and y represent point on the line
m is the slope
b is the y-intercept
The equation of the line requires "m" and "b". We already have "m".
Substitute point (-4, 3) and slope -2/3 into the formula. x=-4; y=3; m=-2/3. Find b by isolating the variable.
y = mx + b
3 = (-2/3)(-4) + b Simplify
3 = 8/3 + b Subtract 8/3 from both sides
b = 1/3
Put b = 1/3 into the formula.
y = -2/3 x + 1/3
10,15,25,40,60 what's next?
Answer:
the answer would be 85
Step-by-step explanation:
because they are added by an increasing value of 5 so 60 plus 25 would be 85
31. In a Mathematics competition, there are 10 questions of equal marks. You get 10 marks for a correct
answer, lose 8 marks for a wrong answer, or no mark for each blank answer. If Jimmy answered 3
questions correctly, 6 questions wrongly, and left 1 question unanswered, how many marks could he
get?
Jimmy can get -18 marks in the Mathematics competition based on his correct, incorrect, and unanswered answers.
Explanation:To calculate the marks Jimmy can get, we need to consider the number of questions he answered correctly, incorrectly, and left unanswered. Since each question carries 10 marks for a correct answer and deducts 8 marks for a wrong answer, we can calculate his marks as follows:
Number of correct answers: 3 * 10 = 30 marksNumber of incorrect answers: 6 * (-8) = -48 marksNumber of unanswered questions: 1 * 0 = 0 marks
To get the total marks, we add up his scores from each category:
Total marks = 30 - 48 + 0 = -18 marks.
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