Answer:
[tex]\textsf{Zeros}: \quad x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Rewrite the given polynomial in the form ax² + bx + c:
[tex]f(x)=2 \sqrt{3}x^2+5x-4 \sqrt{3}[/tex]
To find the zeros, set the function to zero and solve for x using the quadratic formula.
[tex]\implies 2 \sqrt{3}x^2+5x-4 \sqrt{3}=0[/tex]
Quadratic formula:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore,
a = 2√3b = 5c = - 4√3Substituting the values into the quadratic formula:
[tex]\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2\sqrt{3})(-4\sqrt{3})} }{2(2\sqrt{3})}[/tex]
[tex]\implies x=\dfrac {-5 \pm \sqrt {121}}{4\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {-5 \pm 11}{4\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {6}{4\sqrt{3}}, \:\:x=\dfrac {-16}{4\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {3}{2\sqrt{3}}, \:\:x=-\dfrac {4}{\sqrt{3}}[/tex]
[tex]\implies x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}[/tex]
The sum of the roots of a polynomial is -b/a:
[tex]\implies -\dfrac{b}{a}=-\dfrac{5}{2 \sqrt{3}}=-\dfrac{5\sqrt{3}}{6}[/tex]
The sum of the found roots is:
[tex]\implies \left(\dfrac {\sqrt{3}}{2}\right)+\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{5\sqrt{3}}{6}[/tex]
Hence proving the sum of the roots is -b/a
The product of the roots of a polynomial is: c/a
[tex]\implies \dfrac{c}{a}=\dfrac{-4\sqrt{3}}{2\sqrt{3}}=-2[/tex]
The product of the found roots is:
[tex]\implies \left(\dfrac {\sqrt{3}}{2}\right)\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{12}{6}=-2[/tex]
Hence proving the product of the roots is c/a
Therefore, the relationship between the roots and the coefficients is verified.
Answer:
Step-by-step explanation:
Rewrite the given polynomial in the form ax² + bx + c:
To find the zeros, set the function to zero and solve for x using the quadratic formula.
Quadratic formula:
Therefore,
a = 2√3
b = 5
c = - 4√3
Substituting the values into the quadratic formula:
The sum of the roots of a polynomial is -b/a:
The sum of the found roots is:
Hence proving the sum of the roots is -b/a
The product of the roots of a polynomial is: c/a
The product of the found roots is:
Hence proving the product of the roots is c/a
Therefore, the relationship between the roots and the coefficients is verified.
How do I find the domain and range in this graph?
Answer:
Domain: [tex]-4 < x \leq 4[/tex]Range: [tex]0 \leq y \leq 4[/tex]Step-by-step explanation:
The domain is the set of x values, and the range is the set of y values.
Here is the histogram of a data distribution. All class widths are 1.
SO
4
3
2-
2 3
Which of the following numbers is closest to the mean of this distribution?
A. 2
OB. 3
O C. 10
OD. 5
5 6 7 8 9 10
E. 4
The correct answer is option B which is 3
What is mean?
Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
Given data:-
4,3,2
The mean will be calculated as:-
Mean = (4 + 3 + 2) / 3
Mean = 9 / 3
Mean = 3
Therefore the correct answer is option B which is 3
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The points (0, -8) and (10, 2) represent the endpoints of a diameter of a circle. Which of the following represents the equation of this circle?
Answer:
(x-5)²+(y+2)²=200.
Step-by-step explanation:
1) using the given coordinates it is possible to calculate
- the centre of the given circle:
[tex]x_0=\frac{10+0}{2}=5; \ y_0=\frac{2-8}{2}=-2;[/tex]
- the radius of the given circle:
[tex]r=\sqrt{(10-0)^2+(2+8)^2} =\sqrt{200} ;[/tex]
2) finally, the required equation (common form is (x-x₀)²+(y-y₀)²=r²):
(x-5)²+(y+2)²=200.
(3x + 5y = 7
{ 4x - y = 5
Answer:
Step-by-step explanation:
Solution by substitution method
3x+5y=7
and 4x-y=5
Suppose,
3x+5y=7→(1)
and 4x-y=5→(2)
Taking equation (2), we have
4x-y=5
⇒y=4x-5→(3)
Putting y=4x-5 in equation (1), we get
3x+5y=7
⇒3x+5(4x-5)=7
⇒3x+20x-25=7
⇒23x-25=7
⇒23x=7+25
⇒23x=32
⇒x=32/23
→(4)
Now, Putting x=32/23
in equation (3), we get
y=4x-5
⇒y=4(32/23)-5
⇒y=(128-115)/23
⇒y=13/23
∴y=13/23 and x=32/23
6 Solve each equation. Round to the nearest ten-thousandth. Check your answers.
2.
4x = 19
[tex]\huge\text{Hey there!}[/tex]
[tex]\text{4x = 19}\\\\\large\textbf{DIVIDE 4 to BOTH SIDES}\\\\\rm{\dfrac{4x}{4} = \dfrac{19}{4}}\\\\\large\textbf{SIMPLIFY IT!}\\\\\rm{x = \dfrac{19}{4}}\\\\\rm{x = 19 \div 4}\\\\\text{x = 4.75}\\\\\rm{x \approx 4.7500}\\\\\\\huge\text{Therefore, the answer should be: \boxed{\mathsf{4.7500}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Consider the algebraic expression √ 7 x 18 + 12.1 x 15 + π 4 x 6 + 1 9 . What is the degree of this polynomial? Identify the leading coefficient. Identify the leading term.
The degree of the provided polynomial is 18, and the leading term is √7.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have given an expression:
[tex]= \rm \sqrt{7}x ^{18} + 12.1x^{ 15} + \pi 4 x^ 6 + 1 9[/tex]
As we can see in the expression the greatest degree is 18.
So the degree of the polynomial is 18
And the coefficient of the variable which has a height degree is the leading term.
The leading term = √7
Thus, the degree of the provided polynomial is 18, and the leading term is √7.
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Find the slope of every line that is parallel to
the line on the graph
Answer:
[tex] - \frac{1}{6} [/tex]
Step-by-step explanation:
Using the slope formula:
[tex] \frac{ - 1 - 0}{0 - ( - 6)} = - \frac{1}{6} [/tex]
If x is a positive integer, what is the value of x for the equation (x!-(x-3)!)\23=1?
I think the first step is knowing (x!-(x-3)!) equals to 23, but after that i'm stuck, can someone help me?
[tex]\dfrac{x!-(x-3)!}{23}=1\\x!-(x-3)!=23\\(x-3)!((x-2)(x-1)x-1)=23\\(x-3)!((x^3-x^2-2x^2+2x)-1)=23\\(x-3)!((x^3-3x^2+2x)-1)=23[/tex]
23 is a prime number, therefore there are two possibilities:
[tex]\text{I.}\, (x-3)!=1 \wedge x^3-3x^2+2x-1=23[/tex]
or
[tex]\text{II.}\, (x-3)!=23 \wedge x^3-3x^2+2x-1=1[/tex]
[tex]\text{I.}\\(x-3)!=1\\x-3=0 \vee x-3=1\\x=3 \vee x=4[/tex]
Now, we check if any of these solutions is also a solution to the second equation:
[tex]3^3-3\cdot3^2+2\cdot3-1=23\\27-27+6-1-23=0\\ -18=0[/tex]
Therefore, 3 is not a solution.
[tex]4^3-3\cdot4^2+2\cdot4-1=23\\64-48+8-1-23=0\\0=0[/tex]
Therefore, 4 is a solution.
[tex]\text{II.}[/tex]
[tex](x-3)!=23[/tex]
We know that [tex]3!=6[/tex] and [tex]4!=24[/tex], therefore there isn't any [tex]n\in\mathbb{N}[/tex], for which [tex]n!=23[/tex], so there's no solution.
So, the only solution is [tex]x=4[/tex].
has a bag containing twenty balls. There are twice as many yellow balls than blue balls, but the yellow balls are only a third of the red balls. The green balls are the same number as the blue balls. How many are each of the colour ball?
Answer:
Yellow: 4
blue: 2
red: 12
green: 2
NEED HELP ASAP PLEASEE
Answer:
2nd one is the correct
Each conditional statement below is true. Write its converse. If the converse is also true, combine the statements as a biconditional.If x = —10, then x2 = 100.
The converse of the statement will be : if x^2 = 100 then x = -10, which is not true.
How to find the true statement?In order to write a converse of a conditional statement "p then q", will be "q then p" the hypothesis and conclusion interchanges.
Then the converse of the statement will be :
if x^2 = 100 then x = -10,
which is not true.
Since , x = +10, then x^2 = 100
Therefore, if x^2 = 100 then x = -10, which is not true.
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urgent help algebra 2
What is the solution to this system of equations?
Negative 3 x + 5 y = negative 2. 3 x + 7 y = 26.
(4, 2)
(2, 3 and one-third)
no solution
infinitely many solution
The solution to the system of equation is (-4 , 2) , Option A is the right answer.
What are System Of equation ?A set of equation whose factors are common are called system of equations.
It is given in the question
3x +5y = -2
3x +7y = 2
On solving this we get
-2y = -4
y = 2
On substitution in any equation
x = -4
Therefore solution to the system of equation is (-4 , 2) , Option A is the right answer.
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Answer:
A.
Step-by-step explanation:
took tha quiz
I cannot crack this one, somebody please assist me
These [tex]N[/tex] outcomes make up the entire sample space, so
[tex]\displaystyle \sum_{k=1}^N P(e_k) = P(e_1) + P(e_2) + P(e_3) + \cdots + P(e_N) = 1[/tex]
We're given that [tex]P(e_{j+1}) = 2 P(e_j)[/tex] for all [tex]j\in\{1,2,\ldots,N-1\}[/tex], so
[tex]P(e_1) + 2 P(e_1) + 2^2 P(e_1) + \cdots + 2^{N-1} P(e_1) = 1 \\\\ \implies P(e_1) = \dfrac1{1 + 2 + 2^2 + \cdots + 2^{N-1}} = \dfrac1{2^N - 1}[/tex]
Then we can solve the recurrence relation to get the probability of the [tex]j[/tex]-th outcome,
[tex]P(e_{j+1}) = 2 P(e_j) = 2^2 P(e_{j-1}) = 2^3 P(e_{j-2}) = \cdots \\\\ \implies P(e_{j+1}) = 2^j P(e_1) \\\\ \implies P(e_j) = 2^{j-1} P(e_1) = \dfrac{2^{j-1}}{2^N - 1}[/tex]
The probability of getting this sequence of [tex]k[/tex] outcomes is then
[tex]\displaystyle P(E_k) = P(e_1) + P(e_2) + \cdots + P(e_k) = \sum_{j=1}^k \frac{2^{j-1}}{2^N-1} = \frac{2^k-1}{2^N-1}[/tex]
as required.
Some preliminary results: If [tex]S[/tex] is the sum of the first [tex]n[/tex] terms of a geometric series with first term [tex]a[/tex] and common ratio [tex]r[/tex], then
[tex]S = a + ar + ar^2 + \cdots + ar^{n-1}[/tex]
[tex]\implies rS = ar + ar^2 + ar^3 + \cdots + ar^n[/tex]
[tex]\implies S - rS = a(1 - r^n)[/tex]
[tex]\implies S = \dfrac{a(1 - r^n)}{1 - r}[/tex]
which gives us, for instance,
[tex]1 + 2 + 2^2 + \cdots + 2^{N-1} = \dfrac{1 - 2^N}{1 - 2} = 2^N-1[/tex]
Giving out brainliest to whoever answers!
A man has to be at a certain place at a certain time. He finds that he shall be 20 minutes late if he walks at 3 km/h speed and 10 minutes earlier if he walks at a speed of 4 km/h_The distance he has to walk is
Answer:
0.5km or 500m
Step-by-step explanation:
Given Distance = Speed x Time
In this case, we should use the difference in speed and time of the 2 scenarios.
Difference in Time = 20 mins(late) + 10 mins(early)
= 30 mins or 0.5 hour
Difference in Speed = 4km/h - 3km/h = 1km/h
Distance = 1km/h x 0.5 hr = 0.5km or 500m.
Each year the Royal London company gives
its employees a gift box containing 6 bags of
coffee, 4 boxes of tea, and 2 boxes of biscuits.
If in the first three years, the number of
employees grew from 2 to 12 to 18, what was
the total quantity of coffee, tea, & biscuits
distributed by the company in those years?
The total number of tea received in three years is 192.
The total number of coffee received in three years is 128.
The total number of biscuits received in three years is 64.
What is the total quantity of tea, coffee and biscuits distributed in the three years?The total quantity of tea, coffee and biscuits received in the first year = (6 x 2) , (4 x 2) , (2 x 2) = 12, 8, 4 respectively
The total quantity of tea, coffee and biscuits distributed in the second year = (6 x 12) , (4 x 12) , (2 x 12) = 72, 48, 24 respectively
The total quantity of tea, coffee and biscuits distributed in the third year = (6 x 18) , (4 x 18) , (2 x 18) = 108, 72, 36 respectively
Total number of tea received in three years = 108 + 72 + 12 = 192
Total number of coffee received in three years = 8 + 48 + 72 = 128
Total number of biscuits received in three years = 4 + 24 + 36 = 64
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What is the scale factor from AABC to ADEF?
B
48
AA
6
A4 CE
48
6
O A.
C
B. 8
32
D
Answer: 8
Step-by-step explanation:
We are going from a smaller triangle to a larger triangle, so the scale factor is greater than 1.
Eliminate A and D.We know scale factor = (image)/(preimage), so the scale factor is 32/4 = 8
The scale factor of dilation of the triangle is k = 8
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.
Given data ,
Let the first triangle be represented as ΔABC
Let the second triangle be represented as ΔDEF
where the measures of sides of ΔABC are
AB = 6 , BC = 6 and AC = 4
The measure of sides of triangle ΔDEF are
DE = 48 , EF = 48 and DF = 32
The scale factor of dilation k = measure of side DE / measure of side AB
k = 48 / 6
k = 8
Hence , the dilation factor is k =8
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What is the value of this expression when c = -4 and d = 10?
A.
2
B.
9
C.
21
D.
41
The complete question is
"What is the value of this expression when c= -4 and d= 10?
1/4 (c^3+d²)
A.2
B.9
C.21
D.41"
The value of this expression when c = -4 and d = 10 will be option B 9.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
The given expression is
[tex]1/4 (c^3+d^2)\\\\1/4 ((-4)^3+(10)^2)\\\\1/4 ( -64 + 100)\\\\1/4 (36)\\\\9[/tex]
Hence, the value of this expression when c = -4 and d = 10 will be option B 9.
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1. Which of the following numbers is
rational?
A. 0.78
B. 0.303003000
C. √6
D. 0.3841697
Answer:
A. 0.78
Step-by-step explanation:
A rational number is a number that you can express as [tex]\frac{x}{y}[/tex] where [tex]y\neq 0[/tex].
The school play sold $550 in tickets one night. The number of $8 adult tickets was 10 less than twice the number of $5 child tickets. How many tickets were sold for the adults vs the child tickets?
Answer:
This is my answer↓:
Step-by-step explanation:
He school play sold $550 in tickets one night.
The number of $8 adult tickets was 10 less than twice the number of
$5 child tickets.
How many of each ticket were sold
Let say child ticket sold = x
Adult tickets was 10 less than twice the number of child tickets.
=> Adult ticket sold = 2x - 10
Child ticket sold = x
$5 child tickets price
=> Revenue = 5x $
Adult ticket sold = 2x - 10
$8 Adult tickets price
=> Revenue = 8(2x - 10) =16x - 80 $
5x + 16x - 80 = 550
=> 21x = 630
=> x = 30
Child ticket sold = 30
Adult ticket sold = 50
Total ticket sold = 80
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Determine the number of zeros of the polynomial function. f(x) = x^4 − 6x
The factor of the function will be x and (x³ – 6). Then the zeroes of the function will be 0 and √6.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The polynomial function is given below.
f(x) = x⁴ − 6x
Then the factor of the function will be
f(x) = x(x³ – 6)
Then the zeroes of the function will be
x = 0, √6
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Two angles are complentary if the sum of their measures is 90 °. Find two complentary angles such that one of the angles is 165° less than 4 times the other angle
Answer:
51° and 39°
Step-by-step explanation:
x + 4x - 165 = 90
5x = 90 + 165
5x = 255
x = 255 / 5
x = 51
4 x 51 = 204
204 - 165 = 39
2 angles are 51 and 39
John is 5 years younger than David. Four years later David will be twice as old as John. Find their present age.
David will be 10 and John will be 9
A formula for the normal systolic blood pressure for a man age A, measured in mmHg, is given as
P = 0.006A2 − 0.02A + 120. Find the age to the nearest year of a man whose normal blood pressure measures 125 mmHg.
Solving a quadratic equation, the age of the man with a blood pressure of 125 mmHg is of 27 years old.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
The pressure is given by:
P = 0.006A² - 0.02A + 120.
When the pressure is of 125 mmHg, we have that:
0.006A² - 0.02A + 120 = 125.
0.006A² - 0.02A - 5 = 0.
Hence the coefficients are a = 0.006, b = -0.02, c = -5, and the solutions, applying the formula are:
A = -30 and A = 27.
Age has to be positive, hence the man is 27 years old.
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Graph A: A horizontal line goes from (1, 0.5) to (2, 0.5). Another horizontal line goes form (2, 0.2) to (7, (0, 2). Graph B: A curve starts at (0, 0), curves up to (1, 1), and then curves down to (2, 0).
Which graph represents a density curve, and why?
graph A only, because the curve is above the horizontal axis, and the area under the curve from 2 to 7 is 1
graph B only, because the curve is above the horizontal axis, and the area under the curve is equal to 1.57
both graph A and graph B, because both curves are above the horizontal axis, and both areas are positive
neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1
Pictures posted below
Answer: neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1
Step-by-step explanation:
Areas under the graphs:
Graph A
[tex](1)(0.5)+(7-2)(0.2)=1.5\\\\[/tex]
Graph B
[tex]\frac{\pi}{2}(1^{2})=\frac{\pi}{2}[/tex]
As neither of these graphs have an area of 1, neither of them are density curves.
The statement - "neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1" is true.
A few fundamental principles apply to density curves:
A density curve's area beneath it represents probability.A density curve's area under it equals one.Base x height in a uniform density curve equals one.The likelihood that x = a will never occur.The likelihood that x < a is the same as that of x ≤ a.Neither curve of Graph A nor of Graph B has the area under the curve summed up as 1, though the curve is above the horizontal axis.
Hence, because neither graph has an area of 1, even if both curves are above the horizontal axis, the statement "neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1" is true.
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What is the remainder of x^5+2x^4+9x^3-6x^2+3x+3165 divided by x-5
Answer:
8530
Step-by-step explanation:
The remainder is 5⁵ + 2(5)⁴ + 9(5)³ - 6(5)² + 3(5) + 3165 = 8530
Please answer this question!! <3 <4 <5 <6 <9
The correct answer is option C which is the angle LMO is 50°
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.
Given that:-
∠O = 70°
∠L = 60°
∠LMO =?
As we know that the sum of the three angles are 180 degree applying this relation:-
∠LOM + ∠OLM + ∠LMO = 180
70 + 60 + ∠LMO = 180
∠LMO = 180 - 70 - 60 = 50
Therefore the correct answer is option C which is the angle LMO is 50°
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A couple decides that Sophia will drive the first 3/5 of a trip and Toby the last 2/5. The entire trip is A couple decides that Sophia will drive the first 3/5 of a trip and Toby the last 2/5. The entire trip is 500 miles long. How far will Sophia drive?500 miles long. How far will Sophia drive?
Answer:
60 miles
Step-by-step explanation:
miles that Sophia drove = 3/5 x 100 = 60 miles
A fraction is a way to describe a part of a whole. The distance covered by Sophia and Toby is 300 miles and 200 miles, respectively.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
A fraction can also be described in the form of a percentages, to represent the part of the whole.
Given that the length of the entire trip is 500 miles. Also, the first 3/5 of the trip are covered by Sophia and the last 2/5 of the trip are covered by Toby.
Now, the distance covered by Sophia and Toby will be,
Distance covered by Sophia = (3/5) × 500 miles = 300 miles
Distance covered by Toby = (2/5) × 500 miles = 200 miles
Hence, the distance covered by Sophia and Toby is 300 miles and 200 miles, respectively.
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Help me with this please!!!!
Answer:
3
Step-by-step explanation:
Cardinalities are the number of elements in a set.
(A∩B∩C) is the very middle part of the circle, and there are 3 elements there.
