Answer:
A= 3x B= 6/8
Step-by-step explanation:
The value of a is 7, and the value of b is 2√(2) for the given quadratic function f(x) = x² - 14x + 53.
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
The quadratic function f(x) = x² - 14x + 53 is equal to zero when x = a + bi or x = a - bi. This means that the roots of the quadratic equation are a + bi and a - bi.
The roots of a quadratic equation can be found using the quadratic formula:
x = (-b +/- √(b² - 4ac)) / (2a)
In this case, a = 1, b = -14, and c = 53. Substituting these values into the quadratic formula, we get:
x = (-(-14) +/- √((-14)² - 4153)) / (2*1)
x = (14 +/- √(196 - 212)) / 2
x = (14 +/- √(-16)) / 2
Since the square root of a negative number is an imaginary number, the roots of the quadratic equation are a + bi and a - bi, where a = 14/2 = 7 and b = √(-16)/2 = 2√(2).
Therefore, the value of a is 7, and the value of b is 2√(2).
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It is estimated that 89% of senior citizens suffer from sleep disorders and 9% suffer from anxiety. Moreover, 5% of senior citizens suffer from both sleep disorders and anxiety.
(a)Find the probability that a senior citizen suffers from anxiety, given that he or she has a sleep disorder. Round your answer to the nearest hundredth.
(b)Given that a senior citizen suffers from anxiety, what is the probability that he or she also suffers from a sleep disorder? Round your answer to the nearest hundredth.
For a;
[tex]P(a | sd) = p(a AND sd)/P(sd) = 0.06/(0.89) = 0.674[/tex]
For b;
[tex]P(ds | a) = P(ds AND a)/P(a) = 0.06/0.09 =\frac{2}{3}[/tex]
If my calculations are incorrect, then sorry ;/
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What is the solution to this inequality?
−15x>75
x<−5
x>−5
x≥−5
x≤−5
Answer:
x < -5 (the first option)
Step-by-step explanation:
I hope this helps!
The solution of the inequality will be;
⇒ x < - 5
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ - 15x > 75
Now,
Since, The inequality is,
⇒ - 15x > 75
Hence, The solution of the inequality is,
⇒ - 15x > 75
⇒ - x > 75/15
⇒ - x > 5
⇒ x < - 5
Thus, The solution of the inequality is,
⇒ x < - 5
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please help me asap
ty :)
Answer:
y = -1/7x + 1
Step-by-step explanation:
Subtract 3x both sides
21y = 21 - 3x
Divide by 21 both sides
y = 1 - 1/7x
y = -1/7x + 1
solve this
x2 + 14 x + 33 = 0
Answer:
-11, -3.
Step-by-step explanation:
x^2 + 14x + 33 =0
To factor this we need 2 numbers whose product is 33 and whose sum is 14 .
These are 3 and 11, so:
(x + 3)(x + 11) = 0
x = 11, -3.
Dante’s chocolate bar is 36% cocoa. If the weight of the chocolate bar is 73 grams, how many grams of cocoa does it contain round your answer to the nearest tenth?
Answer:
26.3 grams
Step-by-step explanation:
36% = 36/100 = 0.36
73 * 0.36 = 26.28 grams ≈ 26.3 grams
Answer:
i think 26.3 grams
Step-by-step explanation:
0.36×73 = 26.28
When rounded to the nearest tenth, 26.28 should be equal to 26.3
So Dante's the chocolate bar contains 26.3 grams of cocoa.
x+y=3
workout the value of 2x-2y
Answer:
-2
Step-by-step explanation:
x= 1
y= 2
2 times x(1)=2
2 times y(2)=4
2-4= -2
PLEASE HELP MEE i dont really understand this
4(p+1.25)=7 2/5
Answer:
p=0.6
Step-by-step explanation:
Help me out plesseee!!
Step-by-step explanation:
the rate of change is officially
(f(x2) - f(x1)) / (x2 - x1)
but for a line function (as we have here) this is totally easy : it is the slope of the line.
and that means it is the factor of x.
in our case this is -3/2.
because the slope of a line is the ratio "y coordinate change / x coordinate change". and that is exactly corresponding to the general rate of change definition above.
Answer: (f(x2) - f(x1)) / (x2 - x1)
because the slope of a line is the ratio "y coordinate change / x coordinate change".
Step-by-step explanation: HOPE IT HELPS YOU .THANKS .
A,D And E Thats The Answers
Answer:
wait what? hmmm hmmmmmm
How do I solve for x?
Here, the opposite angles of the triangle are equal. If 2 opp. angles in a triangle are equal, then the opposite sides will be equal as well.
So,
16 = x + 36
16 - 36 = x
-20 = x
______
Hope it helps ⚜
Can any one explain this question worth points! plz explain if you can
Answer:
x = 31
Step-by-step explanation:
The given angles are supplementary and their sum is 180 degrees
5x - 16 + x + 10 = 180 add like terms
6x - 6 = 180 add 6 to both sides
6x = 186 divide both sides by 6
x = 31
What the vertex of y=4(x-3)^2+3
Answer:
(3,3)
Step-by-step explanation:
we rewrite in vertex form and use this form to find the vertex (h,k)
The first equation in the following system gives a company's income, in dollars, for selling x baseball caps. The second equation gives the cost of making x baseball caps. Y = 8x y = -0. 01 x2 4x 3,200 The solution of the system is (400, 3,200). How would you interpret this solution?.
The solution of the equation can be determined by substituting the points in the equation and solving it.
The solution of the given equation would be interpreted by solving the equation for the value of x and y.
The solution of the equation is (400, 3200) and it can be determined by using substitution method.
Given that,The first equation in the following system gives a company's income, in dollars, for selling x baseball caps.
The second equation gives the cost of making x baseball caps.
[tex]\rm y = 8x\\\\ y = -0.01 x^2 + 4x + 3200[/tex]
The solution of the system is (400, 3,200).
We have to determine,How would you interpret this solution?
According to the question,The first equation in the following system gives a company's income, in dollars, for selling x baseball caps.
The second equation gives the cost of making x baseball caps.
[tex]\rm y = 8x\\\\ y = -0.01 x^2 + 4x + 3200[/tex]
On solving both the equation,Substitute y = 8x in the equation 2,
[tex]\rm y = -0.01 x^2 + 4x + 3200\\\\ 8x = -0.01 x^2 + 4x + 3200\\\\0.01x^2+8x-4x-3200=0\\\\0.01x (x+800) -4(x+800)=0\\\\(x+800)\ (0.01x-4)\\\\When \ \ x +800=0, \ x = -800\\\\And\ \ 0.01x-4 = 0, \ \ x = \dfrac{4}{0.01} \ \ x =400[/tex]
The value of x is not -800 because the cost can not be negative.
Then the value of x is 400.
Substitute the value of x in equation 1,
[tex]\rm y = 8x\\\\y = 8(400)\\\\y = 3200[/tex]
Hence, The solution of the equation is (400, 3200).
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Help please I’ll give Brainly please answer both I’ll give 5 stars and lines
Answer:
I really cant see the picture that well or, i would help.
Step-by-step explanation:
hey guys can you help me with this question? 20 points :)
Answer:
About 7 units
Step-by-step explanation:
About 7 units would be correct. 1 + 6 is 7
however 6 isn’t an option so the next closet thing is 7
HOPE THIS HELPED :3
Answer pretty sure that’s 7
Step-by-step explanation:
Please help me with this question
Answer:
F
Step-by-step explanation:
Answer:
F
Step-by-step explanation:
You only need to read as far as ...
y ≤
to choose the correct graph. The values in the solution will be less than or equal to those on the boundary line. That means the graph will be shaded below the line, and the line will be solid (because it is part of the solution).
The graph with a solid line and shading below is graph F.
The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel:
(image)
Which statement best describes a flaw in the student's proof?
Angle DBC and angle BDA form a pair of vertical angles, not a pair of alternate interior angles, which are congruent.
Triangles ABD and CDB are congruent by the SAS postulate instead of the SSS postulate.
Triangles ABD and BCD are congruent by the AAS postulate instead of the SSS postulate.
Angle DBC and angle BDA form a pair of corresponding angles, not a pair of alternate interior angles, which are congruent.
The statement that best describes a flaw in the students' proof is;
Option D; Angle DBC and angle BDA form a pair of corresponding angles, not a pair of alternate interior angles, which are congruent.
From the given image, we can see that;
AB ≅ DC
Let us analyze each given option;
A) ∠DBC and ∠BDA are in the same triangle ΔBDC. Now, they can't be a pair of vertical angles because vertical angles are a pair of opposite angles formed when two lines intersect but this is not the case here.
They are also not alternate interior angles because alternate angles are formed when a transverse line intersects two coplanar lines and again that is not the case here.
B) In ΔABD and ΔBDC, we see that;
AB = DC. Also, by theorem of alternate interior angles, we can tell that;
∠ABD = ∠BDC
Similarly, ∠BDA = ∠DBC from alternate interior angles.
Thus, there is one corresponding side and two non-included angles which means the triangles are congruent by AAS Congruency postulate.
C) As seen in B above, this statement is correct because the triangles are congruent by AAS postulate.
D) Corresponding angles lie on the same side of the transversal. In this case, ∠BDA and ∠DBC lie on opposite sides and are even congruent by alternate interior angles.
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If 5 20 times 2 Superscript 2 minus 3 x Baseline = 10 times 2 Superscript negative 2 x Baseline 5, what is the value of x? â€"3 â€"2 2 3.
The value of x is 3.
Given that,
If [tex]5 + 20 \times 2^{2-3x}[/tex],
And Baseline = [tex]10 \times 2^{-2x}+5[/tex]
We have to find,
The value of x?
According to the question,
To determine the value of x in the equation following all the steps given below.
Equation; [tex]\rm 5 + 20 \times 2^{2-3x} = 10 \times 2^{-2x}+5[/tex]
Step1; Subtract 5 from both sides,[tex]\rm5- 5 + 20 \times 2^{2-3x} = 10 \times 2^{-2x}+5-5\\\\\rm 20 \times 2^{2-3x} = 10 \times 2^{-2x}[/tex]
Step2; Divided by 10 on both sides,[tex]\rm 20 \times 2^{2-3x} = 10 \times 2^{-2x}\\\\\dfrac{ 20 \times 2^{2-3x} }{10}= \dfrac{10 \times 2^{-2x}}{10}\\\\\rm 2 \times 2^{2-3x} = 2^{-2x}[/tex]
Step3; Rewrite the term into their power form and add the powers,[tex]\rm 2 \times 2^{2-3x} = 2^{-2x}\\\\2^1 \times 2^{2-3x} = 2^{-2x}\\\\2^{2-3x+1} = 2^{-2x}\\\\[/tex]
Step4; The base is the same on both sides, we equate exponents,[tex]\rm 2-3x+1 = -2x\\\\-3x+2x = -1-2\\\\-x = -3\\\\x=3[/tex]
Hence, The required value of x is 3.
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Tamara wants to rent a jet-ski. Tamara's deal is to pay $60 to rent the jet-ski, plus $12.50 per hour. If
Tamara has $135 how many hours can Tamara use the jet-ski?
Answer:
6 hours.
Step-by-step explanation:
deal: 135-(60+12.5h)=y
let h= # of hrs
135-60=75.
75/12.5=6 hours.
PLEASE HELP
Classify each sequence as arithmetic, geometric or neither:
1.) -1/16, 1/4, -1, 4, -16, …
2.) -5, 10, -15, 20, -25, …
3.) 65, 52, 36, 26, 13, …
[] Neither
[] Arithmetic
[] Geometric
Answer:
1. ARITHMETIC
2. NEITHER
3. GOEMETRIC
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a farm is sold for $457000, which gives a profit of 19%. Find the profit
The answer sheet says it is $73,000
Answer: its 73,000
Step-by-step explanation: the answer sheet has the answers...
1 Name the shapes that are being described. a I have three sides that are all the same length. I have three equal angles. Thave three lines of symmetry and rotational symmetry of order 5. b I have four sides. Thave one line of symmetry and rotational symmetry of order 1. Two of my angles are equal. I have two pairs of equal length sides' C I have six sides. All my sides are the same length. I have six lines of symmetry and rotational symmetry of order
Answer:
a. Equilateral triangle
b. Quadrilaterals
c. Hexagon
Step-by-step explanation:
What's the answer to this?
who was often called the father of modern mathematics because he created analytic geometry and the cartesian coordinate system?
René Descartes was the person who created analytic geometry and the Cartesian coordinate system
Can someone plz help Me?
the answer to your question is C. 6^4
Answer:C? sorry if im wrong
Step-by-step explanation:
Calculate the volume of the cylinder:
10 cm
6 cm
Answer:
60
Step-by-step explanation:
10 ×6
that is the simple answer to your question
How to solve 8.9 times 6
Answer:
53.4
Step-by-step explanation:
8.9 × 6 = 53.4
Hope it help !
what is the following product 3 sqrt 4 times sqrt 3
Answer:
c on edge YW
Step-by-step explanation:
The value of ∛4 × √3 is 2.75 or [tex]\sqrt[6]{432}[/tex].
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given;
Expression,
product 3 sqrt 4 times sqrt 3.
In numerator form:
As per the given expression,
∛4 × √3
Simplifying,
∛4 × √3
= [tex]4^{1/3}[/tex] x [tex]3^{1/2}[/tex]
= [tex]4^{2/6}[/tex] x [tex]3^{3/6}[/tex]
= [tex]\sqrt[6]{16 + 27}[/tex]
= [tex]\sqrt[6]{432}[/tex]
= 2.749
= 2.75
Therefore, the product is 2.75 or [tex]\sqrt[6]{432}[/tex].
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Please help with this question. I dont want another detention
Step-by-step explanation:
Total Students = 450 (Everything within the sample/rectangle)
Choir = 110
Band = 240
Both = 60 (Where both circles overlap)
110+240+60 = 410 (Total students in Choir or Band or Both)
410 ÷ 450 = 0.91111111
Therefore the probability that a student chosen at random is in the choir, band or both out of the sample is 91%
Select the correct answer.
Simplify the following expression.