Answers
The expressions related to the roots of each quadratic equation are listed below:
Case 1 - x² + 3 · x - 9 = 0
Roots: α = - 3 / 2 - 3√5 / 2, β = - 3 / 2 + 3√5 / 2
a) α + β = - 3
b) α² + β² = 27
c) α³ + β³ = - 108
Case 2 - x² + 4 · x - 2 = 0
Roots: α = - 2 - √6, β = - 2 + √6
a) α + β = - 4
b) α² + β² = 20
c) α³ + β³ = - 88
How to determine the roots of quadratic equations and calculate the values of equations based on these roots
This question consists in two parts, find the roots by factoring the quadratic equations by algebra properties and determine the expressions based on the two roots of each expression. A root is a value of x such that the polynomial is equal to zero.
Case 1
x² + 3 · x - 9 = 0
x² + 3 · x = 9
x² + 3 · x + 9 / 4 = 9 + 9 / 4
(x + 3 / 2)² = 45 / 4
x + 3 / 2 = ± 3√5 / 2
x = - 3 / 2 ± 3√5 / 2
The roots are α = - 3 / 2 - 3√5 / 2 and β = - 3 / 2 + 3√5 / 2 and the following expressions are evaluated:
a) α + β = - 3
b) α² + β² = (- 3 / 2 - 3√5 / 2)² + (- 3 / 2 + 3√5 / 2)² = 27
c) α³ + β³ = (- 3 / 2 - 3√5 / 2)³ + (- 3 / 2 + 3√5 / 2)³ = - 108
Case 2
x² + 4 · x - 2 = 0
x² + 4 · x + 4 = 6
(x + 2)² = 6
x + 2 = ± √6
x = - 2 ± √6
The roots are α = - 2 - √6 and β = - 2 + √6 and the following expressions are evaluated:
a) α + β = - 4
b) α² + β² = (- 2 - √6)² + (- 2 + √6)² = 20
c) α³ + β³ = (- 2 - √6)³ + (- 2 + √6)³ = - 88
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Related Questions
simplify 5(x+4)-2(x-3)
Answers
Answer:
3x +26
Step-by-step explanation:
the depth of the water in a tank after t minutes is modeled by f l(t) =3+2.5t measured in inches.find the interpret f(5)
Answers
The function f(5) equals 15.5 inches
What is a function?
A function from either a set X to a set Y provides precisely one item of Y to each item of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. The Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi are credited with the first known attempt to the concept of function. Initially, functions were the idealized vision of how a variable quantity depended on another quantity. A planet's location, for example, is a function of time. Historically, the notion was developed with the infinitesimal calculus at the end of the 17th century, and the functions investigated were differentiable until the 19th century.
The function is solved as
f(5) = 3 + 2.5(5) = 3 + 12.5 = 15.5 inches
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Can you help me please
Which statement describes the graph?
Answers
Answer:
b
Step-by-step explanation:
What is the ratio of the two quantities? 17 seconds to 7 min HELP PLSS WILL BE BRAINLYEST
Answers
Answer:
17 : 420
Step-by-step explanation:
Ratio of two quantities:When finding the ratio of two quantities, both quantities should be in same type.
Convert 7 minutes to seconds.
7minutes = 7 * 60
= 420 seconds
17 seconds : 7 minutes = 17 : 420
The question is asking “Rewrite in simplest terms: 7(9y+2y-6)-9y
Answers
Answer:
[tex]68y-42[/tex]Explanation:
Here, we want to rewrite the given expression
What we have to do is to start by opening up the bracket
To do this, we have to multiply the term on the left with each term inside the bracket
Then we collect the like terms and perform the necessary arithmetic operation
We have this as follows:
[tex]\begin{gathered} \text{ =7(11y-6)-9y} \\ =\text{ 77y-42-9y} \\ =\text{ 77y-9y-42} \\ =\text{ 68y-42} \end{gathered}[/tex]Answer:
68y-42
Step-by-step explanation:
7(9y+2y-6)-9y
Find the expression in simplest terms
Combine like terms
7(11y-6)-9y
Distribute
77y -42-9y
Combine like terms
68y-42
In the isosceles triangle. if <A = 55 find the m<B.
Isosceles triangle
Answers
Answer:
62.5
Step-by-step explanation:
If the perimeter of the rectangle is 46, what is the value of x?
Answers
Answer: 5
Step-by-step explanation:
perimeter = 2 x length + 2 x width
plug in the values
46 = 2(3x+2)+2(x+1)
distribute the 2 into the fraction by multiplying
46 = 6x+4+2x+2
add similar components
46 = 8x+6
subtract 6 to both sides
40 = 8x
divide by 8
5 = x
omar will run at least 28 miles this week, so far he has run 12 miles. What are the possible numbers of additional miles he will run? use t for the number of additional miles he will run white your answer as an inequality solved for t
Answers
The inequality that will define Omar's run is 12 + m ≥ 28.
An inequality in algebra is a mathematical statement that employs the inequality symbol to show how two expressions relate to one another. The phrases on either side of an inequality symbol are not equal. The phrase on the left should be larger or smaller than the expression on the right, or vice versa, according to this symbol. Relationships between two algebraic expressions that are represented by the inequality symbols are known as literal inequalities. The relationship is known as an inequality when the symbols ">", "", "", or "" are used to link two real numbers or algebraic expressions.
For this issue, it is said that Omar would run at least 28 miles this week; he may run more, but 28 miles is his minimum objective.
He had already covered 12 miles.
Afterward, the inequality symbol will be "."
The inequality is therefore 12 + m 28.
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what is 5 + 2 =??? i need to know now
Answers
Answer: 5 + 2 = 7
Step-by-step explanation: its easy
mark receives a score report detailing his performance on a statewide test. on the math section, mark earned a raw score of 39, which placed him at the 68th percentile. this means that
Answers
Mark receives a scale report and on the Math section, he earned a raw score of 39 which is at the 68th percentile, meaning that the total raw score on the Math section is 57
Find out the total score of the Math score, 100th percentile
Given; raw score- 39 which is at the
68th- percentile
For someone to be at the 100th percentile, he or she must have scored all the questions right.
In Mark's case, he had a score of 68 percentile with a score of 39
Total raw score for the Math section;
state; If score of 39 = 68 percentile
? 100 percentile
Cross multiply to solve for the unknown
Thus; 39 * 100 / 68
= 57
Therefore, total raw score on the Math section is 57, which is at the 100th percentile.
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Lines AB and CD are parallel. Find the measure of the three angles in triangle FAB.
136⁰
71⁰
Answers
For the given parallel lines AB and CD, the measure of the angle of the triangle ∠FAB = 25°.
What is defined as the corresponding angles?Corresponding angles are generated when two parallel lines have been intersected by a transversal.The definition of corresponding angles states that when two parallel lines intersect with a third, the angles that occupy the very same relative position at every intersection are said to be corresponding angles to one another."The two lines are considered to be parallel if indeed the corresponding angles inside the two intersection areas are congruent."For the given question;
Line AB || Line CD
From the given diagram,
∠CFD = ∠AFB = 110 (corresponding angles)
Now, in triangle ABF
By the property of triangle; sum of all interior angles of triangle is 180.
Thus,
∠AFB + ∠ABF + ∠FAB = 180°
Put the values;
110° + 45° + ∠FAB = 180°
∠FAB = 180° - 155°
∠FAB = 25
Thus, the measure of the angle ∠FAB = 25° in triangle FAB.
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△PGH is an equilateral, PG=x+5, GH=2x-5 and PH=3x-15. Find the value of x and the perimeter of the triangle.
Answers
The value of x is 10
The perimeter of the triangle is 30 units
What is an equilateral triangle?An equilateral triangle can be defined as a triangle which has all its sides equal or congruent to each other.
The properties of an equilateral triangle includes;
From the information given, we have the sides as;
PG=x+5 GH=2x-5 PH=3x-15Since all of its sides are equal, we have to equate two side, we have;
x + 5 = 2x - 5
collect like terms
x - 2x = -5 - 5
subtract the like terms
-x = -10
make 'x' the subject
x = 10
But the perimeter of an equilateral triangle = 3a = 3(10) = 30 units
Thus, the value is 10
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Which comparison is correct?
A |-3| > |-4|
B |5| > 7
C 7 < |7|
D -5 <-4
Please help!! I need the answer quick as possible thank you!
Answers
The comparison of the inequalities that is correct among the given options is; D: -5 < -4
What is the comparison of the absolute values?We want to compare absolute values.
The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3.
The absolute value of a number can also be described as its distance from zero along real number line.
A) |-3| > |-4|; This is incorrect because the absolute value of - 3 is 3 and the absolute value of - 4 is 4 and 4 is greater than 3 not the other way round.
B) Again, this is incorrect as the absolute value of 5 is 5 which is less than 7.
C) This is incorrect with the same reason as above.
D) This is correct because on a number line, - 5 is less than - 4
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One km is equal to _______.
a.
0.62 ft
b.
3280.8 ft
c.
1.61 ft
d.
5280 ft
Answers
When we try to convert the value of one kilo meter to feet, the value that we obtain is 3280.8 ft.
How do you convert?We know that there are several units that we could use for calculations. t is often common that we need to convert the units from one unit to the other so that we can be able to carry out calculations. The number that allows us to be able to carry out such a a conversion is what we call the conversion factor for that particular operation.
Given that;
1 foot = 0.0003048 kilo meter
We can see that if we seek to convert a value of One km to feet we would have 3280.8 ft
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show work
Solve.
−2/5x −9 < 9/10
Answers
Answer:
X>-99/4
Step-by-step explanation:
Let's solve your inequality step-by-step.
−2/5x−9<9/10
Step 1: Add 9 to both sides.
−2/5x−9+9<9/10+9
−2/5x<99/10
Step 2: Multiply both sides by 5/(-2).
(5/−2)*(−2/5x)<(5/−2)*(99/10)
x>−99/4
Answer:
x>−99/4
can a percent of change be greater than 100%?
Answers
Between 10 P.M. and 7:45 A.M., the water level in a swimming pool decreased by
3/8 in. Assuming that the water level decreased at a constant rate, how much did the water level drop each hour?
Please help asap
Answers
The water level drop each hour by 0.0384 inch
Firstly, the deacrease in water level is takes as per the question
Decrease = 3/8 inches
Decrease=0.375 inches
Then the time interval is calculated
From 10 pm to 7:45 hours will be 9.45 hours
Time interval= (9 + 45/60) hours
Time interval=9.75 hours
Now, the drop in water level per hour is determined, to do so, total water level decreased is divided by the time taken to decrease that water level
that is 0.375/9.75 inches/hour
= 0.03846 inches/hour
Therefore, if between 10 P.M. and 7:45 A.M., the water level in a swimming pool decreased by 3/8 inches and the water level decreased at a constant rate, the water level drop each hour is 0.03846
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The figure above is rotated 270° counterclockwise about the origin. What are the coordinates of W'?
Answers
Answer: The coordinates W' after a rotation 270° counterclockwise about the origin is (3,-1)
Given m
||n, find the value of x.
m
102°
xº
Answers
x=102°(Corresponding angles are equal m || n)
HOPE THIS HELPS
Transform the basic function f(x)=x2 as follows. complete each transformation separately in the order they are given. shift down 5 units and left 77 units. reflect about the y -axis compress vertically by a factor of 2.
Answers
The transformed function becomes; f'(x) = (1/2)[(-x - 77)² - 5] after its shifting and compression.
What is the procedure for obtaining a new function from a parent function?Let us suppose we have such a parent function y=f (x). By simply introducing a constant c, a new function y=g(x) can be generated from the parent function.The following are the function transformation / translation principles: f (x) + b multiplies the function by b.f (x) + b shifts a function b units upward.f (x) − b shifts a function b units downward.f (x + b) shifts a function b units to the left.f (x − b) shifts a function b units to the right.−f (x) reflects a function in x-axis (that is, upside-down)For the given question;
The parent function is given as; f(x) = x².The function is shifted 5 units down, then y coordinates will get reduced by 5 units as; f(x) = x² - 5.Now, there is a shift of 77 to the right, then x coordinates will get reduced by 77 units; f(x) = (x - 77)² - 5.There is a reflection of function about y-axis, then value of x coordinates will change to its negative; f(x) = (-x - 77)² - 5.At last, there is a vertical compress by a factor 2, reduced the function to its half; f'(x) = (1/2)[(-x - 77)² - 5].Thus, the transformed function becomes; f'(x) = (1/2)[(-x - 77)² - 5].
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HELP
What is the slope of the line?
Answers
Answer: -8/3
Step-by-step explanation:
slope is rise/run or y2-y1/x2-x1
so, the two points are (4,-4), (1,4)
-4-4/4-3= -8/3
Help me please :((((((
Answers
100 keed lol keed lol keed
A parallelogram has four angles. You know that one angle is 96. What is the other three angles
Answers
In a recent year, 32.2% of all registered doctors were female. If there were 53,600 female registered doctors that year, what was the total number of registered
doctors?
Round your answer to the nearest whole number.
Answers
Answer:
166,460 doctors registered.
Step-by-step explanation:
32.2% -------- 53,600 female doctors
100% -------- X
X * 32.2% = 100% * 53,600
X = (100% * 53,600) / 32.2%
X = 166,460 doctors
I’m sorry i need at least twenty letters so pleas tell me
What is
13.1×3.70
Answers
Answer:
44.77
Step-by-step explanation:
13.1x3.70=13.1x3.7
37x131=4477
get back the decmial point 44.77
Petra always keeps her 6 bedrooms in her house clean it takes her 15 minutes to clean a single room how many hours will it take her to clean all 6 bedrooms
Answers
Answer:
90 minutes(1hour 30 minutes)
Step-by-step explanation:
If 1 room=15 minutes
Then 6 rooms= ?
=6×15/1
=90 minutes
=1hour 30 minutes
The midpoint of FG is M(6, 9). One endpoint is F(4, 9). Find the coordinates of the other
endpoint G.
Write the coordinates as decimals or integers.
Answers
Answer:
G= (8,9)
Step-by-step explanation:
What is the area of trapezoid ABCD?
Enter your answer as a decimal or whole number in the box. Do not round at any steps.
units²
Trapezoid A B C D on a coordinate plane with vertex A at negative 3 comma 2, vertex B at 1 comma 5, vertex C at negative 7 comma negative 3, and vertex D at 0 comma negative 2. Angle B is shown to be a right angle.
Answers
Given the coordinates above, the area of the trapezoid is approximately 41. See the explanation below.
What is a Trapezoid?A trapezoid is a quadrilateral with at least one set of parallel sides in American and Canadian English. A trapezoid is known as a trapezium in British and other varieties of English.
For the calculation showing the above solution:
Step 1 - Given:
A = (-3,2)
B = (1, 5) = ⊥
C = (-7, -3)
D = (0.-2)
Step 2 - To get the distance between the points we need to use the formula for Distance between two points which is given as:
d=√((x2 – x1)² + (y2 – y1)²).
Distance of Line AB =
√((1 – (-3))² + (5 – 2)²).
= √[(4)² + (3)²]
= √( 16 + 9)
= √25
AB= 5
Repeat this for BC, CD, DA and we'd get the following
BC = 11.313708498985
CD = 7.0710678118655
DA = 5
Step 3 - From the above structure, [see attached] we then apply the formula for the area of a Trapezoid (Trapezium) which is given as:
A = [(a+b)/2] h
Where a = 5
b = 11.313708498985
h = 5
= [(5+11.313708498985)/2] 5
= 40.7842712475
[tex]\approx[/tex] 41
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Add 6.2 to the difference between 4.1 and 1.9 then divide the result by 3
Answers
Difference: the outcome of subtraction.
Let's just start of with the difference between 4.1 and 1.9, because we need the result of this before we do anything else.
1. 4.1-1.9=2.2
2.2 is the difference of 4.1 and 1.9.
2. It says to add 6.2 next.
6.2+2.2= 8.4
Next we need to divide by 3.
3. 8.4/3=2.8.
4. 2.8 is the answer!!
----------------------------
i think this was simple, so good luck!! much love! <33
let f(x)=x^2+3x and g(x)=2x-1 find each function value f(g(-2))
Answers
The composite result function of f( g(-2) ) in the given functions f( x ) = x² + 3x and g( x ) = 2x - 1 is 10.
What is the composite result function of f( g(-2) ) in the given function?A function is simply a relationship that maps one input to one output..
Given the data in the question;
f( x ) = x² + 3xg( x ) = 2x - 1f( g(-2) ) = ?First, set up the composite result function f( g(x) )
f( x ) = x² + 3x
f( g(x) ) = f( 2x - 1 ) = ( 2x - 1 )² + 3( 2x - 1 )
f( g(x) ) = ( 2x - 1 )² + 3( 2x - 1 )
Simplify
f( g(x) ) = ( 2x - 1 )( 2x - 1 ) + 3( 2x - 1 )
f( g(x) ) = 2x( 2x - 1 ) -1(2x - 1 ) + 3( 2x - 1 )
f( g(x) ) = ( 4x² - 2x - 2x + 1 ) + 3( 2x - 1 )
f( g(x) ) = ( 4x² - 4x + 1 ) + 6x - 3
f( g(x) ) = 4x² - 4x + 1 - 6x - 3
f( g(x) ) = 4x² - 4x + 6x + 1 - 3
f( g(x) ) = 4x² + 2x - 2
Now, replace all the occurrence of x with -2 in the function and simplify.
f( g(-2) ) = 4(-2)² + 2(-2) - 2
f( g(-2) ) = 4×4 - 4 - 2
f( g(-2) ) = 16 - 4 - 2
f( g(-2) ) = 10
The composite result function of f( g(-2) ) in the given functions is 10.
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