The polynomial in standard form is equal to 2 · x³ + 12 · x² - 64.
How to derive a cubic equation
Cubic equations have three roots. In this problem we need to derive a cubic equations whose three real roots (r₁, r₂, r₃) and leading coefficient (a) are given. The procedure consists in substituting on factor form of a cubic polynomial and expanding the resulting expression until standard form is obtained.
First, substitute on the factor form of the cubic equation:
y = 2 · (x - 2) · (x + 4)²
Second, expand the polynomial until its standard form is found:
y = 2 · (x - 2) · (x² + 8 · x + 16)
y = 2 · (x³ + 8 · x² + 16 · x - 2 · x² - 16 · x - 32)
y = 2 · (x³ + 6 · x² - 32)
y = 2 · x³ + 12 · x² - 64
The polynomial is equivalent to 2 · x³ + 12 · x² - 64.
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Please Help 2
find (f/g)(m)iff(m)=8m3+5m2-32m-20 and g(m)=8m+5
Diving the polynomial expression f(m) = 8m^3 + 5m^2 - 32m - 20 and g(m) = 8m + 5, as (f/g)(m) using long division gives m^2 - 4
What is long division ?Long division refers to a way of dividing large numbers including polynomials
performing the long division (f/g)(m) gives
divisor 8m + 5
dividend 8m^3 + 5m^2 - 32m - 20
quotient m^2
multiplication (quotient and divisor) = 8m^3 + 5m^2
subtraction (dividend - result of multiplication) = - 32m - 20 new dividend = - 32m - 20
divisor 8m + 5
dividend - 32m - 20
quotient -4
multiplication (quotient and divisor) = - 32m - 20
subtraction (dividend - result of multiplication) = 0
new dividend = 0
The quotient is then added as
m^2 - 4
The second option is the correct option
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I need answer asap thank you
The measure of ∠QTS = 58°
Given; A triangle QPR
PQ = PR
this means that ∠ Q = ∠ R
and QR = QT this means ∠ R = ∠ T
And ST ║ QR
and QT is the transversal
From the above mentioned information we can conclude that
∠QTS = ∠TQR -------------- 1
Thus since ∠ Q = ∠ R
by using angle sum property of triangle we can conclude that
∠ Q + ∠ R = 116 [ exterior angle sum property ]
2 ∠ Q = 116
∠ Q = 58°
this means ∠ TQR = 58°
And from 1 we know that this angle is equal to angle QTS
Thus ∠QTS = ∠TQR = 58°
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You deposit $500 into a savings account that earns interest annually. The function g(x) = 500(1.06)x can be used to find the amount of money in the savings account, g(x), after x years. What is the range of the function in the context of the problem?
ℝ
[500, ∞)
[0, 500]
[0, ∞)
Omar deposited d dollars into a savings account y years ago. ... following expressions could be used to determine the zeros of the function f (x) when f (x).
Step-by-step explanation:
If 8 g of a radioactive substance are present initially and 3 yr later only 4 g remain, how much of the substance will be present after 7 yrs?
Determine if the line segment YX is tangent to circle Z. 30 points
Answer:
XY is tangent to circle Z
Step-by-step explanation:
You want to know if segment XY, measuring 3.6 units, is tangent to circle Z at point X. Segment YZ has length 1.8 units outside the circle, which has radius 2.7 units.
Pythagorean relationIf the triangle XYZ is a right triangle, then we have ...
XY² +XZ² = YZ²
3.6² +2.7² = (1.8 +2.7)²
12.96 +7.29 = 20.25 . . . . . true
Segment XY is a tangent.
Secant relationIf segment YZ is extended across the circle, the lengths of the segments from Y to the circle intersection points are 1.8 and (1.8 +2·2.7) = 7.2. The relation between the secant and the "tangent" will be ...
3.6² = (1.8)(7.2) . . . . . true
This means XY is a tangent.
216. Factor and then calculate the value of the expression
a) a² + ab with a = 6.6, b = 3.4;
b) x2 - xu at x = 0.5, y = 2.5;
c) —5a² — 5ah at a = 4, x = -3
Answer:
a) 66, b) - 1, c) - 20Step-by-step explanation:
Solve as below
a) a² + ab with a = 6.6, b = 3.4;
a² + ab = a(a + b) = 6.6(6.6 + 3.4) = 6.6(10) = 66b) x² - xu at x = 0.5, y = 2.5;
x² - xu = x(x - u) = 0.5(0.5 - 2.5) = 0.5(- 2) = - 1c) -5a² - 5ah at a = 4, h = -3;
-5a² - 5ah = - 5a(a + h) = - 5(4)(4 - 3) = - 20(1) = - 20Answer:
a) 66b) -1 c) -20Step-by-step explanation:
a) a² + ab = ?
→ (6.6)² + (6.6 × 3.4)
→ 43.56 + 22.44
→ 66
So, the answer is 66.
b) x² - xu = ?
→ (0.5)² - (0.5 × 2.5)
→ 0.25 - 1.25
→ -1
So, the answer is -1.
c) -5a² - 5ah = ?
→ -5(4)² - 5(4 × -3)
→ (-5 × 16) - (5 × -12)
→ -80 + 60
→ -20
So, the answer is -20.
When point F
is reflected in the line y = x, the image is located at F"(-7, 1).
The coordinates of F' when reflected in the line y=x is F'(1,-7)
Given:
When point F is reflected in the line y = x, the image is located at F"(-7, 1).
The x-coordinate and y-coordinate are reversed when a point is reflected over the line y = x. The x-coordinate and the y-coordinate switch places and become negated if you reflect over the line y = -x (the signs are changed). The point is on the line y = x. (y, x).
so the point F"(-7, 1) after reflection changes to:
F'(1,-7)
Hence we get the value of F' as (1,-7).
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ax+by=cd
solve for b
Answer:
b=(cd-ax)/y
Step-by-step explanation:
b=(cd-ax)/y
Select the equations of the line that goes through the point 6,-2 and is perpindicular to the line y+2=-2/5(x-10) .
A. y=-2/5x+2
B. y=5/2x-17
C. 5x-2y=34
D. 2x+5y=2
E. y+2=-2/5(x-6)
F. y+2=5/2(x-6)
y + 2 = 5/2 (x - 6) ; 5x-2y=34 ; y=5/2x-17 is the equations of the line that goes through the point (6,-2) and is perpendicular to the line y+2=-2/5(x-10), Hence the correct options are B, C and F.
What is equation of the line?The standard forms of the equation of a line are:
Slope-intercept form:
y = mx + c
Where m indicates the slope of the line and c is the y-intercept
Intercept form:
x/a + y/b = 1
General form of the equation of the straight line, i.e. Ax+By+C = 0
x/(-C/A) + y/(-C/B) = 1
where a = -C/A and b = – C/B
Normal form:
The equation of the line whose length of the normal from the origin is p and the angle made by the normal with the positive x-axis is given by α is given by:
x cos α+y sin α = p
Given,
Point = (6,-2) = (x2,y2)
Equation of line = y+2=-2/5(x-10)
General equation of the line = y - y1 = m ( x-x1 )
After comparing we get,
Slope of the given line = -2/5
As we know both the lines are perpendicular to each other so, product of their slopes must be equal to -1.
m1 × m2 = -1
-2/5 × m2 = -1
We get m2 = 5/2
So the equation of the line having slope 5/2 and passing through (6,-2) is:
y - y2 = m2 ( x-x2 )
y -(-2) = 5/2 (x - 6)
y + 2 = 5/2 (x - 6)
Hence, we get equation of the line as y + 2 = 5/2 (x - 6) .
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Please help me with these sorry for how many there are
Answer: 19.2, 1.7, 15.93, 0.0512
Step-by-step explanation:
We can multiply these straight across but the trick with decimals is that your answer needs to have the same decimal place distance as what you are multiplying. In the first question, we go one decimal place. In the second, we go two decimal places. In the fourth, we go four decimal places.
p=(-3,7); m=-1 graph line containing the point p and having slope m.
The equation of the line is x+y-4=0.
What is an equation?
A formula known as an equation uses the equals sign (=) to express how two expressions are equal.
Main Body:
we know that one point form of a line is
y-y₁= m(x-x₁) , where m= slope
now given is a point (-3,7) and m=-1
y-7 =(-1)(x+3)
x+y-4=0
Hence the answer is x+y-4 =0
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three sides of quadrilateral are the same length,g q. The length of the fourth side is 7 inches. The perimeter of the quadrilateral is 40 inches. write and equation that represents the situation.
The situation can be represented using the equation 3g + 7 = 40
How to determine the equation that represents the situation?From the question, we have the following parameters that can be used in our computation:
Length of three sides = g
Length of the fourth side = 7
Perimeter = 40
The perimeter of a quadrilateral is the sum of the sides of the shape
This means that
P = sum of the 4 sides
So, we have
P = g + g + g + 7
Evaluate
P = 3g + 7
Rewrite as
3g + 7 = 40
Hence. the equation that represents the situation is 3g + 7 = 40
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What is the quotient of 30 and 0.08
Answer:
30 divided by 0.08 will get you 375
Step-by-step explanation:
Find the solutions of the quadratic equation −x^2 + 3x − 3 = 0
The coordinates of the endpoints of
KL
are K(
–
16,10) and L(
–
9,
–
11). Point M is on
KL
and divides it such that KM:LM is 4:3.
What are the coordinates of M?
Write your answers as integers or decimals.
The coordinates M along the directed line segment is (-12, -2)
How to find the coordinates of the point along the directed line segment?The points are given as:
K = (-16, 10)
L = (-9, -11)
The ratio on the segment can be represented as;
KM : LM, m : n = 4 : 3
So, we have the coordinates of the point M that lies along the directed line segment to be
M = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)
So, we have:
M = 1/(4 + 3) * (4 * -9 + 3 * -16, 4 * -11 + 3 * 10)
Evaluate
M = 1/7 * (-84, -14)
Evaluate
M = (-12, -2)
Hence, the coordinates of the point M is (-12, -2)
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What is the value of X? x(x² - 3x - 40) = 0
please show me how u solve it
Answer: x = 0, 8, -5
Step-by-step explanation:
We are trying to solve what value we substitute x into to get the value of 0. We have x outside of (x² - 3x - 40), and we can set that equal to 0. That will be one value of x because we are still left with (x² - 3x - 40). To solve this, we can factor it out into (x-8)(x+5). Set each equal to 0, (x-8) = 0 which leaves us with x = 8, and (x+5) =0, which leaves us with x = -5.
What is the slope-intercept form of the equation of the line shown in the graph?
The equation in slope intercept form is y= (-3/4)x + 95.
What is Linear Function?An equation can be represented by a linear function. The standard form for the linear equation is:
y= mx+b , for example, y=x+4.
Where: m= the slope.
It can be calculated for Δy/Δx.b= the constant term that represents the y-intercept. For the given example: m=1 and b=4.
It is important to inform that the standard form for the linear equation can be called slope-intercept form.
For writing a linear equation, you need two points. From the given graph, it is possible to extract some points, such as: (20,80), (60,50). Then, you should replace the known points in the slope-intercept form (y=mx+b).
For the point (20,80), you can write 80=m*20+b. And for the point (60,50), you can write 50=m*60+b.
Thus, you have:80=20m+b (1)50= 60m +b (2)For solving the previous system, you have to multiply the equation 1 by -1.
Thus,-80=-20m-b (1)50= 60m +b (2)
After that, sum equations 1 and 2.-80+50 = -20m+60m-30=40mm=-30/40m=-3/4
Now, you have y= (-3/4)* x+b.
For finding coefficient b, you should use one of the given points. For example:
(20,80).
y= (-3/4)*x+b for (20,80)80
= -3/4*(20) +b 80
= - 60/4+bb=80 + 60/4b=(320+60)/4b=380/4b
=95
Therefore, the equation in slope intercept form is y= (-3/4)*x + 95.
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find the volume, of the box that is 3ft, 4ft, 6ft
4.
Consider the following amount of energy
used for three different activities:
. 1 minute of walking uses
25 kilojoules of energy
A (4
• 1 minute of jogging uses 84 kilojoules
of energy
1 minute of swimming uses
50 kilojoules of energy
a) How many more kilojoules of energy
would you use in an hour of jogging
than an hour of swimming?
b) To the nearest tenth, how many
minutes of walking would you have to
do to burn up the 1,130 kilojoules in a candy bar
In given word problem ,
a) 2040 more kilojoules of energy would you use in an hour of jogging than an hour of swimming .
b) 45 minutes 2 seconds of walking would you have to do to burn up the 1,130 kilojoules in a candy bar.
What is word problem ?
Our extensive collection of math word problems ranges from addition, subtraction, multiplication, and division to more specialised operations. Mathematical questions that are written as one or more sentences and ask students to use their mathematical understanding to solve problems from "real-life" situations are known as word problems. As a result, for kids to understand the word problem, they need to be familiar with the terminology that goes along with the mathematical symbols that they are already used to.
Here the given ,
=> 1 minute walking = 25 kilojoules
=> 1 minute jogging = 84 kilojoules
=> 1 minute swimming = 50 kilojoules.
a) 1 hour = 60 minutes.
1 hour jogging = 60*84 = 5040 kilojoules.
1 hour swimming = 60*50 = 3000
Then , => 5040-3000=2040 kilojoules.
Therefore 2040 more kilojoules of energy would you use in an hour of jogging than an hour of swimming .
b) x minute of walking = 1130 kilojoules.
=> 25*x=1130
=> x = 1130/25 = 45minutes 2 seconds.
Therefore 45 minutes 2 seconds of walking would you have to
do to burn up the 1,130 kilojoules in a candy bar.
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The perimeter of an ICU ward, that is rectangular in shape, is 258 feet. The width is 37 feet less than the length. Find the dimensions of this ward.
Find Length(ft) and Width(ft)
The dimensions of the rectangle is 83 feet x 46 feet
What is the Perimeter of a Rectangle?
The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P = 2 ( Length + Width )
Given data ,
The perimeter P of the rectangle = 258 feet
Let the length of the rectangle be = L
Let the width of the rectangle be = W
And , The width is 37 feet less than the length. ,
So , W = L - 37
Perimeter P = 2 ( Length + Width )
Substituting the values of L and W in the equation , we get
Perimeter P = 2 ( L + L - 37 )
2 ( L + L - 37 ) = 258
( L + L - 37 ) = 129
2L - 37 = 129
Adding 37 on both sides , we get
2L = 166
Divide by 2 on both sides , we get
Length L of the rectangle = 83 feet
Substituting the value of L in equation ,we get
W = L - 37
Width W of the rectangle = 46 feet
Therefore , Length = 83 feet and Width = 46 feet
Hence , the dimensions of the rectangle is 83 feet x 46 feet
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Complete: (Round your answers to the nearest cent.) picture Method Purchased Cost Recovery Class Recovery Year Cost Recovery MACRS July 20 $ 5,000 7 6 A MACRS Nov. 5 $ 11,000 20 13 B
The completion of the MACRS annual cost recovery on a straight-line basis is as follows:
Method Purchased Cost Recovery Recovery Cost
Class Year Recovery
MACRS July 20 $ 5,000 7 6 A = $833.33
MACRS Nov. 5 $ 11,000 20 13 B = $846.15
What is the MACRS straight-line method?Ordinarily, the MACRS (modified accelerated cost recovery system) depreciation method is the tax-allowed method that ensures that larger deductions for depreciation expense or cost recovery are made in the beginning years and lower deductions for later years.
However, the same deductions are made each year when the straight-line method is used.
The depreciation expense using the MACRS straight-line method is computed by dividing the asset's cost by the recovery year.
Method Purchased Cost Recovery Recovery Cost
Class Year Recovery
MACRS July 20 $ 5,000 7 6 A = $833.33 ($5,000/6)
MACRS Nov. 5 $ 11,000 20 13 B = $846.15 ($11,000/13)
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The next model of a sports car will cost 13.6% less than the current model. The current model costs $42,000. How much will the price decrease in dollars? What
will be the price of the next model?
Answer:
36,288
Step-by-step explanation:
Can anyone help me with this, I need an accurate answer also if possible. -thanks
Answer:
y=x-7
Step-by-step explanation:
we know the y intercept is -7 since when x was 0 g(x) is -7
We write it in slope intercept form which is y=mx+b
m- slope
b- y- intercept
To find slope we do y2-y1/x2-x1
-5+7/2-0
2/2
1
1 is the slope so we just keep it X on the equation and the equation will be
y=x-7
Hopes this helps please mark brainliest
Solve. 4h+8=9h-7 step by step
Answer:
h=3
Step-by-step explanation:
4h+8=9h-7
subtract 4h
8=5h-7
add 7
15=5h
divide 3
h=3
Lorena chooses a golf ball from the bucket at random 4 more times and 3 of the golf balls are blue. what is an experimental probability of choosing a blue golf ball based on Lorena's trials?
The experimental probability of choosing a blue golf ball based on Lorena's trials is 0.75.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true
In this case, Lorena chooses a golf ball from the bucket at random 4 times and 3 times, he picked blue balls.
The probability of picking a blue ball will be:
= Number of times a blue ball was picked / Total number of trials
= 3/4
= 0.75
The probability is 0.75.
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Answer:
60%
Step-by-step explanation:
i actually hope this helps!
Find m/1 and m/2
1
95°
2
m<1 =
m<2=
Answer: 85
Step-by-step explanation:
Does the compound event consist of two mutually exclusive events?
Two dice are rolled. The sum of the dice is a 3 or a 9.
Probability = number of desired event occurrences/number of events in sample space = 9/36 = 1/4
What is meant by probability?Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 signifying impossibility and 1 expressing certainty.
A compound event is made up of two separate events.
Here is a table of probable sums of two die rolls. Die 1 and Die 2 values are listed along the side and top. The figures are roughly near the middle. The sum of Die 1 = 2 and Die 2 = 2 is 4, for example.
Die 2
Die1 1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
Rolling two dice yields 6 * 6 = 36 possible outcomes, or 36 possible sums. There are 36 occurrences in the sample space.
Looking at the table, a 3 or a 9 happens as the sum 9 times, resulting in 9 of the 36 potential occurrences having a sum of 3 or 9.
Probability = number of desired event occurrences/number of events in sample space = 9/36 = 1/4
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290 to 490 percent increase how much did it increase
answer the answer is 200
Step-by-step explanation:
490-290
Larry's tuition for last semester was $5510. If he paid $6080 this semester, his tuition increased by
% (round to the nearest tenth of a percent).
His tuition was increased by 10.34%
What is meant by percentage?A quantity or ratio stated as a fraction of 100 is known as a % in mathematics (from the Latin per centum, "by a hundred").
The Latin word per centum, which means "hundred" or "by the hundred," is the source of the word "percent." The Italian phrase per cento, which means "for a hundred," gradually shrank to become the symbol for "percent," which is now used globally. It finally vanished totally. The word "per" was frequently shortened to "p." Two circles and a horizontal line made up the "cento," which is how the contemporary "%" symbol is now represented.
Given, Larry's tuition for last semester was $5510
% increase= (6080-5510)/5510
=0.10344
=0.10344*100
=10.34%
His tuition was increased by 10.34%
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what does d = math help please ......
Answer:
d = -5
Step-by-step explanation:
[tex]\frac{4}{5}d + 3 = -2 -\frac{1}{5}d\\ \\ \frac{4}{5}d + \frac{1}{5} d = -3 -2\\\\\frac{4+1}{5}d = -5\\\\ \frac{5}{5} d = -5\\\\d = -5[/tex]
Check:
[tex](\frac{4}{5} )(-5) + 3 = (-2) - (\frac{1}{5})(-5)\\\\(\frac{-20}{5} ) + 3 = -2 - (\frac{-5}{5} ) \\\\-4 + 3 = -2 + 1\ = -1[/tex]
