Using the factor theorem, the equation for q is:
[tex]q(x) = 4(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, ..., x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2)...(x - x_n)[/tex]
In which a is the leading coefficient.
In this problem:
Passes through the origin, so x = 0 is a zero, that is [tex]x_1 = 0[/tex].x = i is a zero, and thus, it's conjugate also is, that is, x = -i, hence [tex]x_2 = i, x_3 = -i[/tex]x = 7 - i is a zero, and thus, it's conjugate also is, that is, x = 7 + i, hence [tex]x_4 = 7 - i, x_3 = 7 + i[/tex]Then, the equation is:
[tex]q(x) = a(x - 0)(x - i)(x + i)(x - 7 + i)(x - 7 - i)[/tex]
[tex]q(x) = ax(x^2 - i^2)((x-7)^2 - i^2)[/tex]
Considering that [tex]i^2 = -1[/tex]
[tex]q(x) = ax(x^2 + 1)(x^2 - 14x + 50)[/tex]
[tex]q(x) = ax(x^4 - 14x^3 + 51x^2 - 14x + 50)[/tex]
[tex]q(x) = a(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
q(-1) = -520 means that when [tex]x = -1, q = -520[/tex], and this is used to find a.
[tex]q(x) = a(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
[tex]-520 = a(-1 - 14 - 51 - 14 - 50)[/tex]
[tex]130a = 520[/tex]
[tex]a = \frac{520}{130}[/tex]
[tex]a = 4[/tex]
Hence, the equation is:
[tex]q(x) = 4(x^5 - 14x^4 + 51x^3 - 14x^2 + 50x)[/tex]
A similar problem is given at https://brainly.com/question/24380382
please help me to solve problems
Step-by-step explanation:
4a)
the principle of similar triangles : they have the same angles.
and we do not forget : the sum of all angles in a triangle is always 180 degrees.
a = 180 - 65 - 45 = 70 degrees
b = 65 degrees
c = 70 degrees
b)
same principles.
x = 58 degrees
y = 52 degrees
z = 180 - 58 - 52 = 70 degrees
c)
same principles.
plus the fact that complementary angles around a point on one side of a line are also together 180 degrees.
x = 85 degrees
y = 180 - 40 - 85 = 55 degrees
z = 180 - 85 = 95 degrees
d)
again same principles.
y = 2x (as these 2 angles correspond to each other among the 2 similar triangles).
the angle POQ is again complementary with 87 degrees,
POQ = 180 - 87 = 93 degrees
x + y + 93 = x + 2x + 93 = 180
3x = 87
x = 29 degrees
y = 2x = 2×29 = 58 degrees
The angles in a quadrilateral are 103.8° , 77° , 111.4° and p°. Calculate the value of p.
Answer: 67.8°
Step-by-step explanation:
A quadrilateral's interior angles always add up to 360°.
An equality statement can be set up to satisfy this rule:
103.8+77+111.4+p=360
Collect known values
292.2+p=360
Isolate and solve for p
292.2 (-292.2) +p=360 (-292.2)
p=67.8
Answer:
68.6
Step-by-step explanation:
hello sir / mam!
as the opposite sides of quadrilateral should be 180°
111.4+p=180°
p=180-111.4
p=68.6°
therefore the value of p = 68.6°
hope it helps!
To indirectly measure the distance across a river, Nolan stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Nolan draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.
The length of PR to the nearest foot is 198.94 feet
Find the diagram attached
From the diagram, the triangle PRE and POC are similar triangles.
Let PR = x
Based on similarity theorem;
PR/RE = PR+RO/OC
x/135 = (x+140)/230
Cross multiply
230x = 135(x+ 140)
230x = 135x + 18,900
230x - 135x = 18,900
95x = 18900
x =18900/95
x = 198.94
Hence the length of PR to the nearest foot is 198.94 feet
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The height of a cylinder is 4 millimeters.The circumference of its base is 10 pi mm
[tex]\\ \sf\longmapsto C=10\pi mm[/tex]
[tex]\\ \sf\longmapsto 2\pi r=10\pi mm[/tex]
[tex]\\ \sf\longmapsto 2r=10[/tex]
[tex]\\ \sf\longmapsto r=5mm[/tex]
h=4mm[tex]\\ \sf\longmapsto Volume=V=\pi r^2h[/tex]
[tex]\\ \sf\longmapsto V=\pi (5)^2(4)[/tex]
[tex]\\ \sf\longmapsto V=\pi 25(4)[/tex]
[tex]\\ \sf\longmapsto V=100\pi mm^3[/tex]
volume is 100pi mm³.
What is volume?In mathematics, volume is the space taken by an object.
Here, given that,
The height of a cylinder is 4 millimeters.=h
The circumference of its base is 10 pi mm=2r*pi
So, we get,
r=5
Volume =pi*r²*h
=100pi mm³
Hence volume is 100pi mm³.
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HELP ME PLEASE PLEASE PLEASE
Answer:
#1) 3 different roots, total 6#2) 3 different roots, total 9#3) 3 different roots, total 4Step-by-step explanation:
#1The roots are:
x - 3 = 0 ⇒ x = 3, multiplicity 2x + 1 = 0 ⇒ x = -1, multiplicity 32x + 5 = 0 ⇒ x = -2.5#2The roots are:
x = 0, multiplicity 3x + 2 = 0 ⇒ x = -2x - 4 = 0 ⇒ x = 4, multiplicity 5#3The roots are:
x² - 1 = 0 ⇒ (x + 1)(x - 1) = 0 ⇒ x = -1, x = 1x² + 4x + 4 = 0 ⇒ (x + 2)² = 0 ⇒ x + 2 = 0 ⇒ x = -1, multiplicity 2Rationalize the denominator.
– 5x4
✓4x +7
The question is asking us to make the denominator a rational function by finding a way to remove the square root without changing the value of the overall function.
We can do this by multiplying the denominator and numerator by the √(4x + 7), since multiplying a root term by that root term = the number being rooted (√x × √x = x).
- 5x⁴ × √(4x + 7) = (-5x⁴)(√(4x + 7))
√(4x + 7) √(4x + 7) 4x + 7
Josiah skateboards from his house to school 3 miles away. It takes him 36 minutes.
How many minutes will it take Josiah to skateboard to his friend Sebastian’s house, which is 2 1/2
miles from school, if he travels at the same rate that he did from his house to school?
In the box below, type the number that goes in the blank.
Using the speed - distance relationship, the number of minutes it will take Josiah to cover a distance of 2.5 miles is 30 minutes.
Calculating Josiah's speed :
Speed = (distance ÷ time)Speed = (3 ÷ 36) = 0.08333 miles per minute.
Time taken to cover a distance of 2.5 miles :
Time taken = (Distance ÷ Speed)Time taken = (2.5 ÷ 0.08333) = 30 minutes
Therefore, it will take 30 minutes for Josiah to cover a distance of 2.5 Miles
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3. Which phrase best describes the function of the ATP molecule?
1. Carries energy
2. Destroy energy
3. absorbs energy
4. none of the above
Answer:
1.) Carries energy
Step-by-step explanation:
A good summary of an ATP molecule is a molecule that transfers energy between cells... meaning it carries energy from cell to cell. Furthermore, energy cannot be destroyed, and cannot be absorbed, only changed and transformed. This leaves us with two options, (1. Carries energy, and 4. None of the above). Since we already have a basic understanding of what an ATP molecule does, we can confidently determine that the correct answer is that an ATP molecule can best be described as carrying energy.
The temperature at 6pm is
54℉. The temperature at 10pm
is 42℉. How many degrees did
the temperature fall?
Answer:
12
Step-by-step explanation:
Answer:
12°F??¿??¿????¿??!??????????
1. (3n+2)(n+3)
this is multiplying binomial by a binomial
Using the distributive property with FOIL:
(3n + 2) ( n + 3)
3n² + 9n + 2n + 6
3n² + 11n + 6
It is 12:49 what time it will be 30 minutes from now
Answer:
01:19 PM
Step-by-step explanation:
if its 12:49 then in 30 minutes it'll be 1:19pm
because
in 11 minutes I'll be 1pm and then 30-11= 19
so
1pm + 19 mins = 1:19pm
Hope this helped you- have a good day bro cya)
Answer:
1:19 pm
Hope you have an amazing day!
Solve for t:
t + 7 = 21
A: t= 28
B: t= 14
C: t= -28
D: t= -14
t + 7 = 21
---Subtract 7 from both sides
t + 7 - 7 = 21 - 7
t = 14
Hope this helps!! :)
Answer:
B) t = 14
Step-by-step explanation:
Solve this one following the linear equations beow agebricaly.Express your answer in simplest form.3(6x-4)=24
G.
G
7 cm
8 cm
-
Find volume
Step-by-step explanation:
The volume = [tex](\frac{22}{7} )(7^{2} )(8)[/tex]
= 1232
please give me a brainliest answer
A student graphed f(x) = x and g(x) = -5f(x) + 2 on the same coordinate grid. Which statement describes how the graphs of f(x) and g(x) are related?
The graph of f(x) is translated 5 units up to create the graph of g(x).
The graph of g(x) is translated 2 units down and is less steep than the graph of f(x).
The graph of f(x) is translated 5 units down to create the graph of g(x).
The graph of g(x) is translated 2 units up and is steeper than the graph of f(x).
Answer:
ME TOO
Step-by-step explanation:
Function transformation involves changing the position of a function.
The relationship between f(x) and g(x) is (d) The graph of g(x) is translated 2 units up and is steeper than the graph of f(x).
The functions are given as:
[tex]\mathbf{f(x) = x}[/tex]
[tex]\mathbf{g(x) = -5f(x) + 2}[/tex]
Substitute x for f(x) in g(x)
[tex]\mathbf{g(x) = -5x + 2}[/tex]
The +2 in [tex]\mathbf{g(x) = -5x + 2}[/tex] means that, g(x) is gotten by translating f(x) up by 2 units.
The -5 in [tex]\mathbf{g(x) = -5x + 2}[/tex] means that, g(x) has a steeper slope.
Hence, the correct option is (d)
Read more about function transformations at:
https://brainly.com/question/18213787
Find the slope of (2 , -7 ) and ( -1 , 6 )
A. 4
B. -6
C. -1/6
D. 6
Answer:
-13/3
Step-by-step explanation:
y2 - y1 / x2 - x1
6 - (-7) / -1 - 2
13 / -3
= -13/3
Hello !
Answer:
[tex] \boxed{\sf None \: of \: the \: options \text{:} \: \: m =- \dfrac{13}{3}} [/tex]
Step-by-step explanation:
The slope m of a line passing through two points can be calculated using the following formula:
[tex] \sf m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] \\ [/tex]
Let (x₁ , y₁) = (2 , -7)
Let (x₂ , y₂) = (-1 , 6)
Substitute these values into our formula:
[tex] \sf m =\dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{6 - (-7) }{-1 - 2 } = \dfrac{13}{-3}\\ \\ \implies \boxed{\sf m = -\dfrac{13}{3}} [/tex]
Have a nice day ;)
A scrapyard had 200 tons of recycled steel. They sold 15 tons per day for several days. If there are 80 tons left at the scrapyard, how many days have passed?
Please explain fully.
Answer:
8 days
Step-by-step explanation:
200-80= 120
120 ÷ 15 = 8 days
Answer:
SAME AS WHAT HE SAYS
Step-by-step explanation:
Solve for b. Express your answer as an integer or integers or in simplest radical form. -165= -3-6b^3
Fastest and correct wins brainliest
How many solutions are there to this equation?
4(x-5)=3x+7
A. 1
B. infinitely many
C. 0
Answer:
1
Step-by-step explanation:
4x-20=3x+7
x=27
what is the slope of a line parallel to the line whose equation is 2x + y = 3?
Step-by-step explanation:
Here is the answer to the question
Answer:
-2/1
Step-by-step explanation:
Rewrite equation in point-slope form
y=-2x+3
in y=mx+b, m= the slope
The slope of the line is -2/1
Any lines parallel to this line will have the same slope
<1 and <2 are complementary angles. m<1=2x+34, and m<2=2x+8. find the measure of each angle
Step-by-step explanation:
2x+34=2x+8=90°
4x+42=90°
-42. -42
4x=. 48
÷4. ÷ 4
x= 12 ( divide both sides by 4)
( you need to substitute x)
2(12)+34
measure of angle 1 is equal to 58
2(12)+8
measure of angle 2 is equal to 32
someone help it’s about gradients etc check photo please!! (The coordinates of K and L are (-8, -5)
Answer:
[tex]i) \frac{2}{3} [/tex]
Step-by-step explanation:
[tex] = \frac{y {}^{1} - y {}^{2} }{x {}^{1} - x {}^{ {}^{2} } } [/tex]
[tex] = \frac{ - 5 - ( - 1)}{ - 8 - ( - 2) } [/tex]
[tex] = \frac{ - 4}{ - 6} [/tex]
[tex] = \frac{2}{3} [/tex]
2×[3+2×(10-3)]=
Pa helppppp
Step-by-step explanation:
2 × [3 + 2 × (10 - 3)] =
2 × (3 + 2 × 7) =
2 × (3 + 14) =
2 × 17 = 34
Answer:
34
Step-by-step explanation:
2 × [3 +2 × (10 - 3)]=
2 × (3 + 2 × 7)=
2 × ( 3 + 14)=
2 × 17=
34.
Solve 7!
(Need help with this in Math!)
What number is subtracted from 2.2 which gives you 0.8765
Answer:
1.3235
Step-by-step explanation:
If you take 2.2 and subtract .8765 from it you get 1.3235. If you take that and subtract it from 2.2 you get .8765.
ill give brainlest pls
Answer:
$5.00
Step-by-step explanation:
Answer:
5.00
Step-by-step explanation: this question was already answered but i need the points :p
HELP ASAP PLEASE I BEG TOU
Answer:
The graph below
Step-by-step explanation:
Start at -2 on the y-axis and go up 1/2 every space you go on the x-axis
Hope this Helps
solve for X : 3x²=5x
⇒ 3x² - 5x = 0
⇒ (3x - 5) · x = 0
3x - 5 = 0
x = 0
x = 0, 5/3
Given the overlapping triangles shown at the right. Notice the parallel segments. Find x. 6 х 9 MathBils.com 20
Using the principle of parallel lines, the value of x in the given triangle is calculated to be 8
The smaller triangle can be expressed as :
Side / base = 6/x ----(1)The larger triangle can be expressed as :
Side / base Side = 6+9 = 15 15/20 - - - - - (2)Equating (1) and (2) :
6/x = 15 / 20
15x = 20 × 6
15x = 120
x = 120 / 15
x = 8
Therefore, the value of x in the triangle is 8.
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determine the H.C.F of 12,48,60
Answer:
HCF(12, 48, 60) = 12
Step-by-step explanation:
HCF of 12, 48, 60 is 12 since 12 is largest number which exactly divides all the numbers
Highest common factor (HCF) of 12, 48, 60 is 12.
Hope this helped you- have a good day bro cya)