By the factor theorem,
[tex]3x^2+5x+7=3(x-u)(x-v)\implies\begin{cases}uv=\frac73\\u+v=-\frac53\end{cases}[/tex]
Now,
[tex](u+v)^2=u^2+2uv+v^2=\left(-\dfrac53\right)^2=\dfrac{25}9[/tex]
[tex]\implies u^2+v^2=\dfrac{25}9-\dfrac{14}3=-\dfrac{17}9[/tex]
So we have
[tex]\dfrac uv+\dfrac vu=\dfrac{u^2+v^2}{uv}=\dfrac{-\frac{17}9}{\frac73}=\boxed{-\dfrac{17}{21}}[/tex]
The value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].
What is quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is[tex]ax^{2} +bx+c=0[/tex], where a and b are the coefficients, x is the variable, and c is the constant term.
What is the sum and product of the roots of the quadratic equation?If [tex]ax^{2} +bx+c = 0[/tex] be the quadratic equation then
Sum of the roots = [tex]\frac{-b}{a}[/tex]
And,
Product of the roots = [tex]\frac{c}{a}[/tex]
According to the given question.
We have a quadratic equation [tex]3x^{2} +5x+7=0..(i)[/tex]
On comparing the above quadratic equation with standard equation or general equation [tex]ax^{2} +bx+c = 0[/tex].
We get
[tex]a = 3\\b = 5\\and\\c = 7[/tex]
Also, u and v are the solutions of the quadratic equation.
⇒ u and v are the roots of the given quadratic equation.
Since, we know that the sum of the roots of the quadratic equation is [tex]-\frac{b}{a}[/tex].
And product of the roots of the quadratic equation is [tex]\frac{c}{a}[/tex].
Therefore,
[tex]u +v = \frac{-5}{3}[/tex] ...(ii) (sum of the roots)
[tex]uv=\frac{7}{3}[/tex] ....(iii) (product of the roots)
Now,
[tex]\frac{u}{v} +\frac{v}{u} = \frac{u^{2} +v^{2} }{uv} = \frac{(u+v)^{2}-2uv }{uv}[/tex] ([tex](a+b)^{2} =a^{2} +b^{2} +2ab[/tex])
Therefore,
[tex]\frac{u}{v} +\frac{v}{u} =\frac{(\frac{-5}{3} )^{2}-2(\frac{7}{3} ) }{\frac{7}{3} }[/tex] (from (i) and (ii))
⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{\frac{25}{9}-\frac{14}{3} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{25-42}{9} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} = \frac{\frac{-17}{9} }{\frac{7}{3} }[/tex]
⇒ [tex]\frac{u}{v} +\frac{v}{u} =\frac{-17}{21}[/tex]
Therefore, the value of [tex]\frac{u}{v} +\frac{v}{u}[/tex] is [tex]\frac{-17}{21}[/tex].
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2/7 DIVIDED by 3=please help me
Answer:
2/21.
Step-by-step explanation:
[tex]\frac{2}{7}[/tex] ÷ 3 = (2 / 7) * (1 / 3) = (2 * 1) / (7 * 3) = 2 / 21 = 0.0952380952.
Hope this helps!
Write 3 as 3/1
Now you have 2/7 / 3/1.
When you divide by a fraction change the divide to multiply and flip the second fraction over
Now you have 2/7 x 1/3 now multiply top by top and bottom by bottom to get
2/21
Instructions: Find the missing side. Round your answer to the
nearest tenth
Answer:
73.2
Step-by-step explanation:
you can find the answer using trigonometry relationship
sin31°=41/x
x=41/sin31°. sin31° is approximately equal to 0.56
x=41/0.56
x=73.2
Amanda is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges $111 and allows unlimited mileage. Company B has an initial fee of $55 and charges an additional $0.70 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m.
Answer:
For mileages higher than 80 miles Company A will charge less than Company B
Step-by-step explanation:
Hi, to answer this question we have to write an inequality:
Company A charges $111 and allows unlimited mileage.
Company A =111
Company B has an initial fee of $55 and charges an additional $0.70 for every mile driven
Company B = 55+0.70m
Where m is the number of miles.
Company A has to charge less than Company B
a<b
111 < 55+0.70m
Solving for m
111-55 < 0.70 m
56 < 0.70m
56/0.70 < m
80 < m
For mileages higher than 80 miles Company A will charge less than Company B
Find the square root of the following using division method . iv) 36360
Answer:
190.684
Step-by-step explanation:
To find the square root of 36360, we place a bar over the numbers that we want to find their square root in pairs
, 1 [tex]\dot{3}[/tex] [tex]\overline{63}[/tex] [tex]\overline{60}[/tex]
, 1 1
2, 9 2 [tex]\overline{63}[/tex]
9 261
38, 0 2 60
0 0
.
380, 6 26000
, 6 22800
3806, 8 320000
, 8 304480
38068, 4 1552000
,4
Which gives 190.684
3 63 60
We select the divisor to be the largest number which when squares will be equal to the largest number on the left which is 1
We have 1 * 1 = 1
We subtract it from the 3 to get 2
We add the 1's to get 2
We bring down the next pair which is 63 to form the next dividend, 263
We look for a number which will multiply itself to get 263, which is 9, we then have 29 × 9 = 261
We continue till we arrive at the vertical paired numbers which is 190.684.
Choose the equivalent system of linear equations that will produce the same solution as the one given below 4x-y=-11 2x+3y=5
Answer: x = -2 , y = 3
Step-by-step explanation:
4x-y=-11
2x+3y=5
Solve 4x-y=-11 for y
Add -4x to both sides
4x-y+-4x=-11+-4x
-y=-4x-11
Divide both sides by -1
-y/-1=-4x-11/-1
y=4x+11
Substitute 4x+11 for y in 2x +3y=5
2x+3y=5
2x+3(4x+11)=5
Simplify both sides of the equation
14x+33=5
Add -33 to both sides
14x+33+-33=5+-33
14x=-28
Divide both sides by 14
14x/14=-28/14
x=-2
Substitute -2 for x in y= 4x+11
y=4x+11
y=(4)(-2)+11
Simplify both sides of the equation
y=3
what is the equation of the following line (10 -2) (0 0) a. y= -5x b. -x c. y= 5x d. -1/5x e. y= x f. y= 1/5x
Answer:
Step-by-step explanation:
(0+2)/(0-10)= 2/-10 = -1/5
y - 0 = -1/5(x - 0)
y = -1/5x
solution is D
The total capacity of a water bottle and a mug is 7/8 litre. The capacity of the mug is 1/4 litre. How much greater is the capacity of the water bottle than the mug.
Answer:
The capacity of the water bottle is 2.5 times greater than the mug.
Step-by-step explanation:
We know that the capacity of a water bottle and a mug is 7/8 litre:
[tex]bottle+mug=\frac{7}{8}[/tex]
But we also now that the mug's capacity is 1/4 litre, so the equation above becomes:
[tex]bottle + \frac{1}{4}=\frac{7}{8}[/tex]
Now we want to know how much greater the capacity of the bottle than the mug is. To do this we need to know first what's the capacity of the bottle.
So, we would have:
[tex]bottle=\frac{7}{8}-\frac{1}{4} \\\\bottle=\frac{7}{8}-\frac{2}{8}\\\\\\bottle=\frac{5}{8}[/tex]
Therefore the bottle has a capacity of 5/8 liter while the mug has a 2/8 liter one.
To know how much greater is the capacity of the water bottle than the mug we need to divide these two quantities, so we have:
[tex]\frac{5}{8}[/tex]÷[tex]\frac{2}{8}[/tex][tex]=\frac{5}{8}[/tex]×[tex]\frac{8}{2}[/tex][tex]=\frac{5}{2}=2.5[/tex]
Therefore the capacity of the water bottle is 2.5 times greater than the mug.
If f(x) = |x| + 9 and g(x) = –6, which describes the value of (f + g)(x)? (f+g)(x)≥3 for all values of x (f+g)(x)≤3 for all values of x (f+g)(x)≤6 for all values of x (f+g)(x)≥6 for all values of x
Answer:
(f + g)(x)≥3 for all values of xStep-by-step explanation:
Given the expressions f(x) = |x| + 9 and g(x) = –6, sine f(x) contains the absolute value of a variable x, this absolute value can be negative and positive. Therefore f(x) can be expressed in two forms as shown;
f(x) = x+9 and f(x) = -x+9
If f(x) = x+ 9 and g(x) = -6
(f + g)(x) = f(x)+ g(x)
(f + g)(x) = x+9+(-6)
(f + g)(x) = x+9-6
(f + g)(x) = x+3
Similarly, if f(x) = -x+ 9 and g(x) = -6
(f + g)(x) = f(x)+ g(x)
(f + g)(x) = -x+9+(-6)
(f + g)(x) = -x+9-6
(f + g)(x) = -x+3
(f + g)(x) = 3-x
In both expresson, we have bith x to be positive and negative, hence we can write the value of resulting x as an absolute value as shown;
(f + g)(x) = |x|+3
This shows that (f + g)(x)≥3 for all values of x
help on radical functions
Answer:
A
Step-by-step explanation:
How to do this question plzzz
Hi king,
Let's split it into two prisms.
1st prisim volume:[tex]V_{1}=5cm*10cm*3cm\\V_{1} =150cm^{3}[/tex]
2nd prisim volume:[tex]V_{2}=5cm*10cm*(9cm-5cm)\\V_{2}=5cm*10cm*4cm\\V_{2} =200cm^{3}[/tex]
The prism in the picture:
[tex]V_{final}=150cm^{3} +200cm^{3} \\V_{final}=350cm^{3}[/tex]
Have a good day.
What is the value of f(-1) ?
Answer:
f(-1) = 12
Step-by-step explanation:
Using the graph for f(x) let x=-1
Find the y value when x= -1
f(-1) = 12
pls answer asap i need this answer quick plus the full explanation #4
Answer:
Her Verticle ramp support was 5.5 ft tall.
Step-by-step explanation:
In this type of question, you would need to use the saying "soh cah toa".
Soh Cah Toa is a saying that people use for Sin, Cosine, and tagent. Each of those mean
Sine: opposite/hypotenuse Cosine: Adjacent/hypotenuse and Tagent: Opposite/Adjacent
In this specific question to figure out how tall or high her support is or needs to be have to 20 degree angle off the ground, you will need to use Sin which is opposite over Hypotenuse or x/16
To find the answer in your calculator you would do:
Sin(20)=x/16
First thing you do is the get the x on one side by itself so you would multiply 16 on both sides giving you:
16 × Sin(20)= x
You would then follow to put Sin(20) in your calculator giving you 0.34202014332
After that you multiply that number by 16
5.47232229321
Rounding to the nearest tenth you get answer:
5.5
Helppppp❤️ Please please
Answer:
B and D
Step-by-step explanation:
I think this is the answer
Help please!!! Thanksss
Answer:
6:00 p.m.
hope this helps :)
The area of a rectangular deck, in square meters, is given by the polynomial 40p2 + 24p.
The deck is 8p meters wide.
a) Find the polynomial that represents the length of the deck.
b) Find the polynomial that represents the perimeter of the deck. PLEASE HELP ASAP
Answer:
a. 5p+3
b. 26p + 6
Step-by-step explanation:
a.
Area = length × width
40p² + 24p = length × 8p
Factorise out 8p from both sides
8p(5p + 3) = length × 8p
Divide both sides by 8p
5p + 3 = length
b.
Perimeter = 2(length + width)
"" = 2(5p+3 + 8p)
"" = 2(13p + 3)
"" = 26p + 6
A data-entry clerk spends $86 per week for food. This is 20% of his weekly income. What is the weekly income? Show work please :
Answer:
$430
Step-by-step explanation:
Let the weekly income be x
Money spent on food= $86
% of weekly income spent on food = 20
20% of weekly income in terms = 20/100 * x = x/5
This, income is equal to $86 as given
thus,
x/5 = 86
x = 86*5 = 430
Thus, weekly income is $430.
PLEASE help me with this question!
Answer:
[tex]44^\circ[/tex]
Step-by-step explanation:
The angle measuring [tex]y^\circ[/tex] is formed by two secants intersecting at an exterior point.
The measure of that angle is half the difference between the big intercepted arc and the little intercepted arc.
y = 1/2 (m arc FKB - m arc CGJ)
Plug in the values you know.
56 = 1/2 (156 - m arc CGJ)
Multiply both sides by 2 to clear the fraction.
112 = 156 - m arc CGJ
Subtract 156.
-44 = - m arc CGJ
44 = m arc CGJ
The measure of the little intercepted arc is [tex]44^\circ[/tex].
Given a graph for the transformation of f(x) in the format g(x) = f(kx), determine the k value.
ту
g(x)
f(x)
k= -4
k= -1/4
k= 1/4
k= 4
ASAP!!!!
Answer: C
1/4
Step-by-step explanation:
Given a graph for the transformation of f(x) in the format g(x) = f(kx),
This means that for every value of x, f(x) will take the value it would have had at kx, that is, the graph of f(x) is stretched by a factor of 1/k in the direction of positive x-direction.
Therefore, the value of k will be 1/4.
Answer:
k=4
Step-by-step explanation:
In the standard coordinate plane, how many units separate the points (5, -1) and (5, 12).
Answer:
13
Step-by-step explanation:
Put -1 and 12 in the absolute value form and add them together. You'll get 13.
Number of units separate the points is 13 units.
Distance between two Coordinate:Given that;
Coordinate of first point = (5 , -1)
Coordinate of second point = (5 , 12)
Find:
Number of units separate the points
Computation:
Number of units separate the points = √(x1 - x2)² + (y1 - y2)²
Number of units separate the points = √(5 - 5)² + (-1 - 12)²
Number of units separate the points = √(-13)²
Number of units separate the points = 13 units
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Help! Pls pls pls! Fast!
it is transformed [tex]|x|[/tex] function. moved down by and right by 1 unit,
so $y=|x-1|-1$
What is the volume of the following
rectangular prism?
Answer: 13.5 units³
Step-by-step explanation:
[tex]\dfrac{5}{2}\times \dfrac{27}{5}\quad =\dfrac{27}{2}\quad =\large\boxed{13.5\ units^3}[/tex]
What is the effect of the graph of the equation y=3/7x + 6 is changed to y=3/7x -2?
A. The line is shifted right 8 units
B. The line is shifted down 8 units
C. The line is shifted left 8 units
D. The line is shifted up 8 unit
Answer:
down 8 units
Step-by-step explanation:
going from +6 to -2 goes down 8 units
Answer:
B. The line is shifted down 8 unitsStep-by-step explanation:
f(x) + n - shift the graph n units up
f(x) - n - shift the graph n units down
f(x + n) - shift the graph n units to the left
f(x - n) - shift the graph n units to the right
==============================================
We have y = 3/7x + 6. It has been changed to y = 3/7x - 2.
y = 3/7x + 6 → f(x) = 3/7x + 6
f(x) - 8 = (3/7x + 6) - 8 = 3/7x + 6 - 8 = 3/7x - 2
Can someone help me on this finance problem?
PLSSS HELPFind the next term of the sequence. 1, 8, 27, 64, ..
Answer:
125
Step-by-step explanation:
So you can see that the sequence is all of the perfect cubes so knowing that the next perfect cube we have to find is 5's perfect cube which is 125.
Answer:
192
Step-by-step explanation:
HELPPPPP PLEASEEEE!!!!
Which system of inequalities represents region Z?
Answer:
Hey there!
The two lines in this graph are: y=-1/5x+2, and y=3x-2
Since y=-1/5x+2 is a dotted line, we know that we use the < or > symbols.
Since y=3x-2 is a straight line, we use the ≤ and ≥ symbols.
Thus, for area z, we have y<-1/5x+2, and y≥3x-2
Hope this helps :)
given the equation below which of the following shows the quadratic formula correctly applied? 3x^2-4x-12=0
[tex] {3x}^{2} - 4x - 12 = 0[/tex]
[tex]a = 3[/tex]
[tex]b = - 4[/tex]
[tex]c = - 12[/tex]
Formula:
[tex] \boxed{x = \dfrac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }[/tex]
Replacing:
[tex]x = \dfrac{ -( - 4) \pm \sqrt{ { (- 4)}^{2} - 4(3)( - 12)} }{2(3)} [/tex]
Option: C).
Write each function in standard form. Determine the x-intercepts of the function.
Y=-4(x+2)(x+3)
Answer:
X Intercept (-2,0), (-3,0) and Standard form y = -4x^2 - 20x - 24
Step-by-step explanation:
To write a polynomial in standard form, simplify, and then arrange the terms in descending order.
y = ax^2 + bx + c
y = (−4x−8) (x+3)
Expand (−4x−8) (x+3) using the FOIL Method
y = −4x ⋅ x − 4x ⋅ 3 − 8x−8 ⋅ 3
Simplify and combine like terms.
y = −4x^2 − 20x − 24
Hope this can help
A Pythagorean spiral is constructed by drawing right triangles on the hypotenuse of the other right triangles. Start with a right triangle in which each leg is 1 unit long. Use the hypotenuse of that triangle as one leg of a new triangle and draw the other leg 1 unit long. A spiral has been started below, continue the pattern until a spiral with 12 triangles is formed. 1. Determine the Tangent of the angle at the centre of the spiral for each of the first five triangles. 2. Use this pattern to predict the tangent of the 100th triangle.
Answer:
The angle is determined by dividing 360 by the number of vertexes that it took to complete the circle. The tangent of the 100th triangle would be the same respectively.
Step-by-step explanation:
I remember learning this in kindergarten.
What is the domain of F(x) = In (x)?
A: all real numbers except 0
B: all real numbers
C: all real numbers less than 0
D: all real numbers greater than 0
Answer:
the answer is B
Step-by-step explanation:
In terms of symbols, we would write [tex]x > 0[/tex]
The natural log function, or any log function, is not defined for x = 0 or any negative x value.
Consider the form [tex]\log_b(y) = x[/tex] which is equivalent to [tex]y = b^x[/tex] and notice how the y value slowly approaches zero but never actually gets there. That is one way to see why the inputs of any log function must be larger than 0.
Solve the system of equations below x - y = 5 2x - 3y = 4
Answer:
x=11 y=6
Step-by-step explanation:
making x the subject in the first equation we get
x=y+5 put that in the second equation we also get
2(y+5)-3y=4
2y+10-3y=4
-y=4-10
-y=-6
y=6 use that to also find x from the equation x=y+5 we get
x=6+5
x=11
therefore x=11 y=6