1. If a polynomial function with rational coefficients has -4 and 8 as roots, it means we can factor this polynomial this way :
(x - (-4))(x-8) = (x+4)(x-8) = x² - 8x + 4x - 32 = x² - 4x - 32
1x² - 4x - 32 is a polynomial function of least degree with rational coefficients that satisifies the given conditions. The leading coefficient here is 1, we call this a monic polynomial.
2. There may be something missing in the question here
3. We can use the factoring techniques to find the roots :
x^3 - 5x² + 9x - 45 let us group x^3 with -5x² and 9x with -45 :
(x^3 - 5x²) + (9x - 45) = x²(x - 5) + 9(x - 5)
We can notice now that there is a common factor : (x-5) this allows us to factor again by (x-5) :
Y = (x-5)(x²+9)
This is the maximum we can do on R, but on C the set of complex we can still factor again.
x² + 9 has a negative discriminant : Δ = b² - 4ac where b = 0 , a = 1, c = 9
Δ < 0, Δ = - 36
Applying the formulas for the roots x1 and x2 we get x1 = -3i, and x2 = + 3i
Y = (x-5)(x-3i)(x+3i)
So the solution is S = {5, 3i, -3i} the three roots of the function.
PLEASE HELP ME!!! jacky starts biking to meet up with her friend. she knows that if she bikes at a speed of 10 mph, she will be 3 minutes late. jacky also know that if she bikes at a speed of 12 mph, she will be there 2 minutes before they agree to meet. how much time does she have left before the appointed time?
Answer:
27s
Step-by-step explanation:
d = distance to rendezvous point in miles
t = time of arrival at 10mph, i.e. 3 mins later than appointed time
10 mph = 10 miles per hour = ¹/₆ miles per min
12 mph = ¹/₅ miles per min
t = d/(¹/₆)
t = 6d
5 min = ¹/₁₂ hr
t - ¹/₁₂ = d/(¹/₅)
t = 5d + ¹/₁₂
Elimination of t:
6d = 5d + ¹/₁₂
d = ¹/₁₂ mi
t = 6(¹/₁₂)
t = ¹/₂ min
Time left to appointed time = ¹/₂ - ³/₆₀
= ¹⁰/₂₀ - ¹/₂₀
= ⁹/₂₀.min → 27 seconds
Answer:
27 min
Step-by-step explanation:
rsm
Henry and his little brother made up a game using coins. They flip the coins towards a cup and receive points for every one that makes it in. Henry starts with 15 points, and his little brother starts with 20 points. Henry gets 3 points for every successful shot, and his brother, since he is younger, gets 2 points for each successful shot. Eventually, the brothers will have a tied score in the game. How many additional shots will each brother have made?
Write a system of equations, graph them, and type the solution.
Answer:
After 5 additional shots, the brothers will have a tied score.
Step-by-step explanation:
find equations
henry:
y-int is 15 because that is the starting number. the slope is 3 because that is how much his points are increasing for every successful shot. we can use this information to form this equation:
y = 3x + 15
brother:
y-int is 20 because that is the starting number. slope is 3 because that is how many points he gets for each successful shot. using this information, we can form the following equation:
y = 2x + 20
--
solve
y = 3x + 15
y = 2x + 20
3x + 15 = 2x + 20
x + 15 = 20
x = 5
--
graph
(just use desmos)
In a certain chemical, the ratio of zinc to copper is 3 to 14. A jar of the chemical contains 630 grams of copper. How many grams of zinc does it contain?
Answer:
135 grams of Zinc
Step-by-step explanation:
zinc:copper
3:14
3/14=x/630
x=135
What is y= 3x +4 on a graph
y = 3x +4
3 is the slope. Rise 3 run 1 or up 3 right 1.
4 is the y-intercept
(2x+y)2-y2 if x=-3 y=4 and z=-5
Answer all of the following questions. 3 Points a question. ALSO NO LINKS!
Is 2 a prime number?
Is 3 a prime number?
Is 11 a prime number?
Is 18 a prime number?
Is 20 a prime number?
Is 27 a prime number?
Answer:
no
yes
yes
no
no
yes
Step-by-step explanation:
a prime number cant be devided by any thing other than itself or one
Answer:
Step-by-step explanation:
Is 2 is 3 is 11 is 18 is 20 is 27
-2.3z = -13.8
I need to show work lol
Here are your answers.
it's made by computer.
- BRAINLIEST answerer
Answer:
z = 6
Step-by-step explanation:
- 2.3z = - 13.8 ( divide both sides by - 2.3 )
z = [tex]\frac{-13.8}{-2.3}[/tex] = 6
Use the information given to find the equation of the line using the point-slope formula (y-y_1)=m(x-x_1)). Then convert your answer to slope-intercept form (y=mx+b).
y-intercept of 2 and (4,-1)
If it's possible please a explanation on how you solved it.
Answer:
y=[tex]-\frac{3}{4}[/tex]x+2
Step-by-step explanation:
y=sx+2;
-1=4s+2;
s=-3/4;
y=[tex]-\frac{3}{4}[/tex]x+2
In a company, 90% of the workers are . If 480 work for the company who aren't , how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
Answer:
4720
Step-by-step explanation:
got it from here so should be right.
The length of a rectangle is 5 more than twice the width. Which equation could represent the area of the rectangle in terms of the width?
Answer:
l=5+2w
Step-by-step explanation:
Since the length is twice the width plus 5, the equation would look like :
l=5+2w
A=lw
w=width
2w+5=length
42=w(2w+5)
42=2w2+5w
2w2+5w-42=0
use the quadratic equation
(-5+√25+336)/4
(-5+√361)/4
(-5+19)/4
14/4=3.5
w=3.5 m
2w+5=12 m
3.5 by 12 rectangle
Factorize 2^x+7 + 2^x+6
Answer:
Step-by-step explanation:
[tex]2^{(x+ 7)} + 2^{(x+ 6 )} = 2^{x} * 2^{7} + 2^{x}*2^{6}\\\\=2^{x} *(2^{7} + 2^{6})[/tex]
[tex]= 2^{x} * 2^{6} ( 2+ 1)\\\\= 2^{x} * 2^{6} * 3[/tex]
Britton rotated trapezoid ABCD 180° on the coordinate plane. If angle B is 20° and angle D is 90°, what is the degree measurement of angle B′?
Group of answer choices
20°
70°
90°
180°
Answer:
20°
Step-by-step explanation:
Rotation is one of 3 basic rigid transformation, it will not change the original shape and size. Therefore angle B' should be still 20°
The degree measurement of angle B′ will be same as angle B that is 20°. Then the correct option is A.
What is a transformation of a shape?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object.
From before the refers to the object's initial condition, and Picture, after transformation, refers to the object's ultimate structure and location.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
If the geometry is rotated, then there is no change in anlges.
Britton rotated trapezoid ABCD 180° on the coordinate plane. If angle B is 20° and angle D is 90°.
The degree measurement of angle B′ will be same as angle B that is 20°.
Then the correct option is A.
More about the transformation of the shape link is given below.
https://brainly.com/question/27224339
#SPJ5
combine like the like terms
34w - 4g + 4g - 36w
the answer is -2w (i have the write at least 20 words to dont worry about this)
Answer:
-2w
Step-by-step explanation:
Like terms have same variable.
34w - 4g + 4g - 36w = 34w - 36w - 4g + 4g
= - 2w + 0 = -2w
6 bananas cost the same as 4 oranges. 3 lemons cost the same as 1 orange. 2 limes cost the same as 1 lemon. How many limes cost the same as 1 banana?
If 6 bananas cost the same as 4 oranges. 3 lemons cost the same as 1 orange, one lime costs the same as half of one banana.
Let's assume the cost of one banana is represented by "B" and the cost of one orange is represented by "O". Based on the given information:
6 bananas cost the same as 4 oranges: 6B = 4O
3 lemons cost the same as 1 orange: 3L = 1O
2 limes cost the same as 1 lemon: 2L = 1O
Now, we need to find the cost of one lime in terms of bananas:
From equation 3, we can rewrite it as: L = (1/2)O
Substitute the value of O from equation 2 into the above equation: L = (1/2) * 3L
Now, we have the cost of one lime in terms of lemons. From equation 2, we know 3 lemons cost the same as 1 orange, so we can rewrite it as: L = (1/2) * (1/3)O
Now, substitute the value of O from equation 1 into the above equation: L = (1/2) * (1/3) * 6B
L = (1/2)B
Therefore, one lime costs the same as half of one banana.
To learn more about proportion click on,
https://brainly.com/question/15259359
#SPJ4
Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
______
[tex] \: [/tex]
[tex] \tt5 - 6x = 8x + 17[/tex]
[tex] \longmapsto \tt \: x = \frac{5 - 17}{ - 6 + 8} [/tex]
[tex] \longmapsto \tt \: x = \frac{ - 12}{8 - 6} [/tex]
[tex] \longmapsto \tt \: x = \frac{ - 12}{ 2} [/tex]
[tex] \longmapsto \tt \: x = \boxed{ \blue{ - 6}}[/tex]
-x = 3
HELP ASAP MATHEMATICS
Answer:
x = -3
Step-by-step explanation:
Answer:
x=-3
Step-by-step explanation:
You can just do +x on both sides so: 0=3+x and then -3 on both sides: -3=x.
Assignment
and graphs.
Which of the following properly describe "slope"? Select all that apply.
✓x
y2yi
x₂-x
x₂-x
2 -->
run / rise
rise / run
ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run)
Tutori
M
Answer:
the first option is for sureee
3x - 5 = 7x + 11
x =
Answer:
[tex]3x - 5 = 7x + 11 \\ 7x - 3x = - 11 - 5 \\ 4x = - 16 \\x = - \frac{16}{4} \\ \color{yellow} \boxed{x =-4}[/tex]
Answer:
x= -4
Step-by-step explanation:
3x-5=7x+11
3x-5+5=7x+11+5
3x=7x+11+5
3x=7x+16
3x-7x=7x+16-7x
-4=7x+16-7x
-4x=16
divided each side by -4
x= 16 over -4
divide them and you get -4.
Profit is revenue minus cost. Find the profit if the cost of producing x units of a commodity is
130+25x and the revenue for selling them is x(88-X).
Answer:
[tex]-x^2+63x-130[/tex]
Step-by-step explanation:
When you put that into an equation:
[tex]x(88-x)-(130+25x)[/tex]
Next, solve.
[tex]\mathrm{Apply\:the\:distributive\:law}:\quad \:-\left(a+b\right)=-a-b[/tex]
[tex]-\left(130+25x\right)=-130-25x[/tex]
[tex]=x\left(88-x\right)-130-25x[/tex]
[tex]x(88-x):88x-x^2[/tex]
[tex]=88x-x^2-130-25x[/tex]
[tex]88x-x^2-130-25x =-x^2+63x-130[/tex]
Therefore, the profit if the cost of producing [tex]x[/tex] units is [tex]-x^2+63x-130[/tex], and there may be restrictions depending on conditions.
HELP ME PLEASE RNNN FASTTT
Answer:
The first three are functions
Step-by-step explanation:
4th one fails the Vertical line test.
At Crescent High School, 108 students plan on going to an in-state college and 63 students plan on going to an out-of-state college. What is the ratio of students planning on going to an in-state college to students planning on going to an out-of-state college?
A.
12:7
B.
108:1
C.
7:12
D.
1:108
Explanation:
The ratio we want to find can be thought of in the form in:out
We list the number of "in-state" people first followed by the "out-of-state" people next. A colon separates the two values. So we have the initial ratio of 108:63
Divide both parts by the GCF 9
108/9 = 1263/9 = 7The ratio 108:63 fully reduces to 12:7 meaning there are 12 in-state students for every 7 out-of-state students. The order is important because 7:12 would be incorrect and imply we had 7 in-state vs 12 out-of-state.
Pls help need asap stressing need in 10 mins I will mark as brainliest !! :(
Answer:
C or the min of f(x) is greater
Step-by-step explanation:
2,8 is the vertex which higher than the vertex of g(x)
1/2 divided by (-3) please help
Answer:
-1/6
Step-by-step explanation:
apply fraction rule to get 1/2(-3)
Multiply the numbers to get 1/-6
apply fraction rule to move negative to make
-1/6
1/2 divided by (-3) = -1/6 or -0.1666666667.
What type of angle are 2 and 6?
Answer:
CORRESPONDING ANGLES
Step-by-step explanation:
Answer:
Corresponding angles i believe.
Step-by-step explanation:
Y-2=-3(x-7) written in standard form
4- (-z/3) = 8 Solve for z
Answer:z=12
Step-by-step explanation:
help please
f − –7/3 = 3
Answer:
f=2/3
Step-by-step explanation:
2 . 3² - 1 = blank please hurry up and help
fill in the blank with the letter of the description that best matches the term for the verb porter, match the subject pronoun with the correct form of the verb. i'll mark Brainliest if the answers are correct.
A. portons
B. porte
C. portez
D. portes
E. portent
FILL IN THE BLANK
je ____
tu ____
nous ____
vous ____
ils ____
Step-by-step explanation:
je........porte
tu.......portes
nous.......portons
vous........portez
ils......portent
A classroom has 12 girls for every 4 boys. What is the ratio of boys to total students?
Question 7 options:
4 : 16
12 : 4
4 : 12
12 : 16
Answer:
I don't understand please elaborate more your given question.
Step-by-step explanation:
