3. Use the given information about the polynomial graph to write out the equation.
Degree 5, Roots of multiplicity 2 at x = 3 and x = -2 and a root of multiplicity 1 at x = 4,
y-intercept at (0,12).
Answer:
[tex]f(x)=-\frac{1}{12}(x-3)^2(x+2)^2(x-4)[/tex]
Step-by-step explanation:
The standard form for a polynomial equation in its factored form is:
[tex]f(x)=a(x-p)(x-q)...[/tex]
Where p and q are the zeros and a is the leading coefficient.
We know that the degree of the polynomial is 5.
We are also given roots at x=3 and x=-2. Hence, our factors are (x-3) and (x+2).
These have a multiplicity of two, so we will square them.
We also know that there is a root at x=4. Hence, the factor is (x-4). This has a multiplicity of 1.
Therefore, our polynomial is now:
[tex]f(x)=a(x-3)^2(x+2)^2(x-4)[/tex]
We know that the y-intercept is 12. Therefore, if we substitute in 0 for x, we should get 12 for y. Here, we are solving for our a. Therefore:
[tex]12=a(0-3)^2(0+2)^2(0-4)[/tex]
Evaluate:
[tex]12=a(9)(4)(-4)[/tex]
Evaluate:
[tex]-144a=12[/tex]
Divide both sides by -144:
[tex]a=-1/12[/tex]
Hence, our entire polynomial is:
[tex]f(x)=-\frac{1}{12}(x-3)^2(x+2)^2(x-4)[/tex]
4.
It takes a lady 3 days to wash the windows
inside and out. Her husband can do the job
in 4 days. How fast can they do it together?
PLZ HELP!!!! Explain 72. Determine the value of r so that a line through the points with the coordinates (r, 4) and (-2,3) has
slope 1/4
a. 4.5
b. 6
c. -2
d. 2
9514 1404 393
Answer:
d. 2
Step-by-step explanation:
The point-slope form of the equation for the line can make use of the given slope and point:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
y -3 = 1/4(x +2) . . . . line with slope 1/4 through point (-2, 3)
Filling in the unknown point values, we have ...
4 -3 = 1/4(r +2)
4 = r + 2
2 = r
_____
Alternate solution
The way the question is worded, you seem to be expected to use the slope formula.
m = (y2 -y1)/(x2 -x1)
For the given points and slope, you have ...
1/4 = (3 -4)/(-2 -r)
-2 -r = 4(-1) . . . cross multiply
2 = r . . . . . . . . add r+4 to both sides
Purchased bed for $119.99 bought it at $71.99 the percent difference was 40% or $48.00. How to I write an equation that relates y discount cost to x original cost.
Answer:How was the question asked I bet I could figure it out if you told me that
Step-by-step explanation:
The plumber added an extra $35 to her bill
Answer:
you just add 35 to her bill
Which number is greated 0.3 or -0.7? Explain
Answer:
Step-by-step explanation:
Which number is greater 0.3 or -0.7?
0.3 is greater because it is a positive number. The other one is a negative.
Answer:
0.3 is greater than -0.7
Step-by-step explanation:
If you look at the number line, -0.7 is on the left side of 0, which means is less than 0.
so 0.3 > -0.7
for negative number the bigger is the number, the less is it’s value.
Given
f(x) = 6x^3 +19x²-29x +c where c is a constant
if (x-1) is a factor of f(x),
find value of c
Hence, solve the equation of f(x) =0.
Answer:
[tex]c=4\\x=1, x=\frac{-25+\sqrt{721}}{12},x=\frac{-25-\sqrt{721}}{12}[/tex]
Step-by-step explanation:
See the picture attached
Find the next three terms of each arithmetic sequence.
4. 9, 13, 17, 21, 25, ...
6. 29, 35, 41, 47, ...
5. 4, 0, -4, -8, -12,...
Answer:
(4) 29, 33, 37
(6) 53, 59, 65
(5) -16, -20, -24
Step-by-step explanation:
Find the value of the variable
[tex] \LARGE{ \underline{\underline{ \tt{Required \: answer:}}}}[/tex]
The above quadrilateral is a square because of the marking shown for the equilaterality of sides.
We have,
Side of the square = 13We need to find:
Variable x and y?Solution:
x is the side of the square and y is the diagonal. Hence,
[tex] \large{ \boxed{ \sf{x = 13}}}[/tex]
And for finding the diagonal which can use the Pythagoras theoram where the leg sides (p and b) are the sides of the triangle. Hence,
➝ y = √13² + 13²
➝ y = √338.
[tex] \large{ \boxed{ \sf{y = 13 \sqrt{2} }}}[/tex]
The correct option is Option (D)
☃️[tex] \large{ \purple{ \bf{FadedElla}}}[/tex]
Which of the following pairs of functions are inverses of each other?
Answer:
The answer is (B).
Step-by-step explanation:
A). y = f(x) = 6(x - 2) + 3 ⇔ y = 6x - 12 + 3 ⇔ 6x = y + 9 ⇔ x = [tex]\frac{y+9}{6}[/tex]
g(x) = [tex]\frac{x+9}{6}[/tex] is inverse function of f(x) and ≠ [tex]\frac{x+2}{6}[/tex] - 3
B). y = f(x) = [tex]\frac{5x}{4}[/tex] - 3 ⇔ 4y = 5x - 12 ⇔ x = [tex]\frac{4y+12}{5}[/tex]
g(x) = [tex]\frac{4(x + 3)}{5}[/tex] is inverse of f(x)
What's three digit number closest to 300 using 6, 2, 7, 3
Answer:
326
Step-by-step explanation:
Its hard to explain but you get the idea lol
How many square feet of outdoor carpet will we need for this hole?
Answer:
36 square feet
Step by step explanation:
hope this helps!
What number is 0.001 more than 3.9?
Answer:
3.901
Step-by-step explanation:
Add 0.001 to 3.9.
Answer:
3.901
Step-by-step explanation:
The quadrilateral shown is rotated 90° clockwise about the origin. In which quadrant is the image of the quadrilateral located?
Answer:
Option (2). 1
Step-by-step explanation:
Coordinates of point A, B, C and D are,
A(-4, 4), B(-2, 4), C(-2, 1) and D(-4, 3).
Quadrilateral ABCD when rotated 90° clockwise about the origin,
Rule for the rotation of the vertices,
(x, y) → (y, -x)
Following the rule of rotation coordinates of the image points,
A(-4, 4) → A'(4, 4)
B(-2, 4) → B'(4, 2)
C(-2, 1) → C'(1, 2)
D(-4, 3) → D'(3, 4)
Since all image points have the positive coordinates (x and y coordinates), image quadrilateral A'B'C'D' will be located in 1st quadrant.
Option (2) is the correct option.
Please Help Asap thank you soo much god bless you
1) x ≤ 30
2) 5x + 2x ≥ 14
3) xy ≤ 4
4) y - 5 < 20
Step-by-step explanation:
please mark me as brainlest
how could we graphically visualize the relationshio between the age of a used car and the selling price if a used car
4(3x + 2) = 4(2x + 3) + 4x
Answer:
x = -4
Step-by-step explanation:
4(3x + 2) = 4(2x + 3) + 4x (distribute the 4's on both sides)
12x + 8 = 8x + 12 + 4x (collect like terms)
12x + 8 = 13x + 12 (subtract 12x on both sides)
8 = x + 12 (subtract 12 on both sides)
-4 = x
Hope this helps ya!
solve this expression (4-1/2)*0.6+1.7 show ur work I will give bràinliest
Answer:
3.8
Step-by-step explanation:
Here's how I solved it.
(4-1/2) = 3.5
3.5(0.6) = 2.1
2.1 + 1.7 = 3.8
Lets go through this together!
(4−12)(0.6)+1.7
=72(0.6)+1.7
=2.1+1.7
=3.8
Therefore the answer is 3.8!
If I'm wrong I Apologize May I Have brainliest? <3
10. How many linear feet of cove molding are needed to trim the ceiling of a
12-foot by 16-foot family room?
Answer:
24 look it up on Google and your welcome I hope I'm right good day
how can patterns help me divide multiples of 10?
expand and simply 3(2x+5) - 2(x-4)
Answer:
4x+7
Step-by-step explanation:
6x+15 - 2x-8
Combine like terms
6x-2x=4x
15-8 = 7
4x+7
A pack of cinnamon scented pencils cost $9.00. What is the sales tax rate if the total cost for the pencils with tax is $9.54? _______________% NEED URGENT HELP!!!
well, the pencils are 9 bucks, but they're selling for 9.63, meaning the tax is 0.63 or 63 cents.
now, if we take 9 to be the 100%, what is 0.63 off of it in percentage?
I don’t understand this do any of you do?
Answer:
a reflection across line y, then a translation (1,-5) (right 1, down 5)
Step-by-step explanation:
A(-2,4) → (2, 4) → D(3, -1)
B(-6, 1) → (6, 1) → E(7, -4)
C(-3, 1) → (3, 1) → F(4, -4)
An ant starts walking along a parabola, y(x)=x^2 starting from the point where x=3 He walks until a point where x=3+a where a is a positive number. What is the y-coordinate of the point that he is at now?
plz no bs answers
Answer:
the y co-ordinate > 9
Step-by-step explanation:
I just graphed y = x^2 found the point where the x - axis was 3, found that the y co-ordinate was 9 and if you were to add any positive number the y co-ordinate would only get larger!
Hope this helps!
Abigail (Abby) Boxer, age 45, is a single mother working as a civilian accountant for the U.S. Army. Her Social Security number is 676-73-3311 and she lives at 3456 Alamo Way, San Antonio, TX 78249. Helen, Abby's 18-year-old daughter (Social Security number 676-73-3312), is a dependent child living with her mother, and she does not qualify for the child tax credit due to her age but does qualify for the other dependent credit of $500. Abby received a Form W-2 from the U.S. Department of Defense.
Answer:
Step-by-step explanation:
WHats the question here bud
Jocelyn estimates that a piece of wood measures 5.5 cm. If it actually measures 5.62 cm, what is the percent error of Jocelyn’s estimate?
A. 2.13%
B. 2.18%
C. 12%
D. 46.83%
Answer:
A
okay? Answer A
Juan sells hats and t-shirts for students to wear to athletic events at his school. Yesterday, he sold 23 baseball caps and 20 t-shirts. He earned $200 from t-shirts sales and $287.50 from baseball caps. What is the cost of each baseball cap?
2x+7 the 7 is a what
What do you mean exactly
If angle M is represented by x + 16 and angle G is represented by
X – 40, and angles M and G are complementary, what is the
measure of angle M?
Answer:
the measure of angle M is 73 degrees
Step-by-step explanation:
the sum of complementary angles is 90 degrees. so set up the equation as:
x+16+x-40=90
combine like terms and you get:
2x-24=90
add 24 on both sides and you get:
2x=114
divide by 2 on both sides to isolate x and you get:
x=57
since the equation for angle M is x+16, you substitute 57 for x and you get:
M=57+16
M=73
569,820 divide by 4
569,820 divide by 5
569,820 divide by 10
569,820 divide by 6
569,820 divide by 9
569,820 divide by 3
569,820 divide by 2
and when your done just tell me which one has no remainders (If u tell me the remainders, u get 1 bonus point and that equals........18 POINTS!!)
Answer:
569820/4=142455
569820/5=113964
569820/10=56982
569820/6=94970
569820/9=63313.33333333333333 (remainder)
569820/3=189940
569820/2=284910
Step-by-step explanation: