Answers
Related Questions
Learning Task 1: Write and answer the following in your answer sheet
1. Evaluate the following polynomials in your answer sheet.
f(x) = x4 – 7x2 + 2x - 6
x=1
b. f(x) = 10x3 + 4x2 - 5
x = -3
f(x) = x4 + 5x3 - 2x + 3
a.
at
at
C.
find (2))2
2. Factor each polynomial completely using any method
(x + 1)(x2 – 5x + 6)
b. (x2 - * - 6)(x2 + 6x + 9)
x3 + 3x2 - 4x - 12
a.
C.
LABAR
Answers
Answer:
Evaluating Polynomials:
a. f(1) = -10
b. f(-3) = -239
c. f(2)² = 3125
Factoring Polynomials:
a. (x + 1)(x² - 5x + 6) = (x + 1)(x - 3)(x - 2)
b. (x² - x - 6)(x² + 6x + 9) = (x - 3)(x + 2)(x + 3)(x + 3)
c. x³ + 3x² - 4x - 12 = (x + 3)(x - 2)(x + 2)(x - 2)(x + 2)
A polynomial can be evaluated and factored by long division, factoring and synthetic division methods.
1. Evaluate polynomials
[tex]\mathbf{f(x) = x^4 - 7x^2 + 2x - 6}[/tex]
Substitute 1 for x
[tex]\mathbf{f(1) = 1^4 - 7(1)^2 + 2(1) - 6}[/tex]
[tex]\mathbf{f(1) = 1 - 7 + 2 - 6}[/tex]
[tex]\mathbf{f(1) = -10}[/tex]
[tex]\mathbf{f(x) = 10x^3 + 4x^2 - 5}[/tex]
Substitute -3 for x
[tex]\mathbf{f(-3) = 10(-3)^3 + 4(-3)^2 - 5}[/tex]
[tex]\mathbf{f(-3) = -270 + 36 - 5}[/tex]
[tex]\mathbf{f(-3) = -239}[/tex]
[tex]\mathbf{f(x) =x^4 + 5x^3 - 2x + 3}[/tex]
Substitute 2 for x
[tex]\mathbf{f(2) =2^4 + 5(2)^3 - 2(2) + 3}[/tex]
[tex]\mathbf{f(2) =16 + 40 - 4 + 3}[/tex]
[tex]\mathbf{f(2) =55}[/tex]
Square both sides
[tex]\mathbf{f(2)^2 =3025}[/tex]
Hence, the results of evaluating the polynomials are [tex]\mathbf{f(1) = -10}[/tex], [tex]\mathbf{f(-3) = -239}[/tex] and [tex]\mathbf{f(2)^2 =3025}[/tex]
2. Factor the polynomials
[tex]\mathbf{(x + 1)(x^2 - 5x + 6)}[/tex]
Expand
[tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x^2 - 2x - 3x + 6) }[/tex]
Factorize
[tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x(x - 2) - 3(x - 2) )}[/tex]
Factor out x - 2
[tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x - 3)(x - 2) }[/tex]
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9)}[/tex]
Expand
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = (x^2 +2x - 3x - 6)(x^2 + 3x +3x + 9)}[/tex]
Factorize
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = [x(x +2) - 3(x + 2)][x(x + 3) +3(x + 3)]}[/tex]
Factor out x + 2 and x + 3
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = [(x - 3) (x + 2)][(x + 3)(x + 3)]}[/tex]
Remove square brackets
[tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = (x - 3) (x + 2)(x + 3)(x + 3)}[/tex]
[tex]\mathbf{x^3 + 3x^2 - 4x - 12}[/tex]
Factorize
[tex]\mathbf{x^3 + 3x^2 - 4x - 12 = x^2(x + 3) - 4(x + 3)}[/tex]
Factor out x + 3
[tex]\mathbf{x^3 + 3x^2 - 4x - 12 = (x^2 -4) (x + 3)}[/tex]
Apply the difference of two squares
[tex]\mathbf{x^3 + 3x^2 - 4x - 12 = (x -2)(x+2) (x + 3)}[/tex]
Hence, the results of factoring the polynomials are [tex]\mathbf{(x + 1)(x^2 - 5x + 6) =(x + 1)(x - 3)(x - 2) }[/tex], [tex]\mathbf{(x^2 - x - 6)(x^2 + 6x + 9) = (x - 3) (x + 2)(x + 3)(x + 3)}[/tex] and [tex]\mathbf{x^3 + 3x^2 - 4x - 12 = (x -2)(x+2) (x + 3)}[/tex]
Read more about polynomials at:
https://brainly.com/question/11536910
5x - 3 (x+3) = what to have infinitely many solutions
Answers
Answer: 1/4
Step-by-step explanation: I think that’s the answer! i’m sorry i’m in 8th fe are
yoo i need help... pls
Answers
Answer:
-9x⁹y⁵Step-by-step explanation:
Simplifying:
(-8x⁴y³)*(2x⁵y²) + 7x⁹y⁵ =-16x⁴⁺⁵y³⁺² + 7x⁹y⁵ =-16x⁹y⁵ + 7x⁹y⁵ =(-16 + 7)x⁹y⁵ =-9x⁹y⁵Step-by-step explanation:
-9x⁹y⁵Simplification↑Is 9 correct if now what is it?
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Answer:
4 + 5 = 9
girls: 4/9 (680)
boys 5/9 (850)
total 1530
there are 850 boys and 680 girls.
A cable company charges $70 per month for cable service to existing customers.
a. Write a linear equation representing the relationship between x, the number of months of service, and y, the total amount paid in dollars by an existing customer.
b. For new customers, there is an additional one-time $100 service fee. Repeat the previous problem for new customers.
c. When the two equations are graphed in the coordinate plane, how are they related to each other geometrically?
50 points to answer it. I need help it's the last question of my homework.
Answers
Answer:
a: y=70x
b: y=70x+100
c: They are parallel to each other, with equation b's line being 100 dollars above equation a.
Step-by-step explanation:
They both have the same slope (70), but new customers will have a y intercept of 100 because of the one-time fee.
c)
Step-by-step explanation:
everybody use their cable difference so when you graph out the amount of cable which come with data the previous customers data and cable rates would be different then the new customers and the company should be able to tell that . but it still does happen today
Use the properties of exponents to simplify the expression: 2532
25
3
2
Question 11 options:
A)
125
B)
25
C)
625
D)
5
Question 12 (5 points)
Solve the inequality: (x −3)12+ 2 ≥4
(
x
-
3
)
+
2
≥
4
Question 12 options:
A)
x ≥ 35
B)
x ≥ 11
C)
x ≥ 7
D)
x ≥ 13
Answers
Question
Use the properties of exponents to simplify the expression: [tex]25^{\frac{3}{2}}[/tex]
Answer:
[tex]25^{\frac{3}{2}} = 125[/tex]\
Step-by-step explanation:
Given
[tex]25^{\frac{3}{2}}[/tex]
Required
Simplify
[tex]25^{\frac{3}{2}}[/tex]
Apply the following law of indices
[tex]a^{\frac{m}{n}} = (a^m)^{\frac{1}{n}}[/tex]
So, the expression becomes
[tex]25^{\frac{3}{2}} = (25^3)^{\frac{1}{2}}[/tex]
Express [tex]25^3[/tex] as 15625
[tex]25^{\frac{3}{2}} = (15625)^{\frac{1}{2}}[/tex]
In indices: [tex]a^{\frac{1}{2}} = \sqrt a[/tex]
So, we have:
[tex]25^{\frac{3}{2}} = \sqrt{15625[/tex]
[tex]25^{\frac{3}{2}} = 125[/tex]
Which table of values represents a linear function? A B Y y y 0 7 8 7 1 1 3. --- 2 5 2 -1 4 3 3 -4 7 2 С D 2 y y 3 -2 =7 3 5 -1 -5 2 7 1 0 1 1 9 3 4 -3
Answers
Answer:
it c for sure
Which situation can be represented by the equation y=74x?
Answers
What do you "mean"?
Directions: Convert the following equations from standard form to slope-intercept form.
(10 points)
14. 4x + y = -1
15. 5x - 2y = 14
16. 10x - 2y = -6
17. 8x + y = 12
18. 6x - 10y = 20
Answers
y= 5/2x-7
y=5x+3
y= -8x +12
y= 3/5x-2
If you are good at math please dm me on ig 14lies, or twitt binderelluh1
Answers
Answer:
Okay
Step-by-step explanation:
Interest calculated only on the principle is
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This is urgentttttt!!!!!!
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Answer:
Part A: a. the point 3 units to the left of 7
Part B: b. -4
Step-by-step explanation:
Part A: The expression can be simplified into 7 - 3, and when you subtract a number, you go left on the number line, so the point 3 left of 7
Part B: 7 - 3 = 4, and to get to 0 from 4, you need to subtract 4 or add -4
hurry ASAP 100 points !!!!
Answers
Answer:
I am pretty sure 1=constant independednt, 2 is inconsistent and three is constant dependent
Step-by-step explanation:
I am not positive tho..
Answer:
the first one is y=-5+2x
The Carousel Creators constructed a model of their latest Amusement Park Carousel. What is the scale using 1 cm if the model Carousel houses have a height of 7 cm and the actual Carousel horses are 3.5 meters?
a) 0.5 meters
b) 3.5 meters
c) 0.5 centimeters
d) 3.5 centimeters
Answers
Answer:
c
Step-by-step explanation:
5(-6 + 4)=..................
Answers
Answer:
-10
Step-by-step explanation:
5(-6 + 4)
=-30+20
=-10
Answer:
-10 or just 10 in general
Step-by-step explanation:
System of Equations : Money
Damian has been saving coins he finds on the ground for several months. So far he has found 37 coins that are either pennies or nickels. The combined value of his found pennies and nickels currently is $1.09. What is the system of linear equations, written using standard form, represents the situation if Damian found p pennies and n nickels.
Answers
Answer:
18 nickles 19 pennies
Step-by-step explanation:
value of 1 penny=$0.01
value of 1 nickle=$0.05
0.01p+0.05n=1.09
p+n=37
there are two methods for this system
I.substitution
p+n=37
p=37-n
we replace p in the first relation
0.01(37-n)+0.05n=1.09
0.37-0.01n+0.05n=1.09
0.04n=0.72
n=18 nickels
p+18=37
p=37-18=19 pennies
II.reduction
0.01p+0.05n=1.09
p+n=37
we multiply the second equation by 100
p+5n=109
p+n=37
we calculate the difference between the two relations
p-p+5n-n=109-37
4n=72
n=18
p+18=37
p=19
need help asap please
Answers
Answer:
y=3/4x+1
Step-by-step explanation:
If you rearrange the given equation to slope intercept form, you'll find the slope to be -4/3. If a line is perpendicular to another it'll have the opposite reciprocal for a slope, meaning the new line's slope would be 3/4. If you plug 3/4 and the given point's x and y value into slope intercept form you'll find the b value or y intercept to be 1. Since you now have the slope and the y intercept you can determine the equation to be y=3/4x+1. Hope this helps!
How to Rewrite the expression 4(13-10) using distributive property of multiplication over subtraction
Answers
Answer:
52-40
Step-by-step explanation:
distribute 4 to 13 and 10
put the subtraction sign back in
you will have amazing luck if you help me
Answers
Answer:
b
Step-by-step explanation:
because of the value of the area
b is the answer
there are 56 tulips in a flowerbed. the ratio of tulips to daffodils is 3:5. how many tulips and how many daffodils are there in a flowerbed? (Pls answer correctly)
Answers
Answer:
96
Step-by-step explanation:
3x + 5x = 8x.
8 altogether --> 3 tulips and 5 daisies
16 altogether --> 6 tulips and 10 daisies
24 altogether ---> 9 tulips and 15 daisies
etc
etc
48 altogether --> 12 tulips and 20 daisies
96 altogether --> 15 tulips and 25 daisies
Answer:
55 : 56.6666666667
Step-by-step explanation:
3:5 ÷ 3 = 1 : 1.66666666667 + 55= 56.6666666667
Find the value of x and the measure of the angle labeled 16X".
112
64°
48°
16x
Answers
Answer:
[tex]16x = 48\:(vertically\:opposite\:angles)\\ \boxed{x = 3} \\ angle \: measure \: is \: \boxed{48°}[/tex]
A. is the right answer.Answer:
A
Step-by-step explanation:
Evaluate g(t) for the given values of t.
g(t)=|17-t|
A)g(11)=
B)g(12)=
Answers
Answer:
Step-by-step explanation:
g(t)=|17-t|
A)g(11)=|17-11|
= |6|
= 6
B)g(12)=|17-12|
=|5|
=5
Whiteboard markers cost $4.75 per set at an office supply store. Which equation can be used to determine the price, P, of n sets of these markers? (10 points)
a
P = 4.75n
b
n = 4.75P
c
P equals 4.75 over n
d
n equals 4.75 over P
Answers
Answer: P=4.75n
Step-by-step explanation:
Answer:
P=4.75n
Step-by-step explanation:
b) The price of a computer was $375. In a sale, the price was reduced by 15%. Calcuate the reduction
in the price of the computer
Answers
Select the correct answer.
What are the slope and the y-intercept of the line of best fit on this scatter plot?
Answers
Answer:
A
Step-by-step explanation:
slope is change in y over change in x, line goes down 4, right three whole units, making the slope -4/3
y-intercept is where the line hits the y-axis
the line hits the y-axis at (0,8)
this makes the y-intercept 8
Answer:
The y-intercept is 8 , and the slope is -4/3.
Step-by-step explanation:
Solve the equation. 2/3 t=4/5
A. t= 2/15
B. t= 8/15
C. t= 1 and 1/5
D. t= 1 and 7/15
Answers
Answer:
it's C.
Step-by-step explanation:
make it braintliest please
A painter leans an 18 foot ladder against the house so that the base of the ladder is 4 feet away from the wall. Approximately how far up the side of the house does the ladder reach?
Answers
Answer: 17.5ft
Step-by-step explanation:
Use Pythagorean theorem
A^2 + B^2 = c^2 where c is the hypotenuse
The ladder leaning against the wall is the hypotenuse.
4^2 + b^2 = 18^2
16 + b^2 = 324
324-16 = b^2
308 = b^2
B = 17.5ft
Im giving Brainlest to who answers the best
Answers
Answer:
oop
Step-by-step explanation:
What is the solution to this equation?
X-8 = 15
Α. x= 17
Β. χ= 13
C. χ= 7
D. χ= 23
Answers
Answer:
D.) X=23
Step-by-step explanation:
cause you add 8 to each side then simplify and you get 23
If the Cable Company offers cable for $110 a month but gives a 10% discount for new customers. Find the cost for the new customers.
answer quickly. Thank You!!
Answers
Answer:
$99
Step-by-step explanation:
10% of 110 is 11
110 - 11
99
Answer:
$99
Step-by-step explanation:
First do
10% of 110
Which is 11
Then do
110-11
Which is 99
So the answer is $99