Answer:
[tex]x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)[/tex]
Step-by-step explanation:
[tex]x^3 - 10x^2 -53x - 42[/tex]
The factors of 42 : ±1 , ±2 , ±3 , ±6, ±7, ±14, ±21 , ±42
Using trial and error method we will find the first root of the polynomial.
1 : ( 1 )³ - 10 ( 1 )² - 53 ( 1 ) - 42
1 - 10 - 53 - 42 ≠ 0
Therefore 1 is not a root
-1 : ( -1 )³ - 10 (- 1 )² - 53 (- 1 ) - 42
- 1 - 10 + 53 - 42
53 - 53 = 0
Therefore - 1 is a root of the polynomial.
Therefore ( x + 1) is a factor.
Now by long division or by using synthetic division we can find other factors.
Synthetic Division :
-1 | 1 -10 -53 - 42
| 0 - 1 11 42
|______________________
1 - 11 - 42 0
Therefore ,
[tex]x^3 - 10 x^2 -53x -42 = ( x + 1)(x^2 - 11x +42)[/tex] ------ ( 1 )
Next further factorize x² - 11x - 42
x² - 11x - 42
= x² - 14x + 3x - 42
=x(x - 14) + 3 (x - 14)
=(x + 3 )(x - 14)
Therefore ,
[tex]x^3 - 10 x^2 -53x -42 = ( x + 1)(x + 3) (x - 14)[/tex]
fina a value of the polynomial 5x-4x ^ { 2 } +3 at
(i) x=0
What transformation has taken place on the coordinate grid pleaseee help my final! I'll give rate and heart etc
Answer:
Translation across the coordinate plane
Step-by-step explanation:
Here, we want to get the kind of transformation that has occurred to the shape
from the given coordinate diagram, we can see that A shifted from (2,3) to (-3,6)
B shifted from (2,-2) to (-3,1)
and C shifted from (-1,-4) to (-6,-1)
If we look at these, we can observe that there is a change in the x-axis coordinate in each by (-1-(-6) or 2-(-3) = 5 units
and there is a change in the y-axis value by (3-6) = -3 units
so the transformation here can be represented generally as;
(x -5, y+ 3)
With this, we can see that what we have represented is simply a translation across the coordinate plane
(2a+1) - 4a(2a+1)+4a
Answer:
2a (3-4a)
Step-by-step explanation:
(2a+1)-4a(2a+1)+4a
2a+1-8a²-1+4a
= 2a+4a-8a²
=6a-8a²
= 2a(3-4a)
Answer:
Step-by-step explanation:
Use distributive property: a*(b+c) = (a*b) + (a*c)
-4a*(2a + 1) = -4a*2a + 1*(-4a)
= -8a² - 4a
2a + 1 - 4a(2a + 1) + 4a = 2a + 1 - 8a² - 4a + 4a
= 2a + 1 - 8a²
According to the graph, what is the value of the constant in the equation
below?
A. 0.25
B. 0.5
C. 1
D. 2
Answer:A
Step-by-step explanation:
Answer:
It is A
Step-by-step explanation:
i took the test and it showed it was corrected when i got done checking my test score please choose A.
Question from Venn diagram solving... plz solve. Worth 15 points
Answer:
For this type of problem, it is best to use Venn diagrams as shown in the picture. The areas where the circles intersect are the mutual events that occur together. The area where all circles intersect is denoted as x. These are the students who play all sports. Assuming all of the students play sports in the school, all of the numbers in the circles should add up to 405. The remaining area would be the difference. The solution is as follows:
Students who play tennis and hockey: 45 - x
Students who play hockey and softball: 60 - x
Students who play only tennis and softball: 39 - x
Students who only play tennis:
251 - 45 + x - 39 +x -x = x + 167
Students who only play hockey:
157 - x - 45 + x - 60 + x = x + 52
Students who only play softball:
111 - x - 60 + x - 39 + x = x + 12
The sum of all of these should be 405:
45-x+60-x+39-x+x+167+x+52+x+12 = 405
Solving for x,
x = 30
Therefore, there are 30 pupils who play all sports; 15 pupils who play tennis and hockey; 30 pupils who play hockey and softball; 9 pupils who play tennis and softball; 197 pupil who only play tennis; 82 pupils who only play hockey; and 42 pupils who only play softball.
Step-by-step explanation:
Hope this is correct, if it is wrong then please feel free to critique me and I wil correct my mistake(s). I'm sorry in advance if it is incorrect.
What is the area? Bit confused on this one.
Answer:
x² + 8x + 12
Step-by-step explanation:
see
the length of the entire rectangle = x + 6
breadth of the entire rectangle = x + 2
area of a rectangle = length × breadth
= (x + 6)(x + 2)
= x² + 8x + 12
which is the required polynomial in standard form
Answer:
x^2 + 8x + 12
Step-by-step explanation:
length = x+6
breadth = x+2
ara of rectangle = l*b
=(x+6)(x+2)
=x(x+2) +6(x+2)
=x^2 + 2x + 6x +12
=x^2 + 8x +12
Which of the following describes point H?
Solve this pls I beg
Answer:
-4 < n ≤ 5
Step-by-step explanation:
_________________
The mean of four numbers is 7. Three of the numbers are 5, 7, and 7. What is the fourth number? Explain your reasoning.
Answer:
9
Step-by-step explanation:
The mean is equal to the sum of all numbers divided by the amount of numbers there are. If we represent the mean as m, sum as s, and number of numbers as n, we can write our equation as
m = s/n
Therefore, as we know the mean (7) and number of numbers (4), we can plug those in to find the sum.
7 = s / 4
Multiply both sides by 4
28 = s
We then have our sum. Because we know 3 numbers, and there are 4 total, there is one number left to figure out. Our current sum is 5+7+7 = 19, and we need a sum of 28. The difference between the sums, equivalent to the fourth number, is 28-19=9.
Add the following numbers. -3 + 8 =
Use a calculator to find the r-value of these data. Round the value to three
decimal places
Answer:
-.985
Step-by-step explanation:
What is the first step in solving quadratic equations by finding square roots? a. give the positive and negative answer c. square root both sides to isolate x b. isolate the x squared by using inverse operations d. none of these Please select the best answer from the choices provided A B C D
Answer:
C: isolate the x squared by using inverse operations
Step-by-step explanation:
This method of solving quadratic equation is used when there is only x² term and no x term. Thus;
For example, we have a quadratic equation;
x² - 1 = 80
To solve this by square root method, the first step we have to take is to isolate the x² term by inverse operation which is by addition of 1 to both sides to get rid of the -1 on the left side so that x² can be isolated.
Help Guys which choice is the answer show the work that supports the answer :)??:((( i will extra points if ur not sure of the answer plz don’t answer the question ty:)
Answer:
A
Step-by-step explanation:
area=πr²=π×2²=4π≈4×3.14≈12.56 km²
Answer:
12.56
Step-by-step explanation:
area of circle = pi r^ 2
pi= 22/7
r= 2km
22/7×2×2
22/7×4
22/28
12.56 is ans
Name the marked angle in 2 different ways.
1) angle RQP
2) angle PQR
The product of a number, x, and 18 is 113.4.
Which equation and value of x represent this relationship
Answer:
Step-by-step explanation:
x * 18 = 113.4
x = 6.3
(20 points) thanks so much!!
Step-by-step explanation:
Let us say x=2 and y=1
Using the formula,
=>((2^2)-(1^2))^2+(2(2)(1))^2=((2^2)+(1^2))^2
=>(4-1)^2+(4)^2=(4+1)^2
=>(3)^2+(4)^2=(5)^2
Which is pythogorian triplet
Verify the equation below with each of the values listed for t to find a solution. 4 = 3t – 2 A. t = –6 B. t = –2 C. t = -1/2 D. t = 2
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\text{D) }t=2[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the Answer...}}\\\\4 = 3t - 2\\-----------\\\rightarrow 3t - 2 = 4\\\\\rightarrow 3t - 2 + 2 = 4 + 2\\\\\rightarrow 3t = 6\\\\\rightarrow\frac{3t = 6 }{3}\\\\\rightarrow \boxed{t = 2}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
7
A (0, 2) and B (6,5) are points on the straight line ABCD.
Y
Not drawn
accurately
B (6,5)
(A (0, 2)
0
x
AB = BC = CD
Work out the coordinates of D.
Answer:
(12,8)
LM=24 MN=13 what is KM?
Answer:
ans: KM = 576/13
Step-by-step explanation:
break given triangle to two triangle,
use pythagoras theorem to find LN
now, splited triangle are similar to each other so corresponding sides are proportional to each other
Please help I’ll give brainliest
Answer:
81Step-by-step explanation:
3 exponent 4
[tex] = {3}^{4} [/tex]
= 3 × 3 × 3 × 3
= 81 (Ans)
A ramp 28 ft long rises to a platform. The bottom of the platform is 17 ft from the foot of the ramp. Find x, the angle of elevation of the ramp. Round your
answer to the nearest tenth of a degree.
Answer:
Step-by-step explanation:
Calculate the length of line segment XY in each triangle.
Answer:
XY = 8 cm
Step-by-step explanation:
PQ is a midsegment and is half the length of the 3rd side XY , then
XY = 2 × PQ = 2 × 4 = 8 cm
3(x-1)≤ ½(x+1) -6. Topic is Linear inequalities
Answer:
[tex]x\le \:-1[/tex]
Step-by-step explanation:
[tex]3\left(x-1\right)\le \frac{1}{2}\left(x+1\right)-6[/tex]
[tex]3x-3\le \:-\frac{11}{2}+\frac{1}{2}x[/tex]
[tex]3x\le \:-\frac{5}{2}+\frac{1}{2}x\\[/tex]
[tex]\frac{5}{2}x\le \:-\frac{5}{2}[/tex]
[tex]5x\le \:-5[/tex]
[tex]x\le \:-1[/tex]
x = -1
3(-2) ≤ ½(0) - 6
-6 ≤ 0 - 6
-6 ≤ -6
This is true.
x = -2
3(-3) ≤ ½(-1) - 6
-9 ≤ -½ - 6
-9 ≤ [tex]-\frac{13}{2}[/tex]
This is also true.
Therefore, x ≤ -1.
Question 9 of 10
Which polynomial represents the difference below?
(8x2 +9) - (3x2 + 2x + 5)
Step-by-step explanation:
= (8x² + 9) - (3x² + 2x + 5)
= 8x² + 9 - 3x² - 2x - 5
= 5x² - 2x + 4
Please solve with explanation
Answer:
The amount of wood left is 36 9/16 in
Step-by-step explanation:
Here, we want to get the amount of wood left
To calculate this, we have to subtract what is cut and what is wasted from the original total length
So we have what is left as follows;
45 1/2 - 8 7/8 - 1/16
45 1/2 = 91/2
8 7/8 = 71/8
91/2 - 71/8 - 1/16
(728 - 142 - 1)/16
585/16 = 36 9/16 in
mary selects a piece of candy at random form a jar that contains four peopermint, five cherry, three butterscotch, and two lemon candies. what is the probability that the candy she selects is not lemon?
Answer:
6/7 or 85.7 percent
Step-by-step explanation:
First, you will want to add all of the candies together and find the sum
Then you will want to take away the Lemon candies as you are looking for the probability of NOT choosing those,
so at this point, you should have 12 take that 12, and put it over the total number, so 12/14 then either simplify, or switch to a percentage, or both, and there is your answer.
One of the fastest Times of a recorded for the 50 yard dash is 5.2 seconds the following expression can be used to find how many miles per hour that is what is the missing factor
Answer:
you need to addmission all number
Select the interval where g is negative.
PLSSS HELLPPP!!!
The interval where g is negative is in the domain of -5 ≤ x < 1
The reason for the above selected interval is as follows;
A function is negative over an interval where the graph of the function is
below the x-axis, and the y-coordinate values are negative, excluding
where the y-value is zero. The interval over which a function is negative is
also called the negative region
From the given graph, the function, g(x), we have;
At x = 1, y = g(x) = 0
At x = -5, y = g(x) ≈ -7 and increasing to 0
Therefore at x = -5, g(x) ≈ -7, is negative
Tis negative over the interval -5 ≤ x < 1
Therefore;
The interval where g(x) is negative is -5 ≤ x < 1.
Learn more about intervals of functions here;
https://brainly.com/question/8933368
PLEASE HELPPPPPP Meeeeeee hurrry
Answer: Choice C
1, 3, 6, 8, 10, 12, 13, 13, 16, 18, 19
===========================================================
Explanation:
For each answer choice, there are n = 11 numbers mentioned.
The median will be at slot n/2 = 11/2 = 5.5 = 6, so there are 5 values below the median and 5 values above it. In total, we have 5+1+5 = 11 items overall.
The vertical bar in the box plot represents the median's location. It's at 12, so "12" must be in slot 6 in the answer.
Based on this alone, the answer is between choice A or choice C. These two answers are nearly identical except for one thing: the max for choice A is 20 while the max for choice C is 19.
The answer is choice C because the boxplot shown has the tip of the right whisker at 19, and not 20.
Side note: the data values must be sorted before you can find the median. Luckily, for each answer choice, the values are already sorted for us.
Answer:
It would be Choice C
Step-by-step explanation:
I tried subtracting it but it says it’s wrong so what do I do?
Answer:
70,000 - 20,000= 50,000