Answer:
Step-by-step explanation:
1. Find two numbers that add to make the coefficient of x (in this case, -5) and that multiply to make the constant term multiplied by the coefficient of x^2 (in this case, -2 x 3 = -6)
Two numbers that work are -6 and +1
-6 x +1 = -6
-6 + -1 = -5
2. Split the middle term into the two numbers that you found.
3x^2 -6x +x -2 = 0
I've put the -6 on the left side because in our next step, when we factorise, it will be easier than having the numbers the other way around.
3. Factorise the left side by taking out common factors from each pair. The pairs I'm talking about here are '3x^2 and -6x', and 'x and -2'
3x (x-2) +1 (x-2) = 0
4. You now have two numbers both being multiplied by the term x-2. We can rearrange this equation to give us two brackets being multiplied by each other.
(3x + 1) (x-2) = 0
5. According to the Null Factor Law, if two terms are multiplied together and the result is 0, then one of those terms must be 0. Make both terms equal to 0 and solve each for x.
3x + 1 = 0 x-2 = 0
3x = -1 x = 2
x = -1/3
6. The solutions to this equation are x = 2 and x = -1/3
Answer:
Step-by-step explanation:
Start by separating (not factoring) -5x. For example, we might get {-2x, - 3x} (note how these combine to produce -5x). Might have to try several combinations to find the right one.
Then 3x^2 -5x -2=0 could possibly be x(3x - 2) - (3x - 2), or
x(3x - 2) - 1(3x - 2).
Notice how the factor (3x - 2) shows up twice. If we factor out (3x - 2) we are left with (x - 1). We check these results by multiplying (3x - 2) and (x - 1) together, so we can be sure that the result is the original 3x^2 -5x -2=0.
(3x - 2)(x - 1) = 3x^2 - 3x - 2x + 1 results in 3x^2 - 5x + 2. Unfortunately, the sign of that 2 is incorrect; we'd hoped for -2, not +2.
To check this further, I used synthetic division with 1 as divisor; the remainder is -4, which tells us that (x - 1) is not a factor of 3x^2 -5x -2=0.
Please double check to ensure that you have copied this problem down correctly.
Choose the two steps that are part of factoring the trinomial 6x2 + 17x + 5 by grouping.
a. 6x2 + 9x + 8x + 5
b. (3x + 1)(2x + 5)
c. x(6x + 17) + 5
d. 3x(2x + 5) + 1(2x + 5)
Answer:
b
Step-by-step explanation:
given
6x² + 17x + 5
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 6 × 5 = 30 and sum = 17
The factors are 2 and 15
Use these factors to split the x- term
6x² + 2x + 15x + 5 ( factor the first/second and third/fourth terms )
= 2x(3x + 1) + 5(3x + 1) ← factor out (3x + 1) from each term
= (3x + 1)(2x + 5) → b
The two steps are [tex]3x(2x+5)+1(2x+5)[/tex] and [tex](3x+1)(2x+5)[/tex]. So, options b and d are correct.
Important information:
The given trinomial is [tex]6x^2+17x+5[/tex].Factoring:Splitting the middle term, we get
[tex]6x^2+15x+2x+5[/tex]
After grouping, we get
[tex](6x^2+15x)+(2x+5)[/tex]
Taking out common factors, we get
[tex]3x(2x+5)+1(2x+5)[/tex]
Now, it can be written as:
[tex](3x+1)(2x+5)[/tex]
Therefore, the correct options are b and d.
Find out more about 'Factoring' here:
https://brainly.com/question/2416165
Really need help can someone help me with this problem plz! I need help asap! Someone plz help me plz plz help me!
Answer:
x = 358. / Maximum amount of money for sales = $3,759
Step-by-step explanation:
x + 26 = 384. Inverse operations
-26. -26
x = 358
358($10.50) = $3,759
A three digit number is divided by another three digit number gives 3.724. What are the two numbers?
Answer: the numbers are 250 and 931
Step-by-step explanation:
We have two numbers of 3 digits, A and B such that:
A/B = 3.724
A = 3.724*B
now we can divide the 3.724 in two parts
3.724 = 3 + 0.724
A = (3 + 0.724)*B = 3*B + 0.724*B
So, for now we want to find a number B of 3 digits (i will try to find the smallest possible value of B, because we need to multiplicate B by 3.724 to find A), such that:
0.724*B is an integer.
for example, we can start at B = 1000, and then we will start to reduce the value of B
0.724*1000 = 7240 is an integer, this is an even number, this means that we can take B = 500 and we still will get an integer number.
0.724*500 = 362.
Again, we have an even number, so we can take B = 250 and the result will be also an integer number.
0.724*250 = 181.
Ok, stop here, we can suppose B = 250, then we have:
A = 3.074*B = 3.724*250 = 931
Then the numbers are 250 and 931
I need this answered in two-column proof form. Thanks!
Answer:
You can prove that they are the same because 2 angles opposite each other are equal the same.
Hope this helps
Answer:
I answered this already for you :) Check your other question
What are the long-term and short-term effects of a father's death at age 13?
Answer:
I'm 13 so I'll be able to imagine this.
Step-by-step explanation:
-depression
-worry of afterlife
-insecurity
-increased fear of losing other family members
-untrust
-just general sadness
-feeling like it is your fault/blaming yourself
For the function y = -2x + 4, the input is 3. What is the output?
Answer:
y = -2
Step-by-step explanation:
Plug in 3 for x
y = -2 (3) + 4
y = -6 + 4
y = -2
I hope this helps :))
The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 2008, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, estimate the calendar year in which the number of new cases would reach 543
Answer:
Step-by-step explanation:
I use 84+ CE
stat edit, then fill in the #s
then
vars 5
then
2'nd stat plot, on
then, click stat
Click arrow 1 time to the left to get to Calc
then click (4)(LinReg(ax+b))
then click enter 5 times
(y=-25.31428571x+1000.285714
y=-25.3x+1000.3
now, lets use computer:
y=-25.31(543)+1000.3
y=-12743.03
round to the biggest whole number )
this doesn't really work, so I will put 1999, 2000, 2001, 2002, 2003, 2004 instead of 0, 1, 2, 3, 4, 5 and do the same thing
now I get
y=-25.31428571x+51603.54286
y=-25.3x+51603.5
now, lets use computer:
y=-25.3(543)+51603.5
y=37865.6
round to the biggest whole number:
y=37866
so, year 37866
Using the line of best-fit, it is found that:
The linear regression model is [tex]y = -25.31x + 1000[/tex]The estimate is that the number of cases would reach 543 in the year of 2026.---------------------
The line of best-fit is given by:
[tex]y = bx + a[/tex]
The slope is:[tex]b = \frac{\sum (x - \overline{x})(y - \overline{y})}{\sum (x - \overline{x})^2}[/tex]
After the slope is found, using the means for x and y, the coefficient a is found.---------------------
The means are given by:
[tex]\overline{x} = \frac{0 + 1 + 2 + 3 + 4 + 5}{6} = 2.5[/tex]
[tex]\overline{y} = \frac{1015 + 960 + 950 + 902 + 929 + 866}{6} = 937[/tex]
---------------------
The sums are:
[tex]\sum (x - \overline{x}) = (0 - 2.5) + (1 - 2.5) + ... + (5 - 2.5)[/tex]
[tex]\sum (y - \overline{y}) = (1015 - 937) + ... + (866 - 937)[/tex]
Using a calculator:
[tex]\sum (x - \overline{x})(y - \overline{y}) = -443[/tex]
[tex]\sum (x - \overline{x})^2 = 17.5[/tex]
Thus, the slope is:
[tex]b = -\frac{443}{17.5} = -25.31[/tex]
And
[tex]y = -25.31x + a[/tex]
---------------------
Using the means to find a:
[tex]y = -25.31x + a[/tex]
[tex]937 = -25.31(2.5) + a[/tex]
[tex]a = 1000[/tex]
Thus, the linear regression model is:
[tex]y = -25.31x + 1000[/tex]
---------------------
The number of cases would reach 543 in x years after 2008, and x is found when y = 543. Thus:
[tex]y = -25.31x + 1000[/tex]
[tex]543 = -25.31x + 1000[/tex]
[tex]25.31x = 1000 - 543[/tex]
[tex]x = \frac{1000 - 543}{25.31}[/tex]
[tex]x = 18.1[/tex]
2008 + 18 = 2026
The estimate is that the number of cases would reach 543 in the year of 2026.
A similar problem is given at https://brainly.com/question/21826199
GUYS PLEASE HELP!!!!! WILL GIVE BRAINLIEST FOR BEST ANSWER!!!!
(a) Consider the following statement:
The dress is yellow.
Check all the statements below that are negations of this statement.
It is not the case that the dress is yellow
The dress is not blue
The dress is multicolored
(b) Consider the following conditional statement:
If Mary is wearing tennis shoes, then Mary has been exercising.
What is the conclusion of this statement?
Mary is not wearing gym shorts
Mary has never exercised
It is not true that Mary is wearing gym shorts
Mary is wearing tennis shoes
Mary has been exercising
Answer:
a) It is not the case that the dress is yellow
a) The dress is multicolored
b) Mary has been exercising
step-by-step explanation:
The saying negates that the dress is yellow and saying the dress is multicolored implies that the dress is not just one color or just yellow.
For part b, the condition is, is Mary wearing tennis shoes. The conclusion then is that Mary has been exercising because she is wearing tennis shoes.
subtract the following integer in number line =5 from 3
Answer:
-2
Step-by-step explanation:
3-5= -2
A dolphin jumps 3 feet above sea level to go through a ring. The dolphin starts at the opposite distance below sea level. How far does the dolphin travel from its starting position to the top of it's jump?
Answer:
6 feet
Step-by-step explanation:
The dolphin jumps 3 feet above sea level and it starts from the opposite distance below sea level.
This means that it starts from 3 feet below sea level.
The total distance the dolphin travels from its starting point to the top of the jump is therefore:
3 + 3 = 6 feet
Write the equation of a line that is parallel to 3x-2y=5 and passing through the point (-1,3)
Answer:
y = 3/2 x + 9/2
Step-by-step explanation:
3x - 2y = 5
3x - 5 = 2y
3/2 x - 5/2 = y
y = 3/2 x - 5/2, slope of this line m = 3/2.
For parallel line slope is the same.
y = mx + b
y = 3/2 x + b
Using point (-1,3) , we can find b.
3 = (3/2)*(-1) + b
3 = -3/2 + b
b = 3 + 3/2 = 6/2 + 3/2 = 9/2
y = 3/2 x + 9/2
Which is equivalent to 3v8
Answer:
C.
Step-by-step explanation:
= [tex]\sqrt[3]{8}^{x}\\[/tex]
= Since [tex]\sqrt[3]{} = ^{1/3}[/tex]
= So, It becomes :
= [tex]8^{\frac{x}{3}[/tex]
Can you please help
Solve the equation.
2/3-4x+7/2=-9x+5/6
Answer:
x=-2/3
Step-by-step explanation:
Answer:
x = -2/3
Step-by-step explanation:
don't feel like writing all the fractions but basically isolate the X and the fractions. add them in a calculator divide by the coefficient thats left with x and there you go
Which of the following best describes the perpendicular lines?
Answer:
A perpendicular line is a line that meets a 90 degree angle.
Step-by-step explanation:
Think of the letter L
the top stick of the letter is perpendicular to the bottom stick and it makes a 90 degree angle.
Thats the best way I can explain it.
Hope this helps and please mark me brainliest if it did :)
Answer:
Hey!
Your answer is B. Lines that meet at a 90 degree angle!
Step-by-step explanation:
Just think of an L or something...
The 2 lines meet together and you can then see close to the area they meet at 90 degree angles...
PLZ HLP MEEEEEEEEEEEEEE
Answer:
D
Step-by-step explanation:
The total number of students is 15+12= 27
The ratio of girls to total students is 12/27 = 4/9
Multiply and simplify
V8xyz3 . V10x3y2z
Answer:
Step-by-step explanation:
[tex]\sqrt{8xyz^{3}}*\sqrt{10x^{3}y^{2}z} =\sqrt{8xyz^{3}*10x^{3}y^{2}z}\\\\ =\sqrt{2*2*2*2*5*x^{1+3}*y^{1+2}*z^{3+1}} \\\\\\=\sqrt{2^{4}*5*x^{4}*y{3}*z^{4}} \\\\=2^{2}*x^{2}*y*z^{2}\sqrt{5y} \\\\\\=4x^{2}yz^{2}\sqrt{5y}[/tex]
Catherine reflected the triangle across the x axis. What is the new
triangle?
Answer:
C. (or the third graph)
Step-by-step explanation:
Here is a rectangle ABCD the length of the rectangle is increased by 10% The width of the rectangle is increased by 5% Find the percentage increase in the perimeter of the rectangle
Answer:
7.5 % increase
Step-by-step explanation:
So,first we know that Square is also a special type of Rectangle,
so consider a Square with side 100 unit ,
Initially, After increament in side
Length = 100 unit -(increases by 10% ,So 110% of 100) NEW length = 110 unit
width = 100 unit (increases by 5% ,So 105% of 100) NEW width = 105
initially, Perimeter of Rectangle = 2 x (L + B) = 2 x (100 +100)
= 400 unit
After increment in length and width
Perimeter of New Rectangle = 2 x (L + B) = 2 x (110 +105)
= 430 unit
So we can clearly see that there is an increase of 30 unit in perimeter from initial.
Therefore ,% increase in perimeter will be
(final perimeter - initial perimeter)/initial perimeter x 100
= (430 - 400)/400 x 100
= 7.5 % increase
Answer:
increased by 8%
Step-by-step explanation:
make r the subject of the formula t=r/r-3
Answer:
r = t(r-3)
Step-by-step explanation:
t = r/r-3
r/r-3 = t
r = t x (r-3)
Find the value of k such that the quadratic equation x(x-2k)+6=0 has real and equal roots
Answer:
k= [tex]\frac{x^{2}+6 }{2x}[/tex]
Step-by-step explanation:
x(x−2k)+6=0
Step 1: Add -x^2 to both sides.
−2kx+x2+6+−x2=0+−x2
−2kx+6=−x2
Step 2: Add -6 to both sides.
−2kx+6+−6=−x2+−6
−2kx=−x2−6
Step 3: Divide both sides by -2x.
−2kx /−2x = −x2−6 /−2x
k =
A. all real numbers
B. x≤0
C. x≥4
D. -2≤x≤2
Answer:
D. The true answer is D. -2<x<2
Consider the following equations:
−x − y = 1
y = x + 3
If the two equations are graphed, at what point do the lines representing the two equations intersect?
a
(−1, 2)
b
(−2, 1)
c
(1, −2)
d
(2, −1)
Answer:
The Answer is: (-2,1)
Step-by-step explanation:
what is x if -3x + 6 =39
Answer:
x = -11
Step-by-step explanation:
-3x + 6 = 39
Combine Like Terms
-3x = 33
Divide Each Term then simplify
x = -11
Hope This Helps!
Answer:
x=-11
Step-by-step explanation:
In order to solve for x, we have to get x isolated.
To do that, we must perform the inverse operations to both sides of the equation.
-3x+6=39
6 is being added on to -3x. The inverse of addition is subtraction. Subtract 6 from both sides of the equation.
-3x+6-6=39-6
-3x=39-6
-3x=33
x is being multiplied by -3. The inverse of multiplication is division. Divide both sides by -3.
-3x/-3= 33/-3
x= 33/-3
x=-11
x/3 +2y/3= -1 and x-y/3=9 solve. by elimination method
Answer:
X=51/7, Y= -36/7
Step-by-step explanation:
X/3 + 2y/3 = -1 equ 1
X - y/3 = 9 equ 2
eliminate X/3.
X/3 + 2y/3 = -1..... x 1 ( co-efficient of X in equ2 )
X - y/3 = 9 ...... x 1/3 ( co-efficient of X in equ1 )
X/3 + 2y/3 = - 1 equ 3
-
X/3 - y/9 = 3 equ 4
0 + 7y/9 = -4
y = -36/7
( input the value of y into equ 4 )
X/3 -y/9 = 3
X/3 - (-36/7)/9 = 3
X/3 + 36/63 = 3
X/3 = 3 - 36/63
X/3 = 153/63
63X = 459
X = 459/63
X = 51/7.
A store sells an outfit that consists of a shirt, a tie, and a pair of pants. The store purchases the shirt for $18, the tie for $12, and the pants for $35. The percent of markup is 22%. Find the selling price of the outfit.
Answer:The selling price of the outfit is $79.3
Step-by-step explanation:
18 + 12 + 35 = $65
65* 22% = 14.3
14.3 + 65 = $79.3
or
100% + 22% = 122%
122% of 65
1.22 * 65 = 79.3
How do you graph Y =4 find the slope of a line that is parallel to it
Answer:
Answer is below
Step-by-step explanation:
I graphed the equations on the graph below.
The slope of y = 4 and y = 5 is 0 because the lines are flat and constant, instead of increasing or decreasing.
Kat is painting the edge of a triangular stage prop with reflective orange paint. The lengths of the edges of the triangle are (3x – 4) feet, (x2 – 1) feet, and (2x2 – 15) feet. What is the perimeter of the triangle if x = 4?
Answer:
40 feet
Step-by-step explanation:
Since x=4
3x-4=3(4)-4=12-4=8 feet
x^2-1=4^2-1=16-1=15 feet
2x^2-15=2(4)^2-15=2(16)-15=32-15=17 feet
Perimeter=8+15+17=40 feet
-560.114 a rational or irrational
what is the leading coefficient of the polynomial f(x) defined below:
Explanation:
The leading term of a polynomial is the term with the largest exponent, which in this case that exponent is 4. So the leading term is -3x^4.
The leading coefficient is the coefficient of the leading term. The coefficient of the term -3x^4 is -3.
If the polynomial is written in standard form, then the process is as simple as reading the first coefficient. Otherwise, you may have to sort the terms out first.