a) Solution for x:
x = {x / -3 ≤ x ≥ 2; x≠-2;1)
Interval notation:
(-∞, -3] ∪ (-2, 1) ∪ [2, +∞)
Step-by-step explanation:
Rational Inequality is inequality with rational numbers or expressions.
The symbols in inequality are:
Less than (<)
Greater than (>)
Less than or equal to (≤)
Greater than or equal to (≥)
In fraction or rational expression, the denominator is not 0. A zero-denominator renders the expression undefined.
Given:
(x+3)(x-2)/(x+2)(x-1)≥0
The rational expression:
Numerator: (x+3)(x-2)
Denominator: (x+2)(x-1) where x ≠ -2 and x ≠ 1 because the values -2 or +1 will make the expression undefined
Find the solution for x by equation the factors in enumerator to 0:
x+3 ≥ 0
x ≥ -3
x ≤ -3
x - 2 ≥ 0
x ≥ 2
But:
x ≠ -2
x ≠ 1
Hence:
Solution for x:
x = {x / -3 ≤ x ≥ 2; x≠-2;1)
Interval notation:
(-∞, -3] ∪ (-2, 1) ∪ [2, +∞)
------------------------------------------
b) Take the root of both sides and solve
Inequality Form:
− 4 ≤ x < 2 or x ≥ 3
Interval Notation:
[ − 4 , 2 ) ∪ [ 3 , ∞ ]
May I please receive help?
first, make the line into slope-intercept form.
-3x - 5y = 1
-5y = 3x + 1
y = -3/5x - 1/5
a line parallell to this line has to have the same slope, so it could be but doesn't have to be y = -3/5x - 1
a line perpendicular to y = -3/5x - 1/5 has to have the opposite slope of it.
so, y = 5/3x +1
(((I made up this question so if you can get this you get 51 points// explanation needed prove how to got your answer)))
- multiple choice to make things easier-
Sasha and Frank both have toy cars. Sasha’s car goes 875 meters in 7 minutes. Frank’s car goes 1,232 meters in 11 minutes. Who’s car goes faster and how much faster?
Answer:
Sasha's car moves 13 meters faster than Frank's car
Step-by-step explanation:
I took Sasha's 875 meters and divided it by 7minutes and got 125
Then, I took Frank's 1232 meters and divided it by 11 minutes and got 112
Finally, I subtracted 125 by 112 and got 13 meters
Answer:
125 × 11 = 1375
1375 > 1232
Sashas car goes faster then Frank's
Sashas car goes 143 meters faster then Franks
1 4/9 divided by -2/9
Answer:
6 1/2
Step-by-step explanation:
change 1 4/9 into a improper fraction, which is 13/9, and when dividing fractions flip the second number upside down then multiply. 13/9 times -2/9 is -117/18. simplify, which is 13/2, which is also equal to 6 1/2. hope this helped
how can you be sure that there are no mistakes on your pay stub assuming that you make $10 an hour and that your employer withholds 10 percent for federal taxes?
hiStep-by-step explanation:
order the following numbers from least to greatest.
12
V149
11
Answer:
11 12 v149
thats what I got......
need help asap!!!
(Question:What is 2/3 divided by 4/5?
(Options: 2/3, 5/6, 1 1/5, 3 1/3
Answer:
5/6
Step-by-step explanation:
(Simplify 6 x m x 5
Answer:
30m or 6m5
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
The simplification of the given expression 6 x m x 5 will be 30m.
What is simplification?Simplification is to make something easier to do or understand and to make something less complicated.
The expression is given below.
6 x m x 5
Then the simplification of the expression will be
30m
Where m can be any number.
Then the expression 6 x m x 5 is written as 30m.
More about the simplification link is given below.
https://brainly.com/question/12616840
#SPJ2
Performance task trigonometric identities
#1
[tex]\\ \sf\longmapsto cos75°[/tex]
[tex]\\ \sf\longmapsto cos(45+30)°[/tex]
[tex]\\ \sf\longmapsto cos45cos30+sin45.sin30[/tex]
[tex]\\ \sf\longmapsto \dfrac{1}{\sqrt{2}}\times \dfrac{\sqrt{3}}{2}+\dfrac{1}{\sqrt{2}}\times \dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{\sqrt{3}}{2\sqrt{2}}+\dfrac{1}{2\sqrt{2}}[/tex]
[tex]\\ \sf\longmapsto \dfrac{\sqrt{3}+1}{2\sqrt{2}}[/tex]
#2
[tex]\\ \sf\longmapsto tan\left(-\dfrac{\pi}{12}\right)[/tex]
[tex]\\ \sf\longmapsto tan(-15°)[/tex]
[tex]\\ \sf\longmapsto \dfrac{sin(-15)}{cos(-15)}[/tex]
[tex]\\ \sf\longmapsto \dfrac{-sin15}{cos15}[/tex]
[tex]\\ \sf\longmapsto -\dfrac{\dfrac{\sqrt{3}-1}{2\sqrt{2}}}{\dfrac{\sqrt{3}+1}{2\sqrt{2}}}[/tex]
[tex]\\ \sf\longmapsto -\left(\dfrac{\sqrt{3}-1}{\sqrt{3}+1}\right)[/tex]
Some people advise that in very cold weather, you should keep the gas tank in your car more than half full. Lou's car had 6.4 gallons in the 14-gallon tank on the coldest day of the year. Lou filled the tank with gas that cost $3.90 per gallon. How much did Lou spend on gas?
Answer:
Well,If u meant the cost of 6.4 gallons of gas.Then the answer is 24.96$
But if u meant the full tank(14Gallons),Then its 54.6$
Now pls give me brainliest
please solve fast please
Answer:
see explanation
Step-by-step explanation:
Using identities
sec²x = tan²x + 1
cosec²x = cot²x + 1
cos²x = [tex]\frac{1}{cos^2x}[/tex]
(1)
sin²θ + [tex]\frac{1}{sec^20}[/tex]
= sin²θ + cos²θ = 1
(2)
9sec²θ - 9tan²θ
= 9sec²θ - 9(sec²θ - 1)
= 9sec²θ - 9sec²θ + 9
= 9
(3)
- 8cot²A + 8cosec²A
= - 8cot²A + 8(cot²A + 1)
= - 8cot²A + 8cot²A + 8
= 8
(4)
- 10cosec²β + 10cot²β
= - 10(cot²β + 1) + 10cot²β
= - 10cot²β - 10 + 10cot²β
= - 10
Limits helppppp please!!!!!!
Y=4x+5 If x=-2 What does Y equal?
Answer: -3
Step-by-step explanation:
plug in -2 for x so that the new problem is:
y=4(-2)+5
then, multiply 4 and -2 so that:
y=-8 +5
finally add -8 to 5 to get:
y=-3
Please help me!!!!
.
======================================================
Explanation:
Let's add up the positive values only for now. So we get 172+48 = 220 which represents all the money coming into the account.
Do the same for the negative values. We'll simply add the positive versions of each (ignore the negative signs). So -17 and -40 can be thought of as 17 and 40, which add to 17+40 = 57. Ultimately this result is negative leading us to -57.
In other words, -17 + (-40) = -57
So you can see that adding negatives follows the same rule as positives. The only change is that everything turns negative.
The notation -57 means that 57 dollars is going out in terms of expenses, purchases, withdrawals, fees, etc.
---------------------
To summarize everything so far:
220 dollars in total is coming in57 dollars in total is going outWe subtract those results to find the final balance
balance = moneyIn - moneyOut = 220-57 = 163 dollars
We subtract positive versions of each number.
A ferry boat heads across the river. Due to the current, the boat travels at an angle of 15 degrees north of west. If the boat traveled a total 178 yards, how far did it travel north and how far did it travel west?
46 yards was travelled north while 172 yards was travelled west.
Trigonometric ratios shows the relationship between the sides of a triangle and its angles.
For the question, the distance travelled north and distance travelled west can be determined using trigonometric ratio.
sin(15) = distance travelled north / 178
Distance travelled north = 46 yards
Also:
cos(15) = distance travelled west / 178
Distance travelled west = 172 yards
Hence, 46 yards was travelled north while 172 yards was travelled west.
Find out more at: https://brainly.com/question/2512283
3x +7x -5 +2x +10 simplified is 12x +5
Answer:
yes
Step-by-step explanation:
3x+7x+2x = 12x
-5+10 = 5
so it's = 12x+5
Help Please :)
f(x) = 5x +7
and
g(x) = -2x - 4
f(g(x)) = -2x + ????
Answer:
f(g(x)) = - 10x - 13Step-by-step explanation:
Given functions:
f(x) = 5x +7and
g(x) = -2x - 4Work out the composite f(g(x)):
f(g(x)) = f( -2x - 4) = 5( - 2x - 4) + 7 = -10x - 20 + 7 = - 10x - 13Answer:
f(g(x)) = -10x - 13
???? = - 8x - 13
Step-by-step explanation:
f(x) = 5x +7
and
g(x) = -2x - 4
f(g(x)) = f(-2x - 4) = 5(-2x - 4) + 7
f(g(x)) = -10x - 20 + 7
f(g(x)) = -10x - 13
f(g(x)) = -2x - 8x - 13
use the quadratic formula to solve the equation 4x^2+x-9=0
Answer:
see pics
Step-by-step explanation:
dbdksjhddbbdbsksksodhd pls give brainlist
Answer:
x = (-1 ±[tex]\sqrt{145}[/tex] )/8
Step-by-step explanation:
Quadratic formula: x = (-b ± [tex]\sqrt{b^{2} - 4ac}[/tex] )/(2a)
4x² + x - 9 = 0 ; General form of a quadratic is ax² +bx + c = 0
So a = 4, b = 1, and c = -9
x = -1 ±[tex]\sqrt{1^{2}-4(4)(-9)}[/tex] / 2(4)
x = -1 ± [tex]\sqrt{1 + 144}[/tex] /8
x = -1 ±[tex]\sqrt{145}[/tex] /8
x = (-1 + [tex]\sqrt{145}[/tex])/8 or x = (-1 - [tex]\sqrt{145}[/tex])/8
Please someone help me here
Answer:
A
Step-by-step explanation:
I need to know if these answers are correct or not...
1.
x + (x + 1) + (x + 2) + (x + 3) = 70
4x + 6 = 70
4x = 70 - 6
4x = 64
64/4 =
x = 16
16 + 17 + 18 + 19 = 70
10.
Sca = 336/12 = 28 miles/hr
Scu = 336/14 = 24 miles/hr ->
28 = B + C
24 = B - C ->
28= B + C -> B = 28 - C -> 24 = B - C
-> 24 = 28 - C - C
24 -28 = -2C
-4 = -2C
C = 2 -> B = 28 - 2
= 26 miles/hr
1. Let the four consecutive numbers be x, x+1, x+2, x+3
The sum of four consecutive number is already given to us = 70
Therefore
⇒(x)+(x+1)+(x+2)+(x+3)=70
We need to combine x as we have four x terms in the equation. The next step is to get all of the x’s on one side of the equation and all the numbers on the other side. The same rule applies – whatever you do to one side of the equation, you must do to the other side as well!
⇒4x+6=70⇒4x=64⇒x=16
So, the four numbers are 16, 17, 18 and 19.
Hence, the greatest number among them is 19.
Help it’s urgent :( I’ll mark brainliest
Answer:
x = 4
x = 10
Step-by-step explanation:
x^2 -14x + 40 = 0 ----> factor form
(x - 10)(x - 4) = 0 ---> separate equations
x - 10 = 0 ---> add 10 on both sides
x = 10
x - 4 = 0 ---> add 4 on both sides
x = 4
Answer:
small x= 4
large x= 10
Step-by-step explanation:
hello there!
x^2-14x+40=0
x^2-(10+4)x+40=0
x^2-10x-4x+40=0
pick out the common one!
x(x-10)-4(x-10)=0
(x-10)(x-4)=0
now;
x-10=0
x=10(which is large x)
again:
x-4=0
x=4( which is small x)
hope it helps.. thank u!
A 4 in. by 5 in. photo is enlarged so that its width (shorter dimension) is 5 in.
What is the length of the enlarged photo?
5.25 in.
7 in.
6.25 in.
6 in.
========================================================
Explanation:
The jump from 4 inches to 5 inches is 5/4 = 1.25
In other words, 4*1.25 = 5
So we need to multiply every dimension by the scale factor 1.25 to enlarge the image. The 5 inch dimension then goes to 5*1.25 = 6.25 inches
----------
Here's another way you can solve
(old width)/(old length) = (new width)/(new length)
4/5 = 5/x
4x = 5*5
4x = 25
x = 25/4
x = 6.25
PLEASE HELP AND EXPLAIN
Solve the following equation by factoring 2x^2 - x = 2-4x
Answer:
x=-2, x=1/2
Step-by-step explanation:
> 2x²-x=2-4x
> 2x²-x+4x-2=0
> 2x²+3x-2=0
> 2x(x+2)-(x+2)=0
> (x+2)(2x-1)=0
> x+2=0; 2x-1=0
> x=-2; x=1/2
Add all of the numbers
Answer:
18
Step-by-step explanation:
2 + 1 + 2 + 2 + 3 + 1 + 0 + 0 + 3 + 2 + 0 + 1 + 0 + 1
Get rid of the zeros
2 + 1 + 2 + 2 + 3 + 1 + 3 + 2 + 1 + 1
18
Which equation is the equation of the line, in point-slope form, that has a slope of - 4 and passes through the point (7, 1)?
Answer:
y-1=-4(x-7) is the correct answer
Find the ratio of circles to triangles in the diagram below.
ΟΟΔΔΔ
ΟΟΔΔΔ
ΟΟΔΔΔ
Unsimplified ratio of circles to triangles:
try
Answer:
6:9
Step-by-step explanation:
there are six circle and nine triangle
so the ratio is
6:9
Find the equation of the line with a slope of -3, passing through the point (2,5).
y = -3x + 11
y = -3x - 1
y = 2x + 5
y = -3x + 5
Simplify (2/3 +1/6)
Write the sum in the simplest form
Answer:
5/6
Step-by-step explanation:
2/3 -> 4/6
4/6+1/6= 5/6
Solve for x. The triangles in each pair are similar
Linear and nonlinear
Answer:
Hi im filipino :))
Step-by-step explanation:
Thanks for the points
7 4/5 divided by 1 3/10 (please leave explanation)
Answer:
117/50 or 2 17/50 or 2.34
Step-by-step explanation:
i don't know is just simple
You multiply 7 X5+4 is 39, 39/5 and then multiple