Answer:
The points that lie in the solution set of following system of inequalities are:
Option A (1,-5) and Option C (5,1)
Step-by-step explanation:
We need to find the points that lie in the solution set to the following system of inequalities
[tex]y<-3x+3\\y<x+2[/tex]
We will check each option to identify if they satisfy the given set of inequalities or net.
Option A (1,-5)
We have x=1, y=-5
Putting values and checking
[tex]\\y<-3x+3\\-5<-3(1)+3\\-5<0 \ (true)\\y<x+2\\-5<1+2\\-5<3 \ (true)[/tex]
So, Option A is correct as both values satisfy the given set of equations
Option B (1,5)
We have x=1, y=5
Putting values and checking
[tex]y<-3x+3\\5<-3(1)+3\\5<0 \ (false)\\y<x+2\\5<1+2\\5<3 \ (false)[/tex]
So, Option B is not correct as both values doesn't satisfy the given set of equations
Option C (5,1)
We have x=5, y=1
Putting values and checking
[tex]y<-3x+3\\1<-3(5)+3\\1<-15+3\\1<12 \ (true)\\y<x+2\\1<5+2\\1<7 \ (true)[/tex]
So, Option C is correct as both values satisfy the given set of equations
Option D (-1,5)
We have x=-1, y=5
putting values and checking
[tex]y<-3x+3\\5<-3(-1)+2\\5<3+2\\5<5 \ (false)\\y<x+2\\5<-1+2\\5<-1 \ (false)[/tex]
So, Option D is not correct as both values doesn't satisfy the given set of equations
The points that lie in the solution set of following system of inequalities are:
Option A (1,-5) and Option C (5,1)
Write an equation for the line in the given form.
slope is 5 and (-4, 8) is on the line; point-slope form
Answer:
Y =5x + 12
Step-by-step explanation:
You start with
y-8=5x(x+4)
y=5x+ 12
can someone help asap!!:)
One number is 10 more than another. The sum of twice the smaller plus three times the larger, is 55. What are the two numbers?
9514 1404 393
Answer:
5 and 15
Step-by-step explanation:
Let x represent the smaller number. Then the larger is x+10. The sum is ...
2x +3(x+10) = 55
5x +30 = 55
5x = 25
x = 5
The two numbers are 5 and 15.
__
Check
2·5 + 3·15 = 10 +45 = 55
12y=5x-15
4.2y+6.1x=11
Round to the nearest hundredth.
X=
Y=
Answer:
-15 and 11
Step-by-step explanation:
Find the gradient of the line perpendicular to AB
Find the equation of the line perpendicular to AB and passing through point C
Answer:
a) 3
b) y=3(x-2)-2
Step-by-step explanation:
a)
Step 1: Find the gradient/slope of AB
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]=[tex]\frac{-2-2}{7-(-5)} =\frac{-4}{12} =-\frac{1}{3}[/tex]
Step 2: Find the gradient/slope of the line perpendicular to AB
The slope of the line perpendicular to AB is the reciprocal of the slope of the line AB multiplied by -1, so the slope of the line perpendicular to AB is 3.
b)
Step 1: Find the formula for the equation of a line
If you have a point and the slope, you can use the point-slope form, which is y-y1=m(x-x1).
Step 2: Plug in values to the formula
y-(-2)=3(x-2)
Step 3: Simplify
y+2=3(x-2)
y=3(x-2)-2
[tex]$a)$[/tex] The gradient of a line perpendicular to line [tex]$AB$[/tex] is [tex]$3$[/tex].
[tex]$b)$[/tex] The equation of the line perpendicular to line [tex]$AB$[/tex] and passing through point [tex]$C$[/tex] is [tex]y=-\frac{1}{3}x+\frac{13}{3}[/tex].
What is slope of perpendicular lines?
Lines that are perpendicular lines have slopes that are negative reciprocals.
It is given that the points,
[tex]$A=\left( -5,2 \right)$[/tex]
[tex]$B=\left( 7,-2 \right)$[/tex]
[tex]$C=\left( -2,5 \right)$[/tex]
[tex]$a)$[/tex] We will find the gradient of a line perpendicular to line [tex]$AB$[/tex] by using the slope formula.
So,
By the definition, the slope or gradient of a line describes its steepness, incline, or grade.
[tex]$m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$[/tex] which is equal to [tex]$\tan \left( \theta \right)$[/tex].
Where [tex]$m$[/tex] is the slope and [tex]$\theta $[/tex] is the angle of incline.
So,
Slope [tex]$\left( m \right)=\frac{-2-2}{7-\left( -5 \right)}$[/tex]
[tex]m=\frac{-1}{3}[/tex]
So, The slope of the line perpendicular to [tex]AB[/tex] is the reciprocal of the slope of the line [tex]AB[/tex] which is multiplied by [tex]-1[/tex].
so the slope of the line perpendicular to [tex]AB[/tex] is [tex]3[/tex].
[tex]b)[/tex] We will find the equation of the line perpendicular to [tex]AB[/tex] passing through the point [tex]C[/tex] that is [tex](-2,5)[/tex] by using the formula,
[tex]y=mx+b[/tex]
Here,
[tex]y=5[/tex]
[tex]x=-\frac{1}{3}[/tex]
We will find the [tex]y-[/tex] intercept of the line [tex](b)[/tex] first.
So,
[tex]$5=-\frac{1}{3}\left( -2 \right)+b$[/tex]
[tex]$5=\frac{2}{3}+b$[/tex]
Subtract [tex]\frac{2}{3}[/tex] both side.
So,
[tex]$b=\frac{13}{3}$[/tex]
So, the line perpendicular to [tex]AB[/tex] and passing throught the point [tex]C[/tex] is,
[tex]y=-\frac{1}{3}x+\frac{13}{3}[/tex].
Hence,
[tex]$a)$[/tex] The gradient of a line perpendicular to line [tex]$AB$[/tex] is [tex]$3$[/tex].
[tex]$b)$[/tex] The equation of the line perpendicular to line [tex]$AB$[/tex] and passing through point [tex]$C$[/tex] is [tex]y=-\frac{1}{3}x+\frac{13}{3}[/tex].
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A rectangle has an area of 20 square centimeters. Which of the following could be the rectangle’s length and width?
Answer:
You did not give any options
Step-by-step explanation:
But 20 and 1 or 4 and 5 or 2 and 10 could possibly be the rectangle's length and width.
All but the first answer choice could be the length and width of a rectangle.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
A rectangle has an area of 20 square centimeters.
WE know that The area of the rectangle = length × Width
3 cm and 8 cm = 24 cm^2
This cannot be area of the given reactangle.
1 cm and 20 cm = 20 cm^2.
This is the area of the given reactangle.
2 cm and 10 cm => 20 cm^2
This is the area of the given reactangle.
4 cm and 5 cm => 20 cm^2.
This is the area of the given reactangle.
All but the first answer choice could be the length and width of a rectangle.
The complete question is
Which of the following could be the rectangle’s length and width?
1. 3 cm and 8 cm = 24 cm^2
2. 1 cm and 20 cm = 20 cm^2.
3. 2 cm and 10 cm => 20 cm^2
4. 4 cm and 5 cm => 20 cm^2.
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PLEASE HELP ASAP!!!!!!!!!!!
Find the equation of the line between ( -8, 2) and ( -4, 1)
Answer:
point slope form---> y-2=1/4(x- -8)
slope intercept form---> y=1/4x+4
Step-by-step explanation:
i didnt know which equation you were asking for
A bell tower that is 60 yards tall casts a shadow 32 yards long. If a nearby windmill is
45 yards tall, how long will the windmill's shadow be?
Write your answer as a whole number or a decimal. Do not round.
Answer:
24 yards long
Step-by-step explanation:
60/32 = 45/x
Cross Multiply:
60x = 1440
Divide both sides by 60.
x = 24 yards
Cost of Apples
1 pound of apple is $1.88
if this is a proportional relationship, write an equation relating the weight of the apples (a) to cost (c). If it is not a proportional relationship?
Answer:
Before 1845, “states were allowed to hold elections any time they pleased within a 34-day period before the first Wednesday in December.” What was one effect of this election system?
Voters in states with late elections knew the results of early elections.
Farmers were often unable to get to their polling place in time to vote.
The people who voted first could decide the outcome of most elections.
People spent less time in church because they would often travel to vote on Sundays.
Step-by-step explanation:
what is the greatest common factor of 55+35
Answer:
5
Step-by-step explanation:
this is due soon plz help
Answer:
tre made an error when adding or subtracting. the answer is 05
Simplifying
3.57x + 1.61 = 4.71 + -2.63x
Reorder the terms:
1.61 + 3.57x = 4.71 + -2.63x
Solving
1.61 + 3.57x = 4.71 + -2.63x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2.63x' to each side of the equation.
1.61 + 3.57x + 2.63x = 4.71 + -2.63x + 2.63x
Combine like terms: 3.57x + 2.63x = 6.2x
1.61 + 6.2x = 4.71 + -2.63x + 2.63x
Combine like terms: -2.63x + 2.63x = 0.00
1.61 + 6.2x = 4.71 + 0.00
1.61 + 6.2x = 4.71
Add '-1.61' to each side of the equation.
1.61 + -1.61 + 6.2x = 4.71 + -1.61
Combine like terms: 1.61 + -1.61 = 0.00
0.00 + 6.2x = 4.71 + -1.61
6.2x = 4.71 + -1.61
Combine like terms: 4.71 + -1.61 = 3.1
6.2x = 3.1
Divide each side by '6.2'.
x = 0.5
Simplifying
x = 0.5
HELP ME
solve for X
Answer:
203/11x
Step-by-explanation: I am soo very sorry gave you the wrong answer before but going over it I see it is 203/11x
A number raised to the third power. What is this called???
Answer:
Cubed
Step-by-step explanation:
You can think of it as the volume of a cube where the volume is x to the third power ([tex]x^{3}[/tex], let x = side of the cube) to help you remember. This also goes the same for x to the second power (squared) where it can represent the area of a square which is x².
Hope this helps :)
What is 1 2/3 equal to
What is 6 3/4 equal to
What is -9 7/3 equal to
What is 4 2/7 equal too
Answer:
1 2/3 = 5/3
6 3/4 = 27/4
-9 7/3 = -34/3
4 2/7 = 30/7
Step-by-step explanation:
The hardcover version of a book weighs twice as much as its paperback version. The hardcover book and the paperback together weigh 4.2 pounds. Which system of equations can be used to find h, the weight of the hardcover book, and p, the weight of the paperback?
h = p − 4.2
h = 2p
h = 4.2 − p
p = 2h
h = p − 4.2
p = 2h
h = 4.2 − p
h = 2p
Answer:
the correct option id D.
h = 4.2 − p
h = 2p
The correct equation which can be used to find h, the weight of the hardcover book, and p, the weight of the paperback is,
⇒ h = 2p
⇒ h = 4.2 - p
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The hardcover version of a book weighs twice as much as its paperback version.
And, The hardcover book and the paperback together weigh 4.2 pounds.
Now,
Let the hardcover book weight = h
And, the paperback together weigh = p
Hence. We get;
h + p = 4.2
h = 4.2 - p
And, The hardcover version of a book weighs twice as much as its paperback version.
Hence, We get;
⇒ h = 2p
Thus, The correct equation which can be used to find h, the weight of the hardcover book, and p, the weight of the paperback is,
⇒ h = 2p
⇒ h = 4.2 - p
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A line had a slope of -2/3 and passes through the point (-3, 8). what is the equation of the line?
A y=-2/3x+6
B y=-2/3x+8
C y=6x-2/3
D y=8c-2/3
PLS HURRY IM TIMED ON THIS
Answer:
I think B, but not sure.......
Step-by-step explanation:
I dont need the work, just the answers :)
Write in expanded form.
Answer:
a²*b² /c*d
Step-by-step explanation:
Plzzz help its due by 12
Answer:
THE MAN WHO PUT SOAP IN HIS SOUP SO HE COULD WASH IT DOWN WITH SOMETHING
Step-by-step explanation:
Answer:
me think me made girl mad on brainly
Step-by-step explanation:
Refer to the system of linear equations shown below. Which of the following statements gives the best choice for multiplying to solve this system using the elimination method? 3x−6y=4 6x+11y=−2
I NEED IT URGENtLY
Answer: I just took the test and the answer is Student should show that the solution to the system of equations 7x - y = 4 and 2x - 3y = 1 is the same as the solution to the given system of equations.
Step-by-step explanation:
The solution for the given system of linear equations is (32/69, -10/23).
The given system of equations are 3x-6y=4 and 6x+11y=-2.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Here,
3x-6y=4 ---------(I) and 6x+11y=-2 ---------(II)
Multiply equation (I) by 2, we get
6x-12y=8 ---------(III)
Subtract equation (III) from (II), we get
6x+11y-(6x-12y)=-2-8
⇒ 23y=-10
⇒ y=-10/23
Substitute y=-10/23 in (I), we get
3x-6(-10/23)=4
⇒ 3x+60/23=4
⇒ 3x=4-60/23
⇒ x=32/69
So, solution is (32/69, -10/23)
Therefore, the solution for the given system of linear equations is (32/69, -10/23).
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solve 4 x 9.4 using distributive property. show your work
so it basically 36.16
Step-by-step explanation:
4x9=36
4x4=16
36.16
At Stop n Shop they are selling fried chicken for $1.95 a pound. If Amiyah buys 13.2 pounds how much will she spend?
Answer:
Step-by-step explanation:
Price of one pound = 1.95
Price of 13.2 pounds = 13.2 x 1.95 = 25.74
An NBA Basketball Court is a RECTANGLE that is 94 FEET long and 50 FEET wide. What is the AREA of the Court ? What is the PERIMETER of the Court?
Answer:
perimeter: 288 feet
area: 4700 feet
Step-by-step explanation:
explanation if wanted
Answer:
perimeter: 288 feet
area: 4700 feet
Step-by-step explanation:
How many of you guys think Into The Night by Bath & Body Works smells like men's cologne?
Answer:
It smells soooo good, I love it, but sadly i am not allowed to get it XD
Step-by-step explanation:
Answer:
KIND OF BUT THE BEST ONE IS WARM VANILLA SUGAR AND GLOW I THINK AND VELVET SUGAR I HOOKED YOU UP
Step-by-step explanation:
Simplify 4(2x-3) 7th grade math
Answer:
8x-12
Step-by-step explanation:
Answer:
8x-12Step-by-step explanation:
[tex]4(2x-3)[/tex]
Expand
[tex]4\times 2x = 8x\\\\4\times(-3)=-12\\\\8x-12[/tex]
please help asap!!!! i’ll mark brainlest
Answer:
C. 40 kilograms
Step-by-step explanation:
3.8:(4c+3)=2: 2 2/19
what is c
will give brainiest pls help quick
Answer:
the answer will be be 0.25 for decimal but for a fraction it would be 1/4
Answer:
0.25 is the answer :D
Given the function: f(x) = 7x + 8.
Find the value of y when x = -6.
Answer:
-34
Step-by-step explanation:
7x + 8
7(-6)+8
-42+8
-34
Have a beautiful day! v(⌒o⌒)v
A triangle has vertices at R(1, 1), S(–2, –4), and T(–3, –3). The triangle is transformed according to the rule R0, 270°. What are the coordinates of S'?
(–4, 2)
(–2, 4)
(2, 4)
(4, –2)
Answer:
A
Step-by-step explanation:
Answer:
a.
Step-by-step explanation:
Solve each system by graphing or using a table. Check your answers.
2x+y=−1
−x−2y=−4
Answer:
Step-by-step explanation:
Answer:
The first one: y = 2x - 1
The second one: y = 1/2x + 2
And if the second one is wrong, then it's y = x + 2.
If you can’t see it , it says ... Bella Amman is a sales consultant. She travels all over the country selling her company’s products. Her total monthly expenses for June , July, and August were $4,356.01 , $9,011.20 , and $8,780.00 . What was her average monthly expenditure?
A. $7,382.40
B. $6,565.00
C. $8,090.25
D. $22,147.21
Answer:
A.) $7832.40
Step-by-step explanation:
9,011.20+8,780.00+4,356.01
=22,147.21/3
=7382.40