Find a linear inequality with the following solution set. Each grid line represents one unit.(Give your answer in the form $ax+by+c>0$ or $ax+by+c\geq0$ where $a,$ $b,$ and $c$ are integers with no common factor greater than 1.)
Answers
Answer:
-x + 2y + 1 > 0
Step-by-step explanation:
Let's find the equation of the dashed line first. From the graph, we can see that it has a slope of 1/2 and a y-intercept of -1/2 so using slope-intercept form, the equation of the line is y = 1/2x - 1/2. Since the line is dashed and not solid, we know that we will use either < or > instead of ≤ or ≥, and because we can see that the shaded region is above the dashed line, we know that the linear equation is y > 1/2x - 1/2. However, we want the answer to be in the form ax + by + c > 0 where a, b, and c are integers so therefore:
y > 1/2x - 1/2
= 2y > x - 1
= -x + 2y + 1 > 0
A linear inequality is an expression which make comparison between linear expressions using inequalities. The linear inequality of the graph is: [tex]-x + 2y +1 > 0[/tex]
First, we calculate the slope of the dashed line using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Two points on the graph will be:
[tex](x_1,y_1) = (1,0)[/tex]
[tex](x_2,y_2) = (3,1)[/tex]
The slope (m) is:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{1-0}{3-1}[/tex]
[tex]m = \frac{1}{2}[/tex]
The equation of the line is calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have;
[tex]y = \frac12(x - 1) + 0[/tex]
[tex]y = \frac12(x - 1)[/tex]
Multiply through by 2
[tex]2y= x - 1[/tex]
Now, we convert the equation to an inequality.
The line on the graph is a dashed line. This means that the inequality is either > or <. Also, the upper region of the graph that is shaded means that the inequality is >.
So, the equation becomes
[tex]2y > x-1[/tex]
Rewrite as:
[tex]-x + 2y +1 > 0[/tex]
So, the linear inequality is: [tex]-x + 2y +1 > 0[/tex]
Learn more about linear inequality at:
https://brainly.com/question/19491153
Related Questions
You buy six T-bone steaks that cost $15.99 per pound. The weight that is listed on the package is 5.77 pounds. The scale that weighed the package is accurate to within 1 32 pound. How much per kilogram might you be undercharged or overcharged? (Round to the nearest cent.)
Answers
Answer:
Amount per kilogram, undercharged or overcharged is 0.50
Step-by-step explanation:
Given:
cost of T-bone steaks per pound = $ 15.99
weight listed on package = 5.77 lb
Accuracy of the scale = 1/32 lb
To find:
Amount undercharged or overcharged
Solution:
Let x represent the weight of the package.
Then compute the error in the weight
| x - 5.77 | < 1 / 32
This makes an absolute value inequality
If an inequality is given in the form | x | < a then solution is in the form:
–a < x < a.
If an inequality is in the form | x | > a, then solution splits in the form:
x < –a or x > a.
compute the amount undercharged or overcharged:
First multiply the above inequality by cost of T-bone steaks per pound
15.99 |x - 5.77| < 15.99 (1 / 32)
15.99 |x - 5.77| < 15.99(0.03125)
15.99 |x - 5.77| < 0.4996875
15.99 |x - 5.77| < 0.50
Hence the amount undercharged or overcharged is $0.50
Y = A system of equations. Y equals StartFraction one-half EndFraction x minus 6. X equals negative 4.X – 6 x = –4 What is the solution to the system of equations?
Answers
Answer:
[tex]x = -4, y =-8[/tex] is the solution to the system of equations.
Step-by-step explanation:
Given the system of equations as:
[tex]y= \dfrac{1}{2}x-6[/tex]
and
[tex]x =-4[/tex]
To find:
The solution to the system of equations = ?
Solution:
Here, we are given two equations and two variables i.e. [tex]x[/tex] and [tex]y[/tex].
So, we can solve the system of equations for the values of [tex]x[/tex] and [tex]y[/tex].
Let us first consider the 2nd equation.
[tex]x =-4[/tex] we already have the value of [tex]x[/tex].
Now, let us put the value of [tex]x[/tex] in the 1st equation to find the value of [tex]y[/tex].
[tex]y= \dfrac{1}{2}x-6[/tex]
[tex]\Rightarrow y= \dfrac{1}{2}\times (-4)-6\\\Rightarrow y= -\dfrac{1}{2}\times 4-6\\\Rightarrow y= -2-6\\\Rightarrow \bold{y =-8}[/tex]
So, the solution to the system of equations is:
[tex]x = -4, y =-8[/tex]
Plz help me ! In triangle ABC, angle A = 90° and angle B = 25°. In triangle DEF, angle E =
25° and angle F = 65°. Are the Triangles similar?
Answers
What is the area, in square meters, of the shaded part of the rectangle below?
6 m
14 m
13 m
Answers
Answer:
130 meters squared
Step-by-step explanation:
14-6=8
8*13/2=52
14*13=182
182-52=130 meters
Answer:
130 square metres
Step-by-step explanation:
The shaded area is a trapezium.
Therefore, the rule for its area is base1+base2/2xh
base1=6
base2=14
height = 13
Therefore, 6+14/2 x 13
= 130
Hope that helped!!! k
How to do this question plz answer my question
Answers
Answer:
510,064,471,910,000 m² or 5.1 x 10^14 m²
Step-by-step explanation:
4πr²
if the diameter is 12742, then the radius is 6371
4π(6371)²
510,064,471.91 km²
510,064,471,910,000 m²
Answer:
510064471909788 m²
Step-by-step explanation:
diameter=12742 so the radius r=12742/2=6371=6371*1000=6371000
A=4πr²
A=4π(6371000)²
A=162358564000000π =510064471909788 m²
-7 - p= p +3
How do you do this
Answers
Answer:
-5 = p
Step-by-step explanation:
-7 - p= p +3
Add p to each side
-7 - p+p= p+p +3
-7 = 2p+3
Subtract 3 from each side
-7-3 = 2p+3-3
-10 = 2p
Divide each side by 2
-10/2 = 2p/2
-5 = p
An account pays 8% per year simple interest paid a new one, the amount in the account is $850. How much is the account in year 6?
Answers
Answer:
1258
Step-by-step explanation:
SI = (P x R x T) / 100
SI = Simple Interest
P = Principal
R = Rate
T = Time
SI = (850 x 8 x 6)/100
=> SI = 85 x 8 x 6 /10
=> SI = 680 x 6 /10
=> SI = 68 x 6
=> SI = 408
The total amount after 6 years = Principal + Simple Interest
=> Total Amount = 850 + 408
=> Total Amount = 1258
After 6 years, the amount in account is 1258.
Which of the following is a rational number?
square root of 22, square root of 23, square root of 24, square root of 25
square root of 22
square root of 23
square root of 24
square root of 25
Answers
Answer:
square root of 25 because it equals 5
Step-by-step explanation:
Because the square root of the other they don’t replete or terminate.
square root of 22 is 4.6904157...
square root of 23 is 4.7958315...
square root of 24 is 4.8989794...
square root of 25 is 5
Please help me with this question ASAP.
How many planes of symmetry are there in a regular hexagonal prism?
Answers
Answer:
we have 6 planes of symmetry
Whats the answer? For all of them
Answers
Answer:
cow = 4
pig = 5
chicken = 9
horse = 3
horse + chicken - pig =7
10 People fit comfortably in a 5 feet by 5 feet area. Use this value to estimate the size of a crowd that is 5 feet deep on both sides of the street along a 2-mile section of a parade route.
Answers
Answer:
The size of the crowd that is 5 feet deep on both sides of the street along a 2-mile section of a parade route is 42,240 people
Step-by-step explanation:
The number of people that can fit comfortably in a 5 feet by 5 feet area = 10
Therefore;
The ratio of the number of people per unit area = 10/(5 × 5) = 10/25
The area, A, occupied by the crowd = 5 feet × 2 mile × 2
2 miles = 10,560 feet
∴ A = 5 feet × 10,560 feet × 2 = 105,600 ft²
We then have;
[tex]\dfrac{Number \ of \ people}{105,600} =\dfrac{10}{25}[/tex]
[tex]Number \ of \ people = {105,600} \times \dfrac{10}{25} = 42,240 \ people[/tex]
u need help ASP .
f(x)=1-3X and g (x)=x+4 calculate gf(-2)
Answers
Answer:
gf (-2) = 11
Step-by-step explanation:
[tex]f(x) = 1 - 3x \\ g(x) = x + 4 \\ gf( - 2) = ..[/tex]
[tex]gf = .. \\ g(1 - 3x) \\ = 1 - 3x + 4 \\ = - 3x + 5 \\ gf = - 3x + 5[/tex]
[tex]gf( - 2) = - 3( - 2) + 5 \\ = 6 + 5 = 11[/tex]
Find f(−1) given that f(x)=x3+2x2+3x+4.
A. 10
B. -2
C. 2
D. -10
Answers
Answer:
The answer is option C
Step-by-step explanation:
f(x) = x³ + 2x² + 3x + 4
To find f(-1) substitute the value of x that's
- 1 into f(x)
That's
[tex]f( - 1) = ({ - 1})^{3} + 2 ({ - 1})^{2} + 3( - 1) + 4 \\ = - 1 + 2(1) - 3 + 4 \\ = - 1 + 2 - 3 + 4 \\ = 1 - 3 + 4[/tex]We have the final answer as
[tex]f( - 1) = 2[/tex]Hope this helps you
Can i please get some quick help?
Answers
Answer:
the inverse is the third choice
I NEED HELP, I'VE BEEN STUCK ON THIS...Find the volume of this triangular prism. Enter only the numerical part of your answer in square units.
Answers
Answer:
[see below]
Step-by-step explanation:
Volume of a triangular prism is: [tex]V=\frac{1}{2}bhl[/tex]
We are given the base of 5, the length of 12, and the height of 8. All measurements are in meters.
[tex]V=\frac{1}{2}(5*12*8)\\\\V=\frac{1}{2}(480)\\\\V=240[/tex]
The volume of the prism should be 240 square meters.
Answer:
V = 240 m^3
Step-by-step explanation:
The volume of a triangular prism is
V = Bh where B is the area of the base and h is the height
B = the area of the triangular base
B = 1/2 bh
B = 1/2 *5*12
B = 30 m^2
The volume is
V = 30 * 8
V = 240 m^3
Find x round to the nearest tenth
Answers
Answer:
[tex] X = 70.5 [/tex]
Step-by-step explanation:
The law of Cosine given can be written in another form to make the Cos(C) the subject of the formula. Which is: [tex] cos(C) = \frac{a^2 + b^2 - c^2}{2ab} [/tex]
Where,
a = 20 ft
b = 18 ft
c = 22 ft
C = X
[tex] cos(X) = \frac{20^2 + 18^2 - 22^2}{2*20*18} [/tex]
[tex] cos(X) = \frac{400 + 324 - 484}{720} [/tex]
[tex] cos(X) = \frac{240}{720} [/tex]
[tex] cos(X) = 0.3333 [/tex]
[tex] X = cos{-1}(0.3333) [/tex]
[tex] X = 70.5 [/tex]
Ms. Malle owns a restaurant. Typically 3/20 of the customer’s order fish, while 7/20 of the customer’s order poultry. What fraction of her customers order either fish or poultry?
Answers
A line 8cm Long is measured as 8.04cm. what is the percentage error?
Answers
Answer:
0.04%
Step-by-step explanation:
8.04-8.00
0.4/100
0.04%
please help :) Which sentence is true? A. 9.46 times 10 to the 12 power > 4.0 times 10 to the 13 power B. 9.46 times 10 to the 12 power < 4.0 times 10 to the 13 power
Answers
Answer:
B
Step-by-step explanation:
The problem is simple because they use powers of 10. When something is multiplied by a power of ten, it is essentially moving the decimal point over for every power.
9.46x10^12= 9460000000000
4.0x10^13= 40000000000000
Although 4 itself is less than 9.46, since is is being multiplied by 10^13, it will be one decimal place bigger.
0.017 and 10, please retype the steps you use to set up the problem and type your steps to solve .
Answers
Answer:
0.17
Step-by-step explanation:
0.017 times 10 will equal to 0.17 as you will need to move the decimal point forward by one
If m_ABD
-
83° and m ABC = (x + 10) and mZDBC
(2 + 10) and mZDBC = (4x – 12), what is the measure of each angle?
B
Enter the correct numbers in the boxes.
lo
mABC -
mZDBC =
Answers
Answer:
m<ABC=27°
m<DBC=56°
Step-by-step explanation:
(x+10)+(4x-12)=83
5x-2=83
5x=83+2
5x=85
x=17
m<ABC=(x+10)=(17+10)=27°
m<DBC=(4x-12)=(4*17-12)=56°
Evaluate ƒ(x ) = x 2 + 1 for ƒ(-1). A. 0 B. undefined C. 2
Answers
Answer:
2
Step-by-step explanation:
f(-1)=(-1)²+1=1+1=2
What is the equation for the axis of symmetry of a parabola?
Answers
Answer:
The graph of the parabola is represented by the quadratic function
y = a( x - p )2 + q which has an axis of symmetry represented by the equation of the vertical line x = p.
Step-by-step explanation:
Answer:
x=-b/2a
Step-by-step explanation:
find the area of the 1/4 circle when the radius is 8
Answers
Answer:
Method 1 (using the area of a whole circle and dividing by 4)
First work out the area of the whole circle by substituting the radius of 8cm into the formula for the area of the circle:
A = π ×r²
= π ×8²
= 64π (leave the answer as an exact solution as this need to be divided by 4).
So all you need to do now is divide the answer by 4:
Area of a quadrant = 64π ÷4 = 16π = 50.3 cm² to 3 significant figures.
Method 2 (using ¼ πr²)
Substitute r = 8 directly into the formula A = ¼ πr².
A = ¼ πr².
A = ¼ × π × 8².
A = 50.3 cm²
As you can see it gives exactly the same answer as method 1.
Answer:
64pi / 4 = 16pi, or 50.27
Step-by-step explanation:
We use the area formula:
π * r^2 = Area
Substitute in 8 for r to get 64pi
Then all you have to do is divide 64pi by 4 to find a quarter of the area of the circle, which is 16pi. Or if you want rounded to nearest tenth, 50.27
I'm trying to find 1, 2, & 3 but idk how? Sry if it's sideways I'm new
Answers
Answer:
Step-by-step explanation:
m∠1+∠2=180
2x+40+2y+40=180
2x+2y=180-80
2x+2y=100
x+y=50
x=50-y
m∠1=m∠3
2x+40=x+2y
2x-x=2y-40
x=2y-40
2y-40=50-y
2y+y=50+40
3y=90
y=30
x=50-y=50-30=20
m∠1=2x+40=2×20+40=80°
m∠2=2y+40=2×30+40=60+40=100°
m∠3=x+2y=20+2×30=80°
The length of a rectangle is 3cm longer than its width.If the perimeter of the rectangle is 54cm,find its length in cm.
Answers
Answer:
length = 15 cm
Width = 12 cm
Step-by-step explanation:
Let width = w cm
Length = w + 3
Perimeter of rectangle = 54 cm
2 * (length + width) = 54
2 * (w+3 + w) = 54 {Add like terms}
2 *(2w + 3) = 54
2*2w + 2 * 3 = 54
4w + 6 = 54
Subtract 6 form both sides
4w = 54 - 6
4w = 48
Divide both sides by 4
w = 48/4
w = 12 cm
Length = 12 + 3= 15 cm
Answer:
Length = 15cm
Step-by-step explanation:
let width be x
length = x+3
Perimeter = 2(l + b)
Perimeter = 54cm
equating:
2(x + x + 3) = 54
2(2x +3) = 54
4x + 6 = 54
4x = 54 - 6
4x = 48
x = 48/4 = 12
width = x = 12cm
length = x +3 = 12 + 3 = 15cm
Nine less than the quotient of a number and 2 is 11. Find the number.
Answers
a perfect is to be chosen from a class of 16 girls and 14 boys.what is the probability that the prefect is a girl
Answers
Answer:
8/15Step-by-step explanation:
[tex]16\:girls \\14\:boys\\\\Probability = \frac{Event}{Total \:possible\:outcome}\\\\ Event=16\\\\ Total\:possible\:outcome = 16+14=30\\\\P = \frac{16}{30}\\ \\Probability = \frac{8}{15}[/tex]
A full case of soda contains 24 bottles. Tom filled a partially empty case by putting in seven bottles. How many bottles were in the case before he filled it?
Answers
Answer:
17 bottles
Step-by-step explanation:
full case: 24
he added 7 bottles to fill a case
24-7=17
18 + ?t = 24 what number should be the coefficient of t?
Answers
Answer:
if t is 2 then coefficient will be 3
if t is 3 then coefficient will be 2
Step-by-step explanation:
18 + ?t = 24
subtracting 18 from sides
18 + ?t - 18= 24 -18 = 6
=> ?t = 6 = 2*3
as value of both ? and t is not given thus both can take value of 2 and 3
hence,
if t is 2 then coefficient will be 3
if t is 3 then coefficient will be 2
Answer:
the answer is 123
Step-by-step explanation: