which point lies in the solution set of the inequality 1/2(x+2)+3y<8?
Answers
Note: Options are missing. So, the general solution of the given inequality is shown below.
Given:
The inequality is:
[tex]\dfrac{1}{2}(x+2)+3y<8[/tex]
To find:
The point lies in the solution set of the given inequality.
Solution:
We have,
[tex]\dfrac{1}{2}(x+2)+3y<8[/tex]
It can be written as:
[tex]\dfrac{1}{2}(x)+\dfrac{1}{2}(2)+3y<8[/tex]
[tex]\dfrac{1}{2}x+1+3y<8[/tex]
[tex]\dfrac{1}{2}x+3y<8-1[/tex]
[tex]\dfrac{1}{2}x+3y<7[/tex]
All the points that satisfy the above inequality are in the solution set of the given inequality.
For example (0,0).
[tex]\dfrac{1}{2}(0)+3(0)<7[/tex]
[tex]0<7[/tex]
This statement is true. It means (0,0) is in the solution set.
For example (0,3).
[tex]\dfrac{1}{2}(0)+3(3)<7[/tex]
[tex]9<7[/tex]
This statement is false. It means (0,3) is not in the solution set.
The graph of the inequality [tex]\dfrac{1}{2}x+3y<7[/tex] is shown below.
All the points in the shaded region are in the solution set but the points on the boundary line are not in the solution set.
Related Questions
Find the area of the triangle defined by the coordinates (-3,-4), (-7.0), and (-3, 4).
Answers
i think D is the answer 16
9-3 additional practice circles in the coordinate plane
Answers
Answer:
1. The center is (-5, 6)
The radius is 11
2. The center is (3, -9)
The radius is 6
3. The center of the circle is (-4, -2)
The radius is 3
4. The coordinate of the center of the circle is (2, 2)
The radius of the circle is 4
5. The equation of the circle is (x - 4)² + (y + 3)² = 2²
6. The equation of the circle is (x + 1)² + (x - 10)² = 7²
7. The given point (6, 8) does not lie on the circumference of the circle
8. Yes, the point (√17, 4) lies on the circumference of the circle
9. Please find the attached graph created with the aid of MS Excel
10 Please find the attached graph created with the aid of MS Excel
11. The equation of the circle is (x - a)² + (y - b)² = c²
12. The equation of the circle is x² + y² = 1
Step-by-step explanation:
1. The equation of the circle is (x + 5)² + (y - 6)² = 121
The standard form of the equation of a circle is (x - h)² + (y - k)² = r²
Where;
The center of the circle = (h, k)
The radius of the circle = r
By comparison we have;
h = -5, k = 6, and r = √121 = 11
The center of the circle, (h, k) = (-5, 6)
The radius of the circle, r = 11
2. (x - 3)² + (x + 9)² = 36
Similar to question 1, above, we have by comparison;
h = 3, k = -9, r = √36 = 6
The center of the circle, (h, k) = (3, -9)
The radius of the circle, r = 6
3. From the graph of the circle on the coordinate plane, we have;
The center of the circle = (-4, -2)
The radius of the circle = -1 - (-4) = 3
4. From the graph of the locus of the circle, we have;
The coordinate of the center of the circle, r = (2, 2)
The length of the radius of the circle = The distance from the center to the point (-2, 2)
Therefore, the radius of the circle, r = 2 - (-2) = 4
5. The given radius of the circle, r = 2
The center of the circle, (h, k) = (4, -3)
The equation of a circle in standard form is (x - h)² + (y - k)² = r²
By comparison, we have the equation of the circle given as follows;
(x - 4)² + (y - (-3))² = (x - 4)² + (y + 3)² = 2²
The equation of the circle is (x - 4)² + (y + 3)² = 2²
6. The given radius of the circle, r = 7
The center of the circle, (h, k) = (-1, 10)
The equation of a circle in standard form is (x - h)² + (y - k)² = r²
By comparison, we have the equation of the circle given as follows;
(x - (-1))² + (y - 10)² = (x + 1)² + (y - 10)² = 7²
The equation of the circle is (x + 1)² + (x - 10)² = 7²
7. The given point = (6, 8)
The radius, r = 4
The center of the circle = (3, 5)
The point lies on the circle if the distance. 'd', from the point to the center of the circle = The radius of the circle
∴ d = √((6 - 3)² + (8 - 5)²) = √((3² + 3²) = √(18) = 3·√2
Given that the distance from the point to the center of the circle, d = 3·√2 ≠ 4 = r, the point (6, 8), does not lie on the circumference of the circle
8. The point = (√17, 4)
Radius, r: 9
The center: (0, -4)
The distance from the point to the center of the circle, d = √((√17 - 0)² + (4 - (-4))²) = 9 = r, the radius of the circle
Therefore, given that the distance of the point from the center of the circle = The radius of the circle, the point, (√17, 4), lies on the circumference of the circle
9. The given equation of the circle is (x - 5)² + (y - 1)² = 49
Comparing with the equation of a circle in standard form, we have;
The center of the circle, (h, k) = (5, 1)
The radius of the circle, r = √49 = 7
Please find the attached graph created with the aid of MS Excel
10. The given equation of the circle is x² + (y - 3)² = 25
The center of the circle, (h, k) = (0, 3)
The radius of the circle, r = √25 = 5
Please find the attached graph created with the aid of MS Excel
11. Given that the center of the circle is (a, b) and the radius of the circle is c, the equation of a circle in standard form, (x - h)² + (y - k)² = r², becomes;
(h, k) = (a, b)
r = c
∴ (x - a)² + (y - b)² = c²
12. The diameter of the circle, d = 2 in.
The center of the circle = The origin with coordinates, (0, 0)
Therefore;
The radius of the circle. r = d/2 = 2 in./2 = 1 in.
The center of the circle, (h, k) = (0, 0)
The equation of the circle is therefore;
(x - 0)² + (y - 0)² = 1²
Which gives the equation of the circle as x² + y² = 1.
Is this correct!! Can someone verify!!
Answers
Find the distance between the ordered pairs to
the nearest hundredth.
(1,-8) and (2,4)
Answers
Answer:
12.05
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√(2 - 1)² + [4 - (-8)]²
√(1)² + (12)²
√(1) + (144)
√145
12.05
Solve:
ab^2-(a-c)b-c=?
Answers
Answer:
ab^2-(a-c)b-c
ab^2-ab+bc-c
ab(b-1)+c(b-1)
(b-1)(ab+c)
Solve the equation
3/4x+3-2x= -1/4+1/2x+5
Please help I have tried everything and I haven’t gotten the right answer and it won’t let me move on
Answers
Put in terms of 4 as denominator
3/4x + 12/4 - 8/4x = -1/4 + 2/4x + 20/4
Combine like terms
-5/4x + 12/4 = 2/4x + 19/4
Simplify
12/4 = 7/4x + 19/4
-7/4 = 7/4x
x = -1 :)
Check:
3/4(-1) + 3 - 2(-1) = -1/4 + 1/2(-1) + 5
-3/4 + 3 + 2 = -1/4 - 1/2 + 5
-3/4 + 5 = -3/4 + 5
-3/4 = -3/4 :)
Please help I’ll give brainliest
Answers
Answer:
[tex]A=60m^2[/tex]
Step-by-step explanation:
formula for area of a parallelogram is [tex]A=bh[/tex] where [tex]b[/tex] stands for base and [tex]h[/tex] stands for height.
[tex]A=12(5)[/tex]
[tex]A=60[/tex]
If f(x) = 1 - 2x^3, find the inverse of f.
Answers
f(x) is another way of saying y, so basically tha initial function is y = 1-2x^3.
Change it up to x = 1-2y^3 and solve for y
X - 1 = - 2y^3
(X - 1)/-2 = y^3
So the cube root of ((x-1)/2) = y
Question Progress
Homework Progress
31/ 127 Marks
There are between 24 and 40 students in a
class.
The ratio of boys to girls is 4:7
How many students are in the class?
Answers
Answer:
Step-by-step explanation:
The ratio of boys is 4/11
You need a number that is divisible by 11.
11 represents the number of students in the class. That was obtained by adding 4 and 7 together. So there are 4/11 boys and 7/11 girls.
You could try 33 which is between 24 and 40
4/11 * 33 = 12
There are twelve boys in the class.
7/11 * 33 = 21
There are 21 girls in the class.
21 + 12 = 33 which is exactly what you need.
A music website charges x dollars for individual songs and y dollars for entire albums. Person A pays $5.45 to download 2 individual songs and 3 albums. Person B pays $8.41 to download 5 individual songs and 4 albums. Write a system of linear equations that represents this situation. How much does the website charge to download a song? an entire album?
Answers
Answer:
Amount charged for downloading individual songs = x dollars
Amount charged for downloading an entire album = y dollars
In respect to person A:
6x + 2y = 25.92
3x + y = 12.96
y = 12.96 - 3x
In respect to person B:
4x + 3y = 33.93
Putting the value of y from the first equation in the second, we get
4x + 3(12.96 - 3x) = 33.93
4x + 38.88 - 9x = 33.93
- 5x = - 4.95
x = 0.99 dollars
Putting the value of x in the first equation, we get
y = 12.96 - 3x
= 12.96 - 2.97
= 9.99 dollars
Step-by-step explanation:
John is 8 years younger than Ahmad. If the sum of their ages is 38, how old is John?
Answers
Since John is 8 years younger than Ahmad, the equation would be as follows:
x+x-8=38
Solve for x:
2x-8=38
38+8=46
2x=46
x=23
23 is Ahmad’s age, subtract 8 from this and you’ll get 15 for John’s age.
12) To make 84 tiny pancakes I need 3 /2 cups of mix, and 14 cups of water.
How much mix and water are needed to make 1 dozen tiny pancakes? Write
your answer in ratio format e.g., 0.75 : 1.5*
Answers
Answer:
1 dozen=12. 84/12=7. You answer SHOULD be 7:1 but I haven't done ratios in a while so don't quote me on it.
Step-by-step explanation:
. For the function y= -5x2 - 10x + c, the vertex is (-1,8). What is c? F. -13 G. -3 - J. 13 H. 3
Answers
Answer:
c=3
Step-by-step explanation:
8=-5(-1)^2-10(-1)+c
8=5+c
c=3
Consider this function in recursive form.
A1 = -8
An = 3 + an-1
Enter an equivalent equation written in explicit form where n is the term number.
Type your response in simplest form. Do not type any spaces in your response.
an
An = _____
Answers
Answer:
Step-by-step explanation:
Io
Drag the ordered pairs to match the points shown on the coordinate grid.
Answers
Answer:
A) (3, 6)
B) (2, 3)
C) (4, 2)
D) (6, 0)
Use the slope formula to find the missing coordinate.
m = -7/2 , T(13, 2), W(_, -5)
-11
15
11
Answers
15
Answer:
Solution given;
m = -7/2 , T(13, 2), W(_x, -5)
m=(y2-y1)/(x2-x1)
-7/2=(-5-2)/(x-13)
-7/2=-7/(x-13)
doing crisscrossed multiplication
x-13=2
x=2+13
x=15
Answer:
the answer is 15
Step-by-step explanation:
correct me if I'm wrong thanks
ASAAAPPP PLEASE HELP!!
Answers
Answer:
C is correct
Step-by-step explanation:
Just add the exponents leaving you with 2 squared which is 4
Answer:
[tex]a^b*a^c=a^{b+c}[/tex]
[tex]2x^{1/2} *2^{3/2} =2^{1/2+3/2}[/tex][tex]=2^{4/2}[/tex][tex]=2^2[/tex][tex]=4[/tex]-----------------------
hope it helps...
have a great day!!
Order the numbers −7, 2, −4, 8 from least to greatest
Answers
Got another question for you lovely folk, don’t understand how to do this one either
Answers
Answer:
97.12°
Step-by-step explanation:
the value of the highlight angle =
tan~¹ 1/3 + tan~¹ 5/1 =
18.43° + 78.69° = 97.12°
What are the solutions of the equation x2 + 5x + 6 = 0? A. −3, 2 B. 6, −1 C. 6, 1 D. −3, −2
Answers
Answer:
D. -3,-2
Step-by-step explanation:
Let [tex]x^{2} +5x+6=0=(x+2)(x+3)\\[/tex], then [tex]x+2=0[/tex] or [tex]x+3=0[/tex], thus [tex]x=-2[/tex] or [tex]x=-3[/tex]
p(Febuary 31) Calculate the probability of the event
Answers
Answer:
You can't find the probibilty of the event because it doesn't exist
Step-by-step explanation:
Helppp plzzzzz pointttttts
Answers
Answer:
AD & BE
Step-by-step explanation:
1) AB+BD = AD
2)BC+CE = BE
step by step explanation pls
Answers
Answer:
For the first circle: x=40°
For the second circle: x=94°
Step-by-step explanation:
First circle:
The angle you are trying to figure out is congruent to the 40° angle. This is because they are parallel to one another with a perpendicular intersection.Second circle:
The angle starting in the center of the circle is twice as large as the angle starting at the edge of the circle.You need to do a little math:20+27 = 4747x2 = 94°Marian asked 25 students the following questions in a survey.
1. Are you male or female?
2. Do you wear glasses?
Marian's results are shown below.
There were a total of 15 female students who were surveyed.
• There were 17 students who wear glasses.
Answers
Answer:
Step-by-step explanation:
stuck on this ixl, help me!
Answers
Answer:
-1
Step-by-step explanation:
in negative numbers, it goes the opposite of positive numbers
Brainliest goes to whoever answers correctly I have other questions if you want more points
Answers
Answer:
B, E, F
Step-by-step explanation:
Answer:
B, F
Step-by-step explanation:
A is false; the slope of function Z is 1/4 and the slope of function W is 1/2. 1/2 is greater than 1/4.
B is true. The slope of function Z is less then the slope of function W.
C is false, the y-intercept of function Z is -2 and the y-intercept of function W is -1. They are not the same number.
D is false, the y-intercept of function W is greater than Function Z.
E is false, -3 and -3 are equal
Function W:
y = 1/2x - 1
y = 1/2(-4) - 1
y = -4/2 = -2
y = -2 - 1
y = -3
Function Z:
y = 1/4x - 2
y = 1/4(-4) - 2
y = -1 - 2
y = -3
F is true, if y = -4 for functions W and, they would both be equal.
evaluate the expression 4(n+5)-8 when n =1/4 and m=0.5
Answers
Answer:
17
Step-by-step explanation:
Given
4(n + 5) - 8m ← substitute n = 0.25, m = 0.5 into the expression
= 4(0.25 + 5) - 8(0.5)
= 4(5.25) - 4
= 21 - 4
= 17
Hudson wants to write a letter to his friend. He took out
square paper which covers the total area of 225 feet^2
.
What is the length of any side of the paper?
Answers
Answer:
length = 15 feet.
Step-by-step explanation:
This paper is 15 feet across on any side. Who will deliver this monster?
Area = s^2 where s is the length of 1 side.
Area = 225 feet^2 (You sure this isn't inches).
s^2 = area
s^2 = 225 Take the square root of both sides of the equation.
sqrt(s^2) = sqrt(225)
s = 15
The surface area of the prism is ______ square units. All measurements in the image below are in units. (Input whole number only.)
Numerical Answers Expected!
Answer for Blank 1:
Answers
Answer:
54
Step-by-step explanation:
Surface area of triangular prism = bh + L(s1 + s2 + s3)
Where,
b = 3
h = 4
L = 3.5
s1 = 3
s2 = 4
s3 = 5
Plug in the values into the equation
Area of the triangular prism = 3*4 + 3.5(3 + 4 + 5)
= 12 + 42
= 54 units²
Help me please , show your work