Answers
Answer:
Part 1;
(0, 0)
Part 2;
(0, 2.5)
Step-by-step explanation:
Part 1
The given system of inequalities is presented as follows;
f(x) < x + 4; f(x) > -x - 3; and f(x) < 5
We check each of the points as follows;
The point (0, 0) in the inequality f(x) < x + 4, gives;
f(0) < 0 + 4
f(0) = 0 < (is less than) 0 + 4 = 4
Therefore, (0, 0) is a solution of the inequality f(x) < x + 4
The point (0, 0) in the inequality f(x) > -x - 3, gives;
f(0) < -0 - 3
f(0) = 0 > (is larger than) -0 - 3 = -3
Therefore, (0, 0) is a solution of the inequality f(x) > -x - 3
The point (0, 0) in the inequality f(x) < 5, gives;
f(0) < 5
f(0) = 0 < (is less than) 5
Therefore, (0, 0) is a solution of the inequality f(x) < 5
The point (-6, 0) in the inequality f(x) > -x - 3, gives;
f(-6) = -6 - 3 = 3
The point (-6, 0) with y = 0 < (is less than) f(-6) = 3, therefore (-6, 0) is not a solution to (not included in the graph of) the inequality f(x) > -x - 3 and therefore to the system of inequalities because at x = -6, the values of f(x) > -x - 3 are larger than 3
The point (-3, 4) in the inequality f(x) < x + 4, gives;
f(-3) = -3 + 4 = 1
The point (-3, 4) with y = 4 < (is larger than) f(-2) = 1, therefore (-3, 4) is not a solution to (not included in the graph of) the inequality f(x) < x + 4 and therefore to the system of inequalities because at x = -3, the values of f(x) < x + 4 are less than 1
The point (4, 6) is not a solution to (not included in the graph of) the inequality f(x) < 5 and therefore to the system of inequalities because f(x) is larger than 5 for all x
Therefore, the point which is part of the solution set of the system of inequalities is (0, 0)
Part 2
The given system of inequalities are, f(x) ≥ 2·x + 2; f(x) ≤ -4·x + 3; and f(x) ≤ 6·x + 5
Plotting the given system of inequalities on MS Excel the point which is part of the solution is given by points which are within the triangular intersection area of the three inequalities, with coordinates, (1/6, 7/3), (-3/4, 1/2), and (-1/5, 19/5)
Therefore, the points, (0, 0), (-2.5, 0) are not solutions because, the y-value of the solution area are all higher than the line y = 0
The point (0. 6.5) is not a solution because the points in the triangular solution area all have x-values lesser than x = 6.5
The point which is part of the solution by examination is the point (0, 2.5) which is a point between the lines y = 19/5 = 3.8, y = 1/2, x = -3/4, and x = 1/6.
Related Questions
Find the measure of the missing angle using the exterior angle sum theorm
Answers
Step-by-step explanation:
the sum of angels of a triangle is 180°
130+ ? + (180-160) = 180
130+ ? +20= 180
150+ ? = 180
? = 30°
the missing angle is 30°
Which graph represents a function?
Answers
Answer:
Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.I need help very badly. thanks
Answers
Answer:
Step-by-step explanation:
area of a triangle is 1/2* base * height
1/2* 2.6* 3 is the area of the end of the object , now just multiply by it's length
9*( 1/2* 2.6* 3 )
this looks like choice 3 of the choices
Which equation in slope-intercept form represents a line that is parallel to y=1/2x-2 and passes through the point (-8,1)?
Answers
Answer:
[tex]\displaystyle y=\frac{1}{2}x+5[/tex]
Step-by-step explanation:
We want to find the slope in slope-intercept form of a line that is parallel to:
[tex]\displaystyle y=\frac{1}{2}x-2[/tex]
And passes through the point (-8, 1).
Recall that parallel lines have equivalent slopes.
Since the slope of our given line is 1/2, the slope of our new line must also be 1/2.
We are also given that it passes through the point (-8, 1). Since we are given a slope and a point, we can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute 1/2 for m and (-8, 1) for (x₁, y₁). Hence:
[tex]\displaystyle y-(1)=\frac{1}{2}(x-(-8))[/tex]
Since we want the equation in slope-intercept form, we can isolate y. Distribute:
[tex]\displaystyle y-1=\frac{1}{2}x+4[/tex]
Therefore, our equation is:
[tex]\displaystyle y=\frac{1}{2}x+5[/tex]
which is represented by the table
Answers
Answer:
I think its is C
Anelle is in charge of bringing in dry erase markers for everyone in her math group to use to work on a project. She brings 3 markers for each person in her group and 5 extra markers for everyone to share. If Janelle brings in 23 markers in all, which equation represents the information?
Answers
Answer:
3x + 5 = 23
Step-by-step explanation:
Let x represents the number of persons in her group.
Since she brings 3 markers for each person, then number of markers brought for persons in her group = 3x.
She brings 5 extra markers for each person to share.
Thus, total markers she brought is now;
3x + 5
She brought 23 markers in all.
Thus, equation that represents the information is;
3x + 5 = 23
if f(1) = 2 – 2 anid 9(37)
and g(x) = x2 – 9, what is the domain of g(x) = f(x)?
Answers
Answer:
B
Step-by-step explanation:
Let divide g(x) by f(x)
[tex] \frac{ {x}^{2} - 9 }{2 - x {}^{ \frac{1}{2} } } [/tex]
The domain of a rational function cannot equal zero so let set the bottom function to zero.
[tex]2 - x {}^{ \frac{1}{2} } = 0[/tex]
[tex]x {}^{ \frac{1}{2} } = 2[/tex]
Square both sides
[tex]x = 4[/tex]
Also we can simplify the bottom denomiator into a square root function
[tex]2 - \sqrt{x} [/tex]
The domain of a square root function is all real number greater than or equal to zero because a square root of a negative number isn't graphable.
So we must find a answer that
Disincludes 4 from the intervalDoesnt range in the negative number or infinity)Range out in positve infinityThe answer to that is BF= P(1 + r)!
Rearrange the formula to highlight the present value.
P=
Answers
[tex]\tt\displaystyle\ P(1+r)!= r*(r-1) *(r-2)*(r-3) ..... *1[/tex]
Verify that cos squared A plus Sin squared A is equal to 1 if A is equal to 90 degrees
Answers
Answer:
see explanation
Step-by-step explanation:
To verify cos²A + sin²A = 1 with A = 90° , then
cos²90° + sin²90°
= (0)² + (1)²
= 0 + 1
= 1
In 2004 there were 7,000000 people living alone in great Britain this is four time as many as in 1961, Calculate how many people lived alone in 1961. Express your answer in standard form
Answers
Answer:
1.75 × 10⁶
Step-by-step explanation:
7,000,000 ÷ 4 = 1750000
Which is 1.75 × 10⁶ in standard form
ABCD is a quadrilateral.
a) Calculate the value of x.
b) When ABCD is drawn to scale, would the lines AD and BC be parallel or not? A You must justify your answer without using a scale drawing.
Answers
Answer:
A) 45=x
B) Yes, since both A and B are 90°
6x+90=360
6x=270
x=45
No lines are not parallel
a rectangle consists of two identical squares with a common side. The perimeter of the rectangle is 27 inches. Find its area
Answers
Answer:
40.5 square inches
Step-by-step explanation:
Rectangle consists of two identical squares.
So, if the sides of square = x,
Then, Width of rectangle = x &
Length of rectangle = x +x = 2x
Perimeter of rectangle = 27 inches
2*(length + width) = 27
2*( 2x + x) = 27 {Combine like terms]
2* 3x = 27
6x= 27 {Divide both sides by 6}
x = 27/6
x = 4.5
Width = x = 4.5 inches
Length = 2x = 2*4.5 = 9 inches
Area of rectangle = length *width
= 4.5 *9
= 40.5 square inches
Answer:
40.5
Step-by-step explanation:
By how much does the price of a ticket for the gold section exceed the price for a ticket for the silver section?
Answers
Answer:
$8
Step-by-step explanation:
This system of equations relates the ticket price, in dollars, for seats in the silver (x) and gold (y) sections at a rock concert. x + 2y = 82 3x + y = 96 By how much does the price of a ticket for the gold section exceed the price for a ticket for the silver section?
Two equations are presented in this question
x + 2y = 82 equation 1
3x + y = 96 equation 2
Multiply equation 1 by 3
3x + 6y = 246 equation 3
subtract equation 2 from 3
5y = 150
y = 30
Substitute for y in equation 1
x + 2(30) = 82
x = 82 - 60
x = 22
difference in price = 30 - 22 = $8
x =
Given PQR, R=90º....
Answers
Answer:
RQ = 9 units
Step-by-step explanation:
what is the value of b?
Answers
Answer: The b-value is the middle number, the number next to the X
Write a phrase in words to match each expression.
5+3
——
n
Answers
Answer:
sum of five and 3 is divided by n
help please i need help help
Answers
Answer: here is a picture of all of them I hope this helps :). This picture will clearly show the answers for 1 and 2
Step-by-step explanation:
Which numbers are solutions to the inequality X > 14- 5? Check all that apply.
fractions larger than
14.
decimals larger than 14
145
whole numbers larger than 14
the number 14
fractions smaller than 14
2
Answers
Answer:
fractions larger than 14 and one-half
decimals larger than 14 and one-half
whole numbers larger than 14 and one-half
Step-by-step explanation:
Which numbers are solutions to the inequality x greater-than 14 and one-half? Check all that apply.
Given that the inequality is represented by [tex]x>14\frac{1}{2}[/tex], i.e. x > 14.5
This inequality represent all the set of real numbers which are greater than 14.5. Whereas numbers including 14.5 and below are not involved. Hence the numbers that are a solution to this inequality are:
fractions larger than 14 and one-half
decimals larger than 14 and one-half
whole numbers larger than 14 and one-half
HELPP!
The functions f(x) and g(x) are described using the following equation and table:
f(x)=-4(1.09)x
Answers
Answer:
A: The y-intercept of f(x) is equal to the x-intercept of g(x)
Step-by-step explanation:
From the equation of f(x) given, we have;
f(x) = -4(1.09)^(x)
Now,the y-Intercept will be the point where x = 0.
Thus;
f(0) = -4(1.09)^(0)
f(0) = -4
Now,from the table given for g(x), we can see that at x = 0,g(x) = -4.
Thus,it means that the y-intercept of f(x) is equal to the x-intercept of g(x)
An operator in the plant receives a monthly salary. His rent, which is $849, takes up exactly 1/3 13 of his pay. What is his total pay per month?
Answers
Answer:
Below.
Step-by-step explanation:
(1/3)X = 849
x = 849*3 = 2547
The total pay per month of an operator is equal to $2547.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that an operator in the plant receives a monthly salary. His rent, which is $849, takes up exactly 1/3.
The total monthly salary will be calculated as,
(1/3)X = 849
X = 849 x 3
X= 2547
Therefore, the total pay per month of an operator is equal to $2547.
To know more about an expression follow
https://brainly.com/question/20912045
#SPJ5
Can anyone answer this I’m having trouble
Answers
Answer:
[tex]{ \bf{0.35{ \bar{2}}}} = { \bf{0.352222222....}} \\ = \frac{317}{900} [/tex]
A baseball league is holding registration for both a men's league and a women's league. Only a total of 400 players can register, and each team consists of exactly 10 players. If 24 women's teams have already registered, which inequality could be used to find m, the number of men's teams that can register?
A.
24(10) + 10m < 400
B.
24(10) + 10m > 400
C.
24(10 + 10m) > 400
D.
24(10 + 10m) < 400
Answers
Simplify the expression by combining like
terms:
2b + 7b2 - 2 + 3b - 1 + b
Answers
Answer:
[tex]7b^2+6b-3[/tex]
Step-by-step explanation:
Given:
[tex]2b+7b^2-2+3b-1+b[/tex]
Combine like terms.
[tex]7b^2+6b-3[/tex]
Hope this helps.
Simplify the expression. x^4/ x^7
a x-11
b x-3
c x11
b x3
Answers
Answer:
b
Step-by-step explanation:
[tex]\frac{x^4}{x^7} =x^4 \times x^{-7} =x^{4-7} =x^{-3}[/tex]
(-2x+1) (2x^2-1/3x+2)
Answers
Answer:
JHJHJHJHUJ3480945768
658768
Step-by-step explanation:
684867765543545
Ans x = 0.5
Step-by-step explanation:
[tex]= -4x^{3} + 2x^{2} +\frac{2}{3}x^{2} -\frac{1}{3}x-4x+2\\= -4x^{3}+\frac{8}{3}x^{2} -\frac{13}{3}x+2\\[/tex]
If the equation requires to find x, you can use Casio calculator to solve this by some basic formula:
Step 1: Type [tex]-4x^{3}+\frac{8}{3}x^{2} -\frac{13}{3}x+2[/tex]
Step 2: Press Shift SOLVE (CALC)
Step 3: Press "0" for Solve for X
-> You will find the x is 0.5
10 points 2 questions best one get brainliest
Answers
Answer:
9a. GCF: 16. LCM: 960
9b. GCF: 55. LCM: 275
9c. GCF: 24. LCM: 114
9d. GCF: 40. LCM: 600
10a. GCF: 120. LCM: 1440
10b. 10, 2, 5, 20
10c. 2880, 4320, 5760, 7200
Suppose that partners equally share the profits from a sale of $3,800. Which algebraic expression represents this
situation?
0360040
0 3600-
36000
3800 -
р
HURRRYY IM ALMOST OUT OF TIME SMB HELP!
Answers
Answer:
3600 / p
Step-by-step explanation:
The partners share the company equally so it would be 3600 / p because each person would get an equal share.
If there were 2 partners, each would get 1800.
If there were 4 partners each would get 900.
It makes it so each partner gets and equal amount with this equation
Ion kno this help pls?????????????
Answers
Answer:
[tex]2 {x}^{2} - x - 1 \\ 2 {x}^{2} - (2 - 1)x - 1 \\ 2 {x}^{2} + 2x - 1x - 1 \\ 2x(x + 1) - 1(x + 1) \\ (2x - 1)(x + 1)[/tex]
Abraham set the table for a picnic using round plates. Each plate has a diameter of 8 inches. What is the area of each plate?
Answers
Answer:
50.265
Step-by-step explanation:
Area is radius square times pi. Radius is half of diameter .Diameter is 8 inches. Radius is 4 inches. 4 squared is 16. 16 times pi is 50.265
a 10 foot ladder rests against a vertical wall if the bottom of the ladder slides away from the wall at a speed of 2 ft/s how fast is the angle betwween the top of the ladder and the wall changing when that angle is
Answers
Answer:
d∅/dt = √2/5 Rad/sec
Step-by-step explanation:
According to the Question,
Given That, a 10-foot ladder rests against a vertical wall if the bottom of the ladder slides away from the wall at a speed of 2 ft/s how fast is the angle between the top of the ladder and the wall changing when that angle is π/4.Solution,
Let x be the Distance between the base of the wall and the bottom of the ladder.
and let ∅ be the angle between the top of the ladder and the wall.
Then, Sin∅ =x/10 so, x=sin∅ *10
Differentiating with respect to time t we get,
dx/dt = 10 * cos∅ * d∅ /dt
We have given that dx/dt = 2 ft/s and ∅ =π/4Now, Put these value we get
2 = 10 *(cos(π/4))* d∅/dt
2 = 10/√2 * d∅/dt
d∅/dt = √2/5 Rad/sec
