Which ordered pair is in the solution set fit the system of inequalities shown below?2x-y<3x+2y>-1A. (-2,-1)B. (0,1)C. (1,-2)D.(6,1)
Answers
Given the System of Inequalities:
[tex]\begin{cases}2x-y<3 \\ x+2y>-1\end{cases}[/tex]1. Take the first inequality and solve for "y":
[tex]\begin{gathered} -y<2x+3 \\ (-1)(-y)<(-2x+3)(-1) \\ y>2x-3 \\ \end{gathered}[/tex]Notice that direction of the symbol changes, because you had to multiply both sides of the inequality by a negative number.
Now you can identify that the boundary line is:
[tex]y=2x-3[/tex]Since it is written in Slope-Intercept Form, you can identify that its slope is:
[tex]m_1=2[/tex]And its y-intercept is:
[tex]b_1=-3[/tex]Notice that the symbol of the inequality is:
[tex]>[/tex]That indicates that the line is dashed and the shaded region is above the line.
Knowing all this information, you can graph the first inequality on the Coordinate Plane.
2. Apply the same procedure to graph the second inequality. Solving for "y", you get:
[tex]\begin{gathered} 2y>-x-1 \\ \\ y>-\frac{1}{2}x-\frac{1}{2} \end{gathered}[/tex]Notice that the boundary line is:
[tex]y=-\frac{1}{2}x-\frac{1}{2}[/tex]Where:
[tex]\begin{gathered} m_2=-\frac{1}{2} \\ \\ b_2=-\frac{1}{2} \end{gathered}[/tex]Since the symbol is:
[tex]>[/tex]The line is dashed and the shaded region is above the line.
Knowing this, you can graph the second inequality.
3. Look at the graph of the System of Inequalities:
Notice that:
-The black line is the boundary line of the first inequality and the green line is the boundary line of the second inequality.
- The solution of the system is the intersection region. It is the region where the shaded region of the first inequality and the shaded region of the second inequality, intersect.
4. Plot the points given in the options on the graph of the Systems:
5. You can identify that this point is in the intersection region:
[tex](0,1)[/tex]Therefore, it is a solution.
Hence, the answer is: Option B.
Related Questions
which function has an inverse that is also a function horizontal line test
Answers
If the graph of a function y = f(x) is such that no horizontal line intersects the graph at more than one point, then f has an inverse function.
A. The absolute value function f(x) = | x | is intersected twice by any horizontal line at y > 0. Thus this function does not have an inverse
B. The quadratic function f(x) = x^2 has a graph called parabola. If we plot any horizontal line at y>0, that line will intersect the function twice. This function has no inverse function
The number of cities in a region over time is represented by the function
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For this question, in order to find T(x), we need to multiply the two given functions.
[tex]T(x)=(C\cdot P)(x)[/tex][tex]T(x)=C(x)\cdot P(x)[/tex][tex]=(2.9)(1.05)^x\cdot(1.05)^{3x+5}[/tex][tex]=(2.9)(1.05)^{x+3x+5}[/tex][tex]T(x)=2.9(1.05)^{4x+5}[/tex]Therefore, the answer must be option A.
Of the twenty-two students in a classroom, ten are transfer students, seven are nursing students, four are AAS students and one student is undecided.If three students are chose randomly, without replacement, find the probability that all three students are nursing students.
Answers
Given that:
• There are a total number of 22 students in the classroom.
,• 10 of them are transfer students.
,• 7 are nursing students.
,• 4 are AAS students.
,• 1 student is undecided.
,• Three students are chosen randomly.
Since you need to find the probability that all three students that are chosen randomly are nursing students, you need to set up that this is:
[tex]P(A)[/tex]Where Event A is that one of the students is a nursing student.
Therefore, the probability that three of the chosen students are nursing students can be set up as:
[tex]\begin{gathered} P=P(A)\cdot P(A)\cdot P(A)=P(A)^3 \\ \\ P=P(A)^3 \end{gathered}[/tex]Knowing that the total number of students is 22 and 7 of them are nursing students, you know that:
[tex]P(A)=\frac{7}{22}[/tex]Therefore:
[tex]P=(\frac{7}{22})^3[/tex][tex]P=0.0322[/tex]Hence, the answer is:
[tex]P=0.0322[/tex]In certain deep parts of oceans, the pressure of sea water, P, in pounds per square foot, at a depth of dfeet below the surface, is given by the following equation:4dP = 14 +11If a scientific team uses special equipment to measures the pressure under water and finds it to be 318pounds per square foot, at what depth is the team making their measurements?Answer: The team is measuring atfeet below the surface.
Answers
1) Given this equation for Pressure, we need to plug into p the pressure of 318 lbs/ft² to get the depth according to the model described by this equation.
2) So, we can write out:
[tex]\begin{gathered} P=14+\frac{4d}{11} \\ 318=14+\frac{4d}{11} \\ 11\times318=11\times(14+\frac{4d}{11}) \\ 3498=154+4d \\ 3498-154=4d \\ 3344=4d \\ 4d=3344 \\ \frac{4d}{4}=\frac{3344}{4} \\ d=836ft \end{gathered}[/tex]Note that we multiplied both sides by 11 to get rid of the fraction.
Thus this is the depth below the surface that generates such pressure
Simplify.1,5m^7(-4m^50^2A. -6m^14B. 24m^17C. 24m^14D. 12m^17There is a picture too if you need it.
Answers
The expression can be simplified as,
[tex]\begin{gathered} 1.5m^7(-4m^5)^2 \\ =1.5m^7(16m^{10}) \\ =24m^{17} \end{gathered}[/tex]Thus, option (b) is the correct solution.
5 In nahiangle Bcm. Ireos B = / 13 which function also cauals
Answers
Given data:
The given measurement of angle C is 90 degrees.
The given value of cos(B) =5/13.
The sum of all angles of triangle is,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^{\circ} \\ \angle A+\angle B+90^{\circ}=180^{\circ} \\ \angle A+\angle B=90^{\circ} \\ \angle B=90^{\circ}-\angle A \end{gathered}[/tex]Substitute the above value in the given expression.
[tex]\begin{gathered} \cos (90^{\circ}-A)=\frac{5}{13} \\ \sin A=\frac{5}{13} \end{gathered}[/tex]Thus, the correct answer is sin(A), so the third option is correct.
3 Drag each equation to the correct location on the table. Determine the number of solutions to each equation. Then place each equation in the box that corresponds to its number of solutions. 35 = 2+ +1 2 – 1 = 45 + 3 31 – 2 35 + 1 2x + 3 = 35 – 1 1 2x + 1 = 21 No Solutions 1 Solution 2 Solutions Reset Next All rights reserved. i NE
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Then, it has just 1 solution, and it should be placed in the second column.
[tex]\begin{gathered} 2^x-1=4^x+3. \\ \text{This has no solution} \end{gathered}[/tex][tex]\begin{gathered} 3x-2=3^x+1 \\ \text{This has no solution.} \end{gathered}[/tex]Next;
[tex]\begin{gathered} \frac{1}{2}x+3=3^x-1 \\ \text{This has no solution. It should be in the first column} \end{gathered}[/tex][tex]\begin{gathered} 2x+1=2^x \\ \text{Let x=0,} \\ 2(0)+1=2^0=1 \end{gathered}[/tex]This has one solution, and it should be placed in the second column.
What kind of transformation converts the graph of f(x)=(5x+6)^2 into the graph of g(x)=-(5x+6)^2
Answers
In order to get from
[tex]f(x)=(5x+6)^2[/tex]To
[tex]f(x)=-(5x+6)^2[/tex]You have to reflect across the x-axis.
Remember that the x-axis is the line with equation
[tex]y=0[/tex]Answer: Option A
How much will it cost to buy a low fence to put all the way around the bed? The fencing material costs $0.59 per foot and can only be bought in whole numbers of feet.
Answers
To find the cost we first need to know how many feet of fence we need. To do this we add all the lengths of the sides:
[tex]6+6+8.5=20.5[/tex]Now, since we can only buy whole numbers of feet we need to buy 21 feets of fence, then the total cost is:
[tex]21\cdot0.59=12.39[/tex]Therefore the cost will be $12.39
Find the slope of the line that passes through (54, -61) and (8, -56).
Answers
Answer:
The slope m of the line that passes through the two given points is;
[tex]m=-\frac{5}{46}[/tex]Explanation:
We want to calculate the slope of the line that passes through the given point;
[tex](54,-61)\text{ and }(8,-56)[/tex]Recall that the slope formula can be written as;
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]substituting the given points;
[tex]\begin{gathered} (x_1,y_1)=(54,-61) \\ (x_2,y_2)=(8,-56) \end{gathered}[/tex]We have;
[tex]\begin{gathered} m=\frac{-56-(-61)}{8-54}=\frac{5}{-46} \\ m=-\frac{5}{46} \end{gathered}[/tex]Therefore, the slope m of the line that passes through the two given points is;
[tex]m=-\frac{5}{46}[/tex]
Please help me i have been struggling for two days
Answers
we have the equation
[tex]\log _5(x+1)-\log _2(x-2)=1[/tex]using a graphing tool
see the attached figure
The solution is x=2.90Segment EF is rotated 90° clockwise around the origin and then translated by (-6, y + 7).
The resulting segment E" F" has coordinates E" (-4, 5), F"(-1,-2).
What are the coordinates of the segment EF?
does anyone know this??
Answers
Answer:
E = 2,2 F = 5,-9
Step-by-step explanation:
First, you have to add (6, -7) to both coordinates (that being (-4,5)(-1,-2)
This results in E = 2,-2 and F = -5,-9
Next, you need to rotate both coordinates 90 counterclockwise, resulting in: E being (2,-2) and F being (5,-9)
Hope this helped!
7. 4×= 3yy=-4x + 39. y+2=0x+ 2 = 011.x-5y=45x + y = 4Determine if the graphs will show parallel or perpendicular lines, or neither.
Answers
Given:
[tex]\begin{gathered} 4x=3y \\ y=-4x+3 \end{gathered}[/tex]Sol:.
If the both line are perpendicular then multipilcation of slope is -1 then:
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ \end{gathered}[/tex][tex]\begin{gathered} 3y=4x \\ y=\frac{4}{3}x \\ m_1=\frac{4}{3} \end{gathered}[/tex][tex]\begin{gathered} y=-4x+3 \\ m_2=-4 \end{gathered}[/tex][tex]\begin{gathered} =m_1m_2 \\ =\frac{4}{3}\times-4 \\ m_1m_2\ne-1 \\ \text{That mean its not perpendicular } \end{gathered}[/tex]For parallel line slope are same then its not a parallel line
So line neither perpendicular or parallel.
What is the domain of the function graphed below?
x<7
x_<7
-2_< X_<3
all real numbers
Answers
The given function is defined everywhere except at x = 7 and a higher value than 7 thus x < 7 will be the domain of the function so option (A) is correct.
What is the range and domain of a function?A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
As per the given graph of the function,
The value of the function at x = -1 is -2.
In another place, the graph is not breaking before x = 7.
So, at x > 7 the function is not defined.
The domain of the function will be (-∞ ,7).
Hence "The given function is defined everywhere except at x = 7 and a higher value than 7 thus x < 7 will be the domain of the function".
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The given question is incomplete, the complete question follows with the graph below;
write a linear equation to: slope=2 and goes through point (4, 11)
Answers
When you have to write a linear equation and you have the slope (m) and a point (4, 11) you:
1. Use the standard form of a linear equation:
[tex]y=mx+b[/tex]You know the value of:
m= 2
y= 11
x= 4
You make a substitution:
[tex]11=(2)(4)+b[/tex]You can find then the value of b:
[tex]11=8+b[/tex][tex]b=11-8=3[/tex]Then you have now the data to form the final linear equation:
[tex]y=2x+3[/tex]I need help answering this question, if you can thank you very much.
Answers
Answer: We have to factor out the polynomial which is:
[tex]x^2+6x-16[/tex]The factorization is as follows:
[tex]\begin{gathered} \text{ Method:} \\ \\ (x+a)(x+b)=x^2+(a+b)x+ab \\ \\ \\ ----------------------- \\ \text{ Solution:} \\ \\ x^2+6x-16 \\ \\ \text{ The unknowns }\rightarrow\begin{cases}ab={-16} \\ a+b={6}\end{cases} \\ \\ \\ \text{ The possible values are:} \\ \\ \\ a=8 \\ b=-2 \\ \\ \\ \text{ Because:} \\ \\ \\ (8)\times(-2)=-16 \\ (8)+(-2)=6 \\ \\ \\ \text{ Therefore the factored form is:} \\ \\ \\ (x+8)(x-2)=x^2+6x-16 \end{gathered}[/tex]You want to purchase an automobile for 28,711. The dealer offers you 0% financing for 60 months or a 3,972 rebate. You obtain 5.7% financing for 60 months at the local bank. Which option should you choose
Answers
Answer:
option 1
Step-by-step explanation:
the dealer one ok.......
16 - 2t = 5t +9 Can you help me solve this?
Answers
1=t
add 2t to the second side, so that it is going to be 16=7t+9
now, subtract 9 from the right side: 16-9=7t
7t=7
t=1
roblems in Construction Mathematics me Frandy Ive the following problems. Show your work. Write your answers in the spaces provided. 1. A triangular frame has sides that measure 15-7, 20'-4 and 26-2". What is the total length of the three sides?
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A triangular frame has sides that measure 15-7, 20'-4 and 26-2". What is the total length of the three sides?
Remember that
1 ft =12 inches
Convert all the measure to inches
so
15' 7 "=15(12)+7=187 in
20' 4"=20(12)+4=244 in
26' 2"=26(12)+2=314 in
Right Triangle ABC is pictured below.Which equation gives the correct value for BC?Option 1: sin(32) = BC/8.2Option 2: cos(32) = BC/10.6Option 3: tan(58) = 8.2/BCOption 4: sin(58) = BC/10.6
Answers
Given the image, we are asked which equation gives the correct value for BC?
Explanation
From the image;
[tex]\begin{gathered} A+B+C=180 \\ 32+B+90=180 \\ B=180-90-32 \\ B=58^0 \end{gathered}[/tex]Therefore,
[tex]tan58^0=\frac{opposite}{Adjacent}=\frac{8.2}{BC}[/tex]Answer: Option three
Find the area of the figure.A. 57 square yardsB. 66 square yardsC. 180 square yards D. 234 square yards
Answers
We would section the figure into two shapes as shown below
We can see a trapezium and a rectangle. We would find the area of each figure and add them.
For the trapezium,
Area = 1/2 * (a + b)h
a nd b are the opposite sides of the trapezium while h represents the height.
Thus,
a = 20, b = 24 and h = 9es of the trapezium while h represents the height.
Thu sid
Tyrone's car can travel about 30 miles for each gallon
of gas.
Using d for distance traveled in miles and g for
gallons of gas, write two different equations relating d
and g.
Answers
The equation can be written as d=30g
What is an equation?
An equation can be compared to a scale on which objects are weighed. When the two pans are filled with the same amount of anything (like grain), the scale will balance and the weights will be considered equal. To maintain the scale in balance, if any grain is taken out of one of the balance's pans, an equal amount must be taken out of the other pan. More broadly, if the identical operation is carried out on both sides of an equation, the equation remains in balance. Equations are used to describe geometric shapes in Cartesian geometry. The goal has changed since the equations under consideration, such as implicit equations or parametric equations, contain an unlimited number of solutions.
Tyrone's car can travel about 30 miles for each gallon
So, the equation can be written as d=30g, where d is distance travelled and g is gallons of gas used.
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I am not good at word problems this is a project so need extra help
Answers
M = $6,400
C = $3,600
CD interest = $180
Money market interest = $256
Here, we want to start by completing the chart
We proceed as follows;
Let us take it line by line
a) The rate for the CD account is 5%
Writing this as decimal is 5/100 = 0.05
b) The time for the CD account is 1 year
Next line;
a) Principal invested in money market is $M
b) The time is also 1 year
Next line;
The interest earned on investment is the sum of both
That will be;
0.05c + 0.04m
So, let us write the equations to solve simultaneously;
[tex]\begin{gathered} c\text{ + m = 10,000} \\ 0.05c\text{ + 0.04m = 436} \\ \text{second equation multiplied through by 100;} \\ 5c\text{ + 4m = 43,600} \\ \text{From i;} \\ c\text{ = 10,000-m} \\ \text{put this into the multiplied equation} \\ 5(10,000-m)\text{ + 4m = 43600} \\ 50,000\text{ - 5m + 4m = 43600} \\ m\text{ = 50,000-43600} \\ m\text{ = 6400} \\ c\text{ = 10,000-6400} \\ c\text{ = 3,600} \end{gathered}[/tex]So, let us fill the last parts;
a) $3,600 + $6,400 = Total $10,000 invested
b) CD interest is 0.05 c = 0.05 (3,600) = $180
Money market interest = 0.04M = 0.04 (6,400) =$256
$180 + $256 = $436 total interest
A ball is thrown from an initial height of 1 meter with an initial upward velocity of 7 m/s. The balls height h (in meters) after t seconds is given by the following. h=1+7t-5t^2Find all values of t for which the balls height is 2 meters.Round the answer(s) to the nearest hundredth
Answers
Solution
To find the values of t for which the ball's height is 2 meters
we set h = 2
=> 2 = 1 + 7t - 5t^2
=>5t^2 - 7t + 1 = 0
Using the quadratic formula,
[tex]\begin{gathered} t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ \Rightarrow t=\frac{7\pm\sqrt{\left(-7\right)^2-4\left(5\right)\left(1\right)}}{2\cdot5} \\ \\ \Rightarrow t=1.24s\text{ or }0.16s \end{gathered}[/tex]Therefore, t = 1.23s or 0.16s
Solve the quadratic equation by using the quadratic formula. If the solutions are not real, enter NA. 3x2−5x+1=0 Enter the exact answers.
Answers
The given quadratic equation is,
[tex]3x^2-5x+1=0[/tex]let us use the formula,
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where,
[tex]\begin{gathered} a=3 \\ b=-5 \\ c=1 \end{gathered}[/tex]subistute the values in the formula,
[tex]\begin{gathered} =\frac{-(-5)\pm\sqrt[]{(-5)^2-4\times3\times1}}{2\times3} \\ =\frac{5\pm\sqrt[]{25-12}}{6} \\ =\frac{5\pm\sqrt[]{13}}{6} \\ x=\frac{5+\sqrt[]{13}}{6},x=\frac{5-\sqrt[]{13}}{6} \end{gathered}[/tex]The roots of the quadratic equation are ,
[tex]x=\frac{5+\sqrt[]{13}}{6},x=\frac{5-\sqrt[]{13}}{6}[/tex]Eliminate the y in the following system of equations. What is the result when you add the two equations? [tex]x + y = 8 \\ 5x - 3y = 24[/tex]A: 6x = 32B: 8x = 32 C: x = 0D: 8x = 48
Answers
EXPLANATION
x + y = 8 ----------------------------------------(1)
5x - 3y = 24 ------------------------------------------(2)
If we are to eliminate y in the equations, we first need to multiply through equation (1) by 3.
3x + 3y = 24 ----------------------------------------(3)
Add equation (2) and equation (3).
If we add equation(1) and equation(3) together, -3y will cancel-out 3y.
(5x + 3x) = (24 + 24)
8x = 48
Therefore, the correct option is D. 8x = 48
Differentiate. f(x) = (x3 - 3)2/3 2x f'(x) 3 x 8 х f'(x) 3 | 23-8 2x2 f'(x) 3 S x2 f'(x) 3 8
Answers
1) Let's calculate the derivative of f(x) = (x³-8) ^(2/3)
Let's start applying the power rule :
[tex]undefined[/tex]The top of the hill rises 243 feet above checkpoint 2, which is -162. What is the altitude of the top of the hill?
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The altitude of the top of the hill or the difference in elevation point is 406 feet.
Difference in Elevation PointThe vertical distance between two points is called the difference in elevation. The process of measuring differences in elevation is called levelling , and is a basic operation in topographical surveys.
To determine the difference in elevation between two points, determine the elevation at each point and then calculate the difference.
Point A = 243 feetPoint B = -162 feetThe difference in elevation between the two points is
Point A - Point B = 243 - (-162) = 243 + 162 = 406
The difference in the elevation point is 406 feet.
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1. A train moves at a constant speed and travels 6 miles in 4 minutes. What is its speed in miles per minute? d/t = r time distance t d 4 mins. 6 miles
Answers
Answer: 1.5 miles / minute
Given that:
Distance travelled = 6
Time = 4 minutes
Speed = Distance / time
Speed = 6 / 4
1.5 mile / minute
The one-to-one function f is defined below.
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The inverse function of the relation is f-1(x) = 5x/(7x -6), while the domain and the range are x < 6/7 or x > 6/7 and f(x) < 5/7 or f(x) > 5/7, respectively
How to determine the inverse function?The definition of the function is given as
f(x) = 6x/7x - 5
Rewrite the function as
y = 6x/7x - 5
Next, we swap or switch the variables x and y
So, we have the following equation
x = 6y/7y - 5
Cross multiply in the above equation
This gives
x(7y - 5) = 6y
Open the brackets
7xy - 5x = 6y
Collect the like terms
7xy -6y = 5x
Factor out y
y(7x -6) = 5x
So, we have
y = 5x/(7x -6)
Express as inverse function
f-1(x) = 5x/(7x -6)
Using a graphing calculator, we have
Domain: x < 6/7 or x > 6/7
Range: f(x) < 5/7 or f(x) > 5/7
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