Graph the system of linear inequalities and shade in the solution set. If there are no solutions, graph the corresponding lines and do not shade in any region. 2x + y > 1 Y = greater and equal to 1
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To graph the given system of inequalities first draw the boundary lines of each one:
[tex]\begin{gathered} 2x+y=1 \\ \\ y=1 \end{gathered}[/tex]First inequality:
Find two points (x,y) using the first equation to draw the corresponding line:
When x=0
[tex]\begin{gathered} 2(0)+y=1 \\ y=1 \\ \\ \text{Point: (0,1)} \end{gathered}[/tex]When x=2
[tex]\begin{gathered} 2(2)+y=1 \\ 4+y=1 \\ y=1-4 \\ y=-3 \\ \\ \text{Point: (2,-3)} \end{gathered}[/tex]As the inequality sing is > the line is a dotted line that passes trought points (0,1) and (2,-3)
Second inequality:
A line y=a is a horizontal line in y=a.
As the inequality sing is greater than or equal to the line is a full line in y=1
To find the solution you need to shadow the corresponding area for each inequality and if there is a area shaded by both inequalities it represents the solution:
First inequality: as the inequality sing is > the shaded area is above the boundary line (2x+y=1).
Second inequality: as the inequality sing is greater than or equal to the shaded area is above the boundary line (y=1)
Then, the graph of the system is:
First inequality in red
Second inequality in black
Solution: Area shaded by both inequalities
Related Questions
on232428 29 30 312725 2632 33Y is inversely proportional to the square root of x. True or False: If Y=6 when x = 81, then Y= 9, when x is 36.
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Solution
Step 1
Y is inversely proportional to the square root of x.
[tex]y\text{ = }\frac{k}{\sqrt{x}}[/tex]Step 2
Find the value of k if Y=6 when x = 81.
[tex]\begin{gathered} 6\text{ = }\frac{k}{\sqrt{81}} \\ \\ 6=\text{ }\frac{k}{9} \\ \\ k\text{ = 6}\times9 \\ \\ k\text{ = 54} \end{gathered}[/tex]Step 3
Let find y when x = 36
[tex]\begin{gathered} y\text{ = }\frac{k}{\sqrt{x}} \\ \\ y\text{ = }\frac{54}{\sqrt{36}} \\ \\ y\text{ = }\frac{54}{6} \\ \\ y\text{ = 9} \end{gathered}[/tex]Final answer
True
When the function f(x) is divided by x-3, the quotient is 2x^2 – 5x-5 and theremainder is 9. Find the function f(x) and write the result in standard form.
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We need to find a polynomial in standard form. For this, we have:
Divisor (d):
[tex]Divisor(d)\Rightarrow x-3[/tex]Quotient (q):
[tex]\text{Quotient(q)}=2x^2-5x-5[/tex]Remainder (R):
[tex]R=9[/tex]Then, we know that if we have all of these "components", we can use them using the following formula:
[tex]D=d\cdot q+R[/tex]This is the formula to find the dividend of a division. Then, we have that the function f(x) will be:
[tex]D=(x-3)(2x^2-5x-5)+9_{}[/tex]To solve this, we need to multiply the binomial (x - 3) by the trinomial as follows:
1. The unknown variable x by any of the terms of the trinomial:
[tex]x(2x^2)+x(-5x)+x(-5)=2x^3-5x^2-5x[/tex]2. And we need the latter to the result of multiplying -3 by any of the terms of the trinomial:
[tex]-3(2x^2)-3(-5x)-3(-5)=-6x^2+15x+15[/tex]Now, we need to add both partial results as follows (we need to add like terms):
[tex]2x^3-5x^2-5x-6x^2+15x+15[/tex][tex]2x^3-5x^2-6x^2-5x+15x+15[/tex][tex]2x^3-11x^2+10x+15[/tex]And now, we need to add the remainder:
[tex]D=2x^3-11x^2+10x+15+9\Rightarrow D=2x^3-11x^2+10x+24[/tex]Therefore, the function is:
[tex]undefined[/tex]the dividend of a division. Then, we have
[tex]undefined[/tex]3. Suppose f(x) = x squared - 2x +3 and g(x) = x squared -3. Compute the composition f(g(x)) and simplify.
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The given functions are
[tex]\begin{gathered} f(x)=x^2-2x+3 \\ g(x)=x^2-3 \end{gathered}[/tex]The composition f(g(x)) refers to substituting the x-variables of f(x) for the function g(x).
[tex]f(g(x))=(x^2-3)^2-2(x^2-3)+3[/tex]Then, we solve the power and product. We solve the squared binomial using the following
[tex](a-b)^2=a^2-2ab+b^2[/tex][tex]\begin{gathered} f(g(x))=x^4-2\cdot x^2_{}\cdot3+9-2x^2+6+3 \\ f(g(x))=x^4-6x^2-2x^2+18 \\ f(g(x))=x^4-8x^2+18 \end{gathered}[/tex]Therefore, the composition is[tex]f(g(x))=x^4-8x^2+18[/tex]te the following.a. Estimate the x-intercept(s).b. State whether the leading coefficient is positive or negative.c. Determine whether the polynomial function is cubic or quartic.
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As you can see, the graph has three x-intercepts. These are located at:
x=-2 , x=2 , and x=6.
The x-intercept values are all the values above the x-axis where the function cuts
Now, remember that:
Based in this table, if we look at our graph, we notice that:
If
[tex]\begin{gathered} x\to-\infty,f(x)\to+\infty \\ x\to+\infty,f(x)\to-\infty \end{gathered}[/tex]This situation happens when the leading coefficient is negative and the degree of the polynomial is odd. So,
- The leading coefficient is negative.
- The polynomial function is cubic.
Your neighbor pays you $17 for every 2 hours you work. You work for 8 hours on Saturday. How much does your neighbor own you?
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Your neighbor pays you $17 for every 2 hours you work.
You work for 8 hours on Saturday.
How much does your neighbor own you?
Solution:
Your neighbor pays you $17 for every 2 hours you work.
You work for 8 hours on Saturday.
Total = 17 x (8/2 ) = 17 x 4 = $ 68
the equation 2x^2+10x+1-=0 has two solutions A and B where A
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Given the equation ;
[tex]2x^2+10x+1=0[/tex]The general solution of the equation is :
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]From the given equation ;
a = 2 , b = 10 , c = 1
so,
[tex]\begin{gathered} x=\frac{-10\pm\sqrt[]{10^2-4\cdot2\cdot1}}{2\cdot2}=\frac{-10\pm\sqrt[]{92}}{4} \\ So, \\ x=\frac{-10+\sqrt[]{92}}{4}=-0.102 \\ OR \\ x=\frac{-10-\sqrt[]{92}}{4}=-4.898 \end{gathered}[/tex]So, the solution is :
A = -4.898
B = -0.102
51 divided by 4539 answer
Answers
51/4539 = (51/3)/(4539/3) = 17/1513 = (17/17)/(1513/17) = 1/89 = 0.011
Let f(x)=2x^2 + 5x - 3, g(x)= -x^2 - 4x + 2, and h(x)= -x^2 + 4x - 2. Select all expresions that are equivalent to 3x^2 = x - 1.A. f(x) + h(x) B. f(x) - h(x)C. g(x) + f(x)D. g(x) - h(x)E. h(x) - f(x)F. f(x) + g(x)
Answers
We have three functions
[tex]\begin{gathered} f(x)=2x^2+5x-3 \\ g(x)=-x^2-4x+2 \\ h(x)=-x^2+4x-2 \end{gathered}[/tex]We need to find which expression give us
[tex]3x^2=x-1[/tex]Let us start with the first expression
f(x) + h(x)
[tex]2x^2+5x-3+(-x^2+4x-2)[/tex]Let us add the like terms
[tex](2x^2_{}+-x^2)+(5x+4x)+(-3+\text{ -2)}[/tex][tex]x^2+9x+-5=x^2+9x-5[/tex]Let us find the second expression
[tex]f(x)-h(x)=2x^2+5x-3-(-x^2+4x-2)[/tex]The 2nd bracket must be multiplied by (-)
[tex]2x^2+5x-3+x^2-4x+2[/tex]Add the like term
[tex](2x^2+x^2)+(5x-4x)+(-3+2)[/tex][tex]3x^2+x+-1=3x^2+x-1[/tex]The answer is B
If you try the other answer they will be wrong
In g(x) + f(x) the first terms are -x^2+2x^2 = x^2
So it is not our answer because the first term is 3x^2
In g(x) - h(x) the first terms are -x^2 - (-x^2) = -x^2+ x^2 = 0
So also it is not our answer
In h(x) - f(x) the first terms are -x^2 - 2x^2 = -3x^2
So it is not our answer
In f(x) + g( x) the first terms are 2x^2 + (-x^2) = x^2
So it is not our answer
The correct answer is B
what is the volume 11m 5.3m and 2cm
Answers
The volume of a rectangular prism:
[tex]V=w\cdot l\cdot h[/tex]Then, for the given prism:
Turn the 2 cm into m:
[tex]2\operatorname{cm}\cdot\frac{1m}{100\operatorname{cm}}=0.02m[/tex][tex]\begin{gathered} V=0.02m\cdot5.3m\cdot11m \\ V=1.166m^3 \end{gathered}[/tex]Then the volume of the given prism is 1.166 cubic meters
What is the diameter of XA.12cmB.4cmC.8cmD.2cm
Answers
What is the diameter of X
A.12cm
B.4cm
C.8cm
D.2cm
Remember that
The diameter of a circle is two times the radius
so
in this problem
r=4 cm
that means
D=2*4=8 cm
answer is option CTranslate the sentence into an equation Four more than the product of a number and 7 is 6 Use the variable w for the unknown number
Answers
unknown number = w
four more than the product of a number and 7 is 6
four more = +4
product = multiplication
product of a number and 7 = 7x
four more than the product = 7x+4
is 6 = 6
7x+4=6
Riley and Rhoda plan to buy 2 bags of dog food and a dog collar (x). Each bag of dog food costs $7 and the dog collar costs $4.50. They have $30.Write an inequality and solve :Explain what your solution means for riley and rhoda:
Answers
EXPLANATION
Let's see the facts:
-Riley and Rhoda bags= 2 ---> x
- Bag cost = $7
-Collar cost = $4.5
They can spend $30.
7x + 4.5 ≤ 30
Now, we need to solve the inequality as shown as follows:
Adding -4.5 to both sides,
7x ≤ 30 - 4.5
Simplifying:
7x ≤ 25.5
Dividing both sides by 7:
x ≤ 25.5/7
Simplifying:
x ≤ 3.64 approx 3.64 bags, therefore 3 bags of dog food
Answer: Since the bags are available in full units, with their $30, Riley and Rhoda will buy 0, 1, 2, or 3 bags and 0 or 1 dog tag.
Use synthetic division and the remainder theorem to find P(a). P(x)=x^3+4x^2-3x+6; a=4 P(a)= _______(Simplify your answer.)
Answers
Given:
[tex]P(x)=x^3+4x^2-3x+6;\text{ a=4}[/tex]Let's use synthetic division and the remainder theorem to find P(a).
To use synthetic division, place the numbers which represents the divisor and the dividend in a long division like method.
We have:
Dividend = 1, 4, -3, 6
Divisor = 4
Now, bring down the first number (which is 1), multiply the number by the divisor, place the product under the second number, add both numbers then bring down the result.
Multiply the result by the divisor, place the result under the third number, add the numbers.
Continue with the method until you are done with the third number.
The terms under the boundary line are the results while the last number in the result is the remainder.
We have:
Therefore, the remainder is = 122
Hence, we have:
P(4) = 122
Also, using the remainder theorem, we have:
P(4).
To find P(4), substitute 4 for x in the function and evaluate:
[tex]\begin{gathered} P(4)=4^3+4(4)^2-3(4)+6 \\ \\ P(4)=64+64-12+6 \\ \\ P(4)=122 \end{gathered}[/tex]ANSWER:
P(a) = 122
a man is standing 20m from a large tree. he can see the top of the tree with an angle of elevation of 25 degrees. if the man's eyes are at a height of 2m, what is the height of the tree
Answers
Given:
The distance from the tree to the man = 20m.
The angle of elevation is 25 degrees.
The man's eyes are at a height of 2m.
Required:
We need to find the height of the tree.
Explanation:
Let h be the height of the tree.
[tex]h=2+x[/tex]Since 2m is the distance from the ground to the man's eye.
Consider the triangle ABC.
Here Opposite side =BC=x, Adjacent sides = AB=20m,
Use tan formula.
[tex]tan\theta=\frac{Opposite\text{ side}}{Adjacent\text{ side}}[/tex][tex]\text{ Substitute }\theta=25^o\text{ , Opposite side =x, and Adjacent sides = AB=20m in the formula.}[/tex][tex]tan25^o=\frac{x}{20}[/tex][tex]x=20\times tan25^o[/tex][tex]x=9.3261[/tex]Substitute x =9.3161 in h=2+x .
[tex]h=2+9.3261[/tex][tex]h=11.3261[/tex]Final answer:
The height of the tree is 11.33 m.
The table and scatter plot show the time spent studying, x and the midterm score, y, for each of 10 students.The equation of the line of best fit is y = 3.5x + 16.18 .
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Given
[tex]y=3.5x+16.18[/tex]Observe midterm score
Predicted midterm score
For 12
[tex]\begin{gathered} y=3.5(12)+16.18 \\ y=42+16.18 \\ y=58.18 \end{gathered}[/tex]for 18
[tex]\begin{gathered} y=3.5(18)+16.18 \\ y=63+16.18 \\ y=79.18 \end{gathered}[/tex]A residual is the difference between the observed value and the mean value that the model predicts for that observation
[tex]\begin{gathered} Residue\text{ =58.16-58.16=0} \\ residue\text{ =75-79.18=-4.18} \end{gathered}[/tex]The final answer
Which equation will BEST represent the line if it is translated 2 units down?
Answers
If you have a function f(x) and you translate it a units downward, you obtain a new function g(x) given by:
f(x) = g(x) - a
for the present case, you can notice that the original function has a slope of -3 and a y-intercept of 6, then, based on the general expression for an equation of a line, you have:
y = mx + b
m: slope = -3
b: y-intercept = 6
y = -3x + 6
after the translation you get:
y = -3x + 6 - 2
y = -3x + 4
Hence, the equation y = -3x + 4 represents the trasnlated line
Mia has at most $24 to spend on jewelry. She wants to spend $6 on a pair ofearrings and spend the rest of the money on necklaces. Each necklace costs $9.Which inequality could she use to find the number, x, of necklaces she can buy?A 6x + 9 = 24B9x 24a 6x24 + 9D 9x + 6 5 24
Answers
She has a budget of $24 to spend on jewelry, so we know that the spending has to be less or equal than 24.
There is a spending that is already decided, and is $6 on a pair of earrings.
The rest will be spend on necklaces, wich cost $9 each one. If x is the number of necklaces, the spending on necklaces is 9x.
Then, the total spending is 6+9x and it has to be less or equal than 24, so we can write the inequality as:
[tex]6+9x\le24[/tex]use the long division method to find the result when 4x3 + x2 272 + 18 is divided by 4x - 3. If there is a remainder, express the result in the form q(x) + r(x)/b(x)
Answers
ANSWER:
[tex]x^{2}+x-6[/tex]STEP-BY-STEP EXPLANATION:
We have the following polynomial:
[tex]4x^3+x^2-27x+18[/tex]We must divide it by 4x - 3, using the long division method, therefore:
[tex]4x^3+x^2-27x+18\div \left(4x-3\right)[/tex]We solve it below:
[tex]\begin{gathered} \text{ We divide the leading term of the dividend by the leading term of the divisor:} \\ \\ \frac{4x^3}{4x}=x^2 \\ \\ \text{ We multiply it by the divisor} \\ \\ x^2\cdot(4x-3)=4x^3-3x^2 \\ \\ \text{ We subtract the dividend from the obtained result: } \\ \\ 4x^3+x^2-27x+18-4x^3+3x^2=4x^2-27x+18 \\ \\ \text{ Finally it would be:} \\ \\ x^2+\frac{4x^2-27x+18}{4x-3} \end{gathered}[/tex]Now, we repeat the same procedure:
[tex]\begin{gathered} \text{ We divide the leading term of the dividend by the leading term of the divisor:} \\ \\ \frac{4x^2}{4x}=x \\ \\ \text{ We multiply it by the divisor} \\ \\ x\cdot(4x-3)=4x^2-3x \\ \\ \text{ We subtract the dividend from the obtained result: } \\ \\ 4x^2-27x+18-4x^2-3x=-24x+18 \\ \\ \text{ Finally it would be:} \\ \\ x^2+x+\frac{-24+18}{4x-3} \end{gathered}[/tex]We do the division for the last time and we would have the following:
[tex]\begin{gathered} \text{ We divide the leading term of the dividend by the leading term of the divisor:} \\ \\ \frac{-24x}{4x}=-6 \\ \\ \text{ We multiply it by the divisor} \\ \\ -6\cdot(4x-3)=-24x+18 \\ \\ \text{ We subtract the dividend from the obtained result: } \\ \\ -24x+18-24x+18=0 \\ \\ \text{ Finally it would be:} \\ \\ x^2+x-6 \end{gathered}[/tex]So, the correct answer is:
[tex]4x^3+x^2-27x+18\div\left(4x-3\right)=x^2+x-6[/tex]Could you help me with this is from apex please
Answers
The function is
[tex]f(x)=\frac{1}{9}9^x=9^{-1}\cdot9^x=9^{x-1}[/tex]To get f(3), set x=3 and solve, as follows:
[tex]f(x=3)=9^{3-1}=9^2=81[/tex]Then, the answer is 81, option A
Finding length of hypotenuse d is marked bc I jus needed to press an answer
Answers
Given:
The objective is to find the hypotenuse c of the right triangle.
Consider the right triangle as,
The length of the side c can be calculated using Pythagoras theorem.
[tex]\begin{gathered} AB^2=AC^2+BC^2 \\ c^2=36^2+15^2 \\ c^2=1296+225 \\ c^2=1518 \\ c=\sqrt[]{1518} \\ c=38.96 \\ c\approx39 \end{gathered}[/tex]Hence, option (B) is the correct answere.
The associative property does not work for which operations A. +
Answers
SOLUTION
Associative property works for + (addition) and x (multiplication). It does not work for subtraction and division
Given the triangle, find x to the nearest one hundredth.
Answers
The Solution:
Given:
Required:
Find the value of x.
Applying the Trigonometric Ratio:
[tex]\tan30=\frac{x}{12}[/tex]Cross multiply:
[tex]x=12\tan30=6.9282\approx6.93[/tex]Answer:
6.93
How many gallons is 454 ounces?
Answers
Answer:
3.546875gallons
Explanation:
Using the conversion factor;
1 fluid ounces = 0.0078125 gallons
454 ounces = x
Cross multiply
1 * x = 454 * 0.0078125
x = 3.546875gallons
Hence 454 ounces to gallons is 3.546875gallons
48. Find the x– and y–intercepts of the line: 3x + 4y = –24.A. 3, 4B. 8, 6C. –8, –6D. –3, –4
Answers
Answer:
C. –8, –6
Explanation:
Given the equation:
[tex]3x+4y=-24[/tex](a)x-intercept
The x-intercept is the value of x at which y=0.
When y=0:
[tex]\begin{gathered} 3x+4y=-24 \\ 3x+4(0)=-24 \\ 3x=-24 \\ \text{Divide both sides y 3} \\ \implies x=-\frac{24}{3} \\ x=-8 \end{gathered}[/tex]b)y-intercept
The y-intercept is the value of y at which x=0.
When x=0:
[tex]\begin{gathered} 3x+4y=-24 \\ 3(0)+4y=-24 \\ 4y=-24 \\ \text{Divide both sides by 4} \\ \implies y=-\frac{24}{4} \\ y=-6 \end{gathered}[/tex]The x– and y–intercepts of the line: 3x + 4y = –24 are –8 and –6.
Option C is correct.
help me with geometry homweork
Answers
For a parallelogram, 3y+8 = 2x-4 and 5y = x+8
This is because the parallel sides are equal
3y + 8 = 2x-4 ..........(1)
5y = x+8...............(2)
from equation 2, y =(x+8)/5 .......(3)
substituting for y in equation (1) we have
3(x+8)/5 + 8 = 2x -4
3x+24 +(5x8) =5(2x-4)
3x+24 + 40 = 10x - 20
10x -3x = 40 +24+20
7x = 84
x = 12
From (2) , substituting for x yields
5y = x+8
5y = 12 +8
5y =20
y = 4
What does the constant 1.55 reveal about the rate of change of the quantity?
Answers
Answer:
[tex]\begin{gathered} a)\text{ Growing} \\ b)\text{ 55} \\ c)\text{ second} \end{gathered}[/tex]Explanation:
Here, we want to define the terms in the given exponential equation
The general form is:
[tex]f(t)\text{ = P\lparen1 + r\rparen}^{nt}[/tex]P represents the initial value, while r represents the percentage change and t represents the time frame
if the value inside the bracket is greater than 1, we have an increase
We could rewrite the equation as:
[tex]f(t)\text{ = 570\lparen1 + 0.55\rparen}^{60t}[/tex]This means that:
The function is growing exponentially at a rate of 55% every second
Answer:
Here, we want to define the terms in the given exponential equation
The general form is:
P represents the initial value, while r represents the percentage change and t represents the time frame
if the value inside the bracket is greater than 1, we have an increase
We could rewrite the equation as:
This means that:
The function is growing exponentially at a rate of 55% every second
I have a quiz tomorrow and I need to figure out how to solve a linear equation using a graph ASAP. Can you please help me?
Answers
SOLUTION
The given equations are
[tex]\begin{gathered} x+y=18 \\ y=x+12 \end{gathered}[/tex]The graph of the equations are shown:
Notice that the line intersect at (3,15)
Therefore, the solutions of the system of equations are
[tex]x=3,y=15[/tex]Identify whether the given situation represents one-to-one function. Justify your answer. 10.)The relation pairing a television to universal remote control.
Answers
hello! We have to analyze this sentence and justify the type of function.
The relation pairing a television to a universal remote control.
A universal remote control means that this control works for any television.
So, if we have three models of television, A, B, and C, this remote control would be able to work in all of the TVs, independent of the model.
In this case, we have a situation that represents one-to-many functions, and not a one-to-one function.
Using the same example, if the remote control just works for TV A, it would be a one-to-one function.
the solution to a problem involving a complex number is -4+32i which of the following expressions could be the problem?
Answers
The problems which solution is -4+32i are options B, C, and E
What is the equation of the line that is parallel to the line y = -1/3 x + 4 and passes through the point (6, 5)?a) y = -1/3x + 3b) y = -1/3x + 7c) y = 3x – 13d) y = 3x + 5
Answers
Note that the slope of parallel lines are always equal.
From the given line :
[tex]y=-\frac{1}{3}x+4[/tex]The slope is m = -1/3 and we need the equation of the line that passes through (6, 5)
Using point-slope formula :
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-5=-\frac{1}{3}(x-6) \\ y-5=-\frac{1}{3}x+2 \\ y=-\frac{1}{3}x+2+5 \\ y=-\frac{1}{3}x+7 \end{gathered}[/tex]The answer is B.