Solve the inequalities by graphing. Select the correct graph. y > x y < -x
Answers
The solution to the system of inequalities y > x and y < -x is a V-shaped region in the second and fourth quadrants of the coordinate plane.
Graph attached.
To solve the system of inequalities graphically, you need to shade the regions on the coordinate plane that satisfy both inequalities.
The first inequality is y > x. This means that all points above the line y = x satisfy this inequality.
The second inequality is y < -x. This means that all points below the line y = -x satisfy this inequality.
Now, let's graph both lines and shade the regions that satisfy both inequalities:
Graph the line y = x. This is a straight line with a slope of 1 that passes through the origin (0,0) and goes up and to the right.
Graph the line y = -x. This is also a straight line with a slope of -1 that passes through the origin (0,0) and goes down and to the right.
Graph attached.
The shaded region that satisfies both inequalities is the area between these two lines, below y = -x, and above y = x.
It forms a V-shaped region in the second and fourth quadrants of the coordinate plane.
Therefore, the correct graph should show the shaded V-shaped region that represents the solution to the system of inequalities.
Graph attached.
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Related Questions
Please explain how you worked the problem to find x!
1/x +1/(x+4) =1/5
Answers
[tex]\frac{1]{x} *\frac{x+4}{x+4} +\frac{1}{x+4}*\frac{x}{x}=\frac{x+4}{x*(x+4)}+\frac{x}{x*(x+4)}[/tex] now we can add both of the equation as the denominators have the same value.
[tex]\frac{x+4+x}{x*(x+4)}=\frac{2x+4}{x^{2}+4x} = \frac{1}{5}[/tex] by multiplying both sides by [tex]5*(x^{2}+4x)[/tex]
[tex] 5*(2x+4)=x^{2} +4x[/tex]
[tex] 10x+20=x^{2}+4x[/tex] by subtracting both sides by (10x+20)
[tex] x^{2} -6x -20 = 0[/tex] (by using the quadratic formula)
we will find two answers for this equation
x={[tex]\frac{-6- \sqrt{116}}{-2}[/tex] and [tex] \frac{-6+\sqrt{116}}{-2}[/tex]
Analyze the following budget, with an income of $750, to determine how much can be spent on food for the month. Month________ Budgeted Amount Food $___ Personal Items $20 Cell Phone $75 Entertainment $85 Car Expenses – Gas, Insurance $260 College Savings $250 a. No more than $70 can be spent on food. b. No more than $75 can be spent on food. c. No more than $80 can be spent on food. d. No more than $60 can be spent on food.
Answers
Hope it helps
A monthly of $60 can be spent for food after all the expenses and savings
are sorted.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The numerical form of the given information can be formed as,
$(750 - 20 - 75 - 85 - 260 - 25).
= $60.
So, With an income of $750 and all the expenses including saving for for college worth of $250 the amount that can be spent on food is $60.
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Melissa had a balance of $104 in her checking account at the beginning of the month. She made one additional deposi of $216 and wrote checks $78 , $119 , and $105. What was the balance in her checking account at end of the month
Answers
Answer:
She only had $18 left
Step-by-step explanation:
Is the line through points P(0, 5) and Q(–1, 8) parallel to the line through points R(3, 3) and S(5, –1)? Explain.
a. No, the lines have unequal slopes.
b. Yes, the lines are both vertical.
c. Yes, the lines have equal slopes.
d. No, one line has slope, while the other has no slope.
Answers
m = (y2 - y1)/(x2 - x1)
y2 = 8
x2 = - 1
m = (8 - 5)/(-1 - 0)
m = 3/-1 = -3
Slope RS
m = (y2 - y1)/(x2 - x1)
y2 = 3
x2 = 3
m = (3 - - 1)/(3 - 5)
m = 4/-2 = -2
Conclusion
The slopes are not either 0 or undefined. They are not vertical or horizontal. They are not related by m1*m2 = -1 so they do not relate by right angles. They are not the same.
Answer: A <<<
PLEASE HELP!!!! How can you tell if a triangle can be drawn more than one way?
please explain in detail and be specific.
Answers
Does the point (2 3 , 2) lie on the circle that is centered at the origin and contains the point (0, -4)? Why?
Answers
Answer:
No, because it doesn't satisfy the equation of the circumference
Step-by-step explanation:
A circle is the locus of points on the plane that are equidistant from a fixed point called the center. For a circle whose center is the point
[tex]C=(a,b)[/tex]
and its radius is [tex]r[/tex], the ordinary equation of this circle is given by:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
Since the circle is centered at the origin:
[tex]C=(a,b)=(0,0)\\\\Hence\\\\(x-0)^2+(y-0)^2=r^2\\\\x^2+y^2=r^2[/tex]
Now, let's find [tex]r[/tex] using the data provided. Evaluating the point (0,-4) into the equation:
[tex](0)^2+(-4)^2=r^2\\\\16=r^2\\\\r=\pm 4[/tex]
Thus the equation for the circle given by the problem is:
[tex]x^2+y^2=16[/tex]
In order to corroborate if the the point (2 3, 2) lie on the circle, we need to evaluate it into the equation and check if it satisfy the equation:
Note: I don't know what you mean with 2 3, so I will assume 3 cases:
[tex]2\hspace{3} 3=23\\2\hspace{3} 3=2*3=6\\2\hspace{3} 3=\frac{2}{3}[/tex]
First case:
[tex](23)^2+(2)^2=16\\\\533\neq16[/tex]
It doesn't satisfy the equation, therefore doesn't lie on the circle.
Second case:
[tex](6)^2+(2)^2=16\\\\40\neq16[/tex]
It doesn't satisfy the equation, therefore doesn't lie on the circle.
Third case:
[tex](\frac{2}{3} )^2+(2)^2=16\\\\\frac{40}{9} \neq16[/tex]
It doesn't satisfy the equation, therefore doesn't lie on the circle.
Final answer:
The point (3, 2) does not lie on the circle centered at the origin with a radius of 4 units because when its coordinates are plugged into the circle's equation x² + y² = 16, the result is not equal to the radius squared.
Explanation:
To determine if the point (3, 2) lies on the circle centered at the origin that contains the point (0, -4), we need to see if it satisfies the equation of the circle.
We know the radius of the circle is the distance from the center to the point (0, -4), which is 4 units since all points on a circle are equidistant from the center.
The general equation for a circle centered at the origin (0,0) is x² + y² = r², where r is the radius.
Our circle's equation is x² + y² = 16.
We plug in the coordinates of the point (3, 2) to see if it lies on the circle: 3² + 2² = 9 + 4 = 13, which is not equal to 16. Therefore, the point (3, 2) does not lie on the given circle.
An equilateral triangle has a height of 26 cm. what is the length of each side of the triangle
Answers
Answer:
30.0 cm
Step-by-step explanation:
You want the side length of an equilateral triangle with a height of 26 cm.
Equilateral triangleThe altitude of the triangle divides it into two congruent 30°-60°-90° right triangles. The longer leg is the height: 26 cm. The hypotenuse is the longest of the three sides, which have the ratios ...
1 : √3 : 2
That is, the side of the equilateral triangle is 2/√3 times the altitude.
[tex]s = \dfrac{2}{\sqrt{3}}h = \dfrac{2(26\text{ cm})}{\sqrt{3}}\approx\boxed{30.0\text{ cm}}[/tex]
The length of each side is about 30.0 cm.
__
Additional comment
The side length is an irrational number of cm, approximately 30.022213997.... It rounds to 30.
How do I solve this equation for n? (6x2n)÷8=15
Answers
now we know (6x2n) = 120
so if we re-write this you can make it 6x(2n) = 120
Now we divide by 6 on both sides that gives us (2n) = 20
divide by two and you have your answer
hope this helps
To solve the equation (6x2n)÷8=15 for n, you must perform algebraic operations to isolate n. This involves multiplying by 8, then dividing by 6x, and finally by 2, to arrive at n = 20 / x.
To solve the equation (6x2n)÷8=15 for n, we need to follow several steps. This involves manipulating the equation using algebraic operations until we isolate the variable n on one side. Here is the step-by-step process:
Multiply both sides of the equation by 8 to get rid of the fraction: 6x2n = 15 × 8.Simplify the right side: 6x2n = 120.Divide both sides by 6x to isolate n: 2n = 120 / 6x.Further simplify the right side to get n on its own: n = (120 / 6x) / 2.Complete the calculation based on the values of x that are given: n = 20 / x.If x is known, you can substitute the value of x into the equation to find the value of n. If x is not given, then this is the simplified form of the equation in terms of n and x.
A cube with a volume of 75cm^3 is dilated by a scale factor of 5. What is the volume of the dilated cube?
Answers
in volume
[the scale factor]=∛{[dilated volume]/[initial volume]}
then
[the scale factor]³=[dilated volume]/[initial volume]
[dilated volume]=[initial volume]*[the scale factor]³
[dilated volume]=[75]*[5]³-------> 75*125-------> 9375 cm³
the answer is 9375 cm³
$8000 invested at an APR of 6% for 10 years.
If interest is compounded annually, what is the amount of money after 10 years?
Answers
The formula in finding the maturity value is the following:
A = P (1 + r) ^t
Where A = Maturity value
P = principal amount
r = Annual percentage rate
t = time in years
Substituting the given amount to the formula:
A = $8,000 (1 + 6%) ^10
= $8,000 (1.7908)
= $14,326.40
Therefore, the amount of $8,000 after 10 years compounded annually at 6% is $14,326.40
how many time does 2 go into 19
Answers
When you state the question, "How many times does 2 go into 19", I assume your talking about Long Division. (Not so long in this case)
In this case, we would divide 19 by 2, resulting in 9 with a remainder of 1.
Thats It! :)
I hope I helped, Have a great Day!
Thank you,
Darian D.
In basic division, 2 goes into 19 a total of 9 times with 1 leftover. This demonstrates division and the concept of remainders in mathematics.
Explanation:The student is asking about basic division in mathematics, specifically how many times 2 goes into 19. To find this, we divide 19 by 2.
Doing the division, we get:
19 divided by 2 equals 9 with a remainder of 1.Therefore, 2 goes into 19 9 times with 1 left over.
It's worth noting that there's also a mathematics technique called estimation that might be considered here. If we estimate to the nearest whole number, 2 would go into 19 approximately 9 times since 2 times 9 is 18, which is very close to 19.
There is a two-digit number whose units digit is six less than the tens digit. Four times the tens digit plus five times the units digit equal 51. Find the digits.
Answers
4T + 5U = 51 substitute for T
4(U + 6) + 5U = 51
4U + 24 + 5U = 51
9U + 24 = 51
9U = 27
U = 3
t = U + 6
t = 3 + 6
t = 9
Check
4*t + 5*u = ? 51
4*9 + 5*3 = ? 51
36 + 15 =? 51
51 = 51 It checks.
Answer:
The tens digit number is 9 and the ones digit number is 3.
A candy maker buys a bar of chocolate weighing 162 ounces. About how many pounds does the bar weigh?
Answers
1 pound = 16 ounces
Applying the comversion we have:
(162) * (1/16) = 10,125 pounds
Therefore, the weight of the chocolate bar in pounds is 10,125
Answer:
the bar does weigh 10,125 pounds
solve the proportion
[tex] \frac{3}{4} = \frac{x}{6} [/tex]
Answers
[tex] \frac{3}{4} = \frac{x}{6} [/tex] Multiply 3 by 6 and multiply 4 by x.
4x = 18 Divide by 4.
x = [tex] \frac{18}{4} [/tex] Simplify!
x = [tex] \frac{9}{2} [/tex]
You can check this by comparing the fractions with [tex] \frac{9}{2} [/tex] in the place of x.
[tex] \frac{3}{4} = \frac{ \frac{9}{2} }{6} [/tex] Divide [tex] \frac{9}{2} [/tex] by 6 ( [tex] \frac{9}{2} [/tex] times [tex] \frac{1}{6} [/tex]).
[tex] \frac{3}{4} = \frac{9}{12} [/tex] Simplify!
[tex] \frac{3}{4} = \frac{3}{4} [/tex]
The fractions are equal, so x = [tex] \frac{9}{2} [/tex] .
1) Which two lines are parallel?
I. 5y = -3x-5
II. 5y = -1 - 3x
III. 3y - 2x = -1
a. I. and II.
b. I. and III.
c. II. and III.
d. No two of the lines are parallel.
2) Which do lines are parallel?
I. 3y = -2x - 3
II. 3y = 1 - 2x
III. 4y - 3x = -1
a. I. and II.
c. II. and III.
b. I. and III.
d. No two of the lines are parallel.
Answers
2)a
hope this helps
5) If f(x) = 4x2 - 5x + 7 and g(x) = 3x2 - 2x + 8, find f(x) + g(x).
Answers
f(x) + g(x) = 4x^2 - 5x +7 + 3x^2 - 2x + 8
f(x) + g(x) = 7x^2 - 7x + 15. Don't go any further.
A triangle has sides with lengths of 6 millimeters, 8 millimeters, and 10 millimeters. Is it a right triangle?
Answers
6^2 + 8^2 = 100^2
36 + 64 = 100
100 = 100
Yes, the triangle is a right triangle.
Hope this helps =)
The sides 6 mm, 8 mm and 10 mm forms a right angles triangle.
We have,
The sides of the triangle are of lengths 6 mm, 8 mm and 10 mm.
The longest side length is 10 mm.
Now, the sum of squares of the smaller sides is given as:
6² + 8² = 36 + 64 = 100 = 10²
As, the sum of squares of the smaller sides is equal to the square of the longer side.
So, by the Pythagorean Theorem, the sides form a right triangle.
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The table below shows the average temperature, in degrees Celsius, in Jacob's city over a period of five months:
Month 1 2 3 4 5
Temperature 5 7.2 9.4 11.6 13.8
Did the temperature in Jacob's city increase linearly or exponentially?
Linearly, because the table shows a constant percentage increase in temperature each month
Exponentially, because the table shows a constant percentage increase in temperature each month
Linearly, because the table shows that temperature increased by the same amount each month
Exponentially, because the table shows that temperature increased by the same amount each month
Answers
Answer:
C. Linearly, because the table shows that temperature increased by the same amount each month
Step-by-step explanation:
Which system of equations below has infinitely many solutions?
y = –3x + 4 and y = –3x – 4
y = –3x + 4 and 3y = –9x + 12
y = –3x + 4 and y = -1/3x + 4
y = –3x + 4 and y = –6x + 8
Answers
y = –3x + 4 and 3y = –9x + 12 y=4-3x
y = –3x + 4 and y = -1/3x + 4 x=0, y=4
y = –3x + 4 and y = –6x + 8 x=4/3, y=0
Answer:
y = –3x + 4 and y = –3x – 4 no solution exists
y = –3x + 4 and 3y = –9x + 12 y=4-3x
y = –3x + 4 and y = -1/3x + 4 x=0, y=4
y = –3x + 4 and y = –6x + 8 x=4/3, y=0
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Step-by-step explanation:
In a circle with a radius of 36 3/5 cm, an arc is intercepted by a central angle of 2π7 radians.
What is the arc length?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
cm
Answers
Answer:
The arc length is [tex]32.84\ cm[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=36\frac{3}{5}\ cm=\frac{36*5+3}{5}=\frac{183}{5}\ cm[/tex]
substitute
[tex]C=2(3.14)(\frac{183}{5})=229.848\ cm[/tex]
Remember that
[tex]2\pi[/tex] radians subtends the complete circle of length [tex]229.848\ cm[/tex]
so
by proportion
Find the arc length by a central angle of [tex]2\pi/7[/tex] radians
[tex]\frac{229.848}{2\pi}=\frac{x}{2\pi/7}\\ \\x=229.848*(2\pi/7)/(2\pi)\\ \\x=`32.84\ cm[/tex]
The arc length is approximately 32.81 cm.
Step 1
To find the arc length intercepted by a central angle, we can use the formula:
[tex]\[ \text{Arc Length} = \text{radius} \times \text{central angle} \][/tex]
Given:
- Radius [tex](\( r \)[/tex]) = 36 3/5 cm
- Central angle [tex](\( \theta \)) = \( \frac{2\pi}{7} \)[/tex] radians
First, let's convert the radius to a decimal:
[tex]\[ \text{Radius} = 36 \frac{3}{5} \text{ cm} = 36.6 \text{ cm} \][/tex]
Step 2
Now, we can use the formula to find the arc length:
[tex]\[ \text{Arc Length} = 36.6 \times \frac{2\pi}{7} \]\[ \text{Arc Length} = 36.6 \times \frac{2 \times 3.14}{7} \]\[ \text{Arc Length} = 36.6 \times \frac{6.28}{7} \]\[ \text{Arc Length} = 36.6 \times 0.897 \]\[ \text{Arc Length} \approx 32.808 \][/tex]
Rounded to the nearest hundredth, the arc length is approximately 32.81 cm.
Which of the following is a monomial?
A. 2xyz2
B. 2x + yz
C. 2 + xyz
D. 2x − yz
Answers
So your answer would be A. 2xyz2. Hope it helps! :)
Write an equation that involves multiplication,addition, contains a variable and has a solution of 8.
Answers
Here's an equation:
(Solve for x.)
x=(4+1)*2-2
Hope this helps!
wo groups of students were asked how many pets they had. The table below shows the numbers for each group: Group A 1 2 1 1 3 5 4 2 3 Group B 3 2 3 2 2 2 1 1 2 Based on the table, which of the following is true?
Answers
we know that
The interquartile range is a measure of where the “middle fifty” is in a data set
the interquartile range formula is the first quartile subtracted from the third quartile:
Group A [1 2 1 1 3 5 4 2 3]
Step 1: Put the numbers in order
[1 1 1 2 2 3 3 4 5]
Step 2: Find the median
[1 1 1 2 2 3 3 4 5]
Step 3: Place parentheses around the numbers above and below the median
[(1 1 1 2) 2 (3 3 4 5)]
Step 4: Find Q1 and Q3
[(1 1 1 2) 2 (3 3 4 5)]----> Q1=1 Q3=3
IQRA = Q3 – Q1--------> 3-1=2
Group B [3 2 3 2 2 2 1 1 2]
Step 1: Put the numbers in order
[1 1 2 2 2 2 2 3 3]
Step 2: Find the median
[1 1 2 2 2 2 2 3 3]
Step 3: Place parentheses around the numbers above and below the median
[(1 1 2 2) 2 (2 2 3 3)]
Step 4: Find Q1 and Q3
[(1 1 2 2) 2 (2 2 3 3)]----> Q1=1 Q3=2
IQRB = Q3 – Q1--------> 2-1=1
IQRA=2
IQRB=1
the answer is the option
The interquartile range for Group A students is 1 more than the interquartile range for Group B students
The question about how many pets two groups of students have cannot be answered without the correct data. Typically, such a question would involve computing descriptive statistics or organizing the data into a graph or table for easier comparison and interpretation.
Explanation:Based on the information given in the prompt, which seems to contain a mistake as it does not directly correlate to the question about the two groups of students and their number of pets, we can not effectively conclude which of the following is true regarding the data about Group A and Group B without the appropriate data or statements to compare. Therefore, we need the correct data to proceed with the analysis. Generally, in math problems like this, we would compute the mean, median, mode, or range of the data to compare the two sets, or we could use more advanced statistics if required.
In a correct scenario, you could group the data differently by organizing it into a frequency table or creating a graph to visualize the distribution. Depending on the data shape, you might group it by intervals or categories. Grouping data helps to understand and interpret the data more easily. For instance, it is often easier to see trends and patterns in a histogram or bar chart than in a raw list of numbers.
Jim goes to the store and buy 6 apples for 25 cent each and 10 bananas for 10 cent each Jim has a 10% off coupon Jim will own the store $2. 25 truє σr fαlѕє
Answers
Use the data to create a scatter plot. Year 0 1 2 3 4 Population 3 4 6 11 15 Use the point tool to plot the points from the table in the coordinate grid to create a scatter plot.
Answers
Enter the values in the first two columns of MS excel. Then go on the insert tab and click insert scatter plot. A scatter plot will be made as shown below in the attached picture.
The same plot can be made by hand by simply inserting the correct points on the graph. From the scatter plot we can observe that a positive correlation occurs in the given variables. A straight line can be used to approximate the trend of the data.
Answer:
Refer the attached figure.
Step-by-step explanation:
Given : Data of population
To find : Use the data to create a scatter plot?
Solution :
Data :
Year(x) Population(y)
0 3
1 4
2 6
3 11
4 15
A Scatter Plot has points that show the relationship between two sets of data.
With the help of scatter plot graph,
We plot the points of the data.
Refer the attached figure below.
What is the factored form of x2 - 4x - 5 ?
Answers
Two factors of five that subtract to four
What is the constant term in the expression 4x3y + 8x2 + 6x + 5?
Answers
Answer:
5
Step-by-step explanation:
The constant term is the one with no variables in it: +5.
Answer:
i took the test and its 5.
Which operation is performed in the derivation of the quadratic formula moving from Step 6 to Step 7? subtracting from both sides of the equation squaring both sides of the equation taking the square root of both sides of the equation taking the square root of the discriminant
Answers
as the power 2 from the right side of the equation disappeared
it means that the it's square root has been taken as square root is the opposite of power 2
and it's easily identifiable that it is been square rooted from the right side of the equation as well
Answer:
C
Step-by-step explanation:
Simplify the rational expression. State any restrictions on the variable n^4-11n^2+30/ n^4-7n^2+10
Answers
The given rational expression simplifies to (n^2 - 6)/(n^2 - 2). However, n cannot be equal to ±√2 and ±√5. These are the values that would make the denominator of the original or simplified expression equal to 0.
Explanation:To simplify the given rational expression we must first factor both the numerator and the denominator. The expression is n^4 - 11n^2 + 30/ n^4 - 7n^2 + 10. We recognize this is a quadratic in terms of n^2. Hence, the numerator factors into (n^2 - 6)(n^2 - 5), and the denominator factors into (n^2 - 5)(n^2 - 2).
The simplified version of the expression is (n^2 - 6)/(n^2 - 2) but we need to take into account the restrictions for n which are that n cannot be equal to ±√2 and ±√5. These are the values that would make the denominator of the original or simplified expression equal to 0, thus undefined.
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The rational expression [tex](n^4 - 11n^2 + 30)/(n^4 - 7n^2 + 10)[/tex] simplifies to [tex](n^2 - 6)/(n^2 - 2)[/tex], with restrictions on n being ±√5 and ±√2 since these values would cause the original denominator to be zero.
To simplify the rational expression [tex]n^4 - 11n^2 + 30[/tex] divided by [tex]n^4 - 7n^2 + 10[/tex], we start by factoring both the numerator and the denominator.
Factor the numerator:
→ [tex]n^4 - 11n^2 + 30 = (n^2 - 5)(n^2 - 6)[/tex]
Factor the denominator:
→ [tex]n^4 - 7n^2 + 10 = (n^2 - 5)(n^2 - 2)[/tex]
After factoring, we can eliminate common terms.
The term ([tex]n^2 - 5[/tex]) is present in both the numerator and the denominator and can be cancelled out.
The simplified expression is [tex](n^2 - 6)/(n^2 - 2)[/tex].
We also need to state restrictions on the variable n. These restrictions come from the values that make any denominator zero, which are not allowed.
For the initial fraction, the restrictions are the values of n that make [tex]n^2 - 5[/tex] or [tex]n^2 - 2[/tex] equal to 0. Thus, n cannot be ±√5 or ±√2.
Which terms accurately classify this triangle? Choose exactly two answers that are correct. A. right B. acute C. isosceles D. scalene