PLEASE HELP!!!
Solve this system of equations for x and y. Use the addition method or the substitution method. Check your result:
2x + 4y = 10
x - 2y = 1
How will your solution to the previous problem change if we change it to this system of inequalities?:
2x + 4y ≤ 10
x - 2y > 1
Answers
9514 1404 393
Answer:
(x, y) = (3, 1)
2y +1 < x ≤ 5 -2y where y < 1
Step-by-step explanation:
a) We can add twice the second equation to the first to eliminate y.
(2x +4y) +2(x -2y) = (10) +2(1)
4x = 12 . . . . . simplify
x = 3
3 -2y = 1 . . . . substitute for x in the second equation
2 = 2y . . . . . add 2y-1 to both sides
1 = y . . . . . . divide by 2
The solution is (x, y) = (3, 1).
__
b) The solution for a set of inequalities is generally the intersection of two half-planes. It is not just one point. The solution space is usually represented graphically, but we can write inequalities that express it.
The first inequality tells us that both x and y will be on or below the boundary line, which will have negative slope.
The second inequality tells us x will be above the boundary line with positive slope, and y will be below it. If we consider the boundary lines to cross in an X shape, the solution space will be in the bottom quadrant. This suggests the area can best be represented by expressing x as a range of values in terms of y.
Solving each inequality for x, we get ...
2x +4y ≤ 10 ⇒ x ≤ 5 -2y
x -2y > 1 ⇒ x > 2y +1
These give us the compound inequality ...
2y +1 < x ≤ 5 -2y
Of course, the relation between the limits must hold, so ...
2y +1 < 5 -2y
4y < 4 . . . . . . . add 2y-1
y < 1 . . . . . . divide by 4
The solution is 2y +1 < x ≤ 5 -2y where y < 1.
_____
The graph shows the region that is the solution to the system of inequalities. The vertex point (3, 1) is not part of that region. (It does not satisfy the left boundary condition.) However, that point is the solution to the set of equations. It is where the boundary lines meet.
__
Additional comment
Above, we noted that the inequalities have boundary lines that intersect to divide the Cartesian plane into 4 parts. We called the intersecting lines an X shape. In general, if the solution space is in the left- or right-portion of this shape, the compound inequality defining the solution will be one that bounds y. If it is in the top or bottom of this shape, then the compound inequality will be one that bounds x (as in this problem).
A different generality may apply if the boundary lines have slopes of the same sign.
Related Questions
Find the value of each variable. PLEASE HELP ME
Answers
Given:
A quadrilateral DEFG inscribed in a circle.
[tex]m\angle D=60^\circ, m\angle E=m^\circ, m\angle F=2k^\circ, m\angle G=60^\circ[/tex]
To find:
The value of variables [tex]m[/tex] and [tex]k[/tex].
Solution:
If a quadrilateral is inscribed in a circle then it is a cyclic quadrilateral. The opposite angles of a cyclic quadrilateral angle supplementary angles.
Quadrilateral DEFG inscribed in a circle. So, quadrilateral DEFG is a cyclic quadrilateral.
[tex]m\angle D+m\angle F=180^\circ[/tex] [Supplementary angle]
[tex]60^\circ+2k^\circ=180^\circ[/tex]
[tex]2k^\circ=180^\circ-60^\circ[/tex]
[tex]2k^\circ=120^\circ[/tex]
Divide both sides by 2.
[tex]k^\circ=\dfrac{120^\circ}{2}[/tex]
[tex]k^\circ=60^\circ[/tex]
[tex]k=60[/tex]
Similarly,
[tex]m\angle E+m\angle G=180^\circ[/tex]
[tex]m^\circ+60^\circ=180^\circ[/tex]
[tex]m^\circ=180^\circ-60^\circ[/tex]
[tex]m^\circ=120^\circ[/tex]
[tex]m=120[/tex]
Therefore, the values of the variables are [tex]m=120[/tex] and [tex]k=60[/tex].
A.Calculate the mean,median and mode.(3 points each) 1.)1,2,3,4,5 2.)2,3,4,5,6,6 3.)6,7,5,4,5,6,2,5
Answers
Answer:
Step-by-step explanation:
1.)1,2,3,4,5
mean=sum of all values/number of values
=1+2+3+4+5/5
=15/5
mean=3
Mode :
In the given data, no observation occurs more than once.
Hence the mode of the observations does not exist, means mode=0.
Median
1,2,3,4,5
Middle value is 3 so the median is 3.
2.)2,3,4,5,6,6
mean=sum of all values/number of values
=2+3+4+5+6+6/6
=26/6
mean =4.33
Mode
is that value of the observation which occurs maximum number of times so here mode is 6.
Median
2,3,4,5,6,6
4+5/2
9/2
median=4.5
3.)6,7,5,4,5,6,2,5
mean=sum of all values/number of values
=6+7+5+4+5+6+2+5/8
=40/8
mean =5
Mode
is that value of the observation which occurs maximum number of times so here mode is 5
Median
2,4,5,5,5,6,6,7
5+5/2
10/2
median=5
if someone could help me i would aprshh
Answers
Answer:
Slope: -5/4
Step-by-step explanation:
Use slope (m) formula:
m = y2 - y1 / x2 - x1
m = 5 - 10 / 49 - 45
m = -5/4
Answer:
[tex]-\frac{5}{4}[/tex]
Step-by-step explanation:
Hi there!
Equation for the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
To find the slope of the line, plug in any two points given in the table. For example, we can use the points (49,5) and (53,0):
[tex]=\frac{5-0}{49-53}\\=\frac{5}{-4}[/tex]
Therefore, the slope of the line is [tex]-\frac{5}{4}[/tex].
I hope this helps!
The perimeter of the figure below is 41.6 in. Find the length of the missing side. (Note: diagram is NOT to scale)
Answers
Answer:
[tex]{ \tt{let \: that \: unknown\: side \: be \: x}} \\ { \boxed{ \tt{perimeter = (8 \times side)}}} \\ 41.6 = (3.2 \times 2) + (5.9 \times 5) + x \\ x = 5.7 \:in \\ { \bf{answer : 5.7 \: inches}} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}[/tex]
Help me pleaseeeeeeeeeeeeeeeeeee
Answers
Answer:
Always a parabola or U Shaped
U shaped or by rotating U it will be like intersect symbol.. You can see it in attached file
Evaluate integral tan^6(2x) sec^4(2x) dx.
Answers
Answer:
Is the question original or you simply made it.
The probability of spinning blue on a spinner is 0.3. If the spinner is spun 40 times, estimate how many times you would spin blue. A 3-sided sninner is snun 10 time 1
Answers
Answer:
12 times.
Step-by-step explanation:
That would be 40 * 0.3 = 12.
de moirve's
(√3-i ÷ √3+i)^6 = 1
Answers
(√3 - i ) / (√3 + i ) × (√3 - i ) / (√3 - i ) = (√3 - i )² / ((√3)² - i ²)
… = ((√3)² - 2√3 i + i ²) / (3 - i ²)
… = (3 - 2√3 i - 1) / (3 - (-1))
… = (2 - 2√3 i ) / 4
… = 1/2 - √3/2 i
… = √((1/2)² + (-√3/2)²) exp(i arctan((-√3/2)/(1/2))
… = exp(i arctan(-√3))
… = exp(-i arctan(√3))
… = exp(-iπ/3)
By DeMoivre's theorem,
[(√3 - i ) / (√3 + i )]⁶ = exp(-6iπ/3) = exp(-2iπ) = 1
The system of equations Y equals -1/5 X -6 and Y equals negative 2X +3 is shown on the graph below
Answers
Answer:
The solution of the system is (5, -7)
Step-by-step explanation:
Here we have the system:
y = (-1/5)*x - 6
y = -2*x + 3
We know that this system is graphed below, and the question is incomplete, but I assume that we want to find the solution to this system. If you can see the graph, the solution is just the point where both graphs intersect, but we can find the solution analytically.
We know that:
y = (-1/5)*x - 6
y = -2*x + 3
Then, we can write:
y = (-1/5)*x - 6 = y = -2*x + 3
This leads to:
(-1/5)*x - 6 = -2*x + 3
Now we can solve this for x.
(-1/5)*x + 2*x = 3 + 6
(-1/5)*x + (10/5)*x = 9
(9/5)*x = 9
x = (5/9)*9 = 5
x = 5
now that we know the value of x, we can input this in one of the two equations above to find the correspondent value of y, we will get:
y = -2*x + 3 = -2*5 + 3
y = -10 + 3 = -7
y = -7
Then the solution is:
x = 5 and y = -7, or (5, -7)
Layers of rock wear off during which of the following processes?
A: Expansion B: Contraction C: Exfoliation D: Pressure
Answers
Answer:
Exfoliation
Step-by-step explanation:
Changes in temperature cause rock to expand (with heat) and contract (with cold). As this happens over and over again, the structure of the rock weakens. Over time, it crumbles.
Rocky desert landscapes are particularly vulnerable to thermal stress. The outer layer of desert rocks undergo repeated stress as the temperature changes from day to night. Eventually, outer layers flake off in thin sheets, a process called exfoliation.
holaaaaaaaaaaaaaaaaa plz help i need this quick :)
Quadrilateral ARMY is rotated 90 degrees about the origin. Draw the image of this rotation.
Answers
Answer:
Step-by-step explanation:
If a point (x, y) is rotated 90° counterclockwise about the origin, rule for the rotation will be,
(x, y) → (-y, x)
Therefore, coordinates of the image point after the rotation will be (-y, x).
Following this rule,
Image points of the quadrilateral will be,
A(3, 3) → A'(-3, 3)
R(5, 7) → R'(-7, 5)
M(7, 5) → M'(-5, 7)
Y(5, 1) → Y'(-1, 5)
By graphing the image points we can get the graph of the image quadrilateral A'R'M'Y'.
Answer:
I got my answer on Khan Academy:
please help
Yaritza finds some nickels and pennies in her change purse. How many coins does she have if she has 140 nickels and 130 pennies? How many coins does she have if she has
n
n nickels and
p
p pennies?
Total coins, 140 nickels and 130 pennies: 270
Total coins,
n
n nickels and
p
p pennies:
Submit Answer
Answers
Answer:
270 coins
n + p
Step-by-step explanation:
Given that :
Number of nickels = 140
Number of pennies = 130
The total numbers coins had:
Number of Nickel + number of pennies
140 + 130 = 270 coins
If Number of nickels = n ; number of pennies = p
The total number of coins :
Number of Nickel + number of pennies
n + p
If you put 5 things in your mouth and take 3 out and put them in another hole, how much things are inside of you?
Answers
Answer:
2
Step-by-step explanation:
5-3=2 it's simple really
Answer:
5-3=2
Hope This Helps!!!
What is the area of the figure below
Answers
Answer:
the answer for that is 61.
Step-by-step explanation:
Is it true or false that for all sets A, B, and C, A U (B - C) = (A U B) - C?
Answers
Answer:yes
Step-by-step explanation:66
The given statement A U (B - C) = (A U B) - C is true.
What is a set ?A set is collection of well defined objects.
According to the given question we have to state whether A ∪ ( B - C ) = ( A ∪ B ) - C.
Lets consider we have three sets A, B and C and we also consider they intersect each other.
( B - C ) represents the elements which belongs to B but not in C.
∴ A ∪ ( B - C ) represents the no. of elements which belongs to the set B but not in C union the no. of elements which belongs to A.
AND
( A ∪ B ) - C represents no. of elements which belongs to A or B but not in C.
learn more about sets here :
https://brainly.com/question/8053622
#SPJ2
Alla and Balla together drink 750 milliliters (ml) of water. If Alla drinks 50% more than
Balla, how much does Alla drink?
Answers
Answer:
Step-by-step explanation:
A + B = 750
A = 1.5 B
~~~~~~~~~~~~~~
750-B = 1.5 B
750 = 1.5 B + B
750 = B(1.5 +1)
750 = B (2.5)
B = 300
A = 450
How would this quadrilateral be best classified, and what is the measure of Angle B?
Answers
Answer:
The quadrilateral is Rhombus
B=70°
Step-by-step explanation:
110+110+z+z=360
220+2z=360
2z=360-220
2z=140
z=140/2
Therefore, z=70
So Angle B=70
Since z= Angle B=Angle D
8)
8x + 6
14x - 2
A) 11
C) 8
B) -9
D) -7
Answers
Answer:
C) 8
Step-by-step explanation:
Consecutive angles are equal to 180. So 22x+4+180. Solve that to get x=8. Hope I helped and post more questions :)
which of the following is a geometric sequence?
Answers
Answer:
The right answer is a.
Step-by-step explanation:
PLEASE MARK ME AS A BRAINLIEST
Review the graph.
On a coordinate plane, a circle has center (1, 0) and radius 5. Another circle has center (0, negative 4) and radius 4. Everything inside the second circle and between the first circle is shaded.
Which system of inequalities has the solution set shown in the graph?
25 < (x – 1)2 + y2 and 16 > x2 + (y + 4)2
25 > (x – 1)2 + y2 and 16 > x2 + (y + 4)2
25 < (x – 1)2 + y2 and 16 < x2 + (y + 4)2
25 > (x – 1)2 + y2 and 16 < x2 + (y + 4)2
Answers
Answer:
second option
Step-by-step explanation:
[tex]shaded~area\\(x-1)^2+y^2<25\\and\\(x+4)^2+y^2<16[/tex]
Answer:
A
Step-by-step explanation:
edge
not sure if this is the right question so i dont know if we're thinking about the same question...
Find the midpoint of the line segment.
Answers
Answer:
-2,-3
Step-by-step explanation:
Of the following fractions: 9/19, 5/11, 7/15, and 11/23, which is the largest?
Answers
Answer:
silly question...I used technology to "cheat"
it is 11/23
34155 32775 33649 34485
72105 72105 72105 72105
Step-by-step explanation:
find the equation of the line shown
y =6 x=4
Answers
y - 6 = 0 ................ equation 1
x - 4 = 0 ................ equation 2
What is a cubic function
Answers
Answer:
In mathematics, a cubic function is a function of the form f(x)=ax^3+bx^2+cx+d where the coefficients a, b, c, and d are real numbers, and the variable x takes real values, and a ≠ 0. In other words, it is both a polynomial function of degree three, and a real function.
…aniwwjwwjaoqkqwgahw qjauaaj
Answers
Answer:
Undefined
Step-by-step explanation:
Lim x - - > 1(1 /In(2-x) + 1/(x-1))
To find the limit as x tends to 1
Substitute x = 1 into the function ;
(1 / In(2 - 1) + 1 / (1 - 1))
(1 / In 1) + (1 / 0)
1 / 0 + 1 / 0
Undefined
Help help help help help
Answers
Answer:yo we talking the same test
Step-by-step explanation:
Insta= santiagorez
Answer:
Radius , r = 5 units
Step-by-step explanation:
The standard form of a circle's equation:
[tex](x-a)^2 + (y -b)^2 = r^2 \ , \ where \ (a , b) \ is \ the \ centre\ and\ r \ is \ the \ radius.[/tex]
Given equation :
[tex]x^2 - 2x + y^ 2- 4y = 20\\\\[/tex]
Find radius .
Convert the given equation into standard form.
[tex](x - 1)^2 = x^ 2 - 2x + 1 \\\\(y - 2) ^2 = y^ 2 - 4y + 4\\\\[/tex]
Now add both equations :
[tex](x - 1)^2 + (y - 2)^2 = r^2[/tex]
[tex](x ^ 2 - 2x + 1) + (y^2 - 4y + 4 ) = r^2\\\\(x^2 -2x + y^2 - 4y ) + 1 + 4 = r^2\\\\20 + 1 + 4 = r^2[/tex] [tex][ \ given : \ x^2 - 2x + y^ 2 - 4y = 20 \ ][/tex]
[tex]25 = r^2 \\\\5 = r[/tex]
If the circumference of the circle is 88 cm, then its radius is 14 cm.
true or false?
Answers
Answer:
The radius is approximately 14 cm
Step-by-step explanation:
The circumference
C = 2 * pi *r
88 = 2 * pi *r
Divide by 2
44 = 3.14 *r
Divide by 3.14
44/3.14 = r
14.01273885=r
88/2= 44
Take the area calculate the area of the circle around the answer to the nearest hundredth
Answers
Step-by-step explanation:
we cannot see anything, and you did not describe anything. so, there is nothing to calculate.
Below is the frequency distribution of the score of 40 learners. COMPUTE THE mean,median and mode. (10 points)
Class interval: frequency
56-63 1
48-55 10
40-47 12
32-39 6
24-31 3
16-23 8
Answers
Answer:
Mean = 6.66
Median = 7
Mode = 7.68
Step-by-step explanation:
According to the Question,
Given That, the frequency distribution of the score of 40 learners.Class interval frequency
56-63 1
48-55 10
40-47 12
32-39 6
24-31 3
16-23 8
1). Mean = (Sum of all Observation) / (number of observation)
Mean = 40/6 = 6.66
2) For Median, If there are two number in the middle then you need to find their mean. 1 3 6 8 10 12 middle numbers are 6 and 8.
Median = (6+8) / 2 = 7
3) Mode = 3 × Median - 2 × Mean
Mode = 3×7 - 2×6.66
Mode = 7.68
Kelly used the vertical line test to determine whether or not the curve that she had been given is a function. After conducting the vertical line test, Kelly determined that the curve is a function. Which of the following choices represents the result of Kelly’s vertical line test?
Answers
Answer:
0 or 1
Step-by-step explanation:
Given that Kelley is tasked with having to use vertical line test to determine whether or not a curve is a function. Each vertical line that Kelly draws through her curve must intersect the curve at maximum one point only in order for thecurve to be a function
Answer is 0 or 1 point