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
Triangle A B C is cut by line segment D E. Line segment D E goes from side A C to line A B. The length of A E is 12, the length of E B is 4, and the length of A D is 9. What is the length of Line segment D C? 2 units 3 units 6 units
Answers
Answer: The length of DC is 3 units
Step-by-step explanation:
The Basic proportionality theorem states that if a line is parallel to one side of a triangle and intersects the other two at different points, then the other two sides are divided in the same ratio.
The given image is attached below.
From the BPT theorem, we can say that:
[tex]\Rightarrow \frac{AE}{EB}=\frac{AD}{DC}[/tex]
We are given:
AE = 12 units
EB = 4 units
AD = 9 units
Putting values in above equation, we get:
[tex]\Rightarrow \frac{12}{4}=\frac{9}{DC}\\\\\Rightarrow DC=\frac{9\times 4}{12}\\\\\Rightarrow DC=3 units[/tex]
Hence, the length of DC is 3 units
Answer:
The answer is 3 units
Step-by-step explanation:
What is the slope of the line represented by the equation f(x) = -3x + 7?
A -7
B -3
C 3
D 7
Answers
Answer:
-3
Step-by-step explanation:
in these equations the slope is multiplied by x which is -3 in this one.
Answer:
[tex]-3[/tex]
Step-by-step explanation:
The equation of a line is [tex]y=mx+b[/tex], and m is the gradient which is the slope. Hence, the number with x is the slope, which is [tex]-3[/tex].
Hope that helped.
Please help! What is the domain of the function shown in the graph?
Answers
Answer:
nnmb cgchmfxmgfmv vb , mnio qrstuvwxyz
abcdefghijklmnoprstuvxxyz
Step-by-step explanation:
now i know my abcs next time wont you sing with me
Ms.James shared 5/8 of the candies she had in a bag and had 15 left.How many candies did she have before sharing?
Answers
Answer:
40
Step-by-step explanation:
If you take 15, and divide it by the 3 out of the 3/8 left, you get 5. You then multiply 5 by 8 to get the full amount of candies she had before sharing, 40.
I hope this helped!
Thanks!
Your friend in answering,
~Steve
Answer:
40.
Step-by-step explanation:
If 15 candies are the rest of 3/8, then the total candies were 40.
Lines s and t are perpendicular. If the slope of line s is 5, what is the slope of line t
Answers
If two lines are perpendicular, the product of their slopes is -1
Which expression is not equivalent to 8 + (n – 4)?
12+n
n+4
(8 + n) – 4
(8 – 4) +n
Answers
Answer: n+4
Step-by-step explanation:
Which of the following expressions have a difference of 5? Check all that apply.
VX
0-3-(-8)
-2-3
1-(-4)
07-(-2)
Answers
9514 1404 393
Answer:
A, C
Step-by-step explanation:
A: -3 -(-8) = -3 +8 = 5
B: -2 -3 = -5
C: 1 -(-4) = 1 +4 = 5
D: 7 -(-2) = 7 +2 = 9
__
Differences A and C are 5.
Answer: A: -3- (-8)
B:1 -(-4)
Step-by-step explanation:
in A your subtracting them in B your adding them
The moment generating function for health care costs experienced by a policyholder is given as follows:
Mx(t)= (4/4-t)^3
An insurer reimburses the policyholder for 70% of health care costs experienced by the policyholder. Calculate the expected reimbursement by the insurer for a policyholder.
Answers
Answer:
0.525 = 52.5%
Step-by-step explanation:
Moment generating function ( Mx(t) ) = ( 4 / 4-t)^3
Reimbursement by Insurer = 70%
Determine the expected reimbursement by insurer for policyholder
d/dx (Mx(t) ) = d/dt ( 4 / 4-t)^3 = d/dt (1 - t/4 )^-3
= 3/4 ( 1 - t/4 )^-4 = 3/4
as t → 0
Given that the insurer reimburses 70% = 0.7
expected reimbursement = 0.7 * 3/4 = 0.7 * 0.75 = 0.525
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answers
Answer:
Step-by-step explanation:
Wage = rate / hr * the number of hours worked.
Wage = ?
rate = 15.45
time = 29.25 hours
Wage = 15.45 * 29.25
Wage = 451.91
Name the types of angles shown.
Check all that apply
A supplementary angles
B straight angle
C complementary angle
D right angle
Answers
Answer: C) complementary angle and D) right angle
Step-by-step explanation:
A is wrong because supplementary angles add up to 180 and this shows a right angle not a straight line
B is wrong because this a right angle not a straight angle
C is correct because complementary angles are two angles that add up to 90 degrees. angle EFH is split into EFG and GFH which adds up to 90 degrees.
D is correct because you can see the right angle symbol for angle EFH
The given angles shown in the figure are right angles and complementary angles.
Supplementary angles are two angles that add up to 180 degrees.
A straight angle is an angle that measures exactly 180 degrees.
It is a straight line, so it forms a straight angle.
A complementary angle is a pair of angles that add up to 90 degrees.
∠EFG and ∠GFH together are complementary angles as their sum is 90 degrees.
A right angle is an angle that measures exactly 90 degrees.
∠EFH is a right angle.
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If -9x(x + A) + 2 = (Bx + 2)(3x - 1) + 4, find the constants A and B.I am stuck at the step of solving B,can you help me?write down you steps and answer please
Answers
Answer:
A = -1
B = -3
Step-by-step explanation:
you need to do all the multiplication on both sides and then simply compare the factors of the various powers of x.
so,
-9x² - 9×A×x + 2 = 3×B×x² + 6x -Bx - 2 + 4
-9x² - 9×A×x + 2 = 3×B×x² + (6-B)x + 2
the x-less constants 2 = 2 are correct. now we need to compare the factors for the other parts of x.
we have left and right only one expression of x²
-9x² on the left
3×B×x² on the right
therefore,
-9 = 3×B
=> B = -3
otherwise the equation would not be correct for all values of x.
the only other parts remaining are
-9×A×x = (6-B)x = (6 - -3)x = (6+3)x = 9x
=>
-9×A = 9
-A = 1
A = -1
remember, all parts of the left and of the right side must be equal for the equation to be true in all cases.
Right angle Trigonometry, please help me solve and explain!
Answers
Answer:
5.01
Step-by-step explanation:
Reference angle (θ) = 24.3°
Length of side Opposite to reference angle = 2.06
Let the side length (Hypotenuse) we're looking for be represented as x
Apply SOH:
Sin θ = Opp/Hyp
Substitute the values into the equation
Sin 24.3° = 2.06/x
Multiply both sides by x
x × Sin 24.3° = 2.06/x × x
x × Sin 24.3° = 2.06
Divide both sides by Sin 24.3°
(x × Sin 24.3°)/Sin 24.3° = 2.06/Sin 24.3°
x = 5.01 (nearest hundredth)
PLEASE HELP WILL GIVE BRAINLIEST
Answers
Answer:
Check explanation
Step-by-step explanation:
I'll give you my way of solving it and you can figure it out from there.
<CEA = <DEB due to vertical angles
AE = ED due to midpoint theorem
<CAD = <ADB due to alternating angles theorem
thus two triangles congruent due to ASA
construct a scale of A-sharp major on a treble staff in ascending order only
Answers
Answer: In the picture from the basic music theory website's page on a-sharp major scale
Step-by-step explanation: music theory
A team of researchers wants to determine whether pet owners are generally more satisfied with their lives than non-pet owners. To test their theory, the researchers randomly select 500 pet owners and 500 non-pet owners from several major metropolitan areas in the country. The researchers then interview the individuals, asking them a series of questions. Each response is assessed with a point value that is later translated to a satisfaction indicator. Of the pet owners surveyed, 380 of the 500 were found to be satisfied with their lives, while 336 of the 500 non-pet owners were found to be satisfied.
Would this study be considered an experiment or an observational study?
Answers
Answer:
observational study
Step-by-step explanation:
The side of an equilateral triangle is 12. Its area is
Select one:
a. 144
b. 72
c. 36 √3
d. 48
Answers
Answer:
area is 1/2bh
in an euqilateral triangle, all sides are equal so base and height are 12
1/2 x 12 x 12
1/2 x 144= 72 (B)
Answer: Choice C. [tex]36\sqrt{3}[/tex]
This is the same as writing 36*sqrt(3)
===================================================
Work Shown:
x = 12 = side length of equilateral triangle
A = area of equilateral triangle
A = 0.25*sqrt(3)*x^2
A = 0.25*sqrt(3)*12^2
A = 0.25*sqrt(3)*144
A = 0.25*144*sqrt(3)
A = 36*sqrt(3) .... answer is choice C
Side note: the area approximates to 62.354 square units.
The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 70 and standard deviation 3. (Rockwell hardness is measured on a continuous scale.)a. If a specimen is acceptable only if its hardness is between 67 and 75, what is the probability that a randomly chosen specimen has an acceptable hardness?b. If the acceptable range of hardness is (70-c, 70+c) , for what value of c would 95% of all specimens have acceptable hardness?c. If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten?d. What is the probability that at most eight of ten independently selected specimens have a hardness of less than73.84? [Hint: Y = the number among the ten specimens with hardness less than 73.84 is a binomial variable; what is p?]
Answers
Answer:
a) The probability that a randomly chosen specimen has an acceptable hardness is 0.7938.
b) If the acceptable range of hardness is (70-c, 70+c), then the value of c would 95% of all specimens have an acceptable hardness of 5.88.
c) Expected number of acceptable specimens among the ten is 7.938.
d) Binomial with n = 10 and p = P(X < 73.84)
[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]
Step-by-step explanation:
a )
[tex]P(67 < X< 75) = P( (67 - 70) / 3 < X < (75 - 70) / 3 )\\\\= P( - 1 < Z < 1.67) = 0.9525 - 0.1587 = 0.7938[/tex]
b )
[tex]c = 1.96 * 3 = 5.88[/tex] { Since Z = 1.96 for 95% CI refer table.}
c )
Expected number of acceptable specimens among the ten [tex]= 10 * P(67 < X< 75) \\\\= 10 * 0.7938 = 7.938[/tex]
d )
Binomial with n = 10 and p = P(X < 73.84)
[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]
Question 18 of 28 Which of the following equations can be used to find the length of EF in the triangle below? A. (EA)2 = 242-122 B. (ER2 = 242 +122 O C. EF = 24 - 12 D. EF = 24 + 12
Answers
Answer: A
Step-by-step explanation:
Question 35 of 49
Which description best describes parallel lines?
A. Lines that are not in the same plane and will never intersect
O B. Lines that intersect at a right angle
O C. Lines that intersect
D. Lines that lie in the same plane but will never intersect
SUBM
Answers
Answer:
D.lines that lie in the same plane but will never intersect
Step-by-step explanation:
parallel lie in the same plane but never meet
The table shown gives values of the function y=g(x) for selected values of x.
Answers
Answer: C
Explanation:
A is eliminated because of 3 and 24, 3^2 is 9 and 9 times 3 isnt 24
B is eliminated because of 1 and 6, 2 plus 3 is 5 not 6
C works for all the number sets
D is eliminated because of 1 and 6, again 3 plus 2 is 5 not 6
Find the difference of (4.2x10^3)-(2.7x10^3)
Show work!
Answers
Step-by-step explanation:
Is it helpful ?
plz let me know
carol and jada sold raffle tickets to raise money for a new playground carol sold 2045 tickets jada sold 356 more than carol how many did jada sell
Answers
Henry signed up for a streaming music service that costs $14 per month. The service allows Henry to listen to unlimited music, but if he wants to download songs for offline listening, the service charges $1 per song. How much total money would Henry have to pay in a month in which he downloaded 50 songs? How much would he have to pay if he downloaded s songs?
Cost for 50 songs :
Cost for s songs :
Answers
Answer:
Cost for 50 songs: $64
Cost for s songs: s + 14
Step-by-step explanation:
Since it is $1 per song, if he downloaded 50 songs, it would be $50 extra dollars.
Add this to the monthly charge of 14:
50 + 14
= 64
So, the cost of 50 songs would be $64.
Now, find the cost for downloading s songs.
Each song is $1, so the cost can be represented by s + 14.
The answer is:
Cost for 50 songs: $64
Cost for s songs: s + 14
Evaluate 9(4x – 15) if x = 3.
Answers
Answer:
-27
Step-by-step explanation:
9(4x – 15)
Substitute 3 for x
9((4)(3) - 15)
Multiply (4)(3) = 12
9 ( 12 - 15 )
Subtract 12 - 15 = -3
9(-3)
Multiply 9(-3) = -27
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {-27}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \: 9 \: (4x - 15)[/tex]
Plugging in the value [tex]x = 3[/tex] in the above expression, we have
➼ [tex] \: 9 \: (4 \times 3 - 15)[/tex]
➼ [tex] \: 9 \: (12 - 15)[/tex]
➼ [tex] \: 9 \: ( - 3)[/tex]
➼ [tex] \: - 27[/tex]
Note:-[tex]\sf\pink{PEMDAS\: rule.}[/tex]
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
If the spin rate of the CD is 580 rpm what distance is traveled by the piece of dust (in radians) in 2.9 mins
Answers
Answer:
[tex]d=10568.76rads[/tex]
Step-by-step explanation:
From the question we are told that:
Angular Velocity [tex]\omega=580rpm=>60.74rads/sec[/tex]
Time [tex]t=2.9mins=>174sec[/tex]
Generally the equation for distance d is mathematically given by
[tex]d=\omega*t[/tex]
[tex]d=60.74*174[/tex]
[tex]d=10568.76rads[/tex]
is the sum of two rational numbers sometimes zero ture or false?
Answers
Answer:
True.
Step-by-step explana
-4/5 + 4/5 is 0
find the volume of the cone 3.4 m x 5.5 m
Answers
Answer:
63,5
Step-by-step explanation:
pi r bình pnhân hươnh g
Which statement is true about the end behavior of the
graphed function?
• As the x-values go to positive infinity, the function's
values go to negative infinity.
O As the x-values go to zero, the function's values go to
positive infinity.
• As the x-values go to negative infinity, the function's
values are equal to zero
As the x-values go to positive infinity, the function's
values go to positive infinity.
Answers
Answer:
I believe it is the first choice
Step-by-step explanation:
As the x-values go to positive infinity, the function's
values go to negative infinity is the answer because the x-valures are in the first coordinate which is positive but the functions is going negative because of the line in the 3rd coordinate.
I tried my best, i hope you get it correct.
Please let me know if this is correct or not, if not i will edit my answer.
Please mark brainliest :)
Which is the graph of f(x) = 2 (4)?
5
40.4)
404)
4
(4,4)
3
3
3 2
2
2
2
(2.1)
6,2)
1
5 -4 -3 -2 -14
1
3
4
-5 4 -3 -2 -14
234
-5 6 -3 -2 -14
2
3
4
5
X
-2
-2
نا دیا
-3
-3
4
W4
-5
5
Tu
5
4
(
24)
Answers
Answer:
The Third one
Step-by-step explanation:
Your Welcome :)
Graph of the function is attached below.
Correct option is D.
What is exponential function?As the name suggests, the exponential function contains an exponent. Note, however, that the exponential function has a constant as its base and a variable as its exponent, not vice versa (if a function has a variable as its base and a constant as its exponent, it is a power function). The exponential function can be in one of the following forms:
Definition of exponential function
In mathematics, an exponential function is a function of the form f(x) = aˣ. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0.
Given, exponential function
f(x) = (1/4)4ˣ
exponential function is defined for x∈R
Putting x = 0
f(0) = (1/4)4⁰
f(0) = 1/4
Point on curve is (0,1/4)
Putting x = 1
f(1) = (1/4)4¹
f(1) = (1/4)4
f(1) = 1
Point on curve is (1,1)
Putting x = 2
f(2) = (1/4)4²
f(2) = (1/4)16
f(2) = 4
Point on curve is (2,4)
Putting x = 3
f(3) = (1/4)4³
f(3) = (1/4)64
f(3) = 16
Point on curve is (3,16)
Point (0, 1/4), (1, 1), (2, 4), (3, 16) can be used to draw graph of the function.
Hence, graph of the function is drawn as follows.
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A bag contains 6 black, 4 blue, and 8 white marbles. What is the probability that a marble drawn from the bag will be white?
a.1/18
b.2/5
c.4/9
d.4/5
Answers
Answer:
C.4/9
Step-by-step explanation:
You add the black marbles, blue marbles, and the white marbles together, which equal 18. Out of the 18 marbles, 8 of them are white so it would be 8/18.
but you have to simplify it. 8 and 18 have 2 as the greatest common factor. 8 divided by 2 is 4 and 18 divided by 2 is 9. Finally its 4/9 since you cant simplify it even more.
