Answers
Answer:
[tex]-3\cdot x + 5\cdot y = 6[/tex], [tex]6\cdot x -10\cdot y = 14[/tex] is inconsistent.
Step-by-step explanation:
Two linear equations are inconsistent when each group of coefficients associated with each variable have the same multiple and independent coefficients are different and have the same multiple. Since, the set of variables is [tex](x,y)[/tex], then the following condition must be observed:
[tex]k_{x} = k_{y} \ne k_{c}[/tex] (1)
[tex]k_{x} = \frac{a_{x}}{b_{x}}[/tex] (2)
[tex]k_{y} = \frac{a_{y}}{b_{y}}[/tex] (3)
[tex]k_{c} = \frac{a_{c}}{b_{c}}[/tex] (4)
Now we proceed to check each option:
Option 1: [tex]x + 4\cdot y = 20[/tex], [tex]2\cdot x - y = 7[/tex]
([tex]a_{x} = 1[/tex], [tex]a_{y} = 4[/tex], [tex]b_{x} = 2[/tex], [tex]b_{y} = -1[/tex])
[tex]k_{x} = \frac{1}{2}[/tex], [tex]k_{y} = -4[/tex] (This system is not inconsistent)
Option 2: [tex]3\cdot x + 2\cdot y = -2[/tex], [tex]4\cdot x -y = -2[/tex]
([tex]a_{x} = 3[/tex], [tex]a_{y} = 2[/tex], [tex]b_{x} = 4[/tex], [tex]b_{y} = -1[/tex])
[tex]k_{x} = \frac{3}{4}[/tex], [tex]k_{y} = -2[/tex] (This system is not inconsistent)
Option 3: [tex]8\cdot x + 4\cdot y = 16[/tex], [tex]4\cdot x - 2\cdot y = 6[/tex]
([tex]a_{x} = 8[/tex], [tex]a_{y} = 4[/tex], [tex]b_{x} = 4[/tex], [tex]b_{y} = -2[/tex])
[tex]k_{x} = 2[/tex], [tex]k_{y} = -2[/tex] (This system is not inconsistent)
Option 4: [tex]-3\cdot x + 5\cdot y = 6[/tex], [tex]6\cdot x -10\cdot y = 14[/tex]
([tex]a_{x} = -3[/tex], [tex]a_{y} = 5[/tex], [tex]b_{x} = 6[/tex], [tex]b_{y} = -10[/tex])
[tex]k_{x} =-\frac{3}{5}[/tex], [tex]k_{y} = -\frac{3}{5}[/tex] (This system may be inconsistent)
([tex]a_{c} = 6[/tex], [tex]b_{c} = 14[/tex])
[tex]k_{c} = \frac{3}{7}[/tex] (This system is inconsistent)
Related Questions
Which of the following sets of measurements could be the side lengths of a right triangle?
A) 27, 35, 43
B) 26, 34, 42
C) 25, 33, 41
D) 24, 32, 40
Answers
2 The ratio of beans to rice at T. Blancos place is 2 to 3. There are 27 grains answer of rice on the plate. What is the total number of beans and rice on the plate
Answers
Answer: 45
Step-by-step explanation:
From the question, we are informed that the ratio of beans to rice at T.Blancos place is 2 to 3 and that there are 27 grains answer of rice on the plate. The number of beans would be:
= 2/3 × 27
= 18.
Therefore, the total number of beans and rice on the plate will be:
= 27 + 18
= 45
Rewrite the following equation as a function of x 2x^(4)-625-500=0
Choices are below. Will give 15 points for this.
Answers
Answer:
Option (D) is true.
Step-by-step explanation:
Given the equation
25x⁴ - 625y - 500 = 0
solving in terms of y as a function of x
[tex]25x^4\:-\:625y\:-\:500\:=\:0[/tex]
Step 1: Add -25x⁴ to both sides
[tex]25x^4\:-\:625y\:-\:500\:+\:\left(-25x^4\right)=0+\left(-25x^4\right)[/tex]
[tex]-625y-500=-25x^4[/tex]
Step 2: Add 500 to both sides
[tex]-625y-500\:+500=-25x^4\:+500[/tex]
[tex]-625y=-25x^4\:+500[/tex]
Step 3: Divide both sides by -625
[tex]\frac{-625y}{-625}=\frac{\left(-25x^4\:+500\right)}{-625}[/tex]
[tex]\:\:y=\:\frac{1}{25}x^4-\frac{4}{5}[/tex]
Therefore,
[tex]\:f\left(x\right)=\:\frac{1}{25}x^4-\frac{4}{5}[/tex]
Thus, option (D) is true.
A bottle of laundry detergent costs $4.95 per bottle. If you have a coupon for $2.00 off and your total is $7.90, how many bottles of detergent did you buy? WRITE AN EQUATION AND SOLVE.
Answers
what is 12x-7 where x=4
Answers
Answer:
41
Step-by-step explanation:
12x4=48 -7= 1 and that's my explanation
PLEASE HELP!!!
Suppose a normal distribution has a mean of 50 and a standard deviation of
3. What is P(x<44)?
O A. 0.16
O B. 0.84
O C. 0.975
O D. 0.025
Answers
To solve this problem, we can simply use the formula of normal distribution and substitute the values where required.
The value of P(x <= 44) is 0.025 which is option D
ProbabilityGiven the value of the mean, normal distribution and standard deviation, we can calculate where the value lies
Data;
Mean = 50S.D = 3X = 44But we know that
[tex]z = \frac{x- \mu}{\sigma}[/tex]
Let's substitute the values of x, standard deviation and mean into the equation above
[tex]z = \frac{x-\mu}{\sigma} \\z = \frac{44-50}{3} =-2[/tex]
Solving this further;
[tex]P(z\leq -2) = \frac{1}{2} - \frac{1}{2}(0.9545)\\p(z\leq -2) = 0.025[/tex]
The value of P(x <= 44) is 0.025 which is option D
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Answer:
The answer is 0.16 other guy wrong
Step-by-step explanation:
lil_chris23x 56x34 45x34?? 5yx2X
Answers
Which formula gives the x-coordinates of the maximum values for y= cos()?
O kr for any integer k
Okr for k= 0,+2,t4
O7for any positive integer k
o
for K= 0,+2,+4,
Answers
Answer:
option b
Step-by-step explanation:
just trust
The formula that gives the x-coordinates of the maximum values of
y = cos(x) is kπ for k= 0, 2±, ±4.
Option B is the correct answer.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
The formula that gives the x-coordinates of the maximum values for
y = cos(x) is kπ + π/2 or (2k+1)π/2, where k is any integer.
Now,
This formula corresponds to kπ for k= 0, 2±, ±4
where k can take the values 0, 2, -2, 4, -4, etc.
The cosine function oscillates between -1 and 1, with a period of 2π.
The maximum value of the function is 1, which occurs when the argument of the cosine function is an odd multiple of π/2.
This means that the x-coordinates of the maximum values are given by:
x = kπ + π/2, where k is any odd integer
We can simplify this formula by writing k = 2m+1, where m is any integer, to obtain:
x = (2m+1)π/2
This formula covers all the possible values of k, including positive and negative integers.
For example, when m = 0, we get x = π/2, which is the first maximum value of the function.
When m = 1, we get x = 3π/2, which is the second maximum value, and so on. If we allow m to be negative, we get the values of x for the maximum values of the cosine function in the negative direction.
Therefore,
kπ for k= 0, 2±, ±4
which gives the values of k that correspond to the x-coordinates of the maximum values of y = cos(x).
Learn more about trigonometric identities here:
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The complete question.
Which formula gives the x-coordinates of the maximum values for
y = cos(x)?
- kπ for any integer k
- kπ for k= 0, 2±, ±4
- kπ/7 for any positive integer k
- kπ/2 for K= 0,±2, ±4,
Jay earned $220 during the summer for delivering magazines he bought 5 shirts worth $15 each using his magazine money how much money was left after he bought the shirts
Answers
$220 - $75= $145
Answer:
145
Step-by-step explanation:
Figure ABCD is a kite. Find the
value of x.
Answers
Answer:
X=8
Step-by-step explanation:
2x - 5 = X + 3
-x -x
X - 5 = 3
+5 +5
X=8
2x - 2x -5 = x + 2x + 3
-5 = 3x + 3
-5 -5 = 3x +3-3
-10 = 3x
-10/3 = 3x/3
-3.3333 = X
If the angles of a traingle are in the ratio 2:3:4 , Find Them
Answers
Answer:
40°, 60°, and 80°
Step-by-step explanation:
We know that the sum of the angles of a triangle is equal to 180°.
We can use this equation to solve for these angles:
180 = 2x + 3x + 4x
180 = 9x
20 = x
Then substitute the solution in for x to solve for the angles:
2(20) = 40°
3(20) = 60°
4(20) = 80°
Therefore, the angles are 40°, 60°, and 80°.
PLEASE help i’m a little confused what goes where
Answers
Answer:I think you find the mean mode miden
Step-by-step explanation:
help please!!!! please!!!!
Answers
Answer:
32
Step-by-step explanation:
[tex]\frac{x}{40}=\frac{48}{60} \\ \\ x=32[/tex]
35% of the number of students are boys and if number of girls is 416 then find the total number of students and the number of boys
Answers
Answer:
total students = 640
number of boys = 640-416 = 225
Step-by-step explanation:
percentage of girls = 100-35 = 65%
let total number of students be x
100*416/x = 65
41600/x = 65
x= 41600/x
x= 640
What is the smallest initial velocity that is required to throw a stone 49 feet up on top of a silo?
Answers
Answer: the smallest initial velocity that is required to throw the stone is 56 ft/s
Step-by-step explanation:
We know that;
u = initial velocity
v = final velocity = 0
a = acceleration = -g = -32,
s = distance travelled = 49 feet
V² - u² = 2aS
we substitute
0² - u² = 2 × -32 × 49
0 - u² = -3136
u² = 3136
u = √3136
u = 56 ft/s
Therefore the smallest initial velocity that is required to throw the stone is 56 ft/s
How am I suppose to do my challenges if nothing shows up
Answers
Answer:
umm i dont know ask them oop my fire alarm going off bye
Step-by-step explanation:
What is the area of a rectangle that is 11ft by 2ft?
Answers
Answer: 22 ft²
Step-by-step explanation:
To find the area of a rectangle, we multiply the length and width. It doesn't matter which is which as we get the same answer in the end.
Given information:
Length = 11 ft
Width = 2 ft
Area = length x width
Area = 11 ft x 2 ft = 22 ft²
You'll notice the unit is feet squared or ft², because feet x feet gives us feet².
Raju has some amount saved in his piggy bank. His uncle gave him Rs. 50 as a birthday gift and now Raju has Rs 123 with him.Find how much money he had earlier? ( Write an equation and solve).
Answers
123-50=73
Step-by-step explanation:
its pretty basic, subtract the amount his uncle gave him from what he has now
In addition to his weekly salary, Ethan is paid $16 per delivery.
Last week, he made 5 deliveries, and his total pay was $215. Write a linear equation in
slope-intercept form to find Ethan's total weekly pay T if he makes d deliveries. (please help quickly! I WILL MARK BRAINLEST!!)
Answers
Answer:
Step-by-step explanation:
T=16d=135
The linear equation in slope-intercept form to find Ethan's total weekly pay is T = 16d + 135
A linear equation is in the form:
y = mx + b
where m is the slope of the line, b is the y intercept and y, x are variables.
Let T represent the total money paid to Ethan in a week for d deliveries.
Ethan is paid $16 per delivery, hence m = 16.
T = 16d + b
For 5 deliveries, his total pay was $215. Hence when d = 5, T = 215:
215 = 16(5) + b
215 = 80 + b
b = 135
T = 16d + 135
The linear equation in slope-intercept form to find Ethan's total weekly pay is T = 16d + 135
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Of the 140 7th graders, 15% earn the Presidential Physical Fitness award. How many students earn the award? *
Answers
Answer:
21 students
Step-by-step explanation:
the percent proportion is a/w = p/100
where A is a part of the whole W, and p% or p/100 is the percent
a/140 = 15/100 (Substitute w =140 and p= 15)
a times 100=140 times 15 (cross poducts property)
100a=2100 (Multiply)
100a/100 = 2100/100 (divide both sides by 100)
a = 21 (simplify)
So, 21 students win the award.
b. Some other person's sales tax is $1.61. How much was their subtotal?
Answers
I hope this helps you with you stuff
HELP ME PLEASE AND THANK YOU..
Answers
2600-1500= 1100/5 = 220
find a constant of proportionality that creates a direct proportion to x and y
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
We know that when 'y' varies directly with 'x', we get the equation
y ∝ x
y = kx
k = y/x
Here k is called the constant of proportionality.
Taking an example:
For example, let suppose x and y are directly proportional with x = 4 and y = 10.
We can calculate the constant of proportionality using the formula
k = y/x
substitute x = 4, y = 10 in the equation
k = 10/4
k = 2.5
And at x = 5 and y = 12.5
k = y/x
substitute x = 5, y = 12.5 in the equation
k = 12.5/5
k = 2.5
Therefore, we conclude that a constant of proportionality k = 2.5.
PLEASE HeLP ME!!!! IM TIMED
Answers
Answer:
4 units to the left
Step-by-step explanation:
helpppppppppp pleasssseeee
Answers
The perimeter of a rectangle is 162 inches. what are the dimensions of the rectangle if the length is 7 times than 3 times the width?
Answers
Answer:
3.68 inches × 77.28 inches
Step-by-step explanation:
Given that,
The perimeter of a rectangle is 162 inches.
Let the width is b.
ATQ,
Length = 7 times than 3 times the width
l = 7(3b) = 21b ...(1)
The perimeter of a rectangle is given by :
P = 2(l+b)
Put all the values,
162 = 2(21b+b)
81 = 22b
b = 3.68 inches
Put the value of b in equation (1)
l = 21b
= 21 (3.68)
= 77.28 inches
Hence, the dimensions of the rectangle are 3.68 inches × 77.28 inches
Which expression is not equal to the expression shown?
33 : 3-4
3 x 36
33 x 34
37 : 30
3-3 ÷ 34
ANSWER QUICK AND ILL MARK YOU BRANLIEST
Answers
Step-by-step explanation:
In the given question fourth one is not correct, which can be described as follows:
3-3 =34
0 = 34
that's why it is not correct, and other equation will give a value.
i)
33 ×3-4
= 33 × -1
= -33
ii)
3×36
=108
iii)
37: 30
v)
33×34
= 1122
9) Angeline bought s yards of satin fabric priced ot $8.09 per yard, ond c
yards of cotton fabric priced at $3.79 per yard. Which of the following is on
expression that can be used to determine the amount of money that
Angeline would spend in all on fabric? *
2 points
O 8.09s - 3.79c
O 8.09c +3.79s
8,09c 3.79s
O 8.09s +3.79c
Answers
Answer:
8.09s + 3.79c
Step-by-step explanation:
The $8.09 is pertaining to the satin (s) and the $3.79 is pertaining to the cotton fabric (c).
Answer:
70.77
Step-by-step explanation:
Hope this helps
There are 20 students in my class. Each student needs: .2 cups, 2 plates, 1 party hat and a pair of earphones. My teacher has 2 boxes with plates and forks. Each box contains 8 plates and 10 forks. Would this be enough for the 20 students? Account for each plate and cup. Explain your answer.
Answers
Answer:
Simple, no. This would not be enough.
Step-by-step explanation:
This is because you mentioned that there are 20 students and each of them needed 2 plates. So, there would need to be at least 40 plates. Forks seem irrelevant in this question but if the teacher has 8 plates in 1 box and another 8 in the second box, that would sum up to 16 plates that are available. And the fact that the box doesn't even include the other items, should hint the lack of items available for the students.
This question seemed worded differently. But tried my best. :)
Help pleaseee I’m stuck
Answers
Answer:
Measure of angle S= 30° as both the triangles are similar and similar triangles have thier angles equal.Now,In triangle QRS,
Angle.Q+an.R+an.S=180
(Angle sum property of a triangle.)
Angle.Q+17°+30°=180
Angle.Q=180-
Answer:
7
Step-by-step explanation:
i did this before