Solve the simultaneous equations 2x-5v= 9
3x +4v = -2
Answers
The solution to the simultaneous equations 2x - 5v = 9 and 3x + 4v = -2 is:
x = -23/22
v = -3/22
To solve the system of equations, we can use the elimination method by eliminating one variable from the equations. We can multiply the first equation by 4 and the second equation by 5, so that the coefficients of v in each equation will become equal in magnitude and opposite in sign. This gives us:
8x - 20v = 36
15x + 20v = -10
Adding the two equations eliminates v and gives us:
23x = 26
Therefore, x = 26/23. Substituting x into either of the original equations gives us:
3(26/23) + 4v = -2
Solving for v, we get v = -3/22. Therefore, the solution to the system of equations is x = -23/22 and v = -3/22.
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Related Questions
triangle ABC is defined in the coordinate plane by the points A = 1,1 B = 3,4 and C = 4,2 as shown
Answers
The answer of the question is ,the transformation in (c) will result in a similarity transformation of triangle ABC.
What is Coordinate?A coordinate is numerical value that represent the position of point in space.
We can calculate the side lengths and angles of the triangle ABC.
Side lengths:
AB = sqrt((3-1)² + (4-1)²) = sqrt(13)
BC = sqrt((4-3)² + (2-4)²) = sqrt(5)
AC = sqrt((4-1)² + (2-1)²) = sqrt(10)
Angles:
∠A = arctan((4-1)/(3-1)) ≈ 1.25 radians
∠B = arctan((2-4)/(4-3)) ≈ -1.11 radians
∠C = arctan((2-1)/(4-1)) ≈ 0.32 radians
Now, let's analyze each of the given transformations:
a. T(x, y)(x, y)
This is the identity transformation, which means that the image will be the same as the preimage. Therefore, this transformation will not result in a similarity transformation.
b. T(x, y)(x+2,2y)
This transformation translates the triangle 2 units to the right and scales it vertically by a factor of 2. This will not preserve the ratio of the side lengths and the angles of the triangle, so it will not result in a similarity transformation.
c. T(x, y) (0.5x, 0.5y)
This transformation scales the triangle by a factor of 0.5 in both the x and y directions. This will preserve the ratio of the side lengths and the angles of the triangle, so it will result in a similarity transformation.
d. T(x ,y) (x + 4,y-2)
This transformation translates the triangle 4 units to the right and 2 units down. This will not preserve the ratio of the side lengths and the angles of the triangle, so it will not result in a similarity transformation.
Therefore, the transformation in (c) will result in a similarity transformation of triangle ABC.
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* The complete question is ,
Triangle ABC is defined in the coordinate plane by the points A=(1,1), B = (3, 4), and C = (4, 2), as shown.
Under which transformations will the image of triangle ABC be similar to the preimage?
a. T(x, y)(x ,y)
b. T( x ,y)(x+2,2y)
c. T(x, y) (0.5x, 0.5y)
d. T(x ,y) (x + 4,y-2)
4. A company manufactures model rockets that require igniters to launch. Once an igniter is used to launch a rocket. the igniter cannot be reused. Sometimes an igniter fails to operate correctly. and the rocket does not launch. The company estimates that the overall failure rate. deï¬ned as the percent of all igniters that fail to operate correctly. is 15 percent. A company engineer develops a new ignitcr. called the super igniter. with the intent of lowering the failure rate. To test the performance of the super igniters, the engineer uses the following process. Step 1: One super igniter is selected at random and used in a rocket. Step 2: If the rocket launches. another super ignites is selected at random and used in a rocket. Step 2 is repeated until the process stops. The process stops when a super igniter fails to operate correctly or 32 super igniters have successfully launched rockets. whichever comes ï¬rst. Assume that super igniter failures are independent. (3) If the failure rate of the super igniters is 15 percent, what is the probability that the ï¬rst 30 super igniters selected using the testing process successfully launch rockets? (b) Given that the ï¬rst 30 super igniters successfully launch rockets. what is the probability that the ï¬rst failure occurs on the thirty-ï¬rst or the thirty-second super igniter tested if the failure rate of the super igniters is 15 percent? (c) Given that the ï¬rst 30 super igniters successfully launch rockets. is it reasonable to believe that the failure rate of the super igniters is less than 15 percent? Explain.
Answers
1) The probability is 0.0076
2) The probability is 0.2775
3) Yes it is reasonable because it indicates is that the igniters are more successful than already thought or it would be close to impossible to get those same results by chance.
How to find the probability?1) We are told that the overall failure rate which is the percent of all igniters that fail to operate correctly is 15 percent = 0.15\.
Thus, percentage of success = 85% = 0.85
The probability that the first 30 super igniters selected using the testing process successfully launch rockets is;
P(X = 30) = (0.85)³⁰
= 0.0076
2) Given that the first 30 super igniters successfully launch rockets, the probability that the 1st failure occurs on the 31st or the 32nd super igniter tested if the failure rate of the super igniters is 15 percent is;
P(Y = 31)/P(X = 30) + P(Y = 32)/P(X = 30)
= [(0.15 * 0.85³⁰)/0.85³⁰] + [(0.15 * 0.85³¹)/0.85³⁰]
= 0.2775
3) What the probability in answer 1 above indicates is that the igniters are more successful than already thought or it would be close to impossible to get those same results by chance.
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solve for g:
h/g=4r/t
Answers
Answer:
g4r = ht
g= ht/4r
Step-by-step explanation:
g4r = ht
g = ht/4r
how to find the perimeter of a rhombus
Answers
Answer:
Since each of the four sides of a rhombus has an equal length, the perimeter of a rhombus may be calculated using the formula, Perimeter = 4a, where 'a' denotes the length of the side of a rhombus.
Step-by-step explanation:
The perimeter of a rhombus is calculated by multiplying one of its four equal sides by four 4. Four times the length of one the sides is applied to determine the perimeter of a rhombus.
Which statements are true regarding the system of equations? Check all that apply. 8 x + 10 y = 30. 12 x + 15 y = 60. The lines coincide. The lines are parallel. The slopes are equal. The y-intercepts are different. The system has one solution. The system has an infinite number of solutions. The system has no solution. Mark this and return
Answers
Answer: The lines are parallel.
The slopes are equal.
The y-intercepts are different.
The system has no solution.
Step-by-step explanation:
For a pair of equations: \(a_1x+b_1y=c_1\\\\a_2x+b_2y=c_2\)
They coincide if \(\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}\)
They are parallel if \(\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}\)
They intersect if \(\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}\)
Given equations: \(8 x + 10 y = 30\\ 12 x + 15 y = 60\)
Here,
\(\dfrac{a_1}{a_2}=\dfrac{8}{12}=\dfrac{2}{3}\\\\ \dfrac{b_1}{b_2}=\dfrac{10}{15}=\dfrac{2}{3}\\\\ \dfrac{c_1}{c_2}=\dfrac{30}{60}=\dfrac{1}{2}\)
⇒\(\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}\)
Hence, The lines are parallel.
It has no solution. [parallel lines have no solution]
Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.
\(y=-\dfrac{8}{10}x+\dfrac{30}{10}\Rightarrow\ y=-0.8x+3\)
i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3
Write 12 x + 15 y = 60 in the form of y= mx+c, where m is slope
\(y=-\dfrac{12}{15}x+\dfrac{60}{15}\Rightarrow\ y=-0.8x+4\)
i.e. slope of 12 x + 15 y = 60 is -0.8 and y-intercept =4
i.e. The slopes are equal but y-intercepts are different.
Answer: The lines are parallel.
The slopes are equal.
The y-intercepts are different.
The system has no solution.
Step-by-step explanation:
For a pair of equations:
They coincide if
They are parallel if
They intersect if
Given equations:
Here,
⇒
Hence, The lines are parallel.
It has no solution. [parallel lines have no solution]
Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.
i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3
Write 12 x + 15 y = 60 in the form of y= mx+c, where m is slope
i.e. slope of 12 x + 15 y = 60 is -0.8 and y-intercept =4
i.e. The slopes are equal but y-intercepts are different.
What is the distance from zero called? (I’m doing coordinates)
Answers
Answer:
Step-by-step explanation:
The absolute value, as "distance from zero", is used to define the absolute difference between arbitrary real numbers, the standard metric on the real numbers. Complex numbers [ edit ] The absolute value of a complex number z {displaystyle z} is the distance r {displaystyle r} of z {displaystyle z} from the origin.
Answer:
absolute number
Step-by-step explanation:
To get from point A to point B you must avoid walking
through a pond. To avoid the pond, you must walk 34 meters
south and 41 meters east. To the nearest meter, how many
meters would be saved if it were possible to walk through the
pond? . To the nearest meter, how many meters would be saved if it were possible to walk through the pond?
Answers
p
the rigth awnser is 41 meaters east to were
Step-by-step explanation:
possible to walk through the
. Times to failure of 500 randomly selected light bulbs have a mean of 1500 hours and a standard deviation of 80 hours.
a. At least, what percentage of these light bulbs must have lasted (before failure) between 1300 and 1700 hours?
b. If the relative frequency curve for the failure times has a bell-shape, approximately how many of these light bulbs must have lasted between 1340 and 1580 hours?
Answers
a. At least, what percentage of these light bulbs must have lasted (before failure) between 1300 and 1700 hours?
To determine the percentage of light bulbs that lasted between 1300 and 1700 hours, we must first standardize the values. Standardization makes the calculation easier and allows us to apply Z-Score as follows:Z-Score formula = z = (x - μ) / σWhere;x = 1300 and x = 1700μ = mean = 1500σ = standard deviation = 80Substitute the values into the formula;z₁ = (1300 - 1500) / 80z₁ = -0.25z₂ = (1700 - 1500) / 80z₂ = 0.25Using the standard normal table, the area under the curve between -0.25 and 0.25 is approximately 0.1975 or 19.75%.Therefore, at least 19.75% of these light bulbs must have lasted (before failure) between 1300 and 1700 hours.
b. If the relative frequency curve for the failure times has a bell-shape, approximately how many of these light bulbs must have lasted between 1340 and 1580 hours?
From the empirical rule, we know that if a distribution has a bell-shaped curve, then approximately 68% of the data will fall within one standard deviation of the mean (μ ± σ), 95% will fall within two standard deviations of the mean (μ ± 2σ), and 99.7% will fall within three standard deviations of the mean (μ ± 3σ).Since the range is less than two standard deviations away from the mean, we know that approximately 95% of the light bulbs will last between 1340 and 1580 hours.Therefore, approximately 0.95 * 500 = 475 light bulbs must have lasted between 1340 and 1580 hours.
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Which statements about opposites are true?
Select each correct answer.
The opposite of zero is zero.
A number and its opposite are located the same distance from zero on a number line.
The product of a number and its opposite is always 1.
The opposite of a negative number is always a positive number.
Answers
9514 1404 393
Answer:
A, B, D
Step-by-step explanation:
The "opposite" of a number is that number with its sign changed.
__
The opposite of zero is zero.A number and its opposite are located the same distance from zero on a number line.The opposite of a negative number is always a positive number.Answer:
The "opposite" of a number is that number with its sign changed.
solve in 20 mins i will thumb up thanks
Problem 6 (15 points) Determine if the following systems is a) Linear b) Time-invariant c) Causal. Justify your answer. y(t) = x(t)sinwet 1
Answers
This can be verified by observing that the output signal y(t) does not depend on future input signals x(t + t0) for any value of t0. Therefore, the given system is causal.
The given system is not linear and time-invariant but it is causal. The reasons for this are explained below: The given system is not linear as the output signal is not proportional to the input signal.
Consider two input signals x1(t) and x2(t) and corresponding output signals y1(t) and y2(t). y1(t) = x1(t)sin(we*t) and y2(t) = x2(t)sin(we*t)
Now, if we add these input signals together i.e. x(t) = x1(t) + x2(t), then the output signal will be y(t) = y1(t) + y2(t) which is not equal to x(t)sin(we*t). Therefore, the given system is not linear. The given system is not time-invariant as it does not satisfy the principle of superposition.
Consider an input signal x1(t) with output signal y1(t).
Now, if we shift the input signal by a constant value, i.e. x2(t) = x1(t - t0), then the output signal y2(t) is not equal to y1(t - t0). Therefore, the given system is not time-invariant.
The given system is causal as the output signal depends only on the present and past input signals.
This can be verified by observing that the output signal y(t) does not depend on future input signals x(t + t0) for any value of t0. Therefore, the given system is causal.
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For the straight line defined by the points (3,53)(3,53) and (5,91)(5,91) , determine the slope ( m ) and y-intercept ( b ). do not round the answers.
Answers
The slope (m) of the line is 19 and the y-intercept (b) is -4. The equation of the line can be expressed as y = 19x - 4.
The slope (m) of a straight line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Using the given points (3, 53) and (5, 91), we can substitute the values into the formula:
m = (91 - 53) / (5 - 3)
m = 38 / 2
m = 19
Therefore, the slope (m) of the straight line is 19.
To determine the y-intercept (b), we can use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope and b is the y-intercept.
Using the point (3, 53) and the slope we just calculated (m = 19), we can substitute the values into the equation:
53 = 19(3) + b
53 = 57 + b
Now, solving for b:
b = 53 - 57
b = -4
Therefore, the y-intercept (b) of the straight line is -4.
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WILL GIVE BRAINLIEST AND THANKS. find the value of x
Answers
Answer:
x = 48
Step-by-step explanation:
To solve this problem, one must assume that the segment with a length of (7) bisects the segment with a length of (x).
It is given that the segment with a length of (7) is perpendicular (forms a right angle with) the segment that has a length of (x). This is indicated by the box around one of the angles, signifiying that it is a right angle, or (90) degree angle. Therefore, the triangle with sides measuring (25) and (7) is a right triangle. Thus, one can use the Pythagorean theorem to solve for the base length. Then multiply it by (2) to find the total length of (x).
The Pythagorean theorem states the following:
\(a^2+b^2=c^2\)
Where (a) and (b) are the legs, or sides adjacent to the right angle, and (c) is the hypotenuse or side opposite the right angle.
\(a^2+(7)^2=(25)^2\)
Simplify,
\(a^2+49=625\)
Inverse operations,
\(a^2=576\\\\a=24\)
Multiply this value by (2) to find the total side length of the segment (x),
2(a)
Substitute,
2(24)
Simplify,
48
Please PLEASE help with these two math problems
1. 7^x ÷ 7^y =
2. z^10x^y ÷ z^5 =
Answers
Answer:
14
-25/1
Step-by-step explanation:
Find the value of x and measure of each labeled angle.
Answers
Answer:
6x-45°=4x+5°(vertically opposite angles are equal)
6x-4x=5+45
2x=50
x=50/2
x=25
hope it helps you!
Answer:
x=25
6x-45=6×25-45=105
4x+5=4×25+5=105
Step-by-step explanation:
6x-45=4x+5(Reason:- vertically opposite angle)
or, 6x-4x=45+5
or,2x=50
or,x=25
Any one knows? Please help
Answers
Answer:
1. 12
2.
a can be a triangle (obtuse)
b can be a triangle (acute)
Step-by-step explanation:
At the third step, Han subtracts 39 from 39. How do you know that these numbers represent hundredths?
Answers
Answer: Because 2 places to the right of the the decimal.
Step-by-step explanation:
easy one - giving brainly if correct - show work.
Answers
Answer:
2/3
Step-by-step explanation:
Answer:
you need to do the math then divide numerator by dumerstor then x 100
There are d black and brown horses in a field. There are 16 more black horses than brown horses. Of the horses in the field, only 25% of them are brown. How many are black?
Answers
Answer: 24 black horses
Step-by-step explanation:
Let the number of black horses = bl and
The number of Brown horses = br
Total number of horses = d
Of the horses in the field, only 25% of them are brown. That is,
25% of d = br
0.25d = br ........ (1)
The remaining horses are black. Which will be 100% - 25% = 75%. That is,
75% of d = bl
0.75d = bl ........(2)
But according to the question, there are 16 more black horses than brown horses. That is,
bl = br + 16 ..... (3)
The total number of horses d will be
d = br + bl ...... (4)
Substitute bl in equation 3 into equation 4
d = br + br + 16
d = 2br + 16 ..... (5)
Substitutes equation (1) into the equation (5)
d = 2( 0.25d ) + 16
d = 0.5d + 16
Collect the like terms
d - 0.5d = 16
0.5d = 16
d = 16/0.5
d = 32
Substitute 32 for d in equation (2).
bl = 0.75 × 32
bl = 24 horses.
Therefore, 24 horses are black.
If c cars can be parked in each of the four main rows of the parking lot, what is the expression gor the maximum number of cars that can be parked in the parking lot?
Answers
Answer:
4c
Step-by-step explanation:
We can say that the maximum number of cars can be represented as:
Maximum number of cars = Total of rows × Number of cars per row
In this particular case, we have 4 rows and the number of cars per row is c, thus, the expression above becomes:
Maximum number of cars = 4c
how many license plates can be made using either 3 digits followed by 3 letters, or 3 letters followed by 3 digits?
Answers
Answer:
infinite
Step-by-step explanation:
the law in most states in the usa states there must be 3 letters and 3 numbers so there could be infinite
-hope this helps-
ASAP HELP
Find the variance and standard deviation of the data set below:
0 0.107
1 0.352
2 0.400
3 0.141
Answers
If the standard deviation of a set of data is 6, then the value of variance is 36
The formula for determining variance is variance = √Standard deviation
Variance of a set of data is equal to square of the standard deviation.
If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula
variance = √Standard deviation
Take square root on both sides
Standard deviation² = 6²
Standard deviation= 36
Hence, standard deviation of a set of data is 6, then the value of variance is 36
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a man earns rs4300 per month. He spends 80percent from his income . How much amount does he save in a year.
Answers
Answer:
calcolateľ imc di una persona di 28 anni che peso 90kg e che è 1,55m
Answer:
savings = 10320
Step-by-step explanation:
First, find the percentage of income used.
80% 4300
80 x 4300 = 344000
344000/ 100 = 3440
80% 4300 = 3440
Next, multiply the solution and income by 12.
3440(12) = 41280
4300(12) = 51600
Subtract these two numbers.
51600 - 41280 = 10320
Reduce £20 by 15%
:
:
:
:
:
:
Answers
Answer:
the new value is 17 and the absolute change is -3
Step-by-step explanation:
take 20 and subtract your percentage increase
20 - (15% × 20) =
20 - 15% × 20 =
(1 - 15%) × 20 =
(100% - 15%) × 20 =
85% × 20 =
85 ÷ 100 × 20 =
85 × 20 ÷ 100 =
1,700 ÷ 100 =
Determine whether b can be written as a linear combination of a1 and a2. In other words, determine whether weights x1a1 + x2a2 = b. Determine the weights x1 and x2 if possible. Let a1 = [2 6 -4], a2 = [-2 6 6], and b = [0 36 6]. A. x1 = 3, x2 = 4 B. x1 = 3, x2 = 3 C. x1 = 4, x2 = 2 D. There is no solution.
Answers
The answer is that there is no solution for the given linear combinations.
To determine whether b can be written as a linear combination of a1 and a2, we need to check whether the equation x1a1 + x2a2 = b has a solution for some weights x1 and x2.
Let a1 = [2 6 -4], a2 = [-2 6 6], and b = [0 36 6]. Then we have the system of equations:
2x1 - 2x2 = 0
6x1 + 6x2 = 36
-4x1 + 6x2 = 6
We can solve this system using row reduction:
[2 -2 0 | 0]
[6 6 0 | 36]
[-4 6 0 | 6]
R2 - 3R1 -> R2
R3 + 2R1 -> R3
[2 -2 0 | 0]
[0 12 0 | 36]
[0 10 0 | 6]
R2 / 12 -> R2
[2 -2 0 | 0]
[0 1 0 | 3]
[0 10 0 | 6]
-10R2 + R3 -> R3
[2 -2 0 | 0]
[0 1 0 | 3]
[0 0 0 | -24]
The last row shows that we have an inconsistent system of equations, since 0 = -24 has no solution. Therefore, b cannot be written as a linear combination of a1 and a2.
As a result, the answer is that there is no solution.
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What is the value of q in the equation 0.5q = 6.25?
A. 12.5
B. 6.75
C. 5.75
D. 3.125
Answers
Answer: D
Step-by-step explanation:
3.125 / 0.5 = 6.25
Solve the right triangle. Round your answers to the nearest tenth
Answers
B=40°
a=15.9
c=24.8
EXPLANATION:
B= 180°-(50°+90°) =40°
cosB=opposite/hypotenus
cos(40)=19/c
c=19/cos(40)
=24.8
a^2 + b^2 = c^2
a^2 + 19^2 = 24.8^2
a^2 = 24.8^2 - 19^2
= 615.04 - 361
= 254.04
a= redical(254.04) = 15.9
HOPE THIS HELPS :)
Solve the following
2x=9
Answers
The answer is
=9/2
Hope this helps :)
Let's solve your equation step-by-step.
2x=9
Step 1: Divide both sides by 2.
\(\frac{2x}{2} =\frac{9}{2} \\Answer: x=\frac{9}{2} \\\)
two angles that are located between two coplanar lines on the same side of the transversal are called
Answers
When two angles that are located between two co-planar lines on the same side of the transversal are called Alternate external angles.
Alternate External Angles
The pairs of angles outside the two lines and on either side of a transversal that cuts two lines are referred to as the alternate external angles.
In the given diagram below, the alternate exterior angles are:
∠2 and ∠8
∠1 and ∠7
Hence, when two angles that are located between two co-planar lines on the same side of the transversal are called Alternate external angles.
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i need help pls help
Answers
Answer:
[?] = 4
(the complete term is \(4\frac{1}{2}\ \text{cups}\))
Step-by-step explanation:
\(8\ \text{cups} - 1\frac{1}{3}\ \text{cups} - 2\frac{1}{6}\ \text{cups} = (8-1-2)\ \text{cups} + \frac{-\frac{6}{3} - 1}{6}\ \text{cups} = 5\ \text{cups} + \frac{-3}{6}\ \text{cups} = 5\ \text{cups} + \frac{-1}{2}\ \text{cups} = 4\ \text{cups} + \frac{2 - 1}{2}\ \text{cups}\)
*MEDITATES* OH HELLO HELLO HELLO THERE
*pats seat* COME SIT LETS TALK......LEGEND HAS IT THERE ARE THESE PEOPLE HUNGRY FOR POINTS AND WHOEVER IS FIRST GETS BRAINLIEST!....... OH YOU ARE ONE OF THOSE PEOPLE AREN'T YOU????? WELL HURRY AND SAY SOMETHING RANDOM OR FUNNY!!!!!!! TO GET BRAINLIEST!!!!
Answers
Answer:
Wow, thanks :)
Step-by-step explanation:
You are just too kind :D
Answer:
MEEEEEEE
Step-by-step explanation:
I WAS ON THE TOLITE IN CLASS AND MY CAM TURNED ON THEN MY MOM CAME IN...
2?