So, the given system will have a unique solution when k=,1
A system of linear equations in two variables will have a unique solution when the equations are consistent and independent.
In this case, the system of equations is kx + 3y = k and 3x + ky = k.
One way to check for consistency and independence is by using the determinant of the coefficient matrix and comparing it to the determinant of the system. The determinant of the coefficient matrix is (kk) - (3ky) = k^2 - 3ky and the determinant of the system is k^2 - k.
For the system to have a unique solution, the determinant of the coefficient matrix must be non-zero and equal to the determinant of the system.
Therefore, the system will have a unique solution when k^2 - 3ky = k^2 - k.
Which means that k=1.
This system will have a unique solution when k=1, and the pair of linear equations will be 1x + 3y = 1 and 3x + ky = 1.
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10x-7y=-8 in slope-intercept form
Answer: 10/7x + 8/7
Step-by-step explanation:
Slope intercept form : y = mx + b
10x - 7y = -8
-7y = -10x - 8
7y = 10x + 8
y = 10/7x + 8/7
The monthly cot of driving a car depend on the number of mile driven. Lynn found that in May it cot her $428 to drive 460 mi and in June it cot her $494 to drive 680 mi. (a) Expre the monthly cot C a a function of the ditance driven, d, auming that a linear relationhip give a uitable model
Rate does Lynn's cost increase for every additional mile she drives will be $0.25
The following is the linear relationship between the two variables:
Eq. 1: C f(d) = m*d + k
where m and k are evaluation-needed constants
Find m: We'll determine the angle of the line connecting the points (480, $380) and (800, $460).
Line slope (m) equals $0.25 per mile
Consider one of the two positions and enter (480,$380) in Eq 1 to find k.
k = 380 - 0.25(480) = $260
The line's equation is C f(d) = 0.25*d + 260.
This equation may be used to plot the graph for section a.
The rate of cost per mile is determined by the graph's slope when the units are scrutinized; as a result, $0.25
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60% of tudent like wimming, 40% like dancing, 20% of tudent that like wimming like dancing , how many tudent don't like wimming
So, 40% of students don't like swimming.
We know that 60% of students like swimming, and 40% of students like dancing. We also know that 20% of students that like swimming also like dancing.
First, we can find the number of students that like swimming and dancing by multiplying the percentage of students that like swimming by the percentage of students that like dancing and also like swimming:
20% * 60% = 12%
This means that 12% of students like both swimming and dancing.
To find the percentage of students who don't like swimming, we can subtract the percentage of students who like swimming from 100%.
100-60 = 40%
So, 40% of students don't like swimming.
It's important to note that if the problem had provided a total number of students this information would have been useful to calculate the exact number of students who don't like swimming.
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if a figure is dilated by a factor of 6, the area of the figure will change by a factor of _____.
ANSWER THE QUESTIONS WITH STEPS FOR BRAINLESS
the last answer choice on number 7 is (c) I don’t know
You can find the inverse of any function y=f(x) by reflecting it across the line y=x.
Hence, Option A is correct.
The inverse function is denoted by f-1 or F-1 if the function is denoted by f or F.In mathematics, an inverse function is a function that reverses the action of a function. The inverse of f is denoted if it exists and only if f is a bijective function.The function that "undoes" what f did can be defined as the inverse of f since it "acts on" numbers and transforms them. Alternatively put,A function that can change into another function is referred to as being inverse or anti.To know more about inverse of function here
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4/9of the spectators in a football match are males. If 200 of them are females, how many spectators are there in the competition?
4/9 of the spectators in a football match are males. If 200 of them are females, then the total number of spectators is 360.
What is the proportion?
A proportion is two ratios that have been set equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, 5/10 equals 1/2.
Given that 4/9 of the fans in a football match are men and 200 are women. We must determine the total number of spectators at the football game.
If 4/9 of the total spectators are men, the remaining 5/9 are women.
Let x be the total number of spectators.
Mathematically,
5/9 of x = 200
5/9 × x = 200
5x = 1800
X = 360
As a result, the total number of spectators is 360.
The number of male spectators may also be calculated.
Males + Females = Total number of spectators
360 = Males + 200
Males = 160
Therefore, 4/9 of the spectators in a football match are males. If 200 of them are females, then the total number of spectators is 360.
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How do you find the domain of a function?.
Domain of any function is all the input value of the function for which condition of the function exist.
Domain is set of the input values for which output exist.Let us consider y = f(x) be the function.'y' is the dependent variable and 'x' is the independent variable.All the input values of x for which successful output value exist for the function.y = 2x , x > 4 , x ∈ N.Here. domain is equal to 5, 6, 7, ....∞ implies y = 10, 12, 14, ......Therefore, the domain of the function is its input value for which there exist a successful output value.
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tyler works in a shoe store. the store bought a pair of shoes for 50$, and sold it for 80$. what percentage was the markup?
Answer:160%
Step-by-step explanation:
100%...........50 80:0.5=160
1%..............0.5 50:100=0.5
?.............80
160%...............80
I drove 10 mile north 14 mile eat 16 mile north 2 mile eat 4 mile north how far am I
The total distance traveled is 46 miles.
Distance Traveled:
Distance traveled is the path covered by a body to get from a starting point to an endpoint in a certain period of time, at a certain velocity. Time and velocity play a major role in measuring the distance traveled. The distance travel formula is: d = v x t
To determine the total distance you have traveled, you will need to add up all the distances you have driven in each direction.
You drove 10 miles north, 14 miles east, 16 miles north, and 2 miles east, 4 miles north.
10 miles north + 14 miles east + 16 miles north + 2 miles east + 4 miles north = 46 miles
So, you have traveled 46 miles.
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HELP ME PLEASE!!!!!!!!!!!!!!
Answer:
35
Step-by-step explanation:
35
Answer: 25
Step-by-step explanation:
The ale price of a pring break vacation package i $209. 99 the travel agent aid by booking early, you aved $35. Find the percent decreae in price
The percent decrease in price for booking early for a spring break vacation package is 16.5%.
This was calculated by taking the amount of money saved ($35) and dividing it by the original price of the package ($209.99). Then, the resulting decimal was multiplied by 100 to convert it into a percentage.
Mathematically, the calculation looks like this:
(35/209.99) ×100 = 16.5%.
The 16.5% decrease in price is a substantial savings and could be used to purchase additional items or activities during the vacation. Booking early is often a great way to save money on vacation packages, since travel agents and companies often lower the prices to incentivize travelers to book in advance.
It is important to remember, however, that the savings may not always be 16.5%. Depending on the travel agent or company, the percentage of savings may vary. Additionally, some packages may not offer any savings at all. Therefore, it is important to do research and compare different packages before booking.
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What is an equation with 3 variables called?.
Answer:
Linear equations
Step-by-step explanation:
hope this helps
x-5y=-6
7x-3y=42
Solve each system using substitution
Answer:
Step-by-step explanation:
To solve the system of equations using substitution, we first need to isolate one of the variables in one of the equations. We can start by solving the first equation for y:
x - 5y = -6
y = (x + 6) / 5
Now we can substitute this expression for y into the second equation:
7x - 3y = 42
7x - 3((x + 6) / 5) = 42
Simplifying and solving for x:
(35/5)x - (3/5)x - 18/5 = 42
32x = 210+18
x=57/8
Now we can substitute this value of x back into the first equation to find the value of y:
y = ((57/8) + 6) / 5
y = 21/8
So the solution of the system is (x, y) = (57/8, 21/8).
Can someone help me with this please?
The longest and the shortest distances are 1 mile and 5 miles
The greatest number of miles left is 4.5 miles
How to determine the longest and the shortest distancesFrom the question, we have the following distances that can be used in our computation:
Luke = 3 miles
Logan = 2 miles
This means that
Shortest = 3 - 2 = 1 mile
Longest = 3 + 2 = 5 miles
The compound inequalityRepresent the distance with x
So, we have
3 - 2 < x < 3 + 2
Evaluate
1 < x < 5
The number line is | 1 | 2 | 3 | 4 | 5 |
The greatest number of miles leftIn (a), we have
Longest = 5 miles
So, we have
Greatest = 5 - 0.5
Greatest = 4,5 miles
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Samuel bought a 0.9-liter box of juice and two cans of juice, 350 ml each. What is the total volume of the juice he bought?
Answer:
1.6 L or 1600 mL
Step-by-step explanation:
You want to know the total volume of one 0.9 L box and two 350 mL boxes.
UnitsThe units are related by ...
1 L = 1000 mL
VolumeThen the volumes of the given boxes are ...
0.9 L = 900 mL
350 mL = 0.35 L
You can add the volumes in either of the like units:
900 mL + 2 × (350 mL) = 1600 mL
0.9 L + 2 × (0.35 L) = 1.6 L
The total volume of the juice boxes is 1.6 L or 1600 mL.
__
Additional comment
You can convert the units a couple of ways.
Multiply the unit equivalence equation by an appropriate factor:Because the fraction has equal measures in the numerator and denominator, it does not change the size of the volume. It only changes the units of the volume.
What was the intensity of the earthquake on the Richter scale?.
The intensity of the earthquake on the Richter scale of magnitude 5.3 can be calculated for moderate earthquakes, and a strong earthquake can be estimated at magnitude 6.3.
The idea of a logarithmic earthquake magnitude scale was first developed by Charles Richter in the 1930s to measure the magnitude of earthquakes occurring in Southern California using relatively high frequency data from a nearby seismometer station. Developed. The magnitude of an earthquake is expressed on a scale called the Richter scale. The Richter scale is a base 10 logarithmic scale, meaning that each magnitude is ten times stronger than the last. So 2 is 10 times stronger than 1 and 3 is 100 times stronger. On the Richter scale, the increment is the amplitude of the wave. In the Richter scale, magnitude is represented by whole numbers and decimals. More destructive earthquakes are usually between magnitude 5.5 and 8.9. A truly destructive earthquake is an earthquake that exceeds magnitude 7 on the Richter scale.
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Jacob walks 2/5 kilometres in 1/4 hour. what is jacobs speed in kilometres per hour?
Jacob's speed in kilometers per hour is equal to 8/5 kilometers per hour.
What is speed?In Science, speed can be defined as the distance covered by a physical object or body per unit of time. This ultimately implies that, speed is a scalar quantity because it has magnitude but no direction.
Mathematically, the speed of a physical object or body can be calculated by using this formula;
Speed = distance/time
Substituting the given points into the speed formula, we have the following;
Speed = 2/5/(1/4)
Speed = 2/5 × 4/1
Speed = 8/5 kilometers per hour.
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What is the circumference of a circle with a diameter of 62 centimeters?
Answer:194.78 cm
Step-by-step explanation:
Do the equations 4x 3y 1 5 and 12x 9y 15 represent a pair of coincident lines?.
The given equations do not represent a par of coincident lines. As the equations do not satisfy the conditions.
It is given that the pair of equations are,
4x + 3y - 1 = 5 and 12x + 9y = 15
To determine if the equations represent a pair of coincident lines.
Here we get, a₁ = 4, b₁ = 3, c₁ = -1
a₂ = 12, b₂ = 9, c₂ = -15
So, a₁/a₂ = 4/12 = 3
b₁/b₂ = 3/9 = 3
c₁/c₂ = -1/-15 = 1/15
Therefore,
[tex] \frac{a1}{a2} = \frac{b1}{b2}≠ \frac{c1}{c2} [/tex]
Thus, the given equations do not represent a pair of coincident lines
Now, if you put these equations in any graphing software or here I have used Desmos then you will get the graph (attached image), which further shows that the lines do not coincide.
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What are the 3 types of line graphs?.
The 3 types of line graphs are Simple line graph, Multiple line graph and Compound line graph.
Simple line graph - On the graph, there is only one line drawn.
Multiple line graph - On the same set of axes, many lines are plotted. An excellent way to compare similar objects over the same time period is via a multiple line graph.
Compound line graph - if data can be separated into two or more different categories. Compound line graphs are the name given to this kind of line graph. To represent the component portion of a total, lines are drawn. Part of the total is shown on the line below the top line, which displays the total. The size of each component is indicated by the space between every two lines.
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Write an equation of the line that passes through (−1,3)
and is parallel to the line y=2x+2
.
The linear equation parallel to the line y=2x+2 is:
y = 2x + 5
How to write the equation of the line?A general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
Two lines are parallel if the lines have the same slope, then for example for:
y = 2x + 2
A parallel line will be:
y = 2x + b
And the line must pas through (-1, 3), then:
3 = 2*-1 + b
3 = -2 + b
3 + 2= b
5 = b
Then the linear equation is:
y = 2x + 5
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How do you write 9 more than a number?.
In mathematical notation, you can use the following format to write "9 more than a number":
total + 9
This indicates that you are adding 9 to the original number.
For instance, you can write "9 more than 5" as 5 + 9 = 14 if the integer is 5.
Another option is to use the format: 9 + number.
The outcome is the same as this.
If a variable, such as x, is used to denote the number, you can express "9 more than x" as x + 9 or 9 + x.
This way, you can use the same expression for any number.
In general, when you want to find out a value which is 'x' more than a number 'a', you can use the following mathematical notation:
a + x
This is read as "a plus x".
So ,this indicates that you are adding 9 to the original number.
Therefore, the adding 9 to original number is the answer of this question.
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A small town had a population of 12,000 people in 2001. The population has been decreasing at a rate of 3.5% each year. How many people lived in the town in 2016?
Answer:7032
Step-by-step explanation:
The population of the town in 2016 will be 7032
What is percent of decrease?Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.
Given that, A small town had a population of 12,000 people in 2001. The population has been decreasing at a rate of 3.5% each year.
We know that, Decrease rate =
A = P(1-r)ⁿ
A = final amount
P = initial amount
r = rate
n = years or time
Therefore,
A = 12000(1-0.035)¹⁵
A = 12000(0.965)¹⁵
A = 7032.19
A ≈ 7032
Hence, the population of the town in 2016 will be 7032
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65. Find the slope and y-int
a. 4x + 5y = 7
Answer:
slope = -4/5x
y - int = 7/5
Step-by-step explanation:
4x + 5y = 7
-4x on each side
5y = -4x + 7
divide by 5 on each side
y = -4/5 x + 7/5
What is the inverse of a parabola graph?.
Parabola is called as a curve that is formed by the locus of a point whose distance from a fixed point and from a fixed line is the similar.
This set point is called focus, while the fixed line is known as the directrix of parabola.
Parabola does not have any inverse. Let a parabola having equation y = x^2,
it is graph looks like a U-Shaped curve opening up.
Here does not have an inverse as it fails the horizontal line test.
The inverse equation y=√x, only has the positive input values from the domain of parabola.
If we are constrain the domain to be greater than zero, then only it is possible for the function to pass the horizontal line test.
Therefore, Parabola does not have an inverse.
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The chords PQand RS of a circle are produced to meet at T outside the circle. If O is the centre of the circle, show that PTR=½(POR-QOS)
Answer:
hard one goof luck
Step-by-step explanation:
If 4/3 of water are Enough to water 2/5 of the plants in the house, How much water is necessary to water all the Plants in the house? write an equation to represent the situation, and then find find the answer
Amount of water necessary to water all the plants in the house is 10/3.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given that,
Amount of water needed to water 2/5 of plants = 4/3
Equation representing the amount of water needed to water 5/5 of plants = (4/3) / (2/5)
= (4/3) × (5/2)
= 10/3
Hence 10/3 of water is needed to water all the plants in the house.
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To make 4 cups of rice, Iain needs 5 cups of water. To make 16 cups of rice, he needs 20 cups of water. Write this as a proportion.
4/?=?/?
The proportion when to make 4 cups of rice, Iain needs 5 cups of water and make 16 cups of rice, he needs 20 cups of water is 4/5 = 16/20.
How to calculate the proportion?Proportion in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
In this case, to make 4 cups of rice, Iain needs 5 cups of water and make 16 cups of rice, he needs 20 cups of water. The proportion will be:
4/5 = 16/20
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Is 16 < b + 8, if b = 22 true or false
Answer:
true
because 22+8=30,
and 30 is greater than 16.
Is every triangle 90 degrees?.
A triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 90 degrees.
No, a triangle is not always 90 degrees. In geometry, a triangle is a three-sided polygon with three angles. The sum of the angles in a triangle is always 180 degrees.
This can be proved using the fact that a straight line is 180 degrees. If we draw a straight line, and divide it into two angles, which are supplementary angles. Therefore, these angles add up to 180 degrees. In a triangle, we can draw one straight line and divide it into three angles, which are supplementary angles, therefore the sum of the angles in a triangle is always 180 degrees.
For example, if a triangle has angles of 90 degrees, 60 degrees, and 30 degrees, the sum of these angles is 180 degrees (90+60+30=180).
Therefore, In short, a triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 90 degrees.
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