The two lines in the system of equations will be parallel when the value of k is 15/4.
Let 2 equations of the line be,
ax+by=c1
dx+ey=c2
for lines to be parallel it is necessary that their slopes are equal
we can easily find the slopes of these equations by re-arranging them in the standard equation of a line i.e, y=mx+c
after rearranging we'll get the following equations,
y=(-a/b)x+c1/b
y=(-d/e)x+c2/e
and it should satisfy the given condition,
-a/b=-d/e≠c1/c2
as, if the ratio of the slope is the same as the constants it will become the same line. So, according to the given question
-3/2k must be equal to -2/5
k must be 15/4.
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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.
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).
help plsssssssssssss
Answer:
-28
Step-by-step explanation:
f(-4) = 5(-4) - 2³ = -20 - 8 = -28
HELP ME PLEASE!!!!!!!!!!!!!!
Answer:
35
Step-by-step explanation:
35
Answer: 25
Step-by-step explanation:
The dimensions of a beanbag toss target are given in the diagram below.
12 in
24 in
48 in
What is the measure of the angle of incline, 9, of the target? Enter your answer to the nearest degree in the box below.
0=
The angle of incline, of the target θ = 14.036.
What is the formula for the angle of elevation?The angle of elevation or depression can be calculated using the following formula: t a n = O A, where A is the horizontal distance between the observer and the point and O is the length of the side opposite the angle of elevation or depression, or the object's perpendicular distance from the horizontal line.
To calculate the slope percentage, multiply the result by 100 after dividing the height difference between two points by their separation. The rise is the height difference between two locations. The distance between the locations is known as the run. The result is that (rise / run) x 100 is equal to the percent slope.
Given,
the height of triangle = 12in
base of triangle = 48 in
tan θ = perpendicular / base
tanθ = 12/48
θ = tan ⁻¹( 12/48)
θ = 14.036
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Complete question -
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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What is an equation with 3 variables called?.
Answer:
Linear equations
Step-by-step explanation:
hope this helps
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:
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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A job hotline service charges $25 plus a 4% commission, c, on the first month of earnings if it finds work for a client. Write an equation that represents the total cost, T, to find a job through the hotline. What is the cost if a client earns $1500 the first month? Please someone help!!!!
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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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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There are 67 bikes in the bike
remaining bikes are red.
rack outside a school. Out of all the bikes, 33 are silver. Half of the
Estimate how many bikes are red.
Answer:
17
Step-by-step explanation:
67 minus 33 leaves 34 red bikes but divided that by half gives you 17
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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What system is Y =- 2x 3?.
The equation Y = -2x + 3 is a linear equation in slope-intercept form.
This equation represents a straight line with a slope of -2 and a y-intercept of 3.
The slope -2 tells us that for every unit increase in x, the value of y will decrease by 2. The y-intercept 3 tells us that the line passes through the point (0,3) on the coordinate plane.
It's a line that goes down as the slope is negative and the line can be represented by a graph, that can be easily plotted using the slope and the y-intercept. This equation can be used to model real-world situations like linear regression and many other fields.
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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.
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
Van has 45 new baseball cards. He puts them in a binder that holds 9 cards on each page. How many pages dose he fill?
To find out how many pages Van fills with his new baseball cards, we need to divide the total number of cards by the number of cards that fit on each page.
He has 45 baseball cards and each page holds 9 cards.
So, we can divide 45 by 9.
45 / 9 = 5
Therefore, Van fills 5 pages with his new baseball cards.
It's worth noting that this method gives the number of full pages that are filled and if there are any remaining cards, we have to add one more page for the remaining cards.
Why is addition commutative and subtraction is not?.
Addition is commutative because the order in which two numbers are added does not affect the result.
Commutative property is applicable only for addition and multiplication processes. Thus, it means we can change the position or swap the numbers when adding or multiplying any two numbers.
Addition is commutative because the order in which two numbers are added does not affect the result. For example, 1 + 2 = 2 + 1 = 3. In contrast, subtraction is not commutative because the order in which two numbers are subtracted does affect the result. For example, 1 - 2 = -1, but 2 - 1 = 1. The operation is different when the order of the numbers are changed.
so, addition is commutative because the order in which two numbers are added does not affect the result.
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PLEASE HELP!!!
given m=-1 and b=2, which is the equation of the line?
equation of a line : y=mx+b
Answer : y= -1x+2
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
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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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
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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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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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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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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Ue the entence to anwer the quetion. Mot doctor ay many people who don't get enough leep every night truggle with illne and tre. Which kind of evidence i thi an example of? (1 point)
This kind of evidence is an example of a claim. Hence, the correct answer is option 1.
A claim is a statement or assertion that is made about a particular topic or issue. In this case, the statement is being made by "doctors" and is being presented as evidence of a causal relationship between lack of sleep and negative health outcomes. The statement is not an argument, which would include reasoning or logic to support the claim, nor is it a testimony or excerpt, which would be a statement or quote from a specific person or source.
Option 2, "an argument," is incorrect because it suggests that reasoning or logic is being provided to support the claim. However, in the sentence provided, there is no indication that any reasoning or logic is being presented to support the claim that many people who do not get enough sleep each night suffer from illness and stress. Usually, an argument has a claim and evidence or reasoning to back up that claim.
Option 3, "a testimony or an excerpt," is incorrect because it suggests that a statement or quote is being provided from a specific person or source. However, in the sentence provided, there is no indication of a specific person or source providing the statement. Instead, the statement is being attributed to "doctors" in general rather than any specific individual. A testimony would typically include a statement or quote from a specific person or source, given under oath or affirmation in a formal legal setting.
This question should be provided as:
Use the sentence to answer the question. Most doctors say many people who don't get enough sleep every night struggle with illness and stress. Which kind of evidence is this an example of? Responses:
A claim An argument A testimony or an excerptThe correct answer is option 1.
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associative property commutative property distributive property
Different properties, significance of those properties and their applications in mathematics.
Associative property : Associative law states that the order of grouping the numbers does not matter. This law holds for addition and multiplication but it doesn’t hold for subtraction and division. This can be observed from the following examples.
Addition:
a+ (b+c) = (a+b) + c
Subtraction:
a-(b-c) ≠ (a-b) – c.
Multiplication:
a x (b x c) = (axb) x c
Division:
a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c
Distributive property : This property is used to eliminate the brackets in an expression. The distributive property states that each term inside the bracket should be multiplied with the term outside. This property is very useful while simplifying the expressions and solving the complicated equations.
Addition:
a(b+c) = ab + ac
Subtraction :
a(b-c) = ab – ac
Commutative property : This property states that there is no change in result though the numbers in an expression are interchanged. Commutative property holds for addition and multiplication but not for subtraction and division.
Addition:
a+b = b+a.
Subtraction:
a-b ≠ b-a.
Multiplication:
a x b = b x a
Division:
a ÷ b ≠ b ÷ a.
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