The graph of the given linear equation 2x+3y=6 cuts the Y-axis at A(0,2).
For the graph of linear equation to cut the Y-axis its X-co-ordinate should be zero as abscissa is zero on Y-axis or the equation of Y-axis is x=0. Also the set of coordinates should satisfy the equation.
From the given set of coordinates, A(0,2) B(4,0) C(2,6) D(2,0), it is clear that the graph of the equation 2x+3y=6 cuts the Y-axis at A as it’s X-co-ordinate or abscissa is zero. So, it satisfies the first condition.
To satisfy the second condition the points of a should satisfy the equation given
LHS= 2x+3y
RHS=6
A(0,2)
Substituting the values of x and y in 2x+3y,
2(0)+3(2)=6
Therefore LHS=RHS
Hence, at point A(0,2) the graph of the given equation cuts the Y axis.
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Time vs. Position of Battery Operated Car
5
4
Position (m)
2
0
5
10
Time (s)
15
20
What type of relationship is shown in the graph?
a non-linear, negative relationship
a linear, negative relationship
a linear, positive relationship
O a non-linear, positive relationship
A linear, negative relationship is the type of relationship which is shown in graph of Time vs. Position of Battery Operated Car .
what is linear equation ?A linear equation is an algebraic expression such as y=mx+b. The slope is m, and the y-intercept is B. A "linear equation in two variables" is the term used to describe the previous sentence, which has variables named y and x. Two different variables can be found in bivariate linear equations. Examples of linear equations include 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
The area's 46-16 opposed to 14 is different from the area's 18 and T in a different way. The place is there. It isn't linearly getting farther apart. The lee is actually growing as a result.
Option B, the slanting upwards, is what we're going to go with. Since it will be linear, it isn't option C. It is untrue that the speaking has not been constant over the distance. Because it is a D-option, this increase-decrease is untrue. Option B is the best choice. Absolutely.
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What is the solution of
2+4/9x ≥ 4+x?
Answer:
x < -18/5
this is the answer of you problem
The N71-90 virus will give an infected person a mild rash on their arms once the person has 1 billion of the virus cells in their body. After an initial infection with just one cell, each virus cell will divide into two cells every four hours. After 30 divisions there are 1,073,741,824 cells and the rash starts. Once the rash starts, the immune system kicks in and kills all of the virus cells within an hour. The number of virus cells in the body can be determined using the function where h is the number of hours after infection. If Jolene is infected by one virus cell, how many virus cells will she have after 12 divisions
Jolene will have 4096 virus cells in her body after 12 divisions
Why should we call viruses a cell?Viruses are something more than living or dead, they are both. Maybe we need a new classification of life for them, a life that lives when the environment is favorable and hibernate when it is not.
The function provided to determine the number of virus cells in the body after h hours is 2^h. To find the number of virus cells after 12 divisions, we can plug in 12 for h in the function.
2^12 = 4096.
So, Jolene will have 4096 virus cells in her body after 12 divisions.
Please note that Jolene would not develop a rash after 12 divisions as it would take 30 divisions (120 hours) for the rash to appear.
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3 A sphere is increasing in volume at the rate of 20 in3/s. At what rate is the radius of the sphere increasing when the radius is 4 in.? A.0.982 inls B.0.424 inls C.0.995 inls D.0.025 inls
The rate of increase of the radius is 0.025 in/sec.
What is a sphere?A three-dimensional object with a sphere-like shape. A sphere has no vertices or edges, unlike other three-dimensional shapes. The distances between each point on its surface and its center are equal.
In other words, the distance between any two points on the surface and the sphere's center is equal. The formula for the Volume of the sphere is given by
Volume of sphere = (4/3)πr³
Where, r = radius of the sphere
Here we have
A sphere is increasing in volume at the rate of 20 in³/s.
Here we need to find at what rate the radius of the sphere increases when the radius is 4 in.
Let v = Volume of the sphere at time t
=> Change in Volume = dv/dt = 20
r = Radius of the sphere at time t
As we know, the Volume of the sphere, v = (4/3)πr³
Differentiate the Volume of the sphere with respect to t
=> dv/dt = (4/3)3πr³⁻¹)(dr/dt)
=> dv/dt = 4πr² (dr/dt)
=> 20 = 4πr² (dr/dt)
=> 5 = πr² (dr/dt)
Given that radius, r = 4
=> 5 = π4² (dr/dt)
=> 5 = (22/7) 64 (dr/dt)
=> 5 = 3.14(64) (dr/dt)
=> dr/dt = (5/3.14 × 64)
=> dr/dt = 0.024880573
=> dr/dt = 0.025
Therefore,
The rate of increase of the radius is 0.025 in/sec.
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Which question best describes the diagram above? Answer the question. 120 is 25% of what? 25% of 120 is what? 6 is what percent of 120? 120 is what percent of 25?
Answer:
1. 480
2. 30
3. 5
4. 480%
Step-by-step explanation:
1.
25% = 120
100% = 120 x 4 = 480
2.
100% = 120
25% = 120 : 4 = 25
3.
120 = 100%
6 = 6/120 x 100 = 5%
4.
25 = 100%
120 = 120/25 x 100 = 480%
Ver en español
On the coordinate plane, the segment from R(6,
–
16) to S(14,
–
1) forms one side of a rectangle. The rectangle has an area of 459 square units. Find the perimeter of the rectangle.
Write your answer as a whole number, decimal, or simplified radical. Do not round.
units
The perimeter of the rectangle, given the area and the segment from R ( 6, -16) to S (14, - 1 ) is 88 units
How to find the perimeter ?To find the perimeter, first find the distance between R ( 6, -16) to S (14, - 1 ) which will allow you to find the length of one side. This distance can be found by the formula :
= √((x2 – x1)² + (y2 – y1)²)
= √((14 – 6)² + (-1 – (-16))²)
= 17 units
This means that one side of the rectangle measures 17 units so the other side would be:
Area = Length x Width
459 = 17 x Width
Width = 459 / 17
Width = 27 units
The perimeter of the rectangle is:
= Length + Width + Length + Width
= 17 + 27 + 17 + 27
= 88 units
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What is linear equation 8th class?
An equation in which the highest power of the variable is 1 is known as a linear equation. It is also termed a one-degree equation.
There are two types of linear equations, linear equations in one variable and linear equations in two variables. The standard form of a linear equation in one variable is Ax + B = 0. Where x = variable, A = coefficient and B = constant.
The standard form of a linear equation in two variables is Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always formed in a straight line. That is why it is named a 'linear equation'.
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A fruit company delivers its fruit in two types of boxes: large and small. A delivery of
Weight of each type of box:
Weight of each big box = 18.75 kg
Weight of each small box = 13.75 kg
What is an equation?The relationship between two terms on either side of a letter is represented by a mathematical formula. Often there is a variable and an equals sign.
The definition of an equation in algebra is a formula that shows the equivalence of two mathematical terms. For example, in the expression 6x + 11 = 14 the two terms 6x + 11 and 14 are separated by the "equals" symbol.
To let
Weight of each big box = x
And the weight of each small box = y
Weight of 3 big boxes:
3 times
5 small box weights:
5 years
3x + 5y = 125 .......................(i)
resemble:
9x + 7y = 265 ......................(ii)
Equation (i) multiplied by -3:
-3 (3x + 5y) = 125 * (-3)
-9x - 15y = -375 ...................(iii)
Under (ii) and (iii):
9x + 7y = 265
-9x - 15y = -375
Adding this gives:
-8y = -110
or y = 110/8
or y = 55/4
y = 13.75
From equation (i), we have:
3x + 5y = 125
or 3x + 5(13.75) = 125
or 3x + 68.75 = 125
3x = 125 - 68.75
3x = 56.25
x = 56.25/3
x = 18.75
Each large box weighs:
18.75 kilograms
Weight of each small box:
13.75 kilograms
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To get to his parents' house, Dylan would have to drive due north 8 miles. To get to his
grandparents' house, he would have to drive due east 5 miles. What is the straight-line
distance between the parents' and grandparents' houses? If necessary, round to the nearest
tenth.
When Dylan travels 8 miles due north, the distance between the homes of the parents and grandparents is thus 9 miles.
what is pythagoras theorem ?The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem. The perpendicular, base, and hypotenuse of this triangle are its three named sides. With the aid of the Pythagorean Theorem, we may determine the side lengths of a right triangle by adding the areas of three intersecting squares. The base for more intricate trigonometry ideas, such as the Pythagorean theorem's opposite, is provided by this theorem, which is a very helpful tool.
given
by pythagoras theorem
[tex]c^{2} = a^{2} + b^{2} \\c^{2} = 8^{2} + 5^{2} \\c^{2} = 64 + 25 \\c^{2} = 89 \\c = 9[/tex]
The homes of the parents and grandparents are thus 9 miles apart in a straight line.
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please help it's for a test Which is an x-intercept of the graph of the function y=tan(x-5 pie/6)?
Answer:
5pie/6,0
Step-by-step explanation:
i graphed it
Rover it’ 3/4 of a can of cat food each day Bobo it’ 1/2 of a can of cat food each day cat food cot five dollar for three can it i only aw three can’t fox how much doe it cot for Karen for a 60 day upply of cat food for her to count cat
this question is related to numbers and the solution is as follows,
Rover eats 3/4 can of cat food in a day.
given
in 60 days it will consume 60 x 3/4 cans = 45 cans of cat food
3 cans cost = $5 and a pack contains 3 cans
45 cans is equivalent to= 45/3
= 15 packs
15 packs cost = 15 x $5 = $75
So it will cost $ 75 to feed Rover for 60 days
Bobo eats 1/2 of a can of cat food per day
in 60 days it will consume 60 x 1/2 cans = 30 cans of cat food
3 cans cost $5 and a pack contains 3 cans
30 cans are equivalent to 30/3 = 10 packs
10 packs will cost = 10 x $5 = $50
So it will cost $50 to feed Bobo for 60 days
In total, in 60 days it will cost $75 +$ 50 = $125 to feed both cats in 60 days.
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As calculated from the data we get the result as that $ 125 is required for the cat food of both the cats in a month.
We are given that in 60 days he will consume ,
60 x 3/4 cans
= 45 cans of cat food
The cost of 3 cans cost = $5
and one pack has 3 cans in it.
Therefore, 45 cans is equivalent to
= 45/3
= 15 packs
So , the cost of 15 cans will be ,
15 packs cost = 15 x $5 = $75
Therefore ,$75 is used for 60 days of cat food for Rover.
Now , we know that Bobo eats 1/2 of a can food in a day.
Therefore, in 60 days he will eat,
60 x 1/2 cans
= 30 cans of food
As we know, 3 cans cost $5 and a pack contains 3 cans
Therefore, 30 cans = 30/3 = 10 packs
10 packs will cost = 10 x $5 = $50
So , $50 is spend to feed Bobo , in a month.
Therefore , if will combine their cost we will get that ,
$75 +$ 50 = $125 is required to feed both the cats in one month.
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Arjun is hiking from a mountain lodge to a nearby summit. The probability that he will take the longest trail is 59. The odds against Arjun taking the longest trail are _[blank]_.
What odds best complete the sentence?
Enter your answer as “m:n{}^{\prime\prime} where m and n are the smallest integers possible, like this: 3:2
The odds against Arjun taking the longest trail are 4 : 9 .
How to find the probability ?The probability that when Arjun is hiking from the mountain lodge to the nearby summit, he takes the longest trail, is 5 / 9.
This means that the odds that Arjun will not take the longest trail, or rather, the odds against him taking the longest trail, will be the difference between 1 and the probability that he takes the longest trail:
= 1 - 5 / 9
= 4 / 9
When given as a ratio, this would be:
= 4 : 9
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A triangle has sides with lengths of 33 kilometers, 90 kilometers, and 97 kilometers. Is it a right triangle?
i have to use factorisation in every one of these but im so stuck i dont remember anything. i hope someone could at least solve one of these. i have only the exercises that are noted
16 POINTS
Answer:
12.
V. E=(1-a)(1+a)(1+a^2)(1+a^4)(1+a^8)
Step-by-step explanation:
1-a^16=(1-a^8)(1+a^8)
1-a^8=(1-a^4)(1+a^4)
1-a^4=(1-a^2)(1+a^2)
1-a^2=(1-a)(1+a)
1-a^16=(1-a)(1+a)(1+a^2)(1+a^4)(1+a^8)
What is the quotient of 1. 782 x 109 and 8. 1 x 106 expressed in scientific
notation?
The quotient of 1.782 × 10⁹ and 8.1 × 10⁶ in scientific notation is 2.2 × 10². The result is obtained by using the quotient rule.
What are the rules for exponents?Several rules for exponents are
Product rule → aⁿ × aˣ = aⁿ⁺ˣQuotient rule → aⁿ / aˣ = aⁿ⁻ˣPower of a product rule → (ab)ⁿ = aⁿ × bⁿPower of a quotient rule → (a/b)ⁿ = aⁿ / bⁿPower of a power rule → (aⁿ)ˣ = aⁿˣZero rule → a⁰ = 1Find the quotient of 1.782 × 10⁹ and 8.1 × 10⁶!
Dividing the first number by the second using the quotient rule, it would be
= (1.782 × 10⁹) / (8.1 × 10⁶)
= (1.782/8.1) × (10⁹/10⁶)
= 0.22 × 10⁹⁻⁶
= 0.22 × 10³
In scientific notation, we should write a.b × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
So,
0.22 × 10³ = 2.2 × 10²
Hence, the result of 1.782 × 10⁹ divided by 8.1 × 10⁶ in scientific notation is 2.2 × 10².
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What is the horizontal line on a graph?
The horizontal line of the graph is known as x axis,
The term graph in math is defined as the visual representation of data or the function in math.
Here we have to find the definition for the horizontal line on a graph.
Here we know that the straight line that is mapped from left to right and it is parallel to the X-axis in the plane coordinate system.
On the other hand, we all also know that the straight line that does not make any intercept on the X-axis and it can have an intercept on Y-axis is called horizontal line.
And we all also know that the straight line that is parallel to the x-axis and where all the points on the line have the same y-coordinate and basically all horizontal lines are parallel to each other.
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Evaluate the iterated integral. π/2 0 x 0 x sin(y) dy dx
The answer to the iterated integral after the evaluation is 2.
The iterated integral evaluates to the area of the region bounded by the curves x = 0, x = y, and y = π/2, which can be calculated by setting up a double integral. The outer integral is with respect to x, from 0 to π/2, and the inner integral is with respect to y, from 0 to x.
The integrand is xsin(y), meaning that the area of the region is the integral of xsin(y) with respect to y from 0 to x, and then with respect to x from 0 to π/2. The solution is found by evaluating the inner integral first, which yields -xcos(x), and then evaluating the outer integral. The result is 2, which is the area of the given region.
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whats the awnser i need help
answer:10
Step-by-step explanation:
the graph show it is 1 hour and shows 10 miles and it continues
Answer:
it should be that the miles are 10 times the amount of hours
Step-by-step explanation:
Considering that to bike 10 miles it took 1 hour and to bike 20 miles it took 2 hours it will continue going like that so the miles will always be 10 times the amount of hours
Northlake High School has two lunch periods. Students can eat their lunch in the cafeteria or on an outside patio. About 35% of students who have first lunch eat outside. Compare this with the percentage of second-lunch students who eat outside.
Select the true statement.
A. A smaller percentage of second-lunch students (24%) eat outside.
B. A greater percentage of second-lunch students (39%) eat outside.
c. A greater percentage of second-lunch students (41%) eat outside.
D. A smaller percentage of second-lunch students (18%) eat outside.
A / P / E / X
B. A greater percentage of second-lunch students (39%) eat outside.
From the table above, the percentage second-lunch students who eat outside is calculated as follows:
%= number of students who eat outside/total number of students who have second lunch × 100/1
%=18/46 x 100/1
%=39.1%
What is PercentPercent is usually used to describe data in percentage form. This mathematical science is often used when calculating population percentages, discounts, interest rates, and so on. Percent is a number that represents part or all of the value or goods by forming a ratio of one hundred. Percent has an infinitely high value, while its lowest value is 0 percent. The amount of the percentage is denoted by "%".
History of Percent NumbersThis number was born in ancient Rome to be precise from the collection of auction taxes by using a fraction of 1/100 of the auction value or called centesima rerum venalium. the percent symbol has changed several times. Originally the Latin word percento was used. However, in the next generation, the word percento was changed to two symbols, namely the word per which changed to "/" and cento which changed to "00". Until finally the symbol "%" was known.
Percent formulaThe simple formula for calculating percent is: Percentage (%) = (Total parts)/(Total amount) X 100%. The general percentage formula for calculating the percentage of a number that is considered as part of the whole is written in percent or 100%.
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How many cubic centimetres of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16 cm, the iron being 2 cm thick throughout? If 1 cubic cm of iron weighs 15 g. find the weight of the open box in kg
What are the 3 possible solutions for any quadratic?
There are three basic methods for solving quadratic equations: factoring, using the quadratic formula, and completing the square.
quadratic equations
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax^2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
factoring
factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.
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The day before Gerardo returned from a two-week trip, he wondered if he left his plants inside his apartment or outside
on his deck. He knows these facts:
• If his plants are indoors, he must water them at least once a week or they will die.
• If he leaves his plants outdoors and it rains, then he does not have to water them. Otherwise, he must water them at
least once a week or they will die.
. It has not rained in his town for 2 weeks.
When Gerardo returns, will his plants be dead? Explain your reasoning.
If his plants are indoors, he must water them at least once a week or they will die.
What would you say about an indoor plant?A houseplant is an attractive plant that is cultivated indoors. It is sometimes referred to as a potted plant, potted plant, or an indoor plant. As a result, they are typically seen for ornamental reasons in settings like homes and businesses.Not only do indoor plants improve a room's overall beauty, but studies have also shown that they improve emotions, promote creativity, lower stress levels, and remove air pollutants, all of which contribute to a happier and healthier you. Indoor plants may improve our mood in addition to improving their appearance.If his plants are indoors, he must water them at least once a week or they will die.To learn more about houseplant refer to:
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How do you tell if a log graph is growth or decay?
To tell if a log graph is a growth or decaying, look at the slope of the line. If the slope is positive, then it is growth; if the slope is negative, then it is decay.
A positive slope indicates that the value is increasing over time, while a negative slope indicates that the value is decreasing over time. To find the slope, take two points on the line and calculate the change in the y-value divided by the change in the x-value.
If the answer is positive, the graph is growth; if the answer is negative, the graph is decay. Additionally, you can look at the y-intercept of the graph, which is the value where the line meets the y-axis. If the y-intercept is positive, the graph is growth; if the y-intercept is negative, the graph is decay.
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Click on the assignment icon to receive a printout of this construction assignment. Do the assignment and be ready to give it to your teacher for grading if it is requested.
The Construction is shown below.
What is Perpendicular line?Perpendicular lines are lines that intersect at a right (90 degrees) angle.
Given:
a) Steps for perpendicular line:
To cross the line segment, draw two arcs.Create two more intersecting arcs.Connect the initial point to the intersection of the arcs.b) Perpendicular Bisector for triangle
Draw arcs with the same radius that are centered at X and Y by opening the compass more than halfway.These two arcs come together at two locations. They will be referred to as points P and Q.The line segment M, which is the perpendicular bisector of the line segment S, should be drawn by placing the ruler where the arcs meet (that is, by connecting points P and Q).we are going to proceed in the same way on all three sides of the triangle to draw its three perpendicular bisectors (Ma, Mb and Mc)So, if we extend the bisector they can meet inside, at center and outside the triangle.
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What is the Average Rate of Change of the graph below from -5 < t < 8
Answer:47
Step-by-step explanation
An experiment was conducted to see the effect altitude had on the boiling point of on Effect of Altitude on Boiling Point of Water Boiling Point (°F) 210- 200- 190+ 180- 170- 160- + 0 5,000 10,000 15,000 20,000 25,000 Altitude above Sea Level (ft) Which statement best explains the relationship between altitude and the boilin OA. There is a strong negative correlation between altitude and water's boiling point.
The option that best explains the relationship between altitude and the boiling point is; A. There is a strong negative correlation between altitude and water's boiling point.
How to interpret the correlation relationship?In correlation coefficient, we know that a positive correlation occurs when both x and y values increase at the same time while negative correlation occurs when y value decreases as x value increases.
Now, we see from the given graph that y-values are decreasing with increasing x-values and as such this is a negative correlation.
Now, we want to determine whether it is a strong or weak correlation.
The scatterplot is close to being a straight line and as such the correlation coefficient will be close to - 1 which makes it a strong negative correlation.
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Answer: A is correct
Step-by-step explanation:
took the test
Chris put $5,500 into a savings account that pays 5% interest compounded monthly. How much would be in his account after one month?
Answer:
$5,775
Step-by-step explanation:
The equation is:
A = P( 1 + rt)
We know
P = $5,500
r = 5% = 0.05
t = 1 month
Let's solve
A = 5,500( 1 + 0.05 x 1)
A = 5,500( 1.05)
A = $5,775
So, his account will be at $5,775 after one month.
How does the value of a number change when you divide by 10 100 1000?
Answer: It gets smaller
Step-by-step explanation: When you divide something by anything, the place value of the digits decreases. The digits move to the right since the number gets smaller, but remember, the decimal point does not move.
A pizza has an 18 inch diameter and is sliced into 12 pieces. What is the length of the crust on the edge of one piece of pizza?
answers:
3 pi
4.5 pi
6 pi
1.5 pi
The required length of the curst on the edge of one piece of pizza 1.5 π. Option D is correct.
What is the perimeter?Perimeter is the measure of the figure on its circumference. The perimeter of a circle is given as 2πr, where r is the radius of the circle.
here,
A pizza has an 18-inch diameter
Circumference of pizza = 18π
The pizza is sliced into 12 pieces, and the length of the crust on the edge of one piece of pizza is given as,
= 18π/12
= 1.5π
Thus, the required length of the curst on the edge of one piece of pizza is 1.5 π.
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Please help quickly this is for a big test.
ES=____ units.
Round your answer to the nearest tenth.
That would be [tex] \sqrt{113} [/tex]