The approximate difference in mass between these two animals is 154,000 kg.
Describe Algebra?Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is a broad area of study that includes a wide range of topics, such as equations, inequalities, functions, polynomials, matrices, and more.
Algebraic expressions are composed of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations, on the other hand, are mathematical statements that assert the equality of two algebraic expressions. Inequalities are mathematical statements that assert the relationship between two algebraic expressions using the symbols "<", ">", "<=", or ">=".
Functions in algebra are mappings from one set of numbers to another set of numbers that obey certain rules. These rules may involve properties such as continuity, differentiability, and invertibility.
The difference in mass between these two animals is:
1.7 x 10⁵ kg - 8 x 10⁴ kg = 1.54 x 10⁵ kg
Therefore, the approximate difference in mass between these two animals is 154,000 kg.
To know more about mass visit:
https://brainly.com/question/30189441
#SPJ1
Find the exact value, in terms of a, of each of the following. (HINT: Don't let the variable a scare you! The same strategy you used in Problem 2 still works - draw a point on a circle, assign it coordinates, and find the appropriate trig function’s value.)
a. sin (tan^-1(2/a))
b. cot (cos^-1(a))
Answer:
a. i dk how to do this qn
b. cot (cos^-1(a))
let cos^-1(a) = θ
implies, cosθ = a
from the figure, cotθ = [tex]\frac{x}{\sqrt{1 -x^{2} } }[/tex]
pls mrk me brainliest
A manufacturer buys a new machine that costs $50,000. The estimated useful life for the machine is ten years. The
achine can produce 1,000 units per month. If the machine ran at its capacity for ten years, what would be the fixed cost per unit based on
e cost of the machine per part manufactured? (Round to the nearest penny)
oooo
a) $. 42 / unit
b) $1. 00/unit
c) $4,167 / unit
d) $5,000/unit
The fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit.
What is multiplication ?
Multiplication is a mathematical operation that involves finding the product of two or more numbers or quantities. It is a way of adding a number to itself multiple times. The symbol used to represent multiplication is an "x" or a dot "·". For example, in the expression 5 x 6 = 30, 5 and 6 are multiplied together to give the product of 30. Multiplication can also be represented using parentheses, such as (5)(6) = 30. In addition, multiplication can be done with decimals, fractions, variables, and matrices.
To find the fixed cost per unit based on the cost of the machine per part manufactured, we need to calculate the total number of units produced by the machine over its estimated useful life, and then divide the cost of the machine by that number.
The machine runs at its capacity of 1,000 units per month for 10 years, so the total number of units produced by the machine is:
10 years x 12 months/year x 1,000 units/month = 120,000 units
The cost of the machine is $50,000, so the fixed cost per unit based on the cost of the machine per part manufactured is:
$50,000 ÷ 120,000 units = $0.4167 per unit
Rounding this to the nearest penny gives us the final answer of:
$0.42 per unit (option a)
Therefore, the fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit.
To know more about multiplication visit :
https://brainly.com/question/1135170
#SPJ1
What is the equation of the line?
Answer:
y=-1/4x+1
Step-by-step explanation:
Can someone please help me with this? I need someone to turn these questions into a thesis. Thank you!
Answer:
what kind of thesis are you wanting?
can you guys please help me do this
Select all that apply. Which two rays form BCE? BC CD CE CB
Hi,
The correct answer should be "CE" and "CB" I just had the same question so my answer should be correct.
I hope that this helped you. :)
100 points please help!!
We locate the [tex](5x+4)(x+7)[/tex] in order to solve this trinomial problem.
How do you formulate a trinomial's equation?The quadratic trinomial formula inside one variable has the general form ax2 + bx + c, where a, b, and c are constant terms and none of them are zero. If b2 - 4ac > 0, we're able to factor a quadratic trinomial for any value of a, b, and c. It denotes that, where h and k are real values,
How can you tell if a given equation has a trinomial?A single-term expression is referred to as a monomial, a two-term expression as a factorial, and a three-term expression as a trinomial. a phrase that contains more than three terms is identified only by the quantity of its terms.
Given, [tex]5 x^{2} + 4 x + 35 x + 28[/tex]
Regroup terms into two proportional parts [tex](5 x^{2} + 4 x) + (35 x + 28)[/tex]
Factor Greatest Common Factors out [tex]x (5 x + 4) + 7 (5 x + 4)[/tex]
Factor Greatest Common Factors out [tex](5 x + 4) (x + 7)[/tex]
To know more about trinomial visit:
https://brainly.com/question/23796911
#SPJ1
Find the next term in the arithmetic sequences in which a1 = 5 and d= -4. a2= ?
Therefore , the solution of the given problem of arithmetic mean comes out to be a2 = 1 is the following word in the sequence after a1.
What is arithmetic mean?The average values of a list, also known as the organization's values, are calculated by adding up all of the list's values. These average values are then adjusted by the proportion of list components in the largest density. similar growth patterns can be seen in math. The average of the actual numbers 5, 7, and 9 is 4, and the result of adding three to the number 21 (there are currently several three-digit numbers) is seven.
Here,
Each term in an arithmetic sequence is created by adding a constant difference (d) to the word before it. In order to determine the following term in the series where a1 = 5 and d = -4, we can use the following formula:
=> a = a1 + (n-1)*d
where an is the sequence's nth word.
Inputting a1 = 5 and d = -4 results in:
=> a2 = a1 + (2-1)*d = 5 + (-4) = 1
As a result, a2 = 1 is the following word in the sequence after a1.
To know more about arithmetic mean , visit
brainly.com/question/13000783
#SPJ1
Find the value of x for which PQ and RS are parallel
The value of x for which PQ and RS are parallel, is 83°.
The two parallel lines PQ and RS are stretched from Q to M and S to N, respectively, in the accompanying figure.
In addition, a line from T to O is drawn parallel to PQ and RS.
Now, in the illustration,
∠MPT = 180° - 135°
∠MPT = 45°
The parallel lines MQ and OT are divided by the transversal line PT.
∠MPT = ∠PTO = 45°
∠TRN = 180° - 142°
∠TRN = 38°
A transversal line TR splits the parallel lines NS and OT.
Then, ∠TRN = ∠OTR = 38°
∠PTO + ∠OTR = x
x = 45° + 38°
x = 83°
To learn more about parallel lines link is here
brainly.com/question/16701300
#SPJ4
A Ferris wheel has a diameter of 150 ft. Passengers ride in a carriage around the Ferris wheel. Use your approximation in Question 15 to write an equation relating the total distance traveled to the number of rotations of the wheel. Be sure to define your variables. Show or explain your thinking
To get distance we use formula derived in Question 15, which gives an approximation of the circumference of the wheel based on its diameter which is 471.24nft
[tex]C = \pi d[/tex]
where d: diameter and C: circumference.
With the diameter of 150 feet provided, we can calculate the wheel's circumference as follows:
[tex]C = π(150) = 471.24 ft[/tex]
For our issue, let's define some variables:
n: the number of times the Ferris wheel has rotated
d: the Ferris wheel's circumference
C: the Ferris wheel's circumference
S: the total distance a passenger travels
Given that a passenger travels one circumference every spin, the overall distance after n rotations is roughly equal to:
S ≈ nC
In place of our values, we obtain:
[tex]S = n(471.24) = 471.24n ft[/tex]
So, assuming the Ferris wheel has a 150-foot diameter, we may use the equation S 471.24n to roughly calculate the total distance a passenger would have travelled in ferris wheel spins. However keep in mind that this is just a rough estimate, and it might not be completely correct depending on things like the size of the carriage and the height of the passenger above the ground.
Learn more about distance here:
https://brainly.com/question/15172156
#SPJ1
Sarah bought a pair of shoes at a sale of 20%. If the amound she paid was php 1000, find the mark price
The mark price of the shoes is Php 1250.
Mark price (MP) refers to the original or listed price of a product or service before any discounts, promotions or markdowns are applied. It is the price that a retailer sets for a product with the intention of making a profit.
Since Sarah bought the shoes at a sale of 20%, she paid only 80% of the mark price. This can be expressed as:
80% of MP = Php 1000
0.8MP = Php 1000
To find MP, we need to divide both sides by 0.8:
MP = Php 1000 / 0.8
MP = Php 1250
Learn more about Mark price here
brainly.com/question/27987606
#SPJ4
ECOLOGY: DDT is an insecticide that has been used by farmers. It decays slowly and it is sometimes absorbed by plants that animals and humans eat. DDT absorbed in the mud at the bottom of a lake is degraded into harmless products by bacterial action. Experimental data shows that 10% of the initial amount is eliminated in 5 years(so what would remain?)
a) Find the value of k in the decay formula: y = ae-kt (Pert with different letters)
b) How much of the original amount of DDT is left after 10 years?
c) The U.S. Environmental Protection Agency banned almost all use of DDT in the U.S. in 1972. If none has been used near the lake since then, in what year will the concentration of DDT fall below 25%?
Therefοre , the sοlutiοn οf the given prοblem οf percentage cοmes οut tο be a)k ≈ 0.0279,b)y = 0.593a and c)t ≈ 78.5 .
Describe percentages.In statistics, a percentage is a figure οr an integer that is expressed as a fractiοn οf 100. Additiοnally, the wοrds "pct.," "pct," but alsο "pc" are rarely used. The "%" symbοl, hοwever, is cοmmοnly used tο denοte it. There are nο dimensiοns; the percentage tοtal is flat.
Percentages are really just numbers because the numeratοr is 100. Tο indicate that a number is a percentage, either the percent character (%) οr the text "percent" must appear befοre it.
Here,
a) We can apply the exponential decline equation:
=> [tex]y = ae^{(-kt)} (-kt)[/tex]
[tex]0.9a = ae^{(-5k)} (-5k)[/tex]
Using a to divide both sides:
[tex]0.9 = e^{(-5k)} (-5k)[/tex]
Using both sides' natural logarithms:
ln(0.9) = -5k
calculating k:
[tex]k = -ln(0.9)/5[/tex]
k ≈ 0.0279
Consequently, the decline formula's value of k is roughly 0.0279.
b)
[tex]y = ae^{(-kt)} (-kt)[/tex]
[tex]y = an e^{(-0.0279*10)[/tex]
[tex]y = 0.593a[/tex]
As a result, after 10 years, only about 59.3% of the initial DDT is still present.
c)
[tex]0.25a = ae^{(-0.0279t) (-0.0279t)[/tex]
Using a to divide both sides:
[tex]0.25 = e^{(-0.0279t) (-0.0279t)[/tex]
Using both sides' natural logarithms:
ln(0.25) = -0.0279t
calculating t:
t = -ln(0.25)/0.0279
t ≈ 78.5
Therefore, roughly 78.5 years after the ban in 1972, or in the year 2050, the concentration of DDT will drop below 25%.
To know more about percentage visit:
brainly.com/question/28269290
#SPJ1
Find the zeros of \( f(x) \), and state the multiplicity of each zero. (Order your answers from smallest to largest \( x \) first by real \[ f(x)=x^{4}+12 x^{2}-64 \] \[ x= \] with multiplicity \[ \be
To determine the zeros of f(x) and state the multiplicity of each zero, the following steps should be followed:
Step 1: Determine the roots of the polynomial
To solve for the roots of f(x), use the quadratic formula. f(x) = x⁴ + 12x² - 64
a = 1, b = 12, c = -64
Using the quadratic formula, we have:
x = (-b ± √(b² - 4ac)) / 2a
x = (-12 ± √(12² - 4(1)(-64))) / 2(1)
x = (-12 ± √400) / 2
x = (-12 ± 20) / 2
x₁ = -16
x₂ = 4
x₃ = x₄ = 0
Step 2: State the multiplicity of each zero
After determining the roots of f(x), determine the multiplicity of each root by using the concept of multiplicity. A root has a multiplicity of p if and only if f(x) has a factor of (x - r)ᵖ.
From the quadratic equation above, we have:
x₁ = -16 (multiplicity 1)
x₂ = 4 (multiplicity 1)
x₃ = x₄ = 0 (multiplicity 2)
Therefore, the zeros of f(x) and their multiplicities are: x = -16 (multiplicity 1), x = 4 (multiplicity 1), and x = 0 (multiplicity 2).
The final answer is as follows:
x = -16 with multiplicity 1
x = 0 with multiplicity 2
x = 4 with multiplicity 1.
For further information on Multiplicity, refer below:
https://brainly.com/question/5992872
#SPJ11
(09.04 MC)
What is the area of the sector bound by the center of the circle and arc CD in the circle below? (1 point)
Circle A is shown with a radius labeled 8 feet and a central angle marked 35 degrees.
Answer:
Answer:19.54 square feet.
Quick Check 13.13-3.11 Find the difference. list (3y^(2)+11y-5)/(y^(2)-2y-24)-(2y^(2)+4y-17)/(y^(2)-2y-24)
Answer: pic please so i know some more info thanks
Step-by-step explanation: pic please so i know some more info thanks
First, estimate what you think the quotient should be. Then, solve the problem using long division. Show your work. 2,496 ÷ 8
Answer: 312
Step-by-step explanation:
Estimate: One way to estimate the quotient of 2,496 ÷ 8 is to round 2,496 to the nearest multiple of 8, which is 2,496 rounded to 2,496. Then, we can divide 2,496 by 8, which gives an estimated quotient of 312.
Find b.
(110
116
68°
70°
As a result, the answer tο the fοllοwing questiοn, sum οf all sides οf a hexagοn = 720 where the value οf b = 136.
What is hexagοn?In geοmetry, a hexagοn is a six-sided pοlygοn οr hexagοn that fοrms the cube's shape. Internal angles οf a simple hexagοn add up tο 720°. A hexagοn is a clοsed twο-dimensiοnal pοlygοn with six sides. A hexagοn has six cοrners οn each side. Hexa represents six and gοna represents an angle. Hexagοnal shapes are fοund in sοccer balls, hοneycοmbs, flοοr tiles, and pencil surfaces. A hexagοn is a six-sided pοlygοn in geοmetry. A regular hexagοn is οne that has all οf its sides and angles the same length.
Sum οf all sides οf a hexagοn = (n - 2) × 180°
= (6 - 2) × 180°
= 720°
Frοm the given hexagοn, sum οf all angles
110 + 116 +(180 - 68) + (180 - 70) + 2bx = 720
b = 136
To know more about hexagon visit:
brainly.com/question/3295271
#SPJ1
If the gyration of the outer perimiter of other galaxies are in a spiral elipse what would the probility of the tangent of collisions
The probability of a collision between two galaxies depends on a variety of factors, such as the size, mass, and relative velocities of the galaxies.
The probability of a collision between two galaxies depends on a variety of factors, such as the size, mass, and relative velocities of the galaxies. If the galaxies are in a spiral elipse, then the tangential velocity of the galaxies may be different, and this could affect the probability of a collision. However, without knowing more information about the galaxies, it is impossible to accurately calculate the probability of a collision.
If the galaxies are in a spiral elipse, then it is important to consider the tangential velocity of the galaxies, as this could affect the probability of a collision. Additionally, the relative angular momentum of the galaxies, their proximity to one another, and their respective trajectories also play a role. Without knowing more information about the galaxies, such as their exact positions, velocities, and masses, it is impossible to accurately calculate the probability of a collision.
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
-8(6y-2x-5) Use the distributive property to remove the parentheses.
Answer: -48y+6x+40
Step-by-step explanation: when you multiply two minuses that is +.
In a factory, three machines, J, K and L, are used to make biscuits. Machine J makes 25% of the biscuits. Machine K makes 45% of the biscuits. The rest of the biscuits are made by machine L. It is known that 2% of the biscuits made by machine J are broken, 3% of the biscuits made by machine K are broken and 5% of the biscuits made by machine L are broken. A biscuit is selected at random. Calculate the probability that the biscuit is made by machine J and is not broken.
B. Probability that the biscuit is made by machine and is not broken is:
1-(25% × 2%)
= 50%
c. The probability of breakage: 2% + 3% + 5% = 10%
d. Probability that biscuit is not made by machine = 1-5% = 95%
What do you mean by probability?Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. About an event's outcome, we might be certain or uncertain.
When this occurs, we state that there is a possibility that the event will occur. In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence.
Now from the question,
The probability that the biscuit is made by machine and not broken:
1 - 25% × 2%
= 50%
Now not broken probability = 1- 25% × 2%
Now next, the probability of breakage: 2% + 3% + 5% = 10%
Finally, the probability that biscuit is not made by machine = 1-5% = 95%
To know more about probability, visit:
https://brainly.com/question/30034780
#SPJ1
CAN YOU GUYS HELP ME
The amount of feet the circumference of the outer circle is greater than the circumference of the inner circle is 18.86 feet.
What is a circumference?Circumference is the measure of distance around a circle.
To calculate the how many feet the circumference of the outer circle is greater than the circumference of the inner circle, we use the formula below.
Formula:
ΔC = (C+2πd)-C..................... Equation 1ΔC = 2πdWhere:
ΔC = The amount of feet the circumference of the outer circle is greater than the inner circled = Distance between the inner circle and the outer circleπ = PieFrom the question,
Given:
d = 3 feetπ = 22.7Substitute these values into equation 1
ΔC = 2×22/7×3ΔC = 18.86 feetHence, the difference in circumference between the outer and the inner is 18.86
Learn more about circumference here: https://brainly.com/question/27447563
#SPJ1
NOTE: Answers using z-scores rounded to 3 (or more) decimal places will work for this problem. The population of weights for men attending a local health club is normally distributed with a mean of 174 lbs and a standard deviation of 29-lbs. An elevator in the health club is limited to 35 occupants, but it will be overloaded if the total weight is in excess of 6475 -lbs. Assume that there are 35 men in the elevator. What is the average weight beyond which the elevator would be considered overloaded?
the average weight beyond which the elevator would be considered overloaded is approximately 7616.56 lbs.
What is probability?
Probability is a measure of the likelihood that an event will occur. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probabilities are usually expressed as fractions, decimals, or percentages.
The total weight of 35 men in the elevator can be modeled by the sum of 35 independent and identically distributed normal random variables with mean 174 lbs and standard deviation 29 lbs. Let X be the weight of one man, then the total weight of 35 men is W = 35X.
The mean of W is:
μW = E(W) = E(35X) = 35 E(X) = 35 * 174 = 6090 lbs
The variance of W is:
Var(W) = Var(35X) = 35^2 Var(X) = 35^2 * 29^2 = 899150
The standard deviation of W is:
σW = sqrt(Var(W)) = sqrt(899150) = 947.85
To find the average weight beyond which the elevator would be considered overloaded, we need to find the weight that corresponds to the 95th percentile of the distribution of W, since the elevator is overloaded if the total weight is in excess of 6475 lbs.
Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to the 95th percentile: z = 1.645 (rounded to 3 decimal places).
We can then find the weight w that corresponds to this z-score:
w = μW + z * σW
w = 6090 + 1.645 * 947.85
w ≈ 7616.56
Therefore, the average weight beyond which the elevator would be considered overloaded is approximately 7616.56 lbs.
To learn more about probability from the given link : brainly.com/question/11234923
#SPJ1
What is the cost of 10. 0 gallons of gasoline priced at 1. 449 per gallon?
The cost of 10.0 gallons of gasoline priced at 1.449 per gallon is 14.49.
The cost of 10.0 gallons of gasoline priced at 1.449 per gallon can be determined using the formula Cost = Quantity * Price. To calculate the cost, first multiply 10.0 (the quantity) by 1.449 (the price). This gives the value 14.49, which is the cost of 10.0 gallons of gasoline priced at 1.449 per gallon.
To explain this further, when calculating the cost of an item, we need to take into account both the quantity and the price of that item. The quantity is the amount of the item that we will be purchasing, and the price is the amount that we will be paying for that item. In the case of gasoline, 10.0 gallons is the quantity, and 1.449 is the price per gallon.
To calculate the cost, we need to multiply the quantity by the price. This gives us the cost of the item. In this case, multiplying 10.0 (the quantity) by 1.449 (the price) gives us 14.49, which is the cost of 10.0 gallons of gasoline priced at 1.449 per gallon.
Learn more about total cost here:
https://brainly.com/question/6506894
#SPJ4
I need help with this question please and thank you
Answer:
b = 6
Step-by-step explanation:
step one: Simplify 10^2 to 100
Step two: Simplify 8^2 to 64
Step three: Subtract 64 from both sides
Step four: Simplify 100 - 64 to 36
Step Five: Take the square root of both sides
Step Six: Since 6*6=36, the square root of 36 is 6
Step Seven: Switch sides b = positive 6
I hoped this helped
Pla help algebra1 pls
Answer:
A. 2(4a^3 - 49a)
In this case, you would simply multiply the numbers and leave the a value and exponents alone.
B. 2a(4a^2 - 49)
First, you would distribute(multiply) 2 with the numbers inside the parentheses just like you did for answer A. Then, you would distribute a with the other a values inside the parentheses, you would add this values instead of multiplying it.
F. 2a(2a - 7)(2a + 7)
You would distribute 2a inside the FIRST set of parentheses just like you did before. Then multiply that set of parentheses with the other set of parentheses.
Step-by-step explanation:
I need help with this one
Using Pythagorean theorem, the volume of the cylinder is 201.1 cubic units
What is the volume of the cylinderTo determine the volume of the cylinder, we have to find the height of the cylinder.
using Pythagoras theorem, we can find the height of the cylinder.
13² = 5² + x²
x² = 13² - 5²
x² = 144
x = √144
x = 12 units
The volume of a cylinder is given as
V = 1/3 πr²h
h = height of cylinderr = radius of cylinderv = 1/3 * 3.14 * 4² * 12
v = 64π cubic units
v = 201.1 cubic units
Learn more on volume of cylinder here;
https://brainly.com/question/10390389
#SPJ1
For the complex number z = 12 + i, what is Modifying above z with bar?
The conjugate of the complex number z = 12 + i is [tex]\hat{z}=12-i[/tex]
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
Complex number are in the form a + bi, where a is the real part and b is the imaginary part. Both a and b are real numbers
The conjugate of a complex number z = a + bi is [tex]\hat{z}=a-ib[/tex]
Given that z = 12 + i
The conjugate of z is [tex]\hat{z}=12-i[/tex]
Find more on equation at: https://brainly.com/question/2972832
#SPJ1
10x+2-2x=
what is the answer
Answer:
4
Step-by-step explanation:
10x+2-2x=
10x-2x=2
8x=2
divide both sides by 8
x=2/8
x=4
Unit 8 right triangles and trigonometry homework 4 I need number 10 and 15
Using trigonometric ratios the value for line segment DC is obtained as 30.5 units.
What is trigonometric ratio?Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios. In triangle ABD, the values given are -
∠BDA = 90°,
∠A = 54° and
AB = 20 units
According to the sum property of a triangle.
∠BDA + ∠A + ∠ABD = 180°
Substitute the values into the equation -
90° + 54° + ∠ABD = 180°
144° + ∠ABD = 180°
∠ABD = 180° - 144°
∠ABD = 36°
Now according to trigonometric ratios -
cos θ = Base / Hypotenuse
In triangle ABD -cos 36° = BD / AB
Substitute the values into the equation -
cos 36° = BD / 20BD
= cos 36° × 20BD
= 0.80901 × 20BD
= 16.18
≈ 16.2
Now in triangle BDC, the values given are -
∠BDC = 90°, ∠C = 28° and BD = 16.2
Now according to trigonometric ratios -tan θ = Perpendicular / Base
In triangle BDC -tan 28° = BD / DC
Substitute the values into the equation -
tan 28° = 16.2 / DC
DC = 16.2 / tan 28°
DC = 16.2 / 0.53170
DC = 30.46 ≈ 30.5 units
Therefore, the value for DC is obtained as 30.5 units.
To learn more about trigonometric ratio from the given link
https://brainly.com/question/13276558
#SPJ1
finnd the equation of straight line passing through the point (3a,0) and (0,3b) also shwo that the line passese throught the poinits (a , 2b)
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3a, 0 ) and (x₂, y₂ ) = (0, 3b )
m = [tex]\frac{3b-0}{0-3a}[/tex] = [tex]\frac{3b}{-3a}[/tex] = - [tex]\frac{b}{a}[/tex]
the line crosses the y- axis at (0, 3b ) ⇒ c = 3b
y = - [tex]\frac{b}{a}[/tex] x + 3b ← equation of line
to show that (a, 2b ) lies on the line , substitute x = a into the equation and if y = 2b then the point lies on the line
y = - [tex]\frac{b}{a}[/tex] (a) + 3b = - b + 3b = 2b
then the line passes through the point (a, 2b )