The apothecary system uses the minim as the basic unit of liquid measure and the grain as the basic unit of solid measure.
What is apothecary measurement?
The apothecary system was once a system of weights and measurements used for drug prescription and dispensing. A pound was divided into 12 ounces in the English version, which also divided an ounce into eight drams or drachms and a dram into three scruples, or 60 grains.What are the units of the apothecary system?
The grain, scruple (20 grains), dram (3 scruples), ounce (8 drams), and pound—a ancient scale of weight used in the British Isles for measuring and distributing pharmacological goods (12 ounces).
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If the 4 population assumptions in the hard-weinberg principle are met, what will happen to the allele frequencies?
The Hardy-Weinberg principle states that the frequency of alleles in a large randomly reproducing population will remain constant from generation to generation if certain assumptions are met.
The assumptions are:
No mutations.No migration into or out of the populationNo selection, andNo genetic drift.What is the hardy-Weinberg principle?The Hardy-Weinberg principle, also known as the Hardy-Weinberg equilibrium, model, theorem, or law in population genetics, holds that in the absence of additional evolutionary factors, allele and genotype frequencies in a population would remain constant from generation to generation.A population is not evolving while it is in Hardy-Weinberg equilibrium. Discover how violations of Hardy-Weinberg assumptions result in evolution.
When a population reaches Hardy-Weinberg equilibrium for a gene, it stops evolving and allele frequencies remain constant over generations.Hardy-Weinberg's assumptions include no mutation, random mating, no gene flow, infinite population size, and no selection.If the assumptions for a gene are not met, the population may evolve for that gene (the allele frequencies of the gene may change).Therefore, the Hardy-Weinberg principle states that the frequency of alleles in a large randomly reproducing population will remain constant from generation to generation if certain assumptions are met.
The assumptions are:
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Given below are lease terms at the local dealership. What is the total cash
due at signing?
Based on the various costs resulting from the lease terms at the local dealership, the total cash to pay at signing is $5,480
What is the total cash?This can be found by the formula:
= Down payment + Monthly payment + Security deposit + Acquisition fee
Solving gives:
= 4,100 + 475 + 415 + 490
= $5,480
In conclusion, option A is correct.
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Answer: B. $5005
Step-by-step explanation:
A moving company’s moving rates can be represented by the function f(x) = 3x 400, where x is the number of miles for the move. another moving company’s rates can be represented by the function g(x) = 5x 200. which function represents the difference between the moving companies' rates, h(x) = f(x) – g(x)? h(x) = 2x 200 h(x) = –2x 200 h(x) = 5x – 200 h(x) = 5x 600
The function that represents the difference between the moving companies' rates is:
h(x) = -2x + 200.
How to find the difference of two functions?The difference of two functions is found subtracting the like terms from the functions.
In this problem, the functions for the rates are given as follows:
f(x) = 3x + 400.g(x) = 5x + 200Hence the difference is given by:
h(x) = 3x + 400 - (5x + 200) = 3x - 5x + 400 - 200 = -2x + 200.
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The volume of a sphere is 256/3π cm3.
Work out the surface area of the sphere.
Give your answer in terms of π.
the surface area of the sphere is π/4 cm^3
How to determine the surface areaIt is important to know the formula for surface area and volume of a sphere
Surface area = [tex]\frac{4\pi }{r^2}[/tex]
Volume = [tex]\frac{4}{3} \pi r^3[/tex]
First, let's determine the value of radius, r
The value for volume was given as 256/3π cm3.
[tex]\frac{256}{3} \pi = \frac{4}{3} \pi r^3[/tex]
Pi cancels out and we have cross multiply to get the radius
[tex]256 * 3 = 4 * 3 r^3[/tex]
[tex]12r^3 = 768[/tex]
Make r the subject of the formula
[tex]r = \sqrt[3]{\frac{768}{12} }[/tex]
[tex]r = \sqrt[3]{64}[/tex]
r = 4
Let's substitute to find the surface area
Surface area = [tex]\frac{4\pi }{4^2}[/tex]
Surface area = π/4
Surface area = π/4 cm^3
Thus, the surface area of the sphere is π/4 cm^3
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Please answer this question ASAP!
The traffic lights at three different road crossings change after every 48, 72 and 108 seconds respectively. If they change simultaneously at 8 am, at what time will they change to again?
Answer:
8:07:12 am
Step-by-step explanation:
The lights will change simultaneously after any multiple of the least common multiple of their cycle times.
LCMThe least common multiple of a set of numbers is the product of the highest powers of their prime factors.
48 = 2⁴×3
72 = 2³×3²
108 = 2²×3³
The highest power of the factor 2 is 4. The highest power of the factor 3 is 3, so the LCM of the numbers 48, 72, and 108 is ...
LCM = 2⁴×3³ = 16×27 = 432
The lights will change simultaneously after each period of 7 minutes 12 seconds. They will change simultaneously again at 8:07:12 am.
If the first and the last term of an arithmetic progression, with common difference
[tex]1 \times 1\frac{1}{2} [/tex]
, are
[tex]? \times 2\frac{1}{2} [/tex]
and 19 respectively, how many term has the sequence?
The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.
What is the nth term of an arithmetic sequence?The general form of the nth term of an arithmetic sequence is
an = a1 + (n - 1)d
Where,
a1 - first term
n - number of terms in the sequence
d - the common difference
Calculation:The given sequence is an arithmetic sequence.
First term a1 = [tex]1\frac{1}{2}[/tex] = 3/2
Last term an = [tex]2\frac{1}{2}[/tex] = 5/2
Common difference d = 1/9
From the general formula,
an = a1 + (n - 1)d
On substituting,
5/2 = 3/2 + (n - 1)1/9
⇒ (n - 1)1/9 = 5/2 - 3/2
⇒ (n - 1)1/9 = 1
⇒ n - 1 = 9
⇒ n = 9 + 1
∴ n = 10
Thus, there are 10 terms in the given arithmetic sequence.
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Disclaimer: The given question in the portal is incorrect. Here is the correct question.
Question: If the first and the last term of an arithmetic progression with a common difference are [tex]1\frac{1}{2}[/tex], [tex]2\frac{1}{2}[/tex] and 1/9 respectively, how many terms has the sequence?
Please help !!! Need help !!!
Answer: B. alternate interior angles.
Step-by-step explanation:
Write the equation of the line that passes through
the points (-1, 2) and (6, 3) in slope-intercept form.
The equation of the line that passes through the points (-1, 2) and (6, 3) in slope-intercept form is,
[tex]y=\frac{x}{7} +\frac{15}{7}[/tex]
How to find the equation of a passing line?The equation y = mx often denotes a straight line with a gradient of m that passes through the origin. Y = mx is the equation for a straight line with gradient m that passes through the origin.Y = mx + b is the equation for a line with a slope of m and a y-intercept of (0, b). In order to graph a line expressed in slope-intercept form: Draw the coordinate plane's y-intercept. To locate a different point on the line, use the slope.The three main types of linear equations are slope-intercept form, standard form, and point-slope form.Given: [tex](-1,2)[/tex] and [tex](6,3).[/tex]
The slope of the line passing through[tex](x1,y1)[/tex] [tex](x2,y2)[/tex] is [tex]\frac{y^{2} }{x^{2} } -\frac{y^{1} }{x^{1} }[/tex]
The slope of our line[tex]=\frac{(3-2)}{(6+1)} =\frac{1}{7}[/tex]
Slope intercept from the equation would be [tex]y= 1/7 x +C[/tex]
Find C:
Since [tex](-1,2)[/tex] lies on the line, substitute these in the line equation
[tex]2 = \frac{1}{7(-1)} +c[/tex]
[tex]C=2+\frac{1}{7} =\frac{15}{7}[/tex]
Therefore, the equation in slope intercept form is[tex]y=\frac{x}{7} +\frac{15}{7}[/tex]
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What is the sum?
A
B
C
D
Answer:
[tex]\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]
Step-by-step explanation:
We are given the expression:
[tex]\displaystyle{\dfrac{3}{x^2-9} + \dfrac{5}{x+3}}[/tex]
First, factor the denominator [tex]\displaystyle{x^2-9}[/tex] to [tex]\displaystyle{(x+3)(x-3)}[/tex] via difference of two squares:
[tex]\displaystyle{\dfrac{3}{(x+3)(x-3)} + \dfrac{5}{x+3}}[/tex]
Next, multiply the expression 5/(x+3) by [tex]\displaystyle{x-3}[/tex] both denominator and numerator:
[tex]\displaystyle{\dfrac{3}{(x+3)(x-3)} + \dfrac{5(x-3)}{(x+3)(x-3)}}[/tex]
Add both together since they have same denominator now:
[tex]\displaystyle{\dfrac{3+5(x-3)}{(x+3)(x-3)} }[/tex]
Simplify the numerator:
[tex]\displaystyle{\dfrac{3+5x-15}{(x+3)(x-3)} }\\\\\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]
Therefore, the sum is:
[tex]\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]
Write and solve an equation based on the following question.
8 is the product of 4 and what number?
A 4 = 8x 2
B. 8 = 4x: 4
C 8=4x 2
D. 4 = 8x 1/2
Answer:
D
Step-by-step explanation:
hihihihihuiuiijihihihihihihih
Five pounds is equal to 2.268 kilograms. How many kilograms is 2 pounds?
Mass is the amount of matter that a body possesses and its unit in the international system of units is the kilogram.
How many kilograms is 2 pounds?Knowing that 1 pound is 2.205 kilograms.Therefore ⇒ 2 lb * 1 kg / 2.205 lb = 0.907 kgAnswer: In 2 pounds there are 0.907 kilograms.
10. There are 355 students at Median Middle School. If there 8% of the students were absent on Tuesday, how many students were absent? How many were present?
To solve this question, we simply need to divide the total amount of students by 8% to find out how many students were absent and how many were present.
However, we can't simply multiply it by 8%, so we need to turn that into a decimal.
8% - 0.08
Multiply:
355 x 0.08
= 28.4
Round:
28 kids were absent
Subtract:
355 - 28
= 327
This means that 28 kids were absent, and 327 kids were present.
Emily invests $x at a rate of 3% per year simple interest. After 5 years she has $20.10 interest. I Find the value of x.
The equation be 20.10 = X × 3 × 5/100 then, the value of X = 134.
How to find the value of x?To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.
The formula for Simple Interest exists PTR/100,
where, P = Principal
T = Time period in years
R = Rate of interest per annum.
Simple interest = PTR / 100
20.10 = X × 3 × 5/100
simplifying the above equation, we get
20.10 = 15X / 100
15X = 20.10 × 100 = 2010
X = 2010/15 = 134
X = 134.
Therefore, the value of X exists at 134.
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Cube a and cube b are similar solids. the volume of cube a is 27 cubic inches, and the volume of cube b is 125 cubic inches. how many times larger is the base area of cube b than the base area of cube a?
The base area of cube B is 25/9 times larger than the base area of cube A.
What is area cubic?
Surface area of cube is the sum of areas of all the faces of cube, that covers it. The formula for surface area is equal to six times of square of length of the sides of cube. It is represented by 6a2, where a is the side length of cube. It is basically the total surface area.We know that volume of cube with each side of units is equal to .
First of all, we will find the each side of cube A and B as:
[tex]A^{3} = 27[/tex]
[tex]\sqrt[3]{A^{3} } = \sqrt[3]{27}[/tex]
A = 3
[tex]B^{3} = 125[/tex]
[tex]\sqrt[3]{B^{3} } = \sqrt[3]{125}[/tex]
B = 5
Now, we will find base area of both cubes as:
[tex]\frac{Base area of B}{Base area of A} = \frac{B^{2} }{A^{2} }[/tex]
[tex]\frac{Base area of B}{Base area of A} = \frac{5^{2} }{3^{2} }[/tex]
[tex]\frac{Base area of B}{Base area of A} = \frac{25}{9}[/tex]
Therefore, the base area of cube B is 25/9 times larger than the base area of cube A.
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Pls help
On a graph, sketch f(x)=x+3 and g(x)=x. Is there a way of determining the graph of f(x)+g(x) without solving it algebraically? Explain your thinking below.
The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).
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A skateboard halfpipe is being designed for a competition. the halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 30 ft above the ground. using the ground as the x-axis, where should the base of the halfpipe be positioned? which equation best describes the equation of the halfpipe?
The equation of parabola is given by
(X-h)^2 = 4p(Y-k)^2
2p = 30 - 0
p = 15
4p = 4 × 15
= 60
In this case h = 0
So, we have (h,p) = (0,15)
So we get
We have equation: x^2 = 60(y-15)
y = x^2 / 60 + 15
What is a parabola?A parabola is nothing but a U-shaped plane curve. Any point on the parabola is equidistant from a fixed point called the focus and a fixed straight line known as the directrix. The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax. Some of the important terms below are helpful to understand the features and parts of a parabola. Focus: The point (a, 0) is the focus of the parabola.
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What is 63% of 35. Please tell me how to do it not just answer please!
Answer:
22.05
Step-by-step explanation:
First, convert 63% into a decimal.
To do this, divide it by 100.
[tex] \frac{63}{100} = 0.63[/tex]
Multiply 0.63 by 35.
[tex]35 \times (0.63) = 22.05[/tex]
Answer:
Step-by-step explanation:
.63(35)= 22.05
Multiply .63(35)
For s=5 and t=8, 3st²-s²:
3st²-s² =
Step-by-step explanation:
Given,
s=5
t=8
solution,
= 3st² - s²
= 3*5*8² - 5²
= 3*5*64 - 25
= 960 - 25
= 935
To make cream ice pops, nina uses conical molds that each have a height of 15 cm and a radius of 2 cm. how much ice pop mixture can each mold hold when full? a. 30 pi cubic centimeters b. 10 pi cubic centimeters c. 20pi cubic centimeters d. 60pi cubic centimeters
Answer:
C
Step-by-step explanation:
Givens
r = 2 cm
h = 15 cm
pi = 3.14 The question does not expect a number for pi
Formula
V = (1/3) pi r^2 h Substitute givens into formula
Solution
V = 1/3 * pi * 2^2 * 15 Combine. Remember pi is left as it is
V = 1/3 * pi * 4 * 15
V = 1/3 pi * 60 Divide 60 by 3
V = 20 pi
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
Situation 2 (B)
Step-by-step explanation:
I think it would be B since the power of the gear increases proportionally with the radius.
Study island question below its 8th grade algebra
Answer:
376.8 [tex]units^{2}[/tex]
Step-by-step explanation:
There are a lot of moving parts. We need to find the area of the bottom of the circle the center and the top circle.
The top and the bottom will be the same.
The area of a circle:
a = [tex]\pi[/tex][tex]r^{2}[/tex]
a = 3.14([tex]5^{2}[/tex])
a = 3.14(25)
a =78.5
The center: Think of this as a label on soup can. If you tear the label off it would be a rectangle. To find the area we would multiply the height of the can by the circumference of the circle. They tell us the height is 7 and we can calculate the circumference.
C = [tex]\pi[/tex]d The d is the diameter it is 2 of the radiuses.
C = [tex]\pi[/tex]10
C = 3.14(10)
C = 31.4
Now we multiply 31.4 and 7 together to find the area of the center of the cylinder.
(31.4)(7) = 219.8
The total area:
top 78.5
center 219.8
bottom 78.5
Total 376.8
I need help finding the quotient of this equation in simplified form.
by breaking it down u can write it as
15p^-4/_20p^-12 * q^-6/q^-3
15/-20=-3/4
using law of indices we have
-3/4p^-4+12 * q^-6+3
-3/4p^8q^-3
the answer is the first own
im pulling my hair out with this problem my calculator simplified it to [tex]\frac{1+/-\sqrt{14}}{10}[/tex]
What am i doing wrong?? :')
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+2}x\stackrel{\stackrel{c}{\downarrow }}{-5} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (2) \pm \sqrt { (2)^2 -4(3)(-5)}}{2(3)} \implies x = \cfrac{ -2 \pm \sqrt { 4 +60}}{ 6 } \\\\\\ x= \cfrac{ -2 \pm \sqrt { 64 }}{ 6 }\implies x=\cfrac{ -2 \pm 8}{ 6 }\implies x= \begin{cases} ~~ 1\\ -\frac{5}{3} \end{cases}[/tex]
Answer:
-5/3 and -1
Step-by-step explanation:
I am not sure what you mistake is, but here is my solution. I hope that it helps. I am sorry that you are frustrated. We have all been there.
prove:- sin^2A-cos^2B=sin^2B-cos^2A
Step-by-step explanation:
1: change 'sin²A' and 'cos²B' into (1-cos²A)and (1-sin²A) respectively.
2:open the brackets and put signs accordingly.
3: cancel (-1) and (+1).
4: remaining is your answer.
Suppose you invested $1000 every 3 months over a 15 year period. If money earns an annual rate of 6.5% compounded quarterly, how much would be available at the end of the time period. How much is the interest earned? Show all your calculations
Using the future value formula, it is found that $100,336.67 will be available at the end of the time period, of which $40,336.67 was of interest earned.
What is the future value formula?The future value formula is given by:
[tex]F = P\frac{(1 + i)^n - 1}{i}[/tex]
In which:
P is the periodic payment.i is the equivalent yearly interest rate.n is the number of periods.For this problem, considering the situation described, especially the quarterly compoundings, the parameters are given as follows:
P = 1000, i = 0.065/4 = 0.01625, n = 15 x 4 = 60.
Hence the amount available is given by:
[tex]F = P\frac{(1 + i)^n - 1}{i}[/tex]
[tex]F = 1000\frac{(1 + 0.01625)^{60} - 1}{0.01625}[/tex]
F = $100,336.67
The amount deposited was:
15 x 4 x $1000 = $60,000.
Hence the amount earned in interest was:
$100,336.67 - $60,000 = $40,336.67
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Bank a charges a $35 monthly fee for a checking account debit card with the limited train fashion bank b charges a $15 monthly fee for a checking account and debit card plus $0.70 for each transaction 25 transaction is giving a month
Total charges from bank A exists $15.
Total charges on Bank B spending exists $45.
How to estimate the Total charges on bank B?Given: Bank A charges a $15 monthly fee for a checking account and debit card, with unlimited transactions.
Shade 25 transactions.
Total charges from bank A = $15 monthly
Bank B charged a $35 monthly fee for a checking account and debit card, plus $ 0.70 for each transaction.
She made 25 transactions.
Total charges on bank B = $35 + (0.40)25
Total charges on bank B = $35+10
Total charges on bank B = $45
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Which of the following BEST defines an output? please help me, I've been stuck on this one for a while!
A statement which best defines an output is: B. an output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.
What is a function?A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).
The types of function.In Mathematics, there are different types of functions and these include the following;
Periodic functionInverse functionModulus functionSignum functionPiece-wise defined functionIn this context, we can infer and logically deduce that a statement which best defines an output is that it's the result of a relation or the function rule, which usually are the y-values in a set of ordered pairs, on a table or a graph.
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Complete Question:
Which of the following best defines an output?
A. An output is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.
B. An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.
C. An output is a special type of relation for which there is a rule that pairs each input with exactly one output.
D. An output is a set of ordered pairs in which no y-value repeats.
A piece of PVC material weighs 0.063 pounds per cubic inch. What's the weight of a 36-inch piece of PVC pipe with an outside diameter of 0.82 inches and an inside diameter of 0.75 inches?
The weight of a 36-inch piece of PVC pipe is 0.20 pounds
How to determine the weight of a 36-inch piece of PVC pipe?The given parameters about the 36-inch piece of PVC pipe are
Height, h = 36 inches
Outside diameter, D = 0.82 inches
Inside diameter, d= 0.75 inches
The volume of the PVC pipe is then calculated as:
V = πh(D/2)^2 - πh(d/2)^2
Substitute the known parameters in the above equation
V = 3.14 * 36 * (0.82/2)^2 - 3.14 * 36 * (0.75/2)^2
Evaluate the quotients
V = 3.14 * 36 * 0.41^2 - 3.14 * 36 * 0.375^2
Evaluate the exponents
V = 3.14 * 36 * 0.1681 - 3.14 * 36 * 0.140625
Evaluate the products
V = 19.002024 - 15.89625
Evaluate the difference
V = 3.105774 cubic inches
From the question, we have:
Weight = 0.063 pounds per cubic inch
So, the total weight is
Total weight = 3.105774 cubic inches * 0.063 pounds per cubic inch
Evaluate the product
Total weight = 0.195663762 pounds
Approximate
Total weight = 0.20 pounds
Hence, the weight of a 36-inch piece of PVC pipe is 0.20 pounds
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Describe the design and original dimensions of the photo you chose for Francesca to give as a gift.
Step-by-step explanation:
Transcribed image text: Choosing a Photo Francesca wants to give one of her photographs to a friend as a gift. Help her choose the photograph and determine the style and size of the mat she can afford 1. Describe the design and original dimensions of the photo you chose for Francesca to give as a gift. 2 points: 1 point for describing the photo and 1 point for including the dimensions) Photo description: The photo Shous Francasca and has Friend huagina. Dimensions (including units): The still Photo is a Xg meaning its width is indas and Langth is gind Finding the Total Area of the Photo and Mat 2. Francesca wants to glue her photo on top of a mat that will increase the length of each side. The mat border has a width of x, so the length of each side would increase by 2x inches. Represent the length and width of the mat with an expression. (2 points) Length: Width: 3. The area of the mat is the product of the length and width. Write an expression for area as the product of two binomials. Do not multiply.(1 point)
a man is three times as old as his son. In ten years time, the man will be two times as old as his. Find the age of the son and the father
Answer:
age of son= X
Father's age =3x
After 10 years , father's age= 3x +10
Son's age = X+10
Operations:
3x + 10 =2(x + 10 )
3x + 10 = 2x + 20
X= 10
Therefore, present age of son= 10 years
Father's present age = 30 years
After 10 years son will be 20 years and the father 40 yes which is double
