The merchant needs to fill 60 litres of all types of oils .
What is HCF ?
HCF is the highest common factor, it is the factor in common in more than two numbers.
It is given in the question that
A merchant has 120 litres of oil of one kind, 180 litres of another kind, and 240 litres of the third kind.
He wants to sell the oil by filling the three kinds of equal capacity.
To find the greatest capacity of such a tin , we have to find the highest common factor of the individual capacity.
120=2×2×2×3×5
180=2×2×3×3×5
240=2×2×2×2×3×5
HCF=2×2×3×5=60
The greatest capacity = 60 litres
So the merchant needs to fill 60 litres of all types of oils .
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The table shows values for a quadratic function.
X
y
0
2
3
18
4
32
50
6
72
What is the average rate of change for this function for the interval from x = 2
to x = 4?
16
A
5
The average rate of change for this function for the interval from x = 2
to x = 4 is 20
How to determine the average rate of change?The function is given as:
x y
0 18
2 32
3 50
4 72
The average rate of change at the interval from x = 2 to x = 4 is calculated using:
m = (f(4) - f(2))/(4 - 2)
Using the table values, we have:
m = (72 - 32)/(4 - 2)
Evaluate
m = 20
Hence, the average rate of change is 20
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Graph the line with slope 1/4 and y-intercept -8
Solution: Below! ^^
Detailed explanation:
Hii! I'm sorry, I can't graph the line for you, but I'll try to give you the best possible explanation.
First, note that the question provides us with the info that the y intercept is -8. This is a very valuable piece of information!
This means that the line crosses the y axis (since it's the y intercept) at the point (0,-8). Plot it on the co-ordinate plane.
Next, this question also provides us with the fact that the slope of the line is 1/4. This is yet another valuable piece of information!
What this tells us is: from that point (0,-8), you need to go up 1 unit, then over 4, and so forth, until you obtain a line.
_________
Hope I helped, best wishes & happy studies!
Please reach out to me if any queries arise.
_________
Answer:
Image attached below
Step-by-step explanation:
The line should cross y axis as -8 and should have a point of (0,-8)
The line should have a gradient / slope of 1/4
An automobile tire has a diameter of 59m. What is the circumference of the tire
185.4m (rounded to 1dp)
Circumference of a circle is the diameter times by pi. 59×pi=185.4
Answer:
59 meters
or approximately 185.26 ( using 3.14 for pi)
or 185.3539666 meters using the pi button
Step-by-step explanation:
The circumference is given by
C = pi *d where d is the diameter
C = pi * 59 m
C = 59 pi meters
We can approximate pi by 3.14
C =185.26 meters
or by using the pi button the calculator
185.3539666 meter
The short leg of a 90-45-45 triangle is 5. What is the long leg and the hypotenuse?
The long leg and the hypotenuse of the isosceles right triangle will be 7.07 units.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The short leg of a 90-45-45 triangle is 5.
The right triangle is an isosceles right triangle. Then the two side will be same.
Then the long leg and the hypotenuse will be
H² = 5² + 5²
H² = 25 + 25
H² = 50
H = 7.07 units
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Use the rational zeroes theorem to state all the possible zeroes of the following polynomial:
f (x) = 3x^(6) + 4x^(3) - 2x^(2) + 4
Answer:
All the possible zeroes of the polynomial: f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex] are ±1 , ±2 , ±4 , ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex] , ±[tex]\frac{4}{3}[/tex] by using rational zeroes theorem.
Step-by-step explanation:
Rational zeroes theorem gives the possible roots of polynomial f(x) by taking ratio of p and q where p is a factor of constant term and q is a factor of the leading coefficient.
The polynomial f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex]
Find all factors (p) of the constant term.
Here we are looking for the factors of 4, which are:
±1 , ±2 and ±4
Now find all factors (q) of the coefficient of the leading term
we are looking for the factors of 3, which are:
±1 and ±3
List all possible combinations of ± [tex]\frac{p}{q}[/tex] as the possible zeros of the polynomial.
Thus, we have ±1 , ±2 , ±4 , ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex] , ±[tex]\frac{4}{3}[/tex] as the possible zeros of the polynomial
Simplify the list to remove and repeated elements.
All the possible zeroes of the polynomial: f(x) = [tex]3x^{6} + 4x^{3} - 2x^{2} +4[/tex] are ±1 , ±2 , ±4 , ±[tex]\frac{1}{3}[/tex] , ±[tex]\frac{2}{3}[/tex] , ±[tex]\frac{4}{3}[/tex]
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ratio of pi?
3. whats an estimation that's fraction form?
Answer:
22/7
Step-by-step explanation:
22/7 is not very close to pi, but it is sometimes used as an estimation for pi
Answer:
22/7 is estimation
find the measures of angles of triangle DEF
Answer:
Angle E = 90° Angle D= 55° Angle F = 35°Sum of all the angles of a triangle = 180° ( angle sum property).
Angle D + Angle E + Angle F = 180°
8x - 1 + 5x + 90° = 180°
8x + 5x + 89 = 180
13x = 180 - 89
13x = 91
x = 7.
Angle D = 8x - 1
= 8(7)-1
= 56 - 1
= 55
Angle E = 90° ( given)
Angle F = 5x
= 5 * 7
= 35
Answer:
m∠E: 90°
m∠D: 55°
m∠F: 35°
Step-by-step explanation:
Since the interior angles of a right triangle sum up to 180°, the sum of angles D, E, F will equal 180°. We can then form an equation from that information.
[tex]90+(8x-1)+5x=180\\13x-1=90\\13x=91\\x=7[/tex]
From this, we can plug in the variable.
[tex]mE=90\\mD=55\\mF=35[/tex]
Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.
-x³+4x-15; x+3
Is x + 3 a factor of -x +4x-15?
Yes or no?
Yes, by using the factor theorem and synthetic division method, x + 3 is a factor of -x³ + 4x - 15.
What is the factor theorem?
According to the factor theorem, a given polynomial of f(x) has a factor if and only if f=0.
From the given information:
The factor of -x³ + 4x - 15 is -(x+3)(x² - 3x + 5) = 0Using the synthetic division method:
[tex]\mathbf{= \dfrac{-x^3+4x - 5}{x+3} }[/tex]
[tex]\mathbf{\implies \dfrac{-(x+3) (x^2-3x + 5)}{x+3} }[/tex]
Cancel out the common factors, we have:
[tex]\mathbf{\implies - (x^2-3x + 5)}[/tex]
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Which of the numbers below are whole numbers? Check all that apply.
A. 6830
B. 66
C. 717.59
D. 808
E. 42.3
F. 1/10
Step-by-step explanation:
Anything which has a decimal point is not a whole number
6830 is
66 is
717.59 is not
808 is
42.3 is not
1/10 = 0.1 ergo is not
Which equation has roots of 3 ± √2?
Answer:
D.
Step-by-step explanation:
What is the approximate value of x in the diagram below? (Hint: You will need to use one of the trigonometric ratios given in the table.) sin 40° cos 40° 50° 0.643 0.766 0.839 tan 40° 90°
Answer:
x is approximately 20.89
Step-by-step explanation:
cos(40°) = 16/x
x cos(40°) = 16
x = 16 / cos(40°) = 16/.766 = 20.89
The approximate value of x in the diagram is,
⇒ x = 20.77
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Now, We can formulate by the given figure;
⇒ sin 50° = 16 / x
⇒ 0.77 = 16 / x
⇒ x = 16 / 0.77
⇒ x = 20.77
Thus, The approximate value of x in the diagram is,
⇒ x = 20.77
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If k(x) = 5x-6, which expression is equivalent to (k+ k)(4)?
Example:
[tex](f+g)(x)=f(x)+g(x)[/tex]
To add this, we can substitute in the functions and combine like terms.
Solving the QuestionWe're given:
[tex]k(x)=5x-6[/tex][tex](k+k)(4)=?[/tex]Add k to k:
[tex](k+k)(x) = k(x)+k(x)\\(k+k)(x) = 5x-6+5x-6\\(k+k)(x) = 10x-12[/tex]
Input x as 4:
[tex](k+k)(4) = 10x-12\\(k+k)(4) = 10(4)-12\\(k+k)(4) = 40-12\\(k+k)(4) = 28[/tex]
Answer[tex](k+k)(4)=28[/tex]
(k+k)(4) is equivalent to 28.
What is function ?If we have two non-empty sets X & Y, then each element of X is relative to at least one element of Y. This relation between elements of two sets is called function.
Addition of two functions : If f(x) & g(x) be two functions, then
(f+g)(x) = f(x)+g(x)
What is the required result ?Given, k(x) = 5x-6
Now, Adding function k with k we get,
(k+k)(x) = k(x)+k(x)
= (5x-6)+(5x-6)
= 5x-6+5x-6
= 10x-12
We have to find, (k+k)(4)
∴ (k+k)(4) = (10×4)-12
= 40-12
= 28
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A cab company charges a $5 boarding rate in addition to its meter which is $3
for every mile. What is the equation of the line that represents this cab
company's total charge?
Re
co
Answer:
m3+5
Step-by-step explanation:
m is miles
take the number of miles multiply by3
take that answer add 5
The equation that represents the cab's total charge is y = 3x + 5 , Option A is the correct answer.
What is an Equation ?A statement that relate two expressions with an equal sign is called an Equation.
It is given that
A cab company charges a $5 boarding
Charges for every mile is $3 per mile
Let x be the mile travelled
The cab's total charge is represented by y
then y = 3x + 5
Therefore the equation that represents the cab's total charge is y = 3x + 5 , Option A is the correct answer.
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A radioactive substance decays from 90 mg to 12.6 mg in 29 years according to the exponential decay model y=ae−bx , where a is the initial amount and y is the amount remaining after x years.
Find the b -value.
Use the EXACT b -value to write the exponential decay model for this substance with initial amount 90 mg, then use that model to find the half-life.
Find the half-life.
The half life of the radioactive substance is 10.22 years.
What is Half Life ?Half Life is the amount of time needed by the radioactive substance to reduce to its half concentration (as compared to the initial concentration).
It is given that
y = ae⁻ᵇˣ
here a is the initial amount , y is the amount remaining after x years
a = 90mg at x =0
Value of y = 12.6 mg at x = 29 years
On substitution of value
12.6 = 90 e⁻²⁹ᵇ
0.14 = e⁻²⁹ᵇ
b = 0.0678
The equation is
[tex]\rm y = 90 e^{-0.0678 * x}\\[/tex]
Half life is when the concentration is reduced to half
On 1st half life , the concentration = 90/2 = 45 mg
[tex]\rm 45 = 90 e^{-0.0678 * x}\\[/tex]
x = 10.22 years
Therefore the half life of the radioactive substance is 10.22 years.
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pls answer this math problem
Answer:
-5
Step-by-step explanation:
Substituting x=4 into the equation gives a 2-step linear equation in y. It is solved by isolating the variable and making its coefficient be 1.
__
use x=4When x=4, the equation becomes ...
-3x +9y = -57
-3(4) +9y = -57
-12 +9y = -57
solve 2-step equationThe first step is to "isolate" the variable term (9y) by adding the opposite of the constant that is on the same side of the equation. The result is that the variable term is by itself on one side of the equal sign.
-12 +12 +9y = -57 +12 . . . . . add the opposite of -12
9y = -45 . . . . . . . . . . . . . . simplify
The second step is to make the coefficient of y be 1. We do that by multiplying by its inverse, 1/9. Equivalently, we divide by 9.
(1/9)(9y) = (1/9)(-45) . . . . multiply by the inverse of 9
y = -5 . . . . . . simplify
John can ride his bicycle at a rate of 14 miles per hour. Convert this rate to feet per second_
O 250.33 feet per second
Answer:
Step-by-step explanation:
Givens
r = 14 miles / hour
Problem
Convert to feet per second.
Solution
Later on, you will learn how to solve these kinds of conversion problems using a method called Unit Analysis. Since you likely have not been taught this method, will just use proportions.
1 mile = 5280 feet
14 miles = x Cross multiply
x = 14 * 5280 Simplify
x = 73920 feet
1 hour = 3600 seconds
Answer
r = 73920 feet / 3600 seconds
r = 20.533 feet / secpmd
what is the range of the ordered pairs shown in the graph?
D
Step-by-step explanation:
The points dx are at -1, 1, 2 and 3 so it must be D
Answer:
To find the range,
first see the value of each points -
first = (3,5)
second = (2,0)
third = ( 1,3)
fourth, ( -1, 2)
let's take X Axix to find the range
so the range is ( -1, 1 , 2 ,3)
Option D is correct
area of a trapezium base 8 top6 height 4
The area of a trapezium with base 8 top 6 height 4 is 28 cm².
Given that, base of trapezium (b)=8 cm, top of trapezium (a)=6 cm and height of trapezium = 4 cm.
What is the area of a trapezium?
The trapezium is a quadrilateral with pair of sides parallel. The area of a trapezium is the area enclosed within its four sides.
We know that area of a trapezium [tex]=\frac{1}{2}(a+b) \times h[/tex]
Where a and b are parallel sides of a trapezium.
Now, the area of a given trapezium [tex]=\frac{1}{2}(6+8) \times 4[/tex] cm²
=14×2=28 cm²
Therefore, the area of a trapezium with base 8 top 6 height 4 is 28 cm².
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Mitch needs to do his laundry. It takes him 75 minutes to do each load
when he washes and dries the load. It takes him 43 less minutes if he
hangs up his laundry to dry. He decides to hang up one load of laundry
to dry.
Mitch writes the equation 75r -43 = 332, where x is the number of loads
of laundry he needs to do in order to determine how long it is going to
take him.
The next step Mitch wrote to solve the equation is shown here: 75r = 375
Which property did he use to get to this step?
A
addition property of equality
B
distributive property
C
subtraction property of equality
D
combining like-terms
Answer: [A] addition property of equality
Step-by-step explanation:
Mitch used the addition property of equality because he added 43 to both sides of the equation.
75r - 43 = 332
43 + (75r - 43) = (332) + 43
75r = 375
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Suppose we want to choose 2 colors, without replacement, from the 3 colors red, blue, and green . How many ways can this be done, if the order of choices is relevant
The 2 colors can be chosen in 6 different ways.
In how many ways can the colors be chosen?Here we need to identify the selections and the numbers of options for each.
Here the selections are:
Color 1.Color 2.And the numbers of options for each are:
Color 1: 3 options (there are 3 colors).color 2: 2 options (one is already taken).The total number of combinations is:
C = 3*2 = 6
The 2 colors can be chosen in 6 different ways.
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Put the steps in order to solve the literal equation for y in terms of x.
6x+2y+ 8 = 180
Answer:
x = [tex]\frac{172-2y}{6}[/tex]
Step-by-step explanation:
6x + 2y + 8 = 180 ( subtract 8 from both sides )
6x + 2y = 172 ( subtract 2y from both sides )
6x = 172 - 2y ( divide both sides by 6 )
x = [tex]\frac{172-2y}{6}[/tex]
Evaluate the expression. 7^14/7^15 Evaluate the expression . 714 715
Answer:
1/7
Step-by-step explanation:
Alternative Form: 0.142857, 7^-1
complete the pattern 2, 6, 21, 88, ...
Answer:
445
Step-by-step explanation:
I think it is 445 because each term is +1 and time is the number of terms you want to find.
So
(2+1) time 2 = 6
(6+1) time 3 = 7
(88+1) time 5 = 445
Which expression is equivalent to (r^-7)^6?
Answer:
Step-by-step explanation:
Answer:
[tex]\frac{1}{r^4^2}[/tex] (option B)
Step-by-step explanation:
[tex]\left(a^b\right)^c=a^{bc},[/tex]
So, we need to first multiple -7 × 6 (= -42)
our new value is [tex]r^{-42\\}[/tex]
[tex]\:a^{-b}=\frac{1}{a^b}[/tex]
So, we simplify [tex]r^{-42\\}[/tex] to [tex]\frac{1}{r^4^2}[/tex]
What are the solutions to the following system of equations?
2x − y = 6
y = x2 − 9
(3, 0) and (−1, −8)
(3, 0) and (4, 2)
(−3, 0) and (−1, −8)
(−3, 0) and (4, 2)
Answer:
(3, 0) and (−1, −8)
Equation's:
2x − y = 6y = x² − 9Substitute equation 2 into 12x − (x² − 9) = 6
2x - x² + 9 = 6
-x² + 2x + 9 - 6 = 0
-x² + 2x + 3 = 0
x² - 2x - 3 = 0
x² - 3x + x - 3 = 0
x(x - 3) + 1(x - 3) = 0
(x + 1)(x - 3) = 0
x = -1, x = 3
Find values for yIf x = -1, then y = (-1)² - 9 = -8
If x = 3, then y = (3)² - 9 = 0
Solution Set:(x, y) = (-1, -8), (3, 0)
Help my son please!!!
Answer:
that makes no sence at all i read it over 3 times and still font understand a word of it
sorry :(
Which equation is equivalent to log3(x+5) = 2
Answer:
[tex]3^2=x+5[/tex]
Step-by-step explanation:
Given equation:
[tex]\log_3(x+5)=2[/tex]
Method 1
[tex]\textsf{Using the Log law:} \quad \log_ab=c \:\: \Longleftrightarrow \:\: a^c=b[/tex]
[tex]\implies \log_3(x+5)=2[/tex]
[tex]\implies 3^2=x+5[/tex]
Method 2
Make both sides of the equation the index to base 3:
[tex]\implies \log_3(x+5)=2[/tex]
[tex]\implies 3^{\log_3(x+5)}=3^2[/tex]
Apply the log law [tex]a^{\log_ax}=x[/tex] :
[tex]\implies x+5=3^2[/tex]
Swap sides:
[tex]\implies 3^2=x+5[/tex]
Solve for x
Although the question hasn't asked to solve for x, here is the solution:
[tex]\implies 3^2=x+5[/tex]
[tex]\implies 9=x+5[/tex]
[tex]\implies x=9-5[/tex]
[tex]\implies x=4[/tex]
Check
Substitute the found value of x into the original equation:
[tex]x=4 \implies \log_3(4+5)=\log_39=2 \quad \leftarrow\textsf{correct}[/tex]
[tex]\\ \rm\Rrightarrow log_3(x+5)=2[/tex]
log_a^b=c then b=a^c[tex]\\ \rm\Rrightarrow x+5=3^2[/tex]
[tex]\\ \rm\Rrightarrow x+5=9[/tex]
[tex]\\ \rm\Rrightarrow x=9-5[/tex]
[tex]\\ \rm\Rrightarrow x=4[/tex]
The ratio of apples to oranges is 1 to .
For every apples, there are 6 oranges.
For every 4 apples, there are oranges.
Apples are % of the total number of fruits.
the product of a quarter of 3 more than a number a and 2 times a number b
Answer:
[tex] \frac{1}{4} (3a + 2b)[/tex]
The expression from the given condition is 1/4(3a+4b).
We have given that,
The product of a quarter of 3 more than a number a and 2 times a number b.
What is the quarter?
The quarter means divided into four equal or corresponding parts.
Therefore we get the expression from the given condition is
1/4(3a+4b).
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Which describes how the parent function, f(x) = |x|, is transformed to show the function
f(x) = 0.1|x – 3|?
It is wider and shifted 3 units to the left.
It is wider and shifted 3 units to the right.
It is narrower and shifted 3 units to the left.
It is narrower and shifted 3 units to the right.
It is wider and shifted 3 units to the left , Option A is the right answer.
What is a Function ?Function is a mathematical statement that shows relation between two variables.
The parent function given is
f(x) = |x|
The transformed function is given by
f(x) = 0.1|x -3|
The function is shifted towards the left
and as the scale factor is 0.1 therefore , It is wider
Therefore Option A is the right answer.
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Answer:
The answer for this is B.
Step-by-step explanation:
Figured it out the hard way on EDGE. 2022
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