Answer:
y - 1 = 2(x + 2)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 2 and (a, b) = (- 2, 1), thus
y - 1 = 2(x - (- 2)), that is
y - 1 = 2(x + 2) ← in point- slope form
Today is Arif’s 12th birthday and his father’s 40th birthday. How many years from today will Arif’s father be twice as old as Arif at that time?
A store had 100 t-shirts. Each month, 30% of the t-shirts were sold and 25 new t-shirts arrived in shipments. Which recursive function best represents the number of t-shirts in the store, given that f(0) = 100?
The correct recursive function is: [tex]\[ f(n) = f(n-1) \times (1 - 0.30) + 25 \][/tex]
Let's break down the problem:
At the start, there are 100 t-shirts in the store (f(0) = 100).
Each month, 30% of the current stock is sold, and 25 new t-shirts arrive.
So, if we denote the number of t-shirts in the store at the beginning of the nth month as f(n), we can represent the recursive relationship as follows:
f(n) = f(n-1) * (1 - 0.30) + 25
This equation means that the number of t-shirts in the store at the beginning of the nth month is equal to 70% of the number of t-shirts at the beginning of the previous month (because 30% were sold), plus 25 (because 25 new t-shirts arrive).
In this function:
- [tex]\( f(n) \)[/tex] represents the number of t-shirts in the store at the beginning of the nth month.
- [tex]\( f(n-1) \)[/tex] represents the number of t-shirts in the store at the beginning of the (n-1)th month.
- [tex]\( (1 - 0.30) \)[/tex] represents 70% of the t-shirts from the previous month remaining after 30% are sold.
- [tex]\( + 25 \)[/tex] represents the 25 new t-shirts that arrive each month.
Complete question: A store had 100 t-shirts. Each month, 30% of the t-shirts were sold and 25 new t-shirts arrived in shipments. Which recursive function best represents the number of t- shirts in the store, given that f(0)=100?
a-f(n)=f(n-1) 0.3+25,n>0
b-f(n)=100-f(n-1) = ( 3.3+25 n>0
c-f(n)=f(n-1) -( 0.7+25 n>0
d-f(n)=100-f(n-1) - C 7+25 n>0
Solve each equation. 6x^2+1=13
Answer:
The solution of given equation is x = ±√2
Step-by-step explanation:
It is given that an equation
6x² + 1 = 13
To find the solution of given equation
6x² + 1 = 13 can be written as,
⇒ 6x² = 13 - 1
6x² = 12
x² = 12/6 = 2
x = ±√2
Therefore the solution of given equation is x = ±√2
Jordan is kayaking upstream. The following equation models his speed: f(x) = 2x2 − 4x − 9, where x is Anna's speed relative to land. What is the domain of the function? x ≥ 1 x ≤ −4 x ≥ −9 All real numbers
Answer:
All real numbers
Step-by-step explanation:
The given equation is:
[tex]f(x) = 2 {x}^{2} - 4x - 9[/tex]
where x is Ana's speed.
This is a quadratic function.
A quadratic function is a polynomial function.
All polynomial functions are are continuous and defined for all real values of x.
Therefore the domain of
[tex]f(x) = 2 {x}^{2} - 4x - 9[/tex]
is all real numbers.
Answer:
All real numbers
Step-by-step explanation:
The domain of a continuous parabola is always all real numbers or −∞ ≤ x ≤ ∞ because the ends of the parabola continue forever and when you graph this equation, you see that the ends of the parabola never stops, it continues on and on and on.
Is this right? Or is the answer B?
For this case we must find an expression equivalent to:
[tex]\sqrt [4] {f}[/tex]
By definition of properties of powers and roots we have:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So, rewriting the given expression we have:
[tex]f ^ {\frac {1} {4}}[/tex]
Answer:
Option 1
Answer:
f^(1/4)
Step-by-step explanation:
The fourth power of f, expressed with a rational exponent, is f^(1/4).
The average rate of change of g(x) between x = 4 and x = 7 is 5/6. Which statement must be true?
A. g(7)-g(4)=5/6
B. g(7-4)/7-4=5/6
C. g(7)-g(4)/7-4=5/6 D. g(7)/g(4)=5/6
Answer:
[tex]\frac{g(7)-g(4)}{7-4}=\frac{5}{6}[/tex]
So it looks like C.
Step-by-step explanation:
Average rate of a function g(x) on the interval from x=a to x=b is given by the formula:
[tex]\frac{g(b)-g(a)}{b-a}[/tex].
You can even say:
[tex]\frac{g(a)-g(b)}{a-b}[/tex].
So we have from x=4 to x=7, so the formula becomes:
[tex]\frac{g(7)-g(4)}{7-4}[/tex]
We are given this is equal to 5/6.
Answer:
Its C
Step-by-step explanation:
Given f(x) = -9x + 3 and g(x) = x4, choose
the expression for (fºg)(x).
Click on the correct answer.
-36x4 + 12
(-9x + 3)4
dxt + 3x4
-9x4+3
Answer:
The correct answer is the last one, at the bottom.
Step-by-step explanation:
You need to change in f(x) every 'x' for the expression given in g(x), since you have to build a compound function (fºg)(x).
So F(g(x))= F(x4)=-9*(x4)+3
Resulting (fºg)(x)=-9x4+3 (I only changed 'x' for 'x4', the term +3 is not changed since that is not a variable term, is just a constant number.
If sine theta equals one over three, what are the values of cos θ and tan θ?
cosine theta equals plus or minus four over three, tangent theta equals plus or minus one over two
cosine theta equals plus or minus two times square root of two over three, tangent theta equals plus or minus square root of two over four
cosine theta equals plus or minus four over three, tangent theta equals negative one over two
cosine theta equals plus or minus two times square root of two over three, tangent theta equals negative square root of two over two
Answer:
cosine theta equals plus or minus two times square root of two over three, tangent theta equals plus or minus square root of two over four
Step-by-step explanation:
Given:
sinθ=1/3
θ=19.47 degrees
then
cosθ= cos(19.47)=0.942 = 2(√2/3)
tanθ=tan(19.47)=0.35= √2/4
Hence option two is correct:cosine theta equals plus or minus two times square root of two over three, tangent theta equals plus or minus square root of two over four!
Answer:
So second choice.
[tex]\cos(\theta)=\pm \frac{2\sqrt{2}}{3}[/tex]
[tex]\tan(\theta)=\pm \frac{\sqrt{2}}{4}[/tex]
Step-by-step explanation:
I'm going to use a Pythagorean Identity, name the one that says:
[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex].
We are given: [tex]\sin(\theta)=\frac{1}{3}[/tex].
Inserting this into our identity above gives us:
[tex](\frac{1}{3})^2+\cos^2(\theta)=1[/tex]
Time to solve this for the cosine value:
[tex]\frac{1}{9}+\cos^2(\theta)=1[/tex]
Subtract 1/9 on both sides:
[tex]\cos^2(\theta)=1-\frac{1}{9}[/tex]
[tex]\cos^2(\theta)=\frac{8}{9}[/tex]
Square root both sides:
[tex]\cos(\theta)=\pm \sqrt{\frac{8}{9}}[/tex]
9 is a perfect square but 8 is not.
8 does contain a factor that is a perfect square which is 4.
So time for a rewrite:
[tex]\cos(\theta)=\pm \frac{\sqrt{4}\sqrt{2}}{3}[/tex]
[tex]\cos(\theta)=\pm \frac{2\sqrt{2}}{3}[/tex]
So without any other give information we can't know if cosine is positive or negative.
Now time for the tangent value.
You can find tangent value by using a quotient identity:
[tex]\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}[/tex]
[tex]\tan(\theta)= \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}[/tex]
Multiply top and bottom by 3 get's rid of the 3's on the bottom of each mini-fraction:
[tex]\tan(\theta)=\pm \frac{1}{2 \sqrt{2}}[/tex]
Multiply top and bottom by sqrt(2) to get rid of the square root on bottom:
[tex]\tan(\theta)=\pm \frac{1(\sqrt{2})}{2\sqrt{2}(\sqrt{2})}[/tex]
Simplifying:
[tex]\tan(\theta)=\pm \frac{\sqrt{2}}{2(2)}[/tex]
[tex]\tan(\theta)=\pm \frac{\sqrt{2}}{4}[/tex]
The PTO purchased 6 gallons of ice cream for a party if they served 2/3 cup to each student how many student will be served ice cream?
Please answer fast
Answer:
144 people
Step-by-step explanation:
1 gallon = 4 quarts
6 gallons = 6*4 quarts
6 gallons = 24 quarts
1 quarts= 2 pts
24 quarts = 2*24 = 48 pts
1 pts = 2 cups
48 pts = 48 * 2 cups = 96 cups
We know 6 gallons = 96 cups
96 cups ÷ 2/3 cups per person =
Copy dot flip
96 * 3/2 = 144 people
If the distance between two objects is increased, the gravitational attraction between them will: increase decrease remain the same
WILL GIVE BRAINLIST please help I beg
Answer:
96°
Step-by-step explanation:
An angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc.
x = 168/2 = 84°
A straight angle is 180 degrees
y = 180 - x = 180 - 84 = 96°
Write the sum using summation notation, assuming the suggested pattern continues. -9 - 4 + 1 + 6 + ... + 66
Answer:
Summation notation is:
[tex]\sum_{n=1}^{16}[5(x-1)-9][/tex]
If you prefer it a little more simplified:
[tex]\sum_{n=1}^{16}(5x-14)[/tex]
Step-by-step explanation:
First my favorite part, finding a pattern between the consecutive terms.
This is an arithmetic series because the terms are going up by 5 each time.
So arithmetic sequence, think linear equations:
x | y
1 -9
2 -4
3 1
4 6
..................
n 66
We are going to have to find that n but will will eventually...
The equation for a line in point slope form is [tex]y-y_1=m(x_x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point on the line and m is the slope.
We are already have the slope is 5 (the slope is the common difference in arithmetic sequence).
I'm going to use the first point (1,-9).
So the equation in point slope form is [tex]y-(-9)=5(x-1)[/tex]
Subtract 9 on both sides:
[tex]y=5(x-1)-9[/tex]
Now we need to know how many terms we are adding so what is x if y=66.
[tex]66=5(x-1)-9[/tex]
Add 9 on both sides:
[tex]75=5(x-1)[/tex]
Divide both sides by 5:
[tex]15=x-1[/tex]
Add 1 on both sides:
[tex]16=x[/tex]
We have 16 terms in this sequence where the 16th term is 66.
Summation notation is:
[tex]\sum_{n=1}^{16}[5(x-1)-9][/tex]
You could simplify the 5(x-1)-9.
Distribute: 5x-5-9
Add like terms: 5x-14
Answer:
Step-by-step explanation:
Use complete sentence to describe the net of a rectangular pyramid
Answer:
The net of a rectangular pyramid is consisting of a rectangle, for the base, and there are 4 more triangles that make up the lateral faces, and the triangles make the pyramid.
What is the measure of
Answer:
I think (c) 120 is right answer.
Answer:
C. 120°
Step-by-step explanation:
Since this is an isosceles triangle [two congruent sides], m<B is also 30°. Now, we have to the m<A by using the Interior Angles Theorem [m<1 + m<2 + m<3 = 180°]. So we do this:
60 + m<A = 180; 120 = m<A
I am joyous to assist you anytime.
3. Is the relationship shown by the data linear? If so, model the data with an equation X | Y 1 ,5| 5,10| 9,15| 13,20|
Answer:
[tex]y=\frac{5}{4}x+\frac{15}{4}[/tex]
Step-by-step explanation:
x | y
-------
1 5
5 10
9 15
13 20
This one is linear because as x goes up by the same number so does y. So the ratio of difference of y to difference of x is the same per pair of points.
So a linear equation in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.
To find the slope, I'm going to line up the points vertically and subtract, then put 2nd difference over 1st difference. Like so,
( 1 , 5)
-( 5 , 10)
----------------
-4 -5
So the slope is 5/4 which makes sense since the y's are going up by 5 each time and the x's are going up by 4 each time.
So we have m=5/4. Let's plug that into our y=mx+b.
y=5/4 x+b
To find b, we need to use y=5/4 x+b along with one of the given points.
Choose; it doesn't matter. I like (1,5) I guess.
y=5/4 x +b with (1,5)
5=5/4 (1)+b
5=5/4 +b
Subtract 5/4 on both sides:
5-5/4=b
20/4-5/4=b (Found a common denominator)
15/4=b
The y-intercept is 15/4 so b=15/4.
So the equation for the line in slope-intercept form is y=5/4 x +15/4.
[tex]y=\frac{5}{4}x+\frac{15}{4}[/tex]
Answer:
It is linear.
The equation is 5x - 4y = -15.
Step-by-step explanation:
If it is linear then the slope between consecutive points will be the same.
Slope = (10-5)/(5-1) = 5/4.
slope = (15-10)/ (9-5) = 5/4
slope = (20-15)/ (13-9) = 5/4.
So the data relationship is linear.
y - y1 = m(x - x1)
Using the point (1, 5)
y - 5 = 5/4(x - 1)
y = 5/4x - 5/4 + 5
y = 5/4x + 15/4
4y = 5x + 15
5x - 4y = -15.
x + 5 = -3^x + 4
A. X= -2.25
B. X= 3.75
C. X= -1.25
D. X= 1.25
Answer:
C. X= -1.25
Step-by-step explanation:
x + 5 = -3^x + 4
We change x for -1.25
-1.25 + 5 = -3^(-1.25) + 4
3.75=-0.25+4
3.75=3.75
Same number on both sides, therefore is correct!
I hope you find this information useful and interesting! Good luck!
8. 37.5 ÷2.5 , can y'all please help me with this one and I'm Soo close to getting an 100
Answer:
15
Step-by-step explanation:
37.5÷2.5 goes in 15 times
Answer:
37.5 ÷ 2.5 = 15
If m ∥ k and m ∥ ℓ, then _____
Answer: I think it’s t II k
Step-by-step explanation:
If m is parallel to k and m is also parallel to ℓ, then by the transitive property of parallel lines, k must be parallel to ℓ.
Explanation:If m ∥ k and m ∥ ℓ, then k is parallel to ℓ. In terms of geometry, when a line m is parallel to lines k and ℓ, and all the lines are coplanar, then lines k and ℓ must be parallel to each other as well. This is due to the transitive property of parallel lines which states that if two lines are parallel to the same line, they are parallel to each other. An example of this could be railway tracks: if the sleepers (the wooden blocks) are considered to be line m, which is parallel to both rails (k and ℓ), the rails (k and ℓ) have to be parallel to each other in order for the train to travel smoothly.
Learn more about Transitive Property of Parallel Lines here:https://brainly.com/question/2437149
#SPJ2
Find y. Thank you so much if you can answer!!!
Answer:
Y=3
Step-by-step explanation:
Sin30=y/6
y=6sin30
Y=3
Please HELP me I need it :)
Answer:
C
Step-by-step explanation:
Note that if x = h is a root of a polynomial f(x) then f(h) = 0
Note the sum of the coefficients of the given polynomial
x³ + 4x² + x - 6 is
1 + 4 + 1 - 6 = 0
Hence x = 1 is a root( zero) and (x - 1) is a factor
The pair of values below is from a direct variation. Find the missing number.
(4,6) and (x,3)
Answer:
The answer is 2.
2 since 6/4=3/2
Step-by-step explanation:
Since your relation is a direct variation then the points on your line are of the form y=kx where k is the constant of variation (also called constant of proportionality)
If y=kx then y/x=k.
So all the points in this relation since it is a direct variation will be equal to y-coordinate/x-coordinate.
So we are going to solve this proportion:
[tex]\frac{6}{4}=\farc{3}{x}[/tex]
Again I put y/x from each point. They should have same ratio because this is a direct variation.
Cross multiply:
[tex]6(x)=4(3)[/tex]
[tex]6x=12[/tex]
Divide boht sides by 6:
[tex]x=\frac{12}{6}[/tex]
[tex]x=2[/tex]
Answer:
Step-by-step explanation:
You are solving for the direct variation. This means that the amount of change for is consistent for both x & y:
Note: (x , y) & (x₁ , y₁)
(x , y) = (4 , 6)
(x₁ , y₁) = (x , 3)
Set the two equal to each other:
(4 , 6) = (x , 3)
Find common denominators (y). Remember that what you multiply to one you multiply to the other:
(4 , 6) = (x * 2, 3 * 2) = (2x , 6)
Simplify. Isolate the variable x. Divide:
(4) = (2x)
(4)/2 = (2x)/2
x = 4/2
x = 2
x = 2 is your answer.
Which of the following problems would NOT have a solution?
Six pizzas are shared equally among three people, and you want to know how much each person gets.
Three pizzas are shared equally among two people, and you want to know how much each person gets.
Zero pizzas are shared equally among three people, and you want to know how much each person gets.
Two pizzas are shared equally among zero people, and you want to know how much each person gets.
Answer:
The correct option is D) Two pizzas are shared equally among zero people, and you want to know how much each person gets.
Step-by-step explanation:
Consider the provided information,
We need to identify the option which has no solution,
Consider the option A)
Six pizzas are shared equally among three people, and you want to know how much each person gets.
We can find how much each person gets by dividing the number or pizza with number of people:
Each person gets = 6/3 = 2
That means each person gets 2 pizza.
The problem has a solution.
Consider the option B)
Three pizzas are shared equally among two people, and you want to know how much each person gets.
We can find how much each person gets by dividing the number or pizza with number of people:
Each person gets = 3/2 = 1.5
That means each person gets 1.2 pizza.
The problem has a solution.
Consider the option C)
Zero pizzas are shared equally among three people, and you want to know how much each person gets.
We can find how much each person gets by dividing the number or pizza with number of people:
Each person gets = 0/3 = 0
That means each person gets 0 pizza.
The problem has a solution.
Consider the option D)
Two pizzas are shared equally among zero people, and you want to know how much each person gets.
We can find how much each person gets by dividing the number or pizza with number of people:
Each person gets = 2/0 = No solution
As we know any number divided by 0 has no solution.
Thus, the problem has no solution.
Hence, the correct option is D) Two pizzas are shared equally among zero people, and you want to know how much each person gets.
Solve this (they are all fractions)
6/11=n+7/9
What does r equal
Answer:
[tex]\large\boxed{n=\dfrac{-23}{11}=-2\dfrac{1}{11}}[/tex]
Step-by-step explanation:
[tex]\dfrac{6}{11}=\dfrac{n+7}{9}\qquad\text{cross multiply}\\\\11(n+7)=(6)(9)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(11)(n)+(11)(7)=54\\\\11n+77=54\qquad\text{subtract 77 from both sides}\\\\11n=-23\qquad\text{divide both sides by 11}\\\\n=\dfrac{-23}{11}[/tex]
18. The table shows the amount of money in a savings account after several weeks
Week
Savings
$125
$140
$155
$170
$185
$200
a. Is the sequence arithmetic or geometric? Explain. Find the common difference or common
b. Write a recursive formula for the sequence
c. Write an explicit formula for the sequence
Answer:
a. Arithmetic
b. [tex]a_{n} = a_{n-1} + 15[/tex]
c. [tex]a_{n} = 15n + 125[/tex]
Step-by-step explanation:
A sequence is arithmetic when the difference between one term and the next is a constant. On the other hand, a sequence is geometric when the next term is found by multiplying the previous by a constant.
In this case, the next term of the sequence can be found by adding $15. Therefore, the sequence is ARITHMETIC ✔️
The recursive formula will be the following: [tex]a_{n} = a_{n-1} + 15[/tex]
The explicit formula is the following: [tex]a_{n} = 15n + 125[/tex]
A hook in an office storage closet can hold no more than 6 pounds. An order of jumbo paperclips weighs 2 pounds and an
order of packing tape weighs 3 pounds. If x is the number of orders of paperclips and y is the number of orders of packing
tape, which graph represents how many of each order could be put in a bag hanging from the hook?
Answer:
the first graph: line passing through the points (3, 0) and (0,2), and the shaded region is below the line.Explanation:
1) Find the expression that represents the situation.
The expression that represents the situation is an inequality:
Number of orders of paper clips: xWeight of an order of paper clips: 2 lbsTotal weight of x orders of paper clips: 2xNumber of orders of packing tape: yWeight of an order of packing tape: 3 lbsTotal weight of y orders of packing tape: 3yTotal weight of paper clips and packing tape in a bag: 2x + 3yMaximum weight hold by the hook: 6 lbsHence, the total weight must be less than or equal to (≤) 6 lbs, which is:
2x + 3y ≤ 62) Graph of the inequality 2x + 3y ≤ 6
Line:
Border line: 2x + 3y = 6x-intercept: y = 0 ⇒ 2x = 6 ⇒ x = 6 /2 ⇒ x = 3 ⇒ point (3,0)y-intercept: x = 0 ⇒ 3y = 6 ⇒ y = 6 /3 ⇒ y = 2 ⇒ point (0,2)Shaded region:
Symbol ≤ means that the line is included, which is represented with a solid line, and the region is below the line.
Conclusion: the graph is the line passing through the points (3, 0) and (0,2), and the shaded region is below the line, so that is the first graph of the picture.
Note: strictly speaking, you should include the restrictions that the variables x and y cannot be negative, with which the graph would be only on the first quadrant but those constrains are not handled in the problem.
The graph is also attached.
Answer:
Answer is A
Step-by-step explanation:
What is 2/3 times 3/5 in simplest form
Answer:
[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2}{3}[/tex] × [tex]\frac{3}{5}[/tex]
Cancel the 3 on the numerator/denominator of the fractions leaving
[tex]\frac{2}{1}[/tex] × [tex]\frac{1}{5}[/tex] = [tex]\frac{2}{5}[/tex]
Answer:
2 over 5
Step-by-step explanation:
Over the last 3 evenings, Keisha received a total of 81 phone calls at the call center. The first evening, she received 6 fewer calls than the second evening. The third evening, she received 3 times as many calls as the first evening. How many phone calls did she receive each evening
Answer:
First: 15
Second: 21
Third: 45
Step-by-step explanation:
In order to create the equation we need to represent the evenings with an alebraic term, in thsi case we are going to represent the second evening with an X
Second evening:x
The first night she got 6 fewer calls than the second: Second-6=x-6
The third night she received 3 times the first: 3(first night)=3(x-6)
The equation is First Night plus second night plus third night equals 81.
[tex]First+second+third=81\\x+(x-7)+3(x-6)=81\\x+x-7+3x-18=81\\5x=81+21+6\\5x=105\\x=\frac{105}{5} \\x=21[/tex]
So the first evening he received 15 calls, the second he received 21 and the third one he received 45.
simplify : (x^-2y^-4x^3)^-2
[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x^{-2}y^{-4}x^3)^{-2}\implies (x^{-2}x^3y^{-4})^{-2}\implies (x^{-2+3}y^{-4})^{-2}\implies (x^{1}y^{-4})^{-2} \\\\\\ \stackrel{\textit{distributing the exponent}~\hfill }{(x^{-2\cdot 1}y^{-2\cdot -4})\implies x^{-2}y^8}\implies \cfrac{1}{x^2}\cdot y^8\implies \cfrac{y^8}{x^2}[/tex]
Using equivalent ratios to find a whole \/
Answer:
C.
Step-by-step explanation:
So there are 20 kids with brown hair and this represents 80% of the class total.
So this means 20=.8n since we don't know the total number of kids.
20=.8n
Divide both sides by .8
25=n
So 25 is the total number of kids.
C. is the answer
You could also setup this equation given that 80% is 80/100:
[tex]\frac{20}{\text{ total }}=\frac{80}{100}
To figure out what that total is there you can divide top and bottom of the fraction on right hand side by 4 which gives you the 20 on top and the 25 on bottom.
Box A contained 1.67 kg of flour. Box B contained 8600 g of flour. After same amount of
flour was added to each box, Box B contained 4 times as much flour as Box A. How
much flour was added to each box? Give your answer in kg.
Answer:
The amount of flour added to each box was 0.64 kg
Step-by-step explanation:
Let
x ----> the amount of flour added to each box in kg
Remember that
1 kg=1,000 g
8,600 g=8,600/1,000=8.6 kg
we know that
The linear equation that represent this situation is
(8.6+x)=4(1.67+x)
Solve for x
8.6+x=6.68+4x
4x-x=8.6-6.68
3x=1.92
x=0.64 kg
To solve this problem, we'll use algebra. Let's denote the initial amount of flour in Box A as A and in Box B as B. Also, let the amount of flour added to each box be x (in kilograms).
Given:
A = 1.67 kg
B = 8600 g, which we need to convert to kilograms. Since 1 kilogram is 1000 grams, we get:
B = 8600 / 1000 kg
B = 8.6 kg
After adding x kg of flour to each box, Box B contains 4 times as much flour as Box A. Therefore, we can set up the following equation:
B + x = 4(A + x)
Now, we plug in the values for A and B:
8.6 + x = 4(1.67 + x)
Distribute the 4 on the right side of the equation:
8.6 + x = 6.68 + 4x
Now we'll consolidate like terms:
8.6 - 6.68 = 4x - x
1.92 = 3x
To solve for x, we divide both sides by 3:
x = 1.92 / 3
x = 0.64 kg
So 0.64 kg of flour was added to each box.