Answers
1) The sum of an Octagon is 1080°
And all it's sides are congruent (same size, same angle measure)
And an Octagon has 8 sides
So do,
1080 ÷ 8 = 135°
Each side equals to 135°
2) A triangle adds up to 180°.
We have one angle that's 45° and another angle that has a little □ in it.
That little square (□) is called a right angle which = 90°
So do
90 + 45 = 135
180 - 135 = 45
So the value of x is 45°
Related Questions
Math help pleaseeeee
Answers
Answer:
[tex]x^{\frac{4}{5} }[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{x^{m} }[/tex]
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex], hence
[tex]\sqrt[5]{x}[/tex] = [tex]x^{\frac{1}{5} }[/tex], thus
[tex]x^{\frac{1}{5} }[/tex] × [tex]x^{\frac{1}{5} }[/tex] × [tex]x^{\frac{1}{5} }[/tex] × [tex]x^{\frac{1}{5} }[/tex]
= [tex]x^{\frac{4}{5} }[/tex]
Answer:
[tex] x^{\frac{4}{5} }[/tex]
Step-by-step explanation:
We are given the following expression and we are to determine its most simplified form:
[tex] \sqrt [ 5 ] { x } . \sqrt [ 5 ] { x } . \sqrt [ 5 ] { x } . \sqrt [ 5 ] { x } [/tex]
We know that [tex] \sqrt [ 5 ] { x } [/tex] [tex] = x ^ { \frac { 1 } { 5 } } [/tex]
And since we have four of these like terms so the power of x will become 4, thus making it [tex] x ^4 [/tex].
When [tex] x ^ 4 [/tex] is combined with the square root 5, we get:
[tex]x^4 \times x^{\frac{1}{5}} = x^{\frac{4}{5} }[/tex]
What is the total amount of sap the trees produced that day
Answers
Answer:
wrong its 5gallons
Step-by-step explanation:
A square has a side length of 36 feet. This square is dilated by a scale factor of 2/3 to create a new square. What is the side length of the new square?
Answers
Answer:
24 feet
Step-by-step explanation:
got it right on ttm :)
If the area of a circle is 58 square feet, find the circumference. A. 42.5 ft. B. 4.25 ft. C. 22.35 ft. D. 26.99 ft.
Answers
Answer: OPTION D.
Step-by-step explanation:
The formula for calculate the circumference of a circle is:
[tex]C=2r\pi[/tex]
Where r is the radius.
The formula for calculate the area of a circle is:
[tex]A=r^2\pi[/tex]
Where r is the radius.
Solve for r from [tex]A=r^2\pi[/tex] to calculate it:
[tex]r=\sqrt{\frac{A}{\pi}}\\r=\sqrt{\frac{58ft^2}{\pi}}\\r=4.296ft[/tex]
Subsitute the radius into [tex]C=2r\pi[/tex]. Then:
[tex]C=(2)(4.296ft)\pi=26.99ft[/tex]
Answer:
D. 26.99 ft
Step-by-step explanation:
The formula for area of a circle is
A = πr², where r is the radius. We are given A = 58, so plug that in to find r...
58 = πr² solve for r...
58/π = r² (divide both sides by π)
√(58/π) = r (take the square root of both sides)
now simplify...
(√58)/(√π) = r
[(√58)(√π)]/[(√π)(√π)] = r
[√(58π)]/π = r
The formula for circumference is C = 2πr, where r is the radius....so we have
C = 2π([√(58π)]/π) now simplify...
C = 2√(58π) (the 2 pi's cancel out)
C = 26.9972124 (crunch in your calculator)
Find 4 1/5 · 7 2/3.
A. 28 2/15
B.28 3/10
C. 32 1/5
D. 32 3/5
Answers
Answer:
D. 32 3/5
Step-by-step explanation:
4 1/5 * 7 2/3
Change each number to an improper fraction
4 1/5 = (5*4+1)/5 = 21/5
7 2/3 = (3*7+2)/3 = 23/3
Multiply these together
21/5 * 23/3
483/15
Change this back to a mixed number
15 goes into 483 32 times (32*15 =480) with 3 left over
32 3/5
Answer:
The answer to this problem is C. 32 1/5.
Step-by-step explanation:
Step 1: Multiply the whole number by the denominator then add the numerator to it. Apply this to both fractions individually.
21/5 * 23/3
Step 2: Multiply the fractions.
21/5 * 23/3 = 483/15
Step 3: Simplify the fraction into the simplest form.
483/15 simplifies to 32 3/15 and then simplifies to its simplest form 32 1/5.
1) An apple drops off the apple tree from a height of 8 feet. How long does it take the apple to reach the ground? Use the function f(x) = -16x^2 + c, where c is the initial height of a falling object, to find the answer.
2) Trinette cut a square tablecloth into 4 equal pieces that she used to make two pillow covers. The area of the tablecloth was 3600 square inches. What is the side length of each piece Trinette used to make the pillow covers?
3) Elton earns x dollars per hour at the bookstore. His mother, Evelyn, earns x^2 dollars per hour as a career counselor. Twice Evelyn's wage equals $84.50. What is Elton's hourly wage? Round you answer to the nearest cent.
Answers
Answer:
Part 1) [tex]\frac{\sqrt{2}}{2}\ sec[/tex] or [tex]0.7\ sec[/tex]
Part 2) The side length of each piece Trinette used to make the pillow covers is [tex]30 in[/tex]
Part 3) Elton's hourly wage is [tex]\$6.50[/tex]
Step-by-step explanation:
Part 1)
Let
x------> the time in seconds
we have
[tex]f(x)=-16x^{2}+c[/tex]
In this problem the initial height is 8 ft
so
[tex]f(x)=-16x^{2}+8[/tex]
To find how long does it take the apple to reach the ground, equate the function to zero and solve for x
[tex]0=-16x^{2}+8[/tex]
[tex]16x^{2}=8[/tex]
[tex]x^{2}=1/2[/tex]
[tex]x=\frac{\sqrt{2}}{2}\ sec[/tex]
[tex]x=0.7\ sec[/tex]
Part 2)
step 1
The area of a square tablecloth is
[tex]A=3,600\ in^{2}[/tex]
Divided by 4
[tex]3,600/4=900\ in^{2}[/tex]
step 2
Find the length of each piece
[tex]A=b^{2}[/tex]
so
[tex]900=b^{2}[/tex]
[tex]b=30 in[/tex]
Part 3)
we know that
[tex]2x^{2} =84.50[/tex]
solve for x
[tex]x^{2} =42.25[/tex]
[tex]x=\sqrt{42.25}[/tex]
[tex]x=\$6.50[/tex]
Solve the equation.
8 (4 - x) = 7x + 2
Answers
Answer:
2
Step-by-step explanation:
8 ( 4 - x ) = 7x + 2
(Expand brackets
32 - 8x = 7x + 2
(-7x from both sides)
-15x = -30
(Divide by -15 from both sides)
x=2
Answer:
x = 2
Step-by-step explanation:
8(4 - x) = 7x + 2
Distribute the 8 on the left side.
32 - 8x = 7x + 2
Subtract 7x from both sides.
32 - 15x = 2
Subtract 32 from both sides.
-15x = -30
Divide both sides by -15.
x = 2
if f(x)=x^2+2x-3 and g(x)=x^2-9, find (f/g)(4) and (f+g)(4)
Answers
Answer:
Part 1: Find (f/g)(4) = 3
Part 2: Find (f+g)(4) = 28
Step-by-step explanation:
Part 1: Find (f/g)(4):
(f/g)(4) means divide f function by g function and simplify it. Then plug in 4 into x of that simplified function.
Let's do this:
[tex]\frac{x^2+2x-3}{x^2-9}\\=\frac{(x+3)(x-1)}{(x-3)(x+3)}\\=\frac{x-1}{x-3}[/tex]
Plugging in 4 into x gives us:
[tex]\frac{x-1}{x-3}\\=\frac{4-1}{4-3}\\=\frac{3}{1}\\=3[/tex]
The answer is 3
Part 2: Find (f+g)(4):
(f+g)(4) means add f function and g function and simplify it. Then plug in 4 into x of that simplified function.
Let's do this:
[tex](x^2+2x-3)+(x^2-9)\\=2x^2+2x-12[/tex]
Plugging in 4 into x gives us:
[tex]2x^2+2x-12\\=2(4)^2+2(4)-12\\=28[/tex]
The answer is 28
Answer: the first one is -11 and the second one is 0
step-by-step explanation:
someone answered your question but it was wrong so i had too guess and got the real answers since you know ... i ended up getting it wrong lol so yea
The answer please !!
Answers
Answer:
[tex]\frac{DE}{PQ}=\frac{3}{2}[/tex]
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional
In his problem
If Triangles DEF and PQR are similar
then
The corresponding sides are
DF and PR
FE and RQ
DE and PQ
so
[tex]\frac{DF}{PR}=\frac{FE}{RQ}=\frac{DE}{PQ}=\frac{3}{2}[/tex]
Lines A and B are represented by the equations given below: Line A: 6x + 6y = 24 Line B: x + y = 4 Which statement is true about the solution to the set of equations? (1 point) Select one: a. It is (24, 4). b. There are infinitely many solutions. c. It is (4, 24). d. There is no solution.
Answers
Answer:
I believe it is C
Step-by-step explanation:
since x+y=4 that could mean, 2+2=4 which means x and y has the same value, that is 2.
so if we make the equation
6(2)+6(2)= it WOULD equal to 24, and for that reason I think it is C.
(24,4)
Nathan and Cody are both making pizza dough at different pizzerias. Nathan uses 3 cups of water for every 8 cups of flour. Cody uses 4 cups of water for every 12 cups of flour. Use tables of equivalent ratios to determine who will use more cups of water when Nathan and Cody each use 48 cups of flour.
A.
Nathan will use 8 cups of water and Cody will only use 5 cups of water, so Nathan will use more cups of water.
B.
Cody will use 16 cups of water and Nathan will only use 11 cups of water, so Cody will use more cups of water.
C.
Cody will use 8 cups of water and Nathan will only use 6 cups of water, so Cody will use more cups of water.
D.
Nathan will use 18 cups of water and Cody will only use 16 cups of water, so Nathan will use more cups of water.
Answers
Answer:explanation:
The answer is B because Nathan will use more cups
Answer:
D
Step-by-step explanation:
Nathan uses 3 cups of water for every 8 cups of flour. Cody uses 4 cups of water for every 12 cups of flour. Create tables of equivalent ratios for Nathan and Cody to find who uses more cups of water when each use 48 cups of flour.
When they each use 48 cups of flour, Nathan will use 18 cups of water and Cody will only use 16 cups of water, so Nathan will use more cups of water.
Interest in the trainings offered at the pet shelter decreased from summer to winter. This change can be represented as -83. What is the absolute value of -83?
Answers
It would be 83.
Reason it 83 units away from 0.
I hope this helps :)
Answer:
83
Step-by-step explanation:
What is the answer to this question?
Answers
Answer: [tex]x\geq6[/tex]
Step-by-step explanation:
g°h indicates that you must plug the function h(x) into the function g(x) as you can see below:
[tex]g\°h=\sqrt{(2x-8)-4}[/tex]
Now you must simplify by adding like terms, as following:
[tex]g\°h=\sqrt{2x-12}[/tex]
By definition you have that:
[tex]2x-12\geq0[/tex]
Theen you must solve for x:
[tex]2x\geq12\\x\geq6[/tex]
Therefore, the domain is:
{[tex]x[/tex] ∈R:[tex]x\geq6[/tex]}
Then the answer is [tex]x\geq6[/tex]
Answer:
Restriction on the domain is x ≥ 6.
Step-by-step explanation:
We have given two functions.
g(x) = √x-4 and h(x) = 2x-8
We have to find the restrictions on the domain of (g o f).
(g o h)(x) = g(h(x))
(g o h)(x) = g(2x-8)
(g o h)(x) = √2x-8-4
(g o h)(x) = √2x-12
Hence, 2x-12 ≥ 0
2x ≥ 12
x ≥ 6
Hence, restriction on the domain is x ≥ 6.
So please explain this including the formula please i will give 98 points!!
Answers
Answer:
V =20.4 in^3
Step-by-step explanation:
The formula for volume of a triangular prism is
V = B *h
B is the area of the triangle which is 1/2 b*h
B = 1/2 (2.5) (3.4)
The height is 4.8 in
V = 1/2 (2.5) (3.4) * 4.8
V =20.4 in^3
Answer:
V =20.4 in^3 is your answer
Step-by-step explanation:
If the sphere shown above has a radius of 10 units, then what is the approximate volume of the sphere?
A.
400 cubic units
B.
1,666.67 cubic units
C.
666.67 cubic units
D.
1,333.33 cubic units
Answers
The approximate volume of the sphere is 4188.79 cubic units.
Calculating the volume of a sphere.
A sphere is a three-dimensional round object. The volume of a sphere can be calculated by using the formula [tex]\dfrac{4}{3} \pi r^3[/tex].
In the given question, the radius of the sphere is stated to be 10 units. So, the volume of the sphere can be determined by replacing the value of the radius into the equation. i.e.
[tex]V= \dfrac{4}{3}\pi r^3[/tex]
[tex]V= \dfrac{4}{3} \times \pi \times (10)^3[/tex]
V = 4188.79 cubic units.
Therefore, the approximate volume of the sphere is 4188.79 cubic units.
The area of a square can be found using the equation A= s2, where A is the area and S is the measure of one side of the square. Match the equation for how to slice for the side length of a square to its description.
Answers
Answer: [tex]s = \sqrt{81}[/tex]
Step-by-step explanation: A= s^2, A = 81
81 = s^2
[tex]\sqrt{81} = \sqrt{s^{2} }[/tex]
s = [tex]\sqrt{81}[/tex]
Answer:
Option 2nd is correct
[tex]s = \sqrt{81}[/tex] inches
Step-by-step explanation:
The area of a square can be found using the equation:
[tex]A=s^2[/tex] ....[1]
where,
A is the area of square
s is the measure of one side of the square.
Given that:
A square has an area of 81 square inches.
⇒A = 81
Substitute in [1] we have;
[tex]s^2 = 81[/tex]
⇒[tex]s =\pm \sqrt{81}[/tex]
∵Side of square cannot be in negative.
⇒[tex]s = \sqrt{81}[/tex] inches
Therefore:
A square has an area of 81 square inches →[tex]s = \sqrt{81}[/tex] in
Find the equation of the circle in standard form for the given center (h, k) and radius r: (h, k) = (0, 0), r = 4
Answers
Answer:
[tex]x^2+y^2=16[/tex]
Step-by-step explanation:
The equation of a circle with center (h,k) and radius r is given by the formula;
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Given (h,k)=(0,0) and r=4, we substitute the values to obtain;
[tex](x-0)^2+(y-0)^2=4^2[/tex]
The required equation is
[tex]x^2+y^2=16[/tex]
The standard form of the equation for a circle centered at the origin with a radius of 4 is x2 + y2 = 16.
The equation of a circle in standard form with the center at the origin (0, 0) and a radius of 4 is given by x2 + y2 = r2, where x and y are the coordinates of any point on the circle, and r is the radius.
Plugging the given radius into the equation, we have x2 + y2 = 42. Simplifying this, we get the equation x2 + y2 = 16. This is the standard form of the equation for the given circle.
Triangle ABC undergoes a series of transformations to result in triangle DEF .
Is triangle DEF congruent to triangle ABC ?
Select Congruent or Not congruent for each description.
Answers
question 1 is congruent. 2 is not congruent and 3 is congruent
Answer: 1) Congruent
2) Not congruent
3) Congruent
Step-by-step explanation:
We know that a rigid transformations preserves side-lengths and angle measures of a figure in such a way that the figure doesn't shrink or get enlarger. It creates congruent figures.
The three main rigid transformations are:a) reflections, b) rotations, c) translations
On the other hand a dilation changes the size of the image when the scale factor is not equal to 1. It does not produces congruent images.
Tabitha earns $7 per hour working at the mail. Last week, she worked for 12 1/4 hours. Which best describes how much money she earned?
A- a little less than $65
B- a little less than $77
C- a little less than $84
D- a little less than $90
Answers
Answer:
D
Step-by-step explanation:
7 * 12 = 84
And 1/4 hours which is 7/4 which is $1.25 more.
So she got 85.25 dollars in total, which is a little less than $90.
Beth had planned to run an average of 6 miles per hour in a race. She had a very good race and actually ran at an average of 7 miles per hour, finishing ten minutes sooner than if she had averaged 6 miles per hour. How long was the race? 6 miles? 7 miles? 18 miles? 60 miles? 70 miles?
Answers
Answer:
(x/7) = actual time
Step-by-step explanation:
Conner works 8 1/2 hours and earns $80.75. If Zoey makes an hourly rate that is proportional and earns $118.75, how many hours did she work? Plz show work:)
A. 8 1/2
B. 10
C. 12 1/2
D. 13
Answers
Answer:
Step-by-step explanation:
In 8 hours 30m Corner earns $80.75
In how many hours Zoey earns $118.75
Hours Zoey works= 510*118.75/80.75(converted 8hours into minutes by multiplying with 60)
Solving we get 12 hours 30m.
One way to determine if a given point is on the graph of a linear equation is by checking to see if it is a solution to the equation true or false
Answers
Find the slope or the y-intercept.
How many 1 metre fence panels and how nany 2 metre face panels do you need to put fencing all around the plot?
Please help.
Answers
Answer:
You need 8 2 metre face panels and 2 1 metre face panels
This is because the 2 metre face panels will completely cover the both of the 4 metre sides, and almost cover the 5 metre sides.
Then you will need 1 2 metre face panel for each of the 5 metre sides to complete the fence.
Hope I helped
Step-by-step explanation:
Which table best represents the graph of the equation theta = 45 degrees
Answers
Answer: The first option.
Step-by-step explanation:
The function is:
θ(r) = 45°
so we have a constant function (because r does not apear in the right side of the equation), this means that for every value of r, we have that θ(r) is equal to 45 degrees.
then the correct answer is the first table, because for every value of r we have that the value of theta is the same.
Table 1 best represents the graph of the equation θ(r)= 45°.
It is given that
θ(r)= 45°, which is a constant function.
What is a constant function?For a constant function, the value of the dependent variable is the same for each value of the independent variable.
So, θ will remain constant for all values of r.
r =1, θ=45°
r =2, θ=45°
r=3, θ=45°
r=4,θ=45°
Therefore, Table 1 best represents the graph of the equation θ= 45°.
To get more about function visit:
https://brainly.com/question/2292795
Find the roots of the quadratic function by completing the square: x^2 + 4x - 1 = 0
Answers
Answer:
x = - 2 ± [tex]\sqrt{5}[/tex]
Step-by-step explanation:
Given
x² + 4x - 1 = 0 ( add 1 to both sides )
x² + 4x = 1
To complete the square
add (half the coefficient of the x- term )² to both sides
x² + 2(2)x + 2² = 1 + 2² ← complete the square on the left side
(x + 2)² = 5 ← take the square root of both sides
x + 2 = ± [tex]\sqrt{5}[/tex] ← subtract 2 from both sides
x = - 2 ± [tex]\sqrt{5}[/tex]
roots are x = - 2 - [tex]\sqrt{5}[/tex] or x = - 2 + [tex]\sqrt{5}[/tex]
Final answer:
To find the roots of the quadratic function x² + 4x - 1 = 0, the equation is rearranged, a perfect square is formed by adding (b/2)² to both sides, and the square root is taken to obtain the solutions x = √{5} - 2 and x = -√sqrt{5} - 2.
Explanation:
To find the roots of the quadratic function x² + 4x - 1 = 0 by completing the square, we need to follow a series of steps:
First, we'll arrange the equation so that the x-squared and x terms are on one side, leaving the constant on the other side. In this case, we add 1 to both sides to obtain x² + 4x = 1.
Next, we find the number that needs to be added to x^2 + 4x to make it a perfect square trinomial. This number is (b/2)², where b is the coefficient of x. Here, b is 4, so we need to add (4/2)² = 4 to both sides.
Our equation now reads x² + 4x + 4 = 5. Notice that the left-hand side is a perfect square, as it can be written as (x+2)².
Finally, we take the square root of both sides, giving us x + 2 = √{5} or x + 2 = -√{5}. Therefore, the solutions are x = √{5} - 2 and x = -√{5} - 2.
To check our solutions, we could substitute them back into the original equation and ensure that the left side equals zero.
How would the graph of the function y=x2-8 be affected if the function were changed to y=x2-3
A) the graph would shift 3 units down
B) the graph would shift 5 units to the left
C) the graph would shift 5 units down
D)the graph would shift 5 units up
Answers
Answer:
D) The graph would shift 5 units up.Step-by-step explanation:
f(x) + n - shift the graph n units up
f(x) - n - shift the graph n units down
f(x - n) - shift the graph n units to the right
f(x + n) - shift the graph n units to the left
------------------------------------------------------------------
We have f(x) = x² - 8
f(x) = x² - 8 add 5 to both sides
f(x) + 5 = x² - 3
Therefore your answer is D)
The graph of the function y=x^2-8 would shift 5 units up if changed to y=x^2-3, due to the increase in the constant term.
When comparing the functions y=x^2-8 and y=x^2-3, a change in the constant term represents a vertical shift of the graph. The constant term in the function y=x^2-8 is -8, and in the function y=x^2-3 it is -3. Since -3 is greater than -8 by 5, the graph will be shifted up by 5 units. Therefore, the correct answer to how the graph of the function would be affected is that it would shift 5 units up.
What is the 9th term of the sequence? 3,-12,48,-192,
A. 786,432
B. -196,608
C. -786,432
D. 196,608
Answers
D, 196,608.
The sequence is multiplying by -4 every time.
Answer: The correct option is (D) 196608.
Step-by-step explanation: We are given to find the 9th term of the following sequence :
3, -12, 48, -192, . . .
Let a(n) denote the n-th term of the given sequence.
Then, a(1) = 3, a(2) = -12, a(3) = 48, a(4) = -192, . . .
We see that
[tex]\dfrac{a(2)}{a(1)}=\dfrac{-12}{3}=-4,\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{48}{-12}=-4,\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{-192}{48}=-4,~~.~~.~~.[/tex]
So, we get
[tex]\dfrac{a(2)}{a(1)}=\dfrac{a(3)}{a(2)}=\dfrac{a(4)}{a(3)}=~~.~~.~~.~~=-4.[/tex]
That is, the given sequence is a GEOMETRIC one with first term a = 3 and common ratio d= -4.
We know that
the n-th term of an geometric sequence with first term a and common ratio r is given by
[tex]a(n)=ar^{n-1}.[/tex]
Therefore, the 9th term of the given sequence is
[tex]a(9)=ar^{9-1}=3\times(-4)^8=3\times 65536=196608.[/tex]
Thus, the 9th term of the given sequence is 196608.
Option (D) is CORRECT.
Katie put a $980 item on layaway by making a down payment of 14% of the purchase price. How much does she have left to pay after making the down payment?
Answers
Answer:
$842.8
Step-by-step explanation:
It says that Katie already paid the 14% of the item as a down payment, so she needs to pay the remaining 86% of the item.
To get that, it is:
$980 x 86% = $842.8
(5-2i)+(3+4i)-(-6+2i)
Answers
Simplify
5 - 2i + 3 + 4i - (-6 + 2i)
Simplify brackets
5 - 2i + 3 + 4i + 6 - 2i
Collect like terms
(5 + 3 + 6) + (-2i + 4i - 2i)
Simplify
= 14
The equation (5-2i)+(3+4i)-(-6+2i) simplifies to 14 after adding real parts and imaginary parts separately, resulting in the complex number 14+0i which simplifies to 14.
Explanation:The student's question involves complex number addition and subtraction. To solve the equation (5-2i)+(3+4i)-(-6+2i), we combine like terms, which means separately adding the real parts and the imaginary parts of the complex numbers. The real parts are 5, 3, and 6 (because we subtract a negative, which becomes plus), which add up to 14. The imaginary parts are -2i, 4i, and -2i (again, subtraction of a negative becomes addition), which add up to 0i. Therefore, the final answer is 14+0i, which simplifies to 14.
There are two mixtures. One mixture contains 5% alchol and the other mixture contains 12% alchol. How much of each should be mixed to make 1000 gallons with 10% alchol
Answers
Answer:
to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture that contains 5% alcohol and 285,7 gallons of mixture that contains 12% alcohol.
Step-by-step explanation:
According to the statement, there are two mixtures. One mixture contains 5% alcohol and the other contains 12% alcohol.
We want to make 1000 gallons with 10% alcohol, so we have the following system of equations:
A + B = 1000 gallons. [1]
0.05A + 0.12B = 0.1(1000) ⇒ 0.05A + 0.12B = 100 [2]
(Where 'A' represents the mixture that contains 5% alcohol and 'B' the one that contains 12% alcohol).
Solving the system of equations:
A + B = 1000 ⇒ A = 1000 - B [3]
[3] → [2]
0.05(1000 - B) + 0.12B = 100 ⇒ 50 - 0.05B + 0.12B = 100
⇒ 0.07B = 50 ⇒ B = 714.28 ≈ B=714.3 [4]
[4] → [1]
A + B = 1000 ⇒ A + 714.3 = 1000 ⇒ A = 285,7
Therefore, to make 1000 gallons with 10% alcohol, we need 714.3 gallons of mixture 'A' and 285,7 gallons of mixture 'B'