The value of sin x is [tex]\frac{5}{13}[/tex] and the value of cos y is [tex]\frac{5}{13}[/tex]. The ratio of sin x and cos y is 1.
What is Pythagorean triplet?The Pythagorean Triples, which comprise the three positive numbers a, b, and c, are the integer solutions to the Pythagorean Theorem.
What is Pythagoras theorem?A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem.
The given triangle has sides 12 and 5.
According to the Pythagorean triplet the length of the third side is 13.
The value of sin x is [tex]\frac{5}{13}[/tex].
The value of cos y is [tex]\frac{5}{13}[/tex].
The ratio of sin x and cos y is:
[tex]\frac{sin x}{cos y} = \frac{\frac{5}{13}}{\frac{5}{13}} = 1[/tex]
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Which best describes the relationship between the line that passes through the points (9, –5) and (5, –2) and the line that passes through the points (–4, –2) and (–8, 1)?
A. parallel
B. same line
C. perpendicular
D. neither perpendicular nor parallel
The given two lines are parallel to each other. The correct answer would be an option (A).
What is the slope of the line?The slope of the line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
The lines will be parallel if they have the same slope and they will be perpendicular if the product of the slopes of the two lines is -1.
The slope of the first line can be found using the formula:
m₁ = (-2 - (-5))/(5-9) = -3/4
The slope of the second line can be found using the formula:
m₂ = (1 - (-2))/ (-8 - (-4)) = -3/4
They have identical slope, so the lines will be parallel.
Hence, the given two lines are parallel to each other.
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estimate 718-331 to nearest 100
Answer: 400
Step-by-step explanation: Max has rounded off the difference of two numbers. Max's estimate of the difference is 400.
Given information:
The first number = 718.
The second number = 331
Now, according to the question, Max estimates their difference by taking the number rounded off.
Hence, the rounding off the given number to nearest 100,
we get,
First number as 700 and Second number as 300.
Hence the difference of the obtained number can be written as:
Hence, one can conclude that, max's estimate of the difference is 400.
6. Find m4V.
Y
V
(10x-27)
(2x +29)
X
W
nswers 1-7
Since the total of the inner angles of the rhombus is 360 degrees, the angle mV has a value of 90.
what is angles ?In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that come together at a point in the middle known as the angle's vertex. An angle that is in the plane where the rays are placed can be created by two rays. An angle is also produced when two planes collide. They are known as dihedral angles. In planar geometry, an angle is the form produced by two rays or lines that share a termination. The English word "angle" comes from the Latin word "angulus," which means "horn." The vertex, also known as the sides of the angle, is where the two rays' common terminals meet.
given
m∠V + m∠W + m∠X + m∠Y = 360
10x -27 + 2x + 19 = 180
12x - 8 = 180
188 = 12x
x = 15.66
m∠V + m∠X = 180
2x = 180
x = 90
Since the total of the inner angles of the rhombus is 360 degrees, the angle mV has a value of 90.
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not sure what the answer is
The truth table for ~p ∨ q is as shown below.
~p ∨ q
T
F
T
T
How to construct the truth table for ~p ∨ q?A truth table is a table for evaluating the truth value of a truth-functional compound sentence on the basis of the truth value of its part
The truth tables for negation and disjunction are shown below:
Negation
p ...... ~p
T F
F T
Disjunction
p ..... q ..... p v q
T T T
T F T
F T T
F F T
Note:
T and F stand for True and False respectively.
In disjunction, if one of the inputs is true then the output will be True.
Negation reverses the input i.e if the input is True, the output will be False. The symbol for negation is ~ i.e the negation of p is ~p
Truth table for ~p ∨ q?
p ----- q ----- ~p ----- q ----- ~p ∨ q
T T F T T
T F F F F
F T T T T
F F T F T
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Let $x = -1$. Find the answer to:
Answer:
-1
Step-by-step explanation:
Since -1 to a power will either be negative or postive 1, looking at whether the exponent is odd or even can determine if the answer is -1 or 0 (x + x^2 for instance equals 0 but x + x^2 + x^3 is -1)
[tex]\it (-1)^{2k}=1;\ \ \ (-1)^{2k+1}=-1,\ \ \forall\ k \in\mathbb{N}\\ \\ S=-1+(1-1)+(1-1)+\ ...\ (1-1)=-1[/tex]
←
Find the sample variance and standard deviation.
22, 15, 4, 7, 9
Part 1 of 2
Choose the correct answer below. Fill in the answer box to complete your choice.
(Type an integer or a decimal. Round to one decimal place as needed.)
OA. ²=
OB. s² =
Variance and standard deviation are two common measures of spread in statistics. The standard deviation is √30.25 = 5.5.
What is variance and standard deviation?OB. s² = The sample variance is a measure of the spread of a set of data. To calculate the sample variance, the sum of the squares of the differences between each data point and the mean is divided by the number of data points minus one. In this case, the mean of the data set is (22+15+4+7+9)/5 = 11.
The differences between each data point and the mean are 11-22=-11, 11-15=-4, 11-4=7, 11-7=4, and 11-9=2. The sum of the squares of these differences is (-11)² + (-4)² + 7² + 4² + 2² = 121.
Dividing this by the number of data points minus one, which is 5-1=4, gives us a sample variance of 121/4 = 30.25.
The standard deviation is the square root of the sample variance, so in this case, the standard deviation is √30.25 = 5.5.
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In a right triangle, given legs of lengths 5 and 12, find the length of the hypotenuse.
Answer:
13
Step-by-step explanation:
the using the Pythagorean Theorem A^2+b^2=c^2
5^2 is 25
12^2 is 144
add 144+25=169 then you square root this and it should be 13
Which function represents the graph of f (x) = 1/2 (3)^x
On solving the provided question, we can say that from the graphs the function = [tex]f(x) = 1/2 (3)^x[/tex], it represents a half parabola
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
from the graphs
the function = [tex]f(x) = 1/2 (3)^x[/tex]
it represents a half parabola
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8. Ryan sells cars for a living. He gets paid $50 per day plus
a commission of 2% of the total cost of each car he sells. Ryan's daily
earnings (E) can be represented by the equation E = 0.02x + 50 where x
is the amount of his sales for the day.
a. What does the 0.02 represent in the equation?
b. How much did Ryan make on Monday if he only sold one car
for $4,400?
c. Ryan wants to make $1,000 in a day. What must his daily sales be
to reach this goal? Show all work necessary to justify your answer.
Answer:
a. the 2% commission he receives
b. $138
c. He must make $47,500 in sales
Step-by-step explanation:
a. No work needed
b. E= 0.02 (4,400) +50, which simplifies to E= 88+50 which continues to 138 dollars
c. To find this you already know E, so you can work backwards
1,000= 0.02 (x) + 50
then subtract 50 from each side
950 = 0.02 (x)
then divide both sides by the 0.02 to get X alone
47,500 = X
Tolerance The height and radius of a right circular cylinder are equal, so the cylinder's volume is The volume is to be calculated with an error of no more than 1of the true value. Find approximately the greatest error that can be tolerated in the measurement of expressed as a percentage of
The greatest error that can be tolerated in the measurement of expressed as [tex]\frac{1}{3}%h[/tex]%h.
The given data is the height and radius of a right circular cylinder are equal.
[tex]$$\begin{aligned}V & =\pi h^3 \\\frac{d V}{d h} & =3 \pi h^2 \\d V & =3 \pi h^2 d h\end{aligned}$$[/tex]
A differentiable function is a function in one variable in calculus such that its derivative exists at each point in its entire domain. The tangent line to the graph of a differentiable function is always non-vertical at each interior point in its domain.
A differentiable function does not have any break, cusp, or angle.
Find the derivative of V in terms of h. Then multiply both sides by dh.
The maximum percentage error of the volume is 1%.
[tex]$$\begin{aligned}0.01 \pi h^3 & =3 \pi h^2 d h \\\frac{0.01}{3} h & =d h \\\frac{1}{300} h & =d h\end{aligned}$$[/tex]
The maximum percentage error of the volume is 1% which means
dV=0.01=0.01[tex]\pi[/tex][tex]h^{3}[/tex]. Substitute this into the equation and then solve for
dh.
The maximum error in the height is then [tex]\frac{1}{300}h=\frac{1}{3}[/tex]%h.
Therefore, the greatest error that can be tolerated in the measurement of expressed as [tex]\frac{1}{3}%h[/tex]%h
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i need it in distributive property
There are 24 red peppers and 8 yellow peppers.
What is Distributive property?
By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.
Given that;
Casey has 48 red peppers and 16 yellow peppers.
Now, Divide it into equal part.
Hence, Number of red peppers in two parts = 48/2
= 24
And, Number of yellow peppers in two parts = 16/2
= 8
Thus, After divide into parts, we get;
There are 24 red peppers and 8 yellow peppers.
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Which graph represents the solution to the following sentence?
{x\x>4} U {x|x < -2}
-3 -2 -1 0 1 2345
-4 -3 -2 -1 0 1 2 3 4
-3 -2 -1 0 1 2 3 4 5
Answer: The graph represents the solution to the following sentence is the option number 3:
-3 -2 -1 0 1 2 3 4 5
This is because the set notation {x|x>4} U {x|x<-2} represents the union of all values of x that are greater than 4 and all values of x that are less than -2. The graph shows all the values of x that are greater than 4 and all values of x that are less than -2. The graph also includes the values of x between -3 and 5, it encompasses all the values that are greater than 4 and all values that are less than -2.
The graph represents the solution to the following sentence is (C).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
We have,
{x | x >4 } ∪ {x | x < -2}
Here the set notation {x|x>4} U {x|x<-2} represents the union of all values of x that are greater than 4 and all values of x that are less than -2.
The graph displays all instances of x larger than 4 and all instances of x less than -2.
The graph covers all x values higher than or equal to 4, as well as all x values less than or equal to -2.
It also includes x values between -3 and 5.
Thus, the number line is C.
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Find m
I don’t get it
Find the sum of the first 7 terms of the
following series, to the nearest integer.
10,4, 8/5,…
The required sum of the 7 terms in the geometric sequence is 16.6.
What is geometric progression?Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
Here,
Given geometric series,
10, 4, 8/5 . . . . . .
Common ratio = 4 / 10 = 2/5
first term = 10
the sum of the first seven terms is given as,
S₇ = a[r⁶ - 1] / r - 1
S₇ = 10[{2/5}⁶ - 1] / {2/5 - 1}
S₇ = 16.6
Thus, the required sum of the 7 terms in the geometric sequence is 16.6.
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A city determines that a planned community must have at least 4 acres of developed and open space, and the difference between the number of developed acres, y, and the number of open acres, x, can be no more than 1. Which graph represents the system of inequalities for this scenario?
x + y ≥ 4
y – x ≤ 1
A graph which represents the system of inequalities for this scenario include the following: graph B.
How to write and solve the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of developed acres and number of open acres, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of developed acres.Let the variable y represent the number of open acres.Since a planned community must have at least 4 acres of developed and open space, a linear inequality which represents this situation is given by;
x + y ≥ 4
Additionally, since the difference between the number of developed acres and the number of open acres can be no more than 1, we have;
y – x ≤ 1
Next, we would use an online graphing calculator to graphically solve the system of linear inequalities. Therefore, the required solution for the given system of linear inequalities is the shaded area below the solid line, which is given by graph B.
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Can someone help me pls
The correct solution of the expression 3/4 ( 6x - 4) = 1/2 (x + 4) with the property that justify each step is shown below.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 3/4 ( 6x - 4) = 1/2 (x + 4)
Now, Solve the expression as;
⇒ 3/4 ( 6x - 4) = 1/2 (x + 4)
⇒ 9/2x - 3 = 1/2x + 2 By Distributive property
⇒ 9/2x - 3 - 1/2x = 1/2x + 2 - 1/2x Subtraction property of equality
⇒ (9/2 - 1/2)x - 3 = 2 Combine like terms
⇒ 4x - 3 = 2 Subtraction property
⇒ 4x - 3 + 3 = 2 + 3 Addition property of equality
⇒ 4x = 5
⇒ 1/4 × 4x = 1/4 × 5 Multiplication property of equality
⇒ x = 5/4
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what percent of 40 is 50?
Answer:20
Step-by-step explanation:
Answer:
the percent of 40 is 50
the answer to this is 10
Can someone please actually solve this will mark brainlest and give five stars
In the circle the area of the shaded region and the length of arc ADB is 23/4 π and 23/6 π respectively.
What is length of arc?
The distance along the curved line that makes up the arc is measured using the arc length formula (a segment of a circle). The arc length is, to put it simply, the distance that passes through the curved line of the circle that forms the arc. It should be noted that the arc's length is greater than the separation of its ends along a straight line.
Given that the circle has a center O.
The radius of the circle is 3 yd.
The measure of ∠AOB is 130°.
First find the measure of ∠ADB -
∠ADB = 360° - ∠AOB
Substituting the values in the equation -
∠ADB = 360° - 130°
∠ADB = 230°
Now find the area of the shaded region.
The area of the shaded region can be determined using the formula -
A = (θ/360)πr²
Substituting the values in the equation -
A = (230/360) π(3)²
A = (230/360) π 9
A = 23/4 π or 5.75 π
Therefore, the area of the shaded region is 5.75 π yd².
Now, find the length of the arc ADB.
The length of arc ADB can be determined using the formula -
Arc Length = (θ/360)2πr
Arc Length = (230/360)2π3
Arc Length = 23/6 π or 3.83 π
Therefore, the length of arc is 3.83 π yd.
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Answer one of the following questions
Write an equation in slope-intercept form for the line with y-intercept 7 and slope
-3
Answer: y= -3x+7
Step-by-step explanation:
the equation is y=Mx+b you gave me the slope (-3) and the y-intercept (7) so the answer is y=-3x+7
h(t)=(t+3) 2 +5h, left parenthesis, t, right parenthesis, equals, left parenthesis, t, plus, 3, right parenthesis, squared, plus, 5 Over which interval does h have a negative average rate of change?
The interval over which h(t) has a negative rate of change is given as follows:
(-∞, -3).
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by the following rule:
y = a(x - h)² + k
In which:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.The equation for this problem is given as follows:
h(t) = (t + 3)² + 5.
The leading coefficient is positive, hence the function is concave up.
Considering the t-coordinate of t = -3 at the vertex, the decreasing and increasing intervals are given as follows:
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how can I Write an expression to show 4 thirds times the product of 2 and 1 third.
Answer:
as: 4/3 * (2 * 1/3)
Step-by-step explanation:
Note: parentheses, 2 and 1/3 are being multiplied together first, before being multiplied by 4/3.
Customers who purchased two different computer models were asked if they were happy with their purchase. The results are shown in this table. Drag and drop the correct percentage to complete each statement. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Of those who were not happy with their purchase, about Response area purchased model A, and about Response area purchased model B. 6%18%20%26%36%82% Happy Not happy Purchased Model A 8 2 Purchased Model B 16 9
Of those who were not happy with their purchase, about 20% purchased model A, and about 36% purchased model B.
Illustrate the satisfaction level among customers?Of those surveyed who purchased two different computer models, about 82% reported being happy with their purchase. Of those who were not happy, about 6% purchased model A and 18% purchased model B. This suggests that customers were more satisfied with model A than model B.Additionally, 20% of those who purchased model A were not happy, while 26% of those who purchased model B were not happy. This demonstrates that more customers were unhappy with model B than model A. Overall, it appears that customers were generally satisfied with their purchases, though there is room for improvement in terms of customer satisfaction with model B.This table shows the responses from customers who purchased two different computer models. Of those who were happy with their purchase, 82% purchased Model A and 18% purchased Model B. Of those who were not happy with their purchase, 6% purchased Model A and 26% purchased Model B.This table helps to illustrate the satisfaction level among customers who purchased the two different computer models. This kind of data is useful for companies to identify which models are the most successful, and which ones may require additional improvements.To learn more about to illustrate the satisfaction level among customers refer to:
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A function is represented by the values in the table. x y 2 4 4 8 5 10 7 14 8 16 Choose from the drop-down menu to complete the statement. The function represented in the table___linea
Chose; is or is not
Option A is appropriate since the table's function is linear.
Equation: What is it?The equals sign is used in equations to indicate the equality of two expressions in a formula. The expressions relate two or more variables with each other.
Given that:
x = 2 and y =4
x= 4 and y= 8 and so on.
In all the values given, the value of y is two times the value of x.
Also, these values satisfy the condition of linear expression:
y=mx
where, m =2 for the represented value.
This means that the function is linearly dependent on x.
The function shown in the table is linear.
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Find the curvature of r(t) = (3t, t^2, t^3) at the point (3, 1, 1).
The curvature of r(t) at the point (3,1,1) is 2/3
The curvature of a space curve is given by the formula:
k(t) = |r'(t) x r''(t)| / |r'(t)|^3 where,
r(t) is the position vector of the curver'(t) is the first derivative of r(t) r''(t) is the second derivative of r(t).r(t) = (3t, t^2, t^3)
r'(t) = (3, 2t, 3t^2)
r''(t) = (0, 2, 6t)
So we can substitute these in the above formula:
k(t) = |(3, 2t, 3t^2) x (0, 2, 6t)| / |(3, 2t, 3t^2)|^3
By cross-product, we get
k(t) = |(6t, -6, -6t^2)| / |(3, 2t, 3t^2)|^3
Now substituting the point (3,1,1) we get
k(t) = |(6(1), -6, -6(1)^2)| / |(3, 2(1), 3(1)^2)|^3 = 6/9 = 2/3
So the curvature of r(t) at the point (3,1,1) is 2/3
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Which shows the pre-image of triangle XYZ' before the figure was rotated 90° about the origin?
Answer: 2nd picture
Step-by-step explanation: its rotating 90 degrees
i don’t get this :(
The value of x, which is the measure of the remaining angle, is equal to 180° - 70° - 30°, or 80°.
Find the value of each variable?The sum of the two angles, a and b, is equal to the total of the two angles, x and y, in a linear pair.This relationship can be expressed through the equation a + b = x + y. In this case, a is equal to 70° and b is equal to 30°.To solve for x and y, we must rearrange the equation to solve for each variable individually.First, we can subtract b from both sides to get a = x + y - b. Then, we can add b to both sides to get a + b = x + y.This simplifies to x + y = a + b, or x + y = 70° + 30° = 100°. By subtracting y from both sides, we can solve for x by getting x = 100° - y.To solve for y, we can subtract x from both sides to get y = 100° - x.Since the sum of the two angles is equal to 100°, the value of x must be 90° and the value of y must be 60°.a=70° and b=30° are two angles that together form a straight line.The sum of these two angles is equal to 180°, which is the measure of a straight line.Therefore, the value of x, which is the measure of the remaining angle, is equal to 180° - 70° - 30°, or 80°.The value of y, which is the measure of the remaining angle, is equal to 180° - 70° - 80°, or 30°.Therefore, the value of x is equal to 80°, and the value of y is equal to 30°.To learn more about The Law of Sines refer to:
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Please help will mark Brainly
Therefore , the equation problem is 15 fraction of 72 is the number 480. The expressions published here on left & right sides appear to be equivalent in their relationship.
An equation is what?Mathematical statements with two algebraic in the middle and also the means total (=) sign from either side are called equations. Variables, contractors, diffusion coefficients, terms, and the equatable to sign are just a few of the elements that compose an equation. The "=" sign but also terms both on sides are always necessary when writing an equation.
Here,
Using the value A = 480 as a guide
Let y become the ratio of the number, or the opposite.
It is equivalent to 72%.
The equation that results is
72 is equivalent to x% of 480.
When the expression is condensed, we get
72 = y % x 480
72 = ( y/100 ) x 480
Divide each side by 480 to obtain
y/100 = 0.15
Multiply by 100 on each side to arrive at
y = 15
Consequently, the value is y = 15.
Therefore, out of 480, 72 represents 15%.
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A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x. v(x)
The volume, V of box as a function of x that is V(x) = 4x³ - 64x² + 240x , where x is side of square cut out from each corner.
We have, a box open from top and constituted from rectugular pieces of dimensions 12 inches and 20 inches. As we know, The volume of a box is V
= width (w) × height(h) ×length (l).
Now, equal squares of side x are cut from each corner of box and folded. We draw our box it looks like as seen above figure. We will notice here that the height will be x and that the height and length depend on x. Length of box, l = 20 - 2x and
Width of box, w = 12 - 2x
So the volume is, V(x) = w×h×l
= (12 - 2x)(x)(20 - 2x)
Expand it for further calculation,
V(x) = ( 12 - 2x ) ( 20x - 2x²)
V(x) = 4x³ - 64x² + 240x
Hence, the required volume function is V(x) = 4x³ - 64x² + 240x.
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The volume, V, of a box is defined as V(x) = 4x3 - 64x2 + 240x.
We have a box that opens from the top and is made of rectangular components that are 12 inches and 20 inches in length. As is common knowledge, a box's volume is V.
V = height (h) + width (w) + length (l).
From each corner of the box, equal squares of side x are now cut and folded. We create a box that resembles the image above. Here, we'll see that the height is x and that the relationship between height and length is x-dependent.
Box length, l = 20 - 2x, and
Box width, w = 12 - 2x
Thus, V is the volume (x) = W * H * I
V(x) = (12 - 2x) (x) (20 - 2x)
V(x) = ( 12 - 2x ) ( 20x - 2x²)
V(x) = 240x - 24x² - 40x² -4x³
V(x) = 4x³ - 64x² + 240x
Hence, the required volume function is V(x) = 4x³ - 64x² + 240x.
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You create a recipe for slime by mixing some 20% pure slime and some 80% pure slime to create 1000 gallons of a 65% pure slime mixture. How many gallons of the 20% mixture are needed?
Answer:
We can start solving this problem by using a system of linear equations. Let x be the number of gallons of the 20% pure slime mixture and y be the number of gallons of the 80% pure slime mixture. We know the following:
The total amount of slime mixture is 1000 gallons. This means that x + y = 1000.
The final mixture is 65% pure slime, which means that 0.65 = (0.20)x + (0.80)y. This is because we are mixing 20% pure slime and 80% pure slime to get the final mixture.
We can use these two equations to solve for x, which is the number of gallons of the 20% pure slime mixture needed.
First, we'll use the first equation to solve for y in terms of x:
y = 1000 - x
Then we'll substitute this expression into the second equation:
0.65 = (0.20)x + (0.80)(1000 - x)
Simplifying we get:
0.65 = 0.20x + 800 - 0.80x
0.45x = 200
x = 200/0.45
x = 444.44 gallons
So, you would need 444.44 gallons of the 20% pure slime mixture to make 1000 gallons of a 65% pure slime mixture.
Step-by-step explanation: