The root of f(x) = tan(x) - sqrt(3) is approximately x = 1.7321 using the secant method with initial points x0 = 1 and x1 = 2.
To use the secant method to find an approximation to >/3 correct to within 10^-4, we will follow these steps:
1. Choose two initial points, x0 and x1, such that f(x0) and f(x1) have opposite signs. This ensures that there is at least one root of f(x) between x0 and x1.
2. Calculate the next approximation, xn+1, using the formula:
xn+1 = xn - f(xn) * (xn - xn-1) / (f(xn) - f(xn-1))
3. Continue calculating xn+1 until the desired level of accuracy is reached, i.e., |xn+1 - xn| < 10^-4.
To compare the results to exercise 9 of section 2.2, we need to know the function and initial points used in that exercise. Let's assume that exercise 9 asked us to find the root of the function f(x) = x^3 - 2x - 5 using the secant method and initial points x0 = 2 and x1 = 3.
Using the formula above, we can calculate the next approximations as follows:
x2 = 3 - f(3) * (3 - 2) / (f(3) - f(2)) = 2.384615
x3 = 2.384615 - f(2.384615) * (2.384615 - 3) / (f(2.384615) - f(3)) = 2.094551
x4 = 2.094551 - f(2.094551) * (2.094551 - 2.384615) / (f(2.094551) - f(2.384615)) = 2.094554
We can see that the root of f(x) = x^3 - 2x - 5 is approximately x = 2.0946 using the secant method with initial points x0 = 2 and x1 = 3.
To compare this result to the approximation of >/3, we need to know the function whose root is >/3. Let's assume that it is f(x) = tan(x) - sqrt(3) and that we choose initial points x0 = 1 and x1 = 2. Using the secant method as described above, we can calculate the next approximations as follows:
x2 = 2 - f(2) * (2 - 1) / (f(2) - f(1)) = 1.770188
x3 = 1.770188 - f(1.770188) * (1.770188 - 2) / (f(1.770188) - f(2)) = 1.730693
x4 = 1.730693 - f(1.730693) * (1.730693 - 1.770188) / (f(1.730693) -
f(1.770188)) = 1.732051
We can see that the root of f(x) = tan(x) - sqrt(3) is approximately x =
1.7321 using the secant method with initial points x0 = 1 and x1 = 2.
Therefore, we can conclude that the approximations obtained using the
secant method for these two functions are different, as expected, since
they have different roots and initial points.
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What is the ratio of a circles area?
The ratio of the area of a circle to the area of a square with sides of length equal to the circle's diameter is π/4.
This can be expressed mathematically as A_circle/A_square = π/4, where A_circle is the area of the circle and A_square is the area of the square.
To calculate the area of the circle, use the formula A_circle = πr^2, where r is the radius of the circle. To calculate the area of the square, use the formula A_square = (d^2)/4, where d is the diameter of the circle. Therefore, the ratio of the area of the circle to the area of the square is A_circle/A_square = πr^2/(d^2/4) = 4πr^2/d^2.
For example, if the radius of the circle is 4 cm, then the diameter is 8 cm, and the ratio of the area of the circle to the area of the square is A_circle/A_square = 4π(4^2)/(8^2) = 16π/64 = π/4.
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Which statements and reasons are true and can be used in a proof that m∠8 Select all that apply.
The statements and reasons that are true and can be used in a proof that m∠8 < m∠6 are:
A) m∠6+m∠2+ m∠3 = 180° because the sum of the measures of the interior angles of a triangle is 180°.
C) m∠8+m∠1+m∠2+m∠3+m∠4 = 180° because the sum of the measures of the interior angles of a triangle is 180°.
What is interior angles?Interior angles can be created in geometry in two different ways. In one, parallel lines are cut by a transversal, and in the other, they are inside a polygon. Depending on how large they are, angles are divided into various types. Other angles fall into the category of pair angles because they need to be present in pairs in order to display a particular characteristic. One type of these is interior angles.
Interior angles can be outlined in two different ways:
Angles inside a polygon are referred to as interior angles because they are found inside a polygon, typically. The angles a, b, and c are interior angles in the following figure (a).Interior Angles of Parallel Lines: The angles that are located in the space bounded by two parallel lines intersected by a transversal are also called interior angles.Learn more about Interior angles
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Circle D is shown. Line segment C D is a radius with length 18 centimeters. Which statements are true regarding the area of circle D? Select two options. The area of the circle depends on the square of the radius.
The statements that are true regarding the area of circle D include the following:
A. The area of the circle depends on the square of the radius.
C. The area of circle D is 324π centimeters squared.
How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using this formula:
Area = πr²
Where:
r represents the radius of a circle.
In this context, we can reasonably infer and logically deduce that the area of any circle is directly proportional to the square of its radius.
Substituting the given radius into the formula for the area of a circle, we have the following;
Area of circle = π × 18²
Area of circle = 324π centimeters squared.
Based on the calculations, we can reasonably infer and logically conclude that the area of circle D in terms of pie (π) is equal to 324π centimeters squared.
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Which statements are true regarding the area of circle D? Select two options.
The area of the circle depends on the square of the radius.
The area of circle D is 36π centimeters squared.
The area of circle D is 324π centimeters squared
The area of the circle depends on the square of π.
The area of the circle depends on the central angle.
Mark loads a crate that weighs 22.5 pounds and 12 boxes that each weigh 11.25 pounds onto a truck . what is the total weight of the crate and the boxes
Answer:
157.5 pounds
Step-by-step explanation:
11.25×12=135 then add 135 to 22.5
Plot the points A(3,-2), B(-3, 8), C(-5, -1) on the coordinate axes below. State
the coordinates of point D such that A, B, C, and D would form a
parallelogram.
(Plotting point D is optional.)
The points A(3,-2), B(-3, 8), C(-5, -1) and D(2,16) would form a parallelogram.
How to plot points on graph?
In mathematics, points on a graph are typically plotted on a coordinate plane. The x-coordinate and y-coordinate of each point determine its location on the plane. To plot a point, you will need to know its coordinates (x, y).
To plot the points A(3,-2), B(-3, 8), C(-5, -1) on the coordinate axes, we can start by drawing the x-axis and y-axis, where the x-axis is the horizontal line and y-axis is the vertical line.
We can then locate point A by starting at the origin (0,0) and moving 3 units to the right on the x-axis and 2 units down on the y-axis. Point B can be located by starting at the origin and moving 3 units to the left on the x-axis and 8 units up on the y-axis. Point C can be located by starting at the origin and moving 5 units to the left on the x-axis and 1 unit down on the y-axis.
To form a parallelogram, point D must be opposite of point B and have the same distance from point C and point A. Since a translation of a vector is a linear transformation, D is the translation of vector AB to point C.
The coordinates of point D would be (2,16), which is the translation of point B by the vector (2,8) to point C.
So the points A(3,-2), B(-3, 8), C(-5, -1) and D(2,16) would form a parallelogram.
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Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) is dilated using a scale factor of one fourth to create polygon A′B′C′D′. Determine the vertices of polygon A′B′C′D′.
A′(−0.8, 1.2), B′(−0.4, 0.4), C′(0.8, −0.4), D′(0.8, 0.8)
A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)
A′(−2, 3), B′(−1, 1), C′(2, −1), D′(2, 2)
A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)
With a dilation factor of 1 / 4, Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) would be: A(-1, 1.5), B(-0.5 , 0.5), C(1, -0.5), D(1 , 1). Second option
How to dilate the vertices to scaleThe solution to the problem would be the solution that is gotten when we divide these points by 1/4. This is the dilation factor
we would have:
A(−4, 6), B(−2, 2), C(4, −2), D(4, 4)
= (-4 * 1/4, 6 * 1/4) , B(-2 * 1/4, 2 * 1/4), C(4 * 1/4, -2 * 1/4), D(4 * 1/4, 4 * 1/4)
= A(-1, 1.5), B(-0.5 , 0.5), C(1, -0.5), D(1 , 1)
Hence the second option is correct.
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Answer:A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1).
Step-by-step explanation:
To dilate a point using a scale factor, you multiply both the x-coordinate and the y-coordinate of the original point by the scale factor.
Given the original vertices of the polygon ABCD and a scale factor of one fourth (1/4), we can find the coordinates of the dilated vertices A', B', C', and D':
Original vertex A(-4, 6):
x-coordinate of A': -4 * 1/4 = -1
y-coordinate of A': 6 * 1/4 = 1.5
So, vertex A' is (-1, 1.5).
Original vertex B(-2, 2):
x-coordinate of B': -2 * 1/4 = -0.5
y-coordinate of B': 2 * 1/4 = 0.5
So, vertex B' is (-0.5, 0.5).
Original vertex C(4, -2):
x-coordinate of C': 4 * 1/4 = 1
y-coordinate of C': -2 * 1/4 = -0.5
So, vertex C' is (1, -0.5).
Original vertex D(4, 4):
x-coordinate of D': 4 * 1/4 = 1
y-coordinate of D': 4 * 1/4 = 1
So, vertex D' is (1, 1).
Comparing the calculated coordinates with the options given:
A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)
Among the given options, the correct vertices of polygon A′B′C′D′ are A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1).
B. Exercises
Find the sums or differences.
21, 2,973+56 +37,468 +784
22. 37,205-19,804
23. 861,519-179,321
24. 1,733,642 +18,082+43,605
Perform the indicated operations. Do those inside the parentheses first.
29, (736-565)+189
30. 600-(718-453)
31. (3,264-1,628)+4,356
25. 19+73,048 +314+ 5,080
26. 8,496-6,338
27) 4,000,000-832,971
28. 46,525+273,199 +5,636,024
32. 894+ (1,036-478)
33. 2,457-(986+759)
34. (61,432-38,617)-15,674
Answer:
21. 41,281
22. 17,401
23. 682,198
24. 1,795,329
29. 360
30. 335
31. 5,992
25. 78,461
26. 2158
27. 3167029
28. 5955748
32. 1452
33. 612
34. 7141
Your welcome
Alliosn walks 1/2 mile each 1/5 hour. She continues to walk at the same pace. If allsion walked 1 1/4 miles, hiw long did she walk take
27.5 hrs are long did she walk take to cover distance .
In math, what is a distance?
The length of the segment of the line that connects the supplied two points determines the distance between them.
The shortest segment of a line connecting a point to a line will have a length equal to the distance between them.
Distance covered by Alliosn = 1/2 km
Time taken by Alliosn = 1/5hr
Hence,
speed of peter = Distance/time
= (1/2)/(1/5) km/hr
= 1/10 km/hr
Distance travelled by Alliosn = 1 1/4 km
= 11/4km
Speed = distance/time
1/10 = (11/4) / time
i.e.
Time = 11 * 10/4
= 27.5 hrs
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PLEASE HELP
A boutique in Hampton specializes in leather goods for men. Last month, the company sold 36 wallets and 11 belts, for a total of $3,295. This month, they sold 91 wallets and 10 belts, for a total of $7,599. How much does the boutique charge for each item?
Wallets: $__
Belts: $__
The amount charged by the boutique for each item is given as follows:
Wallet: $79.Belt: $41.How to obtain the price of each item?The price of each item is obtained considering a system of equations, for which the variables are given as follows:
Variable x: cost of a wallet.Variable y: cost of a belt.From the description, the equations are given as follows:
36x + 11y = 3295.91x + 10y = 7599.Simplifying the first equation by 11, we have that:
3.272727x + y = 299.5454
y = 299.5454 - 3.272727x
Replacing on the second equation, the cost of a wallet is given as follows:
91x + 10(299.5454 - 3.272727x) = 7599
58.2728x = 4603.5455
x = 4603.5455/58.2728
x = 79.
Then the cost of a belt is obtained as follows:
y = 299.5454 - 3.272727(79)
y = $41.
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How do you find the center of a transformation?
The center of a transformation refers to the fixed point through which the transformation takes place.
The center of a transformation can be found by the following methods:
Translation: The center of a translation is the point that remains fixed during the transformation.
Rotation: The center of rotation is the point around which the object rotates.
Reflection: The center of reflection is the line of reflection or the point of symmetry.
Dilation: The center of dilation is the point that remains fixed during the transformation and all the distances from it are multiplied by a scale factor.
Combination of Translations, Rotation, Reflection, and Dilation: The center of transformation will be the point of intersection of all the fixed points of above mentioned four transformations.
It is important to note that not all transformations have a center, and some may have multiple centers.
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Simple geometry can compute the height of an object from the object's shadow length and shadow angle using the formula: tan(angleelevation) = treeheight / shadowlength. Given the shadow length and angle of elevation, compute the tree height. Sample output with inputs: 0. 4 17. 5 tree height: 7. 398881327917831.
angle of elevation = 17.5 degrees
shadow length = 4
Computing Tree Height FormulaTo compute the tree height using the given formula, you would need to use the inverse tangent function (arctan) to find the angle of elevation in radians, and then multiply that value by the shadow length.
In this example:
angle of elevation = 17.5 degrees
shadow length = 4
tree height = tan⁻¹ (17.5) × 4
From this, the final output will be 7.398881327917831.
The formula states that the ratio of the tree's height to the shadow's length is equal to the tangent of the angle of elevation. So, by measuring the shadow length and the angle of elevation, we can use the tangent function to calculate the tree's height.
The inverse tangent function (arctan) is used to find the angle of elevation in radians, and then the result is multiplied by the shadow length to get the tree height.
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What is the simplified form of the following expression? rootindex 3 startroot startfraction 4 x over 5 endfraction endroot.
The simplified expression of the ∛4x / 5 is ∛4x / ∛5
Index laws are the rules for simplifying expressions involving powers of the same base number, these laws are also called Laws of indices.
Laws of indices provide us with rules for simplifying calculations or expressions involving powers of the same base. The indices are also known as powers or exponents.
It is represented in the form:
am = a × a × a ×……× a (m times)
we have the law of indices formula:
[tex]\sqrt[a]{b}=b^\frac{1}{a}[/tex]
∛4x / 5 = (4x/5)^1/3
Therefore,
∛4x / 5 = ∛4x / ∛5
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ava read 99 books in 11 months how many books per a month did she read
Why might squaring a number and taking the square root of a number be thought of as opposite operations give an example to justify your answer?
Finding a number's square root is the equivalent as squaring it, or the opposite process. When you multiply the square root of a given integer by itself, you get the original number. Since 8 x 8 equals 64, as fact, 8 is the square root of 64.
What is square roots?It is possible to multiply an integer by its square root in order to obtain the original value. Square root of, end square root is the symbol for this mathematical concept. Contrary to squaring, finding a number's square root is the reverse.
For instance, 3 is squared at 9, 32, and its square root at 9, which is 9, is equal to 3. It is simple to multiply by 9 since it is a perfect square.
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Jorge completed the obstacle course in 18.2 seconds. Kaitlyn finished 3.5 seconds in front of Jorge. Which equation shows Kaitlyn's time?
The equation will be [tex]x-3.2=18.2[/tex] by simple calculation.
What are equations in one step?An algebraic equation that only requires one step to solve is known as a one-step equation. Once you've figured it out, you'll know what the variable's value is that makes the equation true. In order to obtain the variable by itself when solving one-step equations, we perform the inverse (opposite) of the operation that is being applied to the variable.
How do two step equations work?An equation that must be solved in two steps is referred to as a two-step equation. Any constant that is on the same side as the variable must be removed first. To solve, isolate the variable on its own using inverse operations. Keep in mind that anything you do to one side must also be done to the other.
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What is the slope-intercept form the linear equation 2x y 10?
The slope-intercept form of the given linear equation 2x + y = 10 is y = -2x + 10.
If we draw the graph of the linear equation y = mx + c. The result is a line with m as the slope, and c as the y-intercept. This form of the linear equation y = mx + c is called the slope-intercept form, and the values of m and c are real numbers.
The slope, m, of the line represents the steepness of a line. This is also termed a gradient, sometimes. The y-intercept, c, represents the y-coordinate of the point where the graph of the line intersects the y-axis.
Now, change the given equation to slope-intercept form, y = mx + c, where m is the slope and c is the y-intercept.
2x + y = 10
Subtract 2x from both sides of the above equation, we get
y = -2x + 10
This is the required slope-intercept form of the given linear equation.
-- The given question is incorrect, the correct form of equation is
"What is the slope-intercept form the linear equation 2x + y = 10?" --
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Which expression is equivalent to the given expression?
A.
B.
C.
D.
The expression is equivalent to the given expression is 5x²+12x-7: Option C
What is simplification?You should understand that simplification means making an expression more simpler for better understanding
The given expression is
-2x²+8x-9+4x+7x²+2
The first thing to do is to rearrange the expression in the following ways by collecting the like terms
7x²-2x²+8x+4x-9+2
This implies that
5x²+12x-7
Conclusively the simplest form of the expression is 5x²+12x-7
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mr smith gives her class clues about 5 digit mystery numbers the 4 is in a place that is 10 times greater than the 9.
Answer:
Step-by-step explanation:
40
3x+9y=-6 ,-4x-12y=8 solve by substitution method
Latoya' Coffee Shop make a blend that i a mixture of coffee type A and B. In one bag of the blend, there are 6 kilogram of type A. Four bag of the blend are a total of 36 kilogram. How many kilogram of type B are there in one bag?
The Kilograms of type B that are in one bag of the Latoya's Coffee shop blend would be = 3kg
What is a mixture?
A mixture is defined as the combination of two or more components which can or cannot be separated by ordinary methods.
The coffee blend of LaToya shop = Type A and B
A bag of the coffee blend = 6kg of Type A.
4 bags of coffee blend = 36kg
Therefore 4 bags of coffee blend contains = 6 see×4 = 24 kg of Type A
Type B in each bag = 36 - 24 = 12/4 = 3kg.
We are tasked with finding the amount in kilograms of type B coffee present in a bag of coffee.
We already know that in a bag , there are 4kg of type A coffee. Hence, in 6 bags, what we will be having would be 6 * 4kg = 24kg of type A coffee
The total kilograms of coffee in 6 bags of coffee is 48kg. Now we know we have 24kg of type A, the amount of type B coffee present is thus 48kg -24kg = 24kg
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Tell whether the ratios form a proportion.
4 : 12 and 5 : 15
The ratios _____ (do or do not) form a proportion. The cross products are _____ (state the cross product or state "not equal")
Response:
--------------------------------------
--------------------------------------
Talking about the 4:12 and 5:15 can be written in the form of 1:3
What do you mean by ratios?
Mathematical ratios show how many times one number appears in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a fruit plate. The ratio of lemons to oranges is 6:8, while the ratio of oranges to the total amount of fruit is 8:14.
How to address a ratio issue
The total number of shares can be calculated by adding the ratio's component parts.By the total number of shares, divide the entire sum.Add the necessary amount of shares togetherTo know more about Ratios here
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How many images are formed when two plane mirrors are placed at 120?
Three images are formed when two plane mirrors are placed at 120.
assuming an angle of x between the mirror and the object. The previous graphic makes it evident that, regardless of the value of x assumed, the angle of the fourth picture will be more than 180 degrees. A mirror's reflection of the object in question produces a mirror image. The mirror image is what an object seems to be when it is placed in front of a mirror. The reality is quite different from what appears to be the case. No, some messages contain both mirror images and real photographs.
We know that angle = 120
number of images = 360/120
number of images = 3.
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If Elaine has 4 exemptions and makes $520 per week, what will her income tax withholding be according to the following table?
Single Taxpayer, Weekly Withholding
if earnings are at least equal to Column A and less than Column B and the number of claimed exemptions are as numbered
Column A Column B 0 1 2 3 4 5
$0 $50 0 0 0 0 0 0
$50 $75 1 0 0 0 0 0
$75 $100 1 1 0 0 0 0
$100 $150 2 1 0 0 0 0
$150 $200 3 2 1 1 0 0
$200 $250 4 2 1 1 1 0
$250 $300 5 3 2 2 1 0
$300 $400 7 3 2 2 2 1
$400 $500 10 4 3 2 2 1
$500 $600 15 5 3 3 2 1
$600 $750 21 6 4 3 3 2
$750 30 7 5 4 4 3
A. $1. 00
B. $2. 00
C. $3. 00
D. $5. 0
Answer: B $2:00
I Just took it
please help me!! i need it asap
In the rectangle JKLM, diagonal JL= x+7, and diagonal KM=2x+7. What would be the length of JL?
JL has a length of 5.
What is a rectangle ?The internal angles of a rectangle, which has four sides, are all exactly 90 degrees.
At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
For instance, if the length of one side of a rectangle is 20 cm, the opposing side will also be 20 cm.
A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.
It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
According to our question-
3x + 4 = 4x - 1
-3x -3x
4 = x - 1
+1 +1
5 = x
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evaluate the integral ( 4 to 1) 6 + x2 / x^2 dx
So the value of integral [tex]\int\limits^4_1 {\frac{x}{x^2+13} } \, dx[/tex] is 0.51
Define integral:An integral is a mathematical concept used to calculate area or change over an interval, represented by ∫. It is opposite of derivative, with two types: definite and indefinite. Used in many areas of mathematics and physics.
The integral of x/(x^2+13) from x=1 to x=4 can be evaluated using the method of substitution.
Let u = x^2+13, then du/dx = 2x dx
so x dx = du/2
now the integral becomes 1/2 * integral (1/u) du
so intergral is 1/2* [tex]\int\limits {\frac{1}{u} } \, du[/tex]
=> 1/2 [tex]\left \{ {{x=4} \atop {x=1}} \right.[/tex] ln([tex]x^2[/tex]+13)
=> 0.5 ( ln(39)-ln(14))
=>0.51
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Complete question:
evalute integral [tex]\int\limits^4_1 {\frac{x}{x^2+13} } \, dx[/tex]
Find the output, h, when the input,
is -18.
h = 17+ 6
h=?
When the input x is -18, the output h is 14. The answer is obtained using substitution method.
What is substitution method?
One of the algebraic techniques for solving simultaneous linear equations is the substitution approach. It entails changing any variable's value from one equation to the other by substituting it in. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.
Now, we are given h = 17+x/6
So, when the input x is -18, using substitution method,
h=17+(-18/6)
=17+(-3)
=17-3
=14
Hence, when the input x is -18, the output h is 14.
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Use elimination to find the solution to the system of equations.
4x+y=8
3x-2y=6
A. x=6, y=6
B. x=2, y=0
C. x=-3, y=20
D. x=6, y=-16
Answer: To use the elimination method to solve the system of equations, we'll try to eliminate one of the variables by adding or subtracting the equations.
We have:
4x+y=8
3x-2y=6
multiplying the first equation by -2:
-8x-2y=-16
and adding it to the second equation:
3x-2y+(-8x-2y)=6+(-16)
-5x = -10
x = 2
substituting x=2 in the first equation:
4(2)+y = 8
8+y = 8
y = 0
So the solution is x=2 and y=0, that corresponds to the option B.
Sandra drops a brick into a beaker filled with water. Volume increases by 2 liters. Then she uses the density to make a prediction about its weight in kilograms. If the density of the brick is approximately 2 grams per millimeters, what should the prediction be?
The weight of the brick that Sandra dropped is 40 N.
What is the density?We must know that we can be able to define the density as the ratio of the mass to the volume of the object. We know that the density can be regarded as an intrinsic property of the substance.
We can see that;
Density = mass/volume
mass = Density * volume
Volume = 2 L or 2000 mL
Density = 2 grams per millimeters
Mass = 2 * 2000
Mass = 4000 g or 4 Kg
Weight = mass * acceleration due to gravity
Weight = 4 Kg * 10 m/s^2
Weight = 40 N
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Antonio buys five new college textbooks during his first year at school at a cost of $80 each. Used books cost only $50 each. When the bookstore announces that there will be a 50 percent increase in the price of new books and a 20 percent increase in the price of used books, Antonio's father offers him $200 extra. What happens to Antonio's budget line? 1.) Using the line drawing tool, graph Antonio's original budget line. Label this line Upper L 1 .2.) Using the line drawing tool, then graph Antonio's new budget line. Label this line Upper L 2 . Carefully follow the instructions above, and only draw the required objects.
Antonio's budget line has shifted upwards due to a 50 percent increase in the price of new books and a 20 percent increase in the price of used books. His new budget line equation is y = 110x.
Upper L1: y = 80x
Upper L2: y = 110x
Antonio's original budget line (Upper L1) is represented by the equation y = 80x. This equation means that for every x amount of textbook Antonio buys, he will spend 80y in total.
Antonio's new budget line (Upper L2) is represented by the equation y = 110x. This equation means that for every x amount of textbook Antonio buys, he will spend 110y in total.
As a result, Antonio's budget line has shifted upwards due to the increase in both the price of new and used books. Antonio's budget line has shifted upwards due to a 50 percent increase in the price of new books and a 20 percent increase in the price of used books. His new budget line equation is y = 110x.
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