Answers
Answer:
1. [tex](x-3)^2+(y+15)^2=13[/tex]
2. [tex](x+9)^2+(y+14)^2=5[/tex]
3. [tex](x+3)^2+(y+11)^2=\sqrt{51}[/tex]
4. [tex](x+3)^2+(y-0)^2=25[/tex]
For Questions 1-2:Step 1: Formula
The standard form of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex].
The h represents the x value of the coordinates of the circle's center and the k is the y value of the coordinates. The r is the radius.
So in the first problem h is going to be 3 and k is going to be -15. (In this problem the signs are flipped, so if you have a positive number it will be negative in the formula)
After inserting the values in the formula you have your answer of [tex](x-3)^2+(y+15)^2=r^2[/tex]. Now let us find the radius
Step 2: Find the radius
To find the radius of the first two problems what you can do is you can use the distance formula.
To use the distance formula you find have to identify the (x1, y1) and the (x2, y2)
In the first problem, the (x1, y1) would be the center of the circle. The reason for this is that on a graph you have to read it left to right (kinda like English) so to find the values you have to imagine what values would come first, in this case, the center point would come first.
So let us input the values in the formula. The formula is [tex]d = \sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} }[/tex]. This is the distance formula, this formula will be used in this problem.
Okay so the x1 is 3 and the y1 is -15. The x2 is 0 and the y2 is -13. So lets us input these values.
[tex]d = \sqrt{(0-3)^{2}+(-13--15)^2 } \\\\ = \sqrt{(-3)^{2}+(2)^2} \\\\=\sqrt{9+4}\\\\=\sqrt{13}\\\\= 3.605[/tex]
3.605 is our radius.
Now let us write our finished equation.
[tex](x-3)^2+(y+15)^2=\sqrt{13} ^2[/tex] or [tex](x-3)^2+(y+15)^2=13[/tex].
Doing these steps for the next problem gives us our second answer of [tex](x+9)^2+(y+14)^2=5[/tex]
For Questions 3-4:Step 1: Midpoint Formula
To solve this problem you need to use the midpoint formula. The midpoint formula is [tex]\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2}[/tex]. In the first problem, the x1 would be -10, the y1 would be -13. The x2, on the other hand, is 4 and the y2 is -9. Now find the center of the circle.
Step 2: Find the center
To find the center of the circle we need to insert the values of x and the values of y into the midpoint formula. We can do this because they gave us the diameter and the diameter goes through the middle of the circle. So we can do this.
[tex]\frac{-10 + 4}{2} ,\frac{-13+-9}{2}\\\\\frac{-6}{2} ,\frac{-22}{2}\\\\(-3,-11)[/tex]
So (-3, -11) is the center of the circle.
Step 3: Find the radius
Now that we have the center of the circle we can use the distance formula to find the radius. We already have two of the ends of the radius so we can simply use the distance formula with the center and the ends.
[tex]d = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\\\\=\sqrt{(4--3)^2+(-9--11)^2 }\\\\= \sqrt{(7)^2+(2)^2 }\\\\=\sqrt{49+4 }\\\\=\sqrt{51}[/tex]
Step 4: Write your final equation
Know we can insert all the values we have into the standard form of a circle equation.
[tex](x-h)^2+(y-k)^2=r^2\\\\(x+3)^2+(y+11)^2=\sqrt{51} ^2[/tex] or [tex](x+3)^2+(y+11)^2=\sqrt{51}[/tex]. This is our answer.
Doing these steps for the next problem gives us our answer of [tex](x+3)^2+(y-0)^2=25[/tex]
Related Questions
Which is greater 62% or 9/20
Answers
To compare 62% and 9/20, we can convert 62% to a fraction with a denominator of 20:
62% = 62/100 = 31/50
Now we can compare 31/50 and 9/20:
31/50 = 0.62
9/20 = 0.45
Since 0.62 is greater than 0.45, we can conclude that 62% is greater than 9/20.
Which expression is equivalent to 83,120 in expanded form using powers of 10?
A (8×10) + (3 ×104) + (1x10³) + (2x10²)
B (8*10*)+(3×10³) + (1x10³) + (2x10²)
C (8×10¹)+(3×10³) + (1×10²) + (2×10¹)
D (8×10) +(3×10¹) + (1×10¹) + (2×10¹)
Answers
Answer:
The correct answer is B.
83,120 can be written as:
(8 × 10^4) + (3 × 10^3) + (1 × 10^3) + (2 × 10^2)
This is equivalent to option B.
Write an equation to represent the fraction models below
Answers
Identify the reflection of the figure with vertices C(-2,4), D (1,5), and E(1, 2) across the x-axis.
Answers
The coordinates of the reflected figures are C'(-2,-4), D'(1,-5), and E'(1, -2)
Identifying the reflection of the figure with verticesGiven that we have the figure of the vertices CDE
With the coordinates C(-2,4), D (1,5), and E(1, 2)
The transformation is given as
Reflection over the x-axis
The rule of this transformation is
(x, y) = (x, -y)
So, we have
Image = C'(-2,-4), D'(1,-5), and E'(1, -2)
Recall that
the rule of this transformation is (x, y) = (x, -y)
This means that the x-coordinate remains unchanged while the y-coordinate is negated as a result of this reflection.
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PLEASE HELP!
Town A is 7 feet below sea level and Town B is 692 feet above sea level. What is the difference in elevation between Town A and Town B?
A. 685 feet
B. 692 feet
C. 695 feet
D. 699 feet
Answers
Answer:
D. 699 ft
Step-by-step explanation:
Think of a vertical number line with sea level being 0. Town A is +692 ft and Town B is -7 ft.
Difference in elevation = 692 - (-7) = 699
How do you solve this? |3x+8|=x
Answers
The solutions are S={2,4}
Explanation:
Let's rewrite the equation
|3x−8|−x=0
|3x−8|=3x−8, if 3x−8≥0
and
|3x−8|=−(3x−8)=−3x+8, if 3x−8<0
Let f(x)=|3x−8|−x=0
Let's build a variation table
aaaaxaaaaaaaa−∞aaaaaaaa0aaaaaaaaaa83aaaaaaa+∞
aaaaxaaaaaaaaaaaaa−aaaa#color(white)(aaaaa)+#aaaaaaaa+
aaaa|3x−8|aaaaaa−3x+8a#color(white)(aaa)-3x+8#aaaaa3x−8
aaaaf(x)aaaaaaaaaaax=2a#color(white)(aaaaa)x=2#aaaaaax=4
The solutions are S={2,4}
graph{|3x-8|-x [-7.9, 7.904, -3.95, 3.95]}
Let A be a 7×5 matrix with rank equal to 4 and let b be a vector in R8. The four fundamental sub- spaces associated with A are R(A), N(AT ), R(AT ), and N (A).
Answers
The value of R(A) = 4, N(AT ) = 3, R(AT ) = 4, and N (A) = 3.
Given that
Dimension of matrix = 7×5
Rank of matrix = 4
The range space of A,
Which is a subspace of R, is known as R(A).
It is made up of all conceivable linear combinations of A's columns.
The dimension of R(A) = rank of A,
Which is 4 in this case.
The null space of the transpose of A,
Which is also a subspace of R, is designated as N(AT).
All potential answers to the equation ATx = 0,
Where x is a R column vector, are included in it.
N(AT) has a dimension = nullity of A,
which in this case is 3 in this example.
The range space of the transposition of A, is designated as R(AT).
The rows of A are arranged in all conceivable linear configurations.
The rank of A = 4
Thus it equal to dimension of R(AT).
N(A) is the null space of A.
Axe = 0, where x is a column vector in R, are included in it.
The nullity of AT, which is three, is likewise equivalent to the dimension of N(A).
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NEED THE ANSWERS TO ALGEBRA 1B RADICAL EXPRESSIONS UNIT 4 LESSON 8 TEST
1. simplify the radical expression
√20
A. 2√10
B. 5√2
C. 2√5
D. 2
In the attachments are some of the questions.
Answers
The simplified expressions are;
1) 2√5
2) 6x√2
3) 5xk^2√6x
4) 5√1029y^2
What is a radical expression?Any mathematical expression that uses the square, cube, or higher-order roots of a number or variable is referred to as a radical expression. Variables, coefficients, and operators like addition, subtraction, multiplication, and division can also be included.
Mathematical operations like factoring, reducing the denominator, and employing exponent rules can be used to simplify or alter radical equations.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
The given inequality is -3(2x - 5) < 5(2 - x).
The inequality -3(2x - 5) < 5(2 - x) can be solved as follows
-6x+15<10-5x
Add 5x on both the sides of an inequality, we get
-6x+15+5x<10-5x+5x
-x+15<10
Subtract 10 on both the sides of an inequality, we get
-x<-5
Multiply -1 on both the sides of an inequality, we get
x>5
Therefore, an open circle is at 5 and a bold line starts at 5 and is pointing to the right.
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Suppose you roll an eight-sided die numbered 1 through 8 on its faces. What is the probability that you roll a 3 or a 7?
Express your answer as a simplified fraction.
Answers
The probability that you roll a 3 or a 7 is 1/4.
We have, eight-sided die numbered 1 through 8 on its faces.
Now, the probability to roll 3
= 1/8
and, probability of rolling 7
= 1/8
So, the probability that you roll a 3 or a 7
= 1/8 + 1/8
= 2/8
= 1/4
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Mason would receive $10,000 every year for five years. The rate of interest is 10%. What would be the present value of the amount that would be received by Mason at the end of five years?
Answers
The present value of the payments that Mason would receive over five years is $37,901.
How to Calculate the Present Value of Amount?To find the present value of the payments that Mason would receive over five years, we can use the present value formula for an annuity:
PV = PMT x [1 - (1 + r)^(-n)] / r
Where we have:
PV = present value of the payments
PMT = amount of each payment ($10,000 in this case)
r = interest rate per period (10% or 0.10 in this case)
n = total number of periods (5 in this case)
Plug in the values:
PV = $10,000 x [1 - (1 + 0.10)^(-5)] / 0.10
PV = $10,000 x [1 - 0.6209] / 0.10
PV = $10,000 x 3.7901
PV = $37,901
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Solve for x.
Really easy!! I need quick help tho
algebra/geometry
Answers
Answer:
x = -13/7
Step-by-step explanation:
We can solve either by cross-multiplying or by multiplying both sides by the least common denominator, which is the product of the denominators: (5x + 7)(x - 1) in this case.
Both ways will give us the same answer, although cross-multiplying seems much simpler:
[tex]4(x-1)=5(5x+7)\\4x-4=25x+35\\4x=25x+39\\-21x=39\\x=-39/21=-13/7[/tex]
We can check our answer by plugging in -13/7 for x into the equation and see if we get the same answer on both sides:
[tex]4/(5(-13/7)+7))=5/(-13/7-1)\\4/(-65/7+7)=5/(-20/7)\\4/(-16/7)=-7/4\\-7/4=-7/4[/tex]
what is the value of x if 12= 3/x
Answers
The value of the variable x is 1/4
How to determine the valueIt is important to note that algebraic expressions are described as expressions that are made up of terms, variables, constants, factors and coefficients.
Algebraic expressions are also described as expressions that are composed of mathematical or arithmetic operations.
These operations are listed thus;
AdditionMultiplicationDivisionSubtractionBracketParenthesesWe have that;
12= 3/x
cross multiply the values
12x = 3
Make 'x' subject
x = 1/4
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are these right? i’m so confused
Answers
Answer:
Step-by-step explanation:
Hello! Here is a key for you:
Translation up some amount: y + that amount
Translation down some amount: y - that amount
Translation right some amount: x + that amount
Translation left some amount: x - that amount
Reflection across y-axis: (-x, y)
Reflection across x-axis: (x, -y)
7 - Correct
8 - Correct
9 - Correct
10 - This is correct, but your work is incorrect. The formula for reflection across the y-axis is (-x, y). So, you have to take all the points and make their x-values negative. A is located at (-2, -5). -2 = x, so -(-2) = 2 because negative x negative = positive. A' is located at (2, -5), D' is not. C' = (2, 0) is correct, because C is located at (-2, 0). B' = (3, 0) is correct because B was originally at (-3, 0). D' is located at (-2, -2) because D was originally located at (2, -2). So, all you have to do is swap what you wrote for A and D next to the graph, but the graph is completely correct.
11 - Correct
12 - Your answer for 12 isn't visible. I can see you said that P is located at (3, -2) and that P' is located at (-4, -1) which is correct. This means that (x - 7, y + 1) is the correct rule for this question because 3 - 7 = -4 and -2 + 1 = -1.
13. Your answer for 13 is incorrect. This is a reflection across the x-axis, not a translation. So there should be no adding/subtracting in the rule. The formula for reflection across the x-axis is (x, -y). We can find if this graph is a reflection across the x-axis by seeing if each of the prime versions of the original coordinates are a negative y version of the original coordinates.
U is located at (-4, 4), V is located at (-2, 4), and T is located at (-5, 2).
U' is located at (-4, -4), V is located at (-2, -4), and T is located at (-5, -2).
Since U' is located at (-4, -4) and U is located at (-4, 4), the y value turned negative, meaning that U' was a reflection across the x-axis because of (x, -y). Since V' and T' have negative y values of their corresponding original coordinates, Triangle U'V'T' is a reflection over the x-axis.
So, the correct rule you should put for question 13 is (x, -y).
14 - Correct
15 - Incorrect. All y-values turned negative, meaning this is another case of reflection over the x-axis. The correct rule is (x, -y).
16 - Correct
17 - Correct
18 - Correct
19 - Correct
20 - Incorrect. This was a translation over the x-axis, because all y-values turned negative. The correct rule is (x, -y).
For example, J is located at (-1, -1). J' is located at (-1, 1). The y-value turned negative because -(-1) = 1.
--Suggestion: Keep the formulas for the reflection across the x-axis and y-axis by you while doing homework like this.
Reflection across the x-axis formula: (x, -y).
Reflection across the y-axis formula (-x, y).
Translation up/down: (x, y +/- __)
Translation right/left: (x +/-, y)
Apply these formulas to each coordinate, not just one, to see if they all match up.
Good luck! I hope you understand this now.
Question 3. Instructions are below for each part
Answers
Since then, it has spread to other rivers, colonized them, clogged the water intake pipes, and competed with local species for food. Zebra mussels are the method for removing a lot of plankton from the water column.
Here, we have,
The Caspian Sea in Asia is where zebra mussels, or Driessen polymorph, are found naturally.
They arrived in the Great Lakes region in the late 1980s via ballast water from a transatlantic ship.
The Great Lakes, Mississippi, Tennessee, Hudson, and Ohio river basins were all overrun by these mussels within ten years.
The lake's brilliant blue hue is a result of Tahoe's clean air and water.
There is more to this phenomenon than just the fact that Lake Tahoe's surface reflects the sky, which contributes to its blue color.
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complete question:
As you respond to Part A, Part B, and Part C, follow the directions below.
Address all of the instructions in each prompt.
Use evidence from the information provided and your own knowledge of science to support your responses.
Part A
Describe one way scientists near Lake Tahoe can detect if the lake has been impacted by zebra mussels.
Which projection method is preferred in the United States?
The ________ projection method is preferred in the United States. In this type of projection, the object lies below the horizontal plane and behind the vertical plane.
Answers
Answer:
Third Angle Projection method
Step-by-step explanation:
The Third Angle projection method is preferred in the United States. In this type of projection, the object lies below the horizontal plane and behind the vertical plane
Remy drew a rectangle that is 9 inches long and has an area of 45 in.² what is the width of Remy’s rectangle right and solve a division equation to show your thinking
Answers
Answer:
The division equation used to find the width is: 45 divided by 9 equals 5.
Step-by-step explanation:
The formula for the area of a rectangle is A = lw, where A is the area, l is the length, and w is the width. We know that the length of Remy’s rectangle is 9 inches and the area is 45 square inches. We can use this information to solve for the width: 45 = 9w To solve for w, we can divide both sides of the equation by 9: 45/9 = w 5 = w Therefore, the width of Remy’s rectangle is 5 inches. The division equation used to find the width is: 45 divided by 9 equals 5.
Hope this helps.
Priya hiked 1 2/3 miles. Diego hiked 1/2 mile. How much farther did Priya hike than Diego?
Answers
By taking the difference between the distances, we see that Priya hiked (1 + 1/6) miles more than Diego.
How much farther did Priya hike than Diego?To find this, we just need to take the difference betwee the two distances given.
We know that Priya hiked 1 2/3 miles and Diego hiked 1/2 mile, then the difference is:
D = (1 + 2/3) mi - (1/2) mi
D = (1 + 2/3 - 1/2) mi
D = (1 + 4/6 - 3/6) mi
D = (1 + 1/6) mi
We can see that Priya hiked (1 + 1/6) miles more than Diego.
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The distance farther Priya hike than Diego is 1 1 / 6 miles.
How to find distance travelled?Priya hiked 1 2/3 miles. Diego hiked 1/2 mile. Therefore, let's find how much farther Priya hiked than Diego.
Hence,
Distance hiked by Priya = 1 2 / 3 = 5 / 3 miles
Distance hiked by Diego = 1 / 2 miles
Therefore,
Amount of distance farther Priya hiked than Diego = 5 / 3 - 1 / 2
Amount of distance farther Priya hiked than Diego = 10 - 3 / 6
Amount of distance farther Priya hiked than Diego= 7 / 6 miles
Amount of distance farther Priya hiked than Diego = 1 1 / 6 miles
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P is the weighted average of point C and D. Find the coordinates of P under the given conditions
Answers
Coordinates of P = [tex][(3 * xB + xC + 4 * xD) / 8, (3 * yB + yC + 4 * yD) / 8][/tex]
Coordinates of P = [tex][(4 * xC + 2 * xD + 3 * xE) / 9, (4 * yC + 2 * yD + 3 * yE) / 9][/tex]
Leave the directions of point B alone (x1, y1) and the directions of point D be (x2, y2). Then, at that point, the directions of P are:
[tex][(3x1 + x2)/4, (3y1 + y2)/4][/tex]
Let the directions of point A be (x1, y1) and the directions of point E be (x2, y2). Then, at that point, the directions of P are:
[tex][(x1 + 2x2)/3, (y1 + 2y2)/3][/tex]
Leave the directions of point B alone (x1, y1), the directions of point C be (x2, y2), and the directions of point D be (x3, y3). Then, at that point, the directions of P are:
[tex][(3x1 + x2 + 4x3)/8, (3y1 + y2 + 4y3)/8][/tex]
Leave the directions of point C alone (x1, y1), the directions of point D be (x2, y2), and the directions of point E be (x3, y3). Then, at that point, the directions of P are:
[tex][(4x1 + 2x2 + 3x3)/9, (4y1 + 2y2 + 3y3)/9][/tex]
These recipes can be inferred utilizing the weighted typical equation:
[tex][(w1x1 + w2x2 + ... + wnxn)/(w1 + w2 + ... + wn), (w1y1 + w2y2 + ... + wnyn)/(w1 + w2 + ... + wn)][/tex]
where wi is the heaviness of point I and (xi, yi) are the directions of point I. Subbing the given loads and facilitates into the equations for every issue gives the directions of P for each situation.
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The complete question is:
Find the coordinates of P that represent the weighted average of each set of points based on the given conditions. 12. Point B weighs three times as much as point D. 13. Point E weighs twice as much as point A. 14. Point B has a weight of 3 , point C has a weight of 1 , and point D has a weight of 4. 15. Point C has a weight of 4 , point D has a weight of 2 , and point E has a weight of 3.
Quadrilateral H' is the image of quadrilateral H after a sequence of transformations. If quadrilateral H' is congruent to
quadrilateral H, which transformations could have been used?
A. a dilation by a scale factor of 2 followed by a reflection
B. a rotation followed by a dilation by a scale factor of 1/2
C. a reflection, a translation of 1 unit left, and then a dilation by a scale factor of 3
D. a translation of 6 units down, a rotation, and then a reflection
Answers
The transformations that could be used are: D. a translation of 6 units down, a rotation, and then a reflection.
How to Determine the Series of Transformation?If two shapes are congruent to each other, it means they have the same shape and size. The only series of transformation that can be used to produce an image that is congruent to a preimage of a shape is either a translation, rotation, or a reflection. This therefore implies that any transformation that involves a dilation will not produce congruent images of a shape but would rather produce similar images.
Therefore, option A, B, and C, which involves dilation cannot produce quadrilateral H' that is congruent to quadrilateral H.
The series of transformation that can produce that is: D. a translation of 6 units down, a rotation, and then a reflection.
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I need help with this please
Answers
Answer: Felix spent 5 hours doing chores and 3 hours doing homework
Step-by-step explanation:
It says that x represent chores, y represents homework
Answer:
(5, 3)
Step-by-step explanation:
x represents hours of chores y represents hours of homework
6. If Jeremy has a batting average
of 0.5014
and Alex has a batting average of 0.50098
who has the better average?
Answers
Please help with this questions !!!!!!!!
Answers
Based on the information about the angles, the value of x is 10.
How to calculate the value of xFrom the information, n - 2 = 43
Solving for n, we get:
n = 45
The polygon has 45 sides.
sum of interior angles = (n - 2) * 180 degrees
sum of interior angles = (45 - 2) * 180 degrees
sum of interior angles = 7560 degrees
Since the polygon is regular, all of its angles have the same measure, which we are told is (17x+2)°. Let's use this to find x:
sum of interior angles = number of angles * measure of one angle
7560 = 45 * (17x+2)
7560 = 765x + 90
7470 = 765x
x = 10
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if your restaurant serves 50 bowls of french onion soup daily and each serving has 8 ounces of onions per portion?
Answers
To calculate the total amount of onions needed per day, you can multiply the number of servings by the amount of onions per serving.
50 bowls x 8 ounces of onions per bowl = 400 ounces of onions per day.
Therefore, your restaurant will need 400 ounces of onions per day to serve 50 bowls of French onion soup daily
Five friends A, B. C. D and E play different musical instruments. No two friends play the same number of musical instruments. Flute is the only instrument common between C and E. B and C are the only violin players and when D joins them, all three of them play Congo. Only three friends play Guitar. The Cymbal was the only common instrument among all three-A, B and E considered together. Congo is played by most number of friends. More than 2 people play the flute.
Answers
Violin is the instrument played by least number of friends.
Given: We are given that there are five friends A, B, C, D and E. Any two friends do not play the same number of musical instruments. The only instrument that is common between C and E is Flute. B and C are the only players of violin in the whole group and when D joins them, all three of play Congo. There are only three players of Guitar. The Cymbal is the only common instrument among A, B and E. Congo is the most played instrument. Flute is played by more than 2 people.
To Find: We have to find which instrument is played by the least number of friends.
So, we are given that Violin is played by only 2 friends.
We are given that Flute is played by more than 2 people.
Guitar is played by 3 people.
Cymbal is played by at least 3 people i.e., A, B and E
Congo is played by the greatest number of people.
We can see that every instrument other than Violin is played by more than 2 people whereas Violin is played by only 2 people.
Therefore Violin is the least played instrument.
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The owner of an apple orchard has learned from previous experience that, on average, 5% of the harvested apples have blemishes. The owner randomly selects 10 apples from this year’s harvest. What is the probability that 2 of the apples have blemishes?
Answers
The probability that 2 of the apples have blemishes will be 0.0746.
Frequency distribution of the percentage of successful outcomes that might occur in a certain number of trials with the same chance of success. If X~B(n, p), then the probability is given as,
[tex]\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}[/tex]
The probability is calculated as,
P(X = 2) = ¹⁰C₂ * (0.05)² * (0.95)⁸
P(X = 2) = 0.0746
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I need some assistance with this?
Answers
Check the picture below.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{25}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{24} \end{cases} \\\\\\ x=\sqrt{ 25^2 - 24^2}\implies x=\sqrt{ 625 - 576 } \implies x=\sqrt{ 49 }\implies x=7[/tex]
81 − x = 9
(a) Find the exact solution of the exponential equation in terms of logarithms.
(b) Use a calculator to find an approximation to the solution rounded to six decimal places.
Answers
a) The exact solution of the exponential equation [tex]8^{1-x}=9[/tex] in terms of logarithms is: [tex]x=1-(\frac{2}{3}\times \frac{ln(3)}{ln(2)} )[/tex]
b) An approximation to the solution rounded to six decimal places = 0.056642
Consider the exponential equation [tex]8^{1-x}=9[/tex]
Taking ln (log to the base e) on both the sides of above exponential equation,
ln([tex]8^{1-x}[/tex]) = ln (9)
We solve this equation for x.
We know that the rule of logarithm that [tex]log(a^m)=m\times log(a)[/tex]
Using this rule we get,
(1 - x) ln(8) = ln(3²) ............(3² = 9)
(1 - x) × ln(2³) = 2 × ln(3)
(1 - x) × 3 × ln(2) = 2 × ln(3)
1 - x = (2/3) × (ln(3) / ln(2))
x = 1 - [(2/3) (ln(3) / ln(2))]
x = 1 - [(2/3) × 1.584963]
x = 1 - 1.056642
x = 0.056642
This is the required value of x.
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is it possible to convert between pounds and inches or between inches and cups?
Answers
No. It is not possible to directly convert between pounds and inches or inches and cups.
Conversion between unitsIt is not possible to directly convert between pounds and inches or between inches and cups because they are measuring different things.
Pounds are a unit of weight or mass, while inches are a unit of length or distance. Cups are a unit of volume, which is also different from weight or length.
Thus, all other things being equal it is not possible to directly convert between these units.
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Graph this point on the coordinate plane.
(−412, −2)
Answers
The given coordinate point lies in third quadrant which shown in the graph below.
The given coordinate point is [tex](-4\frac{1}{2}, -2)[/tex].
A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.
In the given coordinate point both x-coordinate and y-coordinate are negative.
Hence, the given coordinate point lies in third quadrant which shown in the graph below.
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