The radius line intersects the circle at (4, 8) because the tangent line's slope, which is -1/3, is perpendicular to the radius line's slope of (0, 8), which is 0.
1. Use m = 0 to calculate the slope of the line through point (12, 0).
2. Calculate the radical line's angle between the origin and the tangent point: m = ∞
3. To determine the location where the line touches the circle, use the relationship between the slopes: M2 = -1/M1 = -1/0 = - since M1 M2 = -1
4. To determine a point's coordinates, use the equation for a circle: (x - 8)2 + (y - 8)2 = 82, so (4, 8) (4, 8)
We can use the relationship between the slopes of the tangent line and the radical line from the origin to the tangent point to determine the location where the line contacts the circle. Since the tangent line crosses through point (12,0), its slope is equal to zero. Since the radical line slopes at m2 =, m1 m2 = -1. Accordingly, m2 = -1/m1 = -1/0 = -∞.The coordinates of the spot where the line touches the circle can then be determined using the equation for a circle. (x - 8)2 + (y - 8)2 = 82 is the equation for a circle having the origin as its center and a radius of 8. The coordinates of the place where the line intersects the circle are (4, 8), which can be obtained by substituting in the values for m1 and m2.
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nine delegates, three each from three different countries, randomly select chairs at a round table that seats nine people. let the probability that each delegate sits next to at least one delegate from another country be $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. find $m n$.
The ones we don't want are those. We only want 410 of the 560 total, thus the cost is $097.
Contact nations A, B, and C. At the northernmost position for configurations, someone from A is seated. Since the only thing the problem mentions about how delegates can differ is by their country, I decided to represent people in my solution by their respective nations. Now, we can see that there are nCr(8, 2) * nCr(6, 3) = 560 possible arrangements (8 seats choose 2 for the rest of the A country, 6 seats choose 3 for B). It is clear that configurations with three delegates in a row are the ones we don't want. Take note that scenarios for A, B, and C to be together are still valid despite my placing of A at the start.We now apply the inclusion-exclusion principle. Two cases for an A three in a row. First. A, Master A, A: $20 for B seats at nCr(6, 3). Additionally, there is $20 for each "slant" A set. =$60. *3=180. A and B both: Two cases once more! We identify four ways for B to get three in a row: A, Master A, A, and A. $12 is the same for slant. *3 = $36 (AB, BC, or CA). For all three: This time, we have two of the three aforementioned A circumstances, for a total of six. 180-36+6 Equals 150 in the end. The ones we don't want are those. We only want 410 of the 560 total, thus the cost is $097.
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The vertex form of the function is y = (x +)2+.
The vertex form of the function is [tex]y = (x+4)^{2} - 19[/tex]
Vertex form of function:
The vertex of the function is located at (h,k) of its vertex form, and will be located at the peak or trough of the parabola on a graph. This is the highest or lowest point of the function, depending on its direction.
The vertex form of the equation is written as,
[tex]y = (x+h)^{2} + k[/tex]
Given function is,
y = x² + 8x + 16 - 3 -16
It is observed that,
x² +8x + 16 = (x+4)²
So that, we can write as above function,
y = x² + 8x + 16 - 3 -16 = (x+4)² - 3 -16
or
y = (x+4)² - 19
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please explain correctly how to get the correct answer thank you.
Answer:
Option C
Step-by-step explanation:
First, knowing that two angles on a horizontal line split by a vertical line at any angle is equal to 180 degrees, I try to find which of the combinations of angle x and z equal 180.
A. x = 63, and z = 104 and together they equal 170, so not A
B. x = 76 and z = 63 and together they equal 139 so not B
C. x = 76 and z = 104 and together they equal 180 so it could be C, but we must check D to make sure.
D. x = 63 and z = 76 and together they equal 139 so not D.
From all of this it must be option C
(a) What additional information is needed to prove the triangles are congruent by ASA Postulate? Explain.
(b) What additional information is needed to prove the triangles are congruent by the HLTheorem? Explain.
Part (a)
ASA = angle side angle
To use ASA, we need two angles and a side between those angles. We already have one pair of angles (DFE and GHI). The other pair of angles must be DEF and GIH to have the side sandwiched between the angles.
Answer: We need to know if angle DEF is congruent to angle GIH===================================================
Part (b)
HL = hypotenuse leg
The sides EF and IH are congruent to one another because of the tickmarks. They are the legs of each right triangle. So that takes care of the "L" of "HL". We need to have the hypotenuses congruent to each other to be able to use HL. This theorem only applies to right triangles.
Answer: We need to know if segment DE is congruent to segment GIA cylinder has a radius of 2.5meters. Its volume is 37.5\pi cubic meters. What is the height of the cylinder?
Answer: height = 1.91 m
Step-by-step explanation: Using the formula
V=πr2h
Solving for h
h=V
πr2=37.5
π·2.52≈1.90986m
Can someone show meh pls
The tape diagram represents an equation.
Write an equation to represent the image
w 1.3 2.7
The equation that represents the image will be w + 1.3 = 2.7. And the value of 'w' will be 1.4.
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
The length of both tapes is the same. Then the equation is given as,
w + 1.3 = 2.7
Simplify the equation for w, then we have
w + 1.3 = 2.7
w = 1.4
The equation that represents the image will be w + 1.3 = 2.7. And the value of 'w' will be 1.4.
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4. Dilate the figure with the origin as the center of dilation.
(x,y) → (2x, 2y)
The dilated quadrilateral is A' ( -2 , 4 ) , B' ( 4 , 4 ) , C' ( 6 , -2 ) and D' ( 0 , -2 )
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the quadrilateral be represented as ABCD
Now , the coordinates of ABCD is given as
A ( -1 , 2 ) , B ( 2 , 2 ) , C ( 3 , -1 ) and D ( 0 , -1 )
Now , when the dilation is of the scale of (x,y) → (2x, 2y) about the origin
Substituting the values in the equation , we get
A' ( x , y ) = A ( 2 ( -1 ) , 2 ( 2 ) )
On simplifying the equation , we get
The coordinates of A' is = A' ( -2 , 4 )
The coordinates of B' is = B' ( 4 , 4 )
The coordinates of C' is = C' ( 6 , -2 )
The coordinates of D' is = D' ( 0 , -2 )
Hence , the dilated figure is solved
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What is the area of this compound figure?
Answer: 188in^2
Step-by-step explanation:
You can break the figure into 3 smaller shapes
15 x 5
10 x 5
and 9 x 7
The areas of these smaller shapes are 75, 59 and 63
adding these areas together would get you 188 in squared.
It is first down in a football game. Your team has the ball at your 25-yard marker, and the play is a successful run for 6 yards. A number line from ten to forty with labels at ten, twenty, thirty, and forty. Between each pair of labeled points are four tick marks. Where does the ball end up? Where is the ball relative to where it started? Use the number line to find the answer.
Answer: ddddddddddddddddddddddddddddddddddddddddddddddbddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd
Step-by-step explanation:
on january 28, 1986, space shuttle challenger exploded on takeoff. all seven crew members were killed. following the disaster, scientists and statisticians helped analyze what went wrong. they determined that the failure of o-ring joints in the shuttle's booster rockets was to blame. under the cold conditions that day, experts estimated that the probability that an individual o-ring joint would function properly was 0.977. but there were six of these o-ring joints, and all six had to function properly for the shuttle to launch safely. assuming that o-ring joints succeed or fail independently, find the probability that the shuttle would launch safely under similar conditions. show your work.
The probability of the shuttle launching safely under similar conditions is 0.859, or approximately 86%.
Scientists and statisticians played a crucial role in analyzing the cause of the disaster, which was eventually attributed to the failure of O-ring joints in the shuttle's booster rockets.
To understand the probability of the shuttle launching safely under similar conditions, we need to consider the probability of all six O-ring joints functioning properly. According to experts, the probability of an individual O-ring joint working in cold conditions was 0.977.
Assuming that the O-ring joints succeed or fail independently, we can use the multiplication rule of probability to calculate the probability of all six joints functioning properly.
The multiplication rule states that the probability of two independent events occurring together is the product of their individual probabilities. In this case, the probability of all six joints working properly is:
P(all six joints work) = P(joint 1 works) x P(joint 2 works) x P(joint 3 works) x P(joint 4 works) x P(joint 5 works) x P(joint 6 works)
Plugging in the given probability of an individual O-ring joint working in cold conditions (0.977), we get:
P(all six joints work) = 0.977 x 0.977 x 0.977 x 0.977 x 0.977 x 0.977
P(all six joints work) = 0.977⁶
P(all six joints work) = 0.859
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Help answer this
Two functions are represented below.
Function 1:
Function 2:
x y
-1 3
0 1
1 -1
2 -3
Which statement is true about the y-intercepts of the functions?
A. At least one of the functions does not have a y-intercept.
B. Function 1 and Function 2 have y-intercepts that are equal.
C. Function 1 has a y-intercept that is less than the y-intercept of
Function 2.
D. Function 1 has a y-intercept that is greater than the y-intercept of
Function 2.
Function 1 and Function 2 have y-intercepts that are equal. The solution has been obtained by using slope-intercept form.
What is slope-intercept form?
The line that represents the graph of the equation y = mx + b has a slope of m and a y-intercept of b. The m and b values are real integers, and the slope-intercept form of the linear equation is used.
We are given two functions.
Now, we will represent the functions in the slope-intercept form to find the y-intercept.
Function 1
⇒4x - 2y = -2
⇒2x - y = -1 (Dividing both sides by 2)
⇒ -y = -1 - 2x
⇒y = 2x + 1
So, the y-intercept is 1.
Function 2
We are given two points as (-1,3) and (0,1)
The slope comes out to be = -2
So, b = 3 - (-2)(-1) = 1
So, the y-intercept is 1.
Hence, function 1 and function 2 have y-intercepts that are equal.
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what is the slope of the line
Answer:
slope = [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (5, 2) ← 2 points on the line
m = [tex]\frac{2-0}{5-0}[/tex] = [tex]\frac{2}{5}[/tex]
Marsha uses 8.3 pints of blue paint and white paint to paint her bedroom walls. 3 5 of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls? Express your answer in fraction and decimal form.
Answer:
Step-by-step explanation:
4.8
i got u brainliest please it helps a lot
The triangles are similar.
What s the value of x?
See the attachment for the problem to be answered.
Answer:
?
Step-by-step explanation:
The monster under your bed loves fruit. To appease him you buy 4 pounds of grapes. You also buy some strawberries. Both fruits cost $1.20 per pound. You spend $6. How many pounds of strawberries did you buy?
Answer:
1 pound of strawberries
Step-by-step explanation:
4 x $1.20 = $4.80
$6 - $4.80 = $1.20
one pound is $1.20
What's the percentage if the whole number is 7990 and the part is 19. 16
This means that for part of 19.16 is 0.24% of the total number 7990.Percentage is a way of expressing a number as a fraction of 100. It is commonly used to describe a portion or share of a total quantity.
To find the percentage of a number, we need to multiply the number by the percentage as a decimal and then express the result as a percentage.
In the case of 7990 and 19.16, 19.16 is the part of the whole number 7990. To find the percentage, we need to divide the part by the whole and then multiply by 100.
So, the percentage of 19.16 of 7990 is:
19.16 ÷ 7990 × 100 = 0.24%
This means that 19.16 is 0.24% of the total number 7990.
Percentages are often used in various applications, including calculating interest on loans, determining grades in school, and comparing data between different sets of information. In addition, they are used in various business applications, such as computing taxes, discounts, and determining profits and losses. In conclusion, understanding the concept of percentage is important in various areas of our daily lives and in various professions, as it helps us to make informed decisions and communicate information effectively.
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he accompanying histogram shows the life expectancies at birth for 190 countries as collected by an international health agency.
a) Which would you expect to be larger: the median or the mean? Explain briefly.
b) Which would you report: the median or the mean? Explain briefly.
a) The median would be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean.
b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers.
a) The median is expected to be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean. The mean is calculated by adding all the values together and dividing by the number of values, and if there are any values that are much lower or higher than the rest, this will affect the mean significantly. The median, however, is the midpoint of the values, so outliers have less of an influence on it.
b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers. The median is the midpoint of the values, which means that if there are any values that are much lower or higher than the rest, it will not affect the median as much as it does the mean. This makes the median more accurate in representing the life expectancy of countries, as it is not skewed by outliers. Furthermore, the median is generally more reliable when dealing with skewed distributions, which is often the case with life expectancy data.
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If the sum of two angles is 90 then angles are called ___angles
If the sum of two angles is 90 degrees, then the angles are called complementary angles.
Complementary angles are a type of angle relationship where two angles add up to exactly 90 degrees. In other words, when you add the measures of two complementary angles together, the sum is always equal to 90 degrees.
For example, if angle A measures 30 degrees, and angle B measures 60 degrees, then angle A and angle B are complementary angles, because 30 degrees + 60 degrees = 90 degrees.
Complementary angles are important in geometry and trigonometry, because they often appear in problems involving right triangles. In a right triangle, one of the angles measures 90 degrees, which means that the other two angles must be complementary.
For example, if one angle in a right triangle measures 30 degrees, then the other angle must measure 60 degrees, since 30 degrees + 60 degrees = 90 degrees.
Understanding complementary angles can be useful in a wide range of mathematical and real-world contexts. For example, in construction or engineering, understanding complementary angles can help ensure that structures are built at the correct angle to provide the necessary support and stability.
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Factor the polynomial.
3x³-300x
The result to the factorization of the polynomial is 3x (x + 10) (x - 10).
Polynomial FactorizationFactoring polynomials involves utilizing prime factorization to break the given polynomial down into a product of two or more polynomials. Polynomials can be readily simplified by factoring them.
Writing each term of the longer expression as the product of its elements is the initial step to factorization polynomials.
= 3x³ - 300x
= 3x(x²) - 300x
= 3x(x²) - 3x(100)
= 3x(x² - 100)
= 3x(x² - 10²)
Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = ( a + b ) ( a − b );
where
a = x and b = 10= 3x (x+10) (x−10)
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Let a function f A B be defined by f(x) 11 B-1-2, 1, 0,2- 4¹5) 0. can you make it one to one and onto both? x-1 F x*-2 with A = {-1, 0, 1, 2, 3, 4) and x+2 find the range off. Is the function one to one and onto both? If not, how a whother each of the functions below is one to one, onto both?
Answer:
The function f: A -> B is defined by:
f(x) = { 11, if x = -1 or x = 2,
-1, if x = 0,
-2, if x = 1,
0, if x = 3 or x = 4 }
The range of the function is the set of all possible values of f(x). In this case, the range of f is B = {-2, -1, 0, 11}.
To determine if the function is one-to-one, we need to check if each element in the range has only one pre-image. In other words, we need to check if no two elements in A map to the same element in B. Since each element in B has a unique pre-image in A, the function is one-to-one.
To determine if the function is onto, we need to check if each element in B is the image of some element in A. In this case, every element in B is the image of exactly one element in A, so the function is onto.
Therefore, the function f is one-to-one and onto both.
Topic: Using the rational theorem to find all zeros of a polynomial
Question: 5x^4-26x^3-64x^2+9x-14
The zeroes of 5x^4-26x^3-64x^2+9x-14 are -2, 7 , [tex]\frac{1+i\sqrt{19} }{10}[/tex] and [tex]\frac{1-i\sqrt{19} }{10}[/tex] by Using the rational theorem.
f(x) = [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]
Now, put x = -2
f(-2) = [tex]5(-2)^{4} - 26(-2)^{3} - 64(-2)^{2} +9(-2) -14[/tex]
f(-2) = 0
so, -2 is a zero of f(x)
or (x+2) is a factor of [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]
putting x = 7
f(7) = [tex]5(7)^{4} - 26(7)^{3} - 64(7)^{2} +9(7) -14[/tex]
f(7) = 0
so, (x-7) is a factor of [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex]
Now (x+2)(x-7) would also be a factor so
Divide [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex] by (x+2)(x-7)
or divide [tex]5x^{4} - 26x^{3} - 64x^{2} +9x -14[/tex] by [tex]x^{2} -5x -14[/tex]
The quotient or other factor will be [tex]5x^{2} - x +1[/tex]
[tex]5x^{2} - x +1[/tex]
By factorizing [tex]5x^{2} - x +1[/tex]
The other two zeroes are [tex]\frac{1+i\sqrt{19} }{10}[/tex] and [tex]\frac{1-i\sqrt{19} }{10}[/tex]
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Celine's Cupcakes recorded how many cupcakes it recently sold in each flavor. carrot cupcakes 8 pumpkin cupcakes 1 lemon cupcakes 6 Considering this data, how many of the next 20 cupcakes sold would you expect to be lemon cupcakes?
So we would expect 8 of the next 20 cupcakes sold to be lemon cupcakes.
What is Algebraic expression?
An algebraic expression is a mathematical phrase that consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables can represent unknown values, while the constants represent known values.
Based on the data provided by Celine's Cupcakes, out of the total of 15 cupcakes sold, 6 were lemon cupcakes. This means that the proportion of lemon cupcakes sold is:
6/15 = 0.4
To estimate how many of the next 20 cupcakes sold would be lemon cupcakes, we can assume that the proportion of lemon cupcakes sold will remain the same. Therefore, we can expect that:
0.4 x 20 = 8
Therefore, So we would expect 8 of the next 20 cupcakes sold to be lemon cupcakes.
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My parents give me an allowance of $60 every month. To earn some extra money I get a job. I make $7.50 an hour at this job. In order to have a social life and hang out with my friends, I am going to need at least $260 every month.
What is the APPROXIMATE minimum amount of hours I will have to work to accomplish my goal? (HINT: use whole numbers for your answer)
I would need to work at least 27 hours to make enough money to reach my goal.
What are arithmatic operations?
Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.
Let's start by finding the amount of money I receive from my allowance and how much more money I need to make to reach my goal:
Allowance per month = $60
Amount of money I need for social life = $260
Additional amount of money I need to make = $260 - $60 = $200
Now, let's divide the additional amount of money I need to make by the amount I make per hour to find how many hours I need to work:
$200 ÷ $7.50 per hour = 26.67 hours
Since we can't work a fraction of an hour, we need to round up to the nearest whole number.
Therefore, I would need to work at least 27 hours to make enough money to reach my goal.
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A company charges a shipping fee that is 4. 5% of the purchase price for all items it ships. What is the fee to ship an item that costs 56$?
The shipping charge of an item on the purchase $56 is $2.52.
PercentagePercentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
The percentage of a number is the value of the number out of 100.
For example, in a class, there are 26 boys and 24 girls. So, the percentage of boys in the class is 26/(26+24) × 100 = 26/50 × 100 = 52%, which means out of 100, 52 are boys.
A company charges shipping fee = 4.5% of the purchase price for all items,
Cost of an item =$56
So, shipping fee = 4.5% of 56
= 4.5/100 × 56
= 0.045 × 56
= $2.52
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we just found a linear relationship between and , but these are the transformed variables. what we would like to do now is find the nonlinear relationship between and by transforming back. let be your transformed model, with slope and intercept . what value of do you get? (in this problem, you must round to two significant figures.) unanswered using this, what is the relationship between and in terms of ? use the correct answer from the previous question for the relationship between and as well as and . enter your answer in terms of (type x), (type omega), and your rounded numerical value for only.
The relationship between and in terms of equation is linear model
In statistics, linear relationships are often studied as they provide a simple way to model data. However, not all relationships between variables can be accurately represented using a linear model. In such cases, transforming the variables can sometimes reveal a nonlinear relationship.
When we say we have found a linear relationship between two variables, it means that one variable can be expressed as a linear function of the other.
If we have two variables x and y, a linear relationship between them would be of the form y = mx + b, where m is the slope of the line and b is the y-intercept. This means that as x increases or decreases, y changes in a straight-line fashion.
To find the nonlinear relationship between the original variables, we need to invert the transformation. In this case, we can express y in terms of x by using the inverse of the transformation we applied. Let's say we applied a transformation of the form y' = log(y) and x' = log(x), then we can invert this transformation by taking the exponential of both sides of the equation, giving us
=> [tex]y = e{y'}[/tex] and [tex]x = e^{(x').}[/tex]
Using these equations, we can express the linear model in terms of the original variables as
=> [tex]y = e^{(mx' + b)}[/tex]
Therefore, the relationship between y and x in terms of e and the rounded numerical value is given by
=> [tex]y = e^{(mx' + b)}[/tex]
where m and b are the slope and intercept of the linear model.
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Miss Robert and Mr. Neil have homerooms with the same
perimeter. Mr. Neil's homeroom has a width that
is 1 times the width of Miss Robert's homeroom.
What is the length, /, of Mr. Neil's homeroom?
ft
Miss Robert's
Homeroom
50 ft (w)
33 ft (e)
Mr. Neil's
Homeroom
The length of Mr. Neil's homeroom is (10/11) times the length of Miss Robert's homeroom.
What is the length of Mr. Neil's homeroom?The length of Mr. Neil's homeroom is calculated as follows:
Let's assume that Miss Robert's homeroom has width w and length l, and Mr. Neil's homeroom has width (1¹/₁₀ or 11/10)w and length x.
Both homerooms have the same perimeter, therefore:
2w + 2l = 2(11/10)w + 2x
Simplifying the equation:
2l - 2x = (2/10)w
l - x = (1/10)w
x = l - (1/10)w
To solve for x, we need to express it in terms of l and w.
From the equation above, we can substitute x with l - (1/10)w:
(11/10)w = 2l - x
(11/10)w = 2l - l + (1/10)w
(10/10)w = l + (1/10)w
w = (10/11)l
Substituting w with (10/11)l in the expression for x, we get:
x = l - (1/10)(10/11)l
x = l - (1/11)l
x = (10/11)l
Therefore, the length of Mr. Neil's homeroom is (10/11) times the length of Miss Robert's homeroom.
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Segment AD is an altitude of Triangle ABC.
The figure is not to scale.
Which of the following additional statements would allow us to prove that AB is congruent to AC?
AD is also an internal bisector of ΔABC, this statements prove that AB is congruent to AC.
What is the bisector of the triangle?
The bisector of a triangle is a segment that divides one of its interior angles into two equal parts and continues until it reaches the side opposite that angle. In other words, the bisector of a triangle is a line that divides each interior angle of the triangle into two equal angles.
We have given,
Segment AD is an altitude of ΔABC.
If CD ≅ BD
So, AD is the middle line of the triangle
AD is also an altitude of ΔABC.
So, AD is also an internal bisector of ΔABC
So, AB ≅ AC ............{Thereom of unity of three lines}
Hence, AD is also an internal bisector of ΔABC, this statements prove that AB is congruent to AC.
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Use the factors of the function and the y-intercept to find the standard form of the equation representing Jared’s function.
The equation of the polynomial is P(x) = 0.16875(x + 8)(x - 10)
How to determine the equation of the polynomialFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings:
A root of multiplicity 1 at x = -8
A root of multiplicity 1 at x = 10
y-intercept = -13.5
A polynomial is represented as
P(x) = a * (x - zero)^multiplicity
Using the above as a guide, we have the following:
P(x) = a * (x + 8)(x - 10)
The y-intercept is -13.5
So, we have
a * (0 + 8)(0 - 10) = -13.5
This gives
a = 0.16875
Hence, the expression is P(x) = 0.16875(x + 8)(x - 10)
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Two quadrilaterals are described
The only statement that must be based on the quadrilateral properties is; Option B: Base angles of quadrilateral Z are congruent
How to find the properties of a quadrilateral?Some of the properties of a quadrilateral are;
1) They have four vertices.
2) They have four sides.
3) The sum of all interior angles is 360°.
4) They have two diagonals.
5) A quadrilateral can be regular or irregular.
Now, from the description of Quadrilaterals T and Z, we can say that;
- The base angles of quadrilateral T are not congruent since at least one pair of parallel side is congruent.
- Base angles of quadrilateral z are congruent since opposite sides are congruent.
- Consecutive angles of quadrilateral Z are not congruent
- Opposite angles of quadrilateral T are not supplementary.
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a circle with radius is inscribed in a square and circumscribed about another square as shown. which fraction is closest to the ratio of the circle's shaded area to the area between the two squares?
The fraction that is the ratio of the shaded area of the circle to the area between the two squares is (π−2)/2.
A fraction is a mathematical expression that represents a part or a proportion of a whole.
Let us assume that the radius of the circle is 'r' units. Therefore, the diameter of the circle is 2r units. The diagonal of the inner square is equal to the diameter of the circle, which is 2r units. Hence, the side of the inner square is r√2 units.
Now, let's consider the area of the circle. The formula for the area of a circle is
=> A=πr².
Therefore, the area of the circle is πr².
The area between the two squares is the difference between the area of the outer square and the area of the inner square. The area of the outer square is
=> (2r)²=4r²,
and the area of the inner square is
=> (r√2)²=2r².
Hence, the area between the two squares is
=> 4r²−2r²=2r².
The shaded area of the circle is the area inside the circle but outside the inner square. We can find this area by subtracting the area of the inner square from the area of the circle. Therefore, the shaded area of the circle is
=> πr²−2r²=(π−2)r².
Now, let's find the ratio of the shaded area of the circle to the area between the two squares. We can express this ratio as a fraction. Thus,
ratio = (π - 2)r² / 2r
We can simplify this fraction by canceling out the common factor r^2 in both the numerator and denominator. Thus,
ratio = (π - 2) / 2
This fraction is closest to the ratio of the shaded area of the circle to the area between the two squares.
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