The range of possible values for the third side of the triangle is d)6 < x < 26.
The third side of an acute triangle must be shorter than the sum of the other two sides and longer than the difference between the other two sides. By using the Pythagorean Theorem, we can find the range of possible values for the third side.
The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle equals the square of the hypotenuse. So, for this triangle, we have 10^2 + 16^2 = x^2.
Solve for x: x^2 = 256, so x = √256 = 16.
The third side must be shorter than the sum of the other two sides. So, the maximum value for x is 16 + 10 = 26.
The third side must be longer than the difference of the other two sides. So, the minimum value for x is 16 - 10 = 6.
Therefore, the range of possible values for the third side of the triangle is 6 < x < 26.
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An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.
Which best describes the range of possible values for the third side of the triangle?
x < 12.5, x > 18.9
12.5 < x < 18.9
x < 6, x > 26
6 < x < 26
factor each expression
5a - 25
Answer: 5 (a-5)
Step-by-step explanation:
5 divided by 25 is 5 so that's where 5 came from and then just move the 5 from the a to get just a.
How to convert 145 pounds to kilograms?
Multiply the mass in pounds by 0.45359237 to convert 145 lbs to kilogrammes.
How Do You Convert Lbs To Kg?Add 0.45359237 kg to the given number of pounds to convert it to kilogrammes. For instance, multiply the supplied 5 pounds by 0.45359237 kg to convert 5 lbs to kilogrammes. Consequently, 5 lbs is about equivalent to 2.26796185 kg.It is said that a kilogramme (kg) weighs 2.2 times more than a pound (represented as lbs). Thus, 2.26 pounds are equal to one kilogramme of mass. In light of this, we shall now examine some of the primary variations between the pound and the kilogramme.The imperial unit of mass or weight measurement is the pound.Multiply the mass in pounds by 0.45359237 to convert 145 lbs to kilogrammes. [kg] = 145 * 0.45359237 is the formula to convert 145 pounds to kilogrammes.To learn more about pounds refer to:
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PLS HELP AND SHOW WORK PLS
A librarian has 274 return books. 50 of the books are reserved at her desk, and the remaining books need to be shelved. Each shelf can hold 14 books. write and solve an equation to find the number of shelves needed.
Answer: 16
Step-by-step explanation:
274-50=224/14=16
Answer:
16
Step-by-step explanation:
the equality v · v = kvk 2 holds for all vectors v in r n . True or False
The formula v · v = kvk2 can be seen to hold for all vectors in Rn, as the dot product of a vector and itself is equal to the magnitude of the vector squared.
The formula v · v = kvk2 is true for all vectors v in Rn. This is because the dot product of a vector and itself is equal to the magnitude of the vector squared. The dot product of two vectors is defined as the sum of the products of their components. Therefore, when a vector v is multiplied by itself, the result is the sum of the squares of all its components. The magnitude of a vector is defined as the square root of the sum of the squares of its components. Thus, the formula v · v = kvk2 can be seen to hold for all vectors in Rn, as the dot product of a vector and itself is equal to the magnitude of the vector squared.
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Use cylindrical shells to find the volume of the solid that is generated when the region that is enclosed by y=1/x^3, x=1, x=2, y=0 is revolved about the line x=-1
The volume of the solid that is generated is: [tex]2\pi[/tex][tex][ In|x| - x^-^1]^2_1[/tex]
Now, According to the question:
The formula for the shell method is :
[tex]=\int\limits^a_b {2\pi rh} \, dx[/tex]
where, a and b are the x - bound, which are x=1 and x=2,
So, a = 1 and b = 2
r is the distance from a certain x-value in the interval [1, 2] and the axis of rotation, which is x = -1 .
r = x - (-1) = x + 1
h is the height of the cylinder at a certain x-value in the interval [1, 2], which is [tex]\frac{1}{x^{2} } - 0[/tex] = [tex]\frac{1}{x^{2} }[/tex] (because [tex]\frac{1}{x^{2} }[/tex] is always greater than 0 and h must be positive).
Plugging it all in volume
[tex]\int\limits^2_1 {(2\pi (x + 1)(\frac{1}{x^2} ))} \, dx[/tex]
= [tex]2\pi \int\limits^2_1 { (x + 1)(\frac{1}{x^2} ))} \, dx[/tex]
[tex]2\pi[/tex][tex][ In|x| - x^-^1]^2_1[/tex]
Hence, The volume of the solid that is generated is: [tex]2\pi[/tex][tex][ In|x| - x^-^1]^2_1[/tex]
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in parallelogram WXYZ, diagonals line WY and line XZ intersect at point A. WA = 3x²-105 and AY = 6x. what is line WY? Show your work.
The complete diagonal line WY is 3x² + 6x - 105.
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
The area of a parallelogram is base multiples by height as two triangles form a parallelogram.
Given, In parallelogram WXYZ, diagonals line WY intersect at point A.
WA = 3x² - 105 and AY = 6x, So the line Wy can be obtained by adding
WA and AY.
= 3x² - 105 + 6x.
= 3x² + 6x - 105.
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The required measure of the diagonal AY is given as 84 as per the given condition.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
WA = 3x²- 105,
AY = 6x
Since diagonals of parallelograms bisect each other,
3x²- 105 = 6x
3x² - 6x - 105 = 0
x² - 2x - 35 = 0
(x - 7)(x + 5) = 0
x = 7, -5
A negative value of x can be neglected.
So,
AY = 6x
= 6×7 = 42
Now.
WY = 2AY = 2(42) = 84
Thus, the required measure of the diagonal AY is given as 84 as per the given condition.
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x is gamma, what is cx
"cX" is a function that takes two inputs and returns a scalar result and the value of "cX" depends on the values of the scalar "c" and the constant X.
Gamma (Γ) is a mathematical constant that is used in various areas of mathematics, including probability theory, statistics, and engineering.
The symbol "c" is a constant that represents a scalar multiplier in mathematics. This means that when you multiply a value by "c", you are multiplying it by a constant number. In this case, when we say "cX", we are multiplying the value of X (which is gamma) by the constant "c".
So, in mathematical terms, the expression "cX" can be defined as a function that takes a scalar value (c) and a constant value (X = gamma) as inputs, and returns a scalar result. This function can be used to determine the value of "cX" for a given value of "c".
It is important to note that the value of "cX" depends on the value of the scalar "c". For example, if "c" is equal to 2, then "cX" would be equal to 2 times the value of gamma.
On the other hand, if "c" is equal to 0.5, then "cX" would be equal to 0.5 times the value of gamma.
Complete Question:
Show that if X is gamma distributed and c(> 0) is a constant, then cX is gamma distributed. In particular, if X is chi-squared distributed, then cX is gamma distributed.
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Polygon X is a scaled copy of Polygon Y using a scale factor of 3. Which of the following statements is true?
The area of Polygon Y is [tex]\frac{1}{9}[/tex] the area of Polygon X.
The area of Polygon X is [tex]\frac{1}{9}[/tex] the area of Polygon Y.
The area of Polygon Y is 9 times the area of Polygon X.
The area of Polygon X is 9 times the area of Polygon Y.
Since Polygon X is a scaled copy of Polygon Y using a scale factor of 3, a statement which is true include the following: D. The area of Polygon X is 9 times the area of Polygon Y.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)
Therefore, the area of Polygon X with respect to Polygon Y based on the given scale factor of 3 is as follows;
Area of Polygon X/Area of Polygon Y = 3²
Area of Polygon X/Area of Polygon Y = 9.
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if sqrt a / sprt b =, which statment must be true?
The statement that must be true is (c) x² = a/b
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
√a/√b = x
Take the square root of both sides
So, we have the following representation
a/b = x²
Rewrite the equation as
x² = a/b
Hence, the solution is x² = a/b
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Please help ASAP
A customer at a shipping store is planning to send a package and is considering two options. The customer can send a package for $5, plus an additional $2 per pound. The cost, y, can be represented by the equation y = 5 + 2x, where x represents the amount of pounds of the package. Another option is that the customer can pay a one-time fee of $15 to send the box, represented by the equation y = 15.
Based on the graph of the system of equations, when will the cost of the two shipping options be the same?
A package that weighs 15 pounds will cost $35 for both options.
A package that weighs 15 pounds will cost $25 for both options.
A package that weighs 10 pounds will cost $15 for both options.
A package that weighs 5 pounds will cost $15 for both options.
Answer:
A package that weighs 5 pounds will cost $15 for both options.
Step-by-step explanation:
The equation for the cost of the first shipping option is y = 5 + 2x, where x represents the amount of pounds of the package. The cost, y, increases by $2 per pound of the package. So, if the package weighs 5 pounds, the cost of the first option would be y = 5 + 2 * 5 = $15.
The equation for the second shipping option is y = 15, representing a one-time fee of $15 to send the box. The cost is fixed at $15 regardless of the weight of the package.
Therefore, if the package weighs 5 pounds, the cost of both shipping options would be $15, and the two options would cost the same.
Which of these numbers is not rational
1. v3
2. 0.25
3. 1/5
4. z9
Answer:
√3 is not rational
Step-by-step explanation:
• A rational number is that number that can be expressed as a fraction provided its denominator is not equal to zero.
Forexample;
√3 is irrational because it can not be expressed i to a fraction, but into a long decimal. [√3 = 1.732050....]0.25 is rational because it can be expressed as a fraction [tex]{ \boxed{ \tt{0.25 = \frac{25}{100} = \frac{5}{20} = \frac{1}{4} }}}[/tex]1/5 is already rational as per the definition.√9 is rational because it can be a fraction.[tex] { \boxed{ \tt{ \sqrt{9} = 3 = \frac{3}{1} }}}[/tex]using the substitution u=5x−2, ∫x5x−2−−−−−√ⅆx is equivalent to which of the following?
using the substitution u=5x−2, ∫x5x−2−−−−−√ⅆx is equivalent to ∫u+2 /5 du/5
What is Derivative?
Calculus defines a derivative as the rate at which one quantity, y, changes in relation to another, x. The differential coefficient of y with respect to x is another name for it. Finding a function's derivative is the process of differentiation. A function's derivative is typically represented by d/dx (f(x)) (or df/dx (or Df(x) (or f')). Let's examine the technical definition of a derivative. Two points on a function f(x) curve are (x, f(x)) and ((x + h), f(x + h)), respectively. If so, [f(x + h) - f(x)]/(x + h - x) = [f(x + h) - f(x) / h] will be the slope of the secant line through these points. The second point overlaps the first point in the figure below when the distance between two points is nearly equal to 0 (i.e., as h approaches 0), and the secant line turns into the tangent line. Calculus refers to the slope of the tangent line as the function's derivative.
x = 1/y + 1
y + 1 = 1/x
y = 1/x - 1
differentiating y w.r.t to x
dy/dx=-1/x^2
using subsitution u= 5x-2
then x= u+2/5
∫u+2 /5 du/5
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By rounding to one significant figure, estimate the answers to these questions:
a)
b)
c)
98 + 11
764
19
798
8 x 41
The solution to the division problems after rounding off to 1 significant figure are;
a) 9
b) 40
c) 2
How to round off numbers to one significant figure?The first significant figure of a number is defined as the first digit which is not zero. Hence, the first significant figure of 20,499 is 2 and the first significant figure of 0.0020499 is 2
a) 98 ÷ 11
When this is divided, we have;
8.91
Rounding off to one significant figure gives 9.
b) 764/19
When this is divided, we have;
40.21
Rounding off to one significant figure gives 40.
c) 798/(8 * 41)
When this is divided, we have; 2.43
Rounding off to one significant figure gives 2.
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an ideal gas is contained in a cylinder of fixed length and diameter. 80 j of heat is added while the piston is held in place. the work done by the gas on the walls of the cylinder is
The work done by the gas on the walls of the cylinder is zero, since the piston is held in place. The heat energy added to the gas will cause it to expand, but since the cylinder has a fixed volume, the pressure of the gas will increase without the gas doing any work on the walls of the cylinder.
An ideal gas is a hypothetical gas which follows the ideal gas laws. These laws state that the pressure, volume, and temperature of an ideal gas are related to each other in a predictable and measurable way. In this case, the cylinder has a fixed length and diameter, and the piston is held in place. This means that the volume of the cylinder is fixed and cannot change, even if heat is added to the gas. Therefore, when 80 J of heat is added, the pressure of the gas will increase, but the gas will not do any work on the walls of the cylinder since it cannot expand. Therefore, the work done by the gas on the walls of the cylinder is zero.
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Write an equation that represents the situation.
After the parade, Ameen had 300 pieces of candy. He was allowed to eat 8 pieces of candy each day. Write an equation that represents the number of days he had been eating candy if he has 82 pieces of candy left.
Ameen has been eating the candy for 27 days and now has 82 pieces left
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
Let x represent the number of days he had been eating candy.
Ameen had 300 pieces of candy. He was allowed to eat 8 pieces of candy each day. He has 82 left. This can be represented by:
300 - 8x = 82
8x = 300 - 82
8x = 218
x = 27.25
He has been eating the candy for 27 days
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Rotate the triangle through 180° about the origin.
my worst topic fr
The answer is that the triangle should be here in the image.
Any shape that is 180 degrees turn from (x, y) to (-x, -y).
So pretend a point is on (2, 3), do a 180 degree rotation it will be (-2, -3).
Mark me Brainliest. :D
Answer:
you
Step-by-step explanation:
130 jwphbsmhisjs
zjoshsksn
The pread of a flu viru through a certain population i modeled by y=500/1990e^-. 5(t) where y i the total number of people infected after t day. In how many day will 125 people be infected with the viru?
ln t = 145.69 days day will 125 people be infected with the virus (500/125)/-.005 = t
How many days will it take for 125 people to contract the virus?This question uses the theory of exponential growth and decay.
The equation y=500/1990e^-. 5(t) models the spread of a flu virus through a population, where y is the total number of people infected after t days.
The equation follows an exponential decay curve, where the number of people infected decreases with each passing day. In this case, the rate of decay is -.005.
given below
Step 1: Rearrange the equation to isolate t.
y = 500/1990e^-.005(t)
500/y = 1990e^-.005(t)
500/y = e^-.005(t)
ln(500/y) = -.005(t)
Step 2: Substitute the given values of y (125) and solve for t.
ln(500/125) = -.005(t)
ln(500/125)/-.005 = t
t = 145.69 days
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Factorise fully 3 ( x − 4 ) 2 + 15 ( x − 4 )
The factorization is given as 9x² - 9x - 44
How to factorize the equationFactorize fully 3 ( x − 4 )² + 15 ( x − 4 )
(3x - 4)² + 15(x-4)
(3x - 4)(3x - 4) + 15(x-4)
we have to open the bracket
9x² - 12x - 12x + 16 + 15x - 60
take the like terms in the equation
9x² - 24x + 15x +16 - 60
9x² - 9x - 44
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What’s the function of this?
Answer:
g(x) = 2x +1
Step-by-step explanation:
You want the complete table and the linear function that describes it, given the points (x, g(x)) = (-3, -5) and (-1, -1).
DifferencesWe note the differences between the x-values shown are -1 -(-3) = 2. The corresponding differences between those y-values is -1 -(-5) = 4.
This lets us fill in the values for x=1 and x=3 as being -1+4 = 3, and 3+4 = 7
We observe that the missing x-value corresponds to g(x)=1, which is halfway between g(x)=-1 and g(x)=3. That means its corresponding x-value will be halfway between x=-1 and x=1, at x=0.
The table is shown in the attachment.
Slope-intercept equationThe change in g(x) being 4 when the change in x is 2 means the slope is 4/2 = 2. The y-value of 1 when x=0 means the y-intercept is 1.
These are used to write the slope-intercept form of the equation:
y = mx +b . . . . . . slope is m, y-intercept is b
For a slope of 2 and a y-intercept of 1, the equation is ...
y = 2x +1
When we write that in "functional form", the expression g(x) replaces y:
g(x) = 2x +1
evaluate the function f(x)=5x+2 for f(-4)
Answer:
The answer is -18
Step-by-step explanation:
You plug in -4 and solve
f(-4)= 5(-4) +2
Elizabeth lives in san francisco and works in mountain view. In the morning, she has 3 33 transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same 3 33 choices for her trip home. If elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that she'll use a cab exactly one time?.
The probability that she will choose to use a cab exactly one time is 4/9.
It has been given that In the morning she has 3 transportation choices. And in the evening the same 3 choices.
i) bus
ii) cab
iii) train
Since each choice have an equal chance of being chosen,
The probability of Choosing a bus will be 1/3
The probability of Choosing a cab will be 1/3
The probability of Choosing a train will be 1/3
Now, the Probability of Not Choosing the cab will be the sum of the probabilities of choosing a bus and train i.e, 2/3
Now there will be two possibilities-Either She chooses a cab in the morning and something else in the evening Or She chooses a cab in the evening and something else in the morning.
Therefore, the probability of choosing a cab exactly one time =
( Probability of cab in morning x Probability of no cab in the evening) + (Probability of no cab in morning x Probability of cab in evening)
Probability of choosing a cab exactly once
= 1/3 x 2/3 + 2/3 x 1/3
= 4/9
Therefore, the probability that she will choose to use a cab exactly one time is 4/9.
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An entrepreneur buys some hockey pucks. Each one costs $5.60 and resells for 7.84. What is the mark up price, as a percentage
The percentage mark up of the hockey is 40%
How to determine the percentage mark upFrom the question, we have the following parameters that can be used in our computation:
Selling = 7.84 and cost = 5/60
The markup price can be calculated as follows:
markup price = (selling price - cost price) / cost price * 100%
So, we have
markup price = (7.84 - 5.60) / 5.60 * 100%
Evaluate
markup price = 40%
So, the mark up price is 40%.
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x−(−7)=−10 as an addition problem
The value of the equation x + 17 = 0 is x = -17
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
x - ( -7 ) = - 10 be equation (1)
On simplifying the equation , we get
x + 7 = -10
Adding 10 on both sides of the equation , we get
x + 17 = 0
Now , subtracting 17 on both sides of the equation , we get
x = -17
Hence , the value of equation is x = -17
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consider the case in which the constant a equals 16. plot the graph of y=16x2 .
The graph of y=16x2 is a parabola that is symmetric about the y-axis and opens upwards. Its vertex is at (0,0) and its intercepts are at (0,0) and (±√16,0). As x increases, the graph increases at a faster rate.
The graph of y=16x2 is a parabola that is symmetric about the y-axis and opens upwards. The vertex of the parabola is the point (0,0), which is the point where the parabola changes direction. The y-intercept of the graph is the point (0,0) and the x-intercepts are the points (±√16,0). This means that the graph crosses the x-axis at x=±√16. As x increases, the graph increases at a faster rate. This is because the exponent of x is 2, meaning that the graph is a quadratic equation. When x=0, the graph is at 0, and as x gets larger, the graph increases more quickly. The graph reaches its maximum at x=√16, where y=16. From this point, the graph decreases until it reaches 0 again at x=-√16.
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Which phrases can be represented by the algebraic expression x + 14? select three options.
The phrases can be represented by the algebraic expression x + 14 are Option 2 (A number plus 14), Option 4 (Fourteen more than a number), and Option 5 (A number increased by 14).
Given that we have to find the phrases represented by algebraic expression
Given expression is:
x + 14
This expression means that "x" is increased by 14 or 14 is added to x
Let us check the options one by one
Option 1:
The quotient of a number and 14
So this expression is wrong, since it involves quotient which is not related to given expression
Option 2
A number plus 14
Writing it mathematically,
number + 14
If the number be "x", then we get x + 14
So this option is correct
Option 3
Fourteen less than a number
Writing it mathematically,
number - 14
If the number be "x", then we get x - 14
So this Option is wrong
Option 4
Fourteen more than a number
Here, "more than" means addition
Writing it mathematically,
14 + number
If the number be "x", then we get 14 + x which is same as x + 14
So this option is correct
Option 5
A number increased by 14
Here, "increased by" means addition
Writing it mathematically,
number + 14
If the number be "x", then we get x + 14
So this option is correct
Thus correct options of the algebraic expression x + 14 are option 2, 4, 5.
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Full Question:
Which phrases can be represented by the algebraic expression x + 14? Select three options.
1. the quotient of a number and 14
2. a number plus 14
3. fourteen less than a number
4. fourteen more than a number
5. a number increased by 14
The phrases can be represented by the algebraic expression x + 14 are Option 2 (A number plus 14), Option 4 (Fourteen more than a number), and Option 5 (A number increased by 14).
Given that we have to find the phrases represented by an algebraic expression
Given expression is:
x + 14
This expression means that "x" is increased by 14 or 14 is added to x
Let us check the options one by one
Option 1:
The quotient of a number and 14
So this expression is wrong since it involves a quotient which is not related to the given expression
Option 2
A number plus 14
Writing it mathematically,
number + 14
If the number be "x", then we get x + 14
So this option is correct
Option 3
Fourteen less than a number
Writing it mathematically,
number - 14
If the number be "x", then we get x - 14
So this option is wrong
Option 4
Fourteen more than a number
Here, "more than" means addition
Writing it mathematically,
14 + number
If the number be "x", then we get 14 + x which is same as x + 14
So this option is correct
Option 5
The number increased by 14
Here, "increased by" means the addition
Writing it mathematically,
number + 14
If the number be "x", then we get x + 14
So this option is correct
Thus correct options of the algebraic expression x + 14 are option 2, 4, 5.
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Full Question:
Which phrases can be represented by the algebraic expression x + 14? Select three options.
1. the quotient of a number and 14
2. a number plus 14
3. fourteen less than a number
4. fourteen more than a number
5. a number increased by 14
Simplify: 15²
(pls hurry)
Answer:
225
Step-by-step explanation:
15 x 15 = 225
the size of a bacteria population grows at a rate of p(t) where t is measured in weeks
The bacteria will reach its maximum size at t = 8.94 weeks.
To find when the bacteria will reach its maximum size, we need to find the maximum value of p(t). The first step is to find the derivative of p(t):
dp(t)/dt = -8000(t^2 - 80)/(80 + t^2)^2
Next, we need to find the critical points of this derivative by setting it equal to 0 and solving for t:
dp(t)/dt = 0
-8000(t^2 - 80)/(80 + t^2)^2 = 0
t^2 - 80 = 0
t = √80
t = 4√5
t ≈ 8.94
Since t = 4√5 is the only critical point, we can see that it is a local maximum. To confirm this, we need to find the second derivative and evaluate it at t = 0:
d^2p(t)/dt^2 = 16000t (t^2 - 240) / (80 + t^2)^3
d^2p(t)/dt^2 = 160000 * -160 / (80 + 80)^3 < 0
Since the second derivative at t = 4√5 is less than 0, it is a local maximum.
--The question is incomplete, answering to the question below--
"The size of a bacteria population grows at a rate of p(t) = 8000t/ (80 + t^2) where t is measured in weeks. Determine when the bacteria will reach its maximum size."
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PLEASE HELP!!
look at screen shot for question.
Answer:
Step-by-step explanation:
To evaluate g(-5), you simply plug in -5 for x in the equation:
g(-5) = (-5)²-10 which is 25 - 10 which is 15. Therefore, g(-5) = 15
Can anyone teach me how to do this?
The missing angles and side of the triangle are;
m∠FXD = 44°
EG = 14
m∠FZG = 32°
How to find the angles in a triangle?We are told that the angle bisectors of ΔXYZ are XG, YG and ZG
The parameters are;
∠DYE = 94°
∠FXG = 22°
Thus;
m∠FXD = 2* 22°
m∠FXD = 44°
The sum of angles in a triangle is 180 degrees. Thus;
m∠FZE + 94 + 22 = 180
m∠FZE = 180 - (94 + 22)
m∠FZE = 64°
Thus;
m∠FZG = 64°/2
m∠FZG = 32°
The incenter of a triangle lies at equal distances from the three line segments forming the sides of the triangle, and also from the three lines containing those segments. Thus;
DG = EG = FG = 14
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Essay Worth 10 points)
(05. 07 HC
A coach is assessing the correlation between the number of hours spent practicing and the average number of
the data
Number of hours spent practicing
0 0. 5 1 2001. 5 2 2002. 5 3 2003. 5 4
Score in the game
5 8 11 14 17 20 23 26 29
Part A: Is there any correlation between the number of hours spent practicing and the score in the game? Justify
Part B: Write a function that best fits the data. (3 points)
Part 2: What does the slope and y-intercept of the plot indicate? (3 points)
8
Source C
There is a correlation between the number of hours spent practicing and the score in the game.
Part A: Yes, there is a correlation between the number of hours spent practicing and the score in the game. This is evidenced by the linear trend that is seen in the data, with the score increasing as the number of hours spent practicing increases.
Part B: The function that best fits the data is y = 4x + 5.
Part 2: The slope of the plot indicates that for every hour spent practicing, the score increases by 4 points. The y-intercept indicates that the score is 5 when no hours are spent practicing.
There is a correlation between the number of hours spent practicing and the score in the game.
The function that best fits the data is y = 4x + 5, where the slope indicates that for every hour spent practicing, the score increases by 4 points, and the y-intercept indicates that the score is 5 when no hours are spent practicing.
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