I need help with this problem please and thank you :)
The function f(x) = 3 · (x + 8)² + 4 is the consequence of applying translation and dilation transformations on y = x².
What is the difference between the original function and the transformed function?
In this problem we find a quadratic equation, of which we must infer the series of rigid transformations to be used to obtain a resulting expression. Rigid transformations are transformations applied on functions such that Euclidean distance is not changed. The most used rigid transformations are listed below:
TranslationReflectionRotationDilationContractionAfter comparing the two expressions, we find that this procedure was applied in the following order:
Translation 8 units in the -x direction.Dilation by a factor of 3.Translation 4 units in the +y direction.Finally, we show the procedure to prove this manner:
y = x²
Step 1
y' = (x + 8)²
Step 2
y'' = 3 · (x + 8)²
Step 3
f(x) = 3 · (x + 8)² + 4
The function f(x) = 3 · (x + 8)² + 4 is the consequence of applying translation and dilation transformations on y = x².
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Copy and complete the proof.
Given: C is the midpoint of AE.
C is the midpoint of BD.
AE ≅ BD
Prove: AC ≅ CD
Proof:
Statements Reasons
a. _______ a. Given
b. A C=C E, B C=C D b. _______
c. A E=B D c. _______
d. _______ d. Segment Addition Postulate
e. A C+C E=B C+C D e. _______
f. A C+A C=C D+C D f. _______
g. _______ g. Simplify.
h. _______ h. Division Property
i. AC ≅ CD i. _______
The words that are needed to complete the proof has been added below:
a. AE ≅ BD a. Given
b. A C=C E, B C=C D b. definition of midpoint
c. A E = B D c. definition of congruent segments
d. A C + C E = A E d. Segment Addition Postulate
e. A C + C E = B C + C D e. definition of congruent segments
f. A C + A C = C D + C D f. substitution
g. 2 A C = 2 C D g. Simplify.
h. A C = C D h. Division Property
i. AC ≅ CD i. definition of congruent segments
step I is the required proof
What are congruent segments?This is a term to compare segments that they are have similar properties such as equality in length. For instance using the line asked in the question, line AC is congruent to line CD means that the two lines are equal in length
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2.13 A weird density curve A line segment can be considered a density "curve" as shown
in Exercise 2.1A bekline graph can abe b ended a demiry curve. Figure 2.10
shows such a demity curve.
Figure 2.10 An unusual broken-line" density curve, for Exercise 2.13
0.2
0.4
0.5
0.3
(a) Verify that the graph in Figure 2.10 is a valid density curve.
For each of the following, use areas under this density curve to find the proportion of
observations within the given interval
(b) 0.6 ≤ x ≤0.8
(c) 0≤x≤ 0.4
(d) 0≤x≤02
(e) The median of this density curve is a point between X=0.2 and X=0.4. Explain why.
Regarding the piecewise curve and probabilities, we have that:
a) The figure is a value density curve because the area under the figure is of 1.
b) The probability is: P(0.6 ≤ X ≤ 0.8) = 0.2.
c) The probability is: P(0 ≤ X ≤ 0.4) = 0.6.
d) The probability is: P(0 ≤ X ≤ 0.2) = 0.3.
e) The median is the value of a for which P(0 ≤ X ≤ a) = 0.5, P(0 ≤ X ≤ 0.2) = 0.3 and P(0 ≤ X ≤ 0.4) = 0.6, hence the median of this density curve is a point between X=0.2 and X=0.4.
What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
For this problem, to the left of x = 0.4, we have a linear curve with:
An intercept of 2.Slope of -2.5, as when x increases by 0.4, y decays by 1.Then, considering the constant:
y = -2.5x + 2, x ≤ 0.4.y = 1, 0.4 < x ≤ 0.8.To represent a distribution, it's area over the entire interval has to be of 1. The area is composed by.
A rectangle of dimensions 1 and 0.8.A right triangle with dimensions 1 and 0.4.Hence the total area is:
A = 0.8 x 1 + 0.5 x 0.4 x 1 = 1.
Hence:
The figure is a value density curve because the area under the figure is of 1.
For itens b to d, the probabilities are also given by areas, hence:
0.6 ≤ X ≤ 0.8 = 1 x 0.2 = 0.2.0 ≤ X ≤ 0.4 = 1 x 0.4 + 0.5 x 0.4 x 1 = 0.6.0 ≤ X ≤ 0.2 = 1 x 0.2 + 0.5 x 0.2 x 1 = 0.3.For item e, we have that:
The median is the value of a for which P(0 ≤ X ≤ a) = 0.5, P(0 ≤ X ≤ 0.2) = 0.3 and P(0 ≤ X ≤ 0.4) = 0.6, hence the median of this density curve is a point between X=0.2 and X=0.4.
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9/7 is greater than or less than 3/1
Answer: Less than. (9/7<3/1)
Step-by-step explanation: We know the answer is 9/7<3/1 because 3/1 as a whole number will be 3. If we convert 9/7 into a proper fraction with a whole number, it will be 1 2/7. 3 is greater than 1 and 2/7ths.
Andrew ran 5 miles less than two times the number of miles Bernadette ran. Andrew ran a total of 13 miles. Write an equation to determine how many miles Bernadette ran.
13 = 2x − 5
x − 5 = 2(13)
x/13 = 2(5)
13 + 2x = 5
Answer:
a) 13 = 2x - 5
Step-by-step explanation:
Given that,
→ Andrew ran 5 miles less than 2 times the no. of miles Bernadette ran.
→ Andrew ran a total of 13 miles.
Then the equation will be,
→ 13 = 2 times - 5
→ 13 = 2x - 5
Hence, option (a) is correct.
Draw an isospeles right triangle on the coondinate plane so that the midpoint of its hypotenuse is the origin. Label the coordinates of each vertex.
The isosceles right triangle on the coordinate plane so that the midpoint of its hypotenuse is the origin is shown in the picture.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
It is given that:
Draw an isosceles right triangle on the coordinate plane so that the midpoint of its hypotenuse is the origin.
The coordinate of the origin is (0, 0)
We can take the coordinate of point A and B as (-1, 1) and (1, -1)
The right angle triangle is shown in the attahced picture.
Thus, the isosceles right triangle on the coordinate plane so that the midpoint of its hypotenuse is the origin is shown in the picture.
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If in ∆ABC, the bisectors of ∠B and ∠C intersect each other at O. Prove that ∠BOC = 90° + 1/2∠ A.
ps- pls help istg
It has been proved that if the bisectors of ∠B and ∠C intersect each other at O, then; ∠BOC = 90°+ ¹/₂∠A
How to prove angles?A △ ABC such that the bisectors of ∠ ABC and ∠ ACB meet at a point O.
To prove :
∠BOC = 90° + ¹/₂∠A
Proof :
In △BOC, we have
∠1 + ∠2 + ∠BOC = 180°
In △ ABC, we have, ∠A + ∠B + ∠C = 180°
∠A + 2(∠1) + 2(∠2) = 180°
¹/₂∠A + ∠1 + ∠2 = 90°
∠1 + ∠2 = 90° - ¹/₂∠A
Therefore, in equation 1,
90° - ¹/₂∠A + ∠BOC = 180°
∠BOC = 90°+ ¹/₂∠A
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I need this answered please
Fiona is serving iced tea and lemonade at a picnic. She has only 44 glasses in which to serve the drinks. If x represents the number of glasses of iced tea and y represents the number of glasses of lemonade, which equation represents the number of glasses of ice tea she can serve?
x minus y equals 44
44 plus y equals x
y minus x equals 44
x equals 44 minus y
The number of glasses of iced tea is x = 44 − y.
What is algebra?A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.
Given:
She has only 44 glasses in which to serve the drinks.
x represents the number of glasses of iced tea
y represents the number of glasses of lemonade
According to given question we have
x is the number of glasses of iced tea, and y is the number of glasses of lemonade. The sum is 44,
x + y = 44
Solving for x:
x = 44 − y
Therefore, the number of glasses of iced tea is x = 44 − y.
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Paulina has completed 24 of 42 problems she was assigned for homework. She plans to finish her homework by completing 9math problems each hour,h write an equation to find the number of hours it will take Paulina to complete her math homework assignment
Answer:
Step-by-step explanation:
42=24+9h
Find the slope of the line that passes through (2,1) and (5,6). Simplify your answer and write it as a proper fraction, improper fraction, or integer.
The slope of the line that passes through the given points is equal to 3/5.
Given the following data:
Points on x-axis = (2, 5).
Points on y-axis = (1, 6).
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope = (5 - 2)/6 - 1)
Slope = 3/5
In conclusion, the slope of the line that passes through the given points is equal to 3/5.
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Determine whether the following statements are sometimes, always, or never true. Explain.
If possible, draw an isosceles triangle with base angles that are obtuse. If it is not possible, explain why not.
An isosceles triangle is a triangle with (at least) two equal sides. In the picture above, we have two equal side lengths and the remaining side length. .This property corresponds to two equal angles in a triangle.
verify the following equation:
Find the equation is possible or not?
Yes, it is possible to draw an isosceles obtuse triangle.
An isosceles obtuse triangle is a triangle in which one of its three angles is obtuse (between [tex]90[/tex] and [tex]180[/tex]degrees) and the other two are acute angles.
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Write an explicit formula for each geometric sequence. Then find the first three terms.a₁ =3, r= 3/2
A recursive function allows us to find the value of any term in a geometric sequence by using the previous term in that exact sequence. If the common ratio of that geometric sequence is 9, then each term is nine times the previous term.
The general term for the geometric sequence is
an= a1 * r ^ (n-1)
where an is the nth term, a₁ is the first term, r is the common ratio, and n is its position or number. The term.
where a₁ = 3 and r = 3/2
Sequence: 3, 4.5, 6.75, 10.125, 15.1875, 22.78125, 34.171875, 51.2578125, 76.88671875 ...
3rd value: 6.75.
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For the function f(x) = − 4x + 8, f( – 6) = _.
I need help
Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.) (-6,-4)
The equation of the circle that passes through the point (-6 , -4) and has a center located at the origin is x^2 + y^2 = 52.
Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-6 , -4).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(-6 - 0)^2 + (-4 - 0)^2
radius= √36 + 16
radius = √52
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (0 , 0)
r = √52
(x - 0)^2 + (y - 0)^2 = (√52)^2
x^2 + y^2 = 52
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Write an explicit formula for each sequence. 5,2,-1,-4, . . . .
Formula for arithmetic sequence 5,2,-1,-4, . . . . is an = 3n + 8.
What exactly is an arithmetic sequence?An ordered group of integers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.
This is an A.P. series.
a = 5
d = -3
an = a + (n-1)d
an = a + (n-1)-3
an = a + 3n + 3
an = 5 + 3n + 3
an = 3n + 8
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Describe a different sequence of transformations in which the blue figure is the image of the red figure.
There are two different sequences of transformation.
What is sequence of transformation?
A sequence of transformation is an operator acting on a given space of sequences. Sequence transformations include linear mappings such as convolution with another sequence, and resummation.
What is origin?
A graph in the two-dimensional coordinate plane has the point (0,0) as its origin. The origin is located at the intersection of the vertical and horizontal axes, and the distance to all points can be measured from this point.
Given figure is in which the blue figure is the image of the red figure
The above figure can be transformed in two sequences
a) We could first rotate clockwise 90 degrees from the origin, and then reflect on the x axis. And translate two units right side.
b) We could rotate counter clockwise 90 degrees and then reflect on the y axis. And translate two units upwards.
By these sequence of transformation, blue figure is the image of red figure.
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L
1. If M is between L and N, find MN given:
LN = 6x-5, LM = x + 7, and MN = 3x + 20
M
N
The length of MN is 68.
what is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Given:
LN = 6x-5, LM = x + 7, and MN = 3x + 20
As, M is in between L and N.
LM + MN = LN
x+7 + 3x+ 20 = 6x-5
4x + 27 = 6x -5
-2x = -32
x= 16
So, the length of MN = 3x + 20 = 3 * 16 + 20 = 68
Hence, the length of MN is 68.
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Christine got a prepaid debit card with $20 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 9 cents per yard. If after that purchase there was $17.75 left on the card, how many yards of ribbon did Christine buy?
Find the slope of the line through each pair of points. (1,2) and (2,3)
The slope of the line through each pair of points (1,2) and (2,3) is 1.
How can we determine slope?
Find the coordinates of two points along the selected line.
Find the difference in these two locations' y-coordinates (rise).
Find the difference in these two locations' x coordinates (run). Add the difference in x-coordinates (rise/run or slope) to the difference in y-coordinates.
The formula to calculate slope is -
m = y2 - y1 / x2 - x1
m = 3 - 2 / 2 - 1
m = 1
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To estimate the height of a tree, Dave stands in the shadow of the tree so that his shadow and the tree's shadow end at the same point. Dave is 6 feet 4 inches tall and his shadow is 15 feet long. If he is standing 66 feet away from the tree, what is the height of the tree?
The height of the tree, which Dave is standing 66 feet away from, is 34 feet and 2.4 inches.
If Dave's and the tree's shadows end at the same point, then the length of the shadow of the tree must be the sum of Dave's shadow and his distance from the tree.
tree's shadow = Dave's shadow + distance from the tree
tree's shadow = 15 feet + 66 feet
tree's shadow = 81 feet
Using ratio and proportion, we can solve for the height of the tree.
Dave's height : height of tree = Dave's shadow : tree's shadow
let x = height of the tree
6 feet 4 inches : x = 15 feet : 81 feet
converting feet to inches (1 feet = 12 inches)
76 : x = 180 : 972
Solving for x by evaluating the proportion:
180 x = 76 (972)
x = 410.4 inches
x = 34 feet and 2.4 inches
Hence, the height of the tree is 34 feet and 2.4 inches.
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Find the missing terms of each arithmetic sequence. (Hint: The arithmetic mean of the first and fifth terms is the third term.)... 13/5, a₆, a₇, a₈, 37/5, . . . . . .
The missing term in the sequence is A5 = 5 .
Let's assume for the sake of simplicity that the third term they provided you was >3, and the twenty-fifth is >25. As a result, you put 3 as A sub-one rather than specifying that A sub-3 is 3 and A sub-25 is 25. Here's where things become tough. Set A sub-23 to 25. (why? because 1 to 23 and 3 to 25 are equally distant.
A3=3, A25=25 } A1=3, A23=25
Apply the equation An = A1 + (n-1)D.
(Read: A-sub n = A sub 1 - the nth term - D)
A23(A sub-23)= 3 Plus (23-1)
D 25 = 3 + 22D \s-3 -3
22 = 22D
D = 1
Once more, An = A1 + (n-1)D.
A3 = A1 + (3-1) X 1
3 = A1 + 2
-2 -2
A1 = 1
An = 1 + (n-1) X 1
An = 1 + 1n - 1
An = 1n + 0
So you are left with the general formula An = 1n. You can use this formula to find any term in the sequence, all you got to do is plug in (An) the number you want. In this case, plug in A sub-5 if you want to find the fifth term. You get
An = 1n
A5 = 1X5
A5 = 5
The fifth term in the sequence is 5. (it goes 1,2,3,4,,5,..)
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Prove that: Cos x + Cos(x+ 2pi/3) + Cos (x + 4pi/3) =0
The value of the equation cos x + cos ( x + 2π/3 ) + cos ( x + 4π/3 ) = 0
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the trigonometric equation be represented as A
Now , the value of A is
cos x + cos ( x + 2π/3 ) + cos ( x + 4π/3 ) = 0
Now , the value of cos A + cos B = 2 cos ( A + B / 2 ) cos ( A - B / 2 )
Substituting the values in the equation , we get
cos x + cos ( x + 2π/3 + x + 4π/3 / 2 ) cos ( x + 2π/3 - x - 4π/3 / 2 )
On simplifying the equation , we get
cos x + 2cos ( 2x + 2π / 2 ) cos ( -π/3 )
cos x + 2cos ( x + π ) ( -1/2 )
cos x + ( -cos x ) = 0
So , 0 = 0
Hence , the equation is solved
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PLEASE HELP ME ASAP! Find the approximate side length of a square game board with an area of 205 in2
Answer:
Side length of a square game board is 11.916 inches. Explanation: If the area is 142 ∈2 , as area is square of side length of a square,
Step-by-step explanation:
CodeHS
Using Graphics in JavaScript: Do Now Activity
1) Identify the parts of each circle below.
Answer ?
Parts of each Graph is,
a) Centre = C
Radius = CA = CB = CD
Diameter = BD
b) Centre = S
Radius = SP = SQ = SR
Diameter = PQ
The center of a circle is the center point in a circle from which all the distances to the points on the circle are equal. This distance is called the radius of the circle. Here, point P is the center of the circle.
The distance between the center of the circle to its circumference is the radius.
The diameter of a circle is the distance from a point on the circle to a point. radians away, and is the maximum distance from one point on a circle to another. The diameter of a sphere is the maximum distance between two antipodal points on the surface of the sphere.
Therefore,
Parts of each Graph is,
a) Centre = C
Radius = CA = CB = CD
Diameter = BD
b) Centre = S
Radius = SP = SQ = SR
Diameter = PQ.
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Determine whether each sequence is arithmetic. If so, identify the common difference. 1,1,2,3,5,8, ...........
The sequence 1,1,2,3,5,8, ........... doesn't form an AP as they have the varying common difference.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between these two numerical orders is a fixed number (AP). Arithmetic Sequence is another name for it.
We'd come across a few specific keywords in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be explained in expressed in the form of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' : d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the sequence given is; 1,1,2,3,5,8, ...........
The series contains of given 6 terms.
Let the initial term be 'a₁' = 1.
The second term be 'a₂' = 1.
The third term be 'a₃' = 2.
And, the fourth term is 'a₄' = 3.
For the sequence to form the AP, they must have the equal common difference. So,
d = a₃ - a₂
Substitute the values.
d₁ = 2 - 1
d₁ = 1
Thus, the calculated common difference is 1.
or d = a₅ - a₄ (Put the values)
d₂ = 5 - 3
d₂ = 2
Since, d₁ ≠ d₂
Thus, we can say that the given sequence is not forming an AP.
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The product of 4 and a number plus 17 is 5.”
Answer:
5 - 17 = -12
-12/4 = -3
Answer:
number is - 3
Step-by-step explanation:
let the number be n then the product ( multiplication ) of n and 4 is 4n , so
4n + 17 = 5 ( subtract 17 from both sides )
4n = - 12 ( divide both sides by 4 )
n = - 3
the number n is - 3
If 9(x) = x-2 and h(x) = 4- x, what is the value of (go h) (- 3) ?
Answer: 8/5
Step-by-step explanation:
Find the coordinates of M if N(1.5,2.5) is the midpoint of \overline{M P} and P has coordinates (6,9)
Applying the midpoint formula, the coordinates of point M are: (-3, -4).
How to Apply the Midpoint Formula?The midpoint formula is given as, (x, y) = [(x2 + x1)/2, (y2 + y1)/2].
Given the following:
N(x, y) = (1.5, 2.5)
P(x1, y1) = (6, 9)
M(x2, y2) = (?, ?)
Plug in the values into the midpoint formula
N(1.5, 2.5) = [(x2 + 6)/2, (y2 + 9)/2]
Isolate each coordinate
1.5 = (x2 + 6)/2
2(1.5) = x2 + 6
3 = x2 + 6
3 - 6 = x2
x2 = -3
2.5 = (y2 + 9)/2
5 = y2 + 9
5 - 9 = y2
y2 = -4
Therefore, applying the midpoint formula, the coordinates of point M are: (-3, -4).
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What is the solution of the equation √x+5=√2x-4?
Answer:
x=9
Step-by-step explanation:
[tex]\sqrt{x+5}=\sqrt{2x-4} \\ \\ x+5=2x-4 \\ \\ x=9 [/tex]
On substituting this back into the equation, we see x=9 satisfies it.
