If B is the midpoint of AC, find the length of AC.
10
23
46
None of these choices are correct.
Answers
Answer: [C]: " 46 units ."
______
Step-by-step explanation:
The question (and corresponding image) asks:
" If B is the midpoint of AC, find the length of AC. "
Note:
The midpoint refers to the point in the middle of the line [segment].
In this particular question:
⇒ The line segment; AC is divided into 2 (two) equal segments of the same length:
AB = (x + 13) ; and:
BC = (2x + 3) ; {as per 'posted image'} ;
We are asked to find the length of AC.
[length of AB] + [length of BC] = [length of AC].
(x + 13) + (2x + 3) = [length of AC; for which we solve] :
We shall solving for x ; & then plug in the value to solve.
Note:
[length of AB] = [length of BC] ; Plug in our known values:
⇒ that is; (x + 13) = (2x + 3) ;
So, we have: " x + 13 = 2x + 3 "
_____________________
" x + 13 = 2x + 3 " ;
− x − 3 = − x − 3 " ;
_____________________
0 + 10 = x + 0 ;
→ " 10 = x " ;
↔ {Note: According to the "symmetric property" algebra:
"a = b " ; then " b = a"};
→ " x = 10 " ; {according to the "symmetric property of alm
__________________
Another method:
When we have:
" x + 13 = 2x + 3 " ;
→ Subtract each side of the equation by x ; & subtract each side of the equation by 3 ;
to isolate x on one side of the equation —
[in this case, the 'right-hand' side of the equation];
and to solve for x ; as follows:
" x + 13 = 2x + 3 ";
Now; for each side of the question—on a separate 'left-hand' side; and: on a separate 'right-hand' side basis; we can combine the 'like terms' and simply:
For the left-hand side:
" x + 13 − x − 3 " : Combine the 'like terms":
+ x − x = 0 ; [that is: " +1x − 1x = 0"];
+ 13 − 3 = + 10 ; We have: " 0 + 10 = + 10 ".
Now, For the right-hand side:
" 2x + 3 − x − 3 " : Combine the 'like terms'; as follows:
" + 2x − x = x " ; {that is: " +2x − 1x = 1x = x "} ;
" + 3 − 3 " = 0 " . " x + 0 = x "
So: [left-hand side = right-hand side] ;
→ 10 = x ; ↔ " x = 10 ."
Both methods result in the same value for x ; that is: x = 10 ; which happens to suggest credibility.
Now, to find the length of AC ; which equals:
→ " x + 13 + 2x + 3 " ;
Then, we plug in our calculated value; 10 —for the values of x ;
and solve!
→ " 10 + 13 + (2*10) + 3 " = " 10 + 13 + 20 + 3 " = " 46 units ".
⇒ which corresponds to the correct answer: [C]: " 46 units."
_______
Hope this answer with explanation is helpful.
Best wishes!
_______
Related Questions
I need this answer i dont think this is the right anwser please help
Answers
Answer: 11 ft.
Step-by-step explanation:
Start by listing the variables that you have.
-Total Area=1,848; lot a 33ft wide, 42ft long; lot b xft wide, 42ft long.
- so, our equation looks like 1,848=(33x42)+(42x)
-multiply 33x42=1,386
-subtract 1,386 from both sides to get 462.
-equation should look like 462=42x
-divide by 42 to 11
When archeologists excavate a site, they mark it off with a coordinate grid so that they can easily
identify where artefacts are found and keep a record of the site forever. At the West Kennet Long
Barrow in England, a grave site back to 3600 BCE was found. There are three chambers at the
coordinates (7,9), (17, 33) and (-36,41). It has been said that they form an isosceles triangle with
height twice the length of its base.
Determine whether the statement is true. Justify your answer. Hint: An isosceles triangle has at
least two sides of equal side lengths.
Answers
The distance between the chambers at coordinates (7,9) and (17,33) can be calculated using the distance formula:
distance = √((x2-x1)^2 + (y2-y1)^2)
Plugging in the coordinates, we get:
distance = √((17-7)^2 + (33-9)^2)
distance = √(10^2 + 24^2)
distance = √(100 + 576)
distance = √676
distance = 26
The distance between the chambers at coordinates (7,9) and (-36,41) can be calculated using the same formula:
distance = √((-36-7)^2 + (41-9)^2)
distance = √((-43)^2 + (32)^2)
distance = √(1849 + 1024)
distance = √2873
distance = 53.6
The distance between the chambers at coordinates (17,33) and (-36,41) can be calculated using the same formula:
distance = √((-36-17)^2 + (41-33)^2)
distance = √((-53)^2 + (8)^2)
distance = √(2809 + 64)
distance = √2873
distance = 53.6
Since the distance between the chambers at coordinates (7,9) and (17,33) is not equal to either of the distances between the other pairs of chambers, we can conclude that the statement is not true. The chambers do not form an isosceles triangle, as they do not have at least two sides of equal side lengths
figure abcdef was reflected across the line y = –x to create figure a'b'c'd'e'f'. what are the coordinates of the pre-image of f'?
Answers
(C) F = (2, -4) are the coordinates of the pre-image of F'.
What are coordinates?A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.
So, the result of reflecting Figure ABCDEF across y = -x is A'B'C'D'E'F'.
The transformational rule is:
(x, y) ⇒ (-y, -x)
Which means:
(x, y) ⇒ (-y, -x) ⇒ (4, -2)
In contrast:
-y = 4
-x = -2
Solving for x and y as follows:
y = -4
x = 2
Therefore, (C) F = (2, -4) are the coordinates of the pre-image of F'.
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Complete question:
Figure ABCDEF was reflected across the line y = –x to create figure A'B'C'D'E'F'.
On a coordinate plane, a 6-sided figure has points A prime (negative 2, negative 2), B prime (negative 4, 2), C prime (negative 2, 6), D prime (4, 6), E prime (6, 2), and F prime (4, negative 2).
What are the coordinates of the pre-image of F'?
a. (–2, 4)
b. (4, 2)
c. (2, –4)
d. (–4, –2)
Solve the following system of equations using substitution
-3x+6y=12
2y=x+4
Answers
From the equation, 0 = 0. Therefore, the system of equation has infinite number of solutions.
How to solve system of equation?System of equation can be solved using different method such as elimination method, graphical method and substitution method.
Let's use substitution method to solve the system of equation as follows;
-3x + 6y = 12
2y = x + 4
x = 2y - 4
Hence, let's substitute the value of x in equation(i)
-3(2y - 4)+ 6y = 12
-6y + 12 + 6y = 12
-6y + 6y = 12 - 12
0 = 0
Therefore, the system of equations has infinite solutions.
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Priya invests a sum of money at an interest rate of 8% per year.
At the end of one year, the interest she receives is 1800 rupees.
Work out the value of Priya’s investment at the end of one year.
Answers
The value of Priya's investment at end of the year is Rs. 24300.
Simple Interest:The formula for simple interest is given by
Simple interest, I = PTR/100Where, P = Principal amount, T = Time period, and R = Rate of interest
And the formula for the Amount at end of the time period is given by
Amount, A = P + IHere we have
Priya invests a sum of money at an interest rate of 8% per annum
The interest that she gained after 1 year = 1800 Rs.
Let P be the principal amount i.e Priya's investment
Then calculate Simple interest on P at 8% for 1 year
As we know Simple interest = PTR/100
Interest on P = P(1)(8)/100 = 0.08P
From the given data, interest at end of the year = Rs. 1800
=> 0.08P = 1800
=> P = 1800/0.08
=> P = 22500
The amount that Priya invested = Rs. 22500
As we know Amount = Principal amount + interest
= Rs. 22500 + Rs. 1800
= Rs. 24300
Therefore,
The value of Priya's investment at end of the year is Rs. 24300.
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Spin a spinner numbered 1-8 and you land on 8 twice in a row what is the probability?
Answers
The probability that you land on 8 twice is 1/64
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
We spin a spinner numbered 1-8 twice
The total sample space can be given by considering all the possible values
Hence the total number of spins are 8*8= 64 spins
The possibility that getting 8 twice is only once possible. As it will be only one pair in all the possible values.
Hence, The total probability is 1/64
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Please help me!!!!
Simplify the expression completely.
2 (2.5 -|-6|)
Answers
The value fo the numerical expression 2 × (2.5 -|-6|) will be negative 7.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ 2 × (2.5 -|-6|)
We know that the value inside the mode is always positive, then the expression is written as,
⇒ 2 × (2.5 -|-6|)
⇒ 2 × (2.5 - 6)
Simplify the expression, then the value of the expression is given as,
⇒ 2 × (2.5 - 6)
⇒ 2 × (- 3.5)
⇒ - 7
The value fo the numerical expression 2 × (2.5 -|-6|) will be negative 7.
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14% of americans like to only cook and 48% of americans like to only shop, while 85% enjoy either cooking or shopping. what is the probability that a randomly selected american enjoys both activities?
Answers
The probability that a randomly selected american enjoys both activities is 23 % .
Given :
14 % of americans like to only cook and 48 % of americans like to only shop, while 85 % enjoy either cooking or shopping .
14 % = 0.14
48 % = 0.48
overlapping is 85 % = 0.85
P ( A ) = 0.14
P ( B ) = 0.48
P ( A and B ) = 0.85
we know that,
P ( A or B ) = P ( A ) + P ( B ) - P ( A and B )
= 0.14 + 0.48 - 0.85
= 0.62 - 0.85
= -0.23
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PLEASE HELP ME 100 points if u do pls don't plagiarize the answer look at the image
Answers
Answer:
The given graph is not a direct variation.
Step-by-step explanation:
A direct variation occurs when the rate of change between any two points on a graph is always the same. In this sense, direct variation only occurs when a graph is linear. The given graph is parabolic; its equation is [tex]y = x^2[/tex]. Therefore, it does not exhibit direct variation, as the slope between consecutive points continually changes.
If you want to prove this claim, show that the slope changes between the given points: the rate of change from (2,4) to (3,9) is greater than the rate of change from (0,0) to (2,4).
50 POINTS DUE TODAY, Giselle wants to buy the newest book in her favorite series. She has some money saved but does not want to use all her savings on the book. Giselle’s grandma offers to pay some of the cost of the book for every weed she pulls in her grandma’s garden. The graph shows the cost to Giselle for the purchase of the book after pulling x weeds in her grandma’s garden.
Select True or False to describe each statement.
Answers
Answer:
Step-by-step explanation:
Based on the graph, it appears that Giselle's grandma is offering to pay for a certain percentage of the cost of the book for every weed that Giselle pulls in her garden. The more weeds Giselle pulls, the more money her grandma will contribute, which will reduce the amount that Giselle has to pay for the book. This can be a good way for Giselle to save money on the book without using all of her savings.
1. True, the graph's beginning represents cost before she picks any weeds.
2. False, the graph shows that the cost for he goes into the negatives, showing that she is still able to earn more money from picking weeds.
3.True, from 0 weeds to 5 weeks picked you can see the price change from $18 to $17.
4. True, once she picks 90 weeds she earns the exact amount of money needed to buy the book.
5. False, she would need to pull 90 weeds in order to not spend her own money.
Select all the coefficients in the simplified form of (4y + 5y2-6) - (5y + 27-2²).
A -1
B. 4
C. 5
D. 6
E. 33
Answers
The coefficient of x² in simplified form is 5
What is coefficient ?
A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. They may also be referred to as parameters if the coefficients are variables in and of themselves.
a symbol or number that multiplies another symbol or number (used as a mathematical variable). The coefficient of x in the phrase 3x is 3, and it is a number that represents a quality (such as the metal's coefficient of expansion) of a substance or device.
(4y + 5y² - 6) - (5y + 27 - 2²)
4y + 5y² - 6 - 5y - 27 + 4
5y² - 1y - 29
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Hamza wants to create a bumper sticker with his design. Bumper stickers usually have a height of 3 1/2 inches. What will the width of his sticker be?
Answers
The width of the bumper sticker is 6 1/4 inches .
What is the width of the bumper sticker?In order to determine the width of the bumper sticker, the first step is to determine the relationship between the height of the design and that of the bumper sticker.
The relationship can be determined by dividing the height of the bumper sticker by the height of the design.
Proportion of the heights = 3 1/2 ÷ 2
5/2 ÷ 2
= 5/2 x 1/2 = 5/4 = 1 1/4
Now, multiply the proportion of the heights by the width of the design :
Width of the design = 1 1/4 x 5
5/4 x 5/1 = 25/4 = 6 1/4 inches
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Answer: 6 1/4
Step-by-step explanation: stickers that can be custom screen printed. The most common or average size is probably the 3″ X 11.5″
50 POINTS Giselle wants to buy the newest book in her favorite series. She has some money saved but does not want to
use all her savings on the book. Giselle’s grandma offers to pay some of the cost of the book for every weed she
pulls in her grandma’s garden.
The graph shows the cost to Giselle for the purchase of the book after pulling x weeds in her grandma’s garden.
Select True or False to describe each statement.
(2 points for each correct answer = 10 points)
SELECT True or False
Answers
Answer:
true false false true true
The perimeter is less than
or equal to 51 meters.
10 m
8m
8 m
10 m
Solve the inequality
Answers
(8•2)+(10•2)+x≤51
16+20+x≤51
36+x≤51
x≤51-36
x≤15
Therefore,
(8•2)+(10•2)+15≤51
16+20+15≤51
51≤51
Which of the following Cannot be the sides of a triangle class 7? (a) 4,5,6
(b) 3,4,5
(c) 2,3,4
(d) 1,2,3
Answers
These can not be the sides of a Triangle.
What is a triangle and the response?
Triangles are a particular kind of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here.
Three-sided polygons include triangles. Three triangle angles added together equal 180 degrees.
Property of triangle
Sum of any two sides > third Side
4 , 5 , 6
4 + 5 > 6 , 4 + 6 > 5 , 5 + 6 > 4
3 , 4 , 5
3 + 4 > 5 , 3 + 5 > 4 , 4 + 5 > 3
2 , 3 , 4
2 + 3 > 4 , 2 + 4 > 3 , 3 + 4>2
1 , 2 , 3
1 + 2 = 3
Sum of 1 & 2 is not greater than 3
Hence, these can not be the sides of a Triangle.
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greatest comman factor comman factor x^2+5x
Answers
The greatest common factor of x² + 5x is x. The greatest common factor of x² + 5x is the largest number or expression that can divide evenly into both x² and 5x.
To find the greatest common factor, you can use the prime factorization method.
This involves expressing each term as the product of its prime factors. For example, x² can be written as x × x, and 5x can be written as 5 × x.
The prime factors of x² are x and x, and the prime factors of 5x are 5 and x. The greatest common factor is the product of the common prime factors, which in this case is just x. Therefore, the greatest common factor of x² + 5x is x. The greatest common factor of x² + 5x is the largest number or expression that can divide evenly into both x² and 5x.
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Question 6 If z is a standard normal variable, find the probability. The probability that z is less than 1.13 a. 0.8708 b. 0.8907 c.0.1292 d.0.8485
Answers
If z is a standard normal variable, the probability that z is less than 1.13 is given by: A. 0.8708.
What is the standard normal distribution table?In Statistics, the standard normal distribution table is designed and developed to provide only the area to the left of a specified z-score.
Additionally, since z-score (z₁) and z-score (z₂) are generally symmetric about z = 0 and are negatives of one another, then, by symmetry, the area to the right of z-score (z₂) is always equal to the area to the left of z-score (z₁).
This ultimately implies that, the total areas under a standard normal distribution curve in two tails can be determined by calculating the area to the left of z-score (z₁) and multiplying the value by two (2).
From the z-score table, the area to the left of z-score (z₁ = 1.13) is the same as the probability that z is less than 1.13 and this is given by:
Area to the left of z-score (z₁ = 1.13) = 0.8708.
Probability, P(z ≤ 1.13) = 0.8708.
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If f(x) + x^2[f(x)]^5 = 34 and f(1) = 2, find f '(1). F '(1) = Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y sin 12x = x cos 2y, (pi/2, pi/4)
Answers
To find the derivative of f(x) at x = 1, we can use the formula for implicit differentiation:
d/dx[f(x) + x^2[f(x)]^5] = 0
Substituting the given values, we get:d/dx[f(1) + 1^2[f(1)]^5] = 0
d/dx[2 + 1[2]^5] = 0
Solving for the derivative, we get:d/dx[2 + 1[2]^5] = 0
d/dx[2 + 32] = 0
0 + 32 = 0
Therefore, the derivative of f(x) at x = 1 is 32.
To find the equation of the tangent line to the curve at the given point (pi/2, pi/4), we can use the formula for the slope of a tangent line:
m = f'(x) = d/dx[y sin 12x] / d/dx[x cos 2y]
Substituting the given values, we get:m = d/dx[pi/4 sin 12(pi/2)] / d/dx[pi/2 cos 2(pi/4)]
m = d/dx[pi/4 sin 6pi] / d/dx[pi/2 cos pi/2]
m = 0 / 0
Since the derivative of the numerator is 0 and the derivative of the denominator is 0, the slope of the tangent line is undefined. This means that the tangent line is vertical and parallel to the y-axis.
The equation of the tangent line at the given point is therefore of the form:
x = c
where c is the x-coordinate of the given point, which is pi/2. Therefore, the equation of the tangent line is:
x = pi/2
Note that this is just the equation of a vertical line with an x-intercept at pi/2.
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Find the Amount (A) (Principal Rs 50000 Time = 7 years interest = 3%.
Answers
Answer: Rs 60500
Step-by-step explanation:
Principal = Rs 50000 = p
Time = 7 years = t
Simple interest rate = 3% = r
Interest = p*t*r/100
using above formula,
50000*7*3/100=10500
So, final amount = principal + interest = 50000+10500 = Rs 60500
a bag contains different colored beads. the probability of drawing two black beads from the bag without replacement is 335, and the probability of drawing one black bead is 310. what is the probability of drawing a second black bead, given that the first bead is black?
Answers
The probability of drawing a second black bead, given that the first bead is black, is 1/3 or 0.33.
The probability of drawing two black beads from a bag without replacement is given as 335. The probability of drawing one black bead is also given as 310. To calculate the probability of drawing a second black bead, given that the first bead is black, we can use the formula P(B2|B1) = P(B1 and B2) / P(B1). The probability of drawing one black bead is P(B1) = 310. The probability of drawing the two black beads is P(B1 and B2) = 335. Therefore, P(B2|B1) = 335 / 310 = 1/3 = 0.33.
The probability of drawing two black beads from a bag without replacement is given as P(B1 and B2) = 335. This means that, out of all the possible combinations of beads in the bag, 335 of them contain two black beads. The probability of drawing one black bead is given as P(B1) = 310. This means that, out of all the possible combinations of beads in the bag, 310 of them contain one black bead. To calculate the probability of drawing a second black bead, given that the first bead is black, we can use the formula P(B2|B1) = P(B1 and B2) / P(B1). The probability of drawing one black bead is P(B1) = 310. The probability of drawing two black beads is P(B1 and B2) = 335. Therefore, P(B2|B1) = 335 / 310 = 1/3 = 0.33. This means that the probability of drawing a second black bead, given that the first bead is black, is 1/3 or 0.33.
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What is the answer?
Please help
Answers
-------------------------------------------------------------------------------------------------------------
Answer: 105 frames
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Given: [tex]\textsf{25 frames per second, starts at 0 seconds already played 190 frames}[/tex]
Find: [tex]\textsf{Frame count already played when time = -3.4}[/tex]
Solution: In order to find the number of frames that have already played when the time was equal to -3.4 seconds, we must first figure out long the delay is. We can do this by dividing 25 frames per second from 190 frames which gives us that 7.6 seconds passed before we started counting at 0.
Therefore, if we want to look at -3.4 seconds out of -7.6 seconds that means that 4.2 seconds passes after the initial playing to get to -3.4 seconds. Now we can just multiply 4.2 seconds by 25 frames per second which gives us that about 105 frames have played when the time was equal to -3.4
Work out the volume of the prism. 6 cm 12 cm 2 cm
Answers
Answer:
V = 72 cm³
Step-by-step explanation:
the volume (V) of a prism is calculated as
V = Ah ( A is the area of the triangular face and h is its height )
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 12 and h = 6
A = [tex]\frac{1}{2}[/tex] × 12 × 6 = 6 × 6 = 36 cm² , then
V = 36 × 2 = 72 cm³
Which equation choice could represent the graph shown below?
Answers
By analizying the zeros on the graph, we conclude that the equation that could represent the graph is:
y = (x + 5)²*(x - 3)²
Which equation choice could represent the graph?On the graph, we have a polynomial.
Remember that the degree of the polynomial is related to the zeros of the polynomial. Here we can see that we have two double zeros, one at x = -5 and other at x = 3
We know that are double zeros because the curvature of the polynomial changes there.
Then the equation will be something like:
y = (x + 5)²*(x - 3)²
So that is the correct option, top right.
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WILL MARK AS BRAINLEST!!!!!!!!!!!!!!!!
Answers
C=2(3.14)•r, where r=radius and ≈3.14
Now, simply only the values into the formula; we have a radius of 4in.
D=2(3.14)(4)
Multiply:
D=6.28(4)
D=25.12
Lastly, we must round to the nearest tenth:
D=25.1
So, your answer is 25.1 inches.
The coordinates of the endpoints A B are given. A (7,6) and B (-9,-6). Point K is located on AB so that AK= 3/1. What is the x-coordinate of point K?
Answers
The x-coordinate of the point K that divides AB in 3:1 will be -5.
What is the section of the line?Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
The directions of the endpoints A and B are given. A (7,6) and B (- 9,- 6). Point K is situated on the Stomach muscle with the goal that AK: KB = 3/1.
Then the x-coordinate of the point K is given as,
x = (mx₂ + nx₁) / (m + n)
x = [3(-9) + 1(7)] / (3 + 1)
x = (- 27 + 7) / 4
x = - 20 / 4
x = - 5
The x-coordinate of the point K that divides AB in 3:1 will be -5.
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in the simek and o'brien study, a novice golfer had to sink four consecutive putts before going to the next step. this exemplifies:
Answers
In the Simek and O'Brien study, progressive overload was used by requiring the novice golfer to sink four consecutive putts before moving on to the next step. Progressive Overload.
Progressive overload is the gradual increase of stress placed on the body during physical activity. By requiring the novice golfer to sink four consecutive putts before moving on to the next step, the study is increasing the difficulty of the task and placing additional stress on the body.
Progressive overload is an effective and essential technique for improving physical performance. It involves gradually increasing the intensity of the activity or exercise, which places additional stress on the body and forces it to adapt and become stronger. In the Simek and O'Brien study, progressive overload was used by requiring the novice golfer to sink four consecutive putts before moving on to the next step. This increased the difficulty of the task and allowed the golfer to gradually improve their performance. By gradually increasing the difficulty of the task, the study was able to effectively use progressive overload to improve the golfer's performance.
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(16-24)-(57-77) divided by (-2)
Answers
The answer will be -6 when (16-24)-(57-77) divided by (-2).
What is division?
One of the basic mathematical operations is division, which splits a bigger number into smaller groups with the same number of components. For example, if 20 students need to be divided into groups of five for a sporting event, how many total groups will be created? Dealing with such challenges is made easier by the division operation. In this instance, divide 20 by 5. The result will be 20 x 5 = 4. There will be 4 groups total, each with 5 students. You can verify this number by multiplying 4 by 5 and getting the answer 20, which equals 20.
Here (16-24)-(57-77)/-2
= (-8)-(20)/-2
=12/-2
=-6
Hence the answer will be -6.
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Expectation of Product of Random Variables Proof From the definition of the expected value, the expected value of the product of two random variables is E(X . Y) = EErr-r2 . P(X=Y =r2) where the sum is over all possible values of r1 and r2 that the variable X and Y can take on_ Using the definition above formally prove that if the events X = r1 and Y =r2 are independent (for any r1 and r2) , we have E(X . Y) = E(X) . E(Y). Now; if you have two random variables X and Y and Y=aI+c, show that if E[X2] # E[XJ? , then E(X . Y) # E(X) . E(Y). If you roll a die 6 times in a rOW what is the expected value of the product of the 6 outcomes?
Answers
Look to the photo and you will find the answers there ✔️
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Which of the following quadratic equations has roots 3, 5? a)`x^2-15x+3=0` b)`x^2-8x+15=0` c)`x^2+3x+5=0` d)`x^2+8x-15=0`
Answers
The quadratic equation (B) x²-8x+15=0 has the required roots 3 and 5.
What is a quadratic equation?ax2 + bx + c = 0 is a quadratic equation or a second-order polynomial equation with a single variable.
The algebraic's theorem guarantees that it is a second-order polynomial equation, hence it must have at least one solution.
The answer might be straightforward or challenging.
x2 - 5x - 3x + 15 = 0 are the roots of the quadratic equation x2 - 8x + 15 = 0.
x(x-5)-3(x-5)
(x-3)(x-5)=0
x = 3, 5
So, the correct answer is x² - 8x + 15 = 0.
Therefore, the quadratic equation (B) x²-8x+15=0 has the required roots 3 and 5.
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Which of the following is not a criterion for congruence of ∆ s a SAS B ASA C SSA D SSS?
Answers
(C) SSA is not a requirement for triangle congruence.
What is the congruence of triangles?
Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.
We can move, flip, twist, and turn these triangles to produce the same effect.
When relocated, they are parallel to one another.
Two triangles are congruent if they satisfy all five conditions for congruence.
Right angle-hypotenuse-side (RHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) are the four terms (RHS).
We know that SSA is not the criteria for the congruence of the triangles.
Therefore, (C) SSA is not a requirement for triangle congruence.
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