What is the area of this triangle? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answers
Greetings from Brasil...
We need to use the Cosine Law in Any Triangle, so we can use Heron's formula.
AC² = AB² + BC² - 2.AB.BC.COS B
AC² = 11² + 9² - 2.11.9.COS 63
AC ≈ 10,63
Heron's Formula:
Area = √[P.(P - AB).(P - BC).(P - AC)]
where P = (AB + BC + AC)/2
P = (11 + 9 + 10,63)/2 ⇒ P ≈ 15,31
Area = √[15,31.(15,31 - 11).(15,31 - 9).(15,31 - 10,63)]
Area ≈ 44,21 u.a.
Related Questions
Evaluate ƒ(x) = –x2 + 1 for x = –3. a) 4 b) –4 C) –9 D) –8
Answers
[tex]f(x)=-x^2+1[/tex]
Plug in the value [tex]x=-3[/tex] into this function
[tex]f(-3)=-(-3)^2+1[/tex]
[tex]=-(9)+1[/tex]
[tex]=-8[/tex]
Thus, your answer will be D) -8. Let me know if you need any clarifications, thanks!
Answer:
D. -8
Step-by-step explanation:
We are given
f(x)= -x^2+1
and asked to evaluate f(x) for x= -3. Therefore, we must substitute -3 for x in the function.
f(x)= -x^2+1 for x= -3
f(-3)= -(-3^2)+1
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
First, evaluate the exponent: -3^2
-3^2= -3*-3= 9
f(-3)= -(9)+1
f(-3)=-9+1
Next, add -9 and 1
f(-3)= -8
When f(x)= -x^2+1 is evaluated for x= -3, the result is -8. Therefore, the correct answer is D. -8
Which of the following is an arithmetic sequence?
Answers
Answer:
B: 3,0,-3,-6
Step-by-step explanation:
An arithmetic sequence has constant adding or subtracting. In this case, 3 is being subtracted as a constant.
Sphere A has a diameter of 6 and is dilated by a scale factor of 2 to create sphere B. What is the ratio of the volume of sphere A to sphere B?
Answers
Answer:
8 : 1
Step-by-step explanation:
From the above question, we are given the following parameters
Sphere A has a diameter of 6 and is dilated by a scale factor of 2 to create sphere B.
Volume of a sphere = 4/3πr³
For Sphere A , diameter = 6
Radius = Diameter ÷ 2 = 6÷ 2 = 3
Volume of Sphere A = 4/3 × π × 3³
= 113.09733553 cubic units
Approximately = 113.1 cubic units
We were given a scale factor (k) of 2
Because we are dealing with volume, the scale factor will be cubed
In order to find the Volume of the sphere B
k³ = Volume of Sphere A/ Volume of Sphere B
2³ = 113.1 / Volume of Sphere B
Volume of Sphere B = 113.1/ 2³
= 14.1375 cubic units.
The ration of the Volume of Sphere A to Sphere B
Sphere A: Sphere B
113.1 : 14.14
= 8: 1
Answer:
1:8
Step-by-step explanation:
Took the test and got it right trust
What is the coefficient of b in the expression b² - 5b +18
Answers
Answer: -5
Step-by-step explanation:
A coefficient is a number that a variable is multiplied by.
Hope it helps <3
Answer:
well technically, there are two coefficients
the coefficient of (b^2) is 1 and the coefficient of b (itself) is -5.
But if you sre just looking for the coefficient ot just plain b, it is -5
Step-by-step explanation:
the reason I say the coefficient to (b^2) is 1 because if there is no number in front of the variable, it is automatcally assumed to be 1.
now, as for just plain b, it is -5 because the sign, positive or negative, before a number coefficient gets attached to that number. so, the entire term is -5b, which makes the coefficient to just plain b to be -5
Write the equation of a function whose parent function, f(x) = x + 8, is shifted 2 units to the right.
Answers
This has to do with function transformations. First we can set it up differently, where we are solving for y instead of f(x)
y=f(x)+8
The points of the graph are (x, f(x)+8)
To move the graph to the right, we need to subtract by 2 within the parentheses
y=f(x-2)+8
Now the point would be like (x, f(x-2)+8)
Answer:
[tex]\huge\boxed{f(x - 2) = x + 6}[/tex]
Step-by-step explanation:
f(x) + n - shift the graph n units up
f(x) - n - shift the graph n units down
f(x + n) - shift the graph n units to the left
f(x - n) - shift the graph n units to the right
===========================================
f(x) = x + 8
shift the graph 2 units to the right
f(x - 2) = (x - 2) + 8 = x - 2 + 8 = x + 6
Find an exact value. tangent of seven pi divided by twelve
Answers
(
7
π
12
)
=
−
(
2
+
√
3
)
Explanation:
tan
(
7
π
12
)
=
tan
(
π
−
5
π
12
)
= #-tan((5pi)/12)
=
−
tan
(
3
π
12
+
2
π
12
)
=
−
tan
(
π
4
+
π
6
)
Now using
tan
(
A
+
B
)
=
tan
A
+
tan
B
1
−
tan
A
tan
B
=
−
tan
(
π
4
)
+
tan
(
π
6
)
1
−
tan
(
π
4
)
tan
(
π
6
)
=
−
1
+
1
√
3
1
−
1
×
1
√
3
Multiplying numerator and denominator by
√
3
=
−
√
3
+
1
√
3
−
1
=
−
(
√
3
+
1
)
2
(
√
3
−
1
)
(
√
3
+
1
)
=
−
3
+
1
+
2
√
3
3
−
1
=
−
(
2
+
√
3
Answer: negative 2 minus radical 3
Step-by-step explanation:
We can use the tangent half-angle formula to find the exact value of tangent of 7π/12:
tan(θ/2) = ±√[(1-cosθ)/1+cosθ)]
Here, θ = 7π/6, and cos(7π/6) = -sqrt(3)/2.
Substituting these values, we get:
tan(7π/12) = ±√[(1-(-sqrt(3)/2))/(1+(-sqrt(3)/2))]
= ±√[(2+sqrt(3))/(2-sqrt(3))]
Multiplying the numerator and denominator by (2+sqrt(3)), we get:
= ±√[(2+sqrt(3))^2/(4-3)]
= ±√[(2+sqrt(3))^2]
= ±(2+sqrt(3))
Since 7π/12 lies in the second quadrant, and tangent is negative in the second quadrant, the exact value of tangent of 7π/12 is - (2+√3)
Claim: Most adults would erase all of their personal information online if they could. A software firm survey of randomly selected 583 adults showed that 58 % of them would erase all of their personal information online if they could. Find the value of the test statistic.
Answers
Answer:
Test statistic = 3.863
Step-by-step explanation:
We are told that most adults would erase all of their personal information online if they could. Since the word "most" is used, it means more than 50% or 50 percent.
So, p_o = 0.5
Also, we are told that 58 % of them would erase all of their personal information online if they could.
Thus, p^ = 0.58
Number of randomly selected adults; n = 583
The test statistic formula for hypothesis test for proportion is given by:
z = (p^ - p_o)/[√[p_o(1 - p_o)/n]
Plugging in the relevant values, we have;
z = (0.58 - 0.5)/[√[0.5(1 - 0.5)/583]
z = 0.08/0.02070788416
z = 3.863
find the angle vector (9,7) makes with the x axis
Answers
Answer:
≈ 37.9°
Step-by-step explanation:
Using the tangent ratio
tanΘ = [tex]\frac{y}{x}[/tex] where (x, y ) = (9, 7 )
tanΘ = [tex]\frac{7}{9}[/tex] , thus
Θ = [tex]tan^{-1}[/tex] ([tex]\frac{7}{9}[/tex] ) ≈ 37.9° ( to the nearest tenth )
The system of equations y = negative one-half x + 4 and y = 2x – 1 is shown on the graph below. According to the graph, what is the solution to this system of equations? (2, 3) (3, 2) (–1, 4) (4, –1)
Answers
Answer:
(2, 3 )
Step-by-step explanation:
The solution to a system of equations given graphically is at the point of intersection of the 2 lines.
point of intersection = (2, 3 ) ← is the solution
A function f(x) has x-intercepts of -3 and -5 what is the constant term in the function f(x)=x^2+8x+
Answers
Answer:
[tex]x^{2}[/tex]
Step-by-step explanation:
because x^{2} represents the quadratic equation, so I don't think it will affect it
What is the product?
(negative 3 s + 2 t)(4 s minus t)
negative 12 s squared minus 2 t squared
negative 12 s squared + 2 t squared
negative 12 s squared + 8 s t minus 2 t squared
negative 12 s squared + 11 s t minus 2 t squared
Mark
Answers
Answer:
The answer is
negative 12 s squared + 11 s t minus 2 t squared
Step-by-step explanation:
( - 3s + 2t)( 4s - t)
Expand the terms
We have
- 12s² + 3st + 8st - 2t²
Simplify
We have the final answer as
- 12s² + 11st - 2t²Hope this helps you
Answer:
D. -12s^2+11st-2t^2
. What is the solution set for
|k - 6|+17 = 30
A. (-19, 7}
B. (-7, 19)
C. (-19, 19)
D. {-41, 19)
Answers
Answer:
Hope this is correct and helpful
HAVE A GOOD DAY!
Lydia runs an experiment to determine if a coin is fair by counting the number of times a coin lands heads up. The table shows her data. A 2-row table with 10 columns. The first row is labeled number of coin flips with entries 0, 10, 20, 30 ,40, 50, 60, 70, 80, 90. The second row is labeled number of heads up with entries 0, 7, 12, 18, 23, 30, 35, 38, 42, 45. According to the line of best fit, about how many times would the coin land heads up in 100 flips? 48 50 51 53
Answers
Answer:
b is the right option
Step-by-step explanation:
According to the line of best fit, the coin would land heads up about 52.73 times in 100 flips, which we can round to 53.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
We can use linear regression to find the line of best fit for the given data, which will give us a linear equation that models the relationship between the number of coin flips and the number of times the coin lands heads up.
Using a calculator or statistical software, we can find that the line of best fit for the given data is:
y = 0.4975x + 2.9825
where y is the number of times the coin lands heads up, and x is the number of coin flips.
To find how many times the coin would land heads up in 100 flips, we can substitute x = 100 into the equation and solve for y:
y = 0.4975(100) + 2.9825
y = 49.75 + 2.9825
y ≈ 52.73
Therefore,
According to the line of best fit, the coin would land heads up about 52.73 times in 100 flips, which we can round to 53.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ7
what percentage of the population has a heart rate between 68 and 77
Answers
Answer:
49.87% of the population has a heart rate between 68 and 77.
Step-by-step explanation:
We are given that the mean of the data for the resting heart of adults is 68 beats per minute and the standard deviation is 3 beats per minute.
Let X = the data for the resting heart of adults
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 68 beats per minute
[tex]\sigma[/tex] = standard deviation = 3 beats per minute
Now, the percentage of the population that has a heart rate between 68 and 77 is given by = P(68 < X < 77)
P(68 < X < 77) = P(X < 77) - P(X [tex]\leq[/tex] 68)
P(X < 77) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{77-68}{3}[/tex] ) = P(Z < 3) = 0.9987
P(X [tex]\leq[/tex] 68) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{68-68}{3}[/tex] ) = P(Z [tex]\leq[/tex] 0) = 0.50
The above probability is calculated by looking at the value of x = 3 and x = 0 in the z table which has an area of 0.9987 and 0.50 respectively.
Therefore, P(68 < X < 77) = 0.9987 - 0.50 = 0.4987 or 49.87%
Sophie is riding her bike home when she runs over a nail. It gets stuck to the tire of her bike but does not pop the tire. As she continues to cycle home the nail hits the ground every 2 seconds and reaches a maximum height of 48cm. a) Write a sinusoidal equation that models the nails height off the ground in cm, h, in terms of time,t. Sketch one full revolution of the nail, assuming that sophie first runs over the nail at 0seconds . b) Algebraically determine the height of the nail above the ground at 0.8 seconds. Round your answer to the nearest tenth of a cm
Answers
Answer:
a) The sinusoidal equation is;
The function is h = -24·cos[π(t )] + 24
The sketch of one full revolution is attached
b) The height of the nail at 0.8 seconds is 43.42 cm
Step-by-step explanation:
The sinusoidal equation that models the nails height can be given as follows;
y = A·cos[B(x - C)]+D
A = The amplitude = Half maximum height = 48/2 = 24 cm
The period = 2·π/B = Time to complete one oscillation = 2 seconds
∴ B = 2·π/2 = π
x = t = Time
C = The horizontal shift
D = the vertical shift = 24 cm
y = The height of the nail = h
We have;
h = -24·cos[π(t - C)] + 24
At t = 0, h = 0, therefore, we have;
0 = -24·cos[π(0 - C)] + 24
24·cos[π(0 - C)] = 24
∴ cos[π(0 - C)] = 24/24 = 1
π(0 - C) = 0
C = 0
The function is h = -24·cos[π(t )] + 24
b) The height of the nail at 0.8 seconds is given as follows;
h = -24×cos[π(0.8)] + 24 =
h = 19.42 + 24 = 43.42 cm.
What is the solution to the equation ? 5{n-1 over 10}= 1 over 2
Answers
Answer:
n = 2
Step-by-step explanation:
Given
5( [tex]\frac{n-1}{10}[/tex] ) = [tex]\frac{1}{2}[/tex] ← distribute parenthesis on left side
[tex]\frac{n-1}{2}[/tex] = [tex]\frac{1}{2}[/tex]
Since denominators are both 2 then equate numerators
n - 1 = 1 ( add 1 to both sides )
n = 2
Clarise evaluated this expression.
(66.3 – 14.62) ÷ 0.6 – 0.22
(51.68) ÷ 0.6 – 0.22
(51.68) ÷ 0.42
51.68 ÷ 0.16
32.3
Which errors did Clarise make?
Answers
Answer:
(66.3-14.62)/0.6-0.22
(51.68)/0.6-0.22
(51.68/0.6)-0.22
(86.14667)-0.22
85.92667
pls help me I will give BRANLIEST!!!and follow you back (ー_ー゛)its due in 5minutes
Answers
Answer:
$186.89
Step-by-step explanation:
Let's start by finding the area of the floor.
Area of a trapezium can be found with the formula:
A=(a+b)/2*h
Let's plug our values in.
A=(10+16)/2*7.6
Simplify.
A=26/2*7.6
A=13*7.6
A=98.8
The area of the floor is 98.8 square meters.
Find how many litres of paint are needed.
98.8/1.9=52
He needs 52 liters of paint.
52/5=10.4
He needs 11 5 liter cans of paint.
Each one costs %16.99.
16.99*11=186.89
It would cost $186.89 to buy all the paint he needs.
The amount that two groups of students spent on snacks in one day is shown in the dot plots below. Which statements about the measures of center are true? Select three choices. The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B. The mode for Group A is less than the mode for Group B. The median for Group A is 2. The median for Group B is 3.
Answers
Answer:
The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B.The mode for Group A is less than the mode for Group B.Step-by-step explanation:
First, we can find the measures of center for each group.
Group A
Mode: 1
Median: (1 + 2) / 2 = 3 / 2 = 1.5
Mean: (1 * 5 + 2 * 4 + 3) / 10 = (5 + 8 + 3) / 10 = 16 / 10 = 1.6
Group B
Mode: 3
Median: 92 + 3) / 2 = 5 / 2 = 2.5
Mean: (1 * 3 + 2 * 2 + 3 * 4 + 5) / 10 = (3 + 4 + 12 + 5) / 10 = 24 / 10 = 2.4
From here, we can see that...
The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B.The mode for Group A is less than the mode for Group B.Hope this helps!
Answer:
ABC
Step-by-step explanation:
Help please!!!!!! Thank you
Answers
Answer:
1/4
Step-by-step explanation:
Well see how far each points are from each other.
Start at the red triangle and go up 1, go to the right 4.
Thus,
the rise/run is 1/4.
Hope this helps :)
Answer:
1/4
Step-by-step explanation:
To find the rise/run, you first need to pick two points from the line. You can pick whichever points you want, and you will get the right answer. I will pick (-8, -3) and (8, 1).
Divide the difference of the y's by the difference of the x's.
-3 - 1 = -4
-8 - 8 = -16
-4/-16 = 1/4
The rise/run is 1/4.
Rectangle divided into four rectangles. The perimeters of rectangle #1, #2, #3 #4 are 10 cm, 20 cm, 28 cm and 18 cm respectively. Find the perimeter of big rectangle.
Answers
Answer:
The perimeter of the big rectangle is 38 cm
Step-by-step explanation:
Rectangle 1 and rectangle 2 share the same width, let their width be a cm while Rectangle 3 and rectangle 4 share the same width, let their width be b cm
Rectangle 1 and rectangle 3 share the same length, let their length be x cm while Rectangle 2 and rectangle 4 share the same length, let their length be y cm
The perimeter of a rectangle = 2(length + breadth).
For rectangle 1:
Perimeter = 2(a + x) = 10
a + x = 5 1)
For rectangle 2:
Perimeter = 2(a + y) = 20
a + y = 10 2)
For rectangle 3:
Perimeter = 2(b + x) = 28
b + x = 14 3)
For rectangle 4:
Perimeter = 2(b + y) = 18
b + y = 9 4)
Adding equations 1, 2, 3 and 4 gives:
a + x + a + y + b + x + b + y = 5 + 10 + 14 + 9
a + a + b + b + x + x + y + y =38
2a + 2b + 2x + 2y = 38
2((a + b) + (x + y)) = 38
For the big rectangle, let its width = c = a + b and its length be d = x + y
The perimeter of the big rectangle = 2 (c + d)
Therefore:
2((a + b) + (x + y)) = 38
2(c + d) = 38 cm = The perimeter of the big rectangle
The perimeter of the big rectangle is 38 cm
NEED HELP ASAP WILL AWARD BRAINLIEST!!!!!
Answers
Answer: 69
Step-by-step explanation:
The summer has ended and it’s time to drain the swimming pool. 20 minutes after pulling the plug, there is still 45 000L of water in the pool. The pool is empty after 70 minutes. Calculate how much water was in the pool initially
Answers
Answer:
900L per minute
Step-by-step explanation:
1- 70 - 20 = 50
2- in this 50 min the 45000L was drowned
3- 45000L / 50 = 900L
.. ..
Determine whether the function shown in the graph is even or odd. The graph starts at the top left, continues down through the x axis at negative two to a minimum around y equals negative five, goes up to a maximum on the x axis at y equals negative one, goes back down to a minimum around y equals negative five, and goes back up through the x axis at two.
Answers
Answer:
Might be D
Step-by-step explanation:
took the test and that was the other one i was thinking
Answer: D: The function is odd because it is symmetric with respect to the origin.
Step-by-step explanation:
Please Help! A pair of equations is shown below. x + y = 2 y = one halfx + 5 If the two equations are graphed, at what point do the lines representing the two equations intersect? (4, −2) (−2, 4) (2, 5) (5, −2)
Answers
Answer:
(-2,4)
Step-by-step explanation:
First, put x+y=2 into slope-intercept form: y=-x+2
Second, set the to equations equal to each other: -x+2=1/2x+5
Then, add x to both sides: -x+x+2=1/2x+x+5 to get: 2=3/2x+5
Next, subtract 5 from both sides: 2-5=3/2x+5-5, to get -3=3/2x
Finally, to get the x-value, divide both sides by 3/2: -3(2/3)=3/2x(2/3), to get x=-2
Lastly, substitute -2 for x into one of the equations to find y:
x+y=2
-2+y=2
add 2 to both sides: -2+2+y=2+2, to get y=4
The solution is (-2,4)
Answer:
(- 2, 4 )
Step-by-step explanation:
Given the 2 equations
x + y = 2 → (1)
y = [tex]\frac{1}{2}[/tex] x + 5 → (2)
Substitute y = [tex]\frac{1}{2}[/tex] x + 5 into (1)
x + [tex]\frac{1}{2}[/tex] x + 5 = 2 ( multiply through by 2 to clear the fraction )
2x + x + 10 = 4
3x + 10 = 4 ( subtract 10 from both sides )
3x = - 6 ( divide both sides by 3 )
x = - 2
Substitute x = - 2 into (1) and evaluate for y
- 2 + y = 2 ( add 2 to both sides )
y = 4
Solution is (- 2, 4 )
please help :) Which of these numbers is the greatest? A. 1.9 x 10 to the 5 power B. 9.1 x 10 to the 2 power C. 7.9 x 10 to the 4 power D. 89,900
Answers
Answer: The answer is A.
Step-by-step explanation:
1.9x10^5= 190000
9.1x10^2= 910
7.9x10^4 =79000
please i need this answer in two minutes
1. Sarah serves at a restaurant and makes 20% of what she sells as tips. Her base salary is $10.20 an hour. Each hour she sells an average of $60 of food and drinks. She also makes time and a half when she works over 8 hours during a single shift. Her work week contains three 10-hour shifts, one 5-hour shift, and one 11-hour shift. Using the same income deductions as stated in the previous question, what is Sarah’s annual gross income and annual net income.
Answers
Answer: $55,489.20
Step-by-step explanation:
Given the following information :
Base salary = $10.20 per hour
Overtime pay = $10.20 * 1.5 = $15.3
Average sale per hour = $60
Tips = 20% of sale
Regular shift hour = 8hours
Work week:
3 10-hour shift = 24hrs regular (6 hrs overtime)
1 11 - hour shift = 8hrs regular (3 hrs overtime)
1 5 - hour shift = 5 hours
Total hours per week = 37hrs regular, 9hrs overtime
WEEKLY :
Income from tips = $60 * 46 * 0.2 = $552
Regular pay: 37 * 10.20 = $377.40
Overtime: 9 * $15.30 = $137.70
Total = $(137.70 + 377.40 + 552) = $1067.10
Number of weeks in a year = 52
Annual gross = $1067.10 * 52 = $55,489.20
the figure is cut into 8 equal pieces shade 3/4 of the figure
Answers
Answer:
You have to shade 6 pieces.
Step-by-step explanation:
Hope it helps!
will mark brainliest!!!plz helppp
Answers
Answer:
(5,-6)
Step-by-step explanation:
ONE WAY:
If [tex]f(x)=x^2-6x+3[/tex], then [tex]f(x-2)=(x-2)^2-6(x-2)+3[/tex].
Let's simplify that.
Distribute with [tex]-6(x-2)[/tex]:
[tex]f(x-2)=(x-2)^2-6x+12+3[/tex]
Combine the end like terms [tex]12+3[/tex]:
[tex]f(x-2)=(x-2)^2-6x+15[/tex]
Use [tex](x-b)^2=x^2-2bx+b^2[/tex] identity for [tex](x-2)^2[/tex]:
[tex]f(x-2)=x^2-4x+4-6x+15[/tex]
Combine like terms [tex]-4x-6x[/tex] and [tex]4+15[/tex]:
[tex]f(x-2)=x^2-10x+19[/tex]
We are given [tex]g(x)=f(x-2)[/tex].
So we have that [tex]g(x)=x^2-10x+19[/tex].
The vertex happens at [tex]x=\frac{-b}{2a}[/tex].
Compare [tex]x^2-10x+19[/tex] to [tex]ax^2+bx+c[/tex] to determine [tex]a,b,\text{ and } c[/tex].
[tex]a=1[/tex]
[tex]b=-10[/tex]
[tex]c=19[/tex]
Let's plug it in.
[tex]\frac{-b}{2a}[/tex]
[tex]\frac{-(-10)}{2(1)}[/tex]
[tex]\frac{10}{2}[/tex]
[tex]5[/tex]
So the [tex]x-[/tex] coordinate is 5.
Let's find the corresponding [tex]y-[/tex] coordinate by evaluating our expression named [tex]g[/tex] at [tex]x=5[/tex]:
[tex]5^2-10(5)+19[/tex]
[tex]25-50+19[/tex]
[tex]-25+19[/tex]
[tex]-6[/tex]
So the ordered pair of the vertex is (5,-6).
ANOTHER WAY:
The vertex form of a quadratic is [tex]a(x-h)^2+k[/tex] where the vertex is [tex](h,k)[/tex].
Let's put [tex]f[/tex] into this form.
We are given [tex]f(x)=x^2-6x+3[/tex].
We will need to complete the square.
I like to use the identity [tex]x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2[/tex].
So If you add something in, you will have to take it out (and vice versa).
[tex]x^2-6x+3[/tex]
[tex]x^2-6x+(\frac{6}{2})^2+3-(\frac{6}{2})^2[/tex]
[tex](x+\frac{-6}{2})^2+3-3^2[/tex]
[tex](x+-3)^2+3-9[/tex]
[tex](x-3)^2+-6[/tex]
So we have in vertex form [tex]f[/tex] is:
[tex]f(x)=(x-3)^2+-6[/tex].
The vertex is (3,-6).
So if we are dealing with the function [tex]g(x)=f(x-2)[/tex].
This means we are going to move the vertex of [tex]f[/tex] right 2 units to figure out the vertex of [tex]g[/tex] which puts us at (3+2,-6)=(5,-6).
The [tex]y-[/tex] coordinate was not effected here because we were only moving horizontally not up/down.
Help plz down below with the question
Answers
Answer:
The SAS Postulate
Step-by-step explanation:
SAS means Side-Angle-Side; that is, two sides are equal and an angle between those sides are equal. We're given two sides: TK and TL, and we're given that 1 is congruent to 2. Knowing the latter, we can conclude that the angle between them (let's call it 1.5 for our purposes) will be congruent to itself. Since 1.5 is the angle right in the middle of two congruent sides, our answer is SAS.