Part I: Complete the Square
\(y=-6x^2 + 36x-12\\ \\ y=-6(x^{2}-6x)-12\\\\ y=-6\left((x-3)^{2}-9 \right)-12\\\\y=-6(x-3)^{2}+54-12\\\\\boxed{y=-6(x-3)^{2}+42}\)
Part II: Graph of the function
See the attached image for the complete graph.
After completing the square, the equation of the quadratic is in vertex form, and so the vertex is at (3, 42).
Also, as the coefficient of \(x^2\) is negative, the graph opens down.
Once you figure this out, find the coordinates of some other points on the graph and connect them in the shape of a parabola.
Part III: Line of symmetry
The axis of symmetry is the vertical line passing through the vertex. In this case, it is x = 3.
Part IV: Maximum/minimum value
The maximum/minimum value is the y-coordinate of the vertex. In this case, it is 42.
Help pleaseeeee I would appreciate it
(1) The result of the row operation R₂ ↔ R₃ is [ -5 1 0 8]
[ 8 8 -7 5 ]
[ 2 2 6 -5]
(2) The result of the row operation 3R₁ ↔ R₁ is [24 - 27 -21 - 18]
[8 9 -4 -5]
[2 2 -7 -8]
What is the result of the row operation?
The result of the row operation in the matrix is calculated as follows;
R₂ ↔ R₃, implies changing row 2 and row, and the result would be;
[ -5 1 0 8]
[ 8 8 -7 5 ]
[ 2 2 6 -5]
The result of obtained from 3R₁;
3R₁ = [24 - 27 -21 - 18]
3R₁ ↔ R₁ is determined as; (the row interchange)
[24 - 27 -21 - 18]
[8 9 -4 -5]
[2 2 -7 -8]
Learn more about row operation here: https://brainly.com/question/17490035
#SPJ1
Solve.
4 There are 42 tubes of oil paint on trays. Each tray
holds 6 tubes. How many trays of tubes are there?
Show your work.
7
Answer: 7
Step-by-step explanation:
Since there are 42 tubes and each tray can hold 6 tubes, it will be 42/6 which is 7.
Triangle XYZ is drawn with vertices X(1, 2), Y(2, 5), Z(3, 4). Determine the translation direction and number of units if Y′(2, −2).
7 units down
7 units up
7 units to the right
7 units to the left
So, "down" is the translation direction, while "7 units down" is the number of units.
What is a triangle's three sides?A right triangle's hypotenuse is its longest side, its "opposite" face is the one which faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To define the side of right triangles, we utilize specific terminology.
We must change a point's x and y coordinates by the same amount in order to translate it. Let's calculate the difference between Y and Y′'s coordinates:
Difference in x-coordinates = 2 − 2 = 0
Difference in the y-coordinate = −2 − 5 = −7
This reveals that in the y-direction, Y′ is 7 units lower than Y. Hence, we must translate its entire triangle 7 units down inside the y-direction in order for Y to shift to Y′.
To know more about Triangle visit:
https://brainly.com/question/17335144
#SPJ1
So, "down" is the translation direction, while "7 units down" is the number of units.
What is a triangle's three sides?A right triangle's hypotenuse is its longest side, its "opposite" face is the one which faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To define the side of right triangles, we utilize specific terminology.
We must change a point's x and y coordinates by the same amount in order to translate it. Let's calculate the difference between Y and Y′'s coordinates:
Difference in x-coordinates = 2 − 2 = 0
Difference in the y-coordinate = −2 − 5 = −7
This reveals that in the y-direction, Y′ is 7 units lower than Y. Hence, we must translate its entire triangle 7 units down inside the y-direction in order for Y to shift to Y′.
To know more about Triangle visit:
brainly.com/question/2773823
#SPJ1
can you please help me with this I will mark the BRAINLIEST who ever can help thanks
\(QUESTION:\)
\(WORK\) \(OUT\) \(THE\) \(VALUE\) \(OF\) \(2^{6}\)
Or 2 times 2 times 2 times 2 times 2 times 2 times 2
\(ANSWER:\)
So, 2^6 is:
64
Now, 7^4 is:
2,401
Hope it helps!
\(Grace Rosalia\)
Answer:
a) 2x2x2x2x2x2=64
b)7x7x7x7=2401
write the equation of a line that is perpendicular to the given line that passes through the given point.
y-2=7/3(x+5); (-4,9)
First we must find the opposite-reciprocal of the original slope.
current slope: \(\frac{7}{3}\)
new slope: \(-\frac{3}{7}\)
Using the new slope and the given point, we will plug them into slope-intercept form and solve for b, the y-intercept.
\(9 = -\frac{3}{7}(-4) + b\\\\9 = \frac{12}{7} + b\\\\-\frac{51}{7} = b\)
The y-intercept is \(-\frac{51}{7}\).
Now, we can write the formula for the new line.
Slope-intercept form: \(y = -\frac{3}{7}x - \frac{51}{7}\)
Point-slope form: \(y - 9 = -\frac{3}{7}(x + 4)\)
Find surface area of this rectangle prism
Answer:
Heres this!!
Step-by-step explanation:
The formula to find the surface area of a rectangular prism is A = 2wl + 2lh + 2hw, where w is the width, the l is the length, and the h is the height.
Solve for x:
2x +1°
72 - 99°
Answer: x=20
Step-by-step explanation:
The two angles are vertically opposite so they are equal to each other
7x-99=2x+1
5x=100
x=20
PLS HELP ME
PLS SHOW YOUR WORKING OUT
the formula for y in terms of x and c is y = c⁵ / √x. we can solve this by inversely proportional rule .
what is inversely proportional ?
Two quantities are said to be inversely proportional if an increase in one quantity results in a decrease in the other quantity, and vice versa. In other words, as one quantity increases, the other quantity decreases at the same rate
In the given question,
We are given that 17y is inversely proportional to √(x), which can be written as:
17y ∝ 1/√x
Using proportionality constant k, we can write:
17y = k / √x
Now, we are also given that y = c⁴ when x = c². We can use this information to solve for k:
17y = k / √x
17c⁴ = k / √c²
17c⁴ = k / c
k = 17c⁵
Substituting the value of k in the original equation, we get:
17y = (17c⁵) / √x
Simplifying further, we can write:
y = c⁵ / √x
Therefore, the formula for y in terms of x and c is:
y = c⁵ / √x
To know more about inversely proportional , visit:
https://brainly.com/question/20371514
#SPJ1
A couple purchased a home and signed a mortgage contract for $900,000 to
be paid with half-yearly payments over a 25-year period. The interest rate
applicable is j2 = 5.5% p.a. applicable for the first five years, with the condition
that the interest rate will be increased by 12% every 5 years for the remaining
term of the loan.
(a) Calculate the half-yearly payment required for each five-year interval
9514 1404 393
Answer:
$33,336.83$35,176.68$36,869.23$38,266.75$39,158.08Step-by-step explanation:
The amortization formula can be used to find the payment value.
A = P(r/2)/(1 -(1 +r/2)^(2n))
where P is the principal amount at the beginning of the loan period, r is the annual interest rate, n is the number of years remaining on the loan
The value of A in this scenario is the semi-annual payment.
Initially, the interest rate is 0.055 and the number of years remaining is 25.
After the first 5-year period, the interest rate goes up by 12%, so is multiplied by a factor of 1.12 to become 6.16% per year. The same growth factor is applied to the interest rate at the beginning of each 5-year period.
Of course, the number of years remaining is decreased by 5 years at the beginning of the next 5-year period.
__
The Principal remaining at the end of each 5-year period is the starting principal for the next period. It is calculated from ...
FV = P(1 +r/2)^10 -A((1 +r/2)^10 -1)/(r/2)
Where P is the starting principal, A is the loan payment as calculated above, and r is the annual interest rate.
__
These formulas are built into spreadsheet functions, so the desired set of loan payments can be calculated easily by that technology. The result is attached. In the "# pmts" column is the value used to amortize the loan for the 5-year period. The semiannual payment is calculated as though the loan would be completely paid off in that number of payments, keeping the same interest rate for the duration. Of course, that payment series is interrupted and the loan recalculated at the beginning of the next 5 years.
The half-yearly payments for each 5-year interval are ...
$33,336.83
$35,176.68
$36,869.23
$38,266.75
$39,158.08
_____
Additional comment
The values displayed in the spreadsheet are rounded to the values shown. The values used in calculation have 14 or more significant digits. This means the numbers here may vary from those provided by a lending institution. In the real world, the principal and interest values are rounded to cents with each payment, so actual results may vary by a few cents either way.
Help me answer this.. 20 points
The linear function parallel to the line represented by y = 3x/4 - 1/2 is given as follows:
y = 3x/4 + 1/2.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.When two lines are parallel, they have the same slope.
The slope of the line y = 3x/4 - 1/2 is given as follows:
m = 3/4.
Hence the equation of the parallel line is given as follows:
y = 3x/4 + 1/2.
More can be learned about linear functions at https://brainly.com/question/15602982
#SPJ1
Find the number of ways 66 identical coins can be separated into three nonempty piles so that there are fewer coins in the first pile than in the second pile and fewer coins in the second pile than in the third pile.
There are 331 ways when 66 identical coins can be separated into three nonempty piles
Let the piles have a, b and c coins, with 0<a <b <c. Then, let b=a+k₁, and
c=b+k₂, such that each ki≥1.
The sum is then a+a+k₁+a+k₁+k₂= 66 ⇒ 3a+2k₁+k₂ = 66.
This is simply the number of positive solutions to the equation
3x+2y+z = 66.
If a = 1, then 2k₁ + k₂ = 63⇒ 1≤k₁ ≤31. Each value of k₁ corresponds to a unique value of k₂, so there are 31 solutions in this case.
Similarly, if a = 2, then 2k₁+k₂= 60⇒ 1≤k₁ ≤29, for a total of 29 solutions in this case.
If a = 3, then 2k₁+ k₁= 57 ⇒ 1 ≤ k₁ ≤28, for a total of 28 solutions.
In general, the number of solutions is just all the numbers that aren't a multiple of 3, that are less than or equal to 31.
We then add our cases to get
=1+2+4+....31=1+2+3+...31-3(1+2+3+...10)
=31*(32)/2-3(55)
=31*16-165
=496-165
=331
To know more about identical coins:
https://brainly.com/question/2397962
#SPJ4
Sally can paint a room in 6 hours while it takes Steve 8 hours to paint the same room. how long would it take them to paint the room if they work together
Answer:
It will take them 3.5 hours to paint the room.
Step-by-step explanation:
Step 1: Add the number of hours it takes them together
A. 6 + 8
Step 2: Divide the total number of hours by two (since two people are working together)
B. 12 / 2 = 7 hours
Step 3: Divide by two again since you now have twice the speed
C. 7 / 2 = 3.5 hours
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA 40 POINTS* DONT SKIP :(( .!
Which of the following is a statistical question that can result in numerical data? What is your favorite television show that you watched this week? What is the name of the doctor at Healthy Kids Pediatrics? How many students at your school have a skateboard? What store in the mall are you most likely to purchase apparel from?
Answer:
All of the above, except for 'What is the name of the doctor at Healthy Kids Pediatrics?'
Step-by-step explanation:
What is your favorite television show that you watched this week? - If we define your favourite show as that which you watched most, you could gather data here on time spent watching each show to determine the answer
What store in the mall are you most likely to purchase apparel from? - Similar to before, data on your previous trips to the mall could be gathered to determine which stores you have been to the most often, and using this make a prediction of the most likely you are to purchase apparel from
How many students at your school have a skateboard? - Here data could be gathered by asking which students have a skateboard and which do not
What is the name of the doctor at Healthy Kids Pediatrics? - This question only has an answer, and it would be the name of the doctor
Answer:
How many students at your school have a skateboard?
Step-by-step explanation:
Since it is asking multiple people it can result in data. It can't result in data if it asks just one question to someone
Tristan and his friends made a banner for their back-to-school dance. The banner is rectangular, and it is 15 feet wide and 5 feet tall. What is the area of the banner?
Answer:
(15*5)sq ft
=75 sqft
Step-by-step explanation:
Help!!!! Please
Asap
Answer:
events at A and B are independent because P(A)(B)≠P(A)
It's really hard for me to understand what they are asking.
Answer:
B is the correct answer
Step-by-step explanation:
Angles 1, 2, and 3 added together should make 180 degrees.
So, if angle 2 is 70 degrees, you subtract 70 from 180 (180-70=110) and you're left with 110 degrees.
Angle 1 and 3 add together should make 110 degrees which makes B the only true statement.
A concession stand at the Tennis Center sells a hamburger/drink combination dinner for SS. The profit, y (in dollars), can be
approximated by y = -0.001x2 + 3.6x- 500 where x is the number of dinners prepared.
Find the number of dinners that should be prepared to maximize profit.
What is the maximum profit?
1. Using an exponential equation, the number of dinners that the Tennis Center should prepare to maximize its profits is 1,800.
2. The maximum profit is $2,740.
What is an exponential equation?An exponential equation is an exponential function that has a variable exponent.
Exponential functions are written in the form of y = ab^x, which identifies the common ratio (b) and the y-intercept.
y = -0.001x^2 + 3.6x- 500
y = -0.002x + 3.6 = 0
x = 3.6/.002
= 1800 dinners
y = -0.001(1800)^2 + 3.6(1800) -500 = max profit
= 1.8(1800) + 6,480 -500
= -3,240 + 5,980
= $2,740
Thus, 1,800 dinners are expected to generate a maximum profit of $2,740.
Learn more about exponential equations at https://brainly.com/question/2456547
#SPJ1
A cone with a height of 15 yards has a volume of
475.17 yd³. Find the diameter of the cone.
Answer:
11
Step-by-step explanation:
h = 15 yards
Volume = 475.17 cubic yards
Diameter = 5.5*2 = 11.0 = 11 yards
find x on the following figure
If the perpendicular from chord is x, the length of cord is 11.3 and diameter be 15.5 then the value of x is 4.54.
Given Perpendicular from center to chord is x. The length of cord be 11.3 and the diameter be 15.5.
Perpendicular means a line on other line making an angle of 90 degrees. Cord is the length of line joining two points on a circle and is different from radius or diameter. We know that the formula of calculating the length of chord is as under:
l=\(2\sqrt{r^{2} -d^{2} }\)
now put the value of l=11.3 and r=15.5/2=7.25
11.3=\(2\sqrt{7.25^{2} -x^{2} }\)
11.3/2=\(\sqrt{52.5625-x^{2} }\)
5.65=\(\sqrt{52.5625-x^{2} }\)
squaring both sides
\(5.65^{2} =52.5625-x^{2}\)
31.9225=52.5625-\(x^{2}\)
31.9225-52.5625=-\(x^{2}\)
-20.64=-\(x^{2}\)
20.64=\(x^{2}\)
x=4.54
Hence if the length of cord is 11.3 and diameter is 15.5 then the value of x is 4.54.
Learn more about circle at https://brainly.com/question/24375372
#SPJ10
The ratio of berries to oranges is 10:1. If there are 9 oranges, how many berries are there?
Answer:
90 berries
Step-by-step explanation:
What is the area of the parallelogram 60ftx67ft-52ft
To find the area of a parallelogram, you need to multiply the base by the height. In this case, the given dimensions are 60ft (base) and 67ft (height), and you need to subtract 52ft from the height.
New height = 67ft - 52ft = 15ft
Area of the parallelogram = Base * Height = 60ft * 15ft = 900 square feet.
Therefore, the area of the parallelogram is 900 square feet.
~~~Harsha~~~
mr sharma has 3/4 pounds of swiss cheese and 2/3 pounds of cheddar cheese. he uses 1/4 of the swiss cheese and 1/2 of the cheddar cheese. how many pounds of cheese does mr sharma use
The pounds of cheese that Mr Sharma used is 25 / 48 pounds
How to calculate the value?From the information, Mr sharma has 3/4 pounds of swiss cheese and 2/3 pounds of cheddar cheese. he uses 1/4 of the swiss cheese and 1/2 of the cheddar cheese.
The cheese that was used will be:
= (1/4 × 3/4) + (1/2 × 2/3)
= 3/16 + 1/3
= 9/48 + 16/48
= 25 / 48
He used 25/48 pounds.
Learn more about fractions on:
brainly.com/question/17220365
#SPJ1
someone help please
Answer:
Mean = 7
Step-by-step explanation:
The mean is all the numbers added together divided by the number of numbers.
\(\frac{7+0+11+10}{4}\)
\(\frac{28}{4}=7\)
Answer:
7
Step-by-step explanation:
To find the mean, add up all the numbers then divide by the number of numbers
( 7+0+11+10) /4
28/4
7
The mean is 7
If the figures below are similar with a scale factor of 6:5, find the value of x
Using Scale Factor, the value of x = 33.6.
A scale factor is what?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Scale factor = Dimension of the new shape / Dimension of the original shape is the fundamental formula used to calculate it.
The formula is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is enlarged.
Dimension of the large triangle divided by the little triangle is the formula to utilize.
Based on the accompanying figure,
The little triangle's corresponding side length is 28, whereas the giant triangle's side length is x.
Scale factor = 6/5 Scale factor = 6/5 = 28
x = 33.6
To learn more about Scale factor from given link
https://brainly.com/question/19936821
#SPJ1
Complete Question -
If the figures below are similar with a scale factor of 6:5, find the value of x
Match each function on the left to all points on the right that would be located on the graph of the function. Help!! thanks
Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;
f(x) = 2x + 2 ⇒ (0, 2).
f(x) = 2x² - 2 ⇒ (-1, 0).
\(f(x) = 2\sqrt{x+1}\) ⇒ (0, 2).
What is a function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;
For the ordered pair (0, 2), we have:
f(x) = 2x + 2
2 = 2(0) + 2
2 = 2 (True).
For the ordered pair (-1, 0), we have:
f(x) = 2x² - 2
0 = 2(-1)² - 2
0 = 2 - 2
0 = 0 (True).
For the ordered pair (0, 2), we have:
\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)
2 = 2 (True).
Read more on function here: https://brainly.com/question/10687170
#SPJ1
PLEASE HELP WILL MARK BRAINLIEST!
A portion of the quadratic formula proof is shown. Fill in the missing statement.
Answer: THE ANSWER IS 3 BECAUSE I HAD THIS TEST
RATE BRAINLIEST PLEASE
Step-by-step explanation:
a rectangular room has an area of 384 sq feet with floor tiles covering one part of it and carpet covering the rest. the tile part is 8 ft long. the carpeted part is 24 ft long. what is the width of the room?
8 + 24 = 32 feet long
Area = length x width
384 = 32 x width
Width = 384/32
Width = 12 feet
Answer: The room is 12 feet wide.
Step-by-step explanation: 8+24= the total length of the room. The area of anything divided by either the width or the length always gives you the missing measurement. So, 8+24=32. 384/32=12. You can check any answer you get doing one operation by taking the information you get and preforming the inverse (opposite) operation. Since the opposite of division is multiplication, all you have to do to check your answer is this: 32*12=384.
please answer asap please
A piano mover uses a ramp to move a piano into a house. The doorway to the house is 2 feet above the ground and the ramp starts 7 feet from the doorway. Assuming the ground is level and is perpendicular to the side of the house, what is the approximate length of ramp? You must round your answer to two decimal places.
The ratio of green apples to red apples at a grocery store is 2 to 3. There are 78 red apples at the grocery store. What is the total number of apples at the store?
Answer:
52
Step-by-step explanation:
78 divided by 3 is 26
26 times 2 is 52