The vertex of the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7 is at (2, -5).
The vertex of a parabola in the form of y = a[tex]x^{2}[/tex] + bx + c can be found using the formula x = -b/2a for the x-coordinate of the vertex and then substituting this value into the equation to find the y-coordinate.
For the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7, we can see that a = 3 and b = -12. We can use the formula to find the x-coordinate of the vertex:
x = -b/2a = -(-12)/(2*3) = 2
So the x-coordinate of the vertex is 2. To find the y-coordinate, we can substitute x = 2 into the equation:
g(2) = 3 [tex](2)^{2}[/tex]- 12(2) + 7 = -5
Therefore, the vertex of the function g(x) = 3[tex]x^{2}[/tex] - 12x + 7 is at (2, -5).
So the correct answer is (c) (2, −5).
To learn more about function:
https://brainly.com/question/12431044
#SPJ4
construct a rectangle so that the diagonal is 6 cm and angle between them is 30 degree
Answer:
Let the length of the rectangle be x and the width of the rectangle be y.
Then, we can use the Pythagorean Theorem to find the value of x and y:
x2 + y2 = 62
x2 + y2 = 36
We can use trigonometry to find the value of x and y:
x = 6 sin 30°
y = 6 cos 30°
Therefore, the length of the rectangle is 6 sin 30° cm and the width of the rectangle is 6 cos 30° cm.
Step-by-step explanation:
First of all
You should draw a straight line which is AC=6cm
Then you should take the centre of the line and draw
30 degree in centre. Then you should draw straight line from
30 degree to bisect center point. Then take 3 cm in compass
and join their point.
for every 1,000 babies born in india in 2011, an estimated 50 of them will have died before reaching their first birthday. the rate of 50 deaths per 1,000 births is known as the
The rate of 50 deaths per 1,000 births is known as the infant mortality rate.
What is infant mortality rate?
Infant mortality rate (IMR) is the total number of deaths per 1,000 live births of infants under one year of age. Infant mortality rate is an essential demographic statistic for assessing population health status and identifying health disparities among different groups of the population.
IMR reflects the underlying mortality rate of infants in a society, which can be influenced by several factors, including maternal health, access to healthcare, nutrition, and socio-economic factors.Infant mortality rate (IMR) is the total number of deaths per 1,000 live births of infants under one year of age.
The rate of 50 deaths per 1,000 births is known as the infant mortality rate. The infant mortality rate is considered one of the most critical indicators of a country's health status and is often used to compare the health status of different populations.
for such more question on infant mortality rate
https://brainly.com/question/30557403
#SPJ11
Part A: The line of best fit for this data is y = 5. 3x + 23. Use this equation to make a conjecture about the temperature of the water in the beaker if heated for 6 minutes. Explain your thinking
The line of best fit suggests that the temperature of the water in the beaker after 6 minutes will be approximately 91.8°C. This is because when x = 6, the equation gives us y = 91.8.
The line of best fit for this data is y = 5.3x + 23. This equation can be used to make a conjecture about the temperature of the water in the beaker if heated for 6 minutes. To calculate this, substitute x = 6 into the equation: y = 5.3(6) + 23. Simplifying this equation, we get y = 31.8 + 23, which gives us y = 54.8. This is the temperature of the water in the beaker if heated for 6 minutes, which is approximately 91.8°C. hence, The line of best fit suggests that the temperature of the water in the beaker after 6 minutes will be approximately 91.8°C. This is because when x = 6, the equation gives us y = 91.8.
Learn more about equation here
https://brainly.com/question/28243079
#SPJ4
The Position Vectors of points A,B,C with respect to the origin are 8i-10j, 2i+6j and -10i +4j respectively. If ABCN is a parallelogram find The Position Vector of N. /AN/ and /AB/. Acute angle between AN and AB
Answer:
The Position Vectors of points A,B,C with respect to the origin are 8i-10j, 2i+6j and -10i +4j respectively. If ABCN is a parallelogram find The Position Vector of N. /AN/ and /AB/. Acute angle between AN and AB
What is the value of x?
Answer:
c
Step-by-step explanation:
10 points will be given
Answer : n⁸
:)
mathematical analysis DPM
Answer:
The Distributed Pattern Matching (DPM) problem have provided mathematical analysis and simulation results for establishing the effectiveness of the proposed architecture. DPMS achieves many desirable properties of both the unstructured and structured P2P systems. Like unstructured systems DPMS supports partial keyword matching, utilizes the heterogeneity in peer capabilities, and does not place any hard restriction on index/document placement. Like structured systems, on the other hand, DPMS attains logarithmic bound on search complexity and offers guarantee on search completeness and discovery of rare items. Advertisement traffic in DPMS is comparable to that of DHT-based structured P2P systems. To our knowledge Distributed Pattern Matching (DPM) problem has never been addressed by any research activity in P2P context. 1 The index distribution architecture of DPMS is unique and has been designed specifically to solve the DPM problem. The novel aggregation scheme, proposed in this paper, can effectively reduce storage overhead at the indexing peers without incurring a significant decrease in query routing performance. However, the use of bloom filter for representing indices is not new. Many network applications use bloom filters. A comprehensive list of such applications can be found in [6]. The rest of this paper is organized as follows. Section II highlights and compares the approaches related to DPMS. The architecture and operation of DPMS are presented in section III. Mathematical analysis of search complexity in DPMS is provided in section IV.
please solve question with explanation *TEST REVISION*
Answer:
Step-by-step explanation:
You roll one die. What is the probability that you roll a 6?
Each rectangle is 16% longer than the original. Complete the table with the length of each new rectangle.
It seems that the table has not been provided in the question. However, I can provide a general method to complete the table based on the given information.
If each rectangle is 16% longer than the original, we can calculate the length of each new rectangle by adding 16% of the original length to the original length.
Let L be the original length of the rectangle. Then, the length of the new rectangle would be L + 0.16L = 1.16L.
Using this formula, we can calculate the length of the new rectangle for any given original length. For example, if the original length is 10 cm, then the length of the new rectangle would be:
1.16 x 10 cm = 11.6 cm
Similarly, we can calculate the length of the new rectangle for any other original length and complete the table accordingly.
Express the trig ratios as fractions in simplest terms.
The trig ratios as fractions expressed in simplest terms is :cos(K) = 8 √(17)/17 , sin(L) = 9 √(17)/17
What are trigonometric ratios?Trigonometric ratios are mathematical relationships between the angles and sides of a right-angled triangle. They are ratios of the lengths of two sides of a right triangle in relation to one of its acute angles. The three primary trigonometric ratios are sine, cosine, and tangent, which are commonly denoted as sin, cos, and tan, respectively.
Sine: The sine of a right triangle angle seems to be the ratio of the length of the opposite side towards the length of the hypotenuse.
Cosine: The cosine of an angle in a right triangle is the ratio of the length of the adjacent side to the angle towards the length of the hypotenuse.
Tangent: In a right triangle, the tangent of an angle is really the ratio of the length of the side opposite the angle to the length of the adjacent side.
Given: A right angle triangle JKL, with angle J = 90 degrees, JL = sqrt(17), JK = 8, LK = 9
We can use the following trigonometric ratios:
To find the values of sin(L) and cos(K), we need to identify the opposite, adjacent and hypotenuse sides of the angles L and K.
For angle K:
cos(K) = adjacent/hypotenuse = JK/JL = 8/√(17)
To make the fraction easier to understand, multiply the numerator and denominator by √(17):
cos(K) = (8/√(17)) x (√(17)/√(17)) = (8 √(17))/17
Therefore, cos(K) = 8 √(17)/17
For angle L:
sin(L) = opposite/hypotenuse = LK/JL = 9/√(17)
To make the fraction easier to understand, multiply the numerator and denominator by √(17):
sin(L) = (9/√(17)) x (√(17)/√(17)) = (9 √(17))/17
Therefore, sin(L) = 9 √(17)/17
To know more about fractions, visit:
https://brainly.com/question/10354322
#SPJ1
I need help on my math work
The specified details of the triangle, obtained using the segments joining the midpoints of the sides of the triangle ΔADG and trapezoid ACFG indicates that we get;
4. [tex]\overline{CE}[/tex] is a midsegment of ΔBDF
[tex]\overline{BF}[/tex] is the midsegment of trapezoid ACFG
5. CE = 12 cm, AG = 36 cm
6. m∠2 = 116°, m∠3 = 32°, m∠4 = 58°, m∠5 = 58°, m∠6 = 64°
What is the midpoint of a segment?The midpoint of a segment or the side of a triangle is a point that divides the segment into two parts of the same length.
4. The details of the diagram indicates that the segment [tex]\overline{CE}[/tex] is the midsegment of triangle ΔBDF
[tex]\overline{BF}[/tex] is the midsegment of trapezoid ACFG
5. [tex]\overline{CD}[/tex] is congruent to [tex]\overline{BC}[/tex] by the definition of the midpoint of [tex]\overline{BD}[/tex], similarly;
[tex]\overline{BC}[/tex] is congruent to [tex]\overline{AB}[/tex], by the definition of midpoint of [tex]\overline{AC}[/tex], therefore;
[tex]\overline{CE}[/tex] is the midsegment of triangle ΔBDF, therefore;
CE = (1/2) × BF
CE = (1/2) × 24 cm = 12 cm
CE = 12 cm
ΔBDF and ΔADG and ΔCDE are similar triangles, therefore;
[tex]\overline{BD}[/tex] = (2/3) × [tex]\overline{AD}[/tex]
Similarly, by the relationship between similar triangles we get;
[tex]\overline{BF}[/tex] = (2/3) × [tex]\overline{AG}[/tex]
BF = 24 cm, therefore;
24 = (2/3) × AG
AG = (3/2) × 24 = 36
AG = 36 cm
6. The length of a median of a right triangle, drawn from the right angled vertex, is half the length of the hypotenuse side.
Therefore; ΔACM and ΔABM are an isosceles triangles
m∠1 = m∠3 = 32°
m∠2 = 180° - (32° + 32°) = 116°
m∠2 = 116°
m∠3 = 32°
m∠4 = m∠5 = 90° - m∠1
m∠4 = m∠5 = 90° - 32° = 58°
m∠4 = 58°
m∠5 = 58°
m∠6 = 180° - (m∠4 + m∠5)
m∠6 = 180° - (58° + 58°) = 64°
m∠6 = 64°
Learn more on the midpoint of a segment here: https://brainly.com/question/8075904
#SPJ1
Notebooks at the school store were on sale for $3 off the regular price. Sam bought 4
notebooks on sale and paid a total of $28. Write an equation to find the regular
price of one notebook.
Answer: (28 / 4) + 3 = x; x = the regular price of a notebook not on sale.
Step-by-step explanation: The price of the notebook on sale is $7 and the price of a notebook regularly is $10 (not on sale). Therefore, the equation "(28 / 4) + 3 = x" explains how to come to that value.
witch shapes have atleats one right angle ?? please anwser fluently
Answer:
top left and top right
Step-by-step explanation:
a right angle is 90⁰
Using what you know and learned about angles and triangles over the past few weeks, what is the measure of angle 6?
Answer:
158degrees
Step-by-step explanation:
2 = 68 ( vertically opposite)
4 = 90 (Vertically opposite)
6= 68 +90 = 158( exterior angle is sum of its opposite interior)
A triangle has a 50° angle and two sides that are each 4 centimeters in
Select True or False for each statement about this triangle.
True False
0
One of the angles in the triangle might be 65º.
The triangle might be an equilateral triangle.
Two of the angles in the triangle must measure 50°.
One of the angles in the triangle might be 60°.
C
0
Answer:
1.True
2.False
3.True
4.False
The weekly wages of a man and a boy engaged for the same kind of work is Rs. 80 and Rs. 35 respectively. If the wages of both are increased by the same amount then the men's wage is 8/5 of the boy's wage. What is the increase?
The increase in weekly wages for both the man and the boy is Rs. 40.
Let's assume that the increase in wages for both the man and the boy is x.
After the increase, the man's weekly wage will be Rs. 80 + x and the boy's weekly wage will be Rs. 35 + x.
We know that the man's wage after the increase is 8/5 of the boy's wage after the increase. Mathematically,
80 + x = (8/5)(35 + x)
Simplifying this equation, we get:
80 + x = 56 + (8/5)x
Multiplying both sides by 5, we get:
400 + 5x = 280 + 8x
Subtracting 5x from both sides, we get:
400 = 280 + 3x
Subtracting 280 from both sides, we get:
120 = 3x
Dividing both sides by 3, we get:
x = 40
Therefore, the increase in wages is Rs. 40.
To know more about weekly wages:
https://brainly.com/question/28754816
#SPJ4
9,857 + 310 ÷ 2 - 10 = ?
Answer:
10002
Step-by-step explanation: I think this is correct
Answer:
10002
Step-by-step explanation:
9,857 + 310 ÷ 2 - 10 = 10002
variable is normally distributed with mean and standard deviation . a. find the percentage of all possible values of the variable that lie between and . b. find the percentage of all possible values of the variable that are at least . c. find the percentage of all possible values of the variable that are at most .
The percentage of all possible values of the variable that lie between 10 and 16 is 97.71%, the percentage of all possible values of the variable that are at least 18 is 0.01% and the percentage of all possible values of the variable that are at most 8 is 0.01%.
Given that, variable is normally distributed with mean and standard deviation .
To find the percentage of all possible values of the variable that lie between and .
We can convert the given variable to standard normal variable using Z= (X- μ )/ σ
Therefore, we get, Z1 = (10- 12)/ 1 = -2 And Z2 = (16-12)/1 = 4
Thus, the probability of values that lie between 10 and 16 is given by
P(-2 ≤ Z ≤ 4) = P(Z ≤ 4) - P(Z ≤ -2) = 0.9999 - 0.0228 = 0.9771 = 97.71%.b)
To find the percentage of all possible values of the variable that are at least .Converting the given variable to standard normal variable using Z= (X- μ )/ σ, we get,
Z = (18-12)/1 = 6
The probability of values that are at least 18 is given by
P(Z ≥ 6) = 1- P(Z ≤ 6) = 1- 0.9999 = 0.0001 = 0.01%.c)
To find the percentage of all possible values of the variable that are at most .Converting the given variable to standard normal variable using Z= (X- μ )/ σ, we get,
Z = (8-12)/1 = -4
The probability of values that are at most 8 is given byP(Z ≤ -4) = 0.0001 = 0.01%.
for such more question on percentage
https://brainly.com/question/24877689
#SPJ11
!!!TIMED!!! !!!Please help as fast as possible!!!
Find the value of a.
In right triangle LMN, angles L and M are complementary.
Find the mesure of angle L.
Answer:
Step-by-step explanation:
Every year, Martha and her sister attend 'The Nutcracker' at the Greenpoint Ballet. Last year, orchestra seating cost $60 per ticket. This year, each ticket was 15% cheaper. What was the cost of each ticket this year?
Answer:119.7
Step-by-step explanation:60 divided by 15%
hi i need help checking 12x + 9 = - 15
i know the answer ( x = 2) i just need help checking!!
well actually, your answer is -2
not positive 2
you have to take the 9, and subtract it from the other side (the -15), giving you -24
then you divide -24 by 12, giving you x=-2
this is true because when you plug it back in, you get 12 x -2 = -24
-24 + 9 = -15
Anya has a number of square bricks with a side length of 1 foot that 164) she wants to use to create a rectangular patio in her backyard. At first, she arranges them so the rectangle is 12 bricks long by 3 bricks wide, but then she decides she does not like that arrangement. How can Anya arrange the bricks if she would rather have a square-shaped patio?
Answer: 6 bricks long by 6 bricks wide
Step-by-step explanation:
Since her first arrangement is a 12 x 3 brick patio, we can assume she has 36 bricks. A square has equal lengths of all sides, with this info, she can arrange the 36 bricks into a 6 by 6 patio
alan's camping troop is raising money for a camping trip. the camping troop is selling boxes of popcorn, b, for $3.75 each. each camper starts with a credit of $25. to make the first deposit on the camping trip, alan total sales, f(b), needs to be at least $1100. write an inequality to represent the problem:
Answer:
$3.75b + $25 >= $1100
Step-by-step explanation:
QUESTION 1
If we enter 6 debits of $25 each, the net effect on our account is how many
dollars (indicate if this is negative or positive amount by using a negative sign if the answer is negative).
Andariel went for a ride on her dune buggy in the desert. She rode east for 6 km, then turned 125° to the left for the second stage of her ride. After 5 minutes riding in the same direction, she turned to the left again, and from there travelled the 5.5 km straight back to her starting position.
How far did Andariel travel in the second section of her ride, correct to 2 decimal places?
Applying the laws of cosine, in the second section of her ride, Andariel traveled about 3.012 km, as rounded to 2 decimal places.
What is the law of cosines?The law of cosines is a mathematical formula used to determine the unknown length or angle of a triangle when two sides and an angle or all three sides are known.
Hence, we can think of it as trying to know Andariel's travel distance around a big triangle.
Thus to calculate, using the law of cosines, we have:
[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]
Where in our case:
a = 6 km (distance traveled east)b = x km (distance traveled in the second section)C = 180 - 125 = 55 degrees (angle between a and b)c = 5.5 km (distance traveled straight back to the starting position)If we substitute the values above into the cosine formula, we get:
[tex](5.5)^2 = (6)^2 + (x)^2 - 2(6)(x)*cos(55)[/tex]
[tex]30.25 = 36 + x^2 - 12.0627x[/tex]
Simplifying and rearranging the equation further:
[tex]x^2 - 12.0627x + 5.75 = 0[/tex]
Applying the quadratic formula to simply:
[tex]x = (12.0627 ± sqrt(12.0627^2 - 415.75))/2[/tex]
x = 9.05 or x =3.012.
Remember, we are told Andariel turned left twice and ended up at her starting position, we know that she traveled in a closed loop.
Therefore, the distance she traveled in the second section of her ride must be less than 6 km (the distance she traveled east in the first section). Thus, the distance she traveled last or second section of her ride was 3.012 km.
You can learn more about the law of cosines here https://brainly.com/question/4372174
#SPJ1
Name the marked angle in 2 different ways.
J, K, I
Answer: Where is the image?
Step-by-step explanation:
p+13+q+27 prove that 6=p and q=20
PLEASEE HELP FASTT!!!
To build a large sand castle, Sam takes an old traffic cone and fills it with sand. The cone is 18 in. tall and has a diameter of 7 in
To the nearest cubic inch, how much sand does Sam use?
A) 26 in³
B) 103 in³
C) 231 in³
D) 308 in³
Can u guys factorize this equations please
Answer: Answer is below <3
Step-by-step explanation:
1. —1x²(3x²—7x—5)
2. 14x ² (y²—2x+4x²)
3. 8100m²y4
4. (a5— 7b6) (a5 — 7b6)
5. (m+1) (m+11)
6. (a+1) (a+6)
7. —3x+6
8. (—6a+1) (—6a+1) / 4
9. (x+5)²
10. X² — 7xy—88x
Hope this helps!