will mark brainliest if answered
Answer:
See below
Step-by-step explanation:
The vertex form of a parabola is y = a(x - h)^2 + k
If the leading coefficient is positive, the parabola opens upward, and (h, k) represents the vertex, or turning point.
1a. The leading coefficient is 4, which is positive, meaning the parabola opens upwards. From the vertex form, we can say the vertex(turning point) is (2, 7).
1b. The leading coefficient is -3, which is negative, meaning the parabola opens downwards. From the vertex form, we can say the vertex(turning point) is (-6, 4).
1c. The leading coefficient is -1, which is negative, meaning the parabola opens downwards. From the vertex form, we can say the vertex(turning point) is (-4, -3).
To write the vertex form of a parabola, we need to complete the square. A perfect square trinomial is in the form a^2 + 2ab + b^2. In these cases we are already given a^2 and 2ab.
2a. We can say x^2 corresponds to a^2 because it is a square and 2ab corresponds to 6x. From this, we can say a = x. Now, we can plug that in:
2ab = 6x
2(x)b = 6x
b = 3
Therefore, the last term b^2, is 3^2 or 9. We can add 9 and subtract nine to keep the equation equivalent:
y = x^2 + 6x + 9 - 9 - 2
Now, we can factor the square into (a + b)^2 and simplify:
y = (x + 3)^2 - 11
From this form, the vertex(turning point) will be (-3, -11). Since the leading coefficient is 1, which is positive, the parabola opens upwards, meaning the turning point is a minimum.
2b. We can say x^2 corresponds to a^2 because it is a square and 2ab corresponds to -2x. From this, we can say a = x. Now, we can plug that in:
2ab = -2x
2(x)b = -2x
b = -1
Therefore, the last term b^2, is (-1)^2 or 1. We can add 1 and subtract nine to keep the equation equivalent:
y = x^2 - 2x + 1 - 1 + 11
Now, we can factor the square into (a + b)^2 and simplify:
y = (x - 1)^2 + 10
From this form, the vertex(turning point) will be (1, 10). Since the leading coefficient is 1, which is positive, the parabola opens upwards, meaning the turning point is a minimum.
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 6.2 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 23 samples is 6.4 ppm with a standard deviation of 0.7. Assume the population is normally distributed. A level of significance of 0.02 will be used. State the null and alternative hypotheses.
Answer:
H0 : μ = 6.2
H1 : μ ≠ 6.2
Step-by-step explanation:
Population mean, μ = 6.2 ppm
The hypothesis :
Null, H0 : = The mean level of Ozone is normally 6.2 ppm ;
The alternative hypothesis is the researcher's claim that the current ozone level is not normal, that is it may be higher or lower than the normal value in ppm
Hence, the hypothesis could be written as :
H0 : μ = 6.2
H1 : μ ≠ 6.2
The Marked price of a jacket at a dealer's shop is 2400. The dealer allows a discount of 15% to the retailer. As the company's policies the marked price of the retailer should be the same as the dealer's marked price. What SP should the retailer fix for the jacket? What would its final price be if 10% VAT is imposed? What would be the actual gain of retailer?
Ans
2280,2502,240
Answer:
2400
2640
360
Step-by-step explanation:
the retailer has to sell it for the same price as the dealer.
so, both mark it for 2400 sale price.
if a customer buys it at the retailer, the retailer makes the 15% discount he got from the dealer as profit.
2400 = 100%
1% = 2400/100 = 24
15% = 24×15 = 360
the retailer makes this profit no matter what other fees or taxes are added.
the final price is then including 10% VAT
2400 = 100%
10% = 24×10 = 240
final price = SP + VAT = 2400 + 240 = 2640
Please help as soon as possible! Round your answers to one decimal place, if necessary. Find the mean and median of these data: 2, 5, 13, 15, 18, 20. tysmmm!
Answer:
Mean= 12.2
Median= 14
Step-by-step explanation:
The mean of the data can be calculated as follows
= 2+5+13+15+18+20/6
= 73/6
= 12.2
Mean= 12.2
The median can be calculated as follows
Arrange the numbers in an orderly way
2, 5, 13, 15, 18, 20
= 13+15/2
= 14
Median= 14
prove [tex](x+1)^{2}(x+2)=(x^3+3x+21x+1)[/tex] no files
Answer:
LHS ≠ RHS
Step-by-step explanation:
[tex]LHS =\\\\=(x+1)^2 (x + 2) \\\\=(x^2 + 2x + 1)(x+2)\\\\=x(x^2 + 2x + 1) + 2(x^2 + 2x + 1) \\\\=(x^3 + 2x^2 + x ) + ( 2x^2 + 4x + 2) \\\\=x^3 + 2x^2 + x + 2x^2 + 4x + 2 \\\\=x^3 + 4x^2 + 5x + 2[/tex]
HELP ASAP!! ILL MARK BRAINLIEST! David recorded the ages, in years, of the members of four high school clubs. Each club has the same number of members. A brief description of David’s data is shown.
Music Club: This club has the same number of members older than 16 and younger than 16.
Physics Club: This club has the greatest number of older members.
Sports Club: This club has the greatest number of younger members.
History Club: This club has the oldest member enrolled.
David then made box plots showing his data. Match the labels of the clubs to the box plots. Drag and drop each club into the indicated rectangles.
Answer:
Music club last box
Reason: There are equal number if members
Physics club first box
Reason: There are more older than young people
Sports Club third box
Reason: There are more younger people than older people
History Club takes the second box
Step-by-step explanation:
Hope this helps please like and mark as brainliest
what is the hcf of 11, 13 and 5
Answer:
1
Step-by-step explanation:
The factors of 5 are: 1, 5
The factors of 11 are: 1, 11
The factors of 13 are: 1, 13
Therefore the greatest/highest common factor is 1.
Help me pls it’s number 8, will give brainliest but quickly pls
Write each number in standard form.
Answer:
35010
.08190
- 137000
- .00060041
Step-by-step explanation:
positive exponents add zeros to end and move decimal place to right the amount of the exponent.
negative exponents add zeros to begininng and move decimal to the left.
given a rectangular has a length of 58.5 m and widht of 45 m. Draw a diagram with scake if givrn scale drawing is 1 cm:9m
Answer:
In picture
Step-by-step explanation:
Brainliest please
2. What is the slope of the line 2x + y = 8?
Answer:
Using the slope-intercept form, the slope is 2 .
which value is an import of the function?
-14
12
0
4
si alguien me ayuda en esta doy coronita
Answer: yuh Step-by-step explanation: yuh
Answer:
11/8, 7/4, 8/2
someone reported me
39.63+0.30=24.45+0.80
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{39.63 + 0.30 = 24.45 + 0.80}[/tex]
[tex]\large\textsf{39.63 + 0.30}[/tex]
[tex]= \boxed{\large\textsf{\bf 39.93}}\large\checkmark[/tex]
[tex]\large\textsf{24.45 + 0.80}[/tex]
[tex]=\boxed{\large\textsf{\bf 25.25}}[/tex]
[tex]\large\textsf{\bf 39.93 } \mathsf{\bf \neq }\large\textsf{ \bf 25.25}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: \bf FALSE or NOT TRUE because 39.93 }\mathsf{\neq }\large\textsf{ \bf 25.25}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A rectangle has a length that is 8 less than it’s width w the perimeter is 52 which equation can be used to determine length
Answer:
width?
8-W-52
2(w-8) +2w=52
(W-8)+W=52
2(8-W) +2w=52
If G(X) = 3x+1, then G-1(1) is
Answer:
0
Step-by-step explanation:
To find the inverse, or [tex]G^{-1}[/tex] , we must switch G(x) and x, and then make G(x) [tex]G^{-1} (x)[/tex] as we are finding the inverse, and G(x) represents the starting equation.
[tex]x = 3G^{-1} (x)+1\\x -1 = 3G^{-1} (x)\\\\\frac{x-1}{3} = G^{-1} (x)\\[/tex]
The steps used here are that we firt subtracted 1 from both sides, and then divided 3 from both sides.
To find [tex]G^{-1} (1)[/tex], we simply plug 1 into x in the inverse function, so our answer is [tex]\frac{1-1}{3} =0[/tex]
Using the following image, find GH given HI = 1 and GI =
= 9.
Answer:
8
Step-by-step explanation:
Answer:
[tex]{ \tt{GH =GI - HI }} \\ = 9 - 1 \\ GH = 8[/tex]
You throw a stone with a force of 55.1 N. It accelerates at 41.6 m/s2.
Find the mass of the stone in kg. Round your answer to 1 decimal place.
Answer:
Mass = 1.3 Kilograms.
Step-by-step explanation:
Given the following data;
Force = 55.1 N
Acceleration = 41.6 m/s²
To find the mass of the stone in kg;
Newton's Second Law of Motion states that the acceleration of a physical object is directly proportional to the net force acting on the physical object and inversely proportional to its mass.
Mathematically, it is given by the formula;
Force = mass * acceleration
Substituting into the formula, we have;
55.1 = mass * 41.6
[tex] Mass = \frac {55.1}{41.6} [/tex]
Mass = 1.3 Kilograms
You have $9 and earn $0.75 for each cup of orange juice you sell. Write an equation that represents the total amount $A (in dollars) you have after selling $j cups of orange juice. $A
Answer:
I believe it's A = 0.75j + 9
Step-by-step explanation:
If x or j is the amount of cups of OJ you sell, and you earn $0.75 per cup.
0.75x
The b = 9 which adds to the total amount of money you have
0.75x+9
A is the total money you earn after you sell j cups.
I hope this helps!
Help and explain pleaseeeeeeeeee
Answer:
if f(n) = 4n + 7 and g(n) = 2n + 3, find (g-f)(n)
-2n - 4
f(x) = 2x - 3 and g(x) = 5 - 2x, find f/g (x)
2x - 3 / 5 - 2x
Step-by-step explanation:
Math help please show work
Answer:
7 in
Step-by-step explanation:
Answer:
a = 7 in
Step-by-step explanation:
[tex]Area = \frac{a+b}{2} \times h\\\\26.25 = \frac{a + 10.5}{2} \times 3\\\\26.25 \times 2 = (a+ 10.5) \times 3\\\\52.5 = (A + 10.5) \times 3\\\\\frac{52.5}{3} = a + 10.5\\\\17.5 = a + 10.5\\\\a = 17.5 - 10.5 = 7[/tex]
what is the circumference of a circle diameter of 6 feet?use 3.14 for n
Answer:
18.84 feet.
Step-by-step explanation:
The formula for the circumference of a circle is:
2Pi*radius
The radius would be half the diameter so 3.
2*3.14*3
The Tetrahedron Superyacht designed by Jonathan Schwinge is a regular tetrahedron with edges 20 m
long. The distance r from one corner to the center of the base (shown in the picture below) is 11.5 m.
pecial rig
What is the vertical height h of the tetrahedron?
Round your answer to the nearest tenth of a meter.
% 4 day
h
m
Answer:
16.36 the proof is in the picture
Step-by-step explanation:
Complete the square x2+6x+3
x^2 + 6x + 9
x^2 + 3x + 3x + 9
x ( x + 3 ) + 3 ( x + 3 )
( x + 3 ) ( x + 3 )
( x + 3 ) ^2
Suman and Narayan riding bikes towards each other they are 480 Km apart. The speed of Narayan is 6km/hr faster than Suman. If both meet each other after 6hours find there speeds when both started at same time.
Answer:
Suman 37 km/hr
Narayan 43 km/hr
(extremely sorry if this is wrong!!)
Step-by-step explanation:
We can use the formula distance divided by time is speed.
480/6 = 80.
Their speeds must add up to 80 km/hour
Lets set suman as a variable, lets say s.
Narayan has a speed 6 more than suman so we say 6+s
6+s+s = 80
subtract 6 from both sides
s+s = 74
add like terms
s+s = 2s
2s = 74
divide both sides by 2.
74/2=37
s=37
Suman's speed is 37 km/hr.
Narayan's speed would be 6 more than Suman's so we do 6+37
which makes 43 km/hr
A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 18°33'. When the boat stops, the angle of depression is 51°33'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place. HELP
Answer:
51.33
Step-by-step explanation:
Step-by-step explanation
The angle of depression from the lighthouse is the angle of elevation from the boat. The line of sight from the top of the lighthouse, when depressed, becomes an alternate interior angle of two parallel lines, the line of sight from the top and the boat's movement.From the boat's standpoint, which is what we want anyway, there is a right triangle, with the distance from the lighthouse the adjacent side, the opposite is 200,' and the boat the point desired. The tangent is needed.
From the boat's standpoint, which is what we want anyway, there is a right triangle, with the distance from the lighthouse the adjacent side, the opposite is 200,' and the boat the point desired. The tangent is needed.tangent 18.33 degrees (33 minutes is 33/60 of a degree)=200x
140 divided by 8960 please I need to know.
The value will be 64 when the number 8960 is divided by 140.
What is division?A procedure of dividing anything into equal halves is called division. It is one of the four fundamental operations in math. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given numbers are 8960 and 140. To calculate the quotient divide the number 8960 by 140.
The given number can be divided as below:-
140 ) 8960 ( 64
-840
___________
560
-560
___________
000
Therefore, the value will be 64 when the number 8960 is divided by 140.
To know more about division follow
https://brainly.com/question/25289437
#SPJ2
could someone help me with this please?
Instructions: Find the slope of the line through the points (-13, 16) and (-13, 12). Make sure to simplify
fractions and enter your answers with a foward slash (i.e. "/"). If the slope is undefined enter "undefined.
Answer: undefined
Step-by-step explanation:
Using the slope formula: (y^2 - y^1)/(x^2 - x^1), we can fill in the points:
(12 - 16)/(-13 - - 13) = -4/0
We can’t have a denominator of zero, so this is undefined.
9. How many perpendiculars can we draw to a line from a given point outside the line?
O A. 3
O B. 2.
O C.O
D. 1
Answer:
The answer is D. 1. You can form only 1 perpendicular line.
The length of a regulation soccer field is 110 meters. The diagonal length of the same soccer field is about 133.14 meters. About how wide is the regulation soccer field?
A. 23.14 meters
B. 243.14 meters
C. 172.7 meters
D. 75 meters
Answer:
D
Step-by-step explanation:
Imagine this as a right angle triangle, where the diagonal length is the hypotenuse, the length is one side, and the width is the other.
We can therefore use Pythagoras' Theorem (or Pythagorean Theorem) to solve. The formula for this is a²+b²=c², where c is the hypotenuse, and a and b are the sides.
We can input the values we know to this formula to get the width. This gives 110²+b²=133.14² or 12100+b²=17 726.2596.
From there subtracting 12100 from both sides gives b²=5626.2596.
Square rooting b isolates it, leaving b=75.0083969.
Since the value of the diagonal was approximate, this can be assumed the b is 75m.
**This content involves Pythagoras' Theorem/Pythagorean Theorem, which you may wish to revise. I'm always happy to help!