Answer:
Ok, our function is:
f(x) = 3*(x - 1)^2 + 2.
First, domain:
We should assume that the domain is all the set of real numbers, and then we see if for some value we have a problem.
In this case we do not see any problem (we can not have a zero in the denominator, and there is no function that has problems with some values of x)
Then the domain is the set of all real numers.
Vertex:
Let's expand our function:
f(x) = 3*x^2 - 3*2*x + 1 + 2
f(x) = 3*x^2 -6*x + 2
The vertex of a quadratic function:
a*x^2 + b*x + c is at:
x = -b/2a
here we have:
a = 3 and b = -6
x = 6/2*3 = 6/6 = 1.
And the value of y at that point is:
f(1) = 3*(1 - 1)^2 + 2 = 2
Then the vertex is at: (1, 2)
Range:
The range is the set of all the possible values of y.
Ok, we can see that the leading coefficient is positive, this means that the arms of our quadratic function will go up.
Then the minimal value of our quadratic function is the value at the vertex, y = 2.
This means that the range can be written as:
R = y ≥ 2
So the range is the set of all real numbers that are larger or equal than 2.
Find a formula for the 4th term of the following G.P.S a) 1, 2,4......... b)50, 20, 8......... Pls explain very well.. Thank you.
Answer:
see below
Step-by-step explanation:
The formula for a geometric sequence is
an = a1 * r^ (n-1) where a1 is the first term and r is the common ratio
The common ratio is found by taking the second term and dividing it by the first term
a) 1, 2,4.........
a1 = 1
r = 2/1 = 2
an = 1 * ( 2) ^ (n-1)
Let n = 4
a4 = 1 * 2^ (4-1) = 1 * 2^3 = 8
b)50, 20, 8.........
a1 = 50
r = 50/20= 5/2
an = 50 * ( 5/2) ^ (n-1)
Let n = 4
a4 = 50 * (5/2)^ (4-1) = 50 * (5/2)^3 = 3125/4
Jessie has some nickels, dimes, and quarters in her bank. The number of coins is 30. The expression 0.05n + 0.10d + 0.25q represents the value of the coins, which is $3.45. Jessie has five more nickels than she does quarters. How many of each coin does Jessie have?
Answer:
n = 12 nickels
d = 11 dimes
q = 7 quarters
Step-by-step explanation:
.05n + .1d + .25q = 3.45
n + d + q = 30
n = q + 5
n = 12
d = 11
q = 7
3.7 as a mixed number
Answer:
[tex]3\frac{7}{10}[/tex]
Please tell me if I'm wrong, and maybe consider brainliest if it's correct of course.
how many are 7 raised to 3 ???
Answer:
343
Step-by-step explanation:
7^3 =
7*7*7
343
Solve for x 3(x+7)-14=22
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your equation step-by-step.
[tex]3(x+7)-14=22[/tex]
Step 1: Simplify both sides of the equation.
[tex]3 ( x + 7 ) - 14 = 22\\(3)^(x) + (3) (7) + - 14 = 22[/tex] (Distribute)
[tex]3x + 21 + -14 = 22[/tex]
[tex]( 3x) + (21 + -14 ) = 22[/tex] (Combine Like Terms)
[tex]3x + 7 = 22\\3x + 7 = 22[/tex]
Step 2: Subtract 7 from both sides.
[tex]3x + 7 - 7 = 22 - 7 \\3x = 15[/tex]
Step 3: Divide both sides by 3.
[tex]\frac{3x}{3} = \frac{15}{3} \\x = 5[/tex]
So your answer would be : [tex]\boxed {x = 5}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Point R is on line segment QS. Given QR=3 and QS=17, determine the length RS.
Answer:
14
Step-by-step explanation:
RS = QS - QR
RS = 17 - 3
RS = 14
Answer:
[tex]\large \boxed{14}[/tex]
Step-by-step explanation:
Point R is on the line segment QS.
QS = QR + RS
Solve for RS.
RS = QS - QR
RS = 17 - 3
RS = 14
Which statement describes the graph of x = 4
Answer:
The graph of x=4 is a vertical line parallel to y-axis and having a x-intecept:(4,0) and having no y-intercept
Step-by-step explanation:
So I think that the answer would be this, which means answer 1!! Hope this helps
help me solve please
Answer:
B
Step-by-step explanation:
The side you have drawn in is 4√3 (calculate via pythagoras as √(8²-4²) = √48 = √16·3 = √4²·3 = 4√3)
So the area of the small triangle is 4*2√3 and the area of the small rectangle is 2*4√3. Together makes 4*2√3 + 2*4√3 = 16√3
find the five rational number lying between square of 5/6 and 6/7
Answer:
71/84
Step-by-step explanation:
Answer:
1229/1764, 1231/1764, 179/252, 1255/1754 and 185/252.
Step-by-step explanation:
(5/6)^2 = 25/36
(6/7)^2 = 36/49
LCM of 36 and 49 is 1764
So 25/36 = 25 * 49 / 1764 = 1225/1764
and 36/49 = 36 * 36 / 1764 = 1296/1764
So the 5 rational numbers could be:
1229/1764, 1231/1764, 1253/1764 ( = 179/252), 1255/1764 and 1295/1764 (= 185/ 252).
NEED IN 10 MIN. WILL GIVE BRAINLEST Solve the triangle. B = 36°, a = 41, c = 17
Answer:
Yes this is a Triangle
36 degrees of any side then 41 would connct to 36 and 17 would connects to 36 and 41! If this is Khan Academy your asking out of its a Yes, it is a Triangle
HOPE IM THE BRANLIESS UwUAnswer:
It is a triangle:
Step-by-step explanation:
b² = a² + c² - 2(a)(c)cos(B)
b² = 41² + 20² - 2(41)(20)cos(36)
b² = 754.2121292
b = 27.46292281
b = 27.463
A = 41, B = 27.4, C = 17
Determine the equation of the inverse of y = 1/4 x^3 - 2
All of 4x+8 is under a cube root sign.
=====================================================
Work Shown:
To find the inverse, we swap x and y, then solve for y.
[tex]y = \frac{1}{4}x^3 - 2\\\\x = \frac{1}{4}y^3 - 2\\\\x+2 = \frac{1}{4}y^3\\\\4(x+2) = y^3\\\\4x+8 = y^3\\\\y^3 = 4x+8\\\\y = \sqrt[3]{4x+8}\\\\[/tex]
------------
Side note:
If [tex]f(x) = \frac{1}{4}x^3 - 2[/tex] and [tex]g(x) = \sqrt[3]{4x+8}[/tex], then [tex]f(g(x)) = x[/tex] and [tex]g(f(x)) = x[/tex]for all x values in the domain. Effectively, you use function composition to confirm that we have the correct inverse equation.
According to the graph, what is the value of the constant in the equation
below?
A. 30
B. 72
C. 60
D. 15
Greetings from Brasil...
As stated in the statement:
HEIGHT = CONSTANT ÷ WIDTH
H = C ÷ W
so, isolating the variable C....
C = H · W
choosing any point on the graph...
(2; 30) ⇒ W = 2 and H = 30
C = H · W
C = 30 · 2
C = 60The value of the constant in the equation shown in the figure would be, 60. Hence option C is true.
Given that,
The graph is the relation between Height and width.
As is given in the graph:
Height = Constant / Width
We observe that the graph passes through (2,30), (5,12), (10,6), (30,2)
So, by using any one point we may get the value of constant( since it is a fixed quantity)
Hence, using the point (2,30)
Width = 2
And, Height = 30
So, we get:
Constant = 2 × 30
= 60
To learn more about multiplication visit:
https://brainly.com/question/10873737
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the product 9f 2 numbers is 16/9 . if one number is 5 /2 find the other number
Answer:
The answer is 32/45Step-by-step explanation:
Let the number be x
The product of two numbers is 16/9
That's
x × y = 16/9
One of the numbers is 5/2
That's
y = 5/2
So we have
[tex] \frac{5}{2} x = \frac{16}{9} [/tex]
Multiply through by the LCM
The LCM of 2 and 9 is 18
That's
[tex]18 \times \frac{5}{2} x = \frac{16}{9} \times 18[/tex]
9 × 5x = 16 × 2
45x = 32
Divide both sides by 45
we have the final answer as
[tex]x = \frac{32}{45} [/tex]
Hope this helps you
What is [tex]3^2*3^5[/tex]?
Answer:
[tex]3^7[/tex]
Step-by-step explanation:
[tex]3^2*3^5[/tex]
[tex]\text {Apply Product Rule: } a^b+a^c=a^{b+c}\\\\3^2*3^5=3^{2+5}=3^7[/tex]
A teacher orders 20 copies of a new graphic novel for his class to read. Each of the books weighs the same amount. The total weight of all the books is 10 pounds, What is the weight of 1 book?
Answer:
Each book weighs 1/2 lbs
Step-by-step explanation:
Take the total weight and divide by the number of books
10 lbs/20 books
1/2 lbs per book
Each book weighs 1/2 lbs
Please please please help
Answer:
m = 4
Step-by-step explanation:
9/6=6/m
9m = 36
m = 4
Please answer quickly
Answer:
answer what
Step-by-step explanation:
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Last week Andi had exams in Chemistry and in Spanish. On the chemistry exam, the mean was µ = 30 with σ = 5, and Andi had a score of X = 45. On the Spanish exam, the mean was µ = 60 with σ = 6 and Andi had a score of X = 65. For which class should Andi expect the better grade?
Answer:
Chemistry
Step-by-step explanation:
To solve the above question, we use the z score formula
Andy took two Exams, Chemistry and Spanish. So we find the z score for both exams.
a) Chemistry Exam
On the chemistry exam, the mean was µ = 30 with σ = 5, and Andi had a score of X = 45
z-score is given as: z = (x-μ)/σ
where x is the raw score,
μ is the population mean
σ is the population standard deviation
z = (x-μ)/σ
z = (45 - 30)/5
z = 15/5
z = 3
b) On the Spanish exam, the mean was µ = 60 with σ = 6 and Andi had a score of X = 65.
z-score is given as: z = (x-μ)/σ
where x is the raw score,
μ is the population mean
σ is the population standard deviation
z = (x-μ)/σ
z = (65 - 60)/6
z = 5/6
z = 0.8333333333
Comparing the z score of both Exams,
Andy had a z score of 3 in the Chemistry exam and 0.8333333333 in the Spanish exam.
Therefore, Andy should be expecting a better grade in the Chemistry exam because his z score in the Chemistry exam was higher than that of the Spanish exam.
plz help with equation of the circle will award fastest CORRECT answer with brainliest
Answer:
[tex](x-1)^2+(y-2)^2=6.25[/tex]
Step-by-step explanation:
The equation for a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is the center and r is the radius.
The center is the red dot, which is (1,2). Thus, h=1 and k=2.
To find the radius, you need to use the distance formula. We are given two coordinates: the center (red dot) at (1,2) and a blue dot on the circle at (2.5,4). Find the radius by using the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let (1,2) be x₁ and y₁ and let (2.5,4) be x₂ and y₂. Therefore:
[tex]d=\sqrt{(2.5-1)^2+(4-2)^2}\\d=\sqrt{(1.5)^2+2^2}\\d=\sqrt{2.25+4}\\d=\sqrt{6.25}=2.5[/tex]
Thus, r is 2.5.
Plugging these numbers into the equation, we have:
[tex](x-h)^2+(y-k)^2=r^2\\(x-1)^2+(y-2)^2=2.5^2\\(x-1)^2+(y-2)^2=6.25[/tex]
Which box-and-whisker plot best represents the information from the data?
10 12 15 19 22 22 23 26 30 32
One of the factors of 6x3 − 864x is 4 x2 x + 12 x − 8
Your answer is x + 12
Hope this helped!
Answer:
x+12
Step-by-step explanation:
Correct on test
Samantha is making salad for a party at her house. In the salad recipe that she is using, it takes 3/4 of a pound of boneless chicken breasts to make 5 portions of the salad. She uses 1 1/5 pounds of chicken for every 3 cherry tomatoes used, and 9 cherry tomatoes for every 2 bags of spinach used. If Samantha is making enough salad to use 4 bags of spinach, how many portions of salad will she make?
Answer:
48 portions of salad
Step-by-step explanation:
4 bags spinach = 18 cherry tomatoes = 7.2 lb of chicken
7.2/.75 = 9.6 x 5 = 48
3/4a-1/6=2/3a+1/4? Please i need help!!!!
Answer: a=5
Step-by-step explanation:
1/12a=10/24
24a=120
a= 5
Given that the trinomial x^2+ 11x + 28 has a factor of x +4, what is the other factor?
Answer:
the other factor is (x+7)
Step-by-step explanation:
Given x^2+11x+28
factor into
x^2+7x + 4x + 28
=x(x+7) + 4(x+7)
= (x+4)(x+7)
Answer: the other factor is (x+7)
Given only a compass and straightedge, Greeks were able to construct only
regular polygons and circles, thus leaving many constructions impossible to
complete.
A. True
B. False
A regular heptagon (7-sided figure) cannot be constructed with a compass and straightedge.
Two shaded identical rectangular decorative tiles are first placed (one each) at the top and at the base of a door frame for a hobbit's house, as shown in Figure 1. The distance from W to H is 45 inches. Then the same two tiles are rearranged at the top and at the base of the door frame, as shown in Figure 2. The distance from Y to Z is 37 inches. What is the height of the door frame, in inches?
Answer:
41 inches
Step-by-step explanation:
Let the point at the top of the door on the left be x
Wx + xH = 45
Let the point at the top of the door on the right be c
Yc + cZ = 37
We know the door is
xH + plus the width of the tile
The width of the tile is Yc
xH + Yc
On the right door
cZ + the height of the tile
cZ + Wx
Add the two doors together
xH + Yc + cZ + Wx = 2 times the height of the door
Rewriting
xH + Wx + Yc + cZ = 2 times the height of the door
45+ 37 = 2 times the door height
82 = 2 times the door height
Divide by 2
41 = door height
A rectangular sheet of steel is being cut so that the length is four times the width the perimeter of the sheet must be less than 100 inches . Which inequality can be used to find all possible lengths,l.of the steel sheet
Answer:
w>10
length = 40
Step-by-step explanation:
Let
Width=w
Length=4w
Perimeter is less than 100 inches
Perimeter of a rectangle= 2( Length + width)
100 < 2(4w+w)
100 < 8w+2w
100 < 10w
w > 10
Length =4w
=4 × 10
=40 inches
Answer:
5/2l <100
Step-by-step explanation:
PLATO
The period of y = 2tanx is _____.
Answer:
The period of the function y = 2×tan x is π
Step-by-step explanation:
The tangent function, generally has a period of π radians such that a cycle of the tangent function is completed every π radians
Therefore, where a required number of periods is required to be completed within the π radians range, the number is used to multiply the trigonometric function[ parameter.
From the question, we have;
y = 2×tan x
Which gives the multiplier of the variable x as 1
Therefore, the period of the function y = 2×tan x is π.
Which expression is equivalent to (–2)(a + 6)?
A. –2a + 6
B. 2a + 12
C. –2a – 12
D. –2a + 12
The answer is option c.
Helppppp!!!! Thank you
Greetings from Brasil...
In a triangle the sum of the internal angles is 180 °.... Thus,
Ô = 180 - 30
Ô = 60
The desired area is the area of the rectangle triangle, minus the area of the circular sector whose angle 60
A1 = area of the rectangle triangle
TG B = OA/AB
AB = OA / TG B
AB = 6 / TG 30
AB = 6√3
A1 = (AB . OA)/2
A1 = (6√3 . 6)/2
A1 = 18√3A2 = area of the circular sector
(rule of 3)
º area
360 ------------ πR²
60 ------------ X
X = 60πR²/360
X = 6π
So,
A2 = 6πThen the area shaded is:
A = A1 - A2
A = 18√3 - 6π