The functions f(x) and h(x) have an axis of symmetry of x = 2 and a maximum
How to determine the function?The functions are given as:
f(x) = -x² + 4x + 2g(x) = -(x + 2)² - 5h(x) = -2(x − 1)(x − 3)A quadratic function can be represented as:
y = ax² + bx + c
y = a(x - h)² + k
In both cases, when a < 0; the function has a maximum.
This means that all three functions have a maximum.
Next, we determine the axis of symmetry:
In y = ax² + bx + c, the axis of symmetry is x = -b/2aIn y = a(x - h)² + k, the axis of symmetry is x = hUsing the above forms, we have:
f(x) = -x² + 4x + 2
Axis of symmetry, x = -4/(2 * -1)
x = 2
g(x) = -(x + 2)² - 5
Axis of symmetry, x = -2
h(x) = -2(x − 1)(x − 3)
Expand
h(x) = -2x² - 8x + 8
Axis of symmetry, x = -8/(2 * -2)
x = 2
This means that f(x) and h(x) have an axis of symmetry of x = 2
Hence, the functions f(x) and h(x) have an axis of symmetry of x = 2 and a maximum
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A rectangular garden has an area of 144 ft². If the base is 8 ft long, what is the height?
18 ft
36 ft
64 ft
72 ft
Answer:
The Answer is 18
Hope this helps! :)
Step-by-step explanation:
A triangle has sides of lengths 16,14 and 50 .is the triangle right angle triangle?
Answer:
no
Step-by-step explanation:
using the converse of Pythagoras' identity
If the square on the longest side is equal to the sum of the squares of the other 2 sides, then the triangle is right.
longest side = 50 ⇒ 50² = 2500
16² + 14² = 256 + 196 = 452
since 452 ≠ 2500 then the triangle is not right
A triangle has sides of lengths 16,14 and 50. Is the triangle right angle triangle?
❒ Explanation -:We will solve this question using Pythagoras theorem.
We know,
[tex] \small \boxed{\rm{ c² = a² + b²}}[/tex]
[tex] \small\rm{Where,} [/tex] [tex]\small\sf{ c > a \: and \: c > b}[/tex]
[tex] \small\sf{ 50² = 16² + 14²}[/tex]
[tex]2500 = 256+ 196[/tex]
[tex]2500≠452[/tex]
[tex] \small\bf{ c² ≠ a² + b²}[/tex]
Hence, the triangle is not a right-angled triangle.
NEED HELP ASAP
Question A.) k=5
Question B.) ????
Answer:
b) [tex]f^{-1}(x) = \frac{4x+5}{3}[/tex]
Step-by-step explanation:
b) To find the inverse function, switch the [tex]x[/tex] and [tex]y[/tex] variables and solve for [tex]y[/tex]:
[tex]f(x) = \frac{3x-5}{4}\\y = \frac{3x-5}{4}\\x = \frac{3y-5}{4}\\4x = 3y-5\\4x+5 = 3y\\\frac{4x+5}{3} = y\\f^{-1}(x) = \frac{4x+5}{3}[/tex]
Verify Answer:
[tex]f(1) = \frac{3(1)-5}{4} = -0.5\\f^{-1}(-0.5) = \frac{4(-0.5)+5}{3} = 1[/tex]
Please help with this maze
Answer:
go down then go right
Step-by-step explanation:
What is the Parent Function?
What Are The Transformations?
Answer:
Parent function:
[tex]x^2+y^2=r^2[/tex]
General equation:
[tex](x-h)^2+(x-k)^2=r^2[/tex]
Transformations:
Its a circle with a center of (100,60) and a radius of 15
Name the property used in the equation 1=6n. Then find the value of n.
Answer:
1=6
Step-by-step explanation:
Divide both sides of the equation by the same term
1=6
A student gives the answer to a probability problem as 6/5. tell why this answer must be incorrect.
Answer:
Probability of an event must be from 0 to 1.
Here,6/5 is more than 1 i.e. 1.2.
Hence,the answer is incorrect.
Which relations are functions?
Choose all answers that are correct:
Answer:
A. B and D are functions
Step-by-step explanation:
Functions are either one-to-one or many-to one (x-value --> y value)
C is not a function because -3 (x) maps to 1 and also to 0 (y).
How many sides does a regular n-gon have if the measure of one interior angle is 165?
The supplement of each interior angle has measure
180° - 165° = 15°
and so
n = 360°/15° = 24
since the exterior angles add up to 360° and are all congruent.
Does anybody know this?Find the surface area of the triangular prism the ares of the base is 7.75yd
Answer:
10.308
Sure hope this helps you
An ice-cream from a restaurant costs $3 originally. The price is reduced to $2 one weekend. What is the percent change?
please please please help help help !!
Answer:
The axis of Symmetry divides a line into two equal halves.
Step-by-step explanation
An easy relation to get this value without plotting a graph is x = –b/2a
Where
a = coefficient of x²
b = coefficient of x
From the Question, We need a symmetry of value –½
The only Option that'll give this value is OPTION D
2x – y = 5 – 2x²
Since its a line, Don't forget to make "y" subject before doing any operation.
y = 2x² + 2x – 5
a = 2
b= 2
x = –(2)/2(2)
= –2/4
= –½
nd Distances in the Coordinate Plane
What is the distance between the points (4, 7) and (4,-5)?
0 units
O2 units
O4 units
12 units
Answer:
12 units
Step-by-step explanation:
(4, 7) and (4, -5)
7-(-5)=12
4-4=0
A person can read 24 pages of a book in 1/3 of an hour. What is this person's reading rate in pages per hour?
48
12
72
8
Answer:
72
Step-by-step explanation:
If he reads 24 pages in 1/3 of an hour, he reads 3 times as many pages in 1 hour.
3 × 24 pages = 72 pages
Answer: 72
Nandlal bought 20 dozen notebooks at Rs.156 per dozen.He sold 8 dozens of them at 10% gain and the remaining 12 dozens at 20% gain.What is his gain percent on the whole transaction?
Answer:
[tex]8(156 \times 1.1) + 12(156 \times 1.2) [/tex]
What is the area of this figure
Answer:
105 units²
Step-by-step explanation:
Area of triangle = ½bh
b = 11 + 4
b = 15
A = 2(½15(7))
2 and ½ cancel
A = 15(7)
A = 105 units²
Find the slope from the graph.
Answer:
The answer is -3/2.
Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. what value of x satisfies this equation? round your answer to the nearest hundredth. the value of x is .
The values of x in f(x) = 3|x - 2| + 6 when f(x) = 18 are 6 and -2
How to determine the value of x?The function is given as:
f(x) = 3|x - 2| + 6
The value of f(x) is
f(x) = 18
So, we have:
3|x - 2| + 6 = 18
Subtract 6 from both sides
3|x - 2| = 12
Divide both sides by 3
|x - 2| = 4
Remove the absolute bracket
x - 2 = 4 or x - 2 = -4
Add 2 to both sides
x = 6 or x = -2
Hence, the values of x are 6 and -2
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Connor got to the beach at 9:58 A.M. He hunted for seashells, played in the waves, ate lunch, watched the birds dive in the water, and built a sand castle. He left the beach at 5:26 P.M. How long was he at the beach?
I WILL GIVE BRAINLIEST FOR CORRECT ANSWER
The graph of the system of equations y= 2x+3 and y= x+5 is shown on the coordinate plane (image included). What is the solution to the system of equations?
Answer:
A
Step-by-step explanation:
The answer is A because the point intercepts at (2,7), and answer A has the points (2,7) in it's answer.
What will be the new function g(c) if f(x) = 2^x is translated 2 units down and
3 units left?
Answer:
The new function is
[tex]g(x) = {2}^{x + 3} - 2[/tex]
What is 3-eighths times 4 and 3-sixths times 4?
You will be marked Brainliest if you answer this question correctly!
Please help ASAP
Answer:
As a fraction it would be 4.5
Step-by-step explanation:
3/4 × 6 = 92 = 4 12 = 4.5
Someone please help me before I frl cry
Answer:
Equation: 4x = 128
[tex]m\angle 1 = 84\degree[/tex]
[tex]m\angle 2 = 96\degree[/tex]
Step-by-step explanation:
[tex]m\angle 1+ m\angle 2 =180\degree[/tex] (Linear pair angles)-> (x + 52)° + (3x)° = 180°-> (4x + 52)° = 180° -> 4x + 52 = 180-> 4x = 180 - 52-> 4x = 128 ( This is the required equation)-> x = 128/4-> x = 32[tex]m\angle 1 = (32+52)\degree = 84\degree[/tex][tex]m\angle 2 = (3*32)\degree = 96\degree[/tex]Use the stem-and-leaf plot below to match each term with the correct value. (Round to the nearest whole number.)
Answer:
Step-by-step explanation:
16, 18, 23, 25, 26, 34, 37, 37, 40, 41, 46
( 16 + 18 + 23 + 25 + 26 + 34 + 37 + 37 + 40 + 41 + 46 ) ÷ 11 = 31.181818...
mean ≈ 31
median = 34
mode = 37
Will mark brainlist to whoever answers first
Answer:
the answer is (6,5) pls mark brainest
Answer:
The answer is D.) (6,5)
Step-by-step explanation:
When the first point goes right, you add it, and when the second point goes down, you subtract it
When a figure appears to have depth as you look at it, it is called _____________.
A. perspective
B. solid
C. length
D. net
Answer:
the answer would b B solid
Step-by-step explanation:
because the figure appears to have depth as you look at it so it is solid.
a lawn sprinkler waters a lawn in a circle as shown
Part A
I'm assuming you want the area of a circle with radius 17 yards.
We'll use the formula below
A = pi*r^2
A = (22/7)*17^2
A = (22*17^2)/7
A = 6358/7
A = 908 2/7
The sprinkler covers an area of about 908 2/7 square yards.
You'll type 908 in the left-most box
Then for the other two boxes, you'll have 2 up top and 7 down below to represent the fraction 2/7
The number 908 2/7 is a mixed number.
=======================================================
Part B
You mentioned that the radius reduces to 11 yards here. We'll use the same formula as above and pi = 22/7 approximately
A = pi*r^2
A = (22/7)*11^2
A = (22*11^2)/7
A = 2662/7
A = 380 2/7
The sprinklers can water an area of about 380 2/7 square yards.
This value is also a mixed number
380 is the value in the left most box (it's the whole part)
The other two boxes are filled out the same exact way as the previous part above.
PLEASE HELP!!!
Which of the following is the Best Buy?
1 L for $1.68
0.5 L for $1.29
2 L for $3.40
3 L for $5.07
Answer:
it's 1 L
Step-by-step explanation:
it's pretty easy just do some multiplication
I need help with this question asap please
does anyone know what 3 x (8+2) x 5 is? i really need it for homework due tomorrow thank you!