Answer:
The minimum value of f(x) is greater than the minimum value of g(x).
Step-by-step explanation:
Given
[tex](h_1,k_1) = (3,4)[/tex] --- vertex of f(x)
[tex]g(x) = 4(x - 4)^2 + 3[/tex] --- g(x) equation
Required
Which of the options is true
First, we identify the vertex of g(x)
A quadratic function is represented as:
[tex]g(x) =a(x - h)^2 + k[/tex]
Where:
[tex](h,k) \to[/tex] vertex
So, we have:
[tex](h_2,k_2) = (4,3)[/tex]
[tex]a = 4[/tex]
If [tex]a>0[/tex], then the curve opens upward
From the question, we understand that f(x) also open upward. This means that both functions have a minimum
The minimum is the y (or k) coordinate
So, we have:
[tex](h_1,k_1) = (3,4)[/tex] --- vertex of f(x)
[tex](h_2,k_2) = (4,3)[/tex] --- vertex of g(x)
The minimum of both are:
[tex]Minimum = 4[/tex] ---- f(x)
[tex]Minimum = 3[/tex] ---- g(x)
By comparison:
[tex]4 > 3[/tex]
Hence, f(x) has a greater minimum
Answer:
The minimum value of f(x) is greater than the minimum value of g(x).
Step-by-step explanation:
What is the least common multiple of 50, 41, and 30?
Hello!
[ 50; 41; 30 ] = ?
50 | 2 × 5
5 | 5 => 50 = 2 × 5²
1 |
41 | 41 => 41 = 41
1 |
30 | 2 × 5
3 | 3 => 30 = 2 × 3 × 5
1 |
[ 50; 41; 30 ] = 2 × 3 × 5² × 41 = 2 × 3 × 25 × 41 = 6 × 25 × 41 = 150 × 41 = 6150
Good luck! :)
which statement is correct?
Answer:
Option 3 is correct
tex]\frac{1yd}{36 in}=\frac{7yd}{252 in}[/tex]
Step-by-step explanation:
1.[tex]\frac{1 in}{2.54 cm}=\frac{7 in}{17.68 cm}[/tex]
1 in=2.54 cm
[tex]7 in=2.54\times 7=17.78 cm[/tex]
[tex]\frac{1 in}{2.54 cm}=\frac{1 in}{1 in}=1[/tex]
[tex]\frac{1 in}{2.54 cm}\neq \frac{7 in}{17.68 cm}[/tex]
Hence, it is not correct.
2.[tex]\frac{1 ft}{12 in}=\frac{7ft}{74 in}[/tex]
1 foot=1 2in
[tex] 7ft=7\times 12=84 foot[/tex]
[tex]\frac{1 ft}{12 in}=1[/tex]
[tex]\frac{7ft}{74 in}\neq 1[/tex]
[tex]\implies \frac{1 ft}{12 in}\neq \frac{7ft}{74 in}[/tex]
Hence, it is not correct.
3.[tex]\frac{1yd}{36 in}=\frac{7yd}{252 in}[/tex]
1 yd=36 in
[tex]\frac{1yd}{36 in}=\frac{36}{36}=1[/tex]
[tex]7yd=7\times 36=252 in[/tex]
[tex]\frac{7yd}{252 in}=\frac{252 in}{252 in}=1[/tex]
[tex]\implies \frac{1yd}{36 in}=\frac{7yd}{252 in}[/tex]
Hence, it is correct.
4.[tex]\frac{1 m}{3.28ft}=\frac{7m}{22.86ft}[/tex]
1 m=3.28 ft
[tex]\frac{1 m}{3.28ft}=\frac{3.28}{3.28}=1[/tex]
[tex]7m=7\times 3.28=22.96 ft[/tex]
[tex]\frac{7m}{22.86ft}\neq 1[/tex]
[tex]\frac{1 m}{3.28ft}\neq \frac{7m}{22.86ft}[/tex]
Hence, option is not correct.
Polygon ABCD is rotated 90º counterclockwise about the origin to create polygon A′B′C′D′. Match each set of coordinates to the vertices of polygon A′B′C′D′.
Answer:.
Step-by-step explanation:
find the area of the kite. please help thank you
Answer:
1/2×d1×d2
=1/2× (4+4)(6+3)
=36
Help and explain ( solve using the substitution method )
Answer:
you are posting unvisibile photo pls fix it
Step-by-step explanation:
find the missing side. round to the nearest tenth.
24) HELP ITS DUE IN THE MORNING
A) 14.2
C) 13.8
B) 9.2
D) 15.7
25.
A)37.6
B)30.8
C)45.1
D)5.5
Answer:
24) x = 9.2
25) x = 30.8
Step-by-step explanation:
Given
See attachment for triangles
Solving (24)
To solve for x, we make use of cosine formula
i.e.
cos(40) = adjacent ÷ hypotenuse
So, we have:
cos(40) = x ÷ 12
Multiply both sides by 12
12 cos(40) = x
12 * 0.7660 = x
x = 9.2
Solving (25)
To solve for x, we make use of sine formula
i.e.
sin(25) = opposite ÷ hypotenuse
So, we have:
sin(25) = 13 ÷ x
Multiply both sides by
x sin(25) = 13
Divide by sin(25)
x = 13 ÷ sin(25)
Using a calculator
x = 30.8
What is the height of the parallelogram?
+
A=56 m2
8 m
Answer:
7 m
Step-by-step explanation:
A = base x height
56 = 8 x h
56/8 = h
h = 7
Let A = {a, b, c}, B = {b, c, d}, and C = {b, c, e}. (a) Find A ∪ (B ∩ C), (A ∪ B) ∩ C, and (A ∪ B) ∩ (A ∪ C). (Enter your answer in set-roster notation.)
Answer:
(B n C) = {b,c}
A = {a,b,c}
B= {b,c,d}
C= {b,c,e}
A u (B n C) = {a,b,c}
(A u B) = {a,b,c,d}
(A u B) n C = {b,c}
(A u C) = {a,b,c,e}
(A u B) n (A u C) = {a,b,c}
What is the missing reason for the 3rd
step in the proof below?
Answer:
Multiplication property of the equality
9. Consider the line y = 4x+9. If a second line is perpendicular to this one, what is its slope? please show your work, i will mark brainliest!
Answer:
Slope of the line perpendicular to the given line = [tex]- \frac{1}{4}[/tex]
Step-by-step explanation:
If two are lines are perpendicular to each other,
the product of their slopes = - 1 .
That is ,
[tex]m_ 1 \times m_2 = -1[/tex]
Slope of the given line :
[tex]m_ 1 = 4[/tex]
Hence slope of the line perpendicular to it :
[tex]4 \times m_ 2 = - 1 \\\\\frac{4}{4} \times m_2 = - \frac{1}{4} \\\\1 \times m_2 = - \frac{1}{4}\\\\m_ 2 = \frac{-1}{4}[/tex]
The slope of the line perpendicular to the equation y = 4x + 9 is m = -1/4
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = 4x + 9 be equation (1)
The equation is of the form y = mx + b where m is the slope and b is the y-intercept
Substituting the values in the equation , we get
Slope m = 4
Now , the second line is perpendicular to the line A , the product of slopes of the lines will be -1
So , m₁ x m₂ = -1
4 x m₂ = -1
Divide by 4 on both sides of the equation , we get
m₂ = -1/4
Therefore the value of m₂ is -1/4
Hence , the slope of the line is m₂ = -1/4
To learn more about equation of line click :
https://brainly.com/question/14200719
#SPJ2
Find two positive numbers so that twice their sum equals their product and one number is 10 times the other number. Enter the smaller number first.
Answer:
Step-by-step explanation:
We'll call the 2 numbers x and y. Starting with the last part of that first sentence "one number is 10 times the other number" can be written, in algebraic form:
y = 10x
Now on to the first statement about the numbers: "twice their sum" is 2(x + y) and "equals their product" is = xy. Putting that all together:
2(x + y) = xy and we know that y = 10x so
2(x + 10x) = x(10x) and
[tex]2(11x)=10x^2[/tex] and
[tex]10x^2-22x=0[/tex] and
x(10x - 22) = 0 so
x = 0 or 10x - 22 = 0 which makes
x equal to [tex]\frac{22}{10}=2.2[/tex]
So x = 2.2 and y = 22.
please help me please help me
Answer:
the answer is 1
Step-by-step explanation:
(√4 / √6) + (√6 / √4)
(2 / 2√3) + (2√3 / 2)
√3 / √3
= 1
The ages of Sohail, Afzal and Bilal are 17, 16 and 12 respectively. If the age of Aslam also included the average of the ages is increased by 5. What is the age of Aslam?
Sohail=17
afzal=16
Bilal=12
Aslam=16+5=21
f () = 6x + 4. Find the inverse of f(x).
Answer:
F-1 (x)=1/6x-2/3
Step-by-step explanation:
Use substitution, Interchange the variables, Swap the sides, movthe constant to the right, Divide both sides, Use substitution, and youll find your solution. By the way the -1 is in scientific notation!
help please what is the median
Answer:
The median is 9
Step-by-step explanation:
The median is the number in the middle. The middle of this is 8 and 10, so you plus them and divide by to 2, then it gives 9, so the median is 9.
What is the hardest math problem ever?
Step-by-step explanation:
this is the hardest I think
step below. Question 1 Hexagon AGHBGHCGHD GHEGHFGH is a reflected image of hexagon ABCDEF. The midpoints of the sides of hexagon ABCDEF are also shown. Drag the line of reflection, Għ until the image coincides with the preimage. At this location, if the preimage flips about the line of reflection, it will flip onto itself. In how many different positions can you place GHso the image reflects onto the preimage in this manner? Describe the different positions. Be sure to pass the line of reflection through both vertices and midpoints before answering.
Answer:
Hexagon AGHBGHCGHDGHEGHFGH coincides with hexagon ABCDEF when GH passes through the midpoints of opposite sides; that is, it is a perpendicular bisector of the two sides. HexagonAGHBGHCGHDGHEGHFGH also coincides with hexagon ABCDEF when the line of reflection joins a pair of vertices opposite one another on the hexagon. There are three perpendicular bisectors and three pairs of opposite vertices. In all, there are six lines of reflection that will map the hexagon back onto itself.
Step-by-step explanation:
(c) The perimeter of a rectangle with length 2r cm and width 5 m is 14 m.
Triangle MNO is isosceles. Find the value of y and the measure of Angle O. Y=______
Angle O=_______degrees
Answer:
y = -5
o = 35 degrees
Step-by-step explanation:
If you replace y with -5, the statement 7y = 4y - 15 is correct. You get -35 = -35. Hope this helped!
17.27. How many Social Security numbers (see Exercise 8.12) have their nine digits in strictly increasing order
Answer:
"10 possibilities" is the appropriate response.
Step-by-step explanation:
The numbers will be:
⇒ [tex]123 \ 456 \ 789[/tex]
Now anyway we commence with right and afterwards remove nine from eight and seeing as maintain the sequence growing.
then,
[tex]012345678[/tex][tex]012345679[/tex][tex]012345689[/tex][tex]012345789[/tex][tex]012346789[/tex][tex]012356789[/tex][tex]012456789[/tex][tex]013456789[/tex][tex]023456789[/tex]Thus, the above is the correct answer.
Neeeeed helpppppppppp
Answer:
The answer is x = -3.
Step-by-step explanation:
To solve for (x), start by realizing that line segment IJ and line segment JK sum up to line segment IK, which equals 5. These line segments can then be turned into an equation, and the equation will look like [tex]7+x+2x+7=5[/tex].
Next, begin to solve the equation by combining like terms, which will look like [tex]3x+14=5[/tex]. Then, subtract 14 from both sides of the equation, which will look like [tex]3x=-9[/tex], and divide both sides by 3 and simplify, which will look like [tex]x=-3[/tex]. The final answer is x = -3.
What degree of rotation about the origin will cause the triangle below to map
onto itself?
A.90
B.270
C.360
D.180
A lighthouse casts a 128-ft shadow. A nearby lamppost that measures 5
feet casts an 8-foot shadow. What is the height of the light house, rounded
to the nearest foot? *
Answer: 80 feet
Step-by-step explanation:
We can write these as fractions and do cross multiplication with the numerator being the height of the object while the denominator being the length of the shadow:
5 * 128 = 8x
640 = 8x
80 = x
Thus, the height of the lighthouse is 80 feet tall.
If you vertically compress the absolute value parent function, (x) = |X|, by a
factor of 4, what is the equation of the new function?
O A. g(x) = |4x|
O B. g(x) = 1/4 |x|
O C. g(x) = 4|x|
O D. g(x) = |x-4|
pls mark me as brainlist
thanks a lot
Maths assignment
a^4-16
Answer:
[tex]a^4-16[/tex]
[tex]\left(a^2\right)^2-4^2[/tex]
[tex]\left(a^2+4\right)\left(a^2-4\right)[/tex]
[tex]=\left(a^2+4\right)\left(a+2\right)\left(a-2\right)[/tex]
------------------------
Hope it helps...
Have a great day!!
Step-by-step explanation:
The difference of squares: a² - b² factors to (a - b) (a + b)
Let x⁴ = (x²)²
Let 16 = 4²
Now by difference of squares x⁴ - 16 factors as (x² - 4)(x² + 4)
The front factor, (x² - 4), can factor by difference of squares again as (x - 2)(x + 2)
Please answer this, I need help fast
B
Step-by-step explanation:
If you're using a Casio calculator you can just change the mode to table mode. Put the equations as they are,decide the value of the X axis you want to start at and where you want to end. The step you can use 1 if you want. Press = button. You'll have the co-ordinates. Plot the co-ordinates of each equation and see which one gives a straight line graph. I started at -4 and ended at 5 and I used step 1
The relationship between miles and kilometers is shown in the table below.
Miles
Kilometers
18.2
29.12
29.5
47.20
34.1
54.56
52.8
84.48
How many miles are in 19.08 kilometers?
11.925
17.48
20.68
30.528
Answer:
Step-by-step explanation ithink your are correct because that there 19.08+18.3=11.925
Answer:
11.925
Step-by-step explanation:
Find the surface area or volume of each rectangular prism. (Show work pls)
Answer:
496 in.²
346 mm²
880 in.²
168 cm³
960 m³
420 yd³
Step-by-step explanation:
SA = 2(wl + hl + hw)
SA = 2 · (8 · 16 + 5 · 16 + 5 · 8)
SA = 496
SA = 2(wl + hl + hw)
SA = 2 · (5 · 13 + 6 · 13 + 6 · 5)
SA = 346
SA = 2(wl + hl + hw)
SA = 2 · (4 · 20 + 15 · 20 + 15 · 4)
SA = 880
V = whl
V = 4 · 7 · 6
V = 168
V = whl
V = 10 · 8 · 12
V = 960
V = whl
V = 14 · 3 · 10
V = 420
Please help me with this one!!
Answer:
[tex]21 in^{2}[/tex]
Step-by-step explanation:
The square in the middle has a length and width of 3, so multiply. 9.
All of the triangles have a base of 3 and a height of 2. The area equation for triangles is
[tex]A=bh\frac{1}{2}[/tex]
So base*height is 6. Divide that by 2 or multiply by 1/2.
You get 3. There are 4 triangles, so multiply that by 4. 12.
Add 12 and 9 together, and you get:
[tex]21 in^{2}[/tex]
I hope this helps!
Can someone help me with this math homework please!
Answer:
1. [tex]x=2[/tex]
2. Simplify by combining like terms
3. [tex]x=1[/tex]
4. [tex]k=0.5[/tex]
5. [tex]y=3[/tex]
Step-by-step explanation:
1. [tex]2.5(6x-4)=10+4(1.5+0.5x)[/tex]
Distribute within the parenthesis
[tex]15x-10=10+6+2x[/tex]
Combine like terms
[tex]15x-10=16+2x[/tex]
Isolate the variable expression by using the addition/subtraction properties of equality
[tex]13x=26[/tex]
Isolate the variable by using the division/multiplication properties of equality
[tex]x=2[/tex]
2. Like terms are always combined as soon as possible but never before the distributive property is applied.
3. You can find the solution by comparing the tables.
4. [tex]6k+10.5=3k+12[/tex]
Apply the addition/subtraction properties of equality
[tex]3k=1.5[/tex]
Apply the division/multiplication properties of inequality
[tex]k=0.5[/tex]
5. [tex]y+3=-y+9[/tex]
Addition/subtraction properties
[tex]2y=6[/tex]
Division/Multiplication properties
[tex]y=3[/tex]