Answers
Answer:
option E, C
Step-by-step explanation:
From the graph we will find the equation of g(x).
g(x) is a parabola with vertex ( h, k) = ( 0, 9)
Standard equation of parabola is , y = a (x - h)² + k
y = a (x - 0)² + 9
y = ax² + 9 ---------- ( 1 )
Now we have to find a .
To find a we will take another point through which the parabola passes .
Let it be ( 3, 0).
Substitute ( 3 , 0 ) in ( 1 ) => 0 = a (3 )² + 9
=> - 9 = 9a
=> a = - 1
Substitute a = - 1 in ( 1 ) => y = -1 x² + 9
=> y = - x² + 9
Therefore , g(x) = -x² + 9
Now using the table we will find h(x)
[tex]h(x) = 4^{x}[/tex]
So g(x) = -x² + 9 and [tex]h(x) = 4^{x}[/tex]
Option A : both function increases on ( 0, ∞ ) - False
[tex]\lim_{x \to \infty} g(x) = \lim_{x \to \infty} -x^2 + 9[/tex]
[tex]= - \lim_{x\to \infty} x^2 + \lim_{x \to \infty} 9\\\\= - \infty + 9\\\\=- \infty[/tex]
g(x) decreases on ( 0 , ∞)
[tex]\lim_{x\to \infty} h(x) = \lim_{x \to \infty} 4^{x}[/tex]
[tex]= \infty[/tex]
h(x) increases on ( 0, ∞)
option B : g(x) increasing on (- ∞, 0) - False
g(x) = -x² + 9
g( -2 ) = - (-2)² + 9
= - 4 + 9 = 5
g ( -5) = - ( -5)² + 9
= - 25 + 9 = - 14
As the value of x moves towards - ∞ , g(x) moves towards - ∞
Therefore g(x) decreases on (- ∞, 0)
Option C: y intercept of g(x) is greater than h(x) - True
y intercept of g(x) = ( 0 , 9 )
y intercept of h(x) = ( 0 , 1 )
Option D : h(x) is a linear function - False
Option E : g(2) < h(2) - True
g(x) = -x² + 9
g(2) = -(2)² + 9 = - 4 + 9 = 5
h(x) = 4ˣ
h(2) = 4² = 16
Related Questions
wich is a solution to (x-3)(x+9)=-27?
Answers
Answer:
=0=−6
Step-by-step explanation:
5. What is x in the diagram?
Answers
Answer:
B
Step-by-step explanation:
we rule out all other 3 by the simple fact that the side is 9
Can someone tell me if this is the correct choice?
Answers
Answer:
Step-by-step explanation:
It's not the correct choice. If a root is given, that is the same thing as the solution. We go backwards from a solution to a factor, which is what you need to do here.
If x = 2i is the solution, then the factor is
(x - 2i). Likewise, with the other one.
If x = 3i is the solution, then the factor is
(x - 3i). The leading coefficient of 1 just sits outside the first set of parenthesis, and because multiplication is commutative, it doesn't matter which set you put first. Thus, the one you want looks like this:
f(x) = (x - 2i)(x - 3i) or
f(x) = (x - 3i)(x - 2i).
Jada asked some students at her school how many hours they spent watching television last week, to the nearest hour. Here are a box plot and a histogram for the data she collected.
If anyone trolls imma be very sad :(
Answers
Answer:
100
Step-by-step explanation:
Based on the histogram given :
The vertical axis gives the number of student in the school :
For the range :
0 - 5 = 40
5 - 10 = 30
10 - 15 = 20
15 - 20 = 5
20 - 25 = 3
25 - 30 = 2
Taking the sum :
(40 + 30 + 20 + 5 + 3 + 2) = 100
A steamer travels 36 km upstream and 32 km downstream in 6.5 hours. The same steamer travels 4 km upstream and 40 km downstream in 180 minutes. Determine the steamer's speed in still water and the stream's speed.
Answers
Answer:
The streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h
Step-by-step explanation:
Let v = streamer's speed in still water and v' = stream's speed. His speed upstream is V = v + v' and his speed downstream is V' = v - v'.
Since he travels 36 km upstream, the time taken is t = 36/V = 36/(v + v').
he travels 32 km downstream, the time taken is t' = 32/V' = 32/(v - v')
The total time is thus t + t' = 36/(v + v') + 32/(v - v')
Since the whole trip takes 6,5 hours,
36/(v + v') + 32/(v - v') = 6.5 (1)
Multiplying each term by (v + v')(v - v'), we have
(v + v')(v - v')36/(v + v') + (v + v')(v - v')32/(v - v') = 6.5(v + v')(v - v') (1)
(v - v')36 + (v + v')32 = 6.5(v + v')(v - v') (1)
36v - 36v' + 32v + 32v' = 6.5(v² + v'²)
68v - 4v' = 6.5(v² + v'²) (2)
Also he travels 4 km upstream, the time taken is t" = 4/V = 4/(v + v').
he travels 40 km downstream, the time taken is t'" = 40/V' = 40/(v - v')
The total time is thus t" + t'" = 4/(v + v') + 40/(v - v')
Since the whole trip takes 180 minutes = 3 hours,
4/(v + v') + 40/(v - v') = 3 (3)
Multiplying each term by (v + v')(v - v'), we have
(v + v')(v - v')4/(v + v') + (v + v')(v - v')40/(v - v') = 3(v + v')(v - v') (1)
(v - v')4 + (v + v')40 = 3(v + v')(v - v') (1)
4v - 4v' + 40v + 40v' = 3(v² + v'²)
44v - 36v' = 3(v² + v'²) (4)
Dividing (2) by (4), we have
(68v - 4v')/(44v - 36v') = 6.5(v² + v'²)/3(v² + v'²)
(68v - 4v')/(44v - 36v') = 6.5/3
3(68v - 4v') = 6.5(44v - 36v')
204v - 12v' = 286v - 234v'
204v - 286v = 12v' - 234v'
-82v = -222v'
v = -222v'/82
v = 111v'/41
Substituting v into (2), we have
68v - 4v' = 6.5(v² + v'²)
68(111v'/41) - 4v' = 6.5[(111v'/41)² + v'²]
[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²
[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²
[7548/41 - 4]v' = 6.5[12321/1681 + 1]v'²
[(7548 - 164)/41]v' = 6.5[(12321 + 1681)/1681]v'²
[7384/41]v' = 6.5[14002/1681]v'²
[7384/41]v' = [91013/1681]v'²
[91013/1681]v'² - [7384/41]v' = 0
([91013/1681]v' - [7384/41])v' = 0
⇒ v' = 0 or ([91013/1681]v' - 7384/41) = 0
⇒ v' = 0 or [91013/1681]v' - 7384/41) = 0
⇒ v' = 0 or v' = 7384/41 × 16841/91013
⇒ v' = 0 or v' = 180.097 × 0.185
⇒ v' = 0 or v' = 33.33 km/h
Since v' ≠ 0, v' = 33.33 km/h
Substituting v' into v = 111v'/41 = 111(33.33 km/h)/41 = 3699.63 km/h ÷ 41 = 90.23 km/h
So, the streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h
Find the length of the missing
Answers
Answer:
12
Step-by-step explanation:
using pythagoras theorem
here 15 is hypotenuse since it is opposite 0f 90 degree
9 and x are the other smaller sides of a triangle
according to pythagoras thorem the sum of square of two smaller sides of a triangle is equal to the square of hypotenuse. So,
9^2 + x^2 = 15^2
81 + x^2 = 225
x^2 = 225 - 81
x^2 = 144
x = [tex]\sqrt{144[/tex]
x = 12
Continue the number pattern for the next three terms 1,8,27.....,........,..........
Answers
Answer:
64, 125, 216
Step-by-step explanation:
1, 8, and 27 are perfect cubes, i.e., each is the cube of an integer, and they're perfect cubes of consecutive positive integers:
1 = 1³ = 1×1×1
8 = 2³
27 = 3³
Therefore, the next three-term numbers of the given sequence are:
64 = 4³
125 = 5³ and
216 = 6³
Therefore, the final sequence will look like this:
1, 8, 27, 64, 125, 216
Factorise a² - b²
.......
Answers
Regards,
ArmyCee:)
[tex]\longrightarrow{\green{ (a + b)(a - b) }}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
[tex] ={a}^{2} - {b}^{2} [/tex]
[tex] = (a + b)(a - b)[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
explain by step by step pls :( if u type something wrong ill report u
Answers
Answer:
∠ C = ∠BCD = 30°
Step-by-step explanation:
∠ EDF = ∠GFC = 110° [ corresponding angles ]
Now consider triangle BCF
∠FBC + ∠ABC = 180° [ straight line angle ]
∠FBC + 100° = 180°
∠FBC = 180 - 100 = 80°
∠BFC + ∠GFC = 180° [ straight line angle ]
∠BFC + 110° = 180°
∠BFC = 180 - 110 = 70°
Sum of angles of triangle is 180°
Therefore , in triangle BCF
That is ,
∠F + ∠B + ∠ C = 180°
70° + 80° + ∠C = 180°
∠C = 180 - 150 = 30°
Can someone help me?It's urgent and thank you!
Answers
Answer:
y = square root x2 - 5
Step-by-step explanation:
y=[tex]\sqrt{x} -5[/tex]
(the top option)
Tell whether the equation Y=Y true or false
Answers
Answer:
its true trust biggie on this one fam
Step-by-step explanation:
its true broski
2+2-2-5+5+6+4+8-2+47+28
Answers
Answer:
93
Step-by-step explanation:
So, you basically basic math it, or calculator.
a box contains 6 dimes, 8 nickels, 12 pennies, and 3 quarters. what is the probability that a coin drawn at random is not a dime
Answers
Add all the coins to get total coins:
6 + 8 + 12 + 3 = 29 total coins
Subtract dimes to find total of the coins that are not dimes:
29 -6 = 23
Probability of not picking a dime is the number of coins that aren’t dimes over total coins:
23/29
write an equation for the sentence: the sum of six and twice a number is equal to sixteen minus the number.
URGENT! ONLY HAVE 5 MINUTES!
Answers
Answer:
6+2x=16-x.
Step-by-step explanation:
X will represent the missing number. Sum means 6, twice that number means multiply it by two, equal represents =, minus represents this, therefor the equation 6+2x=16-x represents the correct answer.
A scale model of a sculpture has a scale of 2:53
The height of the model is 20cm.
Find the height of the actual sculpture.
Give your answer in m.
Answers
Answer:
ok so we can simpley this is 1:106
so we multiply
20*106=2120 this is cm so we make it meters...
21.2meters!!!
Hope This Helps!!!
Translate this word problem as a system of equations and then solve using substitution.
The sum of two numbers is 84. One number is three times the other. Find the numbers.
Put your answer in this form:
The numbers are 3 and 6.
Answers
Answer:
The numbers are 21 and 63
Step-by-step explanation:
let one number be x
let the other number be 3 times the other = 3x
3x + x = 84
4x = 84
x = 21
3x = 3×21 = 63
Help please guys if you don’t mind
Answers
Answer:
first
2/5m + 8/5
second
22/5
third
11
If R(x) = 2 – 3x – 1, find R(-2)
a. -3
b. 9
c. -9
d. -11
PLEASE HELP
Answers
Answer:
C
Step-by-step explanation:
C
The output of [tex]R(x) = x^{2} - 3x- 1[/tex] when x = -2 is 9.
What is PEMDAS?PEMDAS exists as an acronym for the terms parenthesis, exponents, multiplication, division, addition, and subtraction.
To estimate the value of R(-2)
Substitute the value of x = -2, then
[tex]R(-2) = (-2)^{2} - 3(-2) - 1[/tex]
By using the PEMDAS order of operations
Calculate exponents, [tex](-2)^2 = 4[/tex]
= 4 - 3(-2) - 1
Multiply and divide (left to right), 3(-2) = -6
= 4 - (-6) - 1
Add and subtract (left to right),
4 - (-6) - 1 = 9
Therefore, the value of R(-2) = 9.
To learn more about the value of a function refer to:
https://brainly.com/question/15712340
#SPJ2
the length of a pond is 1700 CM breadth is 14m and height is 1000 CM if a point is half filled calculate the volume of a water in the pond
Answers
Answer:
1190 m^3
Step-by-step explanation:
l = 1700 cm = 17 m
b = 14 m
h = 1000 cm = 10 m
Total volume = l × b × h
= 17 × 14× 10
= 2380 m^3
since it is half filled ,
Volume is half , so,
volume of water in pond = 2380 ÷ 2
= 1190 m^3
Triangle HIJ is similar to triangle KLM. Find the measure of side MK. Round your answer to the nearest tenth.
Answers
Answer:
[tex]MK\approx 87.7[/tex]
Step-by-step explanation:
By definition, similar polygons have corresponding sides in a constant proportion. Therefore, we can set up the following proportion (ratio of corresponding sides) to solve for [tex]MK[/tex]:
[tex]\frac{20}{13}=\frac{MK}{57},\\MK=\frac{57\cdot 20}{13}\approx \boxed{87.7}[/tex]
Answer:
87.7
Step-by-step explanation:
Like stated previously similar triangle have side lengths with common ratios
*Create a proportionality to solve for MK*
57/13 = MK / 20
Now solve for MK
Multiply each side by 20
57/13 * 20 = 87.7 ( rounded )
MK/20 * 20 = MK
We're left with MK = 87.7
Helppp and explain pleaseeeeee!!!!!!
Answers
Kayleigh has $4500 in a savings account at the bank that earns 0.8% interest per year. How much
interest will she earn in 3 years?
Answers
Answer:
Kayleigh will have a total of $4608.
Step-by-step explanation:
First, you use the formula, I=PRT (Interest=Principal, Rate, Time), then you distribute the numbers: (I=4500x0.8%x3) when you multiply them all, you get $108, then you lastly add 108 to 4500, and you get your final answer of $4608.
Kayleigh will earn $108 in interest over a period of 3 years.
Interest is the additional amount of money that is charged or earned on a principal amount of money. It is typically expressed as a percentage of the principal and is either charged when borrowing money or earned when investing or saving money.
To calculate the interest Kayleigh will earn in 3 years, we can use the formula for simple interest:
Interest = Principal x Rate x Time
Given:
Principal = $4500
Rate = 0.8% = 0.008 (decimal form)
Time = 3 years
Plugging the values into the formula, we have:
Interest = $4500 x 0.008 x 3
Calculating the expression, we find:
Interest = $108
Therefore, Kayleigh will earn $108 in interest over a period of 3 years.
To know more about simple interests follow
https://brainly.com/question/29785550
#SPJ2
Someone help please!!!
Answers
Answer:
10%
Step-by-step explanation:
if the total hours of sports being played is 50 hours, and the time playing soccer is 5 hours, you just divide 5 by 50 (technically will be .1, but to make it a percent you multiply by 100)
2 brothers are 1m 60 cm and 1m 44cm tall. What is their ratio of their height
Answers
Answer: 10:9
Step-by-step explanation:
brother 1- 1m 60cm
brother 2- 1m 44cm
_________________________________________________________
the ratio would be brother 1 : brother 2 => 1m 60cm : 1m 44cm
_________________________________________________________
convert both the values to cm
1m = 100cm
brother 1 would be 100cm + 60cm or 160cm
brother 2 would be 100cm + 44cm or 144cm
_________________________________________________________
[tex]\frac{160}{144} = \frac{10}{9}[/tex] when simplified
the ratio of brother 1 to brother 2 would be 10:9
Al lanzar un dado dos veces consecutivas. ¿Qué probabilidad hay de obtener primero un 3 y luego un numero par?
Answers
Answer:
The probability is 1/12.
Step-by-step explanation:
Number of elements in sample space is 6 . Even numbers are 2, 4 and 6 so the there are 3 three even numbers.
So, the probability of getting 3 on the first chance and then an even number in the second chance is
[tex]P = \frac{1}{6}\times \frac{3}{6}\\\\P = \frac{1}{12}[/tex]
Put these numbers in order from least to greatest.
9.9, 9.5, and 9 4/5
Answers
9 4/5 is equal to 9.8
the average length of string a and string d is 10x cm. the average length of string b and string c is 8x cm . the average length of strings b , c , d is 6x cm . find the length of string a in terms of x
Answers
Answer:
[tex]a = 18x[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{2}(a + d) = 10x[/tex]
[tex]\frac{1}{2}(b + c) = 8x[/tex]
[tex]\frac{1}{3}(b + c+d) = 6x[/tex]
Required
The value of (a)
We have:
[tex]\frac{1}{2}(a + d) = 10x[/tex] --- multiply by 2
[tex]\frac{1}{2}(b + c) = 8x[/tex] --- multiply by 2
[tex]\frac{1}{3}(b + c+d) = 6x[/tex] --- multiply by 3
So, we have:
[tex]\frac{1}{2}(a + d) = 10x[/tex]
[tex]a + d = 20x[/tex]
[tex]\frac{1}{2}(b + c) = 8x[/tex]
[tex]b + c = 16x[/tex]
[tex]\frac{1}{3}(b + c+d) = 6x[/tex]
[tex]b + c + d= 18x[/tex]
Substitute [tex]b + c = 16x[/tex] in [tex]b + c + d= 18x[/tex]
[tex]16x + d = 18x[/tex]
Solve for d
[tex]d = 18x - 16x[/tex]
[tex]d = 2x[/tex]
Substitute [tex]d = 2x[/tex] in [tex]a + d = 20x[/tex]
[tex]a + 2x = 20x[/tex]
Solve for (a)
[tex]a = 20x - 2x[/tex]
[tex]a = 18x[/tex]
Given the interval 0<θ<π/2. Find the angle θ which is formed by the line y = -2x+4 and y = 3x-3
Show your work as well, thank you!
Answers
Answer:
[tex]\rm\displaystyle \theta = \frac{\pi}{4} [/tex]
Step-by-step explanation:
we want to find the acute angle θ (as θ is between (0,π/2)) formed by the line y=-2x+4 and y=3x-3 to do so we can consider the following formula:
[tex] \displaystyle\tan( \theta) = \bigg| \frac{ m_{2} - m_{1} }{1 + m_{1} m_{2} } \bigg | [/tex]
[tex] \rm \displaystyle \implies\theta = \arctan \left( \bigg | \frac{ m_{2} - m_{1} }{1 + m_{1} m_{2} } \bigg | \right)[/tex]
From the first equation we obtain that [tex]m_1[/tex] is -2 and from the second that [tex]m_2[/tex] is 3 therefore substitute:
[tex] \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 3 - ( - 2) }{1 + ( - 2) (3)} \bigg | \right)[/tex]
simplify multiplication:
[tex] \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 3 - ( - 2) }{1 + ( - 6)} \bigg | \right)[/tex]
simplify Parentheses:
[tex] \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 3 + 2 }{1 + ( - 6)} \bigg | \right)[/tex]
simplify addition:
[tex] \rm\displaystyle \theta = \arctan \left( \bigg | \frac{ 5 }{ - 5} \bigg | \right)[/tex]
simplify division:
[tex] \rm\displaystyle \theta = \arctan \left( | - 1| \right)[/tex]
calculate the absolute of -1:
[tex]\rm\displaystyle \theta = \arctan \left( 1\right)[/tex]
calculate the inverse function:
[tex]\rm\displaystyle \theta = \frac{\pi}{4} [/tex]
hence,
the angle θ which is formed by the line y = -2x+4 and y = 3x-3 is π/4
(for more info about the formula refer the attachment thank you!)
Consider two vector-valued functions,
[tex]\vec r(t) = \left\langle t, -2t+4\right\rangle \text{ and } \vec s(t) = \left\langle t, 3t-3\right\rangle[/tex]
Differentiate both to get the corresponding tangent/direction vectors:
[tex]\dfrac{\mathrm d\vec r(t)}{\mathrm dt} = \left\langle1,-2\right\rangle \text{ and } \dfrac{\mathrm d\vec s(t)}{\mathrm dt} = \left\langle1,3\right\rangle[/tex]
Recall the dot product identity: for two vectors [tex]\vec a[/tex] and [tex]\vec b[/tex], we have
[tex]\vec a \cdot \vec b = \|\vec a\| \|\vec b\| \cos(\theta)[/tex]
where [tex]\theta[/tex] is the angle between them.
We have
[tex]\langle1,-2\rangle \cdot \langle1,3\rangle = \|\langle1,-2\rangle\| \|\langle1,3\rangle\| \cos(\theta) \\\\ 1\times1 + (-2)\times3 = \sqrt{1^2 + (-2)^2} \times \sqrt{1^2+3^2} \cos(\theta) \\\\ \cos(\theta) = \dfrac{-5}{\sqrt5\times\sqrt{10}} = -\dfrac1{\sqrt2} \\\\ \implies \theta = \cos^{-1}\left(-\dfrac1{\sqrt2}\right) = \dfrac{3\pi}4[/tex]
Then the acute angle between the lines is π/4.
provide explanation too please !
a piano teacher teaches 8 lessons in 6 hours.
the lessons are all the same length.
how long is one lesson, in minutes?
Answers
1 hour is 60 minutes
6 hours x 60 = 360 total minutes
Divide total time by number of lessons:
360/8 = 45
Each lesson was 45 minutes
what is equivalent to 64 1/4