Range for the given Exponential function [tex]f(x) = 3(16)^{{\frac{3}{4}x}[/tex] is f(x) > 0.
the correction option is a). f(x) > 0
The function given in, the question is exponential function is given by
[tex]f(x) = 3(16)^{{\frac{3}{4}x}[/tex] Which is an exponential function. The domain of the give function is (-∞, ∞).
The function which is in format f(x) = [tex]a^{x}[/tex] where, a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
the Question seems to be incomplete. And options could be
a) f(x) > 0 c) f(x) ≤ 0
b) f(x) < 0 d) f(x) ≥ 0
Simplification of the given equation
[tex]f(x) = 3(16)^{{\frac{3}{4}x}[/tex]
[tex]f(x) = 3(2^4)^{{\frac{3}{4}x}[/tex]
[tex]f(x) = 3(8)^{x}[/tex]
clearly, the range of the exponential function is f(x) > 0.
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Sylvia bought 4 bananas for 50 cents each and 1 apple for 80 cents. Write a numerical expression to represent this situation and then find the total cost.
Answer: 280
Step-by-step explanation:
50 cents for each banana so: 4* 50= 200
200+80
Answer is 280
Mark ran a mean distance of 13.2 km in five days. The next day, Mark ran 20 km.
Find the mean distance Mark ran in the six days.
Answer:
16.6
Step-by-step explanation:
Add the numbers together.
13.2+20=33.2
Now divide the number by 2.
33.2/2=16.6
Hope this helps!
If not, I am sorry.
Divya is solving the following equation for w. 3w -√20-5w = 2 Her first few steps are given below. 3w = √20-5w+2 3w-2= √/20 - 5w (3w - 2)² =(√20 – 5w) 9w² - 12w + 4 = 20 - 5w Is it necessary for Divya to check her answers for extraneous solutions?
Divya should not check her answers for extraneous solution as it's not required in this case.
What is an extraneous solution?It should be noted that an extraneous solution simply means is the transformed equation that's isn't the root of the original equation.
Based on the information given, Divya had already solved the equation and it's not necessary to check the answers for extraneous solution.
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Answer:
No, she shouldn't.
5y + 3= 14
pleaseeeee help
Answer:
5y + 3= 14
subtract 3 from each side
5y=11
divide each side by 5
5y/5=11/5
y=11/5 or 2.2 or 2 1/5
Hope This Helps!!!
Answer:
2.2
Step-by-step explanation:
Properties needed:
Subtraction Property of EqualityDivision Property of Equality
First we need to subtract 3 from both sides because of subtraction property of equality to make both sides equal.
5y + 3 = 14
-3 -3
5y = 11
Then we need to divide 5 from both sides (division property of equality) to get y.
[tex]\frac{5y}{5} = \frac{11}{5}[/tex]
And we get 2.2
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I hope this helps!
Have a great day!
An amusement park charges $7 for adults, $2 for youths, and $0.50 for children. if 150 people enter and pay a total of $100, find the numbers of adults, youths, and children. [hint: these numbers are nonnegative integers.]
The number of adults are 2 . the number of youths are 8
Given charge $7 for adults , $2 for youth and $0.50 for children
Let the number of adults , youths and children be x , y and z
Now it is given that there is total pay of 100
Therefore the equation formed is
7x + 2y +0.50 = 100
Now it is also given that 150 people enter
Therefore
x+y+z=150
x+y+z =150
14x+4y+z=200
Using argument matrix
[tex]\left[\begin{array}{ccc}1&1&1\\14&4&1\end{array}\right] \left[\begin{array}{ccc}150\\200\end{array}\right][/tex]
Corresponding system equation is
x+y+z=150
y+(13/10)z=190
Take z = m (arbitary)
y = 190 - 1.3 m
x = 150 - y
m = 140 x = 2 and y = 8
Hence The number of adults are 2 . the number of youths are 8
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Lilly is a pizza driver. Lilly has to make 4 deliveries.
Delivery 1: 35 Minutes
Delivery 2: 14 Minutes
Delivery 3: 18 Minutes
Delivery 4: 27 Minutes
What is the average amount of time it takes to deliver pizza?
Answer:
23 min 30 sec
Step-by-step explanation:
First, you add 35 + 14 + 18 + 27 which is 94.
Next, you divide 94 by the number of deliveries there were. Which is 4.
94/4 = 23.5.
So your answer would be 23 minutes and 30 seconds.
I Hope This Helped :D
Answer:
23.5 minutes or 23 minutes and 30 seconds
Step-by-step explanation:
1. add all the minutes
35 minutes + 14 minutes + 18 minutes+ 27 minutes = 94 minutes
2. Divide the total amount of minutes by the number of deliveries
94 minutes = 23.5 minutes or 23 minutes and 30 seconds
4 deliveries
You are heading to a drive-in movie and will need exact cash at the entrance for everyone in your car to get in. The cost is $6.50 per person. Write an expression that represents the total cash needed for your car based on the number of people, p, in your car.
Answer:
Using the concept of equation of line, we find that the relationship will be
C = $6.5p.
Step-by-step explanation:
If the cost per head is $6.5 and there are p persons entering the car, then the total amount would be $6.5p.
The final equation would resemble the equation of line y = mx + c.
The expression for the total cost C, would be
C = 6.5p.
Here y = C, x = p, m = 6.5 and c = 0.
So, the expression for the total cost will be the equation of line C = 6.5p.
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3/2 x 7/2= 2^x
A. X= 1
B. X= 3
C. X= 5
D. X= 8
Bookwork code: M29 Calculator allowed The circle below has centre U. BC and DE are tangents to this circle. Work out the size of angle 0. Give reasons for your answer. A 52° B O E Watch video D 27° 0 C Not drawn accurately A Bookwork code : M29 Calculator allowed The circle below has centre U. BC and DE are tangents to this circle . Work out the size of angle 0 . Give reasons for your answer . A 52 ° B O E Watch video D 27 ° 0 C Not drawn accurately A
1) [tex]OA=OB[/tex] (all radii of a circle are equal)
2) [tex]\angle OBA=52^{\circ}[/tex] (angles opposite equal sides in a triangle are equal)
3) [tex]\angle OAB+\angle OBA+\angle AOB=180^{\circ}[/tex] (angles in a triangle add to 180 degrees)
4) [tex]52^{\circ}+52^{\circ}+\angle AOB=180^{\circ}[/tex] (substitution)
5) [tex]\angle AOB=76^{\circ}[/tex] (subtraction)
6) [tex]\angle AOB+\angle BOD=180^{\circ}[/tex] (angles on a line add to 180 degrees)
7) [tex]76^{\circ}+\angle BOD=180^{\circ}[/tex] (substitution)
8) [tex]\angle BOD=104^{\circ}[/tex] (subtraction)
9) [tex]\angle ODE=\angle OBC=90^{\circ}[/tex] (tangents are perpendicular to the radius of a circle at the point of tangency)
10) [tex]\angle ODC=117^{\circ}[/tex] (angle addition postulate)
11) [tex]\angle BOD+\angle OBC+\angle ODC+\angle DCB=360^{\circ}[/tex] (angles in a quadrilateral add to 360 degrees)
12) [tex]104^{\circ}+90^{\circ}+117^{\circ}+\theta=360^{\circ}[/tex] (substitution)
13) [tex]\theta=49^{\circ}[/tex] (subtraction)
(-3, 1)
-5-4-3
(-2,-4)
k
4
4
ob
1
2-
3+
(2/2)
What is the equation, in point-slope form, of the line
that is parallel to the given line and passes through the
point (-3, 1)?
Oy-1= -2(x+3)
Oy-1=-(x+3)
Oy - 1 =
Oy-1 =
(x+3)
(x+3)
Answer:
What is the slope of the line represented by the equation y = y equals StartFraction 4 Over 5 EndFraction x minus 3.x – 3?
Step-by-step explanation:
The equation of line that is parallel to the given line having slope m = -1 and passes through the point ( -3 , 1 ) is y = -x - 2
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
Let the first point be P ( -3 , 1 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
The slope of the line m = -1
Now , the line is parallel to the line passing through P
So , the slopes of the lines are equal
And , the equation of line is y - y₁ = m ( x - x₁ )
On simplifying , we get
y - 1 = -1 ( x - ( -3 ) )
y - 1 = -1 ( x + 3 )
Adding 1 on both sides , we get
y = -x - 3 + 1
y = -x - 2
Hence , the equation of line is y - 1 = -1 ( x + 3 )
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Half the product of two numbers is 36 if one number is 9 what is the other number
Answer:
x=9
y=?
36= 1/2(x*y)
36 *2 = 2* 1/2 (9*y)
72 = 9*y
72/9= 9*y/9
8=y
The other number is 8.
Unit 11: volume & surface area homework 6: surface area of pyramids and cones
The answer for the following part is
What is Volume?Surface area is the amount of space covering the outside of a three-dimensional shape.
Surface Area of Cone,
= πrl + πr²
=3.14*8*15.77 + 3.14* 8*8
= 597.61804 mm²
Surface Area of triangular pyramid,
= apothem * slant height * length
= 73.6 m²
Surface Area pentagonal pyramid
= B + LA
= 247.75 + 5 ( 1/2*12*19.5)
= 247.75 + 5 ( 117)
= 832.75 in²
Surface area of square pyramid
= P*l /2
= 2400 ft²
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PLS I REALLY NEED HELP I NEED TO PASS THIS ASAP
The volume of the cylinder is 1692.46dm³.
How to calculate the volume?It should be noted that the volume of a cylinder is calculated as:
= πr²h
r = radius = 7dm
h = height = 11dm
Volume = πr²h
Volume = 3.14 × 7² × 11
Volume = 3.14 × 49 × 11
Volume = 1692.46dm³
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f(x) = x^2 + 5x - 1 is shifted 3 units left the result is g(x). What is g(x)?
Answer:
A. g(x)=x^2+5x+2
Step-by-step explanation:
f(x) = x^2 + 5x - 1 Shift 3 units to the left. k=3
g(x)=x^2+5x-1+3=x^2+5x+2
g(x)=x^2+5x+2
Hope this helps!
If not, I am sorry.
Which of the following are solutions to the equation below?
(2x+3)^2 = 10
Check all that apply.
Answer:
x = (√10 -3)/2 and (-√10 -3)/2
Step-by-step explanation:
(2x+3)^2 = 10
To solve the equation, take the square root of each side
sqrt((2x+3)^2) = ±√10
2x+3 = ±√10
Subtract 3 from each side
2x+3-3 = ±√10 -3
2x = ±√10 -3
Divide each side by 2
2x/2 = (±√10 -3)/2
x = (±√10 -3)/2
There are two solutions
x = (√10 -3)/2
and (-√10 -3)/2
Answer:
[tex]\large {\textsf{A and D}}\ \implies \sf \sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}[/tex]
Step-by-step explanation:
Given: (2x + 3)² = 10
In order to find the solutions to the given equation, we can take the (square) roots of the equation to find the zeros, which are also known as the x-intercepts. This is where the zeros intersect the x-axis.
Note: when taking the square roots of a quadratic equation, remember to use both the positive and negative roots.
Step 1: Square both sides of the equation.
[tex]\sf \sqrt{(2x + 3)^2} = \sqrt{10}\\\\\Rightarrow 2x+3=\pm\sqrt{10}[/tex]
Step 2: Separate into possible cases.
[tex]\sf x_1 \implies 2x+3=-\sqrt{10}\\\\x_2 \implies 2x+3=\sqrt{10}[/tex]
Step 3: Solve for x in both cases.
[tex]\sf \bold{x_1} \implies 2x+3=-\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=-\sqrt{10}-3\\\\\Rightarrow 2x=-\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{-\sqrt{10}-3}{2}\\\\\Rightarrow x_1=\dfrac{-\sqrt{10}-3}{2}\\\\[/tex]
[tex]\sf \bold{x_2}\implies 2x+3=\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=\sqrt{10}-3\\\\\Rightarrow 2x=\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{\sqrt{10}-3}{2}\\\\\Rightarrow x_2=\dfrac{\sqrt{10}-3}{2}[/tex]
Therefore, the solutions to this quadratic equation are: [tex]\sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}[/tex]
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I need help for solving y in this problem 2x -y =1
Answer:
y = 2x - 1
Step-by-step explanation:
Given equation: 2x - y = 1
We're being asked to solve for y. This is also known as the Slope-Intercept Form. It is represented by the following formula:
y = mx + b
where:
m is the slopeb is the y-intercept (when x = 0)Steps:
1. Subtract 2x from both sides:
[tex]\sf 2x-2x - y = 1-2x\\\\\implies-y=-2x+1[/tex]
2. Divide both sides by -1:
[tex]\sf \dfrac{-y}{-1}=\dfrac{-2x+1}{-1}\\\\\implies y=2x-1[/tex]
This equation has a slope of 2, and a y-intercept of -1.
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Given a b and m/1 = 42°
What is m/6?
Enter your answer in the box.
What is the measure of the unknown angle?
straight angle divided into a one hundred thirty two degree angle and an unknown angle
48°
49°
51°
53°
The work of a student to solve the equation 4(2x − 4) = 8 + 2x + 8 is shown below: Step 1: 4(2x − 4) = 8 + 2x + 8 Step 2: 6x − 8 = 16 + 2x Step 3: 6x − 2x = 16 + 8 Step 4: 4x = 24 Step 5: x = 6 In which step did the student first make an error and what is the correct step? (5 points) Step 2; 8x − 4 = 2(6 + x + 6) Step 2; 8x − 16 = 16 + 2x Step 3; 6x − 2x = 16 − 8 Step 3; 6x + 2x = 16 + 8
A,B, C and D are the four corners of a rectangular plot marked out on level ground. Given that the bearing of B from A is 40 and the bearing of C from A is 90, Find the bearing B frOm C
Answer:
given - a rectangle ABCD
AB = 40
AC. = 90
BC = ?
in triangle ABC
using Pythagoras theorem
(AB) ² + (BC) ² = (AC) ²
(40)² + (BC) ² = (90)²
(BC) ² = (90)²- (40)²
(BC) ² = 8100 - 1600
(BC) ² = 6500
BC =
[tex]20 \sqrt{10} [/tex]
Which currency is it
Answer:
pounds (£)
Step-by-step explanation:
pounds are used in countries such as the UK and South Georgia
Solve for x in the equation
X
O x=-11±25
O x=-11+25
0 x--11+5√/5
Ox--11,5/5
2
x²+11x+121-125
4
=
Answer:
The answer for this question is c
The value of x from the quadratic term equation is x = ( -11/2 ) ± ( 5√5 ) / 2
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² + 11x + 121/4 = 125/4
Subtracting ( 125/4 ) on both sides , we get
x² + 11x + ( 121 - 125 ) / 4 = 0
x² + 11x - 1 = 0 be equation (1)
On simplifying , we get
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
So , x = [ -11 ± √ ( 11 )² - 4 ( 1 ) ( -1 ) ] / 2
On further simplification , we get
x = -11 ± √ ( 121 + 4 ) / 2
x = [ -11 ± √125 ] / 2
x = ( -11/2 ) ± ( 5√5 ) / 2
Therefore , the roots of the equation are x = ( -11/2 ) ± ( 5√5 ) / 2
Hence , the quadratic equations are solved
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Determine whether the given differential equation is exact. If it is exact, solve it. (tan(x)-sin(x)sin*y))dx+cos(x)cos(y)dy=0 g
The differential equation
[tex]M(x,y) \, dx + N(x,y) \, dy = 0[/tex]
is considered exact if [tex]M_y = N_x[/tex] (where subscripts denote partial derivatives). If it is exact, then its general solution is an implicit function [tex]f(x,y)=C[/tex] such that [tex]f_x=M[/tex] and [tex]f_y=N[/tex].
We have
[tex]M = \tan(x) - \sin(x) \sin(y) \implies M_y = -\sin(x) \cos(y)[/tex]
[tex]N = \cos(x) \cos(y) \implies N_x = -\sin(x) \cos(y)[/tex]
and [tex]M_y=N_x[/tex], so the equation is indeed exact.
Now, the solution [tex]f[/tex] satisfies
[tex]f_x = \tan(x) - \sin(x) \sin(y)[/tex]
Integrating with respect to [tex]x[/tex], we get
[tex]\displaystyle \int f_x \, dx = \int (\tan(x) - \sin(x) \sin(y)) \, dx[/tex]
[tex]\implies f(x,y) = -\ln|\cos(x)| + \cos(x) \sin(y) + g(y)[/tex]
and differentiating with respect to [tex]y[/tex], we get
[tex]f_y = \cos(x) \cos(y) = \cos(x) \cos(y) + \dfrac{dg}{dy}[/tex]
[tex]\implies \dfrac{dg}{dy} = 0 \implies g(y) = C[/tex]
Then the general solution to the exact equation is
[tex]f(x,y) = \boxed{-\ln|\cos(x)| + \cos(x) \sin(y) = C}[/tex]
m∠DFG=(2x+6)° and m∠EFG=(3x−11)°. Find the value of x.
The figure shows straight angle D F E that consists of two angles, D F G and E F G.
Answer:
x = 37
Step-by-step explanation:
A straight angle is 180 degrees. That means ∠DFG & ∠EFG have to add together to be 180.
2x + 6 + 3x - 11 = 180 Combine like terms
5x - 5 = 180 Add 5 to both sides
5x = 185 Divide by 5
x = 37
∠DFG = 80°
∠EFG = 100°
a motorcyclist riding North along a straight road at 50 km per hour observes that the wind appeared to have a velocity of 50 km per hour from the direction North 60 degrees West what is the velocity of the wind.
The velocity of the wind will be 50 km per hour.
What is a vector?The quantity which has magnitude, direction and follows the law of vector addition is called a vector.
A motorcyclist riding North along a straight road at 50 km per hour observes that the wind appeared to have a velocity of 50 km per hour from the direction North 60 degrees West.
Then the velocity of the wind will be
Let x be the speed of the wind. Then we have
x² = 50² + 50² - 2 x 50 x 50 x cos 60°
x² = 2500 + 2500 - 2500
x² = 2500
x = 50 km per hour
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??????????????????????????????????????????????????
Answer:
x=20
Step-by-step explanation:
The angles are 'Co-interior Angles', they make a C shape and add up to 180 degrees
so 4x +5x =9x
9x=180
x=20
4x=80
5x=100
Type a number for the types of journals that will be available to you in the new lma
Answer:
Step-by-step explanation:
What are the 6 types of journals?
There are various types of journals including:
academic/scholarly journals.
trade journals.
current affairs/opinion magazines.
popular magazines.
newspapers.
Raya buys a van for £9500 plus VAT at 20%
Raya pays a deposit for the van.
She then pays the rest of the cost in 12 equal payments of £665 each month.
Find the ratio of the deposit Ray pays to the total of the 12 equal payments.
Give your answer in its simplest form.
Step-by-step explanation:
yo thara bhai joginder tu he ek bndr
Y = 4x -2 and y = x +3
Answer:
(0.5,2) and (-3,3)
Step-by-step explanation:
Answer:
Y = 4x -2 is (0.5,2)
y = x +3 is (-3,3)
what is 25:28 in slimpelst from
Answer:
25:28 is the simplest form
Step-by-step explanation:
This is a ratio, think of it like a fraction. You can simplfy it by dividing by common factor.
25 and 28 have no common factors except for 1.
25: 1,5,25
28: 1,2,4,7,14,28
It will stay as 25:28
Answer:
it stays the exact same or 0.893
Step-by-step explanation: