Answer:
s(t) = -4.9t² + 39.2t
Step-by-step explanation:
Given the projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s²
Given
g = -4.9m/s²
v0 = 39.2m/s
s0 = 0m (the initial height)
On substituting into the formula;
s(t) = gt² + v0t + s0
s(t) = -4.9t² + 39.2t + 0
s(t) = -4.9t² + 39.2t
This gives the equation that models the height
Solve each triangle – find any missing side and angle measures. Round answers to the nearest tenth.
Here ABC is a right angle triangle because 1 angle is 90°
BY ASP,
90+56+ angle CAB=180
angle CAB=34°
rounded to nearest = 30°
sin A =opp/hyp
sin 30 = 7/x
1/2=7/x
x=14
rounding to nearest 10
14 =10
AB=10
By Pythagoras Theorem,
AB²=BC²+AC²
AC²=AB²-BC²=10² - 7²
100- 49 = 51
AC=root 51
find dy/dy in terms of x and y
[tex]\frac{dy}{dy}=1[/tex], so I assume you mean "find [tex]\frac{dy}{dx}[/tex]".
We can rewrite this as an implicit equation to avoid using too much of the chain rule, namely
[tex]y = \sqrt[3]{\dfrac{e^x (x+1)}{x^2+1}} \implies (x^2+1) y^3 = e^x (x+1)[/tex]
Differentiate both sides with respect to [tex]x[/tex] using the product and chain rules.
[tex]2x y^3 + 3(x^2+1) y^2 \dfrac{dy}{dx} = e^x(x+1) + e^x[/tex]
[tex]\implies 3(x^2+1) y^2 \dfrac{dy}{dx} = e^x (x+2) - 2x y^3[/tex]
[tex]\implies \dfrac{dy}{dx} = \dfrac{e^x (x+2) - 2x y^3}{3(x^2+1) y^2}[/tex]
Now substitute the original expression for [tex]y[/tex].
[tex]\dfrac{dy}{dx} = \dfrac{e^x (x+2) - 2x \left(\sqrt[3]{\frac{e^x(x+1)}{x^2+1}}\right)^3}{3(x^2+1) \left(\sqrt[3]{\frac{e^x(x+1)}{x^2+1}}\right)^2}[/tex]
[tex]\implies \dfrac{dy}{dx} = \dfrac{e^x (x+2) - \frac{2e^x(x^2+x)}{x^2+1}}{3(x^2+1) \left(\frac{e^x(x+1)}{x^2+1}\right)^{2/3}}[/tex]
[tex]\implies \dfrac{dy}{dx} = e^x \dfrac{x^3-x+2}{3(x^2+1)^2 \frac{e^{2x/3}(x+1)^{2/3}}{(x^2+1)^{2/3}}}}[/tex]
[tex]\implies \dfrac{dy}{dx} = e^{x/3} \dfrac{x^3-x+2}{3(x^2+1)^{4/3} (x+1)^{2/3}}[/tex]
Now, since
[tex]y = \sqrt[3]{\dfrac{e^x (x+1)}{x^2+1}} = \dfrac{e^{x/3} (x+1)^{1/3}}{(x^2+1)^{1/3}}[/tex]
we can write
[tex]\dfrac{dy}{dx} = e^{x/3} \dfrac{x^3-x+2}{3(x^2+1)^{4/3} (x+1)^{2/3}} = \dfrac{e^{x/3} (x+1)^{1/3}}{(x^2+1)^{1/3}} \times \dfrac{x^3-x+2}{3(x^2+1)^{3/3} (x+1)^{3/3}}[/tex]
[tex]\implies \dfrac{dy}{dx} = y \dfrac{x^3-x+2}{3(x^2+1)(x+1)}[/tex]
Focusing on the rational expression in [tex]x[/tex], we have the partial fraction expansion
[tex]\dfrac{x^3 - x + 2}{(x^2 + 1) (x+1)} = a + \dfrac{bx+c}{x^2+1} + \dfrac d{x+1}[/tex]
where we have the constant term on the right side because both the numerator and denominator have degree 3.
Writing everything with a common denominator and equating the numerators leads to
[tex]x^3 - x + 2 = a (x^2+1) (x+1) + (bx+c)(x+1) + d(x^2+1) \\\\ = ax^3 + (a+b+d)x^2 + (a+b+c)x + a+c+d[/tex]
[tex]\implies \begin{cases} a = 1 \\ a+b+d=0 \\ a+b+c = -1 \\ a+c+d=2 \end{cases}[/tex]
[tex]\implies a=1, b=-2, c=0, d=1[/tex]
[tex]\implies \dfrac{x^3 - x + 2}{(x^2 + 1) (x+1)} = 1 - \dfrac{2x}{x^2+1} + \dfrac 1{x+1}[/tex]
and it follows that
[tex]\boxed{\dfrac{dy}{dx} = \dfrac y3 \left(1 - \dfrac{2x}{x^2+1} + \dfrac1{x+1}\right)}[/tex]
Select the correct answer. Which system of equations is represented by this graph? A graph has two diagonal curves. A curve declines through (negative 1, 5), and (2 point 3, negative 5). A curve declines through (negative 5, negative 2) and (2 point 3, negative 5). Both curves intersect at (2 point 3, negative 5). A. B. C. D.
The system of equations represented by the attached graph is y = (x + 3)^2 - 2 and y = -x + 1
How to determine the system of equations?This question will be answered using the attached graph
The curve
The curve is a quadratic function, and it has the following features:
Vertex, (h, k) = (-3, -2)
Point (x, y) = (-1, 2)
A quadratic function is represented as:
y = a(x - h)^2 + k
So, we have:
y = a(x + 3)^2 - 2
Substitute (x, y) = (-1, 2)
2 = a(-1 + 3)^2 - 2
This gives
2 = 4a-2
Solve for a
a = 1
Substitute a = 1 in y = a(x + 3)^2 - 2
y = (x + 3)^2 - 2
The line
The line is a linear function, and it has the following features:
Point (x1, y1) = (-1, 2)
Point (x2, y2) = (-6, 7)
The linear function is calculated as:
y = (y2 - y1)/(x2 - x1) *(x- x1) + y1
So, we have:
y = (7 -2)/(-6 +1) *(x + 1) + 2
Evaluate the quotient
y = -1(x + 1) + 2
Expand
y = -x -1 + 2
y = -x + 1
Hence, the system of equations represented by the attached graph is y = (x + 3)^2 - 2 and y = -x + 1
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How many solutions does the system have? You can use the interactive graph below to find the answer. \begin{cases} 4x-2y=8 \\\\ 2x+y=2 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 4x−2y=8 2x+y=2 Choose 1 answer: Choose 1 answer: (Choice A) A Exactly one solution (Choice B) B No solutions (Choice C) C Infinitely many solutions
[tex]\Huge\boxed{\textsf{A. Exactly one solution}}[/tex]
We have the following system:
[tex]\begin{cases}4x-2y&=8\\2x+y&=2\end{cases}[/tex]
Here, a simple solution to find the answer is to graph the two lines and see how many times they intersect.
I've attached a graph, with [tex]4x-2y=8[/tex] in red and the other equation in blue.
See that the lines only intersect once, at [tex](1.5,-1)[/tex]. This means the system only has one solution.
Answer: No Solution
Let's bring both equations to slope-intercept form. Then we can think about the slopes and the y-intercepts of the lines represented by each equation.
The slope-intercept form of the first equation 2y=4x+62y=4x+62, y, equals, 4, x, plus, 6 is y=2x+3y=2x+3y, equals, 2, x, plus, 3. The second equation y = 2x+6y=2x+6y, equals, 2, x, plus, 6 is already in slope-intercept form.
Hint #22 / 3
The first equation is y = 2x+3y=2x+3y, equals, 2, x, plus, 3, so the slope of its line is 222 and the yyy-intercept is (0,3)(0,3)left parenthesis, 0, comma, 3, right parenthesis.
The second equation is y = 2x+6y=2x+6y, equals, 2, x, plus, 6, so the slope of its line is 222 and the yyy-intercept is (0,6)(0,6)left parenthesis, 0, comma, 6, right parenthesis.
Since both lines have the same slopes but different yyy-intercepts, they are distinct parallel lines.
Hint #33 / 3
Since distinct parallel lines don't intersect, we conclude that the system has no solutions.
What is the ratio?
Help me please!! Thanks so much
Answer: 27:1
Step-by-step explanation:
The ratio of the volumes is equal to the cube of the ratio of the altitudes.
Three quadrilaterals exist such that GHJK ≅ ASDF and GHJK ≅ VBNM.
If MV measures 3 cm, which other segment must measure 3 cm?
A F
KJ
FD
GJ
Among the congruent quadrilaterals, the segment that must also measure 3 cm is: A. A F.
What are Congruent Quadrilaterals?Congruent quadrilaterals have corresponding congruent angles and sides.
Given that, GHJK ≅ ASDF and GHJK ≅ VBNM, it means that all corresponding sides and angles are equal to each other.
MV corresponds to KG and A F. If MV = 3 cm, then one segment that must measure 3 cm is:
A. A F
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Answer: A. A F
same answer as the other person gave but you don't have to read a bunch
which inequality represents all values of x for which the quotient below is defined? sqrt 7x^2 / sqrt3x
Answer:
The Answer is x>0
At a football match, there were 250 more men than women. The number of children was twice the number of women and the number of men was twice the number of women and children combined. How many people were at the match.
Answer:
450 people were at the match
Step-by-step explanation:
So let's make equation :
W = women
M = Men
C = Children
First equation :
M = W + 250
Second equation :
C = 2W
Third equation :
M = 2(W+C)
Let's substitute the second equation into the third :
M = 2(W + 2W)
M = 2W + 4W
M = 6W
Let's substitute this equation into the first one :
6W = W + 250
5W = 250
W = 50
Now we know that that there were 50 women at the match and can substitute this value for the first equation and then the second :
M = 50 + 250
M = 300
This means that there must have been 300 men at the match.
C = 2(50)
C = 100
This means that there must have been 100 children at the match.
Adding all values together gives us :
50 + 300 + 100 =
450 people were at the match
Hope this helped and have a good day
Helppp!! Instructions: Find the missing side. Round your answer to the nearest tenth.
59
X
28
Answer:
x ≈ 14.4
Step-by-step explanation:
using the cosine ratio in the right triangle
cos59° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{28}[/tex] ( multiply both sides by 28 )
28 × cos59° , then
x ≈ 14.4 ( to the nearest tenth )
what is y? i am having trouble figuring out what y is
Answer:
[tex]\sf \boxed{\bf y =5\sqrt{22}}[/tex]
Step-by-step explanation:
45° - 45° - 90° triangle:The ratio of sides of 45 - 45 - 90 triangle is a : a : a√2.
a is the side opposite to 45°.
From the figure, a = 5√11
The side opposite to 90° is a√2.
y = a√2
[tex]\sf = 5\sqrt{11} * \sqrt{2}\\\\ = 5*\sqrt{11*2}\\\\ = 5\sqrt{22}[/tex]
5 Quick algebra 1 questions for 50 points!
Only answer if you know all 5, Tysm! :)
The equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4
How to determine the equations?When a linear equation is represented as:
Ax + By = C
The slope (m) is:
m = -A/B
When the linear equation is represented as:
y = mx + c
The slope is m
A line perpendicular to a linear equation that has a slope of m would have a slope of -1/m
Using the above highlights, the equations of the lines are:
6. y = -2x + 5; (2, 7)
The slope is:
m = -2
The perpendicular slope is:
n = 1/2
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 1/2(x - 2) + 7
Evaluate
y = 1/2x - 1 + 7
This gives
y = 1/2x + 6
7. y = -5; (11, 15)
The slope is:
m = 0
The perpendicular slope is:
n = 1/0 = undefined
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 15
8. Graph ; (-12, 10)
The slope is:
m = (y2 - y1)/(x2 - x1)
Using the points on the graph, we have:
m = (2 - 3)/(3 - 4)
m = 1
The perpendicular slope is:
n = -1
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = -1(x + 12) + 10
y = -x - 12 + 10
Evaluate
y = -x - 2
9. y = -1/6x + 1; (-2, -9)
The slope is:
m = -1/6
The perpendicular slope is:
n = 6
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 6(x + 2) - 9
Evaluate
y = 6x + 12 - 9
This gives
y = 6x + 3
10. 6x + 2y = 14; (12, 0)
The slope is:
m = -6/2
m = -3
The perpendicular slope is:
n = 1/3
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 1/3(x - 12) + 0
Evaluate
y = 1/3x - 4
Hence, the equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4
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Add: -3u^3 + (-7u^3 - 4)
pls answer asap
Answer:
-10u^3 - 4
Step-by-step explanation:
-3u^3-7u^3 = -10u^3
then -4
What is the solution to the system of equations?
y = 2/3x + 3
x =-2
[-2, -15/2 ]
[-2, 5/3]
(-2, 11/6
(-2, 13/3)
Answer:
(- 2, [tex]\frac{5}{3}[/tex] )
Step-by-step explanation:
y = [tex]\frac{2}{3}[/tex] x + 3 → (1)
x = - 2
substitute x = - 2 into (1)
y = [tex]\frac{2}{3}[/tex] × - 2 + 3 = - [tex]\frac{4}{3}[/tex] + [tex]\frac{9}{3}[/tex] = [tex]\frac{5}{3}[/tex]
solution is (- 2, [tex]\frac{5}{3}[/tex] )
Suzanne deposited x dollars to her savings account. Her old balance was $348.50, and her new balance is $532.20. Find the deposited amount.
Answer:
$183.7
Step-by-step explanation:
To find the deposited amount you need to....
[tex]$532.20-$348.50=$183.70[/tex]
Hello!
Subtract the old balance from new balance to find deposit amount.
⇒ Deposit = $532.20 - $348.50
⇒ Deposit = $183.70
Geometry question I need help with the true or false
Answer:
See below
Step-by-step explanation:
SAS says the two triangles are congruent
so side 6x-4 = 3x+8 then x = 4
x= 4 true
x = 3 false ( because we just found it = 4)
Pythag theorem says QT
(6x-4)^2 = QT^2 + 12^2
( 6(4)-4)^2 = 12 ^2 + QT^2
400 -144 = QT^2
QT = 16 true
Which statement is true about this transformation?
It is a rigid transformation because the pre-image and image have the same corresponding angle measures.
It is not a rigid transformation because the corresponding side lengths are not equal.
It can be a rigid or a nonrigid transformation depending on whether the corresponding side lengths have the same measures.
It can be a rigid or a nonrigid transformation because a pair of corresponding angles measures 90°
A true statement about this transformation is: C. It can be a rigid or a nonrigid transformation depending on whether the corresponding side lengths have the same measures.
What is a transformation?In Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. Hence, when an object is transformed, all of the points would also be transformed.
In this scenario, we can logically deduce that triangle J'K'L' can either be a rigid or a nonrigid transformation based on the magnitude of the corresponding side lengths in both triangles, considering that their angles are equal in magnitude.
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Complete Question:
Triangle JKL is transformed to create triangle J'K'L'. The angles in both triangles are shown.
J = 90° J' = 90°
K = 65° K' = 65°
L = 25° L' = 25°
Which statement is true about this transformation?
A. It is a rigid transformation because the pre-image and image have the same corresponding angle measures.
B. It is not a rigid transformation because the corresponding side lengths are not equal.
C. It can be a rigid or a nonrigid transformation depending on whether the corresponding side lengths have the same measures.
D. It can be a rigid or a nonrigid transformation because a pair of corresponding angles measures 90°.
It is a rigid transformation because the pre-image and image have the same corresponding angle measures.
How to determine the true statement?The complete question is added as an attachment
From the image and the preimage triangles, we have that:
The corresponding sides of both triangles are equal
This is identified by the marks I, II and III on the side lengths
Equal corresponding sides represent a rigid transformation
Hence, the true statement about the dilation is (a)
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Prove: Quadrilateral ABCD is a parallelogram
PLEASE HELP
The proof is shown below:
What is a parallelogram?A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal).
As,
<A= 104
<B= 76
As AB || CD,
<A + <D =180
104 + <D =180
<D = 76
and <B + <C =180
76 + <C = 180
<C = 104.
As, opposite angles are equals and AB || CD.
Hence, ABCD is a parallelogram.
For 2 part,
Use m<A = 104° and m<B= 76° to show that <A and <B are same-side interior angles. Then, use AB || CD to show that <A and <D are supplementary angles.
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You flipped a fair coin 10 times. The result were 7 heads and 3 tails. Is the next flip more likely to be heads, tails, or the same likelihood of heads or tails? Explain your answer using complete sentences.
Which of the following is a valid exclusion for the algebraic fraction 8ab^2x/4a^2b - 8ab^2
A. a=/ 0, b =/ 0, a = / b
B. a = / 0, b =/ 0
C. a =/ 0, b =/ 0, a = / 2b
D. b = / 0, a = / b
The valid exclusion of the algebraic fraction is (c) a =0, b =0, a =2b
How to determine the valid exclusion?The expression is given as:
8ab^2x/4a^2b - 8ab^2
Set the denominator to 0
4a^2b - 8ab^2 = 0
Divide through by 4ab
a - 2b = 0
Add 2b to both sides
a = 2b
Hence, the valid exclusion of the algebraic fraction is (c) a =0, b =0, a =2b
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What is the surface area of this hemisphere?
Answer:
1413.7
Step-by-step explanation:
A(sphere) = 4 * π * r².
You can think about it like two times the cap surface area of a hemisphere. Therefore, the hemisphere cap area equals:
Ac = A(sphere) / 2,
Ac = 2 * π * r².
Sam runs 36 km in 2.5 hours, how many km does he run per hour
Answer:
Sarah runs at 14.4km/h
Step-by-step explanation:
36km = 2.5 hours
/ = per or divide
36km/2.5hours = 36 divided by 2.5 = 14.4km/h
f(x) = 5x³ – 2r²
g(x) 3r -7
Answer:
-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9Consider the following figure. (Note that the figure is not drawn to scale.) G 52° 56° 69° I 56° H Order the side lengths FG, GI, FH, GH, and IH from least to greatest. HELP NOW!!!!!
The order of the side lengths from least to greatest is; GH< IH< FG< GI< FH.
What is the order of the side lengths from least to greatest?As with other closed geometric figures, the shortest side length is opposite the smallest angle measure while the longest side length, is opposite the greatest angle measure.
Hence, it follows from the statement above that the order of side lengths is; GH< IH< FG< GI< FH.
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One number is 5 more than 3 times another number.the sum of the numbers is 45. find the numbers
Answer:
35 and 10
Step-by-step explanation:
Let m and n be the numbers
m is 5 more than 3 times n can be written as
m = 3n + 5 ... (1)
Sum of numbers is 45 so m + n = 45 .or
m = 45 - n ... (2)
Equating RHS of (1) and (2) gives us
3n + 5 = 45 - n
Collecting like terms
3n + n = 45 -5
4n = 40
n = 10
Therefore m = 45-10 = 35
Quick Check
In (1) substitute for m and n,
LHS is m = 35
RHS = 3 * 10 + 5 = 35
Imani and Abedi drive to work. Imani drives 66 miles in 1.5 hours. Abedi drives 56 km in 1 hour 15 min. Work out the difference between their average speeds in km/h. 1 mile = 1.6 km
Answer:
0.98 km/h
Step-by-step explanation:
Converting mi to km: 66*1.6 = 105.6 miles
Imani's average: 105.6 miles/ 90 min = 1.73 km/h
Abedi's average: 56 miles/ 75 min = 0.7466 ≈ 0.75 km/h
Difference: 1.73-0.75 = 0.98 km/h
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!
Hello and Good Morning/Afternoon
Let's take this problem step-by-step:
To find the solution to a system of equation
⇒ must set the equations equal to each other
⇒ and solve
Let's put that into action
[tex]x^2-2x+3 = -2x + 12\\x^2-2x+2x+3-12=0\\x^2-9=0\\(x+3)(x-3)=0[/tex]
At this point, to make the whole thing equal zero⇒ either 'x+3' or 'x-3' equals zero
⇒ must find 'x' that satisify either equation
[tex]x-3=0\\x=3\\\\x+3=0\\x=-3[/tex]
Let's find the corresponding f(x) to each x-value
[tex]f(3) = -2(3)+12=-6+12 = 6\\\\f(-3) = -2(-3) + 12=6+12=18[/tex]
Therefore the solutions are (3,6) and (-3,18)
Answer: (3,6), (-3,18)
Hope that helps!
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describe the pattern between the fractions 1/9 and 2/9 and their decimal form
fraction 2/9 is twice the value of fraction 1/9.
What are mathematics operations?
• A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
Here, the given fractions are :
1/9 and 2/9
clearly 2/9 is twice the value of fraction 1/9.
And, there decimal form will be :
1/9 = 0.11
2/9 = 0.22
Here, both are multiple of 11.
Therefore, fraction 2/9 is twice the value of fraction 1/9.
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help me please im in a rush
Answer:
390 m^2
Step-by-step explanation:
So let's start by finding the surface area of the two triangles on the side. Generally the area of a triangle can be calculated as: [tex]\frac{1}{2}bh[/tex]. but since there is two of them, we can calculate the area of both of them by simply canceling out the 1/2 to a 1. So the area of both triangles are 12 m * 5m as given in the diagram. This gives you 60m^2 area for both triangles on the side
Now let's calculate the rectangle on the top. It has a width and length of 13 and 11 m. So multiply these together to get: 143 m^2
Now let's calculate the rectangle that's on the bottom, it has the dimensions 11 and 12m and multiplying these together gets you: 132 m^2\
Now calculate the rectangle all the way in the back, it has the dimensions 5 and 11m, multiplying these together gets you 55 m^2.
Now add all these together: 60m^2 + 143m^2 + 132m^2 + 55m^2 = 390m^2
2 answers btw pls helpp
Question 1 of 5
Select the correct answer.
Which function has a domain of (-♾, ♾)and a range of (-♾, 4)?
PLEASE HELP
A: f(x) = -x^2 + 4
B: f(x) = 2^x +4
C: f(x) = -4x
D: f(x) = x + 4
Answer: A
Step-by-step explanation:
A) Correct. [tex]x^2 \geq 0 \implies -x^2 \leq 0[/tex]
B) Wrong. [tex]2^x > 0[/tex], so the range is [tex](4, \infty)[/tex]
C) Wrong. Linear functions have a range of all real numbers.
D) Wrong. Same logic as C.