The graph of g(x) is an exponential function that crosses the y-axis at y = 3.5, and a horizontal asymptote at y = 3.5
The function is given as:
[tex]g(x) = 2^{x - 1} + 3[/tex]
Set x = 0, to calculate the y-intercept
[tex]g(0) = 2^{0-1} + 3[/tex]
Simplify the exponent
[tex]g(0) = 2^{-1} + 3[/tex]
Express 2^-1 as decimal
[tex]g(0) =0.5 + 3[/tex]
Add 0.5 and 3
[tex]g(0) =3.5[/tex]
This means that the graph of g(x) is an exponential function that crosses the y-axis at y = 3.5
Also, the graph of g(x) has a horizontal asymptote at y = 3.5
Read more about exponential graphs at:
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Answer:
3 graph
Step-by-step explanation:
(2n + 4) + 6 = –9 + 4(2n + 1)
Answer:
n=2.5
Step-by-step explanation:
(2n+4)+6=-9+4(2n+1)
Expand parentheses:
2n+10=-9+8n+4
Combine like terms:
15=6n
Divide both sides by 6:
n=2.5
Hope this helps!
A plane is descending onto the runway with an angle of depression of 55°. If it has 2.8 miles to go before landing (hypotenuse), what is the current altitude of the plane?
A. 4.9 miles
B. 3.4 miles
C. 4 miles
D. 1.6 miles
E. 2.3 miles
Answer:
Option C is correct
Step-by-step explanation:
Given: A plane is descending onto the runway with an angle of depression of 55°. Also, it has 2.8 miles to go before landing.
To find: current altitude of the plane
Solution:
Consider the attached image.
In ΔABC,
[tex]\angle ACB=55^{\circ}[/tex] (Alternate interior angles)
For any angle [tex]\theta[/tex],
[tex]tan \theta[/tex] = side opposite to angle/side adjacent to angle
[tex]\tan C=\frac{AB}{BC}[/tex]
Put [tex]\angle C=55^{\circ}\,,\,BC=2.8\,\,miles[/tex]
[tex]AB=2.8\,\tan 55^{\circ}=3.999\approx 4\,\,miles[/tex]
So, the current altitude of the plane is 4 miles.
Write the simplest form of the expression (64/729)^(−1/6)
Answer:
3/2
Step-by-step explanation:
(64/729)^(−1/6)=(2^6/3^6)^(-1/6)=(2/3)^-1=3/2
please help me!!!! (i only need question 1)
Answer:
28
Step-by-step explanation:
So I just figured out by counting. The top has 8, which means the bottom also has 8. The sides are 3, 2, 1, 1, 2, 3
The total is 8 + 8 + 3 + 2 + 1 + 1 + 2 + 3 = 28
Check the consistency of 2x-3y=7 and x-2y+1=0
Answer:
x = 17, y = 9
or as an ordered pair, (17, 9).
The equations are consistent.
Step-by-step explanation:
2x - 3y = 7
x - 2y = -1 Multiply this equation by -2:
-2x + 4y = 2 Add this to the first equation:
y = 9.
Plug y = 9 into the second equation:
x - 2*9 = -1
x = -1 + 18 = 17.
Order these fractions from least to greatest 7/8 4/6 3/4
Answer:
4/6 , 3/4, 7/8
Step-by-step explanation:
7/8 4/6 3/4
The common denominator is 24
7/8*3/3 = 21/24
4/6* 4/4 = 16/24
3/4 * 6/6 = 18/24
From smallest to largest
16/24, 18/24, 21/24
4/6 , 3/4, 7/8
Find the volume of the cylinder Either enter an exact answer in terms of Pi or use 3.14 or Pi
Answer:
[tex]Volume = 54\,\pi[/tex]
Step-by-step explanation:
Recall the formula for the volume of a cylinder:
[tex]Volume=\pi \,R^2\,H[/tex]
where R is the radius of the cylinder's base, and H is the cylinder's height.
Therefore, in our case the volume becomes:
[tex]Volume=\pi \,R^2\,H\\Volume=\pi \,3^2\,*\,6\\Volume = 54\,\pi[/tex]
Find the 64th term of the following arithmetic sequence.
29,38,47...
Answer:
596
Step-by-step explanation:
I typed in 656 as the other person it was but it wasn't
An arithmetic sequence is a sequence where the difference between each consecutive term is the same.
The nth term of an arithmetic series is given as:
a(n) = a(1) + (n - 1)d
The 64th term of the arithmetic sequence is 596.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
Example:
2, 4, 6, 8, 10 is an arithmetic sequence.
common difference = 2
The first term = 2.
We have,
29, 38, 47,.....
First term = 29
a(1) = 29
Common difference:
= 38 - 29
= 9
Now,
The nth term of an arithmetic series is given as:
a(n) = a(1) + (n - 1)d
The value of the 64th term in the arithmetic sequence.
a(64) = a(1) + (64 - ) x 9
a(64) = 29 + 63 x 9
a(64) = 29 + 567
a(64) = 596
Thus,
The 64th term of the arithmetic sequence is 596.
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LeBron James shot 30 shots per game last season. His season high in shots was 2,000. He wants to earn a different shot per game record next season. How many shots shouldn’t LeBron take per game next season?
Answer:
1700
Step-by-step explanation:
Logan is reading about architecture and learns that trusses can be used to support roofs. He wants to find the measures of the angles on a truss. truss.
Answer:
It could help Logan to first study the constitution and shape of this type of armor in order to make a mental image of the positions of the angles as well as the size.
Step-by-step explanation:
A previous study allows Logan to understand that these types of trusses have a triangular shape and are widely used in the construction of roofs, therefore Logan could use to draw this type of trusses.
An object is launched directly in the air at a speed of 64 feet per second from a platform located 16 feet in the air. The motion of the object can be modeled using the function f(t)=−16t2+64t+16, where t is the time in seconds and f(t) is the height of the object. When, in seconds, will the object reach its maximum height?
Answer:
Step-by-step explanation:
x= -b/2a = -64/2(-16) = 2
showing that the object will reach its highest point at 2 seconds
Please answer correctly !!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!
Answer:
between step 1 and 2 he left off the 5
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!!!!!
Answer:
x^2+6x+8
Step-by-step explanation:
x x x=x^2
x x2= 2x
4 x x=4x
4 x 2= 8
x^2+2x+4x+8
x^2+6x+8
Berto has $12 and 3.75 per gallon how much gas can he get
Answer:
(3.2, 12)
Step-by-step explanation:
Total cost for gas = $12
Cost per gallon = $3.75
Letting total cost of gas be y and number of gallons be x, maximum number of gallons of gas he can buy would be ;
Total cost of gas/ cost per gallon = 12 / 3.75 = 3.2 gallons
Therefore , the coordinate pair (x, y) = (3.2, 12)
Find the surface area of the cylinder. Round to the nearest tenths.
Answer:
The surface area of the cylinder is 251.2cm²
Step-by-step explanation:
To solve this problem we have to calculate the circle area and the lateral area
radius = half of diameter
r = 10/2 = 5cm
To calculate the area of the circle we use the following formula
a = area
r = radius = 5cm
π = 3.14
a = π * r²
we replace with the known values
a = 3.14 * (5cm)²
a = 3.14 * 25cm²
a = 78.5cm²
The area of the circle is 78.5cm²
To calculate the lateral area of the cylinder we use the following formula
a = area =
h = heighti = 3cm
r = radius = 5cm
π = 3.14
a = 2 * π * r * h
we replace with the known values
a = 2 * 3.14 * 5cm * 3cm
a = 6.28 * 15cm²
a = 94.2cm²
The lateral area of the cylinder is 94.2cm²
Now we add the lateral area of the cylinder with 2 times the area of the circle and obtain the area of the cylinder
94.2cm² + (2 * 78.5cm²) = 251.2cm²
The surface area of the cylinder is 251.2cm²
What is the value of p ?
Answer:
B.
Step-by-step explanation:
First find the other two angles in the triangle using supplementary angles.
They are 90° and 55°
Now just subtract them from 180
180 - 90 - 55 = 35°
Which inverse operations could you use to solve the equation m5−8=−6? Select all that apply.
A
Multiply each side by 5 and then add 8 to each side.
B
Add 8 to each side and then multiply each side by 5.
C
Add 8 to each side and then divide each side by 5.
D
Subtract 8 from each side and then multiply each side by 5.
E
Subtract 6 from each side and then multiply each side by 8.
F
Multiply each side by 5 and then add 40 to each side.
Answer:
Correct option: C
Step-by-step explanation:
To solve the equation m*5 - 8 = -6, we can use the following steps:
step1: sum 8 in both sides, to make m*5 be the only term in the left side.
m*5 = 2
step2: divide both sides by 5, then we will have 'm' isolated in the left side.
m = 2/5
So the operations we could use is: add 8 to each side and then divide each side by 5.
Correct option: C
I Need Help With This Question
Attachment below
Answer & Step-by-step explanation:
For this problem, all we have to do is add f(x) to g(x). So, we will add (x -2) to (x² + x - 6).
(x - 2) + (x² + x - 6)
Combine like terms.
x² + (x + x) + (-2 + (-6))
x² + 2x - 8
So, (f + g)(x) is equal to x² + 2x - 8
Write the coordinates of the image of Q(-3,-6) reflected in the line y=x
HELP PLEASE I RLY NEED HELP URGENT
Answer: (-6, -3)
Step-by-step explanation:
We have the point (-3, -6)
And we want to do a reflection over the line y = x.
When we do a reflection of the point (x, y) over the line y = x. the reflected point will be (y, x)
So if our original point is (-3, -6) then the reflected point is (-6, -3)
Select all of the following statements that are true.
All real numbers are natural numbers.
All whole numbers are integers.
All integers are whole numbers.
All natural numbers are rational numbers.
All irrational numbers are dense.
DONE
Answer:
All whole numbers are integer
All natural numbers are rational numbers
Step-by-step explanation:
Answer:
2, 4, 5
Step-by-step explanation:
edge 2021 :)
What is the sum? 8 + (negative 12)
Answer:
your answer is -4!
Step-by-step explanation:
plz mark me brainliest
plz help
solve for q
Answer: -3
Step-by-step explanation:
-3^2=-3*-3=-9
Because the square of q is equal to -9, the square root of -9 is equal to q.
Because of this fact, we can find the square root of -9 to get our answer.
[tex]\sqrt{-9}[/tex] = 3 i.
Therefore, q is equal to 3 i or [tex]\sqrt{-9}[/tex].
Hope this helped! :)
Harpreet took out a payday loan of $500.00. He had to repay $540.00 within 7 days.
A) What was the daily interest on the loan
B) What was the annual interest?
Answer:
a) 1,14%
b) 317%
Step-by-step explanation
J = C . i . t
540 - 500 = 500 . i . 7
40 = 500 . 7 . i
i = 0,0114 = 1,14% within day
-------------------------------------------
J = 500 . 0,0114 . 365 = 2085,71
2085,71 - 500 = 500 . i . 1
1585,71 = 500 . i
i = 3,17 = 317% annual
Jordan has some music books. He will buy 9 new music books each year. He will have 52 music books in 5 years. Rate of change per year = ____ Initial value = _____
What is the factors of 27
Answer:
1, 27, 3, 9,
Step-by-step explanation:
To find the factors of 27 you need to find which whole number times another whole number = 27
We know that 1*27 = 27
We also know that 3*9 = 27
The factors are all the numbers that are used in the multiplication.
In this example the numbers are: 1, 3, 9 and 27
Answer:
1,9,3,27
Step-by-step explanation:
if we break it down we can see:
1x27=27
9x3=27
A rectangular piece of metal is 25in longer than it is wide . Squares with sides 5in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 750in, what were the original dimensions of the piece of metal
Answer:
Step-by-step explanation:
Let width be x
Let lenght be 25 + x
Total ax = (25+x) * x
Square with 5in long are cut from the four corner formed = 750in
(25+x-10) * (x-10) * 5 = 750
(15+x) (x-10) = 150
15x-150+x^2-10x =150
15x -150-150+x^2-10x+0
x^2+15x-300=0
(ax^2+bx+c=0)
The area of the rectangle is 20 square inches. The rectangle is enlarged by a factor of 6.
What is the area of the enlarged rectangle?
120 in.²
720 in.²
2,400 in.²
14,400 in.²
Answer:
B
Step-by-step explanation:
Here, we are told that the rectangle is enlarged by a factor of 6, we now want to calculate the new area of the said rectangle.
Now, for the rectangle to have an area of 20, mathematically the area of a triangle can be calculated using the formula L * B
where L is the length and B is the breadth
our product here is 20, so any product that gives 20 would be a good fit as the value of the width and length of the rectangle
So, let’s say the sides measure 5 inches by 4 inches
Enlarging these by a factor of 6, we have 30 inches by 24 inches
The new area of the rectangle would thus be ;
30 inches * 24 inches = 720 inches^2
Answer:
b
Step-by-step explanation:
Solve
4(2x - 3) = 6x + 2
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4(2x - 3) = 6x + 2
Expand it:
8x - 12 = 6x + 2
+ 12 to both sides
8x = 6x + 14
- 6x from both sides
2x = 14
Divide both sides by 2:
x = 7
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Evaluate:
a = -3, b = 1, and c= -4
-21 - C
Type the correct answer, then press Enter.
Ar
Answer:the answer is -17
Step-by-step explanation:
Please answer correctly !!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!
Answer:
first box: -14[tex](x+7)^2-49=0\\(x+7)^2=49\\(x+7)=\sqrt{49} \\(x+7)=+/-7\\x=-7+/-7\\x=-7+7\,\,and\,\,-7-7\\x=0\,\,and\,\,-14[/tex]
second box: zero
Step-by-step explanation: