Given:
f(x) is an exponential function where f(3) = 18 and f(7.5) = 60.
To find:
The value of f(12), to the nearest hundredth.
Solution:
Let the exponential function be
[tex]f(x)=ab^x[/tex] ...(i)
It is given that [tex]f(3) = 18[/tex]. Substitute [tex]x=3[/tex] in (i).
[tex]f(3)=ab^3[/tex]
[tex]18=ab^3[/tex] ...(ii)
It is given that [tex]f(7.5) = 60[/tex]. Substitute [tex]x=7.5[/tex] in (i).
[tex]f(7.5)=ab^{7.5}[/tex]
[tex]60=ab^{7.5}[/tex] ...(iii)
Divide (iii) by (ii).
[tex]\dfrac{60}{18}=\dfrac{ab^{7.5}}{ab^3}[/tex]
[tex]\dfrac{10}{3}=b^{4.5}[/tex]
[tex]\left(\dfrac{10}{3}\right)^\frac{1}{4.5}=b[/tex]
[tex]b\approx 1.30676[/tex]
Putting [tex]b=1.30676[/tex] in (ii), we get
[tex]18=a(1.30676)^3[/tex]
[tex]\dfrac{18}{(1.30676)^3}=a[/tex]
[tex]a\approx 8.0665[/tex]
Putting [tex]a=8.0665[/tex] and [tex]b=1.30676[/tex] in (i), we get
[tex]f(x)=8.0665(1.30676)^x[/tex]
Putting x=12, we get
[tex]f(12)=8.0665(1.30676)^{12}[/tex]
[tex]f(12)=200.0024[/tex]
[tex]f(12)\approx 200.00[/tex]
Therefore, the value of f(12) is about 200.00.
find the missing dimension of the cylinder round your answer to the nearest tenth volume = 592ft ³
Answer:
10ft
Step-by-step explanation:
volume= 502 ft³
or, πr²h= 502ft³
or, h= 502/(π×4²)
or, h= 9.98~10
What is 7x2 - 4 + 6x3 - 4x - X4 in standard form?
A 4 - 4x + 7x2 + 6x3 – X4
B. 46-4 - x) + x2(7 + 6x - x2)
C. X4 + 6x3 + 7x2 - 4x - 4
D. –X4 + 6x3 + 7x2 - 4x - 4
Help ASAP
Answer:
the answer is b
Step-by-step explanation:
hope I'm right
Answer:
D. –x^4 + 6x^3 + 7x^2 – 4x – 4
Step-by-step explanation:
When writing in standard form you have to put the monomials from greatest to least according to their exponent.
[tex]-x^4+6x^3+7x^2-4x-4[/tex]
The first number is [tex]-x^4[/tex] because 4 is the greatest exponent we see, then comes [tex]+6x^3[/tex] which is next because it has the second greatest exponent. And so on and so on.
If 2A:3B =5:6 and 3B:2C =36:15, then find A:C
Answer:
Step-by-step explanation:
2A:3B
= 5:6
3B:2C
= 36:15
A:C
= ?:?
2A/3B x 3B/2C
=5/6 x 36/15
=1/1 x 6/3
=1/1 x 2/1
=2
3B and 3B got canceled
For 2A and 2C, the 2 in front of A and C, got canceled as we are cross multiplying.
So I think the answer is
A:C
=1:1 ??
My answer could be wrong.
What is the solution?
WILL GIVE BRAINLIEST
Answer:
its d
Step-by-step explanation:
If m and n are the zeroes of the polynomial 6y 2 -7y – 2, find a polynomial whose zeroes are 1/m and 1/n
Answer:
[tex]y^2-\frac{7}{2}y+3[/tex]
Step-by-step explanation:
Given polynomial is,
6y² - 7y - 2
Fro the zeros of the given polynomial,
6y² - 7y - 2 = 0
6y² - 4y - 3y - 2 = 0
2y(3y - 2) - 1(3y - 2) = 0
(2y - 1)(3y - 2) = 0
(2y - 1) = 0
y = [tex]\frac{1}{2}[/tex]
(3y - 2) = 0
y = [tex]\frac{2}{3}[/tex]
Therefore, zeros of this polynomial are m = [tex]\frac{1}{2}[/tex] and n = [tex]\frac{2}{3}[/tex]
If a polynomial has zeros as [tex]\frac{1}{m}[/tex] and [tex]\frac{1}{n}[/tex] then the zeros will be [tex]\frac{3}{2}[/tex] and 2.
Polynomial will be,
[tex](y-\frac{3}{2})(y-2)[/tex]
= [tex]y(y-2)-\frac{3}{2}(y-2)[/tex]
= [tex]y^2-2y-\frac{3}{2}y+3[/tex]
= [tex]y^2-\frac{7}{2}y+3[/tex]
Write the number in scientific notation.
0.00000515
Answer:
Hi! The answer to your question is D. 5.15 x [tex]10^{-6}[/tex]
Step-by-step explanation:
☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆☆*: .。..。.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
Stay Safe!!!
- Brooklynn Deka
What are the integer solutions to the inequality below?−4≤x<0
4 boxes again
Answer:
-4/-3/-2/-1
Step-by-step explanation:
TGGGGGGGFFFGGGGGGGHTTGTGTGGGHTTGTGTGGTTG
Step-by-step explanation:
TTTGTGTGGGGGGTGDSDJSDQWINE33DHJJJK
find the measure of the angle indicated
Answer:
105
Step-by-step explanation:
x + 25 + 80 = 180
x + 105 = 180
x = 75
x + y = 180
75 + y = 180
y = 105
What's the missing angle?
Answer:
125 and 55
Step-by-step explanation:
The total angle degree of (2x+3) and (x-6) is 180. So, you add both, and set the equation equal to 180 degrees.
2x+3+x-6=180
3x-3=180
3(x-1)=180
x-1=60
x=61
Substitute that for your angles, and you get your answers.
Round your answer to the nearest percent.
Answer:
32%
Step-by-step explanation:
[tex]71 \div 219 = 0.32[/tex]
Please help if you know the answer please
If a car travels 180 km on 12 liters of gas, how many km per liter does the car get? Express in simplest form.
Answer:
5 kilo-meters per liter of gas
Step-by-step explanation:
180 divided by 12 would be 180 / 12 = 5 km per liter
(P.S., pls mark me brainliest, and have a nice day)
how much would a $75 video game be with 8.25% sale tax
Answer:
1 Simplify 75\times 875×8 to 600600.
600\div 25
600÷25
2 Simplify 600\div 25600÷25 to 24
24
Step-by-step explanation:
John is going to the store. His house is located 3 miles south and 4 miles east from the store, as shown below. What is the shortest distance from his house to the store? Explain
Answer:
5 miles
Step-by-step explanation:
It is a right triangle, with 3 miles down, and 4 miles to the right
the shortest distance would be and southeast line.
Using the Pythagorean theorem, you get:
3^2 + 4^2 = x^2
9 + 16 = x^2
25 = x^2
x = 5
Simplify the expression: - ( 4x + 10)
Answer:
-4x-10
hope it help
Answer:
-4x-10
Step-by-step explanation:
Find the missing side
Answer:
15.9
Step-by-step explanation:
because the x side it's the same as 15 but it's slanted a little bit out so there is a bit more to 15
Answer:
A
Step-by-step explanation:
1. Which expression has a value of -28? > A (-20) + 18 : (-3) B 2 – (2) + 48 = (-2) C-3 · 2 – (-22) D -4.5 - 8 Past due. This attempt will be submitted late. Last sav
please help. will mark brainliest
Marriane can say hello in more than 7 languages. Which number line could represent this situation?
Answer:
A) x > 7
Step-by-step explanation:
Since it's more than, the inequality would be >
Since it's >, that means it's an open circle
So,
x > 7
please help_________
Answer:
[tex]11\sqrt{797}\pi[/tex]
Step-by-step explanation:
[tex]A=\pi r \sqrt{h^2+r^2}[/tex]
the radius is 22/2 = 11 in
h is 26 in
substitute: [tex]\pi \left(11\right)\sqrt{\left(26^2\right)+\left(11^2\right)}[/tex]
= [tex]11\sqrt{797}\pi[/tex]
Answer:
286π in²
Step-by-step explanation:
The lateral area (A) of the cone is calculated as
A = πrs ( r is the radius and s the slant height )
Here r = 22 ÷ 2 = 11 and s = 26 , then
A = π × 11 × 26 = 286π in²
can anyone help me to sove it?
In a bakery at night, there are some cupcakes with some flies hovering over them. How many cupcakes are there if both the following statements are true: 1. If each fly lands on a cupcake, one fly doesn’t get a cupcake. 2. If two flies share each cupcake, there is one cupcake left out.
How many people were surveyed altogether?
25
50
40
15
The end points of PG are given. Find the length of segment PQ using the Pythagorean therom p(-4.3) and q(0,5)
Answer:
4.5 cm
Step-by-step explanation:
Given that the end points of PG are given. Find the length of segment PQ using the Pythagorean theorom p(-4.3) and q(0,5)
Solution
Using the formula;
Length PQ = sqrt ( (X - x)^2 + ( Y - y)^2 )
Length PQ = sqrt( ( 0 + 4 )^2 + ( 5 - 3 )^2)
Length pq = sqrt ( 4^2 + 2^2)
Length PQ = sqrt ( 16 + 4 )
Length PQ = sqrt ( 20 )
Length PQ = 4.47 cm
Therefore , the length PQ is 4.5 cm approximately.
pleasee helpppp i need the answer
Answer:
7x-30
Step-by-step explanation:
Please give me BRAINLIEST and THANKS lol <( ̄︶ ̄)>
plaz anser kwik!!!!!!
Answer:
14
Step-by-step explanation:
First we substitute x for 6 and y for 2.4
4(6+2.4)
______ -> 33.6 / 2.4 -> 14
2.4
Find the equation of this line.
9514 1404 393
Answer:
y = 1/2x + 1
Step-by-step explanation:
The slope of the line is "rise"/"run", where "rise" is the vertical distance between two points separated by a horizontal distance of "run".
Here, two points are marked that are 4 units apart horizontally (run = 4). The right-most point is 2 units above the left-most point (rise = 2). The slope between these points is ...
m = rise/run = 2/4 = 1/2
The line crosses the y-axis at y=1, so the "y-intercept" is b=1.
These values can be put into the "slope-intercept form" equation for a line.
y = mx + b . . . . . . line with slope m and y-intercept b
y = 1/2x + 1 . . . . . matches the required answer form
What is the total surface area of the rectangular pyramid whose net is shown?
Answer: 2203.96
Step-by-step explanation:
A university has 29,670 students. In a random sample of 255 students, 17 speak three or more languages. Predict the number of students at the university who speak three or more languages.
A student’s performance in Test 1 and Test 2 for all the 6 subjects has to be compared graphically for the current academic year. Which form of graph would be appropriate in this case? *
Bar Graph
Histogram
Double Bar Graph
Answer:
Double Bar Graph
Step-by-step explanation:
A double bar graph would be suitable to show the performance of test 1 and 2 in all 6 subjects