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.
Please help if you know the answer please
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:
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.
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.
What is the total surface area of the rectangular pyramid whose net is shown?
Answer: 2203.96
Step-by-step explanation:
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 many people were surveyed altogether?
25
50
40
15
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 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:
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
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
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.
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
Round your answer to the nearest percent.
Answer:
32%
Step-by-step explanation:
[tex]71 \div 219 = 0.32[/tex]
What is the solution?
WILL GIVE BRAINLIEST
Answer:
its d
Step-by-step explanation:
please help. will mark brainliest
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
Simplify the expression: - ( 4x + 10)
Answer:
-4x-10
hope it help
Answer:
-4x-10
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]
pleasee helpppp i need the answer
Answer:
7x-30
Step-by-step explanation:
Please give me BRAINLIEST and THANKS lol <( ̄︶ ̄)>
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
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
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 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
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.
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.
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
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
can anyone help me to sove it?
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