Answer:
[tex]f(10) = 173[/tex]
Step-by-step explanation:
Given
Exponential Function
[tex](x_1,y_1) = (3,10.125)[/tex]
[tex](x_2,y_2) = (6,34.2)[/tex]
Required
Determine f(10)
We have that
[tex]y = ab^x[/tex]
First, we need to solve for the values of a and b
For [tex](x_1,y_1) = (3,10.125)[/tex]
[tex]10.125 = ab^3[/tex] --- (1)
For [tex](x_2,y_2) = (6,34.2)[/tex]
[tex]34.2 = ab^6[/tex] ---- (2)
Divide (2) by (1)
[tex]\frac{34.2}{10.125} = \frac{ab^6}{ab^3}[/tex]
[tex]\frac{34.2}{10.125} = \frac{b^6}{b^3}[/tex]
[tex]3.38= b^{6-3}[/tex]
[tex]3.38= b^{3}[/tex]
Take cube root of both sides
[tex]b = \sqrt[3]{3.38}[/tex]
[tex]b = 1.5[/tex]
Substitute 1.5 for b in [tex]10.125 = ab^3[/tex]
[tex]10.125 = a * 1.5^3[/tex]
[tex]10.125 = a * 3.375[/tex]
Solve for a
[tex]a = \frac{10.125}{3.375}[/tex]
[tex]a = 3[/tex]
To solve for f(10).
This implies that x = 10
So, we have:
[tex]y = ab^x[/tex] which becomes
[tex]y = 3 * 1.5^{10[/tex]
[tex]y = 3 * 57.6650390625[/tex]
[tex]y = 172.995117188[/tex]
[tex]y = 173[/tex] -- approximated
Hence:
[tex]f(10) = 173[/tex]
Find the values of a and b so that the linear system has the given solution.
Given Solution: (2, 1)
Equation 1: ax - by'= 4
Equation 2: bx - ay = 10
Answer:
The values are a=6, b=8
Step-by-step explanation:
System of Equations
We are given the system of equations:
ax - by = 4
bx - ay = 10
And it's known the solutions are: x=2, y=1.
Plugging in the solutions:
2a - b = 4 [1]
2b - a = 10 [2]
Now we have to solve the system above. Multiply [1] by 2:
4a - 2b = 8
Now we add with [2]:
3a = 18
a = 18/3 = 6
a = 6
From [2]:
2b - 6 = 10
2b = 16
b = 16/2 = 8
b = 8
The values are a=6, b=8
Simplify |3 - 11| - (15+ 3+2)2
Answer:
-26
Step-by-step explanation:
so, the absolute value of 3 and 11 together is 14.
14-(15+3+2)2
14-(20)2
14-40
-26
Determine the quotient of 1 and 2 over 3 divided by 4 over 5 . (2 points)
1 and 1 over 3
1 and 8 over 15
2 and 1 over 12
2 and 5 over 6
Answer:
2 and 1 over 12
Step-by-step explanation:
[tex]1 \frac{2}{3} \div \frac{4}{5} \\ \\ = \frac{1 \times 3 + 2}{3} \div \frac{4}{5} \\ \\ = \frac{5}{3} \times \frac{5}{4} \\ \\ = \frac{25}{12} \\ \\ = 2 \frac{1}{12} \\ [/tex]
A rectangle of area seven square centimetre is cut into three equel rectangle what is the area of each
7cm^2=2.33cm^2 for each rectangle
factor the following
42x+28y
Answer:
To find the GCF, do the prime factorization of both numbers.
42 = 2 x 3 x 7
28 = 2 x 2 x 7
The GCF uses the numbers that appear in BOTH, 2 x 7 = 14 is the GCF of the numbers. There is no variable GCF because there isn't a variable that appears in both.
Taking out the GCF gives you:
14(3x + 2y)
Step-by-step explanation:
Answer:
14(3x + 2y)
Find the GCF.
It is 14.
Use the distributive property.
Then, multiply each term.
Can someone answer please
Answer:
it's 222
cuz 74•3= 222
....
Answer:
She right
Step-by-step explanation:
find the difference between (-2,3) and (6,3)
Answer:
5.099
Step-by-step explanation:
Answer:
The difference between (-2,3) and (6,3) is 8
Step-by-step explanation:
pls help due soon! lol
Answer:
If there's a point after 2: 13.2
If there's no a point after 2: 1320
Step-by-step explanation:
A= 6[tex]s^{2}[/tex]
Two numbers/variables touching like this means to multiply!
s=2.20
6x2.20= 13.2
-------------------------------------------------------------------------------------
If there is no point, same process, not same answer.
s=220
6x220= 1320
I hope this helped you! If you are still confused, comment so I could give you more info. :D
I need help please.Please
Answer:
Store A
Step-by-step explanation:
Store A
50/100=0.5
0.5×5=2.5
The watch will be 50-2.5=47.5
Store B
60/100=0.6
0.6×20=12
The watch will be 60-12=48
So the watch price in store A is better
Answer:
You should buy from Store A because you're paying $0.50 less than if you were to buy from Store B.
Step-by-step explanation:
First, don't subtract if it's a percentage. You will want to multiply to get the amount you're removing from the original price.
Let's look at Store A. $50 and 5% discount. 50 * 0.05 = 2.5. Remove 2.5 from 50.
50 - 2.5 = 47.5
When you buy from Store A, you will pay $47.5
Let's look at Store B. $60 and 20% discount. 60 * 0.20 = 12. Remove 12 from 60.
60 - 12 = 48
When you buy from Store B, you will pay $48
Ultimately, Store A is the best option because you're paying less.
Mark paid $54.60 to fill his car's gas tank. The gas tank was empty and the cost of gasoline was $3.90 per gallon.
23) You are late for work. You have two options for getting to work. You may take the bus which takes on average 40 minutes with a standard deviation of 12 minutes. Or you can cycle which takes on average 50 minutes with a standard deviation of 2 minutes. Compare these two distributions.
You leave your house at 8.05 am and are supposed to start work at 9.00 am.
Which option would you choose if you will be fired if you are even a few minutes late?
Answer:
either of them because you wont be late because it only takes 52 minutes for both
Step-by-step explanation:
because
Shawn sells 36 vehicles in 4 weeks. Brett sells 56 vehicles in 7 weeks. Who sells more vehicles per week
Answer:
Shawn
Step-by-step explanation:
Shawn sells 36/4 = 9
Brett sells 56/7=8
Therefore , Shawn sells more vehicles per week
Answer: Shawn
Step-by-step explanation:
36 ÷ 4 = 9
56 ÷ 7 = 8
9 is greater than 8 and bc if we divide the numbers it equals how many vehicles per week.
CAN SOMEBODY PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
x-intercept=-2
y-intercept=3
Create the f(x) function based on the table. Answer should be in function notation
Answer:
It will be
f(x)=x+4
A box contain five red balls, a ball is drawn at random, what is the possibility that the ball will be red?
Answer:
yes because it says it only has red balls it didn't say any other color or something
1 over 4 as a decimal
Hey there!
If you want to CONVERT a FRACTION INTO a DECIMAL , all you have to do is this SIMPLE step!
Which is to DIVIDE the NUMERATOR from the DENOMINATOR
The numerator is the TOP number
The denominator is the BOTTOM number
Now let’s solve for your answer
1/4 = 0.25 because 0.25 • 4 = 1
Answer: 0.25 ☑️
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
Evan is making a table that will be created of the figure below. The table top is a triangle attached to a rectangle. To purchase the right amount of paint he needs to know the area of the table top He can only spend 10 on paint which is enough to cover 150ft of surfaces area. What is the max length of the base of the the rectangle he can build
Answer:
23 ft
Step-by-step explanation:
The computation of the maximum length of the base of the triangle is as follows:
Area of triangle is = 4 × 6 ÷ 2
= 12 ft²
Now the maximum area of the rectangle is
= 150 - 12
= 138 ft²
L = ?
W = 6 ft
Area of rectangle is = L × W
L × 6 = 138
L = 138 ÷ 6
= 23 ft
On a very cold morning, it was -7°F. As the day went on, the temperature rose 3 degrees each hour. Which equation shows the temperature over time?
A.y=-3x-7
B.y=-3x+7
C.y=3x-7
D.y=3x+7
Answer:
The equation shows the temperature over time will be:
[tex]y = 3x - 7[/tex]Hence, option (C) is correct.
Step-by-step explanation:
We know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
where m is the rate of change or slope and b is the y-intercept
Let 'y' be the temperatureLet 'x' be the time in the hour
Given that one very cold morning, it was -7°F.
Thus, the y-intercept = b = -7
Given that as the day went on, the temperature rose 3 degrees each hour.
Thus, the rate of change = slope = m = 3
Thus, substituting m = 3 and b = -7 in the equation
[tex]y = mx+b[/tex]
[tex]y = 3x + (-7)[/tex]
[tex]y = 3x - 7[/tex]
Therefore, the equation shows the temperature over time will be:
[tex]y = 3x - 7[/tex]Hence, option (C) is correct.
3415 base 7 ×(-432base 7)
Ignore the negative sign, since that only affects the sign of the final product
3415₇ × 432₇
You can compute the product by considering the digit expansion, by which I mean first expanding each number as sums of powers of 7:
3415₇ = 3000₇ + 400₇ + 10₇ + 5₇
(It's the same thing as writing, for example, the decimal 3415 as 3000 + 400 + 10 + 5, just in a different base.)
Similarly,
432₇ = 400₇ + 30₇ + 2₇
Then apply the distributive property:
= (3000₇ + 400₇ + 10₇ + 5₇) × (400₇ + 30₇ + 2₇)
= 3000₇ × (400₇ + 30₇ + 2₇)
… + 400₇ × (400₇ + 30₇ + 2₇)
… + 10₇ × (400₇ + 30₇ + 2₇)
… + 5₇ × (400₇ + 30₇ + 2₇)
= {12}00000₇ + {9}0000₇ + 6000₇
… + {16}0000₇ + {12}000₇ + {8}00₇
… + 4000₇ + 300₇ + 20₇
… + {20}00₇ + {15}0₇ + {10}₇
where I use the curly braces to indicate products (written in base 10) of digits that exceed 6. Anything in these braces needs to be properly converted to base 7. For example,
{12}₇ = 7 + 5 = 15₇
So you would have
= 1500000₇ + 120000₇ + 6000₇
… + 220000₇ + 15000₇ + 1100₇
… + 4000₇ + 300₇ + 20₇
… + 2600₇ + 210₇ + 13₇
Add everything up:
• In the 7⁰ place,
3₇
• In the 7¹ place,
1₇ + 1₇ + 2₇ = 4₇
• In the 7² place,
2₇ + 6₇ + 3₇ + 1₇ = {12}₇ = 15₇
• Carry the 1 (underlined). In the 7³ place,
2₇ + 4₇ + 1₇ + 5₇ + 6₇ + 1₇ = {19}₇ = 25₇
• Carry the 2. In the 7⁴ place,
1₇ + 2₇ + 2₇ + 2₇ = {7}₇ = 10₇
• Carry the 1. In the 7⁵ place,
2₇ + 1₇ + 5₇ + 1₇ = {9}₇ = 12₇
• Carry the 1. In the 7⁶ place,
1₇ + 1₇ = 2₇
So, we end up with
3415₇ × 432₇ = 22045543₇
and thus
3415₇ × (-432₇) = -22045543₇
Use the table below to answer the question.
Price Quantity Supplied of T-shirts Quantity Demanded of T-shirts
$5
0
300
$10
100
100
$25
300
50
$50
400
0
At the highest price of $50, producers supply _____ T-shirts and consumers demand _____T-shirts.
100, 100
0, 300
400, 0
Answer: 400,0
Step-by-step explanation:
I just took this on Ody
What is the slope for these graphs ?
an amusement park sold 46 child tickets. The other 4 tickets it sold were adult tickets. What is the ratio of the number of adult tickets to the number of child tickets? Select all correct ratios
Answer:
2:46
1:23
Step-by-step explanation:
24x2+10x-4
Please help me
Answer:
the answer is 8!
Step-by-step explanation:
hope this helped! <3
Which The following radical functions is graphed below
Answer:
Option A
Step-by-step explanation:
From the graph attached,
Vertical asymptote of the given function → x = -4
Horizontal asymptote → y = 0
Oblique asymptote → None
Therefore, graph that has been given in the picture is,
F(x) = [tex]\frac{1}{(x+4)^2}[/tex]
Option (A) will be the answer.
(8x+1)÷5=3x-6
find x
Answer:
31/7
Step-by-step explanation:
8x+1 = 15x-30
31 = 7x
(31/7) = x
Answer:
8x + 1 =3x-6
--------
5
8x+1=15x-30
8x-15x= -30-1
-7x=-31
x=31
---
7
x=4.42
equation of a line in slo[e-intercept form given the slope = 6 and it passes through the point (1, 8)
Answer:
math way
Step-by-step explanation:
Which is the equation of a line that is perpendicular to the line
y
=
−
5
x
+
11
?
Answer:
y=1/5x
Step-by-step explanation:
hopefully that helped
3. Leeland can eat 1 hotdog in 20 minutes. What is his unit rate in hotdogs
per hour?
A 1/2 a hotdog per hour
B 1 hotdogs per hour
C 2 hotdogs per hour
D hotdogs per hour
Answer:
Hi how are you doing today Jasmine
Answer:
i think more then the awnsers that are givin or im just being a dummy
Step-by-step explanation:
Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x?
Answer:
X=1 = i√19 Put a vertical line through the second = sign
Step-by-step explanation:
when writing this .....put a line under all the + signs 0k and / is divided by 2
2 + √4-4(1)(20)
2 + √4-80 /2
x=2 +√76/2
x=2 +2i√19 the twos cancel out
1 +i√19
answer the following questions:
1. 2/3 is what percent of 1/4?
2. 2/3 is what percent of 1/6?
Answer:
1. 37.5%
2.25%
Step-by-step explanation:
1.
2/3 and 1/4
What percent = x/100
0.25/2/3=x/100
25=2/3x
x=37.5
37.5%
2/3 and 1/6
1/6/2/3=x/100
16 2/3=2/3x
25%
Hope this helps plz hit the crown :D
Answer:
THANKS
Step-by-step explanation: