Answer:
Step-by-step explanation:
The given expression represents exponential growth. The expression is written as
20,000(1.05)^t
Where
20000 represents the initial population of the town in 2005.
1.05 represents the rate at which the population is increasing each year after 2005. The actual growth rate is
0.05 × 100 = 5%
t represents the number of years after 2005
Therefore, the complete sentence would be
The population of the town is increasing by 5% each year.
Please help!!
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He started at 90 kilograms and gained weight at a constant rate of 8 lbs. a week.
a. Write a function to represent this situation. Use x and y as your variables.
b. What would his weight be after 8 weeks?
Answer:
A. y=90+8x
B. After 8 weeks he would be 154 pounds.
Step-by-step explanation:
You use the equation and plug in your x variable as 8 and you get 154 as the y.
Help ASAP please ! Explain too!
Answer: D
Step-by-step explanation:
simplify
Answer:
When dealing with area (2 dimensions) when we deal with a one dimensional quantity (distance) it changes a 2 dimensional quantity by the square of the difference.
Comparing a 3, 4, 5 triangle to a 6, 8, 10 triangle, the larger triangle has 4 times the area of the smaller triangle.
20) 6 / 4 = 1.5 1.5 ^2 = 2.25
Therefore, ABC's area is 2.25 larger than A'B'C's area.
21) 21 / 7 = 3 and 3^3 = 9
Therefore, ABC's area is 9 times larger than A'B'C's area.
Step-by-step explanation:
Convert the expression 9 1/2to radical form.
Answer:
Radical Form is 1/√9
Step-by-step explanation:
Also, the decimal version is 0.3 repeating
Answer:
[tex]\sqrt[2]{9}[/tex]
Step-by-step explanation:
To find radical form with fractions , put the whole number (i.e 9) inside the square root, the denomination in the top of the square root (i.e 2) and the numerator is the power of the number inside the square root (in this case it is one so you would not put it there.)
What is the value of cos(150°)?
Final answer:
The value of cos(150°) is -0.866.
Explanation:
The value of cos(150°) can be determined using the unit circle or trigonometric ratios. Since 150° is in the second quadrant, the cosine value is negative. In the second quadrant, the reference angle is 180° - 150° = 30°. The reference angle corresponds to the angle on the unit circle with the same cosine value.
In the first quadrant, the cosine value is positive. The cosine of 30° is 0.866 (approximately). Since the angle is in the second quadrant, the cosine value will be the same but negative. Therefore, the value of cos(150°) is -0.866.
given that f(x)=19x+6, what’s f(3)
Answer:
f(3)=63
Step-by-step explanation:
We want to find out what y is, when x is equal to 3.
f(x)=19x+6
To solve for f(3) substitute 3 in for x.
f(3)=19(3)+6
Multiply
f(3)=57+6
Add
f(3)=63
What are the period and amplitude of the function?
Answer:
Period is 4, Amplitude is 3.5
Step-by-step explanation:
The Period is how far in the x direction for a function to repeat. This function repeats at (1,5), (5,5), etc. 5-1 = 4 difference between points which is the period.
The Amplitude is defined as the vertical distance from the center. The maximum vertical distance is 5 and the minimum is -2. 5-(-2) = 7. 7/2 = 3.5. 3.5 is the average which is the amp.
The solution is :Period is 4, Amplitude is 3.5, of the function.
What is wavelength?The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.
The wavelength is also defined as the distance between two locations in a wave that have the same oscillation phase.
here, we have,
The Period is how far in the x direction for a function to repeat.
This function repeats at (1,5), (5,5), etc.
5-1 = 4 difference between points which is the period.
we have,
The Amplitude is defined as the vertical distance from the center.
The maximum vertical distance is 5 and the minimum is -2.
5-(-2) = 7.
7/2 = 3.5.
3.5 is the average which is the amp.
To learn more about the wavelength refer to the link;
brainly.com/question/7143261
#SPJ3
Price, in dollars, of bicycles: 150, 134, 136, 120, 145, 170, 125, 130, 145, 190, 140 box plots
Answer:
Arrange this data in numerical order:
120, 125, 130, 134, 136, 140, 145, 145, 150, 170, 190
We have 11 observations.
Minimum = 120
First quartile = 130
Median = 140
Third quartile = 150
Maximum = 190
Check for outliers:
130 - 1.5(150 - 130) = 100
150 + 1.5(150 - 130) = 180, so 190 is an outlier.
See the attachment.
3(x-2)<2(x+9)How do you slove this??
Answer:
x<24
Step-by-step explanation:
3(x-2)<2(x+9)
Distribute
3x - 6 < 2x+18
Subtract 2x from each side
3x-2x -6 < 2x-2x+18
x - 6 < 18
Add 6 to each side
x-6+6 <18+6
x<24
A rectangle has a height of w^2 +3w+9 and a width of w^2+2 what’s the area
Answer:
Two solutions were found :
w = 1
w = -4
Step-by-step explanation:
w =(-3+√25)/2=(-3+5)/2= 1.000
or:
w =(-3-√25)/2=(-3-5)/2= -4.000
Answer: w^4+3w^3+11w^2+6w+18
Step-by-step explanation:
Gasoline is sold by the gallon. If 5 gal costs $17.35, how much would 12 gal cost?
Answer: $41.64
Step-by-step explanation: $17.37/5=3.47, so 3.47 x 12 = $41.64
How do you find Radius with just the circumference? An Equation Would be
Preferred. Thanks
answer:
c =
[tex]2\pi r[/tex]
or
[tex]\pi \: d[/tex]
Answer:
To find the radius with just the circumference is with this formula:
R = C ÷ (2 × π)
Or just divide the circumference by 2 times pi.
Here's an example:
The circumference is 26
R = C ÷ (2 × π)
R = 26 ÷ (2 × 3.14)
R = 26 ÷ 6.28
R = 4.140127388535032 or 4.1
Hope this helped
which unit could be used to measure area? yards ,miles ,square inches and pounds.
Answer:
square inches
Step-by-step explanation:
like u can do
square yards
square miles
but it has to have a "square"
so it is square inches
Answer:
square inches
Step-by-step explanation:
Did quiz
witch table has the constant of proportionality between y and x of 8/5
table 1 table 2 table 3
4 32/5 2 14/5 5 20/3
10 16 6 42/5 9 12
11 88/5 20 28 12 16
Answer:
Table 1
Step-by-step explanation:
Constant of proportionality is simply the ratio of y to x. In each of the given tables, the second column is y and the first is x.
Table 1:
4 32/5
10 16
11 88/5
Let's find the constant of proportionality for each row:
R1: (32/5) / 4 = 8/5
R2: 16/10 = 8/5
R3: (88/5) / 11 = 8/5
Thus, since this matches the requirements and all three rows have the same constant, Table 1 is the answer.
If you check the other two tables in the same way, you'll see that neither has a constant of proportionality of 8/5.
Hope this helps!
Answer:
Table 1
Step-by-step explanation:
y = (8/5)x
32/5 = 8/5 × 4
32/5 = 32/5
16 = 32/5 × 10
16 = 16
88/5 = 8/5 × 11
88/5 = 88/5
Find the 4th term in the sequence with the following definition: See picture for sequence.
Please need help badly!!
Answer:
a₄ = - 37
Step-by-step explanation:
To find the 4 th term using the recursive formula and a₁ = - 2
a₂ = 2a₁ - 3 = 2(- 2) - 3 = - 4 - 3 = - 7
a₃ = 2a₂ - 3 = 2(- 7) - 3 = - 14 - 3 = - 17
a₄ = 2a₃ - 3 = 2(- 17) - 3 = - 34 - 3 = - 37
Which point is located at (4,8)?
A) A
B) B
C) C
D) D
Answer:
C
Step-by-step explanation:
Start at the origin
Go to the right 4 units
Go up 8 units
We will end up at point C
Answer:
The coordinate of C is (4,8)
NEED HELP ASAP!
Use the net as an aid to compute the surface area of the triangular prism.
A) 108 cm2
B) 120 cm2
Eliminate
C) 132 cm2
D) 170 cm2
Answer:
Hi There the correct answer to this is C) 132 cm2
Step-by-step explanation:
All you really need to do is 1 base = 8 × 6 = 48
2 sides = 2(5 × 6) = 60
2 triangles = 2(8 × 32) = 24
SA = 48 + 60 + 24 = 132 cm2
So Hope That Helps!
Answer:
132 cm^2
Step-by-step explanation:
Given the function h(a) = -x^2+ 7x + 14, determine the average rate of change
of the function over the interval 1 < x < 8.
Answer:
Submit Answer
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Answer:
- 2
Step-by-step explanation:
The average rate of change of h(x) in the closed interval [a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [a, b ] = [1, 8 ], thus
f(b) = f(8) = - 8² + 7(8) + 14 = - 64 + 56 + 14 = 6
f(a) = f(1) = - 1² + 7(1) + 14 = - 1 + 7 + 14 = 20
average rate of change = [tex]\frac{6-20}{8-1}[/tex] = [tex]\frac{-14}{7}[/tex] = - 2
PLEASE ANSWER ASAP !!!!!
The difference of 3 times a number and 15 is no less than the square of the number.
Select the inequality that represents this relationship.
+
OA. 3.+ 15 > 12
O B. 3. s
OC. 31 < x2
OD. 3.-
I AL
GELABAIE VREME
O
FALSE
the First
Reset
Next
Answer: D
Hope this helps!
sorry about the first answer
|x+3|=-2
This answer does not have two solutions...why?
Step-by-step explanation:
|x+3| = -2 doesn't have a solution because the exact values can't be negative
Pls i need help my brain won't think straight
Rocky because of the product rule which says that when multiplying two terms with the same base you add the exponents.
(1, 5)(2, 8)(3, 11)(4, 14)(5, 17)(6, 20)(7, 23) A) y = 3x - 2 B) y = 3x + 2 C) y = -3x + 2 D) y = 1 3 x - 2 3
Answer:
y = 3x+2
Step-by-step explanation:
First we need to find the slope
m = (y2-y1)/(x2-x1)
= (23-20)/(7-6)
=3/1
We know the slope is 3
Using the slope intercept form of a line
y= mx+b where is the slope and b is the y intercept
y = 3x+b
Using a point (1,5)
5 = 3(1)+b
Subtract 3 from each side
5-3= 3-3+b
2 = b
y = 3x+2
Answer:
B) y = 3x + 2
Step-by-step explanation:
Slope: (8 - 5)/(2 - 1)
= 3/1 = 3
y = 3x + c
5 = 3(1) + c
c = 5 - 3
c = 2
y = 3x + 2
What's |5| + |–7|?
Question 8 options:
A)
–12
B)
–2
C)
12
D)
2
Answer:
C) 12
Step-by-step explanation:
Absolute value always means it is the positive version of the number
This switches -7 to 7 and 5 stays the same.
5 + 7 = 12
The absolute value returns the "positive version" of a number. This means that if the number is already positive, it does nothing. Otherwise, it gets rid of the negative sign.
So, you have
[tex]|5|=5,\quad |-7|=7[/tex]
and thus
[tex]|5|+|-7|=5+7=12[/tex]
I need to find x and y
Answer:
[tex]x = - 2 \\ y = - 4[/tex]
Step-by-step explanation:
[tex] - 2x + 2y = - 4 \: \: \: \: \: \\ i.e. \: \: \: - x + y = - 2 \: \: \: \: \: \: \: ...(1)\\ \\ 3x + 3y = - 18 \\ i.e. \: \: \: \: \: \: x + y = - 6\: \: \: \: \: \: \: ...(2)[/tex]
From (1) we get
[tex] x = 2 + y[/tex]
Now put x = 2 + y in equation (2)
[tex]2 + y + y = - 6 \\ 2 + 2y = - 6 \\ 2y = - 6 - 2 \\ 2y = - 8 \\ \\ y = - \frac{8}{2} \\ \\ y = - 4[/tex]
now put y = -4 in equation (1) we get
[tex] - x + ( - 4) = - 2 \\ - x - 4 = - 2 \\ x + 4 = 2 \\ x = 2 - 4 \\ x = - 2[/tex]
The number of users on a website has grown exponentially since its launch. After 2 months, there were 90 users. After 4 months, there were 810 users. Find the exponential function that models the number of users x months after the website was launched. Write your answer in the form f(x)=a(b)x.
Answer:
10(3)^x
Step-by-step explanation:
The function contains the points (2,90) and (4,810). Use the general form y=abx to write two equations:
90=ab^2 and 810=ab^4
Solve each equation for a:
a=90/b^2 and a=810/b^4
Since a=a, set the other sides of the equations equal and solve for b.
90/b2=810/b4
Cross multiply, then divide and simplify as follows:
90b^4=810b^2
b^4/b^2=810/90
b^2=90
b^3
Now, use the value of b and the point (2,90) to find the value of a.
90=a(3^2)
a=10
So, substitute answers in original equation for a final answer of f(x)=10(3)^x.
What is the measure of AC?
Answer:
41°
Step-by-step explanation:
∡ABC = (DE+AC)/2 = 39°
AC = 39*2-DE = 78° - 37° = 41°
What is the y- intercept of y= -3x
Answer: (0,0) or y=0
In order to find the y-intercept, we need to find the point that crosses the y-axis. To find that x=0 or (0,y)
When x=0, y=0 on the graph since there are no transformations.
Simplify each expression.
[tex] \frac{2x - 16}{8x ^{3} + 56x {}^{2} } \times \frac{x + 7}{x ^{2} - 7x - 8 } [/tex]
Answer:1
Step-by-step explanation: yea
Answer:
[tex]\frac{1}{4x^2\left(x+1\right)}[/tex]
Step-by-step explanation:
[tex]\frac{2x-16}{8x^3+56x^2}\cdot \frac{x+7}{x^2-7x-8}[/tex]
You first factor things out.
[tex]\frac{x-8}{4x^2\left(x+7\right)}\cdot \frac{x+7}{x^2-7x-8}[/tex]
You then multiply. (Cancel common factor, X+7)
[tex]\frac{x-8}{4x^2\left(x^2-7x-8\right)}[/tex]
You factor again.
[tex]\frac{x-8}{4x^2\left(x+1\right)\left(x-8\right)}[/tex]
Then cancel out common fact x-8.
So therefore, you get the final answer,
[tex]\frac{1}{4x^2\left(x+1\right)}[/tex]
Solve cot x + 2cot x * sin x = 0 for U^ <= x<=180
Answer:
Step-by-step explanation:
hello :
cot x + 2cot x sin x = 0 0≤ x≤ 180
cotx(1+2sinx) =0 means : cotx=0 or 1+2sinx=0
1) cotx=0 so : cosx=0 and sinx ≠ 0 because cotx = cosx/sinx
when : 0≤ x≤ 180 : x=90°
2) 1+2sinx=0 means : sinx = -1/2
when : 0≤ x≤ 180 : no solutions because : sinx ≥ 0
conclusion : one solution : x=90°
The answer an example how to do it
Answer:
≈ 1347 mi²
Step-by-step explanation:
The shaded area is the difference between the outer area and the inner area
shaded area = outer - inner
= πr₁² - πr₂²
where r₁ = 14 + 11 = 25 and r₂ = 14, thus
A = π × 25² - π × 14² = 625π - 196π = 429π = 429 × 3.14 ≈ 1347 mi²
Answer:
Step-by-step explanation:
Area of the shaded region = Area of the Outer circle - Area of the inner circle
Outer circle:
r = 14+11 = 25 mi
Area = πr² = π*25²
Inner Circle:
r = 14 mi
Area = πr² = π*14²
Area of shaded region = π*25² - π*14²= π(25² - 14²)
= 3.14*(625 - 196)
=3.14*429
= 1347.06 mi²
Angel has finished 75% of an art project that has taken
him a total of 9 hours so far. If he continues to work at
the same rate, how many hours will it take for him to
complete the entire project?
Answer: 12 hours
Step-by-step explanation: For this problem we will write a percent equation to solve for 100% and how many total hours it will take angel to finish the entire project.
Lets write a equation to solve for w, total amount of hours.
9/w = 75/100
9/w x w = 75/100 x w
9 = 75w/100
9 x 100/75 = 75w/100 x 100/75
w = 12
So, it will take Angel 12 hours to finish his entire project.
Final answer:
Angel will need 3 more hours to complete the art project, for a total of 12 hours when he continues to work at the same rate.
Explanation:
Angel has completed 75% of his art project in 9 hours. To find out how much time it will take to complete the entire project, we need to determine the time taken to complete 100% of the project. First, we calculate the time taken for 1% of the work, which is 9 hours divided by 75 (the percentage completed so far). This gives us 0.12 hours per percent.
Now, we can find out the total time for 100% completion by multiplying 0.12 hours by 100, which totals 12 hours. Since Angel has already completed 9 hours of work, the remaining time to finish the project is 12 hours minus 9 hours, which equals 3 more hours of work.