Answer: D. Reflect across the x-axis, and then reflect again over the x-axis.
Explanation:
If we reflect over the x axis, and then reflect over that same axis again, then we arrive at the original image. Nothing has changed. This is because the two reflections effectively cancel each other out.
It's like taking one step forward, then taking one step back. You haven't moved at all.
The population, P, of six towns with time t in years are given by the following exponential equations:
(i) P = 1000 (1.08) Superscript t (ii) P = 600 (1.12) Superscript t
(iii) P = 2500 (0.9) Superscript t (iv) P = 1200 (1.185) Superscript t
(v) P = 800 (0.78) Superscript t (vi) 2000 (0.99) Superscript t
Which town decreasing the fastest?
a.
ii
c.
iii
b.
v
d.
vi
Please select the best answer from the choices provided
A
B
C
D
Given:
The population, P, of six towns with time t in years are given by the following exponential equations:
(i) [tex]P=1000(1.08)^t[/tex]
(ii) [tex]P = 600 (1.12)^2[/tex]
(iii) [tex]P =2500 (0.9)^t[/tex]
(iv) [tex]P=1200 (1.185)^t[/tex]
(v) [tex]P=800 (0.78)^t[/tex]
(vi) [tex]P=2000 (0.99)^t[/tex]
To find:
The town whose population is decreasing the fastest.
Solution:
The general form of an exponential function is:
[tex]P(t)=ab^t[/tex]
Where, a is the initial value, b is the growth or decay factor.
If b>1, then the function is increasing and if 0<b<1, then the function is decreasing.
The values of b for six towns are 1.08, 1.12, 0.9, 1.185, 0.78, 0.99 respectively. The minimum value of b is 0.78, so the population of (v) town [tex]P=800 (0.78)^t[/tex] is decreasing the fastest.
Therefore, the correct option is b.
Cos 600 degrees solved by double angle formula (20 points)
show work please :)))
Answer:
[tex] \rm\cos({600}^{ \circ} ) =-1/2 [/tex]
Step-by-step explanation:
we would like to solve the following using double-angle formula:
[tex] \displaystyle \cos( {600}^{ \circ} ) [/tex]
there're 4 double Angle formulas of cos function which are given by:
[tex] \displaystyle \cos(2 \theta) = \begin{cases} i)\cos^{2} ( \theta) - { \sin}^{2}( \theta) \\ii) 2 { \cos}^{2}( \theta) - 1 \\iii) 1 - { \sin}^{2} \theta \\ iv)\dfrac{1 - { \tan}^{2} \theta}{1 + { \tan}^{2} \theta } \end{cases}[/tex]
since the question doesn't allude which one we need to utilize utilize so I would like to apply the second one, therefore
step-1: assign variables
to do so rewrite the given function:
[tex] \displaystyle \cos( {2(300)}^{ \circ} ) [/tex]
so,
[tex] \theta = {300}^{ \circ} [/tex]Step-2: substitute:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \cos ^{2} {300}^{ \circ} - 1[/tex]
recall unit circle thus cos300 is ½:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \left( \dfrac{1}{2} \right)^2 - 1[/tex]
simplify square:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2\cdot \dfrac{1}{4} - 1[/tex]
reduce fraction:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = \dfrac{1}{2} - 1[/tex]
simplify substraction and hence,
[tex] \rm\cos({600}^{ \circ} ) = \boxed{-\frac{1}{2}}[/tex]
SOMEONE PLEASE HELP ME OUT ON THIS. PLEASE!
n= 1. then a1= 7+3(1)
How to solve it.
Answer:
I think this is right for the 2nd problem
Step-by-step explanation:
a1=7+(3)(1)
Step 1: Simplify both sides of the equation.
a1=7+(3)(1)
a=7+3
a=(7+3)(Combine Like Terms)
a=10
a=10
Answer:
a=10
20) solve:
[tex] {8}^{2} + 2 = [/tex]
21) solve:
[tex]4(2x + 5y = [/tex]
22) simplify the expression
[tex]4( {2}^{2} + 30) - 4 = [/tex]
please help have a lot of math to do today
Answer:
115 in.^2
Step-by-step explanation:
The total surface area is the sum of the areas of the square base and the 4 congruent triangular faces.
SA = b^2 + 4 * bh/2
SA = (5 in.)^2 + 4 * (5 in.)(9 in.)/2
SA = 25 in.^2 + 2 * 45 in.^2
SA = 115 in.^2
PLEASE SOMEONE SOLVE B) I ALREADY KNOW 1. A) Is 75.875m^2
The diameter of a $1 coin is 26.5 mm. Find the area of one side of the coin. Round to the nearest hundredth.
The area of one side of the coin is 41.605 mm².
Given that, the diameter of a $1 coin is 26.5 mm.
We need to find the area of one side of the coin.
What is the area of a circle formula?The area of a circle formula is A=πr².
Now, radius=26.5/2=13.25 mm.
Area of a coin=3.14×13.25=41.605 mm².
Therefore, the area of one side of the coin is 41.605 mm².
To learn more about the area of the circle visit:
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You have two squares. The larger square has a side of 3 more than the smaller square. If the combined area of the two squares is 89 cm squared. What is the length of the smaller square.
A. 3
B. 5
C. 8
D. 10
(2/1.3)+(2/3.5)+(2/5.7)+ ... + (2/97.99) > 98%
Step-by-step explanation:
gxhkmnjggggffffffcccccccccccc
What is the measure of m?
6
24
n
m
m =
[?]
Enter
the measure of m is24 according to the questions
Point S lies between points R and T on Line segment R T. A line contains points R, S, T. The space between R and S is 2 x. The space between S and T is 3 x. If RT is 10 centimeters long, what is ST?
Answer:
[tex]ST = 6cm[/tex]
Step-by-step explanation:
Given
[tex]RS =2x[/tex]
[tex]ST = 3x[/tex]
[tex]RT = 10[/tex]
Required
Find ST
From the question, we understand that S is between R and T.
So:
[tex]RS + ST = RT[/tex]
Substitute known values
[tex]2x + 3x = 10[/tex]
[tex]5x =10[/tex]
Divide both sides by 5
[tex]x =2[/tex]
Given that:
[tex]ST = 3x[/tex]
[tex]ST = 3 * 2[/tex]
[tex]ST = 6cm[/tex]
Answer:
C or 6 centimeters
Step-by-step explanation:
Which statement is true about this quadratic equation?
y = 12 – 11x + 7
A.
There is one real solution.
B.
There are two complex solutions.
C.
There are two real solutions.
D.
There is one complex solution,
The statement that is true about the quadratic equation is (b) There are two complex solutions.
Identifying the statement that is true about the quadratic equationFrom the question, we have the following parameters that can be used in our computation:
y = 12 – 11x + 7
Express properly
So, we have
y = 12x² – 11x + 7
Next, we calculate the discriminant using
d = b² - 4ac
Where
a = 12
b = -11
c = 7
Substitute the known values in the above equation, so, we have the following representation
d = (-11)² - 4 * 12 * 7
Evaluate
d = -215
This value is less than 0
This means that it has complex solutions
Read more about quadratic functions at
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Read is solving the quadratic equation 0 equals X over two minus 2X -3 using the quadratic formula which shows the correct substitution of the values ABC into the quadratic formula quadratic formula X equals negative B+
Answer:
[tex]x = \frac{-(-2) \± \sqrt{(-2)^2 - 4*1*-3}}{2*1}[/tex]
Step-by-step explanation:
Given
[tex]0 = x^2 - 2x -3[/tex]
Required
The correct quadratic formula for the above
A quadratic equation is represented as:
[tex]ax^2 + bx + c = 0[/tex]
And the formula is:
[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
So, we have:
[tex]0 = x^2 - 2x -3[/tex]
Rewrite as:
[tex]x^2 - 2x - 3 = 0[/tex]
By comparison:
[tex]a= 1; b = -2; c = -3[/tex]
So, we have:
[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]x = \frac{-(-2) \± \sqrt{(-2)^2 - 4*1*-3}}{2*1}[/tex]
Please help explanation if possible
Answer: y = -3x + 5
Step-by-step explanation:
slope = m
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-4)}{1-3}=\frac{6}{-2}=-3[/tex]
y = mx + b, (3,-4), (1,2), m = -3
(both points work for the y = mx + b equation)
[tex]y=mx+b\\2=-3(1)+b\\2=-3+b\\b=5\\y=-3x+5[/tex]
Find the missing side. Round your answer to the nearest tenth. 19, 36
Answer:
x=110.6
Step-by-step explanation:
sin(19)=36/x. x=36/sin(19)=110.6
BRAINLIET TO THE FIRST.....AND PLZZ HURRY.....
What is the volume of the oblique cone? Round to the nearest tenth.
Formula for the volume of a cone: V = 1/3 x pi x r^2 x h
Since this is a right cone, the height is given as 8.5 and the radius is 4.
V = 1/3 x pi x 4^2 x 8.5
V = 1/3 x pi x 16 x 8.5
V = 1/3 x pi x 136
V = 45 1/3 pi
V = 142.4 cubic units
Hope this helps!
Answer:
142.4 units^3
Step-by-step explanation:
We use the same formula for volume as for a cone
V = 1/3 pi r^2 h
V = 1/3 pi (4)^2 ( 8.5)
= 1/3 pi (16)(8.5)
Letting pi = 3.14
=142.34666667
Rounding to the nearest tenth
= 142.4
Can anyone answer this for me?
Answer:
y = 2 - [tex]x^{2}[/tex]
Step-by-step explanation:
[tex]x^{2}[/tex] results in a parabola (U-shape). Adding a negative in front of it flips the parabola to look like an upside-down U.
The 2 makes it shift up two decimal spots to (0,2).
12.915 to 2 decimal places
Answer:
12.92
Step-by-step explanation:
rounding the 1 hundredth up to 2 because of the 5 thousandth
Answer:
12.915 to 2.d.p :12.92Step-by-step explanation:
See explanation in attached image
a sum of money Doubles itself in 5 years what is rate of simple interest
Step-by-step explanationIf you are reading this say
thank u
Can someone pls help with this
here it is :)
do check properly, I have given step by step instructions:)
do give feedback on my answer, would appreciate it!
Answer:
900000
Step-by-step explanation:
[tex]30*10^{4}[/tex]
=3*10000
=30000
=30*30000
=900000
A particle moves along a line with a velocity v(t)=t2−t−6, measured in meters per second. Find the total distance the particle travels from t=0 seconds to t=4 seconds.
The total distance the particle travels from t=0 seconds to t=4 seconds would be 11.33 meters.
Used the concept of integration that states,
In Maths, integration is a method of adding or summing up the parts to find the whole. It is a reverse process of differentiation, where we reduce the functions into parts.
Given that,
A particle moves along a line with a velocity v(t) = t² - t - 6, measured in meters per second.
Now the total distance the particle travels from t=0 seconds to t=4 seconds is,
D = ∫₀⁴ |(t² - t - 6)| dt
D = ∫₀⁴ (t²) dt - ∫₀⁴ (t) dt - ∫₀⁴ (6) dt
D = (t³/3)₀⁴ - (t²/2)₀⁴ - 6 (t)₀⁴
D =| (64/3) - (16/2) - 6 (4)|
D = | (64/3) - 8 - 24 |
D = | (64/3) - 32|
D = 11.33 meters
Therefore, the total distance is 11.33 meters.
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Name the property shown by the statement a + b + 2 = 2 + a + b
Complete the statements.
f(4) is
f(x) = 4 when x is
Find the value of m if x + m is a factor of x^2 - 5mx + 3
Answer:
+or- sqrt(3/4)
Step-by-step explanation:
If x + m is a factor, that means that when x = -m the equation equals 0. Sub -m into x
0 = (-m)^2 - 5m(-m) + 3
0 = m^2 - 5m^2 + 3
0 = -4m^2 + 3
Factorise
0 = -4(m^2 - 3/4)
0 = -4(m + sqrt(3/4))(m - sqrt(3/4))
:. m = +or- sqrt(3/4)
Guys please help me solve this problem, yes I will mark brainliest
Given that the vertex is at (50, 1000), the max profit is $1000 when 50 items are produced
The graph below could be the graph of which exponential function?
Answer:
B
Step-by-step explanation:
please show work it’s for calc
Answer:
24
Step-by-step explanation:
The question is asking for the net area from x=3 to x=10.
It gives you the net area from x=3 to x=5 being -18.
It gives you the net area from x=5 to x=10, being 42.
Together those intervals make up the interval we want to find the net area for.
-18+42=42-18=24
Answer:
[tex]\displaystyle \int\limits^{10}_3 {f(t)} \, dt = 24[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Property [Splitting Integral]: [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int\limits^{5}_3 {f(t)} \, dt = -18[/tex]
[tex]\displaystyle \int\limits^{10}_5 {f(t)} \, dt = 42[/tex]
[tex]\displaystyle \int\limits^{10}_3 {f(t)} \, dt[/tex]
Step 2: Integrate
[Integral] Rewrite [Integration Property - Splitting Integral]: [tex]\displaystyle \int\limits^{10}_3 {f(t)} \, dt = 24 = \int\limits^5_3 {f(t)} \, dt + \int\limits^{10}_5 {f(t)} \, dt[/tex][Integrals] Substitute: [tex]\displaystyle \int\limits^{10}_3 {f(t)} \, dt = 24 = -18 + 42[/tex]Simplify: [tex]\displaystyle \int\limits^{10}_3 {f(t)} \, dt = 24[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
SEE QUESTION IN IMAGE
Answer:
c) 11.5Step-by-step explanation:
Total frequencies:
6 + 15 + 20 + 7 + 2 = 50Median group is the containing the middle - 25th and 26th frequencies. This is the 11-15 interval.
Estimated median formula:
Estimated Median = L + ((n/2) − B)/G* w, whereL - lower class boundary of the group containing the median = 10.5 n - total number of values = 50 B - cumulative frequency of the groups before the median group = 6 + 15 = 21 G - frequency of the median group = 20 w - group width = 5Substitute values and work out the number:
Estimated Median = 10.5 + (50/2 - 21)/20*5 = 11.5Can somebody help me with this question
Answer:
900°
Step-by-step explanation:
The interior angles sum = 180° ( n - 2 )
~~~~~~~~
n = 7
180° ( 7 - 2 ) = 900°
Answer:
900 degrees
Step-by-step explanation:
just apply the formulas discussed in class !
The sum of interior angles in a triangle is 180°. To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°.
The number of triangles in each polygon is two less than the number of sides.
The formula for calculating the sum of interior angles is:
(n−2)×180∘ (where n is the number of sides)
in our case we have 7 sides.
so, we could split this polygon into 5 triangles.
each of these triangles would have an angle sum of 180°.
so, the angle sum of the polygon is
5×180 = 900°
if 20,x,y,z,25 are in AP .find the value of X,y,z.
Answers:
x = 21.25y = 22.5z = 23.75=============================================================
Work Shown:
AP = arithmetic progression, which is the same as arithmetic sequence
d = common difference
x = 20+dy = 20+2dz = 20+3dNotice how we scale up the d terms d, 2d, 3d, counting up by 1 each time.
So that must mean 25 is the same as 20+4d
20+4d = 25
4d = 25-20
4d = 5
d = 5/4
d = 1.25
and therefore,
x = 20+d = 20+1.25 = 21.25y = 20+2d = 20+2*1.25 = 22.5z = 20+3d = 20+3*1.25 = 23.75We could convert these to fraction form, but I find decimal form is easier in this case.
