To measure sound, we use the measure decibel which in fact is a logartimic funcion of the amplitude of a soud
To measure eartquakes, we use the Richter scale whci is a logaritmic function of the amplitude of the force of an earthquake
To calculate how long a body has been dead, the coroner must know how long the body temperature has not been at 98.6 degrees. Because the rate of the body cooling is proportionate to temperature differences between the body and its surroundings, the answer is found by calculating exponential decay using logarithms.
The radius of a circle is 7 in. Find its area in terms of pi
Answer:
49π
Step-by-step explanation:
πr^2 <---- The formula for the area of a circle.
let "a" represent area of the circle.
a = π × 7^2
Simplify by the use of the exponent.
7^2 = 49
Your answer:
49π
A medicine is applied to a burn on a patient’s arm. The area of the burn in square centimeters decreases exponentially and is shown on the graph
EXPLANATION
The function that represents the exponential decay is as follows:
[tex]f(x)=ab^x[/tex]Where a=initial amount and b= decay coefficient
Since the initial amount is 8cm^2, the is the value of the coefficient a is 8.
[tex]f(x)=8b^x[/tex]Now, we need to compute the decay rate:
We can obtain this by substituting two given values, as for instance (0,8) and (1,6) and dividing them:
[tex]\frac{6}{8}=\frac{8}{8}\frac{b^1}{b^0}[/tex]Simplifying:
[tex]\frac{3}{4}=0.75=b[/tex]The value of b is 3/4:
[tex]y=8\cdot0.75^x[/tex]1) There will be 3/4 of the burn area each week.
2) The equation representing the area of the burn, after t weeks will be the following:
[tex]y=8\cdot(\frac{3}{4})^x[/tex]3) After 7 weeks, the area will be represented by the following expression:
[tex]y=8\cdot(\frac{3}{4})^7[/tex]Computing the power:
[tex]y=8\cdot\frac{2187}{16384}=1.068cm^2[/tex]
10. (09.02 MC)Which of the following tables shows the correct steps to transform x2 + 8x + 15 = 0 into the form (x - p)2 = q?[p and q are integers) (5 points)
To transform
[tex]x^2+8x+15=0[/tex]Make it a perfect square
since 8x/2 = 4x, then
We need to make 15 = 16 for 4 x 4 = 16, so add 1 and subtract 1
[tex]\begin{gathered} x^2+8x+(15+1)-1=0 \\ x^2+8x+16-1=0 \end{gathered}[/tex]Now we will make the bracket to the power of 2
[tex]\begin{gathered} (x^2+8x+16)-1=0 \\ (x+4)^2-1=0 \end{gathered}[/tex]Add 1 to both sides
[tex]\begin{gathered} (x+4)^2-1+1=0+1 \\ (x+4)^2=1 \end{gathered}[/tex]The answer is C
A Ferris wheel has a radius of 12 meters and takes 16 seconds to complete one full revolution. The seat you are riding in, takes 4 seconds to reach the top which is 28 meters above the ground. Write a sine or cosine equation for the height of your seat above the ground as a function of time.
EXPLANATION
Given that the wheel has a radius of 12 meters and it takes 16 seconds to complete one full revolution, if we call t to the time in seconds and since the top of the wheel is 28 meters above the ground, the bottom is 4 meters above the ground.
Now, we need to consider that the equation that applies is the following:
[tex]height=16-12\cos \theta[/tex]As theta is the angle between the radius from the center of the wheel to the bottom and the rider's coordinate, we need to represent the angle as a function of the time. We have that it takes 16 second to complete one full revolution, this means that the wheel rotates 360 degrees in 16 seconds. Now, we can use the angular velocity: w= 360/16 = 22.5 degrees/s
Then, we need to represent the angular velocity in radians, as 360 degrees is 2π radians, the obtained angular velocity would be: w = 2π/16 = π/8 rad/s
Hence the appropiate equation as a function of the time would be as follows:
[tex]h=16-12\cdot\cos (\frac{\pi t}{8})[/tex]
1277 concert tickets were sold for a total of $16,267. If students paid $11 and nonstudents paid $17, how manystudent tickets were sold?
Hello there. To solve this question, we'll have to remember some properties about system of equations.
Given that 1277 concert tickets were sold, for a total of $16,267, knowing that students paid $11 and non-students paid $17, we have to determine how many students tickets were sold.
Let's start labeling the variables we have. Say x is the number of tickets sold for students, while y is the number of tickets sold for non-students.
The total number of tickets sold can be found by adding how many students and non-students tickets were sold, i.e.
[tex]x+y=1277[/tex]To find the total amount collected, we have to multiply the number of each ticket sold by its respective fee, adding everything as follows:
[tex]11\cdot x+17\cdot y=16267[/tex]With this, we have the following system of equations:
[tex]\begin{cases}x+y=1277 \\ 11x+17y=16267\end{cases}[/tex]We can solve it using the elimination method. It consists in multiplying any of the equations by a factor (usually the easier equation) that when added to the other equation, one of the variables are cancelled out.
In this case, multiply the first equation by a factor of (-11)
[tex]\begin{cases}-11x-11y=-14047 \\ 11x+17y=16267\end{cases}[/tex]Add the two equations
[tex]\begin{gathered} -11x-11y+11x+17y=-14047+16267 \\ 6y=2220 \end{gathered}[/tex]Divide both sides by a factor of 6
[tex]y=370[/tex]Now we plug it back into the first equation in order to solve for x (i. e the number of tickets sold for students)
[tex]\begin{gathered} x+y=1277 \\ x+370=1277 \\ x=1277-370 \\ x=907 \end{gathered}[/tex]This is how many tickets were sold to students.
graphing a parabola of the form y=ax squared 2
The graph of the parabola given by the equation:
[tex]y=\frac{1}{4}x^2[/tex]has a vertex when y=0 which happens iff
[tex]\begin{gathered} \frac{1}{4}x^2=0 \\ x^2=0 \\ x=0 \end{gathered}[/tex]Therefore the graph is:
The vertex has coordinates (0,0). Now, two points to the left of the vertex that are on the parabola have coordinates (-2,1) and (-4,4). Two points that are to the right of the parabola have coordinates
I need help on 2 please Directions: Find the value of x. Round each answer to the nearest tenth.
The angle indicated is a right angle, so the triangle is a right triangle.
Thus, we can apply the Pythagora's Theorem:
[tex]a^2+b^2=c^2[/tex]Where c is the hypotenuse, the angle opposite to the right angle, and a and b are the legs.
x is the hypotenuse in this case, so:
[tex]\begin{gathered} 22^2+27^2=x^2 \\ x^2=484+729 \\ x^2=1213 \\ x=\sqrt[]{1213} \\ x=34.8281\ldots\approx34.8 \end{gathered}[/tex]So the question is A local theater sells admission tickets for $9.00 on Thursday nights, where n is the number of customers M(n) the amount of money the theater takes What is the domain of M( n ) in this context
We have the function M(n):
M( n ) = 9 · n
which describes the amount of money the theater takes.
Since the domain of a function refers to the values n can take and n is the number of costumers
In this particular case we do not have a restriction of the number of costumers. Then n can take the following values:
n = 0, 1 , 2, 3, ...
Domain: all non- negative integers
If the maximum capacity of the theater is 100 costumers then
n = 0, 1, 2, 3, ..., 100
Therefore its domain would correspond to
Domain: all non- negative integers less than or equal to 100
Find the area of a shaded region shown below, which was formed by cutting an isosceles trapezoid out of the top half of a rectangle. The width of the rectangle is 32 in, the height of the rectangle in 24 in. The leg of the isosceles trapezoid is 15 in.
Step 1: Redraw the diagram and label it.
From the figure, the hypotenuse of triangles A and B is 15 in and the height is 12 in. We can apply the Pythagoras theorem to find the base.
Let base of the triangle A and B be the adjacent.
Opposite = 12
Adjacent = ?
Hypotenuse = 15
[tex]\begin{gathered} Next,\text{ apply the Pythagoras theorem to find the adjacent.} \\ \text{Opposite}^2+Adjacent^2=Hypotenuse^2 \\ 12^2+Adj^2=15^2 \\ 144+Adj^2\text{ = 225} \\ \text{Collect like terms.} \\ \text{Adj}^2\text{ = 225 - 144} \\ \text{Adj}^2\text{ = 81} \\ F\text{ ind the square root of both sides.} \\ \sqrt[]{Adj^2\text{ }}=\text{ }\sqrt[]{81} \\ \text{Adj = 9 in} \end{gathered}[/tex]The area of the shaded region = Area of A + Area of B + Area of C
[tex]\begin{gathered} \text{Area of A = }\frac{Base\text{ x Heigth}}{2} \\ \text{Base = 9} \\ \text{Height = 1}2 \\ \text{Area of A = }\frac{9\text{ x 12}}{2} \\ =\text{ }\frac{108}{2} \\ =54in^2 \\ \text{Area of B = }\frac{Base\text{ x Height}}{2} \\ =\text{ }\frac{9\text{ x 12}}{2} \\ =\text{ }\frac{108}{2} \\ \text{= 54 in}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of rectangle C = Length }\times\text{ Breadth} \\ Lenght\text{ = 32} \\ \text{Breadth = 12} \\ \text{Area of C = 32 x 12} \\ =384in^2 \end{gathered}[/tex]Therefore,
Area of the shaded region = 54 + 54 + 384 = 492 inches square
Final answer
Area of the shaded region = 492 inches square
An adult elephant drinks about 225 liters of water each day. Is the number ofdays the water supply lasts proportional to the numberof liters of water the elephant drinks?Is it proportional
An elephant drinks 225 liters of water per day, then in 2 days it drinks 2*225 = 450 liters, in 3 days it drinks 3*225 = 675 liters.
time (days) | 1 | 2 | 3
water (L) | 225 | 450 | 675
If an elephant drinks more water per day, the number of days the water supply lasts decrease. Then these two variables are inversely proportional.
Solve the system by the method of your choice. Identify inconsistent systems and systems with dependent equations, using set notation to express solution sets
The given system of equations is
[tex]\begin{gathered} y=3x+5\rightarrow(1) \\ 5x-2y=-7\rightarrow(2) \end{gathered}[/tex]Substitute y in equation (2) by equation (1)
[tex]5x-2(3x+5)=-7[/tex]Simplify the left side
[tex]\begin{gathered} 5x-2(3x)-2(5)=-7 \\ 5x-6x-10=-7 \end{gathered}[/tex]Add the like terms on the left side
[tex]\begin{gathered} (5x-6x)-10=-7 \\ -x-10=-7 \end{gathered}[/tex]Add 10 to both sides
[tex]\begin{gathered} -x-10+10=-7+10 \\ -x=3 \end{gathered}[/tex]Divide both sides by -1
[tex]\begin{gathered} \frac{-x}{-1}=\frac{3}{-1} \\ x=-3 \end{gathered}[/tex]Substitute x in equation (1) by -3 to find y
[tex]\begin{gathered} y=3(-3)+5 \\ y=-9+5 \\ y=-4 \end{gathered}[/tex]The solution of the system of equations is {(-3, -4)}
Since the system has only one solution then it is an independent consistent system.
I don’t know the answer for this one and others I need help
x = 1, y = 3
Explanation:The given system of equations is:
y = 4x - 1.......................(i)
y - 2x = 1..................(ii)
Substitute equation (i) into equation (ii)
4x - 1 - 2x = 1
4x - 2x = 1 + 1
2x = 2
x = 2/2
x = 1
Substitute x = 1 into equation (i)
y = 4x - 1
y = 4(1) - 1
y = 4 - 1
y = 3
The solution to the system of equations is x = 1, y = 3
Find all possible rational roots of f(x)=4x^3-13x^2+9x+2
Polynomial
[tex]f(x)=4x^3+13x^2+9x+2[/tex]I need help with this question Subtraction:3+(-4) = ?
Given:
We have to use subtraction
[tex]3+(-4)[/tex]To find: Solve the above expression?
Explanation:
Here we use the subtraction operation to solve the given expression.
We know the operator property,
[tex]\begin{gathered} (+)(-)=(-) \\ (-)(-)=(+) \\ (+)(+)=(+) \\ (-)(+)=(-) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} =3+(-4_) \\ \\ =3-4 \\ \\ =-1 \end{gathered}[/tex]Thus, 3+(-4) = -1.
Answer: 3+(-4) = -1.
The figure on the left is a trapezoidal prism. The figure on the right represents its base. Find the volume of this prism. 13 ft 10 ft 10 ft 2 ft 13 ft 12 ft 13 ft 20 ft 13 ft 5 ft 10 ft 5 ft The area of the trapezoidal base is 8 ft2, the height is ft. Therefore, the volume is IN
volume of the trapezoidal prism is
[tex]V=A_b\times h[/tex]then, area of the trapezoidal base
[tex]\begin{gathered} A_b=\frac{1}{2}(b1+b2)h \\ A_b=\frac{1}{2}(10+20)\times12 \\ A_b=\frac{1}{2}(30)\times12 \\ A_b=\frac{360}{2}=180 \end{gathered}[/tex]area of the trapezoidal base = 180 ft^2
height = 2ft
so, the volume is:
[tex]\begin{gathered} V=180\times2 \\ V=360 \end{gathered}[/tex]volume = 360 ft^3
A square ABCD has the vertices A(n,n), B(n,-n), C(-n,-n), and D(-n,n). Which vertex is in Quadrant II?Answers:A.CB.DC.BD.A
Given:
A square ABCD has the vertices A(n,n), B(n,-n), C(-n,-n), and D(-n,n).
In quadrant II, the cordinates of the x have negative sign and coordinates of y axis have poistive sign.
Thus, the vertex is in Quadrant II is D(-n,n).
The dot plot shows the hourly pay rate for ten employees at best books bookstore.
We will have the following:
The strongest case he can make is the mean hourly rate since Levi's current pay rate is well bellow the average hourly pay rate.
(U.LL.2) A perfectly cube-shaped smelly candle has a volume of 125 cubic kilometers. What is the area of each side of the smelly candle?
25 square kilometers
Explanation
the volume of a cube is given by:
[tex]\begin{gathered} \text{Volume}=\text{side}\cdot\text{side}\cdot\text{side} \\ \text{volume}=(side)^3 \end{gathered}[/tex]Step 1
Let
volume = 125 cubic kilometers
Step 2
replace and solve for "side"
[tex]\begin{gathered} \text{Volume= side}^3 \\ 125km^3=side^3 \\ \text{cubic root in both sides} \\ \sqrt[3]{12}5km^3=\text{ }\sqrt[3]{side^3} \\ 5\text{ km= side} \end{gathered}[/tex]Step 3
now, we have the length of a side, to find the area, make
Area of a square is
[tex]\begin{gathered} \text{Area= side }\cdot side \\ \text{Area}=side^2 \end{gathered}[/tex]replace to find the area
Let side = 5 km
[tex]\begin{gathered} \text{Area}=(5km)^2 \\ \text{Area = 25 km}^2 \end{gathered}[/tex]
Find x, where a=14 degrees and b=22 degrees. Find the measure of each angle of the polygon. Shown below.
To answer this question, we need to remember that the sum of the interior angles of a quadrilateral is equal to 360º (in fact, we can divide a quadrilateral into two triangles, and the sum of interior angles of a triangle is equal to 180º).
Then, we have that a = 14º and b = 22º, then we can state the next equation:
[tex](2x+14^{\circ})+(3x+22^{\circ})+2x+x=360^{\circ}[/tex]And now, we can solve the equation for x as follows:
1. Add the like terms as follows:
[tex](2x+3x+2x+x)+14^{\circ}+22^{\circ}=360^{\circ}[/tex][tex]8x+36^{\circ}=360^{\circ}[/tex]2. Subtract 36º from both sides of the equation:
[tex]8x+36^{\circ}-36^{\circ}=360^{\circ}-36^{\circ}\Rightarrow8x=324^{\circ}[/tex]3. Divide both sides by 8 as follows:
[tex]\frac{8x}{8}=\frac{324^{\circ}}{8}\Rightarrow x=40.5^{\circ}[/tex]Therefore, the value for x = 40.5º
Then, we can find the values for the measure of angle A as follows:
[tex]m\angle A=2(40.5^{\circ})+14^{\circ}=95^{\circ}[/tex]The measure of angle B is
[tex]m\angle B=3(40.5^{\circ}_{})+22^{\circ}=143.5^{\circ}[/tex]The measure of angle C is
[tex]m\angle C=x^{\circ}=40.5^{\circ}[/tex]The measure of angle D is
[tex]m\angle D=2(40.5^{\circ})=81^{\circ}[/tex]A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. the premium antifreeze solution contains 90% pure antifreeze. the company want to obtain 180 gallons of a muxture that contains 45% pure antifreeze how many and how many gallons of the premium antifreeze solution must be mixed
Answer:
Both should be 90 gallons
Explanation:
Let the gallons of pure water used = x gallons
Since the company want to obtain 180 gallons of a mixture, the gallons of 90% pure antifreeze needed = (180-x) gallons
We therefore have that:
90% of (180-x) gallons = 45% of 180 gallons
[tex]\begin{gathered} 0.9(180-x)=0.45\times180 \\ 162-0.9x=81 \\ 0.9x=162-81 \\ 0.9x=81 \\ x=\frac{81}{0.9} \\ x=90 \end{gathered}[/tex]• The number of gallons of pure water used = 90 gallons
• The number of gallons of premium antifreeze solution
= 180-90
= 90 gallons.
1. Write an equation of the line that is parallel to the linewhose equation is 4y + 9 = 2x and passes through thepoint (7,2)
First let's put the equation 4y + 9 = 2x in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept. So we have that:
[tex]\begin{gathered} 4y+9=2x \\ 4y=2x-9 \\ y=\frac{2x-9}{4} \\ y=\frac{1}{2}x-\frac{9}{4} \end{gathered}[/tex]The slope of this equation is 1/2. In order to the second line be parallel to this line, it has to have the same slope. Also, since the second line passes through the point (7, 2), we have:
[tex]\begin{gathered} y=\frac{1}{2}x+b \\ (7,2)\colon \\ 2=\frac{1}{2}\cdot7+b \\ 2=\frac{7}{2}+b \\ b=2-\frac{7}{2}=\frac{4-7}{2}=-\frac{3}{2} \end{gathered}[/tex]So the second equation is:
[tex]y=\frac{1}{2}x-\frac{3}{2}[/tex]Write an exponential equation using y = a(b)^x“ thatrepresents the growth or decay of the situation.A house was purchased for $370,000. The house has anannual appreciation rate of 3%. Please write a let statementand an equation that represents the house's value over time.
Let:
PV = Initial value = 370000
r = appreciation rate = 3% = 0.03
x = time
the equation will be given by
[tex]\begin{gathered} y=PV(1+r)^x \\ so\colon \\ y=370000(1+0.03)^x \\ y=370000(1.03)^x \end{gathered}[/tex]Emily reads 22 pages per hour. In all, how many hours of reading will Emily have to do this week in order to have read a total of 44 pages?
Answer:
The number of hours of reading it will take Emily to read a total of 44 pages is;
[tex]2\text{ hours}[/tex]Explanation:
Given that Emily reads 22 pages per hour.
Her rate of reading is;
[tex]r=22\text{ pages/hour}[/tex]The amount of time she needs to read 44 pages will be the number of pages divided by the rate;
[tex]\begin{gathered} t=\frac{\text{number of pages}}{\text{rate}}=\frac{44}{22}\text{hour} \\ t=2\text{ hours} \end{gathered}[/tex]Therefore, the number of hours of reading it will take Emily to read a total of 44 pages is;
[tex]2\text{ hours}[/tex]hello can you help me with this trigonometry question read carefully of how it has to be answered
Area of a circle = πr²
Replacing with radius = 8.4 in:
Area of a circle = π(8.4)²
Area of a circle = 221.6708 in²
This area corresponds to 2π radians. To find the area corresponding to 2.37 radians, we can use the next proportion:
[tex]\frac{2\pi\text{ rad}}{2.37\text{ rad}}=\frac{221.6708^{}}{x^{}}\text{ }[/tex]Solving for x:
[tex]\begin{gathered} 2\pi\cdot x=221.6708\cdot2.37 \\ x=\frac{525.359796}{2\pi} \\ x=83.6136\text{ sq. in} \end{gathered}[/tex]When asked to find f ( g ( x ) ), what should you do? plug f (x) into g (x)plug g (x) into f (x)multiply f (x) by g (x)none of the above
From the given question,
f(g(x)) means,
Plug g(x) into f(x)
Hence, the correct option is B
Select the correct answer.378Convert4 to rectangular form.OA.Y = -1OB.y = 1O C.y =O D.O E.I = -1
The Solution.
Assuming the radius is 1.
[tex]x=\cos (\frac{3\pi}{4})=-\sin (\frac{3\pi}{4})[/tex]Therefore,
[tex]\begin{gathered} x=-y \\ or \\ y=-x \end{gathered}[/tex]So, the correct answer is option D
Flnd the value of x for the triangle or rectangle. Then find the length of the sides of the triangle or rectangle.Q1: Perimeter = 18 meters Q2: Perimeter = 23 feet
The perimeter of a rectangle is given by:
P = 2w + 2h
Where:
w = width = 2x
h = height = x
P = 18
Replacing the data into the equation:
18 = 2(2x) + 2(x)
18 = 4x + 2x
18 = 6x
Solving for x:
x = 18/6
x= 3
Therefore:
w = 2(3) = 6m
h = 3m
---------------------------------------------------------------------------------
P = x + 2x + (x + 3)
23 = 3x + x + 3
23 = 4x + 3
Solving for x:
23 - 3 = 4x
20 = 4x
20/4 = x
5 = x
Therefore its sides are:
x = 5 ft
2x = 2(5) = 10ft
x + 3 = 5 + 3 = 8ft
Select the correct answer.In triangle ABC, AB = 12, BC = 18, and m B = 75° what are the approximate length of side AC and measure of A?O AAC = 18.9;m SA = 66.99OB.OC.AC = 20.3 m A = 34.8°AC = 18.9: m A = 37.8°AC = 20.31 m A = 58.9°ODResetNext
Draw the triangle ABC.
Determine the length of side AC.
[tex]\begin{gathered} (AC)^2=(AB)^2+(BC)^2-2\cdot AB\cdot BC\cdot\cos B \\ =(12)^2+(18)^2-2\cdot12\cdot18\cdot\cos 75 \\ =356.190 \\ AC=\sqrt[]{356.19} \\ =18.87 \\ \approx18.9 \end{gathered}[/tex]So side AC is equal to 18.9 m.
Determine the measure of angle A.
[tex]\begin{gathered} \frac{AC}{\sin B}=\frac{BC}{\sin A} \\ \frac{18.9}{\sin75}=\frac{18}{\sin A} \\ \sin A=\frac{18}{18.9}\cdot\sin 75 \\ A=\sin ^{-1}(0.9199) \\ =66.9 \end{gathered}[/tex]So mesure of angle A is 66.9 degree.
Find the slope and y-intercept of the line shown below.10-8-6-co +4-2--10-8-64-2-2- 2 4 6 8 10~ 60--4-X-6--8--10-
Looking at the graph
we have a horizontal line
the equation is
y=-5
The slope of a horizontal line is equal to zero
so
m=0
The y-intercept is the point (0,-5)
therefore
b=-5
The answer is
m=0b=-5Remember that
y=mx+b
substitute
m=0
b=-5
y=(0)(x)-5
y=-5
Hi, can you help me to find (Ir possible) the complement andsupplement of the angle of exercise
The angle is given 24 degree.
To determine the complement angle ,
[tex]90^{\circ}-24^{\circ}=66^{\circ}[/tex]To determine the supplement angle ,
[tex]180^{\circ}-24^{\circ}=156^{\circ}[/tex]