SOLUTION
We want to solve for v in
[tex]F=\frac{mv^2}{R}[/tex]This means we should make v the subject, that is make it stand alone. This becomes
[tex]\begin{gathered} F=\frac{mv^2}{R} \\ m\text{ultiply both sides by }R,\text{ we have } \\ F\times R=\frac{mv^2}{R}\times R \\ R\text{ cancels R in the right hand side of the equation we have } \\ FR=mv^2 \end{gathered}[/tex]Next, we divide both sides by m, we have
[tex]\begin{gathered} FR=mv^2 \\ \frac{FR}{m}=\frac{mv^2}{m} \\ m\text{ cancels m, we have } \\ \frac{FR}{m}=v^2 \\ v^2=\frac{FR}{m} \end{gathered}[/tex]Lastly, we square root both sides we have
[tex]\begin{gathered} v^2=\frac{FR}{m} \\ \sqrt[]{v^2}=\sqrt[]{\frac{FR}{m}} \\ \text{square cancels square root, we have } \\ v=\sqrt[]{\frac{FR}{m}} \end{gathered}[/tex]Hence the answer is
[tex]v=\sqrt[]{\frac{FR}{m}}[/tex]Dylan looked at the function .and said, "This function is always greater than 0, so 0 is the absolute minimum." Explain why Dylan is incorrect.
Given data:
The given function is f(x)=4(1/2)^x.
The given function always greater than zero, the given function never become equal to zero, the asymptote at y=0.
Thus, zero can't be consider as the absolute minima of the function.
If m<9 = 97° and m<12 = 114°, find the measure of each missing angle.
1) Since we have a pair of parallel lines cut by transversal ones then we can state the following conclusions about the angles formed
2) Let's set our table
m∠1
m∠2
m∠3
m∠4
m∠5 = 83º ∠9 and ∠10 are supplementary angles
m∠6 = 97º ∠6 and ∠7 are consecutive interior angles (supplementary)
m∠7 = 114º ∠7 and ∠12 are alternate interior angles (congruent)
m∠8 =66º ∠8 and ∠11 are alternate interior angles (congruent)
m∠9 =97º Given
m∠10 = 180 - 97 =83º ∠9 and ∠10 are supplementary angles
m∠11 = 180º -114º = 66º ∠11 and ∠12 are supplementary angles
m∠12 = 114º Given
m∠13 = 83º ∠10 and ∠13 are Vertical angles
m∠14 = 97º ∠9 and ∠14 are Vertical angles
m∠15= 114º ∠12 and ∠15 are Vertical angles
m∠16 = 66º ∠11 and ∠16 are Vertical angles
The slope of this regression line is 0.8 .What does this tell you about the relationship between the amount of fertilizer and the height of the seedlings?
The slope of a line shows the relation between a unitary increment in the x-variable and the corresponding change in the y-variable.
In this case, the x-variable represents the amount of fertilizer, in grams, and the y-variable represents the height of the seedings, in cm.
Then, the slope of 0.8 means that when the x-variable increases in 1 unit, the y-variable increases 0.8 units. Or more specifically, for each additional gram of fertilizer used, the height of the seedings increases by about 0.8 cm on average.
What is the quotient? 7-^1/7^2
Hello there. To solve this question, we'll have to remember some properties about powers.
We have to determine the following quotient:
[tex]undefined[/tex]In your own words, describe the location of each point on a coordinate plane. Be specific. 1. (0,4)2.(2,5) 3.(-3, 6)
Locations on the coordinate plane are described as ordered pairs. An ordered pair tells you the location of a point by relating the point's location along the x-axis (the first value of the ordered pair) and along the y-axis (the second value of the ordered pair)
1. Point ( 0, 4)
The coordinate of ( 0, 4) is on the y-axis, because x = 0 and y = 4.
The point ( 0, 4) is on the y-axis at y = 4
2. Point ( 2, 5 )
Starting from the origin, go along the x-axis 2 units in a positive direction (right) and along the y-axis 5 units in a positive direction (up).
3. P( -3 , 4 )
Starting from the origin, go along the x-axis 3 units in a negative direction (left) and along the y-axis 4 units in a positive direction (up).
(10,-5)(10-9) what is the linear equation
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
point 1 (10 , - 5) x1 = 10 y1 = -5
point 2 (10, - 9) x2 = 10 y2 = -9
linear equation = ?
Step 02:
Slope formula
[tex]m\text{ = }\frac{y2\text{ -y1}}{x2-x1}[/tex][tex]m\text{ = }\frac{-9-(-5)}{10-10}=\frac{-9+5}{0}=\frac{-4}{0}=\infty[/tex]The answer is:
The equation of the line is a vertical line in x = 10, since the slope is infinite.
Whats the vertex of f(x)= 2x^2-8
Can someone help me with this? How do I figure this out?
We are given the following radical expression:
[tex]\sqrt[]{a+b}[/tex]We are asked to determine the equivalent exponential expression. To do that we will use the following relationship:
[tex]\sqrt[]{x}=x^{\frac{1}{2}}[/tex]Applying the relationship we get:
[tex]\sqrt[]{a+b}=(a+b)^{\frac{1}{2}}[/tex]Therefore, the right answer would be B.
Rewrite the expression 8m^6/4m^9 using the rules of exponents
Answer:
Rewrite the expression 8m^6/4m^9 using the rules of exponents
Step-by-step explanation:
8 ÷ 4 = 2
m^6 ÷ m^9
exponent rule in a division problem is you subtract them so...
6 - 9 = -3
you can't have a negative exponent so it would be 2 over m^3
If you have a negative exponent the rule is "flip it" meaning you flip the sign but when you do that it becomes a fraction. so... 2/m^3
A regular polygon has 20 sides. If one of its angles measures (5h − 12)°, what is the value of h?
h = 38.4
h = 34.8
h = 33.6
h = 30
Answer:
h = 34.8
Step-by-step explanation:
(20 - 2) × 180 = 3240
3240 ÷ 20 = 162
5h - 12 = 162
+ 12 to cancel out the -
5h = 174
÷ 5 to cancel out 5 × h
h = 34.8
The total area of a polygon is 176 sq.ft. Find the value of x in the drawing
Answer:
x=6 ft
Explanation:
The given polygon is a trapezium in which:
• The parallel sides are a=16 ft and b=(16+2x) ft
,• The height, h = 8 ft
,• Area = 176 sq.ft.
The area of a trapezium is calculated using the formula:
[tex]\begin{gathered} A=\frac{1}{2}(a+b)h \\ a,b\text{ are the parallel sides} \\ h\text{ is the perpendicular height} \end{gathered}[/tex]Substitute all the known values:
[tex]\begin{gathered} 176=\frac{1}{2}\times8(16+16+2x) \\ 176=4(32+2x) \end{gathered}[/tex]Divide both sides by 4.
[tex]\begin{gathered} \frac{176}{4}=32+2x \\ 44=32+2x \end{gathered}[/tex]Subtract 32 from both sides:
[tex]\begin{gathered} 44-32=32-32+2x \\ 12=2x \end{gathered}[/tex]Divide both sides by 2.
[tex]\begin{gathered} \frac{12}{2}=\frac{2x}{2} \\ x=6\text{ feet} \end{gathered}[/tex]The value of x in the drawing is 6 feet.
Answer:
X=6
Step-by-step explanation:
First multiply 8 by 16 to get 128. Then subtract that from 176 to get 48. Then divide by to because there are two triangles to get 24, so each triangle is 24 square feet. Find a number that multiplied by 8 equals 48 (this will be x). The reason that I did this is because of the formula for area of a triangle (B*H/2=A). After you divide by 48 by 2 you will get 24. The number that was multiplied by 8 is x (x=6).
Find the area of the shape shown below. 7 3
To find the area of the figure you can divide the figure into to smaller shapes
calculate the area of each of the smaller figures.
for the square
[tex]\begin{gathered} A=s\cdot s \\ A=3\cdot3 \\ A=9 \end{gathered}[/tex]For the triangle the base is the difference between the longest side which is 7 and the side on the square which is 3
[tex]7-3=4[/tex]find the area of the triangle
[tex]A=b\cdot\frac{h}{2}[/tex][tex]\begin{gathered} A=4\cdot\frac{3}{2} \\ A=\frac{12}{2} \\ A=6 \end{gathered}[/tex]Add both areas to find the area of the figure
[tex]\begin{gathered} A_T=9+6 \\ A_T=15 \end{gathered}[/tex]Lin ran 234 miles in 2/5 of an hour. Noah ran 823 miles in 4/3 of an hour.Who ran faster, Noah or Lin?How far would Lin run in 1 hour?How far did Noah run in 1 hour?How long would it take Lin to run 1 mile at that rate?How long would it take Noah to run 1 mile at that rate?
Given:
• For Lin:
Distance = 234 miles
Time = 2/5 of an hour
• For Noah:
Distance = 823 miles
Time = 4/3 of an hour
Let's determine who ran faster.
Let's find the time of each runner by multplying by 60.
Where:
60 minutes = 1 hour
To determine the speed of each of them, apply the formula:
[tex]speed=\frac{dis\tan ce}{time}[/tex]• To find Lin's speed, we have:
[tex]\text{ Lin's sp}eed=\frac{dis\tan ce}{\text{time}}=\frac{234}{\frac{2}{5}\ast60}=\frac{234}{24}=9.75\text{ mph}[/tex]Therefore, Lin's speed is 9.75 miles per hour.
• To find Noah's speed, we have:
[tex]undefined[/tex]5.65 less than a number equals 49
Let
x ------> the number
the algebraic expression is equal to
x-65=-49
solve for x
adds 65 both sides -------> by addition equality property
x=-49+65
x=16
the number is 16
Use the substitution method to solve the system of equations.3x + 2y = 13y = x - 1O A. (2,1)O B. (2,3)O C. (3,2)O D. (1,2)
3x + 2y = 13
y = x - 1
We want to substitute the second equation into the first equation.
In the first equation, everytime we see "y" substitute x-1
3x +2y = 13
3x + 2( x-1) = 13
Distribute
3x +2x -2 = 13
Combine like terms
5x -2 = 13
Add 2 to each side
5x-2+2 = 13+2
5x = 15
Divide each side by 5
5x/5 = 15/5
x = 3
Noe we can find the value of y by using the second equation
y = x-1
y = 3-1
y =2
The solution is
( 3,2)
how many killer whales are there when there are 5 million beluga whales
We know that the number of og beluga whales varies directly as the number of killer whales, that means that we can write a relation of the form:
[tex]y=kx[/tex]where y is the number of beluga whales, x is the number of killer whales and k is the constant of proportionality.
To answer the question we first need to find k, to do that we plug the values x=23 and y=14 in the equation above and solve for k:
[tex]\begin{gathered} 14=k23 \\ k=\frac{14}{23} \end{gathered}[/tex]Now that we know k the relation is:
[tex]y=\frac{14}{23}x[/tex]Finally to find the number of killer whales if there are 5 millions of beluga whales we plug y=5 in the equation above and solve for x:
[tex]\begin{gathered} 5=\frac{14}{23}x \\ x=\frac{5\cdot23}{14} \\ x=8.21 \end{gathered}[/tex]Therefore when there are 5 millions beluga whales we have 8.21 millions of killer whales.
I get a whole number so I’m not taking steps correctly
The sum of the given matrices is not possible to calculate as the order of both the matrix are different.
To add two matrices both matrices must be of the same order.
[3 -8] is of order 1 × 2
[4 -5 -6] is of order 1 × 3
Since the two matrices are of different orders it is not possible for the two matrices to be added.
Although direct sum or Kronecker sum could be used to add the matrices but the correct symbol for them is not used.
Hence the required result is impossible .
A matrix, also spelled "matrices," is a rectangular table or array of characters that are arranged in rows and columns to represent a mathematical object or a property of one.
Matrix representations of linear mappings in linear algebra allow for explicit computations. Because of this, matrices are studied extensively in linear algebra, and most properties and actions of abstract discrete mathematics may be explained in terms of matrices.
To learn more about matrix visit:
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At a town fair, for one of the game booths contestants pick a single card from a standard deck, and payouts are based on the cards chosen. Find the probability of your card being a club and a 6
Recall,
Probability = number of favorable outcomes/number of total outcomes
The number of cards in a standard deck of cards is 52. There is only one 6 of clubs. Thus, the probability of selecting a a club and a 6 is
1/52
write a polynomial function in standard form with the given zeros. This is not a test nor homework, I am preparing for the ACT and my teacher said these problems would be on there and therefore I need help1. -1, 3, 42. -3, 0, 0, 53. -2 multiplicity 34. (x+3)^2(x+1)
For question 1
The zeros of the polynomial are -1, 3 , 4, it means x = -1, x=3 and x=4
therefore,
[tex]\begin{gathered} x\text{ + 1, , x-3, and x-4 are factors of the polynomial} \\ \text{ f(x)= (x+1)(x-3)(x-4) } \\ f(x)=(x^2-3x+x-3)(x-4)^{} \\ =(x^2\text{ -2x -3)(x -4)} \\ =x^3-4x^2-2x^2+8x-3x+12 \\ f(x)=\text{ }x^3-6x^2+5x+12 \end{gathered}[/tex]For question 2
The zeros of the polynomial are -3, 0, 0, 5 it means x = -3, x=0, x=0 and x=5
therefore,
[tex]\begin{gathered} (x+3),\text{ (x-0), (x-0), and (x-5) are factors} \\ f(x)=\text{ (x+3) (x) (x) (x-5)} \\ =x^2(x+3)(x-5)=x^2(x^2-5x+3x-15)=x^2(x^2-2x-15) \\ f(x)=x^4-2x^3-15x^2 \end{gathered}[/tex]For question 3
The zeros of the polynomial are -2, -2, -2 it means x = -2, x=-2, , x=-2
therefore,
[tex]\begin{gathered} (x+2),(x+2),(x+2)\text{ are factors of the polynomial} \\ f(x)\text{ = (x+2)(x+2)(x+2)} \\ =(x^2+2x+2x+4)(x+2)=(x^2+4x+4)(x+2) \\ =x^3+2x^2+4x^2+8x+4x+8 \\ f(x)=x^3+6x^2+12x+8 \end{gathered}[/tex]Angle AED is 146 degrees. Ray EC bisects angle AED. What is the measure of angle AEC?
STEP 1
We draw a diagram to represent the information.
[tex]\begin{gathered} <\text{AEC}=\frac{In conclusion, the answer is 73 degreesLet D be the event that a randomly chosen student enjoys drawing. Let S be the event that a randomly chosen studentplays sports. Identify the answer which expresses the following with correct notation: The probability that a randomlychosen student plays sports, given that the student enjoys drawing.
ANSWER
P(S|D)
EXPLANATION
The notation P(A|B) always reads as "the probability of A given B"
If the events are
D: student enjoys drawing
S: student play sports
The probability that a randomly chosen student plays sports, given that the student enjoys drawing is: P(S|D)
what is the slope when the rise is -10 and the run is 2
Slope intercdpt form of line
Then
Rise means elevation over y axis
Run means displacement along X axis
Now the Slope m = ( Rise/Run ) = (-10/2) = -5
So its a line directed down with slope -5
(when slope is negative, line goes down)
Create an equation could be used to find the volume, V, of the cylindrical tank. DO 0 TT sin cos tan sin-cos'tan а в E 1 = vo 0 < A p CSC sec cot log log in 1 Part B Question
Given:
V denotes the volume of the water tank.
r represents the radius of the tank.
h represents the length of the water tank.
The volume of cylindrical tank is expressed as,
[tex]V=\pi\times r^2\times h[/tex]Given that the length of tank h = 20 feet.
The equation becomes,
[tex]\begin{gathered} V=\pi\times r^2\times20 \\ V=20\pi(r^2) \end{gathered}[/tex]Answer:
[tex]V=20\pi(r^2)[/tex]6 out of 20 students at a school assembly were first grade students. What percentage of students. at assembly were first grades
We are given that 6 out of 20 students at a school assembly were first-grade students.
What percentage of students at the assembly were first-grades students?
To find the percentage of students, divide 6 by 20 and then multiply the result by 100.
[tex]\begin{gathered} =\frac{6}{20}\times100\% \\ =0.3\times100\% \\ =30\% \end{gathered}[/tex]Therefore, 30% of students at the assembly were first-grade students.
parallelogram pqrs has diagonals PR and SQ that intersect at T find the value of X and Y
If a parallelogram PQRS has diagonals PR and SQ that intersects at T, then, T is the midpoint of PR and T is the midpoint of SQ
Given
[tex]\begin{gathered} PT=y \\ TR=3x+1 \end{gathered}[/tex][tex]y=3x+1[/tex]Also
[tex]\begin{gathered} QT=3y \\ TS=4x+13 \end{gathered}[/tex][tex]3y=4x+13[/tex]Now we are going to solve the system of equations with two unknowns
[tex]\begin{gathered} y=3x+1 \\ 3y=4x+13 \end{gathered}[/tex]Substitute equation 1 into 2
[tex]\begin{gathered} 3(3x+1)=4x+13 \\ 9x+3=4x+13 \\ 9x-4x=13-3 \\ 5x=10 \\ x=\frac{10}{5} \\ x=2 \\ \end{gathered}[/tex]x = 2
Substitute x = 2 into equation 1
[tex]\begin{gathered} y=3x+1 \\ y=3(2)+1 \\ y=6+1 \\ y=7 \end{gathered}[/tex]y = 7
The answer would be x = 2, y = 7
Find the slope of the line passing trough the given points point (3 , 2). Point (1, -1)
For this question we will use the formula for the slope of a line passing through two points:
[tex]s=\frac{y_2-y_1}{x_2-x_1}\text{.}[/tex]Substituting the given points we get:
[tex]s=\frac{-1-2}{1-3}=\frac{-3}{-2}=\frac{3}{2}\text{.}[/tex]Answer:
[tex]\frac{3}{2}\text{.}[/tex]if eddie buy carrots and her discount is 35% and the original price of the carrots is $7.40 how much did she pay
First, find what is 35% of $7.40 equal to. To do so, multiply 7.40 times 35/100:
[tex]7.4\times\frac{35}{100}=2.59[/tex]Then, the discount is equal to $2.59. To find the final price, substract the discount (2.59) from the original price (7.4):
[tex]7.4-2.59=4.81[/tex]Therefore, the price that she paid was:
[tex]\text{ \$4.81}[/tex]You spend 51/2hours at the park this week. You spend 210 fewer minutes at the library than you do at park. How many minutes do you spend at the library?
Solution
Given:
Time spent at the park =
[tex]\begin{gathered} 5\text{ }\frac{1}{2}\text{ hours} \\ \end{gathered}[/tex]Convert this time to minutes
[tex]\begin{gathered} \text{Recall that } \\ \text{1 hour = }60\text{ minutes} \\ 5\frac{1}{2}\text{ hours = 5}\frac{1}{2}\text{ x 60}=\frac{11}{2}\text{ x 60 = 330 minutes} \\ \\ \end{gathered}[/tex]Time spent at the library is 210 minutes fewer than that spent at the park.
This implies the time spent at the library is
[tex]\begin{gathered} \text{Time spent at the park minus 210 minutes} \\ =330\text{ minutes - 210 minutes} \\ =120\text{ miutes} \end{gathered}[/tex]The answer is 120 minutes
what percent of $717 is $239?
what percent of $717 is $239?
we have that
717 represent the 100%
so
Apply proportion
100/717=x/239
solve for x
x=(100/717)*239
x=
Find the conditional relative frequency that a student surveyed prefers cats as pets, given that the student is a girl
To find the relative frequency asked, you have to divide the number of girls who prefer cats by the number of girls:
[tex]\frac{6}{28}\approx0.2143\Rightarrow21.43\text{percent}[/tex]About 21.43% of the girls prefer cats as pets