Answer:
[tex] x=2 \pm \sqrt{7} [/tex]
Step-by-step explanation:
Given this form ax^2+bx=k, here are my steps for completing the square while answer your question:
First step: Divide both sides by what is in front of x^2. You want the coefficient of x^2 to be 1. To do this for your question, divided both sides by 3.
This gives us x^2-4x = 3.
Second step: We are ready to begin the completing the square process at this step. We are going to add (b/2)^2 on both sides. For this question b=-4.
So we will be adding (-4/2)^2 on both sides.
This gives us x^2-4x+(-4/2)^2=3+(-4/2)^2.
Third step: I like to simplified the things inside the square and I do not actually apply the square at this step. It makes a later step easier in my opinion.
So this step gives us x^2-4x+(-2)^2=3+(-2)^2.
Fourth step: I'm actually going to write the left hand side as a square. Just drag the things that are inside the squares down into ( )^2.
This is what I mean x^2-4x+(-2)^2=(x-2)^2.
So at the end of this step we have (x-2)^2=3+(-2)^2.
Fifth step: I'm going to simplify the right hand side.
This step gives us (x-2)^2=7
Sixth step: We are ready to square root both sides.
This gives us [tex] x-2=\pm \sqrt{7} [/tex]
Seveth step: Get x by itself like you normally would with a linear equation. My step here is just to add 2 on both sides.
Final answer: [tex] x=2 \pm \sqrt{7} [/tex]
[tex]3x^2-12x=9\\x^2-4x=3\\x^2-4x+4=7\\(x-2)^2=7\\x-2=\sqrt7 \vee x-2=-\sqrt7\\x=2+\sqrt7\vee x=2-\sqrt7[/tex]
Write a rational function that has the specified characteristics.
Answer:
a) f(x) = (x-5)/((x-3)(x-10))
b) f(x) = (x-4)/((x+4)(x^2+1))
c) f(x) = 2(x-1)(x+1)/((x+3)(x-4))
d) f(x) = -2(x+5)(x-3)/((x+2)(x-5))
e) f(x) = -3(x^2-1)(x-2)/(x(x^2-9))
Step-by-step explanation:
Ordinarily, we think of a horizontal (or slant) asymptote as a line that the function nears, but does not reach. Some of these questions ask for the horizontal asymptote to be zero and for a function zero at a specific place. That is, the actual value of the function must be the same as the asymptotic value, at least at one location.
There are several ways this can happen:
add a vertical asymptote on the same side of the zero as the required vertical asymptote. The function will cross the horizontal asymptote and then approach from the new direction.add a vertical asymptote on the other side of the zero from the required asymptote. The function zero will then be between the asymptotes, and the function will approach the asymptote in the expected way. (See the attachment)add complex zeros in the denominator. The function will cross the horizontal asymptote and approach it from the new direction. This does not add any asymptotes to the function.To make the horizontal asymptote be zero, the degree of the denominator must be greater than the degree of the numerator. That is, there must be additional real or complex zeros in the denominator beyond those for the required vertical asymptotes.
__
a) f(x) = (x-5)/((x-3)(x-10)) . . . . vertical asymptote added at x=10 to make the horizontal asymptote be zero
__
b) f(x) = (x-4)/((x+4)(x^2+1)) . . . . complex zero added to the denominator to make the horizontal asymptote be zero
__
c) f(x) = 2(x-1)(x+1)/((x+3)(x-4)) . . . . factor of 2 added to the numerator to make the horizontal asymptote be 2. Numerator and denominator degrees are the same. (See the second attachment.)
__
d) f(x) = -2(x+5)(x-3)/((x+2)(x-5)) . . . . similar to problem (c)
__
e) f(x) = -3(x^2-1)(x-2)/(x(x^2-9)) . . . . similar to the previous two problems (See the third attachment.)
_____
You remember that the difference of squares factors as ...
a² -b² = (a-b)(a+b)
so the factor that gives zeros at x=±3 can be written (x²-9).
To write a rational function with specific characteristics, define the characteristics and use factors to create the desired asymptotes and holes.
Explanation:To write a rational function with specific characteristics, we need to define the characteristics first. For example, let's say we want a function with a vertical asymptote at x = 2, a horizontal asymptote at y = 0, and a hole at x = -3. We can write the rational function as:
f(x) = (x + 3)(x - 2) / (x - 2)
In this function, the factor (x - 2) in both the numerator and denominator creates the vertical asymptote at x = 2. The (x + 3) factor in the numerator creates the hole at x = -3, and the horizontal asymptote at y = 0 is determined by the highest power of x in the numerator and the denominator being the same, which is x^1.
Learn more about Rational Functions here:https://brainly.com/question/27914791
#SPJ3
Drag the tiles to the boxes to form correct pairs.
Multiply the pairs of numbers and match them to their products.
Answer:
Answer in the picture.
Answer:
[tex](-7)(-1.2)\leftrightarrow 8.4[/tex]
[tex](-2\frac{1}{2})(-2)\leftrightarrow 5[/tex]
[tex](2.5)(-2)\leftrightarrow -5[/tex]
[tex](7)(-1.2)\leftrightarrow -8.4[/tex]
Step-by-step explanation:
Product rule of signs:
(+)(+) = (+)
(+)(-) = (-)
(-)(+) = (-)
(-)(-) = (+)
Using these signs simplify the given expression.
[tex](-7)(-1.2)=8.4[/tex]
It means (-7)(-1.2) is equivalent to 8.4.
[tex](-2\frac{1}{2})(-2)=(-\frac{5}{2})(-2)=5[/tex]
It means [tex](-2\frac{1}{2})(-2)[/tex] is equivalent to 5.
[tex](2.5)(-2)=-5[/tex]
It means (2.5)(-2)- is equivalent to -5.
[tex](7)(-1.2)=-8.4[/tex]
It means (7)(-1.2) is equivalent to -8.4.
In one town 79% of adults have health insurance.What is the probability that 4 adults selected at random feom the town all have health insurance round to the nearest thousandth if necessary
Answer:
0.390 to the nearest thousandth or 39%.
Step-by-step explanation:
That would be 0.79^4
= 0.3895.
The probabilities are multiplied because each selection is independent.
The probability that 4 adults randomly selected from a town with 79% health insurance coverage will all have health insurance is approximately 0.389.
The probability that 4 adults selected at random from a town where 79% of adults have health insurance, will all have health insurance. To solve this, we use the concept of independent events in probability. Since each selection is independent, and the probability that one adult has health insurance is 0.79, the probability that all four adults have health insurance is the product of their individual probabilities.
So the calculation would be:
0.79 times 0.79 times 0.79 times 0.79
This equals approximately 0.389 or rounded to the nearest thousandth, 0.389.
Line C: y = x + 12 Line D: y = 3x + 2 Which of the following shows the solution to the system of equations and explains why? (A) (4, 14), because one of the lines passes through this point.(B) (4, 14), because the point lies between the two axes(C) (5, 17), because both lines pass through this point(D) (5, 17), because the point does not lie on any axis
Answer:
C)
Step-by-step explanation:
We are given with a pair of linear equations,
y=x+12
y=3x+2
Let us solve them for x and y
In order to solve them we subtract first equation from the second ,
0=2x-10
Adding 2x on both sides we get
2x=10
Dividing both sides by 2 we get
x=5
Now replacing this value of x in first equation
y=5+12=17
Hence the solution of the two equations is (5,12)
And by solution of a linear pair of equations, we mean that both the lines passes through that point.
Match the operation on the right with its inverse operation on the left
Answer:
Multiplication with division
Subtraction with addition
Division with multiplication
addition with subtraction
Step-by-step explanation:
they are the opposite of each other... just that simple :))
hope this helps.
Answer:
Multiplication matches with division.
Subtraction matches with addition.
Division matches with multiplication.
Addition matches with subtraction.
Step-by-step explanation: Addition adds to something while subtraction takes away something. Dividing a number gets it much smaller, and multiplying gets a number much bigger.
Find the angle between the given vectors to the nearest tenth of a degree. u = <6, 4>, v = <7, 5>
Answer: 1.8°
Step-by-step explanation:
To calculate the angle between the vectors u and v we use the formula of the dot product.
The dot product between two vecotores is:
[tex]u\ *\ v = |u||v|*cosx[/tex]
Where x is the angle between the vectors
As we know the components of both vectors, we calculate the dot product by multiplying the components of both vectors
[tex]u=6i + 4j\\v=7i +5j[/tex]
Then:
[tex]u\ *\ v = 6*7 + 4*5[/tex]
[tex]u\ *\ v = 42 + 20[/tex]
[tex]u\ *\ v =62[/tex]
Now we calculate the magnitudes of both vectors
[tex]|u|=\sqrt{6^2 + 4^2}\\\\|u|=2\sqrt{13}[/tex]
[tex]|v|=\sqrt{7^2 +5^2}\\\\|v|=\sqrt{74}[/tex]
Then:
[tex]62 = 2\sqrt{13}*\sqrt{74}*cosx[/tex]
Now we solve the equation for x
[tex]62 = [tex]cosx=\frac{62}{2\sqrt{13}*\sqrt{74}}\\\\x=arcos(\frac{62}{2\sqrt{13}*\sqrt{74}})\\\\x=1.8\°[/tex]
Ancient paintings were found on cave walls in South America. The Carbon-14 in the paintings was measured and was found to be 19% of the original weight. How old were the paintings?
A. 3,839
B. 9,239
C. 13,839
D. 19,239
Answer: C. 13,839 (the answer is not among the given options, however the result is near this value)
Step-by-step explanation:
The exponential decay model for Carbon- 14 is given by the followig formula:
[tex]A=A_{o}e^{-0.0001211.t}[/tex] (1)
Where:
[tex]A[/tex] is the final amount of Carbon- 14
[tex]A_{o}=[/tex] is the initial amount of Carbon- 14
[tex]t[/tex] is the time elapsed (the value we want to find)
On the other hand, we are told the current amount of Carbon-14 [tex]A[/tex] is [tex]19\%=0.19[/tex], assuming the initial amount of Carbon-14 [tex]A_{o}=[/tex] is [tex]100\%[/tex]:
[tex]A=0.19A_{o}[/tex] (2)
This means: [tex]\frac{A}{A_{o}}=0.19[/tex] (2)
Now,finding [tex]t[/tex] from (1):
[tex]\frac{A}{A_{o}}=e^{-0.0001211.t}[/tex] (3)
Applying natural logarithm on both sides:
[tex]ln(\frac{A}{A_{o}})=ln(e^{-0.0001211.t})[/tex] (4)
[tex]ln(0.19)=-0.0001211.t[/tex] (5)
[tex]t=\frac{ln(0.19)}{-0.0001211}[/tex] (6)
Finally:
[tex]t=13713.717years[/tex] This is the age of the paintings and the option that is nearest to this value is C. 13839 years
Quadrilateral ABCD is reflected across the x-axis and then reflect across the y-axis to form quadrilateral A?B?C?D?. If the coordinates of vertex A are (-7, 3), what are the coordinates of vertex A??
Answer:
A'(7,-3)
Step-by-step explanation:
We were given the coordinates, A(-7,3) of quadrilateral ABCD and we want to find the image of A after a reflection across the x-axis followed by a reflection in the y-axis.
When we reflect A(-7,3) across the x-axis we negate the y-coordinate to obtain: (-7,-3).
When the image is again reflected in the across the y-axis, we negate the x-coordinate to get (--7,-3).
Therefore the coordinates of A' after the composed transformation is (7,-3).
Answer:
it is c
Step-by-step explanation:
Nick recently started a landscaping company. He began with 3 3 clients. Thanks to word-of-mouth referrals, his clients double each month. How many clients will Nick have after one year?
Answer:
6144 clients
Step-by-step explanation:
Number of clients in the beginning = 3
The number of clients doubled each month. This means for every month the number of clients was 2 times the previous month. This can be modeled by a geometric sequence, with first term as 3 and common ratio of 2.
The general formula for the geometric sequence is:
[tex]a_{n}=a_{1}(r)^{n-1}[/tex]
Here,
[tex]a_{1}[/tex] is the first term of the sequence which is 3
r is the common ratio which is 2 and n represents the number of term.
We need to calculate the number of clients after 1 year i.e. after 12 months. So here n will be 12. Using these values, we get:
[tex]a_{12}=3(2)^{12-1}=6144[/tex]
Thus, after 1 year the company started by Nick will have 6144 clients
Answer:
12,288
Step-by-step explanation:
all i did was multiple the previous outputs by 2.
3
6
12
24
48
96
192
384
768
1536
3072
6144
12288
NEED HELP FAST!!!!!!!!!!!
John the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 3 clients who did Plan A and 5 who did Plan B. On Saturday there were 9 clients who did Plan A and 7 who did Plan B. John trained his Friday clients for a total of 6 hours and his Saturday clients for a total of 12hours. How long does each of the workout plans last?
Answer:
45 minutes each
Step-by-step explanation:
Set Plan A clients as x and Plan B clients as y to make a system of equations, the constant is the number of hours worked.
3x+5y=6
9x+7y=12
Now solve using substitution or elimination. I will use elimination.
-9x-15y=-18 I multiplied the whole first equation by -3 to eliminate x.
9x+7y=12, add the equations
-8y=-6 solve for y
y= 3/4 of an hour or 45 minutes
Next plug y into either equation
3x+5(3/4)=6 Solve for x.
3x+15/4=6
3x=2.25
x=0.75, also 45 minutes
To check plug in each variable value to each equation to see if they work if you need to.
Simplify. –2.2 – 3.1 A. 0.9 B. 5.3 C. –5.3 D. –0.9
Answer:
C. -5.3
Step-by-step explanation:
Simply add the negatives straight across to arrive at your answer.
I am joyous to assist you anytime.
Answer: C.-5.3
Step-by-step explanation: I could be wrong
Solving Quadratic Equations posttest
A.
B.
C.
D.
Answer:
D. [tex] x = 3 \pm \sqrt{10} [/tex]
Step-by-step explanation:
[tex] x^2 - 6x - 1 = 0 [/tex]
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
a = 1; b = -6; c = -1
[tex] x = \dfrac{-(-6) \pm \sqrt{(-6)^2 - 4(1)(-1)}}{2(1)} [/tex]
[tex] x = \dfrac{6 \pm \sqrt{36 + 4}}{2} [/tex]
[tex] x = \dfrac{6 \pm \sqrt{40}}{2} [/tex]
[tex] x = \dfrac{6 \pm \sqrt{4 \times 10}}{2} [/tex]
[tex] x = \dfrac{6 \pm 2 \sqrt{10}}{2} [/tex]
[tex] x = 3 \pm \sqrt{10} [/tex]
Draw the following regular polygons inscribed in a circle:
pentagon
hexagon
decagon
dodecagon (12-gon)
For each polygon, include the following information in the paragraph box below:
What was the central angle you used to locate the vertices? Show your calculation.
What is the measure of each interior angle of the polygon? Show your calculation.
What is the relationship between the central angle and the interior angle?
As the number of sides increases, how do the angles change?
please help !! PLZ HELP WILL MARK BRAINLIEST
Answer:
first attachment has pentagon and decagonsecond attachment has hexagon and dodecagoncomputation info explained belowStep-by-step explanation:
1, 2. Central Angle, Interior Angle
See the 3rd attachment for the values. (Angles in degrees.)
The central angle is 360°/n, where n is the number of vertices. For example, the central angle in a pentagon is 360°/5 = 72°.
The interior angle is the supplement of the central angle. For a pentagon, that is 180° -72° = 108°.
These formulas were implemented in the spreadsheet shown in the third attachment.
3. Angles vs. Number of Sides
The size of the central angle is inversely proportional to the number of sides. In degrees, the constant of proportionality is 360°.
_____
Comment on the drawings
The drawings are made by a computer algebra program that is capable of computing the vertex locations around a unit circle based on the number of vertices. The only "work" required was to specify the number of vertices the polygon was to have. The rest was automatic.
The above calculations describe how the angles are computed. Converting those to Cartesian coordinates for the graphics plotter involves additional computation and trigonometry that are beyond the required scope of this answer.
These figures can be "constructed" using a compass and straightedge. No knowledge of angle measures is required for following the recipes to do that.
Answer:
The other guy is right but I wrote this
Step-by-step explanation:
Please show me how you did it
Using the law of sin.
Sin(angle) = Opposite leg / hypotenuse
Sin(33) = x / 23
Solve for x:
Multiply both sides by 23:
x = sin(33) * 23
x = 12.5267
Rounded to the nearest hundredth = 12.53 cm.
Check the picture below.
make sure your calculator is in Degree mode.
If f(x) = x - 1 and g(x) = x3, what is (g•f)(8)?
Enter the correct answer
I will assume that you meant to type (g o f)(8).
First we find f(8).
f(8) = 8 - 1 or 7.
We now find g(f(8)), which means g(7).
g(7) = 7^3 or 343
Answer:
(g o f)(8) = 343
Answer:7^3
Step-by-step explanation:
f(8)=8-1=7
g(f(8))= 7^3
PLEASE HELP ME WITH THIS MATH QUESTION
Answer:
area of circle = 9/64 π square inches
Step-by-step explanation:
Points to remember
Area of circle = πr²
Where 'r' is the radius of circle
It is given that diameter of circle = (3/4) in
Therefore radius r = diameter/2 = (3/4)/2 = 3/8 in
To find the area of circle
Area = πr²
= π(3/8)²
= π * 9/64
= 9/64 π square inches
The correct answer is 9/64 π square inches
PLEASE HELP ME WITH THIS MATH QUESTION
Answer:
The measure of arc EF = 146°
Step-by-step explanation:
From the figure we can see two circles with same center.
From the figure itself we get measure of arc AB is same as measure of arc EF, measure of arc Ac is same as measure of arc ED and measure of arc BC is same as arc FD.
The measure of arc AB = 146°
Therefore the measure of arc EF = 146°
Janice is trying to earn $30 to buy a necklace. She has saved $5.25. She earns $2.25 per hour weeding her grandmother's garden and she earns $5.50 per hour selling seashells at the flea market. Will Janice have enough to buy the necklace if she works in the garden for 2 hours and at the flea market for 4 hours? Use the inequality 2.25y + 5.50z + 5.25 ? 30. Yes, because the total will be $26.50. Yes, because the total will be $31.75. No, because the total will be $25.25. No, because the total will be $46.50.
Answer:
Yes, because the total will be $31.75
Step-by-step explanation:
Let
x -----> number of hours weeding grandmother's garden
z ----> number of hours selling seashells at the flea market
we know that
The inequality that represent this situation is
[tex]2.25x+5.50z+5.25\geq30[/tex]
so
For x=2 hours, z=4 hours
substitute in the inequality
[tex]2.25(2)+5.50(4)+5.25\geq30[/tex]
[tex]4.50+22+5.25\geq30[/tex]
[tex]31.75\geq30[/tex] -----> is true
therefore
Janice will have enough to buy the necklace
Answer:
yes
Step-by-step explanation:
because the total will be $31.75.
The product of two positive numbers is 750. The first number is 5 less than the second number. The equation x(x – 5) = 750 can be used to find x, the value of the greater number. What is the value of the greater number? 15 25 30 50
Answer:
30
Step-by-step explanation:
You can try the answer choices to see what works.
15·10 ≠ 750
25·20 ≠ 750
30·25 = 750 . . . . the larger number is 30
50·45 ≠ 750
Answer:
The value of the greater number is 30.
Step-by-step explanation:
We need to find the values of x that satisfy the equation :
[tex]x(x-5)=750[/tex]
Working with the equation ⇒
[tex]x(x-5)=750[/tex]
[tex]x^{2}-5x=750[/tex]
[tex]x^{2}-5x-750=0[/tex]
Given an equation with the form
[tex]ax^{2}+bx+c=0[/tex]
We can use the quadratic equation to find the values of x
[tex]x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex] and
[tex]x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
With [tex]a=1\\b=-5\\c=-750[/tex] we replace in the equations of x1 and x2 ⇒
[tex]x1=\frac{-(-5)+\sqrt{(-5)^{2}-4.(1).(-750)}}{2.(1)}=30[/tex]
[tex]x1=30[/tex] is a solution of the equation [tex]x^{2}-5x-750=0[/tex]
Now for x2 ⇒
[tex]x2=\frac{-(-5)-\sqrt{(-5)^{2}-4.(1).(-750)}}{2.(1)}=-25[/tex]
[tex]x2=-25[/tex] is a solution of the equation [tex]x^{2}-5x-750=0[/tex]
Given that both numbers are positive ⇒
[tex]x>0[/tex] and [tex](x-5)>0\\x>5[/tex]
Therefore, x2 is not a possible value for the greater number
The greater number is [tex]x1=30[/tex]
Is the pythagorean theorem only for right triangles
Yes, the Pythagorean Theorem only works with right triangles.
You can use it to solve for the hypotenuse, or either one of the sides depending on the information you are provided with.
Answer:
yes
Step-by-step explanation:
Find the value of x if m arc ADC = (4x + 4)° and m angle ABC = 150°.
Answer:
The measure of angle x is 74°
Step-by-step explanation:
we know that
The inscribed angle measures half of the arc that comprises
so
∠ABC=(1/2)[arc ADC]
substitute the given values
150°=(1/2)[4x+4]
300°=[4x+4]
4x=300-4
4x=296
x=74°
the vertex of this parabola is at (5,-4). which of the following could be its equation?
Answer:
Option D
Step-by-step explanation:
The equation of a parabola in vertex form is
[tex]y = a(x - h)^{2} + k[/tex]
Where (h,k) is the vertex.
We were given the vertex as (5,-4). This implies that:
h=5, k=-4, we can see that a=2 is the leading coefficient of all the options.
We substitute the values to get:
[tex]y = 2(x - 5)^{2} + - 4[/tex]
Or
[tex]y =2( {x - 5)}^{2} - 4[/tex]
If f(x) = 2x – 8 and g(x) = √x-5
what is (fºg)(30)?
Answer:
2.
Step-by-step explanation:
(f o g)(x) = 2(√(x-5)) - 8
So (f o g)(30) = 2 √(30-5) - 8
= 2 * √25 - 8
= 2* 5 - 8
= 2.
To find (f ° g)(30) for the functions f(x) = 2x - 8 and g(x) = √x-5, you first calculate g(30), which is 5, and then apply f to this result to get f(5) = 2. Therefore, (f ° g)(30) equals 2.
If f(x) = 2x - 8 and g(x) = √x-5, we want to find (f ° g)(30). The notation (f ° g)(x) means we apply g(x) first and then apply f(x) to the result of g(x). Thus, we first find g(30).
Calculate g(30):
g(30) = √(30 - 5)g(30) = √25g(30) = 5
Now that we have g(30), we apply f to this value:
f(g(30)) = f(5)f(5) = 2(5) - 8f(5) = 10 - 8f(5) = 2
Therefore, (f ° g)(30) = 2.
A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.)
Answer:y = 18(1.15)^x
Step-by-step explanation:
g o o g ; e
Answer:
The required equation is [tex]y = 18(1.15)^x[/tex].
Step-by-step explanation:
Consider the provided information.
The Initial value of poster = $ 18
After 1 year amount of increase = $ 20.70
With the rate of 15% = 0.15
Let future value is y and the number of years be x.
[tex]y = 18(1.15)^x[/tex]
Now verify this by substituting x=1 in above equation.
[tex]y = 18(1.15)^1=20.7[/tex]
Which is true.
Hence, the required equation is [tex]y = 18(1.15)^x[/tex].
URGENT PLEASE HELP ME WITH THIS MATH QUESTION PLEASE FILL ALL BLANKS
Answer:
see explanation
Step-by-step explanation:
Translate 4 units to the left and then reflect over the x- axis
The decimal form of 43% is
Answer:
.43
Step-by-step explanation:
If I see % in a number I like to think of it as times 1/100 or divided by 100 (those are the same thing).
So we are doing 43 divided by 100 (or 43/100) which gives you .43 .
Anytime you divide by 100 you have to move the decimal left twice. (43 is 43. so 43. divided by 100 is .43)
Example
23.5%=.235
Why?
23.5 divided by 100 is .235
Another example
4%=.04
Why?
4. divided by 100 is .04
Many newspapers carry a certain puzzle in which the reader must unscramble letters to form words. how many ways can the letters of emdangl be arranged? identify the correct unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters.
The sequence "emdangl" rearranges to "mangled" (an appropriately fitting word scramble solution).
There are 7 letters in the sequence "emdangl", so there are 7! = 7*6*5*4*3*2*1 = 5040 different permutations of the seven letters. The exclamation mark is shorthand to represent factorial notation. Factorials are the idea of multiplying from that integer counting down until you get to 1. The reason why this works is because we have 7 letters to pick from for the first slot, then 6 for the next, and so on until all seven slots are filled out.
Since there is one solution ("mangled") out of 5040 total permutations, this means the probability of getting the solution just by random chance/guessing is 1/5040
Use a calculator shows that 1/5040 = 0.0001984 approximately.
The word 'emdangl' can be arranged in 5040 ways. The probability of randomly selecting one arrangement is 1/5040.
Explanation:The word 'emdangl' has 7 letters. To find the number of ways the letters can be arranged, we use the formula for permutations of distinct objects, which is n-factorial (n!). For this word, there are 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 ways to arrange the letters.
Now, let's determine the probability of randomly selecting one arrangement of the given letters. Since there is only one correct unscrambling, the probability is 1 out of the total number of arrangements, which is 1/5040.
Learn more about Permutations here:https://brainly.com/question/23283166
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Jane and Lee had dinner at The Palace The bill totaled $20 30 with tax The service
was good, so they decided to leave a 15% tip. What is 15% of $20 30. to the
nearest cent?
Answer:
$3.45
Step-by-step explanation:
$20.30 / 10 = $2.30 = 10%
$2.30 / 2 = $1.15 = 5%
$2.30 + $1.15 = $3.45 = 15%
Use the unit circle to find the value of sin 3π/2 and cos 3π/2. Show work please!
Answer:
Step-by-step explanation:
3π/2 is equivalent to 270°. The "opposite side" for this angle is -2; the adjacent side is 0, and the hypotenuse is 2.
Thus, sin 3π/2 = opp/hyp = -2/2 = -1, and
cos 3π/2 = adj/hyp = 0/2 = 0.
Answer:
[tex]sin\frac{3\pi}{2}=-1[/tex] and [tex]cos\frac{3\pi}{2}=0[/tex]
Step-by-step explanation:
We are given that a unit circle
We have to find the value of [tex]sin\frac{3\pi}{2}[/tex] and [tex]cos\frac{3\pi}{2}[/tex] by using the unit circle
Radius of circle=r=1 unit
We know that
[tex]x=r cos\theta[/tex] and [tex]y=r sin\theta[/tex]
We [tex]\theta=\frac{3\pi}{2}[/tex]
Then x=[tex]1\cdot cos\frac{3\pi}{2}[/tex]
[tex]x=cos (2\pi-\frac{\pi}{2})[/tex]
[tex]x=cos \frac{\pi}{2}[/tex] ([tex]cos(2\pi-\theta)=cos\theta[/tex])
[tex]x=0 (cos\frac{\pi}{2}=0)[/tex]
[tex]y=1\cdot sin\frac{3\pi}{2}[/tex]
[tex]y=sin(2\pi-\frac{\pi}{2})[/tex]
[tex]y=-sin\frac{\pi}{2}[/tex] ([tex]sin(2\pi-\theta)=-sin\theta[/tex])
[tex]y=-1[/tex] ([tex]sin\frac{\pi}{2}=1[/tex])
Hence, [tex]sin\frac{3\pi}{2}=-1[/tex] and [tex]cos\frac{3\pi}{2}=0[/tex]
I am having a hard time with this proof of vertical angles. The choices for them are at the bottom.
Answer:
Angles 1 and 3 are verical: Given
Angles 1 and 3 are formed by ntersecting lines:
Definition of vertical angles.
Angles 1 and 2 are a linear pair and angles 2 and 3 are a linear pair:
Definition of linear pair.
1 and 2 are supplementary, and 2 and 3 are supplementary:
Linear Pair Theorem
Angles 1 and 3 are congruent:
Congruent Supplement Theorem
Step-by-step explanation:
The first is given because it tells you it is given.
The second is the definition of vertical angles. Vertical angles are angles formed by two intersecting lines.
The third statement is the definition of linear pair. Linear pair is a pair of adjacent angles formed by two lines that intersect.
The fourth statement comes from the theorem of linear pairs. Linear pair theorem states that if you have 2 angles that are a linear pair, then they are supplementary.
The fifth statement comes from the congruent supplement theorem. It says if 2 angles are supplementary to the same angle, then they are congruent to each other.