we have the expression
sin(x − y) − sin(x + y)
Remember that
sin(x-y)=sinxcosy-cosxsiny
and
sin(x+y)=sinxcosy+cosxsiny
Substitute in the given expression
sinxcosy-cosxsiny-[sinxcosy+cosxsiny]
Remove the parenthesis
sinxcosy-cosxsiny-sinxcosy-cosxsiny
Combine like terms
-2cosxsiny
therefore
The answer is
−2(cos x)(sin y)Below is a savings plan for Adrienne. Use this table to answer the questions below. # of Months Saving Account Balance $85 6 $105 9 $120 $145 $165 18 Ich 13. How much money will Adrienne have saved in 24 months? 11 months? 14. How much money will Adrienne have saved after only 1 month? 5 months? 15. In how many months will Adrienne have saved $1257 $1907 16. What is the rate of change? 17. What was more challenging about this problem than the other problem with the table? How can knowing the rate of change help you in answering questions in this problem? 18. what is the y-intercept 19. what is the algebraic equation for Adrienne's saving plan?
ANSWERS
13. $195 (24 months) and $130 (11 months)
14. $80 (1 month) and $100 (5 months)
15. 10 months ($125) and 23 months ($190)
16. 5
18. 75
19. y = 5x + 75
EXPLANATION
To answer all of these questions we have to find the equation first.
The equation that relates the account balance (y) to the number of months saving (x) is,
[tex]y=mx+b[/tex]Where m is the slope - also called rate of change, and b is the y-intercept.
The slope of a line passing through points (x1, y1) and (x2, y2) is,
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]We can find the slope by choosing any two pairs of (# of months, account balance). Let's find it with the pairs (2, 85) and (6, 105),
[tex]m=\frac{105-85}{6-2}=\frac{20}{4}=5[/tex]The slope of the line is 5, so for now, the equation is,
[tex]y=5x+b[/tex]To find the y-intercept we have to replace y and x with any pair of points from the table and solve for b. Let's use the first one,
[tex]\begin{gathered} 85=5\cdot2+b \\ b=85-10 \\ b=75 \end{gathered}[/tex]The y-intercept is 75. And the equation is y = 5x + 75.
To find the answers to the questions in parts 13 and 14, we just have to replace x by the number of months given and solve:
• 24 months,
[tex]y=5\cdot24+75=120+75=195[/tex]• 11 months,
[tex]y=5\cdot11+75=55+75=130[/tex]• 1 month,
[tex]y=5\cdot1+75=80[/tex]• 5 months,
[tex]y=5\cdot5+75=25+75=100[/tex]To solve the two questions in part 15 first we have to solve the equation for x. Subtract 75 from both sides,
[tex]\begin{gathered} y-75=5x+75\cdot75 \\ 5x=y-75 \end{gathered}[/tex]And divide both sides by 5,
[tex]\begin{gathered} \frac{5x}{5}=\frac{y-75}{5} \\ x=\frac{1}{5}y-15 \end{gathered}[/tex]So if we want to find the number of months until she saved $125, we have to replace y with 125,
[tex]x=\frac{1}{5}\cdot125-15=25-15=10[/tex]And the same applies to $190,
[tex]x=\frac{1}{5}\cdot190-15=38-15=23[/tex]Tell whether a correlation is likely in thissituation. If so, tell whether there is acausal relationship. Explain yourreasoning.the age of your parents and the length ofyour hair
A correlation is not likely between the age of your parents and the length of your hair.
This is owing to the fact that the length of your hair is a factor entirely dependent on your individual biological composition and lifestyle choices.
Write the equation for a parabola with a focus at (6, 7) and a directrix at x = 1.
ANSWER
[tex]\text{ The equation of the parabola is; \lparen y - 7\rparen}^2\text{ = 10\lparen x - 3.5\rparen}[/tex]EXPLANATION
Given that;
The focus of the parabola is (6, 7)
The directrix is 1
Follow the steps below to find the equation of the parabola
Step 1; Write the general formula of the parabola equation
[tex]\text{ \lparen y - k\rparen}^2\text{ = 4p\lparen x - h\rparen}^[/tex]Recall, that the vertex of the parabola midway between the focus and directrix
Hence, h can be calculated below has
[tex]\begin{gathered} \text{ h = }\frac{\text{ k}}{\text{ 2}} \\ \\ \text{ h = }\frac{7}{2} \\ \text{ h = 3.5} \end{gathered}[/tex]Also, p is the distance of vertex to directrix
p = 6 - 3.5
p = 2.5
Step 2; Substitute the calculated data into the formula in step 1
[tex]\begin{gathered} \text{ \lparen y - 7\rparen}^2\text{ = 4}\times2.5\text{ \lparen x - 3.5\rparen} \\ \text{ \lparen y - 7\rparen}^2\text{ = 10\lparen x - 3.5\rparen} \end{gathered}[/tex]Answer:
x=(y-7)^2/10 +7/2
Step-by-step explanation:
khan
Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 86 km slower than the other. If the two planes are 9450 h kilometers apart after 5 hours, what is the rate of each plane?
Let 'd' be the distance that the faster plane travels, then the distance that the slower plane travels is:
[tex]9450-d[/tex]Now, let 's' be the speed of the faster plane, then similarly, the speed of the slower plane is:
[tex]s-86[/tex]We have the following equation for the faster plane:
[tex]d=5\cdot s[/tex]and the equation for the slower plane is:
[tex]9450-d=5\cdot(s-86)[/tex]Now we can do the substitution d=5s on the second equation to find the value of s:
[tex]\begin{gathered} d=5s \\ \Rightarrow9450-5s=5\cdot(s-86)=5s-430 \\ \Rightarrow9450+430=5s+5s=10s \\ \Rightarrow10s=9880 \\ \Rightarrow s=\frac{9880}{10}=988 \\ s=988 \end{gathered}[/tex]We have that the speed of the faster plane is s=988 km/h. Now we can find the speed of the slower plane:
[tex]s-86=988-86=902[/tex]Finally, we can check the answer by finding the distance traveled:
[tex]\begin{gathered} 9450-d=5\cdot(902) \\ \Rightarrow d=9450-5\cdot(902)=9450-4510=4940 \\ \text{and} \\ d=5(988)=4940 \end{gathered}[/tex]Therefore, the speed of the faster plane is 988 km/h and the speed of the slower plane is 902 km/h
standard deviation of 0.37, 0.13, 0.06,0.15,0.29
A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. Tables of the standard normal distribution are frequently used to show different regions of the normal distribution.
How do I calculate standard deviation?First, determine the mean. Step 2: Calculate the square of each data point's variance from the mean. Add the values from Step 2 in Step 3. Divide by the total number of data points in step 4.
Mean = 0.37+0.13+0.06+0.15+0.29\s=1.00
It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.
Standard deviation is the square root of variance, which is the average squared deviations from the mean. Both metrics capture distributional variability, although they use different measurement units:
The units used to indicate standard deviation are the same as the values' original ones (e.g., minutes or meters).
The units used to express variation are substantially greater.
To learn more about standard deviation refer to:
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A triangle has a 45 degree angle, a 624 degree angle, and a side 5 feet in length.Select True or False for each statement about this type of triangle.TrueFalseThe triangle must be a scalene triangle.The triangle must be an acute triangle.The triangle must contain another angle that is 623 degrees.
The addition of the three angles of a triangle is equal to 180°, then the measure of the third angle is:
x = 180° - 45° - 62.5°
you download 2 movies and 3 songs the next week you download 1 movie and 5 songs.what is the total cost of the downloads?
Price of downloads of number of movies and songs is given by function g(x) =2x and f(x) = (x/2) +2 respectively , then total cost of the downloads of total 3 movies and 8 songs is equal to 12 dollars.
As given in the function,
Price of downloads of number of movies represented by
g(x) = 2x
where x is the number of movies
Price of downloads of number of songs represented by
f(x) = (x /2) +2
where x is the number of songs
Total number of downloads
First week
Number of movies downloads = 2
Number of songs downloads =3
Next week
Number of movies downloads = 1
Number of songs downloads = 5
Total movies = 2+1
=3
Cost of downloads 3 movies
g(3)= 2(3)
=6
Total songs =3+5
= 8
Cost of downloads8 songs
f(8)= (8/2) +2
=6
Total cost of the downloads = 6 +6
= 12 dollars
Therefore, price of downloads of number of movies and songs is given by function g(x) =2x and f(x) = (x/2) +2 respectively , then total cost of the downloads of total 3 movies and 8 songs is equal to 12 dollars.
The complete question is :
The price for digital downloads of music is represented by the linear function f(x) shown on the graph. The price for digital downloads of movies is represented by g(x) = 2x, where x is the number of movies downloaded and g(x) is the total cost in dollars. Graph of a line with equation f of x equals one half times x plus 2. The x-axis is labeled Number of Songs, and the y-axis is labeled Price in Dollars.
You download 2 movies and 3 songs the next week you download 1 movie and 5 songs. What is the total cost of the downloads?
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What is the b-value of y= 4cos(8pix)A. 8 pi xB. 0C. 8 piD. 4What is the period of the same function?A. 2piB. 1/4C. 4D. 8pi
Answer:
C. B-Value = 8π
B. Period =1/4
Explanation:
The standard form of the trigonometric function is given as:
[tex]y=A\cos (Bx-C)+D[/tex]Comparing the given equation:
[tex]y=4\cos (8\pi x)[/tex]We see that the B-value of the function:
[tex]\begin{gathered} Bx=8\pi x \\ B=8\pi \end{gathered}[/tex]The B-Value is 8π.
In the standard form given above, the period of the function is calculated below.
[tex]\begin{gathered} \text{Period}=\frac{2\pi}{B} \\ =\frac{2\pi}{8\pi} \\ =\frac{2}{8} \\ \text{Period}=\frac{1}{4} \end{gathered}[/tex]The period of the function is 1/4.
On a track for remote controlled racing cars, racing car A completes the track in 36 seconds, while racing carB completes in 24 seconded If they both start at the same time after how many seconded will they be side by side againConvert the answer to show how many minute and seconded it would take for them to be side by side again
Okay, here we have this:
Here we need to identify how many seconds will it take for the two cars to meet again, therefore for this we are going to find the least common multiple of the two numbers (36, 24):
To do this, we will first decompose each number, and then we will multiply each factor the greatest number of times that it occurs in any of the numbers:
36=2*2*3*3
24=2*2*2*3
LCM(36, 24)=2*2*2*3*3
LCM(36, 24)=72 seconds.
Finally we obtain that the two cars will take 72 seconds to meet again, this is equivalent to 1 minute and 12 seconds.
2n-5=11Two step equation
You have the following equation:
|2n + 5| = 11
In order to solve the previoues equation for n, you take into account that an equation with an absolute value has two solutions. In this case you have:
2n + 5 = 11
2n + 5 = - 11
That is, the equation must be solved for both cases.
For the first equation you have:
2n + 5 = 11 you add 5 both sides
2n = 11 - 5
2n = 6 divide by 2 both sides
n = 6/2
n = 3
For the second equation you have:
2n + 5 = -11 add 5 both sides
2n = -11 - 5
2n = -16 divide by 2 both sides
n = -16/2
n = -8
Hence, the solutions to the given equation are:
n = {3,-8}
(2x-1) (3x-1)=15my choices area)3b)0c)-6d)-1
(2x-1) + (3x-1) = 15
2x - 1 + 3x - 1 = 15
rearrange
2x + 3x - 1 -1 = 15
5x -2 = 15
5x = 15 + 2
5x = 17
Divide both sides by 5
x = 17/5
= 3.4
Rounding to 3
Option a)3
) Which replacement for a makes this not a function?
Here, f(x) is a function if corresponding to every image there exist a unique pre-image.
So, f(x) is not a function if a an x value repeats.
Here, the other x values are 4, 9, 12.
If the 'a' is any of these x value f(x) is not a function.
Therefore, for f(x) to be not a function 'a' should be chosen as 4.
Hence, the correct option is first option.
i need help with my homewrok PLEASE CHECK WORK number 6
Given: The graph of an exponential function as shown in the image
To Determine: The equation of the given graph
Solution
The general equation of an exponential equation is
[tex]\begin{gathered} y=ab^x \\ a=vertical\text{ stretch} \\ b=common-ratio \end{gathered}[/tex]Let us pick a point from the graph and the value of common ratio to solve for a
Please note that the common ratio is 2 because the processing power doubles every year
So
[tex]\begin{gathered} Point:(0,60),b=2 \\ y=ab^x \\ 60=a(2)^0 \\ 60=a(1) \\ 60=a \\ a=60 \end{gathered}[/tex]Let us substitute a and b into the general equation would given us
[tex]y=60(2)^x[/tex]Hence, the equation is
y = 60 (2)ˣ
Sorry for the bad photo quality! I will write out what the question is asking (geometry)Write or draw a counter example to the following conditionals #18: if a polygon is a quadrilateral, then it has four right angles
The given statement is,
If a polygon is a quadrilateral, then it has four right angles.
To write a counterexample to the given statement:
The statement, "If a polygon is a quadrilateral, then it has four right angles" is not always possible.
Because rhombus is one such figure which has four sides and none of its angles are right angles.
Thus, a counterexample for the statement, "If a polygon is a quadrilateral, then it has four right angles" is Rhombus.
There are 13 balls numbered 1 through 13 placed in a bucket. What is the probability of reaching into the bucket and randomly drawing two balls numbered 12 and 2without replacement, in that order? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Explanation
We are given the following:
• 13 balls numbered 1 through 13 placed in a bucket.
We are required to determine the probability of randomly drawing two balls numbered 12 and 2 without replacement, in that order.
This is achieved thus:
The probability of randomly selecting a ball numbered 12 from the bucket is:
[tex]Pr.(12)=\frac{1}{13}[/tex]The probability of randomly selecting 2 from the bucket after the first selection is:
[tex]Pr.(2)=\frac{1}{12}[/tex]Therefore, the probability of randomly selecting two balls numbered 12 and 2 is:
[tex]\begin{gathered} Pr.=\frac{1}{13}\times\frac{1}{12} \\ Pr.=\frac{1}{156} \end{gathered}[/tex]Hence, the answer is:
[tex]\frac{1}{156}[/tex]the figure below is a net for a right rectangular prism. its surface area is 252 m^2 and the area of sine of tye faces are filled in below. find the area of the missing faces and the missing dimension
Notice that:
[tex]Total\text{ Area=72m}^2+36m^2+72m^2+36m^2+2A=252m^2.[/tex]Solving the above equation for A, we get:
[tex]\begin{gathered} 2A=252m^2-(\text{72m}^2+36m^2+72m^2+36m^2), \\ 2A=36m^2, \\ A=\frac{36m^2}{2}, \\ A=18m^2. \end{gathered}[/tex]Now, recall that the area of a rectangle is given by the following formula:
[tex]Area=height*length.[/tex]Therefore:
[tex]A=6m*?=18m^2.[/tex]Solving for ?, we get:
[tex]?=\frac{18m^2}{6m}=3m.[/tex]Answer:The area of the missing face is
[tex]18m^2.[/tex]The length of each missing side is:
[tex]3m.[/tex]Circle terms and simplify the expression50+3(-10)+2(-20)
The given expression is
[tex]50+3(-10)+2(-20)[/tex]First, we solve the products.
[tex]50-30-40[/tex]Then, we sum.
[tex]-20[/tex]Therefore, the answer is -20.g(x)=1/2x−4. Evaluate g(10) please help me
Hello there. To solve this question, we'll need to plug in the value of x to find the value of the function in that point.
Let g(x) = 1/(2x - 4).
To evaluate g(10), we need to plug in x = 10 to the function
g(10) = 1/(2*10 - 4)
Multiply the values
g(10) = 1/(20 - 4)
Subtract the values
g(10) = 1/16.
QUESTION 2
To calculate the average rate of change of the amount of money, we'll need to use the slope formula.
The slope m of a line passing through two points (x0, y0) and (x1, y1) is given by: m = (y1-y0)/(x1-x0)
As you can see on the graph, in the 0-th month, Sarah had $200 in her account. In the 12-th month, she had $500.
Which means we have the points (0, 200) and (12, 500)
Using the slope formula, we get:
AVG = (500 - 200)/(12-0)
Subtract the values
AVG = 300/12
AVG = 25
This is the average rate of change of the amount of money. If you wanted the instantaneous rate of change, we would be talking about derivatives. In this case, the values would be equal since we dealing with a line and the slope is the leading coefficient of the line equation.
Find the area of the pentagon in the diagram below. A 15 square inches B 20 square inches C25 square inches D 28 square inches
we divide the pentagon into two figures
Trapezium
trapezium area
[tex]\begin{gathered} A=\frac{(B+b)\times h}{2} \\ \\ A=\frac{(6+2)\times4}{2} \\ \\ A=16 \end{gathered}[/tex]the are of the trapezium is 16 square in
Triangle
triangle area
[tex]\begin{gathered} A=\frac{b\times h}{2} \\ \\ A=\frac{6\times3}{2} \\ \\ A=9 \end{gathered}[/tex]the area of the triangle is 9 square in
Total area
Sum the areas to find the area of the pentagon
[tex]\begin{gathered} 16+9 \\ =25 \end{gathered}[/tex]the pentagon area is 25 square inches
Question 10 (5 points)Find the area of the shaded portion if we know the outer circle has a diameter of 4 mand the inner circle has a diameter of 1.5 m.
Hello there. To solve this geometry question, we'll need to remember how to find the area of an annulus.
Let's start by drawing the circles:
Remember that the area of the shaded area, between the outer and inner circle, called annulus, can be calculated by subtracting the area of the outer circle and the area of the inner circle:
The area of a circle with diameter D is given by:
[tex]\pi\cdot\text{ }\frac{D\text{\textasciicircum{}2}}{4}[/tex]topic is hard for me to understand, help is appreciated
Answer:
Given vector v is,
[tex]\vec{v}=-24\vec{i}-7\vec{j}[/tex]$$=-24\vec{i}-7\vec{j}$$To find the unit vector that has the same direction as the vector v is,
Unit vector u is,
[tex]\vec{u}=\frac{\vec{v}}{\lvert\vec{v}\rvert}-----(1)[/tex]we have that,
To find a unit vector with the same direction as a given vector, we divide the vector by its magnitude.
The magnitude of a vector formula is used to calculate the length of a vector and is denoted by |v|. The magnitude of a vector is always a positive number or zero it cannot be a negative number.
[tex]\lvert x\vec{i}+y\vec{j}\rvert=\sqrt[]{x^2+y^2}[/tex]we get,
[tex]\lvert\vec{v}\rvert=\sqrt[]{24^2+7^2}[/tex][tex]=\sqrt[]{625}[/tex][tex]=25[/tex][tex]\lvert\vec{v}\rvert=25[/tex]Substitute the values in equation (1), we get
[tex]\vec{u}=\frac{-24\vec{i}-7\vec{j}}{25}[/tex][tex]\vec{u}=\frac{1}{25}(-24\vec{i}-7\vec{j})[/tex]Answer is:
[tex]\vec{u}=\frac{1}{25}(-24\vec{i}-7\vec{j})[/tex]The exponential models describe the population of the indicated country, A, in millionthe greatest growth rate? By what percentage is the population of that country increaCountryhas the greatest growth rate.
We are given the following logistic growth function P(x)
[tex]P(x)=\frac{90}{1+271e^{-0.122x}}[/tex]The function P(x) models the percentage of Americans who have coronary heart disease.
Here x is the age.
Let us find the percentage of 55-years old who have some coronary heart disease.
Substitute x = 55 into the function
[tex]\begin{gathered} P(55)=\frac{90}{1+271e^{-0.122(55)_{}_{}}} \\ P(55)=\frac{90}{1+271e^{-6.71_{}}} \\ P(55)=\frac{90}{1+0.33} \\ P(55)=67.7\% \end{gathered}[/tex]Therefore, the percentage of 55-years old with some coronary heart disease is 67.7% (rounded to one decimal)
What is 38,050,000 expressed in scientific notation?А. 3.805 x 108ОООв. 0.3805 x10^8С. 0.38 х 10-8D. 3 805 x 107
By definition, Scientific Notation has the following form:
[tex]a\cdot10^b[/tex]Where "a" is a number greater than or equal to 1, but less than 10 and "b" is an Integer.
In this case, you have this number:
[tex]38,050,000[/tex]To express it in Scientific notation, follow these steps:
-The decimal point must be after the first digit (which must not be zero), so you must move de the decimal point 7 spaces to the left, so "b" will be positive.
-Then, the exponent "b" will be 7.
So, you get 38,050,000 expressed in scientific notation is :
[tex]=3.805\cdot10^7[/tex]what is 3/5 as an equation or fraction?use an equation to write each fraction or product as a multiple of a unit fraction 3/5
Answer:
Writing as a multiple of a unit fractions, we have;
[tex]\frac{3}{5}=3\times\frac{1}{5}[/tex]Explanation:
Given the fraction;
[tex]\frac{3}{5}[/tex]A unit fraction is of the form;
[tex]\frac{1}{n}[/tex]where n is a positive integer.
Writing as a multiple of a unit fractions, we have;
[tex]\frac{3}{5}=3\times\frac{1}{5}[/tex]Complete the square rational only:Solve the equation for all values of x by completing the square.x^2 + 4x + 3 = 0
Problem:
Solve the equation for all values of x by completing the square.
x^2 + 4x + 3 = 0
remember the following:
To solve
[tex]ax^2\text{ + bx +c= }0[/tex]by completing the square, we carry out the following steps:
1. Transform the equation so that the constant term, c, is only on the right-hand side. In our case:
[tex]x^2\text{ + 4x = -3}[/tex]2. If a , the leading coefficient (the coefficient of the term x^2), is not equal to 1, divide both sides by a. Notice that in our case a = 1. Then, we don't do this step.
3. Add (b/2a)^2 to the right and the left side of the equation, that is:
[tex]x^2\text{ + 4x + (}\frac{b}{2a})^2\text{= -3 + (}\frac{b}{2a})^2[/tex]in our case note that b = 4 and a = 1, so we have:
[tex]x^2\text{ + 4x + (}\frac{4}{2})^2\text{= -3 + (}\frac{4}{2})^2[/tex]this is equivalent to say:
[tex]x^2\text{ + 4x + (2})^2\text{= -3 + (2})^2\text{ = -3+4}[/tex]this is equivalent to say
[tex]x^2\text{ + 4x + (2})^2=1[/tex]this is equivalent to say:
[tex](x+2)^2=1[/tex]now, we take the square root of both sides of the equation
[tex]\sqrt[]{(x+2)^2}=\sqrt[]{1}[/tex]this is equivalent to say:
[tex]x+2^{}=\pm1[/tex]solve for x
[tex]x=\pm1\text{ - 2}[/tex]then, we have two solutions:
[tex]x=1-2\text{ = -1}[/tex]and
[tex]x=-1-2\text{ = -}3[/tex]the two roots(zeros) are x = -1 and x = -3
The next model of a sports car will cost 5.5% less than the current model. The current model costs $34,000. How much will the price decrease in dollars? What will be the price of the next model?Decrease in price dollars?
Okay, here we have this:
Considering the provided information, we are going to calculate the requested decrease in dollars and price of the next model, so we obtain the following:
Decrease in dollars=Current price * Percent decrease
Decrease in dollars=$34000 * 5.5%
Decrease in dollars=$1870
Here we obtain that the decrease in dollars will be $1870.
Let's find now the price of the next model:
Price of the next model=Price of the current model - Decrease in dollars
Price of the next model=$34000-$1870
Price of the next model=$32130
Finally we obtain that the decrease in dollars will be $1870 and the price of nnext model is $32130.
determine weather the degree of the function is even or odd and weather the function itself is even or odd.
Answer:
The function is odd.
Explanation:
A function is classified as odd if
[tex]f(x)=-f(-x)[/tex]Graphically, this means if a function has a positive value at x = a (to the right of the y-axis), then it must have a negative value at x = -a (to the left of the y-axis).
To prove that our function is odd, we take a few examples from the graph
[tex]\begin{gathered} f(2)=-f(-2)_{} \\ f(6)=-f(-6) \end{gathered}[/tex]and so on.
Hence, our function is odd!
It was reported in a department meeting that over the past year and your hospital increased the number of employees by 4%. last year there were 389 people employed; how many are employed this year? Round to a whole number.
Since the number of employees increased by 4%, then, find what is 4% of 389 equal to. That corresponds to the amount of new employees.
To find what is 4% of 389, multiply 389 by 4/100:
[tex]389\times\frac{4}{100}=15.56\approx16[/tex]Rounded to the nearest whole number, there are 16 new employees.
Add 16 to 389 to find the total amount of employees this year:
[tex]389+16=405[/tex]Therefore, the number of employees this year is 405.
identify the following sequence as geometric, arithmetic, or neither 25, 50, 75, 100
Arithmetic sequence.
Explanation:From the question, we are to determine whether 25, 50, 75, 100 is an arithmetic or geometric sequence:
An arithmetic sequence is identified by a common difference. First, let us check whether the sequence is arithmetic.
Determine the common difference:
[tex]\begin{gathered} d=100-75=75-50=50-25 \\ d=25 \end{gathered}[/tex]Since the sequence has a common difference, therefore the sequence is an arithmetic sequence.
Graph the following ellipse and state its center and vertices
EXPLANATION:
Given;
We are given the following equation of an ellipse;
[tex]9x^2+36x+4y^2-8y=-4[/tex]Required;
We are required to graph the ellipse and state its center and vertices.
Step-by-step solution;
[tex]\begin{gathered} Re-write\text{ }in\text{ }standard\text{ }form: \\ \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1 \end{gathered}[/tex]We now have;
[tex]\begin{gathered} Our\text{ }ellipse\text{ }is\text{ }in\text{ }the\text{ }form: \\ \frac{(x-(-2)^2}{4}+\frac{(y-1)^2}{9}=1 \\ Hence: \\ \\ \frac{(x+2)^2}{2^2}+\frac{(y-1)^2}{3^2}=1 \end{gathered}[/tex]With the center given as (h, k), we now have
[tex]Center=(-2,1)[/tex]Also,
[tex]a=2,b=3[/tex]Using a graphing tool, the graph would now appear as follows;
The vertices as shown in the graph are found at the point;
[tex]\begin{gathered} (h,k+b) \\ (h,k-b) \\ Hence: \\ (-2,1+3),(-2,1-3) \\ \\ Vertices=(-2,4),(-2,-2) \end{gathered}[/tex]Therefore,
ANSWER:
[tex]\begin{gathered} Center=(-2,1) \\ \\ Vertices)=(-2,4),(-2-2) \end{gathered}[/tex]