Domain : Domain of a function is the set of input values for which the function is real and defined.
Given function is :
[tex]y=\sqrt[]{x+3}+3[/tex]Since if x less than - 3 then the square root will be into the form of complex number i,
So x ≥ -3
So Domain will be : x ≥ -3
Interval notation : [ -3, infinity)
Range : Range is the set of all the output values of the function :
The range of the funtion is:
[tex]f(x)\ge3[/tex]Intervale notation : [3, infinity)
Domain = x ≥ -3, [-3, inifinity)
Range : f(x)≥3, Interval notation [ 3, infinity)
Answer : A)
Domain x ≥- 3
Range y ≥ 3
What is the difference of the complex numbers below? (6+81)-(1-21 ) O A. 7+10) O O O B. 5+10) O C. 5+67 O 0 7 D. 7 +62
we have the expression
[tex](6+8i)-(1-2i)[/tex]Remove parenthesis
[tex]6+8i-1+2i[/tex]Group similar terms
[tex](6-1)+(8i+2i)[/tex]Combine like terms
[tex]5+10i[/tex]The answer is option BA baseball player has a batting average of 0.33. What is the probability that he has exactly 4 hits in his next 7 atbats? Round to 3 decimal places.The probability is
Given that the player can or cannot hit the ball, then this situation can be modeled with the binomial distribution.
Binomial distribution formula
[tex]P=_nC_xp^x(1-p)^{n-x}^{}[/tex]where
• P: binomial probability
,• nCx: number of combinations
,• p: probability of success in a single trial
,• x: number of times for a specific outcome within n trials
,• n: number of trials
Substituting with n = 7, x = 4, and p = 0.33, we get:
[tex]\begin{gathered} P=_7C_4(0.33)^4(1-0.33)^{7-4} \\ P=35(0.33)^4(0.67)^3 \\ P\approx0.125 \end{gathered}[/tex]The probability is 0.125
f(x)=x4-6x2 + 3 (b)(6 pts) Find the intervals where f is concave up and where it is concave down. Locate all inflection points. (You may write on the next page if you need more space for this question.)
The inflection points are (-√3, -6), (0, 3), and (√3, -6). The interval where the function is concave up is (-∞, -1)∪(1, ∞). The interval where the function is concave down is (-1, 1).
We are given a function f(x). The function f(x) is defined as x^4 - 6x² + 3. We need to find all the inflection points of the curve. To find the points of inflection, we need to differentiate the equation of the function with respect to the variable "x". After differentiation, the equation is f'(x) = 4x³ - 12x. We now equate this equation with zero, to get the values of "x".
4x³ - 12x = 0
4x(x² - 3) = 0
So, the values of "x" are ±√3 and 0. Put these values in the original equation to get the corresponding y-coordinates. The points of inflection are (-√3, -6), (0, 3), and (√3, -6). Now we need to find the intervals where the function is concave up and where it is concave down. For this, we need to differentiate the previous equation once again with respect to "x". After differentiation, the equation is f''(x) = 12x² - 12. We now equate this equation with zero, to get the values of "x". If the result is negative, then the function is concave downward. If the result is positive, then the function is concave up.
12x² - 12 = 12(x² - 1) = 0
The values of "x" are -1 and 1.
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[tex]\displaystyle\sum_{ k = 1}^{ n } ( - 21 + 5k) = 996[/tex]Solve for "n" value.
Given an equation to solve for n:
[tex]\sum ^n_{k\mathop=1}(-21+5k)=996[/tex]The expansion of the given sum is as follows:
[tex]\begin{gathered} -21+5(1)+(-21+5(2))+(-21+5(3))+\cdots+(-21+5n)=996 \\ -21n+(5+10+15+\cdots+5n)=996 \\ -21n+5(1+2+3+\cdots+n)=996 \\ -21n+5(\frac{n(n+1)}{2})=996 \\ -21n+\frac{5}{2}(n^2+n)=996 \\ -42n+5(n^2+n)=1992 \\ -42n+5n^2+5n=1992 \\ 5n^2-37n-1992=0 \end{gathered}[/tex]Now, factorise the above quadratic equation:
[tex]\begin{gathered} 5n^2+83n-120n-1992=0 \\ n(5n+83)-24(5n+83)=0 \\ (5n+83)(n-24)=0 \end{gathered}[/tex]Use zero product rule in the equation to get:
5n + 83 = 0 or n - 24 = 0 which implies n = -83/5 and n = 24.
Neglect the negative solution of the equation to get n = 24.
Thus, the answer is 24.
According to the graph, what is the solution to this system of equations? O (-4,-3) 0 (-3,-4) O (-5, 5) O (5,-5)
The intersection of the 2 lines is the point of the solution of the graph . Using the graph above , the meeting point of the 2 lines are
[tex](-4,-3)[/tex]Use systems to solve :The length of a rectangle is 2 cm more than itswidth. If the perimeter is 52 cm, find the width.
ANSWER
The width is 12 cm
EXPLANATION
The length L of the rectangle is 2 cm more than its width W. With this we have one equation:
[tex]L=W+2[/tex]Then the perimeter is 52cm, which is the sum of the sides of the rectangle:
[tex]P=W+W+L+L=2W+2L[/tex]Therefore the system to solve is:
[tex]\begin{cases}L=W+2 \\ 52=2W+2L\end{cases}[/tex]Using the substitution method we can solve just for W. Replace L in the second equation by its value in terms of W from the first equation:
[tex]52=2W+2(W+2)[/tex]Use the distributive property to eliminate the parenthesis:
[tex]52=2W+2W+4[/tex]Add like terms:
[tex]52=4W+4[/tex]And solve for W:
[tex]\begin{gathered} 4W=52-4 \\ 4W=48 \\ W=\frac{48}{4} \\ W=12 \end{gathered}[/tex]Therefore, the width of the rectangle is 12cm
Reduce to lowest terms 24/36
To reduce to the lowest terms we notice that:
[tex]\frac{24}{36}=\frac{6\cdot4}{6\cdot6}=\frac{6\cdot2\cdot2}{6\cdot2\cdot3}[/tex]now, we can eliminate the 6 and 2 that repeat in the numerator and denominator, thereforew the fraction in lowest terms is:
[tex]\frac{2}{3}[/tex]At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 32 minutes and a standard deviation of 5 minutes. What is the probability that a randomly selected customer will have to wait less than 21 minutes, to the nearest thousandth?
Given:
[tex]\begin{gathered} mean(\mu)=32 \\ Standard-deviation(\sigma)=5 \end{gathered}[/tex]To Determine: The probability that a randomly selected customer will have to wait less than 21 minutes, to the nearest thousandth
Solution
Using normal distribution formula below
[tex]P(Z<\frac{x-\mu}{\sigma})[/tex]Substitute the given into the formula
[tex]\begin{gathered} P(Z<\frac{21-32}{5}) \\ =P(Z<-\frac{11}{5}) \\ =P(Z<-2.2) \end{gathered}[/tex][tex]\begin{gathered} P(X<-2.2)=1-P(X>-2.2) \\ =1-0.986097 \\ =0.01390345 \\ \approx0.014(Nearest\text{ thousandth\rparen} \end{gathered}[/tex]Hence, the probability that a randomly selected customer will have to wait less than 21 minutes, to the nearest thousandth is 0.014
What would be the transformation of point A when reflected across the x-axis?(1, -2)(-1, 2)(-1, -2)(1, 2)
Given:
The coordinates of point A is (-1, 2).
To find:
The reflection of point A across the x-axis.
Solution:
It is known that the reflection of a point (x, y) about the x-axis is (x, -y).
So, the reflection of point A is (-1, -2).
Thus, option C is correct.
a low-wattage radio station can be heard only within a certain distance from the station. on the graph below, the circular region represents that part of the city where the station can be heard, and the center of the circle represents the location of the station. which equation represents the boundary for the region where the station can be heard,help I need the explanation for it
In order to find the equation that represents this boundary, let's use the equation of the circumference below:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where r is the radius and the center of the circumference is the point (h, k).
Looking at the image, we can see that the circumference is centered at (-6, -1), and its radius is equal 4 units.
So we can write the following equation, using h = -6, k = -1 and r = 4:
[tex](x+6)^2+(y+1)^2=16[/tex]Therefore the correct option is the second one.
a line intercepts the point (-2, 1) and it has a slope of 2 input the correct values into the point slope formula. y- ? = ? ( x- ?)
We know that the point-slope forumal is given by:
[tex]y-y_1=m(x-x_1)[/tex]where the terms: m, y₁ and x₁ are numbers.
Given that the line passes through a given points we have that:
m is the slope of the line
y₁ is the y value of that given point
x₁ is the x value of that given point
In this case we have that
1. It has a slope of 2, then m = 2
2. The line intercepts the point (-2, 1). Since (-2, 1) = (x₁, y₁) then
x₁ = -2 and y₁ = 1
We have that
m = 2
x₁ = -2
y₁ = 1
Let's replace those values in the first formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \downarrow \\ y-1=2(x-(-2)) \\ y-1=2(x+2) \end{gathered}[/tex]Answer- the point-slope formula of this line is: y - 1 = 2(x + 2)Comelius conducts an experiment where he selects a letter tile from the tiles shown, records the letter, then replaces it in the bag The table shows the results after 50 trialsA 1 0E 18T 18U 4What is the relative frequency that a letter was T? Express your answer as a fraction in simplest form
Relative frequency of T = 9/25
Explanation:Total number of T's = 18
Total number of A's = 10
Total number of E's = 18
Total number of U's = 4
Total = 18 + 10 + 18 + 4 = 50
Relative frequancy = number of time the letter occurred/total letters
Relative frequency = 18/50
To the simplest form:
Relative frequency of T = 9/25
Determine whether the relation is a function. y=4x-1 with inputs x= -3, x= -2, and x= -1
Given the equation:
[tex]y=4x-1[/tex]This is a linear relation, and particularly, it is a function because each x-value has one and only one y-value given by the equation above.
We evaluate this function for x = -3, x = -2, and x = -1:
[tex]\begin{gathered} x=-3\Rightarrow y=4(-3)-1=-13 \\ \\ x=-2\operatorname{\Rightarrow}y=4(-2)-1=-9 \\ \\ x=-1\operatorname{\Rightarrow}y=4(-1)-1=-5 \end{gathered}[/tex]Problem 12a) solve for x, 3(-2x +5) = 9(x-5), x=b) x = –27, x =
The given equation is
[tex]3(-2x+5)=9(x-5)[/tex]Dividing by 3 both sides, we get
[tex]\frac{3\mleft(-2x+5\mright)}{3}=\frac{9\mleft(x-5\mright)}{3}[/tex][tex]-2x+5=3(x-5)[/tex]Multiplying 3 and (x-5) as follows.
[tex]-2x+5=3\times x-3\times5[/tex][tex]-2x+5=3x-15[/tex]Adding 15 on both sides, we get
[tex]-2x+5+15=3x-15+15[/tex][tex]-2x+20=3x[/tex]Adding 2x on both sides, we get
[tex]-2x+20+2x=3x+2x[/tex][tex]20=5x[/tex]Dividing by 5, we get
[tex]\frac{20}{5}=\frac{5x}{5}[/tex][tex]4=x[/tex]Hence the value of x is 4.
9) write in standard formthrough: (4,4), parallel to y=-6x + 5
Data
Point (4, 4)
Equation
y = -6x + 5
Procedure
As the straight line is parallel we use the same slope of the original straight line.
m = -6
Now we will calculate y-intercept
[tex]\begin{gathered} b=y-mx \\ b=4-(-6)\cdot4 \\ b=4+24 \\ b=28 \end{gathered}[/tex]The equation would be:
[tex]y=-6x+28[/tex][tex]6x+y=28[/tex]Now in the standard form: 6x+y=28
what doesnt belong and why? please someome help me will make brainlist
The one that doesn't belong is 4² = 4² + 4²
Explanation:
2² = 2 × 2
4² = 4 × 4
4² is not equal to 4² + 4²
this is because 4² + 4² = 16 + 16 = 32
while 4² = 4 × 4 = 16
The one that doesn't belong is 4² = 4² + 4²
Approximate the median in each of the three graphs. Explain how you determined the answer.
The median is the centermost data in a set of values.
Since these graphs are for the year 2013, meaning, these graphs contained 365 days of recorded temperature.
For 365 days, the centermost data would be the 183rd day.
Let's take a look at each graph what is the temperature on the 183rd day when data is arranged from lowest to the highest temperature.
As we can see above, the first two bins of the histogram only cover 180 days. Since we are looking for the 183rd day, we moved to the third bin. Hence, the median temperature for City A is between 65 to 75 ℉.
For City B,
The 183rd day in City B is found on the interval 55-75. Hence, the median temperature for City B is between 55-75℉.
Lastly, for City C:
As we can see in the graph above, the 183rd day is approximately closed to the third bin. Hence, for the 183rd day, we can say that the temperature is between 65 to 75℉. The median temperature for City C is between 65 to 75℉.
I need help with the transition from red to blue
5 units left and 2 units down
finding percent proportions
The total number is 80, Among them 30% are under the age of 7, so the number of players under the age of 7 is,
[tex]30\times\frac{80}{100}[/tex]Janet, Li Na, and Katie have 68 beads altogether.Janet has 3 times as many beads as Li Na.Katie has 5 more beads than Janet.How many beads does Katie have?
EXPLANATION:
Given;
We are told that Janet, Li Na and Katie all have a total of 68 beads.
We are also told that;
(i) Janet has 3 times as many beads as Li Na
(ii) Katie has 5 more beads than Janet.
Required;
We are required to find out how many beads Katie has.
Step-by-step solution;
From the conditions given, Janet has 3 times as many beads as Li Na. That means if Li has an y number of beads, Janet's would be times 3.
Therefore, if Li Na is L and Janet is J, then it means;
[tex]\begin{gathered} Li\text{ }Na=l \\ Janet=3l \end{gathered}[/tex]Also we are told that Katie has 5 more beads than Janet. That means, if Katie is K, then;
[tex]\begin{gathered} Janet=3l \\ Katie=3l+5 \end{gathered}[/tex]Bear in mind that they all have a total of 68 beads. Hence, we add up their beads as follows;
[tex]\begin{gathered} LiNa+Janet+Katie=68 \\ l+3l+3l+5=68 \end{gathered}[/tex][tex]7l+5=68[/tex]Subtract 5 from both sides;
[tex]7l+5-5=68-5[/tex][tex]7l=63[/tex]Divide both sides by 7;
[tex]\frac{7l}{7}=\frac{63}{7}[/tex][tex]l=9[/tex]This means Li Na has 9 beads. If Katie's bead is given by the expression 3l + 5, then she will have;
[tex]\begin{gathered} Katie=3l+5 \\ Katie=3(9)+5 \\ Katie=18+5 \\ Katie=23 \end{gathered}[/tex]ANSWER:
Katie has 23 beads.
Marco says that -2/3 * -45 * 9 + 9 * 2/3 * 4/5 both have a product of 4 and 4/5 explain whether or not Marco is correct
Question:
Solution:
Since 4 4/5 is a mixed number, we have that
[tex]4\text{ }\frac{4}{5}\text{ = }\frac{(4\text{ x 5 ) + 4}}{5}\text{ = }\frac{24}{5}=\text{ 4.8}[/tex]On the other hand, notice that:
[tex]-\frac{2}{3}\text{ x -}\frac{4}{5}\text{ x 9 = }\frac{24}{5}\text{ = 4.8}[/tex]thus:
[tex]-\frac{2}{3}\text{ x -}\frac{4}{5}\text{ x 9 = }\frac{24}{5}\text{ = 4 }\frac{4}{5}[/tex]Now, notice that:
[tex]9\text{ x }\frac{2}{3}\text{ x }\frac{4}{5}=\text{ }\frac{9\text{ x 2 x 4}}{3\text{ x 5}}\text{ = }\frac{72}{15}\text{ = }\frac{24}{5}\text{ = 4.8}[/tex]thus:
[tex]9\text{ x }\frac{2}{3}\text{ x }\frac{4}{5}=4\text{ }\frac{4}{5}[/tex]Then, we can conclude that both expressions have a product of 4 4/5.
Karl borrowed $5,700 from the bank for a year at 9% simple interest. What was the amount he paid back to the bank?
Simple interest = PRT /100
where P is the principal
R is the rate
T is the time in year
From the question
P=$5700 R=9 T=1
substitute the values into the formula;
S.I = 5700 x 9 x 1 /100
=$513
Amount pay back = $5700 + $513 = $6,213
Write the equation in slope-intercept form through the point (3, 1) and is perpendicular to the y-axis and graph
Write the equation in slope-intercept form through the point (3, 1) and is perpendicular to the y-axis and graph
step 1
we know that
If the line is perpendicular to the y-axis, that means that the line is parallel to the x-axis
so
Its a forizontal line
the slope is equal to zero
therefore
the equation is
y=1
using a graphing tool
see the attached figure
please wait a minute
Line a is parallel to line b line a passes through the points (1,7) and (2,-4)Line b passes through the point (6,14)The equation of line b is y=__
Given:
Line a is parallel to line b.
Line a passes through the points (1,7) and (2,-4).
Line b passes through the point (6,14).
The objective is to find the equation of the line b in slope intercept form.
For parallel lines the slope of the two lines will be equal.
Consider the coordinates of the line a as,
[tex]\begin{gathered} (x_1,y_1)=(1,7) \\ (x_2,y_2)=(2,-4) \end{gathered}[/tex]The slope of line a can be calculated as,
[tex]\begin{gathered} m_a=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-4-7}{2-1} \\ =-11 \end{gathered}[/tex]Since both are given as parallel lines, the slop of line b will be,
[tex]m_b=-11[/tex]If the line b passes throught the point (6,14), the equation can be represented as,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-14=-11(x-6) \\ y-14=-11x+66 \\ y=-11x+66+14 \\ y=-11x+80 \end{gathered}[/tex]Hence, the equation of line b is y = -11x+80.
etec dego BoildName4-1Amber is saving money to buy a bicycie. She saves $60 hergrandfather gave her, and plans to save an additional $5 eachweek. How much will Amber save after wweeks?Total sawingeUse a bar diagram to represent the amountAmber will save after w weeks.S60Amber will save 60Sw dollarsWeeklyvingsMoney from grandfatherafter w weeks.Reggie drives 10 miles from the airport to the highway. Once on the highway, he drives ata speed of SS miles per hour What is Reggie's total distance from the airport h hours afterreaching the highway?1. Complete the bar diagram.Total distance55 mites per hourDitanceHourly distance on highwayhụhwY
Valencia, this is the solution:
Distance Reggie will drive from the airport to the highway = 10 miles
Distance per hour once on the highway = 55 miles
Let h to represent the number of hours Reggie will drive on the highway
In consequence,
Reggie will drive a total distance of 10 + 55h miles from the airport
Compare the numbers oS and 0.05. How many times 0.05 is 0.5? Use place value to explain how you know
We will look at the process of decimal point shifts as follows:
[tex]0\text{.05}[/tex]For the above decimal to be manipulated in such a way such that the result is:
[tex]0.5[/tex]Here we see that the digits in the given decimal and the result are exactly the same. However, the placement of decimal point ( . ) has been changed. Such changes in decimal point places are usually accompained by number multiples of ( 10 ).
Now there are two possibilities for the decimal point to move i.e to the right or to the left. If we move the decimal point to the left then we are reducing the value of the decimal ( smaller number ). In such cases we divide the given decimal by multiples of ( 10 ).
Vice versa, If we move the decimal point to the right then we are increasing the value of the decimal ( larger number ). In such cases we multiply the given decimal by multiples of ( 10 ).
The decimal number given to us is smaller than the result decimal. i.e:
[tex]0.5\text{ > 0.05}[/tex]Hence, the given decimal number must be multipled by multiples of 10.
The general rule in moving the decimal point in either multiplying or dividing the multiples of ( 10 )s. Is to count the number of " 0 s" in the this multiples. E.g if we divide:
[tex]\frac{0.2}{10}\text{ = 0.02}[/tex]In above example we divided by ( 10 ). This has ( one zero ). Hence, we will move the decimal point to the left by ( one place ). Another example:
[tex]\frac{236.58}{10000}\text{ = 0.023658}[/tex]In above example we divided by ( 10000 ). This has ( four zeros ). Hence, we will move the decimal point to the left by ( four places ).
The same case applies to multiplication of multiples of 10; however, the only difference is the direction of decimal point moving i.e right.
So with the help of above guidelines and example we see that:
[tex]0.05\cdot10^x\text{ = 0.5}[/tex]We need to determine the number of zeroes for ( 10s ) for which there is only a one place shift to the right side by the decimal point.
The value must be ( x = 1 ). That is we multiple the given ( 0.05 ) by ( 10 ). 10 has only one zero which allow the decimal point to travel to the right side by one digit place. Hence,
Answer:
[tex]\textcolor{#FF7968}{10}\text{\textcolor{#FF7968}{ times 0.05 is 0.5}}[/tex]Given: F(x) = 3x^2+ 1, G(x) = 2x - 3, H(x) = xF(x) + G(x) =
Explanation
to add two functions just add like terms,Like terms" are terms whose variables and their exponents, are the same
so
Step 1
let
[tex]\begin{gathered} f(x)=3x^2+1 \\ g(x)=2x-3 \end{gathered}[/tex]hence
[tex]f(x)+g(x)=3x^2+1+2x-3[/tex]we can see the only pair of like terms ar +1 and (-3), so
[tex]\begin{gathered} f(x)+g(x)=3x^2+1+2x-3 \\ \text{add like terms} \\ f(x)+g(x)=3x^2+2x-2 \end{gathered}[/tex]I hope this helps you
what digit is in the
7 more than t
The algebraic expression is:
[tex]t+7[/tex]Answer: t + 7
7. Given an arithmetic sequence, find a26if a4 = 71 and a32 = 1. 8. Given a geometric sequence, find az ifa1 = 729 and a2 = – 243.
Arithmetic sequence
a= 26
a4 = 71
a32 = 1.
an = a1 + (n-1)d
a4 = a1 + (3)*d
71 = a1 + (3)*d (I)
a32 = a1 + (31)*d
1 = a1 + 31 d (II)
to find a1 and d we subtract (II)- (I)
1 = a1 + 31 d (II)
-( 71 = a1 + (3)*d) (I)
________________
-70 = 0 28 d
-70 = 28 d
d= -70/ 28
d= -5/2
Replacing d in (I)
71 = a1 - (3)(5/2)
a1= 71 + (3)(5/2)
a1= 78.5
The arithmetic sequence is
an = a1 + (n-1)d
an = 78.5 + 2.5 (n-1)
Verifying
a4 = 78.5 - 2.5 (3) = 78.5 -7.5= 71
a32 = 78.5 +2.5 (31) =78.5 -77.5 = 1
a26 = 78.5 + 2.5 (25) = 78.5 - 62.5 = 16
Give me some minutes
______________________
Answer
a26 = 16
I need a deep explanation we are doing this in school pulled out my notes and still don't understand.
For an isosceles triangle, two sides are equal and for right triangle o angle should be of 90 degree.
Let the third point coordinate be (x,y).
The distane between given point (-2,-4) and (4,-4) is 6.
The on angle is 90 degree which means one side is perependicular to the given side.
The coordinate of third point must be equal to (4,y) or (-2,y).
As triangle is isosceles so distance between point (4,y) and (4,-4) is equal to 6.
[tex]\begin{gathered} 6=\sqrt[]{(4-4)^2+(y+4)^2} \\ 6=(y+4) \\ y=6-4 \\ =2 \end{gathered}[/tex]Thus coordinate of third point can be (4,2).
Second case if third point is (-2,y).
Distance between point (-2,y) and (-2,-4) is 6, as triangle is isosceles triangle.
[tex]\begin{gathered} 6=\sqrt[]{(-2+2)^2+(y+4)^2} \\ 6=(y+4) \\ y=2 \end{gathered}[/tex]Thus third coordinate can be (-2,2).
As from the options only (4,2) is correct.