we have the set
15,17,21,6,3
so
from least to greatest
3,6,15,17,21because3<6<15<17<21Problem N 2
we have
-55, 143, 18, -79, 44, 101
from least to greatest
-79, -55, 18, 44, 101, 143what is the area of a rectangle with a width of 4y and a length of 6y?
area of the rectangle = width x length
[tex]\begin{gathered} A=4y\times6y \\ A=24y^2 \end{gathered}[/tex]If the function y=-f(x-4)+3 were graphed, write the transformations to the graph of y = f(x) in theorder that they occur.
The parent function is y = f(x)
The derived function is y = -f(x - 4) + 3
The sequence of transformations that was done to the graph of y = f(x) is:
• The function y = f(x) is shifted to the right by 4 units to become y = f(x - 4)
,• The function y = f(x-4) is dilated by a factor of -1 to become y = -f(x - 4). This also means a 180 degrees rotation
,• The function y = -f(x - 4) is shifted up by 3 units to become y = -f(x - 4) + 3
In summary, the transformations done to graph of y = f(x) in the order that they occur are:
0. Translation to the right by 4 units
,1. Dilation by a factor of -1
,2. Translation upwards by 3 units
Peter has a salary of 108.00 kina per fortnight plus a 8½% commission on her sales . In the last two weeks he sold six radios at 430,289,360.how much is he paid
Data:
• Fixed salary: 108 kina
,• Commission: 8.5% = 0.085
Procedure:
0. Calculating the commissions of each sale:
[tex]430\cdot0.085=36.55[/tex][tex]289\cdot0.085=24.57[/tex][tex]360\cdot0.085=30.60[/tex]2. Adding the commission to the fixed salary:
[tex]108.00+30.60+24.57+36.55=[/tex][tex]=108.00+91.72[/tex]Answer: $199.72
if a tree 20 meters tall casts a shadow 30 meters long, what is the angle of elevation from the shadow to the tip of the tree, to the nearest degree?
sketch the situation
a trigonometric function that is a relation between the angle of elevation and the 2 sides of the rectangles is the tan
[tex]\tan \theta=\frac{opp}{adj}[/tex][tex]\tan \theta=\frac{20}{30}=\frac{2}{3}[/tex]find the inverse
[tex]\begin{gathered} \tan ^{-1}(\frac{2}{3})=\theta \\ \theta=33.69º \end{gathered}[/tex]after rounding the angle of elevation is 34º.
an auditorium has 288 seats distributed evenly and 9 rolls finding unit rate of seats per row
Solution
For this case we have the total of seats 288 , and the number of rolls is 9
Then we can find the unit rate like this:
288/9 = 32
Then the final answer is:
32 seats/row
This is a Calculus 1 Problem. Show ALL your work, giving proper context, and make sureIt is written neatly, legibly, and with appropriate organizations. MUST SHOW ALL THE JUSTIFICATION OF THE PROBLEM!!!Question 1(1)
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
step 1: Write the given function
[tex]f(x)=\frac{\sqrt{x+a^2}-a}{x},a>0[/tex]STEP 2: Get the domain of f(x)
[tex]\begin{gathered} The\:domain\:of\:a\:function\:is\:the\:set\:of\:input\:or\:argument\:values\:for\:which\:the\:function\:is\: \\ real\:and\:defined \\ \\ Combine\:real\:regions\:and\:undefined\:points\:for\:final\:function\:domain \\ x\ge \:-a^2 \end{gathered}[/tex]Hence, the domain of f will be:
[tex]x\ge-a^2[/tex]
Vector A of magnitude 365.2 and direction 0= 210.79 degrees
If we take the vector A and rotate it till it reaches 270° we would have the following figure
As we can see there's no horizontal component, the horizontal component is zero, and the vertical component is the vector magnitude.
Rewrite as equivalent rational expressions with denominator (x – 2)(x – 5)(x – 6)
Rewriting the first term, we have:
[tex]\begin{gathered} \frac{7}{x^2-7x+10} \\ \frac{7}{(x-5)(x-2)}(\text{ Factoring the quadratic expression}) \\ \frac{7\cdot(x-6)}{(x-5)(x-2)(x-6)}(\text{ Multiplying on both sides by (x-6))} \\ \frac{7x-42}{(x-5)(x-2)(x-6)}(\text{ Distributing)} \end{gathered}[/tex]Rewriting the second term, we have:
[tex]\begin{gathered} \frac{4x}{x^2-8x+12} \\ \frac{4x}{(x-6)(x-2)}(\text{ Factoring the quadratic expression}) \\ \frac{4x\cdot(x-5)}{(x-6)(x-2)(x-5)}(\text{ Multiplying on both sides by (x-5))} \\ \frac{4x^2-20x}{(x-6)(x-2)(x-5)}(\text{ Distributing)} \end{gathered}[/tex]The answers are:
[tex]\frac{7x-42}{(x-5)(x-2)(x-6)},\frac{4x^2-20x}{(x-6)(x-2)(x-5)}[/tex]The answer to part A is 7 and the answer to part B is 51. Solve part C.
The ways a waiter and a dishwasher are paid are different. A waiter has a flat $25 dollars daily wage so despite having a lower payment per hour than a dishwasher is logical and expected that a waiter earns more money in the short run. However, as working hours increase the inportance of that fixed daily payment decreases and the contribution to the total payment given by the payment per hour begins to dominate.
It's easy to see this in the graph of both wages. Both are straight lines but the one representing a waiter's wage starts with an offset whereas that of a dishwasher starts at 0. However, since the later receives a better hourly payment the slope of its graph is higher and at some point it surpasses the wage of the waiter. This also happens at a reasonable number of hours (7 hours) because the difference between payments per hour (which define the slopes of the lines) is not minimal.
The function f is defined as follows.f(x) = -2x2-5If the graph of fis translated vertically upward by 3 units, it becomes the graph of a function h.Find the expression for h(x)
Given:
f(x) = -2x² - 5
To find:
The function for h(x) after a vertical translation of 3 units upwards
Translation rules:
[tex]\begin{gathered} f(x\text{ + a\rparen = translation to the left} \\ f(x\text{ - a\rparen: translation to the right} \\ f(x)\text{ + b: translation upward} \\ f(x)\text{ - b: translation downward} \end{gathered}[/tex]From the above, a translation of 3 units upward will involve adding 3 units to the function of f(x)
[tex]\begin{gathered} h(x)\text{ = f\lparen x\rparen + 3} \\ h(x)\text{ = -2x}^2\text{ - 5 + 3} \\ \\ h(x)\text{ = -2x}^2\text{ - 2} \end{gathered}[/tex]In calculus early transcendental functions Can I solve for x if the base number isn’t the same? 7^4x-1=3^5x
the Given:
The equation is,
[tex]7^{4x-1}=3^{5x}[/tex]Explanation:
Take a natural log on both sides of the equation and simplify it.
[tex]\begin{gathered} \ln (7^{4x-1})=\ln (3^{5x}) \\ (4x-1)\ln 7=5x\ln 3 \\ 4x\ln 7-\ln 7=5x\ln 3 \\ 4x\ln 7-5x\ln 3=\ln 7 \\ x(4\ln 7-5\ln 3)=\ln 7 \\ x=\frac{\ln 7}{4\ln 7-5\ln 3} \end{gathered}[/tex]So value of x is,
[tex]x=\frac{\ln 7}{4\ln 7-5\ln 3}[/tex]In the triangle below , RT=ST, find the measure of
Given the triangle RST
As shown:
m∠T = 110
And RT = ST
So, it is an isosceles triangle
so, m∠R = m∠S = x
The sum of the angles of the triangle = 180
So,
[tex]\begin{gathered} m\angle R+m\angle S+m\angle T=180 \\ x+x+110=180 \\ 2x=180-110 \\ 2x=70 \\ x=35 \end{gathered}[/tex]So, the answer will be:
m∠TRS = 35°
Abby already owns 18 necklaces, and additional necklaces are priced at 2 for a dollar. Howmuch money does Abby need to spend on new necklaces in order to own a total of 36necklaces?
Let be "x" the amount of money (in dollars) Abby needs to spend on new necklaces, in order to own a total of 36 necklaces.
According to the information given in the exercise, the cost of 2 additional necklaces is $1.
Since she already has 18 necklaces, you can identify that she needs 18 new necklaces in order to own 36 necklaces.
Knowing the above, you can set up te following proportion:
[tex]\frac{1}{2}=\frac{x}{18}[/tex]Now you must solve for "x" in order to find its value. You can do it by multiplying both sides of the equation by 18. Then, you get:
[tex]\begin{gathered} (18)(\frac{1}{2})=(\frac{x}{18})(18) \\ \\ x=9 \end{gathered}[/tex]Therefore, the answer is: She needs to spend $9.0 in order to own a total of 36 necklaces.
Why is the line a good fit for the data shown in the scatter plot?
Explanation:
There is a linear association between the variables x and y if we can see how the data follows a straight line trend. In this case, we can see that in general when the x variable increase, the y variable decrease with a considerable slope. So, we can say that there is a strong linear association.
Therefore, the
Provide the missing statement and reasons for the following proof:Given: 9(2 – 6) +41 = 75Prove: I=889ReasonStatement$1 9(x-6) + 41 - 75R1S2. 9(x - 6) - 34R2.S3| |R3 Distributive PropertyS4 9x = 88R488S5 * -R5
Given:
[tex]9(x-6)+41=75[/tex]Explanation:
Solve the equation to obtain the value of x.
[tex]9(x-6)+41=75\text{ (Given)}[/tex]Substract 41 from both sides of equation.
[tex]9(x-6)+41-41=75-41\text{ (Substract 41 from both sides)}[/tex]Apply distributive property .
[tex]9\cdot x-9\cdot6=34\text{ (Distributive property)}[/tex]Add 54 to both sides of equation.
[tex]9x-54+54=34+54\text{ (Add 54 to both sides of equation)}[/tex]Divide both sides of equation by 9.
[tex]\begin{gathered} \frac{9x}{9}=\frac{88}{9} \\ x=\frac{88}{9}\text{ (Divide both sides by 9)} \end{gathered}[/tex]Answers:
R1: Given
R2: Subtract 41 from both sides of equation (Subtractiove property of equality)
S3: 9*x -9*6 = 34
R4: Add 54 to both sides of equation (Additive property of equality)
R5: Divide both sides of equation by 9 (Division property of equality)
Need help answering this question it will eventually have 4 parts
Hello! I need some assistance with this homework question for precalculus, please?HW Q9
Answer: 0
Explanation:
Recall, the inverse of an exponential function is a logarithmic function. Thus, if
y = = logb x, then
where b is the base of the logarithm
x = b^y
The given expression is
loga 1 = ?
Let loga 1 = t
by applying the rule above,
1 = a^t
Recall, if we raise any variable to the power of zero, the value is 1. Thus,
1 = a^0
1 = 1
Thus, t = 0
loga 1 = 0
Thus, the correct option is 0
Square the binomial.(3x – 7)^2simplify your answer
Answer:
[tex]9x^2-42x+49[/tex]Explanation:
Here, we want to square the binomial
We proceed as follows:
[tex]\begin{gathered} (3x-7)^2\text{ = (3x-7)(3x-7)} \\ \end{gathered}[/tex]We can further breakdown this as follows:
[tex]\begin{gathered} 3x(3x-7)-7(3x-7) \\ =9x^2-21x-21x+49 \\ =9x^2-42x+49 \end{gathered}[/tex]how do we find the values of x and y.
Given:
A matrix
[tex]\begin{bmatrix}{10x} & {} \\ {18} & {}\end{bmatrix}=\begin{bmatrix}{4} & {} \\ {6y} & {}\end{bmatrix}[/tex]Required:
To find the values of x and y.
Explanation:
Two matrices are said to be equivalent matrices if they have the same rank.
The given matrices are equivalent, so their corresponding element will be equal.
[tex]\begin{gathered} 10x=4 \\ x=\frac{4}{10} \\ x=\frac{2}{5} \end{gathered}[/tex][tex]\begin{gathered} 18=6y \\ y=\frac{18}{6} \\ y=3 \end{gathered}[/tex]Final Answer:
The values of x and y are as:
[tex]\begin{gathered} x=\frac{2}{5} \\ y=3 \end{gathered}[/tex]At a restaurant only 4 out of 12 people ordered an appetizer. Which of the following shows the fraction of people who could NOT order an appetizer?
At a restaurant, only 4 out of 12 people ordered an appetizer. Which of the following shows the fraction of people who could NOT order an appetizer?
_____________________________________________
4 out of 12 people ordered an appetizer
4/ 12 = 1/3
1/3 ordered an appetizer
________________
1 = 3/3
the unit (the total of people),
3/ 3 - 1/3 = 2/3
2/3
________________________
Answer 2/3 = 8/12 could NOT order an appetizer.
Question 5 of 10, Step 1 of 13/10CorrectJustin recently drove to visit his parents who live 240 miles away. On his way there his average speed was 11 miles per hour faster than on his way home (he ran intosome bad weather). If Justin spent a total of 8 hours driving find the two rates.
Given,
The distance, D = 240 miles
The average speed was 11 miles per hour.
Solution:
Let x be the speed.
Then, (x+11) will be the average speed.
The time taken to cover outward bound is
[tex]Time=\frac{240}{\left(x+11\right)}hrs......\lparen1)[/tex]The time taken to cover homeward bound is
[tex]Time=\frac{240}{x}\text{ hrs......\lparen2\rparen}[/tex]Add both equations (1) and (2)
[tex]\begin{gathered} Time\text{ + Time = 8 hrs} \\ \frac{240}{\left(x+11\right)}+\frac{240}{x}=8 \\ \frac{240x+240\left(x+11\right)}{x\left(x+11\right)}=8 \\ \frac{240x+240x+2,640}{x\left(x+11\right)}=8 \end{gathered}[/tex][tex]\begin{gathered} 480x+2640=8\lparen x^2+11x) \\ 480x+2640=8x^2+88x \\ 8x^2+88x-480x-2640=0 \\ 8x^2-392x-2640=0 \end{gathered}[/tex]Divide the equation by 5.
[tex]\begin{gathered} x^2-49x-330=0 \\ x^2+6x-55x-330=0 \\ x\left(x+6\right)-55\left(x+6\right)=0 \\ \lparen x+6)\left(x-55\right)=0 \end{gathered}[/tex]Thus, the value of x is
[tex]x=55,-6[/tex]Justin's average speed to his parents house is 55 mph.
Justin's average speed from his parent's house is
[tex]\begin{gathered} x+11=55+11 \\ =66\text{ mph} \end{gathered}[/tex]could u guys help me out thank u so much
To simplify an algebraic fraction, we will simplify the numbers and the variables
[tex]\frac{12wxy}{20xy}[/tex]Since the simplest form of 12/20 is
[tex]\frac{12}{20}=\frac{\frac{12}{4}}{\frac{20}{4}}=\frac{3}{5}[/tex]Since x/x = 1 and y/y = 1, then
The simplest form of the fraction is
[tex]\frac{12wxy}{20xy}=\frac{3w}{5}[/tex]You can write it as
[tex]\frac{3}{5}w[/tex]Find the y - intercept of the line formed by: −1x+4y=23
Solve for y on the expression:
[tex]-1x+4y=23[/tex]Add both sides by 1x:
[tex]-1x+1x+4y\text{ =23+1x}[/tex][tex]4y=\text{ 23+1x}[/tex]Divide both sides by 4:
[tex]\frac{4y}{4}=\frac{23+1x}{4}[/tex][tex]y\text{ =}\frac{23}{4}+\frac{x}{4}[/tex]Where 1/4 is the slope and 23/4 represents the y-intercept.
The ordered pair for the y-intercept is (0.23/4).
Graph the quadratic function f(x)=(x-2)^2
Answer
The graph of the function f(x) = (x - 2)² is presented below
Explanation
To graph a function, it is usually better to expand it.
f(x) = (x - 2)²
= (x - 2) (x - 2)
= x (x - 2) - 2 (x - 2)
= x² - 2x - 2x + 4
= x² - 4x + 4
So, logically, we then insert different values of x into this function and obtain corresponding values of y. This set of ordered pairs are now plotted and joined together for the graph.
The graph of this function is then plotted and presented under 'Answer' above.
Hope this Helps!!!
Hello, can you please help me solve question number 8 !
1
Explanation:[tex]8)\text{ }\sin A\text{ cosA tanA + }\frac{2\sin Acos^3A}{\sin\text{ 2A}}[/tex][tex]\begin{gathered} \sin A\text{ cosA tanA + }\frac{2\sin Acos^3A}{\sin\text{ 2A}} \\ \tan \text{ A = }\frac{\sin A}{\cos A} \\ \sin A\text{ cosA }\times\frac{\sin A}{\cos A}\text{ + }\frac{2\sin Acos^3A}{\sin\text{ 2A}} \\ =\text{ sinA(sinA) + }\frac{2\sin Acos^3A}{\sin\text{ 2A}} \end{gathered}[/tex][tex]\begin{gathered} =sin^2A\text{ + }\frac{2\sin Acos^3A}{\sin\text{ 2A}} \\ =\text{ }\frac{\sin ^2A(sin2A)+2sinAcos^3A}{\sin \text{ 2A}} \\ \sin 2A\text{ = 2sinAcosA} \\ =\text{ }\frac{\sin ^2A(sin2A)+2sinAcos^3A}{2\sin \text{ AcosA}} \\ =\text{ }\frac{\sin ^2A(2sinA\cos A)+2sinAcos^3A}{2\sin \text{ AcosA}} \end{gathered}[/tex][tex]\begin{gathered} =\text{ }\frac{\sin^2A(2sinA\cos A)+2sinAcos^3A}{2\sin\text{ AcosA}} \\ =\frac{2\sin ^3A(\cos A)+2sinAcos^3A}{2\sin \text{ AcosA}} \\ =\frac{2\sin ^3A\cos A+2sinAcos^3A}{2\sin \text{ AcosA}} \\ =\text{ }\frac{\cos A(2\sin ^3A)+\cos A(2sinAcos^2A)}{2\sin \text{ AcosA}} \end{gathered}[/tex][tex]\begin{gathered} =\text{ }\frac{\cos A(2\sin^3A)+\cos A(2sinAcos^2A)}{2\sin\text{ AcosA}} \\ =\frac{\cos A\lbrack(2\sin^3A)+(2sinAcos^2A)\rbrack}{\text{cosA(}2\sin A)} \\ =\frac{(2\sin^3A)+(2sinAcos^2A)}{2\sin A} \\ =\frac{2\sin A(\sin ^2A+cos^2A)}{2\sin A} \end{gathered}[/tex][tex]\begin{gathered} =sin^2A+cos^2A \\ \text{reca ll:} \\ \text{ sin}^2x+cos^2x\text{ = 1} \\ \\ \text{Hence, }sin^2A+cos^2A\text{ = 1} \end{gathered}[/tex]The ages of the people in the fifth row at the ball game were 12,12,11,5,2,34,37,50,52,10,10,12,16,29,8. Find the following mean median mode range
1) Let's find the mean by adding them up and dividing by the number of data points:
[tex]\begin{gathered} \bar{x}=\frac{12+12+11+5+2+34+37+50+52+10+10+12+16+29+8}{15} \\ \bar{x}=20 \end{gathered}[/tex]2) To fnd the mMedian, i.e. the middle number. We need to arrnge oan rderly from the least to the greaseest as our first step:
[tex]2,\:5,\:8,\:10,\:10,\:11,\:12,\:12,\:12,\:16,\:29,\:34,\:37,\:50,\:52[/tex]Since there is an odd umber oof data points, we can pick the number that evenly divides it into two groups:
The number that divides into two groups of 7 numbers to the left and 7 numbers to the right is 12.
3) Mode is the number that repeats itself the most in any data set:
[tex]12[/tex]which number has the same absoulute value as -2? -1/2 , 1/2. 0. or 2
which number has the same absoulute value as -2? -1/2 , 1/2. 0. or 2
we know that
The absolute value as -2 is
[tex]\mleft|-2\mright|=2[/tex]so
verify each number
1) -1/2
[tex]|-\frac{1}{2}|=\frac{1}{2}[/tex]2) 1/2
[tex]|\frac{1}{2}|=\frac{1}{2}[/tex]3) 0
[tex]|0|=0[/tex]4) 2
[tex]|2|=2[/tex]therefore
the answer is 2
If quadrilateral below is a kite, find the missing measures
A quadrilateral is a polygon having four sides, four angles, and four vertices. ∠1=72, ∠2=43, ∠3=43,∠4=360,∠5=18,∠6=47,∠7=72 are the missing angles.
What is Quadrilateral?A quadrilateral is a polygon having four sides, four angles, and four vertices
The given quadrilateral is a Kite.
We need to find the missing angles.
The total angle of kite is 360 degrees.
Please find the attached Diagram,
In triangle ABE, 90+18+∠1=180
∠1=72
In triangle CDE, 90+43+∠6=180
∠6=47
In triangle BCE, 90+47+∠3=180
∠3=43
∠5=18
∠7=72
∠2=43
∠4=360
Hence ∠1=72, ∠2=43, ∠3=43,∠4=360,∠5=18,∠6=47,∠7=72 are the angles.
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Find the equation of the line that is parallel to y=4x+1 and contains the point (1,1)
SOLUTION
The given equation is:
[tex]y=4x+1[/tex]Notice that the slope of the given equation is 4.
Recall the slopes of parallel line are equal.
Therefore the slope of the required line is 4.
Since the slope of the required line is 4 and it is given that the line contains the point (1,1)
Then the equation of the line using Point-Slope Form is:
[tex]\begin{gathered} y-1=4(x-1) \\ y-1=4x-4 \\ y=4x-4+1 \\ y=4x-3 \end{gathered}[/tex]Therefore the required equation is:
[tex]y=4x-3[/tex]I need help with my math
To solve the system of equations graphically, you must draw a line that represents each equation, then find the point of intersection between the 2 lines, this point is the solution of the system
Let us do that
[tex]y=-\frac{1}{2}x-6[/tex]Let us choose a value of x to find y
Let x = 0
[tex]\begin{gathered} y=-\frac{1}{2}(0)-6 \\ y=0-6 \\ y=-6 \end{gathered}[/tex]The first point on the line is (0, -6)
Let x = 2
[tex]\begin{gathered} y=-\frac{1}{2}(2)-6 \\ y=-1-6 \\ y=-7 \end{gathered}[/tex]The second point on the line is (2, -7)
We will do the same for the 2nd equation
[tex]y=-3x+4[/tex]At x = 0
[tex]\begin{gathered} y=-3(0)+4 \\ y=0+4 \\ y=4 \end{gathered}[/tex]The first point is (0, 4)
Let x = 2
[tex]\begin{gathered} y=-3(2)+4 \\ y=-6+4 \\ y=-2 \end{gathered}[/tex]The second point on the line is (2, -2)
Now we will draw each line using the points above
The red line represents the first equation
The blue line represents the second equation
The two lines intersected at the point (4, -8)
Then the solution of the system is (4, -8)