Let's begin by listing out the information given to us:
Both triangles have Line BD equal
[tex]BD=BD[/tex]Line AB equals Line CD
[tex]AB=CD[/tex]Angle A equals Angle C
[tex]m\angle A=m\angle C[/tex]Hence, Triangle ABD is congruent to Triangle CDB
Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas.tan(u) = 13/5, 0 < u < /2
The first step to answer this question is to find tan(2u) by using the double angle formula:
[tex]\begin{gathered} tan(2u)=\frac{2tan(u)}{1-tan^2(u)} \\ tan(2u)=\frac{2(\frac{13}{5})}{1-(\frac{13}{5})^2} \\ tan(2u)=\frac{\frac{26}{5}}{1-\frac{169}{25}} \\ tan(2u)=\frac{\frac{26}{5}}{-\frac{144}{25}} \\ tan(2u)=-\frac{65}{72} \end{gathered}[/tex]It means that tan(2u) is -65/72.
The next step is to rewrite the equations for sin(2u) and cos(2u) to have them in terms of the least number of variables possible, this way:
[tex]\begin{gathered} sin(2u)=2sin(u)cos(u) \\ sin(2u)=2sin(u)\frac{sin(u)}{tan(u)} \\ sin(2u)=\frac{2sin^2(u)}{tan(u)} \end{gathered}[/tex][tex]\begin{gathered} cos(2u)=cos{}^2(u)-sin^2(u) \\ cos(2u)=1-sin^2(u)-s\imaginaryI n^2(u) \\ cos(2u)=1-2sin^2(u) \end{gathered}[/tex]If we rewrite tan(2u) in terms of sin(2u) and cos(2u) we will have:
[tex]\begin{gathered} tan(2u)=\frac{sin(2u)}{cos(2u)} \\ tan(2u)=\frac{\frac{2s\imaginaryI n^{2}(u)}{tan(u)}}{1-2sin^2(u)} \end{gathered}[/tex]We know the values of tan(2u) and tan(u), so we can solve the equation for sin^2(u).
[tex]\begin{gathered} tan(2u)=\frac{2sin^2(u)}{tan(u)(1-2sin^2(u))} \\ -\frac{65}{72}=\frac{2s\imaginaryI n^2(u)}{\frac{13}{5}(1-2s\imaginaryI n^2(u))} \\ -\frac{65}{72}\cdot\frac{13}{5}\cdot(1-2sin^2(u))=2sin^2(u) \\ -\frac{169}{72}(1-2sin^2(u))=2sin^2(u) \\ -1+2sin^2(u)=\frac{72}{169}\cdot2sin^2(u) \\ -1+2sin^2(u)=\frac{144}{169}sin^2(u) \\ 2sin^2(u)-\frac{144}{169}sin^2(u)=1 \\ \frac{194}{169}sin^2(u)=1 \\ sin^2(u)=\frac{169}{194} \end{gathered}[/tex]Using this value we can find the values of sin(2u) and cos(2u):
[tex]\begin{gathered} sin(2u)=\frac{2sin^2(u)}{tan(u)} \\ sin(2u)=\frac{2\cdot\frac{169}{194}}{\frac{13}{5}} \\ sin(2u)=\frac{65}{97} \end{gathered}[/tex][tex]\begin{gathered} cos(2u)=1-2sin^2(u) \\ cos(2u)=1-2\cdot\frac{169}{194} \\ cos(2u)=1-\frac{169}{97} \\ cos(2u)=-\frac{72}{97} \end{gathered}[/tex]It means that sin(2u)=65/97, cos(2u)=-72/97 and tan(2u)=-65/72.
Gregory left a $8 tip on a $46 restaurant bill. What percent tip is that? Give your answer to two decimal places if necessary.
Answer:
17.39%
Step-by-step explanation:
Considering that $46 was the restaurant bill and Gregory left an extra tip of $8, the percent is:
[tex]\begin{gathered} \frac{8}{46}=0.1739\text{ } \\ \end{gathered}[/tex]0.1739 = 17.39%
This tip represents 17.39%.
I need help but not all are boxes are used
Given:
[tex]y=3x-5\text{ and y=-6x+4}[/tex]Aim:
We need to find the solution to the given system of equations.
Explanation:
Consider the equation y =3x-5.
Substitute y =-6x+4 in the equation y =3x-5.
[tex]-6x+4=3x-5[/tex]Solve for x.
Add 6x to both sides of the equation.
[tex]-6x+4+6x=3x-5+6x[/tex][tex]4=3x-5+6x[/tex][tex]4=9x-5[/tex]Add 5 to both sides of the equation.
[tex]4+5=9x-5+5[/tex][tex]9=9x[/tex]Divide both sides by 9.
[tex]\frac{9}{9}=\frac{9x}{9}[/tex][tex]x=1[/tex]Substitute x =1 in the equation y =3x-5.
[tex]y=3(1)-5[/tex][tex]y=-2[/tex]The solution of the given system of equations is x=1 and y =-2.
Final answer:
[tex](1,-2)[/tex]How much should be invested now at an interest rate of 6.5% per year, compounded continuously l, to have $3500 in four years.Round your answer to the nearest cent.
Okay, here we have this:
Considering the provided information we are going to replace in the formula of continuous compound interest:
[tex]\begin{gathered} A=Pe^{rt} \\ 3500=Pe^{(0.065\cdot4)} \end{gathered}[/tex]Now, let's solve for P:
[tex]\begin{gathered} P=\frac{3500}{e^{0.26}} \\ P=$2,698.68$ \end{gathered}[/tex]Finally we obtain that should be invested $2,698.68.
The organizer of a conference is selecting workshops to include. She will select from 6 workshops about chemistry and 7 workshops about biology. In how many ways can she select 4 workshops if 2 or fewer must be about chemistry?
Given that there are 6 workshops about chemistry and 7 workshops about biology.
So the total number of workshops available are,
[tex]\begin{gathered} =6+7 \\ =13 \end{gathered}[/tex]The number of ways of selecting 'r' objects from 'n' distinct objects is given by,
[tex]^nC_r=\frac{n!}{r!\cdot(n-r)!}[/tex]The total number of ways of selecting 4 workshops having no workshop about chemistry is calculated as,
[tex]\begin{gathered} n(\text{ 0 chemistry)}=^7C_4 \\ n(\text{ 0 chemistry)}=\frac{7!}{4!\cdot(7-4)!} \\ n(\text{ 0 chemistry)}=\frac{7\cdot6\cdot5\cdot4!}{4!\cdot3!} \\ n(\text{ 0 chemistry)}=\frac{7\cdot6\cdot5}{3\cdot2\cdot1} \\ n(\text{ 0 chemistry)}=35 \end{gathered}[/tex]The total number of ways of selecting 4 workshops having exactly 1 workshop about chemistry is calculated as,
[tex]\begin{gathered} n(\text{ 1 chemistry)}=^7C_3\cdot^6C_1 \\ n(\text{ 1 chemistry)}=\frac{7!}{3!\cdot(7-3)!}\cdot\frac{6!}{1!\cdot(6-1)!} \\ n(\text{ 1 chemistry)}=\frac{7\cdot6\cdot5\cdot4\cdot3!}{3!\cdot4!}\cdot\frac{6\cdot5!}{1!\cdot5!} \\ n(\text{ 1 chemistry)}=\frac{7\cdot6\cdot5\cdot4}{4\cdot3\cdot2\cdot1}\cdot6 \\ n(\text{ 1 chemistry)}=210 \end{gathered}[/tex]The total number of ways of selecting 4 workshops having exactly 2 workshops about chemistry is calculated as,
[tex]\begin{gathered} n(\text{ 2 chemistry)}=^7C_2\cdot^6C_2 \\ n(\text{ 2 chemistry)}=\frac{7!}{2!\cdot(7-2)!}\cdot\frac{6!}{2!\cdot(6-2)!} \\ n(\text{ 2 chemistry)}=\frac{7\cdot6\cdot5!}{2!\cdot5!}\cdot\frac{6\cdot5\cdot4!}{2!\cdot4!} \\ n(\text{ 2 chemistry)}=\frac{7\cdot6}{2\cdot1}\cdot\frac{6\cdot5}{2\cdot1} \\ n(\text{ 2 chemistry)}=315 \end{gathered}[/tex]Consider that the number of ways to select 4 workshops if 2 or fewer must be about chemistry, will be equal to the sum of the individual cases when the number of chemistry workshops in the selection are either 0 or 1 or 2.
This can be calculated as follows,
[tex]\begin{gathered} \text{ Total}=n(\text{ 0 chemistry)}+n(\text{ 1 chemistry)}+n(\text{ 2 chemistry)} \\ \text{Total}=35+210+315 \\ \text{Total}=560 \end{gathered}[/tex]Thus, the total number of ways is 560.
A cube is dilated by a factor of 3.5.The volume of the resulting cube is ___ times the volume of the original cube.
A volume of a cube is given by V=L^3 where L is its side length. If a cube is dilated by a factor of 3.5, it means that its sidelength is increased by a factor of 3.5, i.e. if S is the first length, the new length L satisfies L=3.5*S. Now, the old cube's volume v was v=S^3, after it has expanded to the new sidelength L its new volume V is V=L^3. Using the equation L=3.5*S we can replace L in the equation for V like follows:
V=(3.5*S)^3
Expanding the product we get
V=[(3.5)^3]*(S^3)=42.875*(S^3)
We previously noticed that the prior volume of the cube was v=S^3. Replacing v for S^3 in the previeus equation gives us:
V=42.875v
Thus, the factor by wich the volume of the original cube was scaled up is 42.875
how do I write an equation as a multiple of a unit fraction using 3×3/7
EXPLANATION
An equation can be written as a multiply of a unit fraction using the following relationship:
[tex]x(3\cdot\frac{3}{7})[/tex]What is the ratio of fish to dinosaurs?3 dinosaurs 10 fish
Answer
10/3
or 3.33
Solution
[tex]\frac{10\text{ fish}}{3\text{ dinosaurs}}\text{ = }\frac{10}{3}=3.33[/tex]add 3 feet 6 in add 3 feet 6 in + 8 ft 2 in + 4in + 2ft 5in what does that add up to
We want to find the sum of;
3 feet 6 in + 3 feet 6 in + 8 ft 2 in + 4in + 2ft 5in.
Recall that;
[tex]1\text{ feet = 12 inches}[/tex]Adding we have;
[tex]undefined[/tex]Erica's marks in eight consecutive mathematics examinations were:94,83,75,52,71,68,75,49
(a) The total marks Erica scored is the sum of the given marks:
total = 94 + 83 + 75 + 52 + 71 + 68 +75 + 49 = 567
(b) The mean is given by the quotient between the total and the number of marks, as follow:
mean = 567/8 = 70.875
301123233What Happened When the Crossword Puzzle Champion Died?Find the graph of the solution set of each inequality below in the corresponding column of graphs. Notice the letter next to it.Write this letter in each box containing the number of that exercise. Keep working and you will find out about this grave event.x<2(10 x<1 0 4x is less than 2-3 -2 -1 0 1 2 3-3 -2 -1 0 1 2X<2D++++-3 -2 -123-3 -2 -1 0 1 2 33 x>2+ 12 -3 2 A +++ +13 x>-3-3 -2 -1 0 1 2-3 -2 -1 0 1 2 3(5) x 114 #-1 ++++-3 -2 -10 1 2 3x < -1 A+++ 6 0 >-3 -2 -12-3 -2 -1 0 1 2 3x>-1 E+6 0 6 +++-3 -2 -1 0 1 2-3 -2 -1 0 1 2 318 0
I'm doing it on my notebook, hold on, it's easy
[tex]5 \times 5[/tex]what is 5 times 5
5 times 5 = 25
5 x 5 = 25
5 + 5 + 5+ 5 +5 = 25
Answer:
answer is going to be 25
Step-by-step explanation:
so pretend you have 5 bags of 5 apples, this should stand for 5(bags of apples) and 5(apples in each bag), if you add the apples all together it will be 25 in total, or just try adding 5 five times: 5+5+5+5+5
Use this graph of y = 2x2 - 12x + 19 to find the vertex. Decide whether thevertex is a maximum or a minimum point.TV-5O A. Vertex is a minimum point at (1,3)B. Vertex is a minimum point at (3,1)C. Vertex is a maximum point at (1,7)D. Vertex is a maximum point at (3,1)
For a parabola, the vertex is the critical point, in other words, it is the maximum or the minimum of the function.
From the graph, we can see that the minimum (the minimum value of y) of the graph is 1. The vertex is the point (3,1).
Moreover, as we mentioned the vertex is always the minimum or the maximum, in this case, it is the minimum since the rest of the graph is 'above' that point.
The answer is option B. Vertex is a minimum point at (3,1)
A group of workers can plant 334 acres in 118 days. What is the unit rate in acres per day? Write your answer as a fraction or a mixed number in simplest form.
Number of acres = 334
Number of days = 118 days
unit rate = Number of acres/Number of days
Unit rate = 334 acres/114 days
2 is common to both numerator and denominator
Divide both by 2:
Unit rate = 167/57
No other number asides 1 is common to both the numerator and denominator
Hence, the unit rate in acres per day is 167/57
In mixed fraction = 2 53/57
Content attributionQUESTION 441 POINTThe area of a rectangle is 19.68 square centimeters. The width is 4.8 centimeters. What is the length?Provide your answer below:centimetersD0
In order to calculate the length of the rectangle, we can use the formula for the area of a rectangle:
[tex]A=L\cdot W[/tex]Where A is the area, L is the length and W is the width.
If the area is equal to 19.68 cm² and the width is equal to 4.8 cm, let's calculate the length:
[tex]\begin{gathered} 19.68=4.8\cdot L\\ \\ L=\frac{19.68}{4.8}\\ \\ L=4.1\text{ cm} \end{gathered}[/tex]Therefore the length of the rectangle is equal to 4.1 cm.
Find the range of the function for the given domain: {-4, 0, 4}
f(x)=x²-2
O {-14, 2)
O {-14, 2, 18)
O {-2, 14)
O (-18, -2, 14)
Answer:
{-2,14}
Step-by-step explanation:
f(-4) = f(4) = 14
f(0) = -2
So I am struggling in math and I could use some help to try and get through it
Given the functions:
[tex]\begin{gathered} f(x)=-5x+2 \\ g(x)=-2x²-3 \end{gathered}[/tex]to find f(7), we can make x = 7 on the function f to get the following:
[tex]\begin{gathered} f(7)=-5(7)+2=-35+2=-33 \\ \Rightarrow f(7)=-33 \end{gathered}[/tex]in a similar way, we can find g(5) by making x = 5 on the function g:
[tex]\begin{gathered} g(5)=-2(5)²-3=-2(25)-3=-50-3=-53 \\ \Rightarrow g(5)=-53 \end{gathered}[/tex]therefore, f(7) = -33 and g(5) = -53
n - 3 over 10 = 3 over 5
The given expression is
[tex]\frac{n-3}{10}=\frac{3}{5}[/tex]First, we multiply by 10 on each side.
[tex]\begin{gathered} 10\cdot\frac{n-3}{10}=\frac{3}{5}\cdot10 \\ n-3=6 \end{gathered}[/tex]Then, we sum 3 on each side.
[tex]\begin{gathered} n-3+3=6+3 \\ n=9 \end{gathered}[/tex]Therefore, the solution is 9.If f(x) is a third degree polynomia function, how many distinct complex roots are possible?
Complex roots always appear in pairs, actually if a+ib is a root then a-ib is also a root. Then, at most there are 2 complex roots in a third degree polynomial.
what is the value of B ( area of the base) for the following triangular prism?40 ft^248 ft^260 ft^224ft^2
SOLUTION:
The base of the prism is a triangle and the formula for finding the area of a triangle is "half base multiplied by height".
From the figure of the prism given the base and height of the triangle is 6 ft and 8 ft.
[tex]\begin{gathered} \frac{1}{2\text{ }}\text{ x 6 x 8} \\ \\ \frac{48}{2} \\ \\ 24ft^2 \end{gathered}[/tex]CONCLUSION:
The area of the base of the given triangular prism is 24 squared feet ( the fourth option).
Solve each inequality). 2|4t-1|+6>20
To answer this question we will use the following property:
[tex]|a|>b>0\text{ if and only if }a>b\text{ or }a<-b.[/tex]Subtracting 6 from the given inequality we get:
[tex]\begin{gathered} 2|4t-1|+6-6>20-6, \\ 2|4t-1|>14. \end{gathered}[/tex]Dividing the above inequality by 2 we get:
[tex]\begin{gathered} \frac{2|4t-1|}{2}>\frac{14}{2}, \\ |4t-1|>7. \end{gathered}[/tex]Then:
[tex]4t-1>7\text{ or }4t-1<-7.[/tex]Solving the above inequalities we get:
1)
[tex]4t-1>7.[/tex]Adding 1 to the above inequality we get:
[tex]\begin{gathered} 4t-1+1>7+1, \\ 4t>8. \end{gathered}[/tex]Dividing the above by 4 we get:
[tex]\begin{gathered} \frac{4t}{4}>\frac{8}{4}, \\ t>2. \end{gathered}[/tex]The above inequality in interval notation is:
[tex](2,\infty).[/tex]2)
[tex]4t-1<-7.[/tex]Adding 1 to the above inequality we get:
[tex]\begin{gathered} 4t-1+1<-7+1, \\ 4t<-6. \end{gathered}[/tex]Dividing the above result by 4 we get:
[tex]\begin{gathered} \frac{4t}{4}<-\frac{6}{4}, \\ t<-\frac{3}{2}. \end{gathered}[/tex]The above inequality in interval notation is:
[tex](-\infty,-\frac{3}{2}).[/tex]Answer:
[tex](-\infty,-\frac{3}{2})\cup(2,\infty).[/tex]There are 25
students in an
Algebra class. 9 of
them got an A on
the test. What
percent of them
scored an A?
Answer:
36%
Step-by-step explanation:
First, you would write that as a fraction, which would be 9/25. Then, you'd convert the fraction to a percentage by getting the denominator to 100. Multiply the numerator and denominator by 4 to achieve this. The answer would be 36/100, which translates to 36%.
Consider the relation y = −3|x + 5| − 6. What are the coordinates of the vertex?
Solution:
Given the relation below
[tex]y=-3|x+5|-6[/tex]The general form, an absolute value function is
[tex]y=a|x-h|+k[/tex]The vertex coordinates are (h, k)
Solving to find the vertex below
[tex]\begin{gathered} x+5=x-h \\ 5=-h \\ h=-5 \\ k=-6 \\ (h,k)\Rightarrow(-5,-6) \end{gathered}[/tex]Hence, the coordinates of the vertex is
[tex](-5,-6)[/tex]You buy a house for $299,00. If you make a 20% down payment, how much would you pay in total per month for the 30 year loan if you pay $3200/year in taxes, $1050/year in insurance and $28/month forthe home owners association?
Charlene calculated that the monthly patyment, including interests is $ 692.88.
Taxes = $ 3,200 annually, if we divide it by 12, we will find the monthly amount, this way:
3,200/12 = $ 266.67
Insurance = $ 1,050 annually, if we divide it by 12, we will find the monthly amount, this way:
1,,050/12 = $ 87.50
Home owners association = $ 28
Therefore, the monthly payment would be:
692.88 + 266.67 + 87.50 + 28
You can finish the calculation, Charlene!
[tex]x2 = 49[/tex]what's the answer
Solve the equation:
[tex]x^2=49[/tex]The simplest method to solve the equation is to apply the square root on both sides of the equation:
[tex]\sqrt{x^2}=\sqrt{49}[/tex]Since the square and the square root are inverse functions, they cancel out, leaving us with the equation:
[tex]x=\sqrt{49}[/tex]We must find a number such that its square results in 49. That number is 7. But we must recall that there is another number that produces 49 when squared. That number is -7.
This gives us two solutions. It can be written:
[tex]x=\pm7[/tex]The equation has two solutions:
x = 7, x = -7
Convert the measurement. 12 in/sec = ft/min
kmartinez2849, this is the solution:
Let's recall that:
1 inch/second = 5 feet/minute
Thus:
12 inch/second = 5 * 12 feet/minute
12 inch/second = 60 feet/minute
Let's recall that:
1 feet = 12 inches
1 minute = 60 seconds
Therefore:
1 inch/second * 60 = 60 inches/minute
Converting inches to feet
60 inches = 5 feet
In conclusion, 5 feet/minute
5.True or False: The ordered pair (0, 3) is a solution to the equationy = -5x + 3.
You have the following equation:
y = -5x + 3
in order to determine if the point (0,3) is solution of the previous equation, replace the values of x = 0 and y = 3, and verify if the equation is consistent, as follow:
3 = -5(0) + 3
3 = 3
the equation is consistent for the given point, then, the point (0,3) is a olution of the given equation
adrienne earns 98$ for working 8 hours. if she earned 453.25$, how many hours did she work?
Answer: 37 hours
Step-by-step explanation:
98/8 = 12.25
453.35/12.25 = 37
Simplify:6.2n - 8.3 + -9.1 + 1.4n
ANSWER
7.6n - 17.4
EXPLANATION
We have the expression that we want to simplify.
We have:
6.2n - 8.3 + (-9.1) + 1.4n
The first step is to collect like terms:
=> 6.2n + 1.4n - 8.3 - 9.1
Now, simplify:
7.6n - 17.4
That is the answer.
For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.Part A: Write a function in for the geometric sequence where the first term is 11 and the common ratio is 4 .Part B: Find the first five terms in the geometric function.Part C: In one paragraph, using your own words, explain your work for Step A and Step B.
Remember that the formula for a geometric sequence is:
[tex]a_n=a_1\cdot r^{n-1}[/tex]PART A:
With the data given, the formula for the sequence is:
[tex]a_n=11_{}\cdot4^{n-1}[/tex]PART B:
[tex]\begin{gathered} a_1=11\cdot4^{1-1}\rightarrow a_1=11 \\ a_2=11\cdot4^{2-1}\rightarrow a_2=44 \\ a_3=11\cdot4^{3-1}\rightarrow a_3=176 \\ a_4=11\cdot4^{4-1}\rightarrow a_4=704 \\ a_5=11\cdot4^{5-1}\rightarrow a_5=2816 \end{gathered}[/tex]PART C:
For part A, we took the general formula for the geometric sequence and plugged in the first term and the common ratio provided.
For part B, we replaced n for all the numbers from 1 through 5 to get the first 5 terms of the sequence.