Given BD bisects ∠ABC, complete the flowchart proof below. Note that the last statement and reason have both been filled in for you.
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In order to prove that the triangles are congruent, we can write the following statements and reasons:
first box in the first row:
statement: BD bisects angle ABC
reason: given
first box in the second row:
statement: angle ABD congruent to angle DBC
reason: A segment bisector divides a segment into two congruent segments.
second box in the second row:
statement: angle ADB congruent to angle BDC
reason: given
third box in the second row:
statement: side AB congruent to side BC
reason: given
Since we have two pairs of congruent angles and one pair of congruent sides that are not between the angles, we can prove the triangles congruent by case AAS.
Related Questions
Points D, C, B, and A are collinear.What is the slope of DC in simplest form?5BСSlope of DC = [?]D
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Given points D, C, B and A are colinear (they lie on the same line), you can determine that the slope of AB and the slope of DC are the same.
By definition:
[tex]Slope=\frac{Rise}{Run}[/tex]In this case, you can identify that:
[tex]\begin{gathered} Rise=5 \\ Run=1 \end{gathered}[/tex]Therefore, you can determine that:
[tex]\begin{gathered} Slope\text{ }of\text{ }DC=\frac{5}{1} \\ \\ Slope\text{ }of\text{ }DC=5 \end{gathered}[/tex]Hence, the answer is:
[tex]Slope\text{ }of\text{ }DC=5[/tex]2) The debate team with 18 members is to choose four officers: captain, co-captain, treasurer, and secretary. How many ways can those officers be selected?
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We have 18 members that can be positioned in 4 positions.
As the positions are different from each other, the order matters.
Then, this is a permutation of 18 elements in 4 places with no repetition.
The number of permutations can be calculated as:
[tex]\begin{gathered} P(n,r)=\frac{n!}{(n-r)!} \\ P(18,4)=\frac{18!}{(18-4)!}=\frac{18!}{14!}=18\cdot17\cdot16\cdot15=73440 \end{gathered}[/tex]We could have derived this by doing this analysis:
We have 18 to choose for captain.
Then, we have 17 left to choose for co-captain.
Finally 16 can be chosen for treasurer and 15 are left for secretary.
Then, the posible teams are 18*17*16*15=73440.
Answer: we can select them in 73,440 ways.
Find the area to the left of x=73 under a normal distribution curve with mean=71 and standard deviation =2 .Round your answer to four decimal places.
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To find the area to the left of x=73 under a normal distribution curve:
1. Find the corresponding z, use the next formula:
[tex]z=\frac{(x-\operatorname{mean})}{\text{standard deviation}}[/tex][tex]\begin{gathered} z=\frac{73-71}{2} \\ \\ z=\frac{2}{2} \\ \\ \\ z=1 \end{gathered}[/tex]2. Find the z-score corrsponding to z=1, use a z score table:
The area to the left of z is equal to the corresponding z-score.
Then, the area to the left of x=73 is 0.8413Which one of the following graphs is the graph of:if x > 0If(x) = -1 if x = 0 ?-3if x < 0OA.GB.Ax
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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Explain the given piecewise function
We look for where x is greater than zero and f(x) will be x
Where x equals 0 and the f(x) will be -1
Where x is less than 0 and f(x) will be -3
Hence, the correct graph will be:
OPTION D
According to the manual, a battery in a cellular phone loses 2% of its charge eachday. Assume the battery is 100% charged. Write an equation to represent thepercent charge, P, as a function of the number of days, d, since the battery wascharged and use it to determine the number of days until the battery in only 50%charged.
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a.) According to the manual, a battery in a cellular phone loses 2% of its charge each
day.
b.) Assume the battery is 100% charged.
Let,
P = the percent charge
d = the number of days since the battery was charged
The equation will be:
P = 100 - 2d
Let's determine the number of days until the battery in only 50% charged.
P = 100 - 2d
50 = 100 - 2d
2d = 100 - 50
2d = 50
2d/2 = 50/2
d = 25
Therefore, the battey will be only 50% charged in 25 days.
Find a logarithmic function to model the dataf(x) = 60.73(0.95)xf(x) = 0.93(60.73)xf(x) = 60.04 – 8.25 ln xf(x) = 8.25 – 60.04 ln x
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Evaluate the logarithmic functions provided at different values of x to see which matches better the data from the y column:
1) f(x)= 60.04 - 8.25 * ln(x)
[tex]\begin{gathered} f(1)=60.04-8.25\ln (1) \\ =60.04 \\ \\ f(2)=60.04-8.25\ln (2) \\ =54.32\ldots \\ \\ f(3)=60.04-8.25\ln (3) \\ =50.97\ldots \\ \\ f(4)=60.04-8.25\ln (4) \\ =48.60 \\ \\ f(5)=60.04-8.25\ln (5) \\ =46.76 \\ \\ f(6)=60.04-8.25\ln (6) \\ =45.26\ldots \\ \\ f(7)=60.04-8.25\ln (7) \\ =43.98\ldots \end{gathered}[/tex]2) f(x) = 8.25 - 60.04 * ln(x)
[tex]\begin{gathered} f(1)=8.25-60.04\ln (1) \\ =8.25 \\ \\ f(2)=8.25-60.04\ln (2) \\ =-33.36\ldots \\ \\ f(3)=8.25-60.04\ln (3) \\ =-57.71\ldots \\ \\ f(4)=8.25-60.04\ln (4) \\ =-74.98\ldots \\ \\ f(5)=8.25-60.04\ln (5) \\ =-88.38\ldots \\ \\ f(6)=8.25-60.04\ln (6) \\ =-99.32\ldots \\ \\ f(7)=8.25-60.04\ln (7) \\ =-108.58\ldots \end{gathered}[/tex]The rest of the given functions are not logarithmic.
We can see from the computed values for the given logarithmic functions, that the one which best fits the data, is: f(x)=60.04-8.25*ln(x).
Therefore, the answer is:
[tex]f(x)=60.04-8.25\ln (x)[/tex]2.90change repeating decimal to fraction?
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The given number is 2.90.
As you can notice this is a decimal number which is also rational. To express as a fraction, we divide it by 100 to get rid of the decimal point, then we simplify, as follows
[tex]\frac{290}{100}=\frac{145}{50}=\frac{29}{10}[/tex]Therefore, the equivalent fraction is 29/10.
In the figure below, AC || DE, BD measures 8 m, AD measures 12 m, and BE measures 6 m. Find the length of BC.
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Answer:
BC = 15 units===============
Parallel lines divide the transversal into proportional segments.
Set ratios and find the missing lengthBD/AD = BE/ED8/12 = 6/ED2/3 = 6 / EDED = 6*3/2ED = 9Find BCBC = BE + EDBC = 6 + 9BC = 156n+36=0solve the following equation if n=10
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According to the given data we have the following equation:
6n+36=0
So, if the value of n=10 we would solve the equation as follows:
We would substitue the variable of n with 10, so:
6n+36=0
6(10)+36=0
60+36=96
Therefore, the value of the equation 6n+36 when n=10 would be 96
The function graphed is of the form y=a sin bx or y=a cox bx, where b>0. Determine the equation of the graph.
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The equation is of the form y=asinbx
The amplitude of the graph is a=3 unit
The period is
[tex]\frac{\pi}{2}[/tex]Thus,
[tex]\frac{2\pi}{b}=\frac{\pi}{2}\Rightarrow b=4[/tex]Thus the equation becomes,
y=3sin(4x)
A department store is holding a drawing to give away free shopping sprees. There are 9 customers who have entered the drawing: 3 live in the town of Gaston, 2 live in Pike, and 4 live in Wells. Two winners will be selected at random. What is the probability that both winners live in Pike? Write your answer as a fraction in simplest form.
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We need to find the probability that the two winners line in Pike.
We know that 2 out of the 9 customers who entered the drawing live in Pike.
Thus, the probability of the first winner line in Pike is:
[tex]\frac{2}{9}[/tex]Then, considering the first winner live in Pike, there are left 8 customers, and 1 of them live in Pike. Thus, the probability that the second winner lives in Pike is:
[tex]\frac{1}{8}[/tex]Now, the probability that the first one lives in Pike and the second one also lives in Pike is the product of the two probabilities we found:
[tex]\frac{2}{9}\times\frac{1}{8}=\frac{2}{9\times8}=\frac{1}{9\times4}=\frac{1}{36}[/tex]Therefore, the probability that both winners live in Pike is:
[tex]\frac{1}{36}[/tex]Line c passes through the points (3, - 5) and (6, 1) . Line d passes through the points (6, - 4) and (2, - 2) Find the slope of each line and determine whether lines c and d are parallel , perpendicular , or neither . Explain your answer ...
Answers
Answer:
The slope of line c is 2.
The slope of line d is -1/2.
Lines c and d are perpendicular
Step-by-step explanation:
Slope of a line:
When given two points of a line, the slope is given by the change in y divided by the change in x.
Parallel lines: Have the same slope
Perpendicular lines: The multiplication of their slopes is -1.
Line c:
Passes through points (3,-5) and (6,1).
Change in y: 1 - (-5) = 1 + 5 = 6
Change in x: 6 - 3 = 3
Slope: 6/3 = 2
The slope of line c is 2.
Line d:
Passes through points (6,-4) and (2,-2)
Change in y: -2 - (-4) = -2 + 4 = 2
Change in x: 2 - 6 = -4
Slope: 2/-4 = -1/2
The slope of line d is -1/2.
Relationship between the lines:
They have different slopes, so they are not parallel.
Multiplication of the slopes:
2*(-1/2) = -2/2 = -1
Since the multiplication of their slopes is -1, Lines c and d are perpendicular.
at Mr.neelys farm, there were 75 sheep and 60 cows what is the ratio number of cows to the number of sheep's at Mr.neelys farm
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Answer:
The ratio of the number of cows to the number of sheeps in the farm is;
[tex]\begin{gathered} \frac{4}{5} \\ Or \\ 4\colon5 \end{gathered}[/tex]Explanation:
Given that;
there were 75 sheep
and 60 cows
We want to find the ratio of the number of cows to the number of sheeps in the farm;
[tex]\text{ratio}=\frac{\text{ number of cows }}{\text{ number of sh}eeps}=\frac{60}{75}[/tex]reducing the ratio to the least form;
[tex]\text{ratio=}\frac{60}{75}=\frac{4}{5}[/tex]Therefore, the ratio of the number of cows to the number of sheeps in the farm is;
[tex]\begin{gathered} \frac{4}{5} \\ Or \\ 4\colon5 \end{gathered}[/tex]estimate 8426 divided by 36 so that it only has one non zero digit.
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Given:
[tex]\frac{8426}{36}[/tex]Required:
To estimate 8426 divided by 36.
Explanation:
[tex]\begin{gathered} \text{ 234.05} \\ 36)8426 \\ \text{ 72} \\ ----- \\ \text{ 1226} \\ \text{ 108} \\ ------- \\ \text{ 146} \\ \text{ 144} \\ ------ \\ \text{ 200} \\ \text{ 180} \\ -------- \\ \text{ 20} \end{gathered}[/tex]Therefore,
[tex]\frac{8426}{36}=234.05555[/tex]Final Answer:
[tex]234.05[/tex]insert parentheses to make the expression true, 382/292-101+8=10
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Answer:
(382/(292-101))+8=10
(382/191)+8=10
(2)+8=10
10=10
c and 217 more is equal to 198
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c and 217 more means c+217
equal to 198 means =198
the complete sentence means
c+217=198
The question is in the image. Answer the question 4.
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Step 1
Given;
[tex]coordinate\text{ points\lparen5,-12\rparen}[/tex]Required; To find the value of θ
Step 2
We use the trigonometric function Toa to find the required angle.
[tex]\begin{gathered} tan\theta=\frac{opposite}{Adjacent} \\ opposite=-12 \\ adjacent=5 \\ tan\theta=\frac{-12}{5} \\ \end{gathered}[/tex][tex]\begin{gathered} Using\text{ pythagoras} \\ (-12)^2+(5)^2=hypotenuse^2 \\ hypotenuse=\sqrt{144+25}=13 \\ Sin\theta=\frac{opposite}{Hypotenuse}=\frac{-12}{13} \end{gathered}[/tex][tex]\begin{gathered} cos\theta=\frac{adjacent}{hypotenuse}=\frac{5}{13} \\ csc\theta=\frac{1}{sin\theta}=\frac{1}{\frac{-12}{13}}=\frac{13}{-12} \end{gathered}[/tex][tex]\begin{gathered} sec\theta=\frac{1}{cos\theta}=\frac{1}{\frac{5}{13}}=\frac{13}{5} \\ cot\theta=\frac{1}{tan\theta}=\frac{1}{\frac{-12}{5}}=\frac{5}{-12} \end{gathered}[/tex]Solve the equation (the answer might be no solution or all real numbers)-30= -10(q-1)6+(c+8)=136-(c+8)=13-(c-4)=13-36= -3(2-5m)4-10(n+4)=-56
Answers
We have to find the solution for this equations.
a) -30 = -10(q-1)
[tex]\begin{gathered} -30=-10(q-1) \\ q-1=\frac{-30}{-10} \\ q-1=3 \\ q=3+1 \\ q=4 \end{gathered}[/tex]b) 6+(c+8) = 13
[tex]\begin{gathered} 6+(c+8)=13 \\ c=13-6-8 \\ c=-1 \end{gathered}[/tex]c) 6-(c+8)=13
[tex]\begin{gathered} 6-(c+8)=13 \\ 6-13=c+8 \\ -7=c+8 \\ -7-8=c \\ c=-15 \end{gathered}[/tex]d) -(c-4)=13
[tex]\begin{gathered} -(c-4)=13 \\ c-4=-13 \\ c=-13+4 \\ c=-9 \end{gathered}[/tex]f) -36= -3(2-5m)
[tex]\begin{gathered} -36=-3(2-5m) \\ \frac{-36}{-3}=2-5m \\ 12=2-5m \\ 5m=2-12 \\ 5m=-10 \\ m=\frac{-10}{5} \\ m=-2 \end{gathered}[/tex]g) 4-10(n+4)=-56
[tex]\begin{gathered} 4-10\mleft(n+4\mright)=-56 \\ 4+56=10(n+4) \\ 60=10(n+4) \\ \frac{60}{10}=n+4 \\ 6=n+4 \\ n=6-4 \\ n=2 \end{gathered}[/tex]Calculate the X value a. 4: 7 = x: 5x: 8 = 99 :5
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Start writing the proportion as a fraction
[tex]\begin{gathered} 4\colon7\rightarrow\frac{4}{7} \\ x\colon5\rightarrow\frac{x}{5} \end{gathered}[/tex]then, the ratios must be the same meaning we can equal the fractions
[tex]\begin{gathered} \frac{4}{7}=\frac{x}{5} \\ \text{cross-multiply and solve for x } \\ x=4\cdot\frac{5}{7} \\ x=\frac{20}{7} \end{gathered}[/tex]repeat the same procedure for b
[tex]\begin{gathered} x\colon8\rightarrow\frac{x}{8} \\ 99\colon5\rightarrow\frac{99}{5} \\ \text{then,} \\ \frac{x}{8}=\frac{99}{5} \\ x=8\cdot\frac{99}{5} \\ x=\frac{792}{5} \end{gathered}[/tex]k= 12, r=4%, po=$10,000, n=25 using the compound interest formula
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The compound interes formula is given by:
[tex]P_N=P_0(1+\frac{r}{k})^{Nk}[/tex]where P0 is the principal (the initial amount), r is the interes rate (in decimal form), k is the number of times the interest is compounded and N is the time elapsed.
Plugging the values given we have:
[tex]\begin{gathered} P_N=10000(1+\frac{0.04}{12})^{12\cdot25} \\ =27,137.65 \end{gathered}[/tex]Therefore the future amount is $27,137.65 and the interest earned is $17,137.65.
Х о 1 2 3 4 у -5 4 13 22 31
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We can take any 2 points both from x and y and use the equation of a line formula to find out the equation of the line represented by the points in the table.
Let's take the points:
[tex]\begin{gathered} (x_1,y_1)=(0,-5) \\ (x_2,y_2)=(1,4) \end{gathered}[/tex]The equation of a line formula is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Let us plug in the points into this formula and do a little algebra to re-arrange the equation in the slope-intercept form, which is y = mx + b. The steps are shown below:
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-(-5)=\frac{4-(-5)}{1-0}(x-0) \\ y+5=\frac{4+5}{1}(x) \\ y+5=\frac{9}{1}(x) \\ y+5=9x \\ y=9x-5 \end{gathered}[/tex]The slope-intercept form is given by:
[tex]y=9x-5[/tex]Where 9 is the slope and -5 is the y-intercept (y-axis cutting point)
what is 30% off 10? How u get answer
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We are asked to find out what is 30% off 10?
30% off 10 means that there is a discount of 30% and you are supposed to pay only the remaining 70%
100% - 30% = 70%
So you can simply find the 70% of 10
[tex]70\%\: of\: 10=\frac{70}{100}\times10=7[/tex]Therefore, 30% off 10 is equal to 7
There is another way to find out 30% off 10
First, you find 30% of 10 and then subtract the result from the original amount
[tex]\begin{gathered} 30\%\: of\: 10=\frac{30}{100}\times10=3 \\ 10-3=7 \end{gathered}[/tex]Therefore, 30% off 10 is equal to 7
"The sum of 5 and a number results in 14."
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We are given the phrase "The sum of 5 and a number results in 14." which suggest that we should find such a number. Let x be the number we are looking for, the phrase "The sum of 5 and a number" translates to the equation x+5,, since we are adding 5 to the number.
The part "results in 14" means that after adding 5, we end up having 14 as a result, this means we have
[tex]x+5=14[/tex]Now, we proceed to solve this equation for x by simply subtracting 5 on both sides. Once we do so, we get
[tex]x=14-5=9[/tex]so in this case the number we were looking for is x=9.
What is the measure of ZXYZ shown in the diagram below?S36°TХ114"ZO A. 78O B. 39OC. 36ОD. 75
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In order to calculate the measure of angle XYZ, we can use the following property of secant lines to a circle:
[tex]\begin{gathered} XYZ=\frac{1}{2}(XZ-ST) \\ \text{XYZ}=\frac{1}{2}(114-36) \\ \text{XYZ}=\frac{1}{2}\cdot78 \\ \text{XYZ}=39\degree \end{gathered}[/tex]So the correct option is B.
DAC BAD.What is the length of BD?Round to one decimal place.
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Notice that we have two triangles with the SAME angle, abd with also a common side (the same length) AD.
we can use the law os sines in the smaller triangle and specially using the sides that are known.
for example, we can state in the first (smaller) triangle that:
[tex]\frac{\sin(\theta)}{2}=\frac{\sin (D)}{5.9}=\text{ }\frac{\sin(C)}{AD}[/tex]For the full triangle ABC we have the following law of sines:
[tex]\frac{\sin(2\theta)}{2+\text{?}}=\text{ }\frac{\sin(C)}{8.1}=\frac{\sin (B)}{5.9}[/tex]For the medium triangle ADB the law of sines goes as:
[tex]\frac{\sin(\theta)}{?}=\frac{\sin(B)}{AD}=\frac{\sin(180-D^{})}{8.1}=\frac{\sin (D)}{8.1}[/tex]Now, we need to find common variables to combine equations based on the law of sines.
Notice as well that sin(180-a) = sin(a) this is a trig identity, so we are going to replace this in the last trig identity for triangle ADB
Now, we have the following relationships from the veri first law of sines:
[tex]\sin (\theta)=\frac{2\cdot\sin (D)}{5.9}[/tex]and from the last law of sines we have the folloowing relationship:
[tex]\sin (\theta)=\frac{?\cdot\sin (D)}{8.1}[/tex]so we can equal both sine expressions since they are from the same angle, and try to solve for the unknown "?" in the equation:
[tex]\begin{gathered} \frac{2\cdot\sin(D)}{5.9}=\frac{?\cdot\sin (D)}{8.1} \\ \frac{2}{5.9}=\frac{?}{8.1} \\ \frac{2\cdot8.1}{5.9}=\text{?} \end{gathered}[/tex]whre we have eliminated sin(D) as common factor in both equations (this is correct as long as sin*D) is not equal to zero, which cleary is not the case here)
Therefore our unknown "?" is 2*8.1 / 5.9 = 2.7457 which rounded to one decimal is 2.7
Find the x-intercept(s) and the coordinates of the vertex for the parabola y=x² + 4x - 5. If there is more than one x-Intercept, separate them with commas.DD:x-intercept(s):5?vertex:00
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SOLUTION
Step 1 :
In this equation, we are expected to find the x-intercept(s)
of the vertex and the co-ordinates of the vertex of the parabola :
[tex]y=x^2\text{ + 4x - 5}[/tex]Step 2 :
[tex]\begin{gathered} \text{Given y = x}^2\text{ + 4 x - 5,} \\ y=x^2\text{ + 4 x + (}\frac{4}{2})^2\text{ - 5 - (}\frac{4}{2})^2\text{ ( Completing the square method )} \\ \\ y=(x+2)^2\text{ - }9 \\ \text{The vertex of the parabola, ( h, k ) }=\text{ ( -2 , -9 )} \end{gathered}[/tex]Step 3 :
We need to solve for the x-intercepts,
[tex]\begin{gathered} \text{Given y = x}^2\text{ + 4 x - 5} \\ \text{Factorising the Quadratic Function, we have that:} \\ y=x^2\text{ - x + 5 x - 5 } \\ y\text{ = x ( x -1 ) + 5 ( x - 1 )} \\ y\text{ = ( x - 1 ) ( x + 5 )} \\ \text{Setting y = 0, we have ( x - 1 ) = 0 or ( x + 5 ) = 0} \\ x\text{ = 1 or x = -}5\text{ } \end{gathered}[/tex]CONCLUSION:
The vertex of the parabola, ( h, k ) = ( -2 , -9 )
The x - intercepts are : x = 1 or x = -5
Convert 0.111... to a repeating fraction. simplify if you can
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Explanation:
To convert from a repeating decimal number to a fraction we have to do the following steps:
1. Let 'x' be the repeating decimal:
[tex]x=0.111\ldots[/tex]2. Let 'n' be the number of decimals that repeat. In this case n = 1
3. Multiply both sides of point 1 by 10^n:
[tex]10x=1.111\ldots[/tex]4. Substract (1) from (3) to eliminate the repeating part:
[tex]\begin{gathered} 10x-x=1.111\ldots-0.111\ldots \\ 9x=1 \end{gathered}[/tex]5. Solve for x:
[tex]\begin{gathered} 9x=1 \\ x=\frac{1}{9} \end{gathered}[/tex]6. Simplify: in this case, it is the simplest form for this fraction
Answer:
0.111... as a fraction is 1/9
How do you graph Y=5 on a graph. This is a linear equation. I know how to do it when they give an x too. But I don’t know what to do with just a y=5?
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The equation y=5 represents something we know as a constant function. In a constant function, y, always, no matter what, takes the same value and is the value of the constant. In this case, the constant is 5, it means that for all values of x, y will always be 5.
In a graph, a constant function is an horizontal line, parallel to the x axis, that cuts the y axis at y=c, c is the constant. It means that the graph of y=5 will be an horizontal line that has a y intercept of 5.
What is the standard deviation of the data?Some teenagers collected trash for a beach cleanup.The data for the number of pounds of trash collected byeach teenager are shown below.26, 26, 21, 22, 20, 25, 35O pounds4.66 pounds5.03 poundso 25.33 pounds
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determine the slope of a vertical line, and the slope of a horizontal line.
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The slope of a vertical line is undefine
The slope of a horizontal line is zero