Answers
Given:
AD is angle bisector of angle BAC.
AB = AC.
The objective is to prove BD = DC.
Step 1:
Statement: AD is angle bisector of angle BAC.
Reason: Given.
Step 2:
Statement:
[tex]\angle BAD=\angle\text{DAC}[/tex]Reason: Definition of angle bisector.
Step 3:
Statement:
[tex]AB\cong AC[/tex]Reason: Given
Step 4:
Statement: AD = AD.
Reason: Reflexive.
Step 5:
Statement:
[tex]\Delta BAD\text{ }\cong\text{ }\Delta CAD[/tex]Reason: By SAS criteria.
Step 6:
Statement:
[tex]BD\cong DC[/tex]Reason: By Corresponding parts of congruent triangles (CPCT).
Hence, the required results are obtained.
Related Questions
Which equation represents a horizontal line that passes through the point (2, 7)? А x=2 В y = 2 C X= 7 D y=7
Answers
It is important to know that horizontal lines are represented by the equation y = k, where k is a real numbers.
In this case, if the equation passes thorugh (2,7), then the equation would be y = 7.
Hence, the answer is D.The population of a certain town was 10,000 in 1990. The rate of change of the population, measured in people per year, is modeled by P prime of t equals two-hundred times e to the 0.02t power, where t is measured in years since 1990. Discuss the meaning of the integral from zero to twenty of P prime of t, d t. Calculate the change in population between 1995 and 2000. Do we have enough information to calculate the population in 2020? If so, what is the population in 2020? Explain your answers.
Answers
Given the function of the rate of change of the population:
[tex]P(t)=200e^{0.02t}[/tex]The integral of this function will be the value of the population growth of the town from 1990 to 2010. This is because P(t) is the rate of change of population, its integral will be the antiderivative, that is the population of the town.
To calculate the change in population we have to find the integral from 5 to 10 of P(t):
[tex]\begin{gathered} \int_5^{10}200e^{0.02t}dt \\ 200\int_5^{10}e^{0.02t}dt \\ 200\cdot\frac{e^{0.02t}}{0.02} \\ 10000e^{0.02t} \\ (10000e^{0.02(10)})-(10000e^{0.02(5)}) \\ 1162.3 \end{gathered}[/tex]The change in population can not be a decimal number, so we can round it to 1162.
To calculate the population in 2020 we have to find the integral from 0 to 30 of P(t) and then add it to 10000 which was the initial population (we already know the integral so we're just going to evaluate it):
[tex]\begin{gathered} 10000e^{0.02(30)}-10000e^{0.02(0)} \\ 8221.2 \\ 10000+8221.2=18221.2 \end{gathered}[/tex]It means that the population in 2020 is 18221 (Remember that we round it because it is not possible to have a decimal value for the population of the town).
A car travels 238 miles in 4 hours and 15 minutes. How many miles does it travel per
hour?
Answers
We can conclude that the distance traveled in 1 hour is 57 miles after doing some mathematical operations.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out by the arithmetic operators.So, the distance traveled in 1 hour:
Distance traveled in 4 hours and 15 minutes = 238 milesThen divide 238 by 4.15 as follows:
238 ÷ 4.1557.34Rounding off: 57 miles
Therefore, we can conclude that the distance traveled in 1 hour is 57 miles after doing some mathematical operations.
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Residents in a city are charged for water usage every three months. The water bill is computed from a common fee, along with the amount of water the customers use. The last water bills for 40 neighborhood residents are displayed in the histogram below. A histogram titled Neighborhood Monthly water bill has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 1; 125 to 150, 2; 150 to 175, 5; 175 to 200, 10; 200 to 225, 13; 225 to 250, 8. Which interval shows the greatest change in water bills? $150–$175 $175–$200 $200–$225 $225–$250
Answers
$200-$225 interval shows the greatest change in water bills
What is Histogram?A diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.
The interval which contains the median water bill is $200 - $225
The tabulated data is given in the attachment.
The median class = Cummulative frequency / 2
The median class = 40 / 2
The class interval which contains the 20th frequency.
This is the 200 - 225 class
The interval which contains the median water bill is $200 - $225
Hence $200-$225 interval shows the greatest change in water bills
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Answer:
C)$200–$225
Step-by-step explanation:
edge 2023
In places where there are crickets, the outdoor temperature can be predicted by the rate at which crickets chirp. One equation that models the relationship between chirps and outdoor temperature is , where c is the number of chirps per minute and f is the temperature in degrees Fahrenheit.
Suppose 110 chirps are heard in a minute. If it is 75°F outside, about how many chirps can we expect to hear in one minute? Do not include units (chirps) in your answer. Round your answer to the nearest whole number.
Answers
Answer:
The crickets do not chirp at all below 40 degrees and at 75 degrees they chirp about 161 times per minute.
Write an inequality that represents the graph below
Answers
An inequality that represents the given graph is; 2 < x < ∞.
What is referred as the term inequality?In mathematics, an inequality is a link between two expressions as well as values that aren't equal to each other.Inequality results from a lack of balance. For instance, suppose you would like to buy a new vehicle that costs $250 but only have 225. It is also a inequality because you are comparing these two non-equal numbers.For the given question.
The inequality is given by the values of the number line.
The value is starting from 2 and goes up to infinity.
But, It is a hollow dot at 2 means 2 is with open interval, as 2 will not be taken for the value of x.
The values lies between, (2, ∞)
Thus, the inequality that represents the given graph is; 2 < x < ∞.
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M=W(1+rt) (solve the following formula for "t"
Answers
Given the following formula given in the exercise:
[tex]M=W\mleft(1+rt\mright)[/tex]You can solve for the variable "t" by following the steps shown below:
1. You must apply the Disrtributive proprerty on the right side of the equation:
[tex]\begin{gathered} M=(W)\mleft(1)+(W)(rt\mright) \\ M=W+Wrt \end{gathered}[/tex]2. Now you need to apply the Subtraction property of equality by subtracting "W" from both sides of the equation:
[tex]\begin{gathered} M-(W)=W+rtW-(W) \\ M-W=Wrt \end{gathered}[/tex]3. Finally, you can apply the Division property of equality by dividing both sides of the equation by "Wr":
[tex]\begin{gathered} \frac{M-W}{Wr}=\frac{Wrt}{Wr} \\ \\ t=\frac{M-W}{Wr} \end{gathered}[/tex]The answer is:
[tex]t=\frac{M-W}{Wr}[/tex]I can’t figure this out I need help. I’ve been stuck on it for about an hour and a half.
Answers
SOLUTION
From the question, we are told to distribute the multiplication across in
[tex](4v^4-6z^5).4z^4[/tex]This means we should expand.
This becomes
A train travels 150 km in 2 hours and 30 minutes. What is its average speed?
Answers
Answer:
It's average speed is 48 km per hour
Step-by-step explanation:
Answer:
60 km/hr
Step-by-step explanation:
150 km / 2.5 hr = 60 km/hr
CD is the mid segment of trapezoid WXYZ.-What is the value of X?-What is XY?-What is WZ?
Answers
The midsegment theorem states that the length of the midsegment is equal to half the length of the base. From the information given,
midsegment = CD = 22
base = XY = 4x + 1
By applying the midsegment theorem, we have
CD = 1/2XY
22 = 1/2(4x + 1)
By crossmultiplying, we have
22 * 2 = 4x + 1
44 = 4x + 1
4x = 44 - 1
4x = 43
x = 43/4
x = 10.75
Thus,
Substituting x = 10.75 into XY = 4x + 1, it becomes
XY = 4(10.75) + 1
XY = 43 + 1
XY = 44
Substituting x = 10.75 into WZ = x + 3, it becomes
WZ = 10.75 + 3
WZ = 13.75
Is (-2,-6) a solution to the equation y = 3x?
Oyes
Ono
Answers
Answer:
yes
Step-by-step explanation:
if y = -6,
3x = -6
x = -2
Answer:
yes
Step-by-step explanation:
y = 3x?
Let x = -2 and y = -6
-6 = 3(-2)
-6 = -6
This is a true statement so (-2,-6) is a solution to the equation y = 3x
The hypotenuse of right triangle XYZ is 28 and m
Answers
Solution
For this case we can do the following:
m < X = 60
One angle in a right triangle needs to be 90º
So then we can find the measure of the other angle like this.
180 -90-60 = 30º
We can find the following identity:
[tex]\sin 60=\frac{y}{28}[/tex]And solving for thw leg opposite we got:
[tex]y=28\cdot\sin 60=24.25[/tex]
Put 3/4, -1/2, -1/4 in order from least to greatest.
Answers
Answer:
-1/2, -1/4, 3/4.
Explanation:
If we draw the number in a number line, we get:
So, if we order them from least to greatest, we get:
-1/2, -1/4, 3/4.
Answer:
-1/2, -1/4, 3/4
Step-by-step explanation:
Rotate this hexagon 180º.
(0, -8)
(3, -8)
(6,-5)
(6, 1)
(3, 2)
(0, 2)
Answers
After rotation the coordinates of the hexagon is (0, 8), (-3, 8), (-6, 5), (-6, -1), (-3, -2), (0, -2)
Upon rotation of this hexagon by 180
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
After rotation, the co- ordinates change from
(0, -8) → (0, 8)
(3, -8) → (-3, 8)
(6,-5) → (-6, 5)
(6, 1) → (-6, -1)
(3, 2) → (-3, -2)
(0, 2) → (0, -2)
Therefore, after rotation the coordinates of the hexagon is (0, 8), (-3, 8), (-6, 5), (-6, -1), (-3, -2), (0, -2)
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17. The rent for a store is GH¢420.00 a year.
What is the rent for the store in six
months?
Answers
Answer:
GH¢210Step-by-step explanation:
The rent is 420 a year.
6 months is half a year.
The rent for 6 months is half the rent for a year:
420/2 = 210What are the dimensions of the rectangle with Maximum area?
Answers
Let x be the length of the rectangle and y be the width of the rectangle, then we can set the following equations:
[tex]\begin{gathered} 2x+2y=40, \\ A=x\cdot y\text{.} \end{gathered}[/tex]Solving the first equation for x we get:
[tex]\begin{gathered} 2x=40-2y, \\ x=\frac{40}{2}-\frac{2y}{2}, \\ x=20-y\text{.} \end{gathered}[/tex]Substituting x=20-y in the second equation we get:
[tex]\begin{gathered} A=(20-y)\times y, \\ A=20y-y^2. \end{gathered}[/tex]Now, we will use the first and second derivative criteria to find the maximum.
The first and second derivatives are:
[tex]\begin{gathered} A^{\prime}(y)=20-2y. \\ A^{\prime\prime}(y)=-2. \end{gathered}[/tex]Since the second derivative is a negative number that means that A(y) reaches a maximum when A´(y)=0.
Solving A´(y)=0 for y we get:
[tex]\begin{gathered} 20-2y=0, \\ 20=2y, \\ 10=y\text{.} \end{gathered}[/tex]Now, substituting y=10 in x=20-y, we get:
[tex]x=20-10=10.[/tex]Answer:
Length 10 yards.
Width 10 yards.
I need help with this question parts a - e
Answers
Given:
650 lb of coffee is sold when the price is $4 per pound,
400 lb of coffee is sold at $8 per pound.
To find:
A) List the data points
B) The slope of line joining the points
C) Interpretation of meaning of slope of line
D) linear equation of data using point slope form
E) Using the function we need to predict the number of consumers buying at $6 per pound
Step-by-step solution:
A) Data points of the given data:
Data points:
(4,650) and (8,400)
B) The slope of the line joining the points:
[tex]\begin{gathered} Slope=\frac{y_2-y_1}{x_2-x_1} \\ \\ Slope=\frac{400-650}{8-4} \\ \\ Slope\text{ =-62.5} \end{gathered}[/tex]C) Interpretation of meaning of slope of line:
Slope here means that:
When there is an increase in the price of coffee then the weight of coffee decreases.
Weight per dollar of coffee decreases at the rate of 62.5
D) linear equation of data using the point-slope form:
Applying point-slope form:
y - y1 = m(x - x1)
y - 650 = -62.5(x - 4)
y = -62.5x + 900
In function notation it can be represented as:
S(P) = -62.5P + 900
E) Using the function we need to predict the number of consumers buying at $6 per pound
To predict that, we will simply put the value of P equal to 6 in the given function:
S(P) = -62.5P + 900 At P = 6
S(P) = -62.5(6) + 900
S(P) = 525
Thus we can say that 525 customers will buy at $6 per pound.
Sun lei bought a computer for $1800. The total cost, including tax, came to $1890. What is the tax rate?
Answers
Given:
Cost of computer without tax $1800.
Total cost including tax is $1890
[tex]\text{Tax amount =1890-1800}[/tex][tex]\text{Tax amount = \$90}[/tex]Let the tax rate be x
[tex]90=1800\times\frac{x}{100}[/tex][tex]\frac{90}{18}=x[/tex][tex]x=5[/tex]Tax rate is 5%
In isosceles △ABC where AC≅BC, altitiude CD is drawn. If AC= 17 and AB= 30. Determine the altitiude of the triangle.
Answers
By definition, an Isosceles triangle is a triangle that have two congruent sides, and the altitude divides the triangle into two equal Right triangles.
Remember that a Right triangle is a triangle that has an angle whose measure is 90 degrees.
Based on this, you know that:
[tex]\begin{gathered} AD=BD=\frac{AB}{2} \\ \\ AC=BC \end{gathered}[/tex]Knowing that:
[tex]\begin{gathered} AB=30 \\ AC=17 \end{gathered}[/tex]You get that:
[tex]\begin{gathered} AD=BD=\frac{30}{2}=15 \\ \\ AC=BC=17 \end{gathered}[/tex]The Pythagorean Theorem states that:
[tex]a^2=b^2+c^2[/tex]Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.
So you can identify that, for this case:
[tex]\begin{gathered} a=17 \\ b=15 \\ c=CD \end{gathered}[/tex]Where "CD" is the altitude of the triangle.
Therefore, substituting values and solving for "CD", you get this result:
[tex]\begin{gathered} 17^2=15^2+CD^2 \\ \sqrt[]{17^2-15^2}=CD \\ CD=8 \end{gathered}[/tex]The answer is: Option (1)
What is 372.7332 rounded to the nearest thousandth?
Please help rn I have until 3pm
Answers
Nandita earned 224 dollars last month. she earned 28 dollars by selling cards at a craft fair and the rest of the money by babysitting. Complete an equation that models the situation and can be used to determine x, the number of dollars Nandita earned last month by babysitting.
Answers
the selling price of each card is = 28 $
let she sold x number of cards,
so, the equation is,
28x = 224
x = 224/28
x = 8
thus, the answer is number of cards sold by nandita is 8
so, the equation is
28x = 224
Find the critical value (tα/2) for a 99% confidence interval if the sample size is 15. Round your answer to three decimal places.
tα/2 =
Answers
The critical value (tα/2) for a 99% confidence interval for the sample size 15 is 2.977 .
We have to find the critical value tα/2 for 99% confidence interval, we are given the sample size.
First we will find the alpha value to get the critical value.
=100%-99%
=1-0.99
=0.01
α=0.01
α/2=0.01/2
α/2=0.005
degrees of freedom(df)= n-1=15-1=14
We will use degrees of freedom and α/2 values to find the critical value that is tα/2.
By using the t table we get the critical value of tα/2=2.977.
Therefore, the critical value for 99% confidence interval with sample size 15 is 2.977.
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Determine the open intervals on which the function is increasing, decreasing, or constant.(Enter your answers using interval notation. If an answer does not exist, enter DNE.)
Answers
Given:
[tex]f(x)=\sqrt{x^2-4}[/tex]To find:
The interval at which the function is increasing, decreasing and constant.
Explanation:
We know that,
For a function, y = F(x), if the value of y is increasing on increasing the value of x, then the function is known as an increasing function.
For a function, y = F(x), if the value of y is decreasing on increasing the value of x, then the function is known as a decreasing function.
According to the graph,
The function is increasing in the interval,
[tex][2,\infty)[/tex]Because, if x increases from 2, the value of y increases.
The function is decreasing in the interval,
[tex](-\infty,-2][/tex]Because, if x increases from negative infinity, the value of y decreases.
As we know, a constant function is a function whose output value is the same for every input value.
Here, the function is not constant at any of the intervals.
Final answer:
Increasing:
[tex][2,\infty)[/tex]Decreasing:
[tex](-\infty,-2][/tex]Constant: DNE.
2) Convert this fraction into a mixed number in lowest terms 60/25
Please I need step by step explanation.
Answers
The given fraction 60/25 into a mixed number would be 2 2/5 in the lowest terms.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
First, we have to find the whole number,
Determine how many times the denominator enters the numerator. Divide 60 by 25 and preserve just the numbers to the left of the decimal point:
⇒ 60 / 25 = 2.4000 = 2
Then, find a new numerator :
Multiply the result by the denominator and subtract it from the original numerator.
⇒ 60 - (25 x 2) = 10
Now, put together
To obtain this, keep the original denominator and use the solutions from Steps 1 and 2:
⇒ 2 10/25 ⇒ 2 2/5
Thus, the given fraction 60/25 into a mixed number would be 2 2/5 in the lowest terms.
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Use the equation below and the indicated value to find an ordered pair that is a solution.
y=2x-1 Let x = 4.
The ordered pair is 4.
Answers
The ordered pair is 4 is 7.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
Given that,
The equation is
y = 2x-1
Substitute the value of x =4
y = 2x-1
y = 2×4-1
y = 7
The value of y at x = 4 is 7.
Hence, the ordered pair of 4 is 7.
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Here is an ordered set of sample data.87 109 156 166 204210 279 416 500 534592 609 655 677 777837 873 998Identify the 5 number summary: (min, Q1, median, Q3, max).
Answers
Solution:
A boxplot is a standardized way of displaying the dataset based on a five-number summary: the minimum, the maximum, the median, the first quartile, and the third quartile.
The general representation for a box plot is given below;
Comparing this to the box plot given in the question, the following can be deduced;
[tex]\begin{gathered} \text{minimum, }\min =11 \\ lowerquartileQ_1=12 \\ \text{Median}=15 \\ \text{upper quartile, Q}_3=17 \\ \max imum,\text{ max=20} \end{gathered}[/tex]Therefore, the answer as arranged is;
[tex](11,12,15,17,20)[/tex]The interquartile range, IQR is given by;
[tex]\begin{gathered} Q_3-Q_1 \\ \text{where;} \\ Q_3=17 \\ Q_1=12 \\ \\ \text{IQR}=17-12 \\ \text{IQR}=5 \end{gathered}[/tex]Therefore, the interquartile range is 5.
Steve files head of household. In 2022, he received $23,000 in social security benefits, $10,000 in taxable retirement income, and $4,000 in interest and dividend income. Using the Social Security Benefits Worksheet - Line 6a and 6b, determine Steve's taxable social security benefits.
Answers
Steve's taxable social security benefits is zero.
Since Steve declares himself as the head of the home, his social security payments, which range from $25,000 to $34,000, will be subject to a 50% tax.
Retirement income, interest income, and dividend income are not considered social security benefits for determining the limit. Nevertheless, in the case at hand, the social security benefits total $23,000, which is less than the maximum of $25,000 and is thus not taxable.
As a result, Steve's Social Security benefits are not taxable.
Hence the taxable amount on Steve on social security benefits is Zero.
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I am having trouble with the last two questions. I worked through finding the slope and y-intercept with a previous tutor, before we got disconnected.6. Express this equation as a function D of P and find its domain.7. How many shirts per month will be demanded if the price is $27?
Answers
Data:
[tex]m=-\frac{203}{152}\approx-1.3355[/tex][tex]b=\frac{11227}{152}\approx73.862[/tex]Equation as a function of D of P
[tex]D(P)=-1.3355\cdot P+73.862[/tex]Answer (6):
• Domain
[tex](-\infty,+\infty)[/tex]To know how many shirts per month will be demanded if the price is $27, we have to use P = $27:
[tex]D(27)=-1.3355\cdot27+73.862\text{ }\approx37.80[/tex]Answer (7): $37.80
The number of students in the tutoring center was recorded for 27 randomly selected times. The data is summarized in the frequency table below. What is the class width for this frequency distribution table
Answers
The class width for this frequency table is 5.
What is class width?The class width is described as the distance between the lower class of two consecutive classes.
How to calculate class width?One can calculate class width by finding the difference between the two consecutive lower classes.
In the figure above, the first two classes are described as
0-4
5-9
So, the lower classes of these intervals are 0,5
Thus the difference between them is 5
Therefore, the class width for this frequency distribution table is 5.
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The weights of a certain brand of candies are normally distributed with a mean weight of 0.8543 g and a standard deviation of 0.0519 g. A sample of these candies came from a package containing 469 candies, and the package label stated that the net weight is 400.3 g. (If every package has 469 candies, the mean weight of the candies must exceed
400.3
469=0.8536 g for the net contents to weigh at least 400.3 g.)
Answers
Given,
The weight of candies normally distributed ;
Mean weight of candies = 0.8543 g
Standard deviation, σ = 0.0519 g
Sample of candy came from a packet of 469 candies
Net weight of the packet = 400.3 g
Average weight of the candies in the packet;
[tex]x_{avg} =[/tex] ∑xi/n = 400.3/469 = 0.8535
The population standard deviation (sigma=0.0519 g) is the standard deviation for a confectionery that was chosen at random (sample size n=1).
The z-score can be used to determine the likelihood that an element has a weight greater than 0.8536z = (X - μ) / (σ/√n) = (0.8536 - 0.8535) / (0.0519/√1) = 0.0001/0.0519 = 0.002
P(X > 0.8536) = P(z > 0.002) = 0.4992
A randomly chosen candy has a probability P=0.4992 of weighing at least 0.8536 g.
The z-score needs to be computed if the sample now has n=441 candies and we want to know the likelihood that the mean weight is at least 0.8543 g:z = (X - μ) / (σ/√n) = (0.8543 - 0.8535) / (0.0519/√441) = 0.0008/0.0024 = 0.3288
P(X > 0.8543) = P(z > 0.3288) = 0.37115
A sample of 441 candies chosen at random has a probability P=0.3712 of having an average weight of at least 0.8543 g.
We may determine the likelihood that, for a package of 469 candies and using the mean of 0.8535 g that we previously determined, the average weight is at least 0.8556 g in order to be more certain of the claim that the mean weight is 0.8556 g.z = (X - μ) / (σ/√n) = (0.8556 - 0.8535) / (0.0519/√469) = 0.0021/0.0024 = 0.89
P(X > 0.8556) = P(z > 0.89) = 0.18673
Given that the likelihood is P=0.187, the brand's claim that it delivers the amount promised to customers on the label needs to be reevaluated.
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