Please finish the following proof using the "prove steps" and write the two-column statements.
Answers
Based on the AAS congruence theorem, ΔADB ≅ ΔCDB. The two-column proof for this is explained below.
What is the AAS Congruence Theorem?The AAS congruence theorem states that two triangles are equal or congruent to each other if they have two pairs of congruent angles and a pair of non-included congruent sides.
We are given that ∠ADB and ∠CDB are right angles, therefore, they are congruent to each other. We are also given that ∠A ≅ ∠C.
Also, BD ≅ BD based on the reflexive property of congruency.
Therefore, according to the AAS congruence theorem, ΔADB ≅ ΔCDB.
The two-column proof would be stated as shown below:
Statement Reasons
1. ∠ADB and ∠CDB are right angles 1. Given
2. ∠A ≅ ∠C 2. Given
3. BD ≅ BD 3. Reflexive property
4. ΔADB ≅ ΔCDB 4. AAS congruence theorem
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Related Questions
Nora has a coupon for $3 off of a calzone. She orders a beef and olive calzone, and her bill, with the discounted price is $9.49. What is the regular price of the calzone? Make sure to round your answer to the nearest cent. Do not place a dollar sign as it will not be needed for this question.
Answers
Explanation
We are given the following information:
• Nora has a coupon for $3.
,• Nora orders a beef and olive calzone.
,• Her bill after the discount is $9.49
We are required to determine the regular price of the calzone.
If we aren’t including tax and we assume that both beef and calzone are the same price then:
[tex]\begin{gathered} Calzone\text{ }price=\frac{9.49+3}{2}=6.245 \\ Calzone\text{ }price\approx6.25 \end{gathered}[/tex]Hence, the price of the calzone is approximately 6.25
Identify the local extrema on the graph below. Type your answer as a coordinate (x,y). If there is not a local maximum/minimum then type "none".positive (opening up) absolute value graph with vertex at (1,-3)Local minimum is at the coordinate AnswerLocal maximum is at the coordinate Answer
Answers
The graph is given and local minima from the graph is
[tex](1,-3)[/tex]And the local maxima is none.
A local little league has a total of 70 players, of whom 80% are right-handed. How many right-handed players are there? There are right-handed players.
Answers
there are (0,80)(70)=56 right handed players
Tickets to a show cost $5.50 for adults and $4.25 for students. A family is purchasing 2 adult tickets and 3 student tickets.
Estimate the total cost.
What is the exact cost?
If the family pays $25, what is the exact amount of change they should receive?
Answers
The exact cost is $23.75 for the show, and the exact change they should get is $1.25.
An adult ticket to the show costs $5.50
A student ticket to the show costs $4.25.
A family buys two adult tickets and three student tickets. This would imply that the total cost of two adult tickets would be
⇒ 2 × 5.5 = $11
It also implies that the total cost of three student tickets is
3 × 4.25 = $12.75
The total cost of two adult tickets and three student tickets is
⇒ 11 + 12.75 = $23.75
If the family pays $25, the exact change they should get is
⇒ 25 - 23.75 = $1.25
Thus, the exact cost is $23.75 for the show, and the exact change they should get is $1.25.
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Jessica bought a house at auction for $82,500. The auction company charges a 15% premium on the final bid. how much will jessica pay for the house
Answers
First, we need to find the 15% of $82,500 as:
[tex]82,500\cdot15\text{ \% = 82,500 }\cdot\frac{15}{100}=12,375[/tex]It means that Jessica will pay $82,500 for the house plus $12,375 to the auction company. So, in total, Jesica will pay for the house:
$82,500 + $12,375 = $94,875
Answer: $94.875
How many 1 hour days is 240 hours?
Answers
Answer:
The answer to your question is,
10 days in 240 hours
I hope this helps :)
Answer:
`10 days are in 240 hours
Step-by-step explanation:
We know 1 day is 24 hours. So if we divide 240 by 24, we get 12.
Note: Figure is not drawn to scale.If h= 13 units and r= 4 units, then what is the approximate volume of the cone shown above?OA. 52 cubic unitsOB. 69.337 cubic unitsOC. 2087 cubic unitsOD. 225.337 cubic units
Answers
The volume of a right circular cone is computed as follows:
[tex]V=\pi r^2\frac{h}{3}[/tex]where r is the radius and h is the height of the cone.
Substituting with r = 4 units and h = 13 units, we get:
[tex]\begin{gathered} V=\pi4^2\frac{13}{3} \\ V=\pi16\frac{13}{3} \\ V=\frac{208}{3}\pi\approx69.33\pi \end{gathered}[/tex]What is the volume of this sphere?
Use a ~ 3.14 and round your answer to the nearest hundredth.
Radius =3 m
cubic meters
Answers
Explanation
We are asked to get the volume of the sphere
The volume of a sphere is given by
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \\ where\text{ r = radius =3m} \\ \pi=3.14 \end{gathered}[/tex]The volume of the sphere will be
[tex]V=\frac{4}{3}\times3.14\times3^3=113.04m^3[/tex]Therefore, the volume of the sphere will be 113.04m³
Would you Please Solve it and explain little[tex]14(.5 + k) = - 14[/tex]
Answers
To solve the given equation, we first apply the distributive property on the left side.
So, we have:
[tex]\begin{gathered} 14(0.5+k)=-14 \\ 14\cdot0.5+14\cdot k=-14 \\ 7+14k=-14 \\ \text{ Subtract 7 from both sides of the equation} \\ 7-7+14k=-14-7 \\ 14k=-21 \\ \text{ Divide by 14 from both sides} \\ \frac{14k}{14}=-\frac{21}{14} \\ k=-\frac{21}{14} \end{gathered}[/tex]Finally, we simplify.
[tex]\begin{gathered} k=-\frac{3\cdot7}{2\cdot7} \\ $$\boldsymbol{k=-\frac{3}{2}}$$ \end{gathered}[/tex]Therefore, the solution of the given equation is -3/2.
I dont really get it or what it is asking
Answers
ANSWER
• A vertical plane that cuts through the top vertex, perpendicular to the base,: ,triangle
,• A horizontal plane, that cuts through the pyramid, parallel to the base:, ,square
,• A vertical plane that cuts through the base and two opposite lateral faces:, ,trapezoid
EXPLANATION
• A vertical plane that cuts through the top vertex, perpendicular to the base,: if we draw a rectangle perpendicular to the base that passes through the vertex,
Hence, the cross-sectional shape is a triangle.
• A horizontal plane, that cuts through the pyramid, parallel to the base:, if it is a plane parallel to the base, then it should have the same shape as the base,
Hence, the cross-sectional shape is a square.
• A vertical plane that cuts through the base and two opposite lateral faces:, again, we can draw this plane. The cross-sectional shape will have one pair of parallel sides and one pair of non-parallel sides,
Hence, the cross-sectional shape is a trapezoid.
The taxes on a house assessed at $71,000 are $1775 a year. If the assessment is raised to $114,000 and the tax rate did not change, how much would thetaxes be now?
Answers
Solution:
Given:
[tex]\begin{gathered} \text{House assessed at \$71,000} \\ \text{Tax paid in a year = \$1775} \end{gathered}[/tex]The tax rate paid for the year is;
[tex]\begin{gathered} r=\frac{1775}{71000}\times100 \\ r=2.5\text{ \%} \end{gathered}[/tex]If the assessment is now raised to $114,000 and the tax rate did not change, then the tax paid on the house will be;
[tex]\begin{gathered} \text{Tax}=2.5\text{ \% of \$114,000} \\ \text{Tax}=\frac{2.5}{100}\times114000 \\ \text{Tax}=\text{ \$2,850} \end{gathered}[/tex]Therefore, the tax paid on the house with an assessment of $114,000 is $2,850
Seniors at a high school are allowed to go off campus for lunch if they have a grade of A in all their classes or perfect attendance. An assistant principal in charge of academics knows that the probability of a randomly selected senior having A's in all their classes is 0.1. An assistant principal in charge of attendance knows that the probability of a randomly selected senior having perfect attendance is 0.16. The cafeteria staff know that the probability of a randomly selected senior being allowed to go off campus for lunch is 0.18. Use the addition rule of probability to find the probability that a randomly selected senior has all As and perfect attendance.
Answers
Given:
Probability a randomly selected senior has A = 0.1
Probability a randomly selected senior has a perfect attendance = 0.16
Probability a randomly selected senior is being allowed to go offf campus: P(A or B) = 0.18
Let's find the probability that a randomly selected senior has all As and a perfect attendance using addition rule for probability.
Apply the formula below:
P(A or B) = P(A) + P(B) - P(A and B)
Rewrite for P(A and B):
P(A and B) = P(A) + P(B) - P(A or B)
P(A and B) = 0.1 + 0.16 - 0.18
Therefore, the probability that a randomly selected senior has all As and perfect attendance is
In Millersburg, the use of landlines has been declining at a rate of 10% every year. If there are 42,000 landlines this year, how many will there be in 7 years?If necessary, round your answer to the nearest whole number.
Answers
To calculate how many landlines will be used in 7 years you have to apply the exponential decay
[tex]y=a(1-r)^x[/tex]Where
a is the initial value
r is the decay rate (this value is given as a percentage, you have to use it expressed as a decimal)
x is the time interval that has passed
We know that there are 42000 landlines this year
The declining rate is 10% → expressed as a decimal value r=0.1
The time-lapse is 7 years
[tex]\begin{gathered} y=42000(1-0.1)^7 \\ y=20088.47 \end{gathered}[/tex]In 7 years there will be 20088.47 landlines
nWhich graph shows the solution set of the compound inequality 1.5x-1 > 6.5 or 7X+3 <-25?-1010O-1050510-10-5510+-105010Mark this and returnSave and ExitNextSubmit
Answers
Solving the first inequality >>>
[tex]\begin{gathered} 1.5x-1>6.5 \\ 1.5x>6.5+1 \\ 1.5x>7.5 \\ x>5 \end{gathered}[/tex]Solving the second inequality >>>>
[tex]\begin{gathered} 7x+3<-25 \\ 7x<-25-3 \\ 7x<-28 \\ x<-\frac{28}{7} \\ x<-4 \end{gathered}[/tex]So, the solution set will be all numbers less than -4 and all numbers greater than 5.
We will have open circle at -4 and 5 and arrows to both sides.
From answer choices, second option is the right graph.
Can I Plss get help on this homework number 1
Answers
1.
given the equation
[tex]y=0.32x-20.53[/tex]where
x= number of times at bat
y=number of hits
y=? when x=175
then
[tex]y=0.32(175)-20.53[/tex][tex]y=56-20.53[/tex][tex]y=35.49[/tex]then
Correct answer is option A
A player who is at bat 175 times should expect 35 hits
Janelle alternates between running and walking. She begins by walking for a short period, and then runsfor the same amount of time. She takes a break before beginning to walk again. Consider the four graphsbelow. Which graph best represents the given situation?
Answers
the answer is letter C
letter C best represents a situation in which Janelle starts walking and then running.
We can know this by the slope of the lines.
Which of the following sets number could not represent the three sides of a right triangle
Answers
Given 4 sets of three sides of a triangle
We will find Which of the following sets of numbers could not represent the three sides of a right triangle
First, for any right triangle, the sum of the square of the legs is equal to the square of the hypotenuse
The hypotenuse is the longest side of the triangle
We will check the options:
a) { 11, 60, 61}
[tex]11^2+60^2=121+3600=3721=61^2[/tex]So, option a represent a right triangle
b) {46, 60, 75 }
[tex]46^2+60^2=2116+3600=5716\ne75^2[/tex]So, option (b) does not represent a right triangle
No need to check the other options
So, the answer will be {46, 60, 75}
Evaluate an exponential function that models a real world problem
Answers
Answer:
• Initial value: $26,000.
,• Value after 12 years: $1,319
Explanation:
The value of a car model that is t years old is given by the function:
[tex]v(t)=26,000(0.78)^t[/tex](a)The Initial Value
At the initial point of purchase, the value of t=0.
[tex]\begin{gathered} v(0)=26,000(0.78)^0 \\ =26000\times1 \\ =\$26,000 \end{gathered}[/tex]The initial value is $26,000.
(b)Value after 12 years
When t=12:
[tex]\begin{gathered} v(12)=26,000(0.78)^{12} \\ =1318.6 \\ =\$1,319 \end{gathered}[/tex]The value of the car after 12 years is $1,319 (correct to the nearest dollar).
DiaporamGiven the diagram below and the following statements. GliProve that mZHIW90".HEZGIW and ZHW are supplementaryReasonmZGIH+mZHIW-180°ReasonEnter the unknown statements and reasons to complete theflow chart proof. You can click the Organize button at anytime to have the tutor automatically organize the nodes inthe flow chart .StatementSubtraction Property ofConclusion
Answers
Step 1
Perpendicular lines are lines that meet at right-angles or 90°
Step 2
First statement: Definition of right angles
Second statement:
Refer to the table which summarizes the results of testing for a certain disease. A test subject is randomly selected and tested for the disease. What is the probability the subject has the disease given that the test result is negative. Round to three decimal places as needed.Positive Test ResultNegative Test ResultSubject has the disease879Subject does not have the disease27312
Answers
Answer: 0.021
First, we will find the total number of results by adding up all the subject results in the table:
[tex]87+9+27+312=435[/tex]Now, we know there are 435 total results. We are asked to find the probability that the subject has the disease given that the test result is negative.
Looking at the table, we can see that the number of subjects that has the disease despite having negative results is 9. We will then divide these results by the total number of subject results to find the probability being asked:
[tex]P=\frac{9}{435}=0.020689\approx0.021[/tex]With this, we know that the probability of the subject having the disease given the results is negative is 0.021.
Find all the roots of y = x4 + 7x3 + 25x2 - 11x – 150
Answers
Given the equation :
[tex]y=x^4+7x^3+25x^2-11x-150[/tex]to find the roots of he function , y = 0
so,
[tex]x^4+7x^3+25x^2-11x-150=0[/tex]the factors of 150 are;
1 x 150 , 2 x 75 , 3 x 50 , 5 x 30 ,
We will check which number give y = 0
so, when x = 1 , y = -128
When x = -1 , y = -120
when x = 2 , y = 0
So, x = 2 is one of the roots
so ( x - 2 ) is one of the factors of the given equation :
Make a long division to find the other roots:
so,
[tex]\frac{x^4+7x^3+25x^2-11x-150}{x-2}=x^3+9x^2+43x+75[/tex]See the following image:
Now , we will repeat the steps for the result
the factors of 75
1 x 75 , 3 x 25 , 5 x 5
We will check which number give y = 0
when x = 1 , y = 128
when x = -1 , y = 40
When x = 3 , y = 312
when x = -3 , y = 0
so, x = -3 is another root
So, ( x + 3 ) is one of the factors
so, make a long division again to find the other roots:
[tex]\frac{x^3+9x^2+43x+75}{x+3}=x^2+6x+25[/tex]See the following image :
Now the last function :
[tex]x^2+6x+25=0[/tex]a = 1 , b = 6 , c = 25
[tex]D=\sqrt[]{b^2-4\cdot a\cdot c}=\sqrt[]{36-4\cdot1\cdot25}=\sqrt[]{36-100}=\sqrt[]{-64}=i\sqrt[]{64}=\pm8i[/tex]which mean the last equation has no real roots
So,
the roots of the given equation is just two roots
So, the answer is the roots of the given eaution is x = 2 and x = -3
1. A taxi driver records the time required to complete various trips and the distance for each trip. time (minutes) The equation for the line of best fit is y=0.50x + 0.40. Which of the following statements BEST interprets the slope of the line of best file A. For every 0.50 minute increase in time, the distance increases by 1 mile. B. For every 1 minute increase in time, the distance increases by 0.50 miles. C. For every 0.54 ninute increase in time, the distance decreases by 1 mile. . D. For every 1 minute increase in time, the distance decreases by 0.50 miles.
Answers
Given
Equation
y = 0.5x + 0.4
Procedure
Slope = 0.5
Intercept = 0.4
B. For every 1 minute increase in time, the distance increases by 0.50 miles.
See attached question answer in in terms of log and a fraction
Answers
Given:
[tex]\int_4^{\infty}\frac{1}{x^2+x}\text{ dx}[/tex]To find:
the integral
[tex]\begin{gathered} First,\text{ we will re-write the expression} \\ \frac{1}{x^2+x}\text{ = }\frac{1}{x^2(1\text{ + }\frac{1}{x})} \\ \\ let\text{ u = 1 + 1/x} \\ u\text{ = 1 + x}^{-1} \\ \frac{du}{dx\text{ }}\text{ = 0 + \lparen-1}x^{-1-1})\text{ = -1x}^{-2} \end{gathered}[/tex][tex]\begin{gathered} \frac{du}{dx}\text{ = -x}^{-2} \\ \\ du\text{ = -x}^{-2}dx \\ du\text{ = }\frac{dx}{-x^2} \\ \\ \int_4^{\infty}\frac{1}{x^2+x\text{ }}dx\text{ = }\int_4^{\infty}\frac{1}{x^2(1\text{ +}\frac{1}{x})}dx \\ \\ Substitute\text{ for u and du in the expression:} \\ \int_4^{\infty}\frac{1}{x^2(u)}dx\text{ = }\int_4^{\infty}\frac{dx}{-x^2(u)}=\int_4^{\infty}-\frac{du}{u} \\ \end{gathered}[/tex][tex]\begin{gathered} -\int_4^{\infty}\frac{du}{u}=-\int_4^{\infty}ln\text{ u \lparen differentiation rule\rparen} \\ \\ \int_4^{\infty}ln(1+\frac{1}{x})=\int_4^{\infty}ln(\frac{x+1}{x})=\int_4^{\infty}ln(x+1)\text{ - ln\lparen x\rparen} \\ \\ -\int_4^{\infty}ln(1+\frac{1}{x})=-\int_4^{\infty}ln(x+1)\text{ - ln\lparen x\rparen = }\int_4^{\infty}ln(x)\text{ - ln\lparen x+1\rparen} \\ \\ -\int_4^{\infty}ln(1+\frac{1}{x})=\text{ \lbrack\lparen}\lim_{x\to\infty}(ln(x)\text{ - ln\lparen x+1\rparen\rbrack- \lbrack lnx - ln\lparen x+1\rparen\rbrack}_{x=4} \\ \\ -\int_4^{\infty}ln(1+\frac{1}{x})=\text{ \lbrack}\frac{x}{x+1}\text{\rbrack}_{\infty}\text{ - ln\lbrack}\frac{x}{x+1}]_4 \\ \\ -\int_4^{\infty}ln(1+\frac{1}{x})=0\text{ - ln\lbrack}\frac{4}{4+1}] \\ \\ -\int_4^{\infty}ln(1+\frac{1}{x})=\text{ -ln\lbrack}\frac{4}{5}] \end{gathered}[/tex][tex]-\int_4^{\infty}ln(1+\frac{1}{x})\text{ = ln\lparen}\frac{5}{4})[/tex]the fraction of 1 yard that is 4 inches is?
Answers
We need to remember
1 yard= 36 inches
x yard = 4 inches
x is the fraction of the yard that is 4 inches
[tex]x=\frac{4}{36}=\frac{1}{9}[/tex]1/9 of yard is 4 inches
A wildlife park manager is working on a request to expand the park. In a random selection during one week, 3 of every 5 cars have more than 3 people insideIf about 5,000 cars come to the park in a month, estimate how many cars that month would have more than 3 people inside.
Answers
Determine the ratio of cars that have more than 3 people.
[tex]\frac{3}{5}[/tex]Since in a month 5000 cars comes to park. Then cars with more than 3 people are,
[tex]\begin{gathered} \frac{3}{5}\cdot5000=3\cdot1000 \\ =3000 \end{gathered}[/tex]Answer: 3000
Trey has bought 10 pounds of dog food. He feeds his dog2/5pounds for each meal. For how many meals will the food last?Write your answer in simplest form
Answers
ANSWER
25 meals
EXPLANATION
Trey has 10 pounds of food to give to his dog. To know for how many meals the food will last we have to divide the total amount of food by the amount of food he gives the dog in each meal,
[tex]10\colon\frac{2}{5}[/tex]To divide this we can use the KCF rule:
• K,eep the first fraction. In this case the first number is a whole number, which we can think of as a fraction with denominator 1.
,• C,hange the division sign into a multiplication sign.
,• F,lip the second fraction.
[tex]10\colon\frac{2}{5}=10\times\frac{5}{2}[/tex]And to multiply we just multiply the numerators and the denominators,
[tex]10\times\frac{5}{2}=\frac{10\times5}{1\times2}=\frac{50}{2}[/tex]To write it in simplest form we have to simplify the fraction. Note that 50 is an even number, so it is divisible by 2. 50 divided by 2 is,
[tex]\frac{50}{2}=25[/tex]Hence, the food will last 25 meals
20. Damilola wrote the equation h = 2d + 1 to represent the height of hisplant, h, after a certain number of days. In this relationship, he identified has the dependent variable, and d as the independent variable. Do youagree? Why or why not?*
Answers
As we can see we have the next equation
[tex]h=2d+1[/tex]where h is the dependent variable and d is the independent variable
So we agree, because d does not depend on the height, but the height depends on the days
In order words
An independent variable is a variable that represents a quantity that is modified in an experiment. In this case d
A dependent variable represents a quantity whose value depends on how the independent variable is modified. In this case h
Determine if the side lengths could form a triangle. Use an inequality to justify your answer.16 m, 21 m, 39 m
Answers
We can draw the following triangle
the triangle inequality state that
[tex]|a-b|where | | is the absolute value. In our case, if we apply this inequality we obtain[tex]|21-39|which gives[tex]\begin{gathered} |-18|since 21m is between 18m and 60m, the values 16m, 21mn and 39m can form a triangle.All questions relate to the equation y=9 x^2-36 x+37Got it.1. Which way does the parabola open? Your answerYour answerYour answer2. What is the minimum value of y?Your answer3. What is the maximum value of y?Your answer5. What is the axis of symmetry?7. What is the y-intercept?Your answer8. Rewrite the equation in vertex form.
Answers
Given the parabola:
[tex]y=9x^2-36x+37[/tex]Part 1
To determine the way the parabola opens, we consider the coefficient of x².
• If the coefficient is positive, it opens downwards.
,• If the coefficient is negative, it opens upwards.
In this case, the coefficient of x²=9 (Positive).
The parabola opens downwards.
Part 2
The minimum value of the parabola occurs at the line of symmetry.
First, we find the equation of the line of symmetry.
[tex]\begin{gathered} x=-\frac{b}{2a};a=9,b=-36,c=37 \\ \therefore x=-\frac{(-36)}{2\times9} \\ x=2 \end{gathered}[/tex]Find the value of y when x=2.
[tex]\begin{gathered} y=9x^2-36x+37 \\ y=9(2)^2-36(2)+37 \\ =36-72+37 \\ Min\text{imum value of y=1} \end{gathered}[/tex]Part 3
Since the graph has a minimum value, the maximum value of y will be ∞.
Part 5
As obtained in part 2 above, the axis of symmetry is:
[tex]x=2[/tex]Part 6
The vertex is the coordinate of the minimum point.
At the minimum point, when x=2, y=1.
Therefore, the vertex is (2,1).
Part 7
The y-intercept is the value of y when x=0.
[tex]\begin{gathered} y=9x^2-36x+37 \\ y=9(0)^2-36(0)+37 \\ y=37 \end{gathered}[/tex]The y-intercept is 37.
Part 8
We rewrite the equation in Vertex form below:
[tex]\begin{gathered} y=9x^2-36x+37 \\ y-37=9x^2-36x \\ y-37+36=9(x^2-4x+4) \\ y-1=9(x-2)^2 \\ y=9(x-2)^2+1 \end{gathered}[/tex]Hey I need help on this math problem ignore the lines across the answer choices it’s a glitch I can’t change it and the lines don’t mean that the answer choice is wrong
Answers
Solution:
Given:
Two box plots for city A and city B.
A box plot with its representations is shown:
From the box plot given:
For City A :
[tex]\begin{gathered} City\text{ A:} \\ Q_3=78 \\ Q_1=76 \\ Interquartile\text{ range \lparen IQR\rparen}=Q_3-Q_1 \\ IQR=78-76 \\ IQR=2 \end{gathered}[/tex]For City B :
[tex]\begin{gathered} City\text{ B:} \\ Q_3=78 \\ Q_1=68 \\ Interquartile\text{ range \lparen IQR\rparen}=Q_3-Q_1 \\ IQR=78-68 \\ IQR=10 \end{gathered}[/tex]From the IQR calculated, the correct answer is:
The interquartile range for city B is greater.