It will take 16hr 30min for Mrs. Smith to catch up.
To find how many hours will it take Mrs smith to catch up:Let,
t + 3 = Time of Mr. Smith
t = Time of Mrs. Smith
v1 = 55 mph the speed of Mr. Smith
v2 = 65 mph the speed of Mrs. Smith
Formula: Distance = speed × time
v1 ( t + 3) = v2t
55 ( t + 3 ) = 65t
65t = 55t + 165
65t - 55t = 165
10t = 165
t = 16.5 hr
t = 16 hr 0.5 × 60 min
t = 16 hr 30 min
Therefore, it will take 16hr 30min for Mrs. Smith to catch up.
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A recent article claims that the state of Illinois has low tuition rates for its colleges and universities. Cate decides to research the cost of tuition for different colleges in Illinois. The average tuition in Illinois is $28,950 with a standard deviation of $3,470. Which type of inference test should Cate use
One sample Z Test is used by cate.
According to the statement
The average tuition in Illinois is $28,950 with a standard deviation of $3,470.
Assuming we have a large enough sample, since we are testing one group's mean relative to a hypothesized value, this would be a one-sample z-test.
So, One sample Z Test is used by cate.
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Using that income equation, after how many years will the income be $300? Round your answer correct UP TO TWO (2) decimal digits.
The number of years based on the equation is 24 years.
How to illustrate the information?The information is incomplete. An overview will be given. Let the income equation be represented as I = 60 + 10x where x represents the years taken.
Therefore i = 60 + 10x
60 + 10x = 300
10x = 300 - 60
10x = 240
x = 240/10
x = 24
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What's the explicit rule for the sequence 3, -6, 12, -24, 48, ...?
Answer:
[tex]a_{n}[/tex] = 3 [tex](-2)^{n-1}[/tex]
Step-by-step explanation:
there is a common ratio between consecutive terms , that is
- 6 ÷ 3 = 12 ÷ - 6 = - 24 ÷ 12 = 48 ÷ - 24 = - 2
this indicates the sequence is arithmetic with explicit rule
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 3 and r = - 2 , then
[tex]a_{n}[/tex] = 3 [tex](-2)^{n-1}[/tex]
Answer:
[tex]\sf \dfrac{-3}{2}(-2)^n[/tex]
Step-by-step explanation:
Explicit formulas are used to represent all the terms of the geometric sequence with a single formula.
[tex]\sf \boxed{\bf t_n = ar^{n-1}}[/tex]
a is the first term.
r is the common ratio.
r = second term ÷ first term.
3 , - 6 , 12, - 24, 48 ,........
a = 3
r = -6 ÷ 3 = -2
[tex]\sf t_n = 3*(-2)^{(n-1)}\\\\[/tex]
[tex]\sf = 3*(-2)^{n}*(-2)^{-1}\\\\ =3*(-2)^n*\dfrac{-1}{2}\\\\= \dfrac{-3}{2}(-2)^n[/tex]
Check:
[tex]\sf t_1 =\dfrac{-3}{2}*(-2)^1=\dfrac{-3}{2}*(-2) = 3\\\\\\t-2 = \dfrac{-3}{2}*(-2)^2 = \dfrac{-3}{2}*4=-6\\\\\\t_3=\dfrac{-3}{2}*(-2)^3=\dfrac{-3}{2}*(-8)=12[/tex]
If A, B, C, and D, are the only possible outcomes of an experiment, find the probability of D using the table below. . Group of answer choices 1/4 3/7 4/7 1/7
Using it's concept, the probability of D is 4/7.
What is a probability?
A probability is given by the number of desired outcomes divided by the number of total outcomes.
Researching this problem on the internet, A, B and C all have a probability of 1/7. The sum of all probabilities is of 1 = 100%, hence:
[tex]3 \times \frac{1}{7} + P(D) = 1[/tex]
[tex]P(D) = 1 - \frac{3}{7}[/tex]
[tex]P(D) = \frac{4}{7}[/tex]
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The average daily maximum temperature in Syracuse is 21.85°C, and the average daily minimum temperature is -4.7°C. The average daily maximum temperature is
°C higher than the average daily minimum temperature.
By applying the definition of difference, we find that the average daily maximum temperature in Syracuse is 26.55 °C higher than the average daily minimum temperature.
What is the difference between the average daily maximum temperature and the average daily minimum temperature?
Herein we must find the difference bewteen the two temperatures, defined as the subtraction of the minimum temperature from the maximum temperature:
x = 21.85 °C - (- 4.7 °C)
x = 26.55 °C
By applying the definition of difference, we find that the average daily maximum temperature in Syracuse is 26.55 °C higher than the average daily minimum temperature.
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Jina needs to solve a problem that involves using a different type of units for angle measure. The problem given to her to calculate 6/5 * 240
The value of the expression 6/5 * 240 is 288
How to calculate the expression?The expression is given as:
6/5 * 240
Divide 240 by 5
6 * 48
Multiply 6 and 48
288
Hence, the value of the expression 6/5 * 240 is 288
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Solve for m.
[tex] \frac{5}{4 - m} = \frac{ - 3}{m + 2}[/tex]
A. [tex] - \frac{11}{3} [/tex]
B. [tex] - 11[/tex]
C. [tex] - \frac{7}{3} [/tex]
D. [tex] - 3[/tex]
Hello,
[tex] \frac{5}{4 - m} = \frac{ - 3}{2 + m} [/tex]
[tex]5(2 + m) = - 3(4 - m)[/tex]
[tex]10 + 5m = - 12 + 3m[/tex]
[tex]5m - 3m = - 12 - 10[/tex]
[tex]2m = - 22[/tex]
[tex]m = \frac{ - 22}{2} [/tex]
[tex]m = - 11[/tex]
→ Answer B
Variable m cannot be equal to any of the values −2,4 as division by zero is undefined. Multiply both sides of the equation by (m − 4)(m + 2), the lowest common denominator of 4−m,m + 2.
−(2 + m) ×5 = (m −4 )( −3 )To find the opposite of 2+m, find the opposite of each term.
(−2 −m) ×5 = ( m−4 )( −3 )Use the distributive property to multiply −2−m by 5.
−10 −5m = ( m−4 )( −3 )Use the distributive property to multiply m−4 by −3.
−10 −5m =−3m + 12Add 3m to both sides.
−10 − 5m + 3m =12Combine −5m and 3m to get −2m.
−10 −2m = 12Add 10 to both sides.
−2m = 12 + 10Add 12 and 10 to get 2.
−2m = 22Divide both sides by −2.
m = 22 / -2Divide 22 by −2 to get −11.
m = −11Therefore, the correct option is "B".
Matt's family traveled 3/8 of the distance to his grandmother’s house on Saturday. They traveled 3/5 of the remaining distance on Sunday. What fraction of the total distance to his grandmother’s house was traveled on Sunday?
Answer:
3/8
Step-by-step explanation:
Let's use a sample number of 100 miles
If 3/8 was traveled the first day, then 37.5m were traveled on the first day.
Now on Sunday, there are 62.5m remaining in the trip. They travel 3/5 of that, meaning they went 62.5 * 3/5m. This turns out to be 37.5 miles that were traveled on Sunday.
37.5/100 = 3.8
PLEASE HELP IM STUCK
Step-by-step explanation:
we have
2y = 4x - 9
and we want it to look like
...x + ...y = -9
simple.
the y term is already on the left side. we need to move the x term to the same side.
what do we do ? we subtract the term we want to get rid of on one side from both sides (we always have to do changes in both sides of the equation, or we change the whole meaning of the equation).
2y = 4x - 9 | -4x on both sides
-4x + 2y = -9
and we are finished. that's it.
Answer:
-4x + 2y = -9
Step-by-step explanation:
Pre-Solving InformationWe are given the equation 2y=4x-9, and we want to convert it into standard form.
Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0.
SolvingNotice how in standard form, x and y are on the same side. Currently, x and y are on different sides.
Therefore, we first need to get x and y on the same side.
We can do this by subtracting 4x from both sides.
2y = 4x - 9
-4x -4x
_____________
-4x + 2y = -9
As indicated by the -9 on the left side, we have solved the question, and are now done.
Hence, the answer is -4x + 2y = -9.
Total area=
Help me please thanks so much
The total area of the regular pentagon prism is 485 square units
How to determine the surface area?The given parameters are:
Base area = 50
Height = 11
Base = 7
Start by calculating the total area of the 5 sides using
Sides = n * Height * Base
Sides = 5 * 11 * 7
Sides = 385
The total surface area is
Total = 2 * Base area + Sides
This gives
Total = 2 * 50 + 385
Evaluate
Total = 485
Hence, the total area of the regular pentagon prism is 485 square units
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If a = √3-√11 and b = 1 /a, then find a² - b²
If [tex]b=\frac1a[/tex], then by rationalizing the denominator we can rewrite
[tex]b = \dfrac1{\sqrt3-\sqrt{11}} \times \dfrac{\sqrt3+\sqrt{11}}{\sqrt3+\sqrt{11}} = \dfrac{\sqrt3+\sqrt{11}}{\left(\sqrt3\right)^2-\left(\sqrt{11}\right)^2} = -\dfrac{\sqrt3+\sqrt{11}}8[/tex]
Now,
[tex]a^2 - b^2 = (a-b) (a+b)[/tex]
and
[tex]a - b = \sqrt3 - \sqrt{11} + \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{9\sqrt3 - 7\sqrt{11}}8[/tex]
[tex]a + b = \sqrt3 - \sqrt{11} - \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{7\sqrt3 - 9\sqrt{11}}8[/tex]
[tex]\implies a^2 - b^2 = \dfrac{\left(9\sqrt3 - 7\sqrt{11}\right) \left(7\sqrt3 - 9\sqrt{11}\right)}{64} = \boxed{\dfrac{441 - 65\sqrt{33}}{32}}[/tex]
What is the equation of the line described below written in slope-iWhat is the equation of the line described below written in slope-intercept form?
the line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0
The equation of a line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0 is y = -1/2x + 1
Equation of a lineA line is the shortest distance between two points. The equation of a line in point-slope form and perpendicular to a line is given as;
y - y1 = -1/m(x-x1)
where
m is the slope
(x1, y1) is the intercept
Given the following
Point = (4, -1)
Line: 2x-y - 7 = 0
Determine the slope
-y = -2x + 7
y= 2x - 7
Slope = 2
Substitute
y+1 = -1/2(x -4)
Write in slope-intercept form
2(y + 1) = -(x - 4)
2y+2 = -x + 4
2y = -x + 2
y = -1/2 + 1
Hence the equation of a line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0 is y = -1/2x + 1
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Answer:
y = - (1/2) x + 1
what does -16t^2 mean in h(t)=5+100t-16t^2
-16t^2 represent the position on the graph on the negative side.
According to the statement
we have given equation is h(t)=5+100t-16t^2 -(1)
And we have to find representation of -16t^2
we know that the equation number (1) represent the Quadratic Equation
And in this we have to solve the Quadratic Equation and find the representation of the given terms. then
h(t)=5+100t-16t^2
5+100t-16t^2 = 0
16t^2 -100t-5 = 0
In this equation 16t^2 represent the equation on the graph.
It means that it shows the position on the graph.
Overall, -16t^2 represent the position on the graph on the negative side.
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Use the drawing tool(s) to form the correct answer on the provided number line. Consider the given functions. Function 1 Function 2 Graph shows a polynomial function plotted on a coordinate plane with vertical axis g of x. A curve enters quadrant 3 at (minus 5, minus 40), goes through (minus 4, 0), (minus 2, 32), (0, 15), (2, 0), and exits quadrant 1 at (4, 30). Represent the interval where both functions are decreasing on the number line provided.
Both functions decrease at (-1, 2)
How to determine the decreasing intervals of the function?The complete question is added as an attachment
The polynomial function f(x) is represented by the graph.
From the graph, the polynomial function decreases at (-2, 2)
The absolute function is given as;
f(x) = =5|x + 1| + 10
The vertex of the above function is
Vertex = (-1, 10)
Because a is negative (a= -5), the vertex is a maximum.
This means that the function decreases at (-1, ∞)
So, we have
(-2, 2) and (-1, ∞)
Combine both intervals
(-1, 2)
This means that both functions decrease at (-1, 2)
See attachment 2 for the number line that represents the interval where both functions are decreasing
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please help with question!!
A. 6x²-2x+5, is the quotient of the polynomial.
The coordinates of three vertices of a rectangle are (3,7), (-3,5), and (0,-4). What are the coordinates of the fourth vertex
The coordinates of the fourth vertex are (6, -2)
What are the coordinates of the fourth vertex?The coordinates of three vertices of a rectangle are given as: (3,7), (-3,5), and (0,-4).
Calculate the slope of the first two coordinates using
m = (y2 - y1)/(x2 - x1)^2
Substitute the known values in the above equation
d = (7 - 5)/(3 + 3)
Let the fourth coordinate be (x, y)
Calculate the slope of the other two coordinates using
m = (y2 - y1)/(x2 - x1)^2
Substitute the known values in the above equation
m = (y + 4)/x
Equate both slope equations
(y + 4)/x = (7 - 5)/(3 + 3)
Simplify the fraction
(y + 4)/x = 1/3
Cross multiply
x = 3y + 12
Let y = -2
So, we have:
x = 3 *-2 + 12
Evaluate
x = 6
Substitute x = 6 and y = -2 in (x, y)
This gives (6, -2)
Hence, the coordinates of the fourth vertex are (6, -2)
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What is the value of the expression below when w= 5 and x =9
The value of the expression 9w + 5x when w= 5 and x =9 is 90
Algebraic expression9w + 5x
When
w = 5 and x = 9
9w + 5x
= 9(5) + 5(9)
= 45 + 45
= 90
Complete question:
What is the value of the expression below when w = 5 and x = 9? 9w + 5x
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What can you say about the continuous function that generated the following table of values?
table
x y
0.125 -3
0.5 -1
2 1
8 3
64 6
A.not enough information to answer the question
B. the function has more than one x-intercept
C.the function has exactly one x-intercept
D.the function has no x-intercept
Option C. The function that has the table here has exactly one x-intercept.
How to find the interceptAs the signs of the functions are changing, we can see that there is a crossing to the x axis.
This tells us that the zero value that we see is the x intercept and there is no other x intercept in the question.
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Identify the property being demonstrated for each expression.
3+ (5 + 7) = (3+5)+7
(3)[5(7)] = (3)[7(5)]
Intro
5+0=5
Dor
what are the more approprite measures of center and spread for this data set? select two choices: one for the center and one for the spread. please help asap!!
Based on the data set, B. Better measure of center: median. C. Better measure of spread: interquartile range (IQR).
What measures of center and spread are best?The measure of center should be the median because the mean will be affected by the outliers on the left side.
The IQR will be the best measure of spread because the standard deviation is also affected by the outliers.
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Find the missing side. Round your answer to the nearest tenth.
Answer:
x = 19.1
Step-by-step explanation:
Because this is a right triangle, we can use trigonometry.
Thus, we must use either sine (opposite / hypotenuse), cosine (adjacent / hypotenuse), or tangent (opposite / adjacent).
If we use 33 as the reference angle, the side measuring 16 is the adjacent side and x is the hypotenuse.
Thus, we can use cosine:
[tex]cos 33=\frac{16}{x} \\x*cos33=16\\x=19.0778=19.1[/tex]
Alejandro wants to determine the average shoe size of all of the male students in his school. Which sample is likely to yield the most biased results?.
The sample that is likely to yield the most biased results is; B) every member of the boys’ basketball team
How to identify a bias in sampling?The sample that is likely to yield the most biased results is; B) every member of the boys’ basketball team.
The reason option B is the most biased is because members of a basketball team are typically taller than other people. We know that taller people generally have larger feet, and larger shoe sizes, than shorter people. Thus, choosing only people from this area would lead to a biased sample.
The missing options are;
A) every tenth boy on the school’s phone list
B) every member of the boys’ basketball team
C) every boy in a randomly selected ninth-, tenth-, eleventh-, and twelfth-grade gym class
D) every fifth boy who walks through the front doors of the school in the morning
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Answer:
B)
Step-by-step explanation:
ANSWER THIS QUESTION FIRST=BRANIEST
Answer:
18
Step-by-step explanation:
first we divide both parties by 5 making it so that 1/6 =3 and then we multiply by 6 to make it 6/6 = 18
The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). Which graph represents g(x)? On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10). On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8). On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10). On a coordinate plane, a parabola opens up. It goes through (negative 8, 8), has a vertex at (negative 5, negative 11), and goes through (negative 2, 8). Mark this and return
The quadratic function g(x) = (x - 5)² + 1 passes through the points (2, 10) and (8, 10) and has a vertex at (5, 1).
How to analyze quadratic equations
In this question we have a graph of a quadratic equation translated to another place of a Cartesian plane, whose form coincides with the vertex form of the equation of the parabola, whose form is:
g(x) = C · (x - h)² - k (1)
Where:
(h, k) - Vertex coordinatesC - Vertex constantBy direct comparison we notice that (h, k) = (5, 1) and C = 1. Now we proceed to check if the points (x, y) = (2, 10) and (x, y) = (8, 10) belong to the parabola.
x = 2
g(2) = (2 - 5)² + 1
g(2) = 10
x = 8
g(8) = (8 - 5)² + 1
g(8) = 10
The quadratic function g(x) = (x - 5)² + 1 passes through the points (2, 10) and (8, 10) and has a vertex at (5, 1).
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Answer: B
Step-by-step explanation:
looked at the points from the dude above, or below, anyway i hope this helps
x: -1/2
-6(x-2):
por favor necesito una respuesta
The value of the expression if x = -1/2 is 15
Function and valuesGiven the expression below shown;
f(x) = -6(x - 2)
If the value of x is -1/2, hence;
f(-1/2) = -6(-1/2 - 2)
Simplify
f(-1/2) = -6(-5/2)
f(-1/2) = 6 * 5/2
f(-1/2) = 3 * 5 = 15
Hence the value of the expression if x = -1/2 is 15
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The line l cuts the y-axis at (0, 5). l also passes through the point (2, 1). find the equation of the line which is parallel to l and which passes through the point (3, 0).
Answer: [tex]y=-2x+6[/tex]
Step-by-step explanation:
The slope of line l is
[tex]\frac{5-1}{0-2}=-2[/tex]
Since parallel lines have the same slope, the slope of the line we need to find is -2.
Substituting into point-slope form,
[tex]y=-2(x-3)\\\\y=-2x+6[/tex]
Twenty new members are elected to an agency every two years. The agency has 100 members on average overall. How long does a member hold his/her position at the agency
The time that a member hold his/her position at the agency is approximately 0.1 year.
Given that twenty members are elected to an agency every two years and there are 100 members on a average overall.
We have to find the time that a member hold his position at the agency.
To calculate the time we have to use multiplication which means product of two numbers.
In 2 years agency elected 20 members. It shows like under:
2 years=20 members
We require 100 members at one end so we will multiply by 5 both sides.
10 years=100 members
Now take 100 to left side of equal to sign.
10/100=1 member
1 member=1/10
=0.1
Hence a member holds 0.1 year at the agency.
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Tests show that the hydrogen ion concentration of a sample of apple juice is 0.0003 and that of ammonia is . find the approximate ph of each liquid using the formula , where is the hydrogen ion concentration.
The pH value of the apple juice is 3.5, is the correct answer.
The pH value of the ammonia is 8.9, is the correct answer.
The question seems to be incomplete and complete question is shown below
Tests show that the hydrogen ion concentration of a sample of apple juice is 0.0003 and that of ammonia is 1.3 x 10-9. Find the approximate pH of each liquid using the formula pH = -log (H+), where (H+) is the hydrogen ion concentration The pH value of the apple juice is___ The pH value of ammonia is____
1.pH of apple juice
A. 8.11
B. 1.75
C. 3.5
D. 2.1
2. pH of ammonia
A. 1.1
B. 7.0
C. 5.4
D. 8.9
The pH of a solution is defined as the logarithm of the reciprocal of the hydrogen ion concentration [H+] of the given solution.
From the formula;
pH = -log[ H⁺ ]
Given the data in the question.
For the Apple juice
hydrogen ion concentration H⁺ = 0.0003
pH of the apple juice pH = ?
pH = -log[ H⁺ ]
pH = -log[ 0.0003 ]
pH = 3.5
The pH value of the apple juice is 3.5
For the ammonia
hydrogen ion concentration H⁺ = 1.3 × 10⁻⁹
pH of the ammonia pH = ?
pH = -log[ H⁺ ]
pH = -log[ 1.3 × 10⁻⁹]
pH = 8.9
The pH value of the ammonia is 8.9
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13.222.. - 1.3222.. = ??
Answer:
Answer
Answer in decimal
11.8998
Can someone help me out on these geometry questions? ASAP!!!
Write formal proofs the LL Theorm.
Question 6
1) [tex]\overline{AB} \cong \overline{BD}[/tex], [tex]\overline{CD} \perp \overline{BD}[/tex], O is the midpoint of [tex]\overline{BD}[/tex], [tex]\overline{AB} \cong \overline{CD}[/tex] (given)
2) [tex]\angle ABO, \angle ODC[/tex] are right angles (perpendicular lines form right angles)
3) [tex]\triangle ABO, \triangle CDO[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\overline{BO} \cong \overline{OD}[/tex] (a midpoint splits a segment into two congruent parts)
5) [tex]\triangle ABO \cong \triangle CDO[/tex] (LL)
Question 7
1) [tex]\angle ADC, \angle BDC[/tex] are right angles), [tex]\overline{AD} \cong \overline{BD}[/tex]
2) [tex]\overline{CD} \cong \overline{CD}[/tex] (reflexive property)
3) [tex]\triangle CDA, \triangle CDB[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\triangle ADC \cong \triangle BDC[/tex] (LL)
5) [tex]\overline{AC} \cong \overline{BC}[/tex] (CPCTC)
Question 8
1) [tex]\overline{CD} \perp \overline{AB}[/tex], point D bisects [tex]\overline{AB}[/tex] (given)
2) [tex]\angle CDA, \angle CDB[/tex] are right angles (perpendicular lines form right angles)
3) [tex]\triangle CDA, \triangle CDB[/tex] are right triangles (a triangle with a right angle is a right triangle)
4) [tex]\overline{AD} \cong \overline{DB}[/tex] (definition of a bisector)
5) [tex]\overline{CD} \cong \overline{CD}[/tex] (reflexive property)
6) [tex]\triangle ADC \cong \triangle BDC[/tex] (LL)
7) [tex]\angle ACD \cong \angle BCD[/tex] (CPCTC)