In ΔABC shown below, ∠BAC is congruent to ∠BCA:
Triangle ABC, where angles A and C are congruent
Given: Base ∠BAC and ∠ACB are congruent.
Prove: ΔABC is an isosceles triangle.
When completed (fill in the blanks), the following paragraph proves that Line segment AB is congruent to Line segment BC making ΔABC an isosceles triangle.
Construct a perpendicular bisector from point B to Line segment AC.
Label the point of intersection between this perpendicular bisector and Line segment AC as point D:
m∠BDA and m∠BDC is 90° by the definition of a perpendicular bisector.
∠BDA is congruent to ∠BDC by the definition of congruent angles.
Line segment AD is congruent to Line segment DC of a perpendicular bisector.
ΔBAD is congruent to ΔBCD by_____1_______.
Line segment AB is congruent to Line segment BC because____2_____.
Consequently, ΔABC is isosceles by definition of an isosceles triangle.
Refer to the image attached.
Given: [tex]\angle BAC[/tex] and [tex]\angle ACB[/tex] are congruent.
To Prove: [tex]\Delta[/tex]ABC is an isosceles triangle.
Construction: Construct a perpendicular bisector from point B to Line segment AC.
Consider triangle BAD and BCD,
[tex]\angle BAC = \angle ACB[/tex] (given)
[tex]\angle BDA = \angle BDC = 90^\circ[/tex]
(By the definition of a perpendicular bisector)
[tex]AD=DC[/tex] (By the definition of a perpendicular bisector)
Therefore, [tex]\Delta ABD \cong \Delta BDC[/tex] by Angle Side Angle(ASA) Postulate.
Line segment AB is congruent to Line segment BC because corresponding parts of congruent triangles are congruent.(CPCTC)
Final answer:
By constructing a perpendicular bisector from B to AC in triangle ABC, we use the RHS Congruence rule and CPCTC to prove that AB is congruent to BC, thus showing that triangle ABC is isosceles.
Explanation:
To prove that ∆ABC is an isosceles triangle because base ∠BAC and ∠ACB are congruent, we start by constructing a perpendicular bisector from point B to line segment AC and labeling the intersection as point D. By definition, m∠BDA and m∠BDC are 90°, and ∠BDA is congruent to ∠BDC. Also, AD is congruent to DC because D is the midpoint of AC. Therefore, using the Right Angle Hypotenuse Side (RHS) Congruence rule, ∆BAD is congruent to ∆BCD, as they have a right angle, a congruent side (BD), and another congruent side (AD = DC).
Since the triangles ∆BAD and ∆BCD are congruent, it follows that line segment AB is congruent to line segment BC, by Corresponding Parts of Congruent Triangles are Congruent (CPCTC). Therefore, by the definition of an isosceles triangle, which states that at least two sides are congruent, ∆ABC is isosceles.
I need help solving these please help...
What is 3/5 as a decimal? answers:
a. 0.75
b. 0.3
c. 0.12
d. 0.15
How do you completely factor 2x^3 + 16y^3
The cost of seeing a weekday show is 2/3 the cost of a weekend show. in one month, andy spent $42.50 for 4 weekday shows and 3 weekend shows. find the price of a weekday show and the price of a weekend show
Answer:
x = weekday shows
y = weekend shows
x = 2/3y
4x + 3y = 42.50
4(2/3y) + 3y = 42.50
8/3y + 3y = 42.50
8/3y + 9/3y = 42.50
17/3y = 42.50
y = 42.50 * 3/17
y = 127.50/17
y = 7.50
x = 2/3y
x = 2/3(7.50)
x = 15/3
x = 5
so weekday shows (x) cost $ 5 and weekend shows (y) cost $ 7.50
Step-by-step explanation:
What's 44/8 as a mixed number
Subtract the following polynomials, then place the answer in the proper location on the grid. Write your answer in descending powers of x.
Subtract 2x^2 - 6x - 4
from 4x^2 - 4x + 3. ...?
The correct answer is: 2x^2+2x+7
What is the minimum number of colors required to color in the following map if no two adjacent regions can have the same color? In a complete sentence, explain how you got your answer
the principal will randomly choose 6 students from a large school to represent the school in a newspaper photograph. the probability that a chose student is an athlete is 30%. (assume that this doesn't change) What is the probability that 4 athletes are chosen? ...?
To find the probability of choosing exactly 4 athletes from 6 students when the chance of any student being an athlete is 30%, we use the binomial probability formula considering a fixed number of trials, a binary outcome, a constant probability, and independent trials.
Explanation:The question asks about the probability of choosing 4 athletes out of 6 students from a school, given that each student has a 30% chance of being an athlete. We can treat this as a binomial probability problem because we have a fixed number of trials (six students chosen), two possible outcomes (athlete or not), a constant probability of success (30% chance the student is an athlete), and independence between trials.
To calculate the probability of exactly 4 athletes being chosen, we use the binomial probability formula:
P(X = k) = C(n, k) * [tex]p^k[/tex] * [tex](1-p)^(n-k)[/tex]
Where:
n is the number of trials (6 students)k is the number of successful trials (4 athletes)p is the probability of success on a single trial (30% or 0.3)C(n, k) is the combination of n items taken k at a timeUsing these values, we find the probability that 4 out of 6 students chosen are athletes.
The point (-3,11) is a solution of which of the following systems?
y≥x-2
2x+y≤5
y>x+8
3x+y>2
y>-x+8
2x+3y≥7
y≤-3x+1
x-y≥-15
please help!! Choose the equation below that represents the line passing through the point (−5, 1) with a slope of 3/2
A: y − 5 = 3/2 (x + 1) B: y + 1 =3/2 (x − 5) C: y + 5 = 3/2 (x − 1) D: y − 1 = 3/2 (x + 5)
Pete wants to make turkey sandwiches for two friends and himself. He wants each sandwich to contain 3.5 ounces of turkey.how many ounces of Turkey does he need?
A population of 240 birds increases at a rate of 16% annually. Jemel writes an exponential function of the form f(x) = abx to represent the number of birds after x years. Which values should she use for a and b?
Answer:
[tex]\boxed{\boxed{a = 240, b = 1.16}}[/tex]
Step-by-step explanation:
General exponential function for growth or decay is,
[tex]y=a(1\pm r)^{x}[/tex]
Where,
a = initial value,
r = rate of change
+ is used for growth and - is used for decay.
As here, the number of birds increasing so, the exponential function is,
[tex]y=a(1+r)^{x}[/tex]
And initial value a = 240, r = rate of change = 16% = 0.16
Putting the values,
[tex]y=240(1+0.16)^{x}\\\\y=240(1.16)^{x}[/tex]
Comparing this with the given equation [tex]y=ab^{x}[/tex]
Hence, a = 240, b = 1.16
Answer:
The value of a is 240 and b is 1.16.
Step-by-step explanation:
Given,
The initial population of the birds = 240,
Annual rate of increasing = 16 %,
Hence, the population of birds after x years
[tex]P=240(1+\frac{16}{100})^x[/tex]
[tex]=240(1+0.16)^x[/tex]
[tex]=240(1.16)^x[/tex]
We can put P = f(x), ( because, f(x) also shows the population of birds after x years )
[tex]\implies f(x) = 240(1.16)^x[/tex] --------(1)
According to the question,
[tex]f(x) =ab^x[/tex] --------(2),
From equation (1) and (2),
a = 240 and b = 1.16
What is the value of the function y = 2x - 3 when x = –1?
A.
–5
B.
2
C.
–1
D.
3
Sandy walks 26 miles in a month. how many miles will she have walked in 2 years
Final answer:
Sandy walks 312 miles in a year, so over 2 years, she would walk 624 miles. As a reference point, a marathon runner with an average speed of 9.5 mi/h would take approximately 2.76 hours to run a 26.22 mi marathon.
Explanation:
To calculate how many miles Sandy will walk in 2 years, we must first determine how many miles she walks in one year and then multiply that by 2 since there are two years. Sandy walks 26 miles in a month. Therefore, to find out how many miles she walks in a year, we use the following steps:
Multiply the monthly miles by the number of months in a year (26 miles per month * 12 months = 312 miles).
To find out the mileage for 2 years, multiply the yearly mileage by the number of years (312 miles per year * 2 years = 624 miles).
Therefore, Sandy will have walked 624 miles in 2 years.
If a marathon runner averages 9.5 mi/h, the calculation to determine how long it takes him or her to run a 26.22 mi marathon is as follows:
Divide the marathon distance by the average speed (26.22 mi / 9.5 mi/h).
The result gives us approximately 2.76 hours, which is the time it takes to complete the marathon
16-2b=b+7
solve equation
Solve the following system of equations. Enter the y-coordinate of the solution. Round your answer to the nearest tenth.
5x+2y=21
-2x+6y=-34
...?
Answer:
The y-coordinate of the solution would be [tex]-\frac{64}{17}[/tex]
Step-by-step explanation:
Given system of equations,
5x+2y = 21 ----------(1)
-2x+6y = -34 ---------(2),
2 × Equation (1) + 5 × Equation (1),
We get,
4y + 30y = 42 - 170
34y = -128
[tex]\implies y = -\frac{128}{34}=-\frac{64}{17}[/tex]
A ballplayer catches a ball 3.0s after throwing it vertically upward. With what speed did he throw it, and what height did it reach?
Answer:
d=11, vo=15m/s
Step-by-step explanation:
use first and second kinematic equation, plug in T as 1.5 since that is when it reaches the top. G=-9.8 m/s^2, thats gravity or acceleration in this case.
A 5 ft woman is standing next to a tree. her shadow is 10 ft long the trees casts a shadow that is 116 ft long. how tall is the tree? worksheet
An explorer in the dense jungles of equatorial Africa leaves his hut. He takes 40 steps northeast, then 80 steps 60 degrees north of west, then 50 steps due south.Assume his steps all have equal length. Save him from becoming hopelessly lost in the jungle by giving him the displacement, calculated using the method of components, that will return him to his hut. ...?
Which set of points is not coplanar?
points A, B, E
points A, B, C, E
points B, C, D
points A, B, C, D
we know that
Coplanar points are three or more points which lie in the same plane. Remember that a plane is a flat surface which extends without end in all directions. Any three points in 3-dimensional space determine a plane.
case a) points A, B, E
Any group of three points determines a plane
so
The points A,B,E are coplanar
case b) points A, B,C,E
The four points do not belong to the same plane
so
The points A,B,C,E are not coplanar
case c) points B, C, D
Any group of three points determines a plane
so
The points B, C, D are coplanar
case d) points A,B, C, D
The base of the pyramid is a flat surface, the four points lie in the same plane
so
The points A,B, C, D are coplanar
therefore
the answer is the option
points A, B, C, E are not coplanar
Write an equation to solve the problem.
Two buses leave Houston at the same time and travel in opposite directions. One bus averages 55 mi/h and the other bus averages 45 mi/h. When will they be 400 mi apart? ...?
ok guys this is for connexus introduction to solving equations: practice
1. B, h=2A/b 2. C, v=h+5t^2/t 3. D, 23 4. D, -81 5. A, 17/7 6. D, 8 7. A, 4 hours 8. C, width is 4.5; length is 7.5 9. C, never true 10. B, sometimes true
-hope this helps you guys out :3 your welcome
Sydney is cutting the crust from the edges of her sandwich. The dimensions, in centimeters, of the sandwich is shown.
Which expression represents the total perimeter of her sandwich, and if x = 1.2, what is the approximate length of the crust?
Answer:
The answer is B. I looked at the picture of his problem. I just did the test.
I just knew the answer beforehand.
Step-by-step explanation:
Solve for x.
A triangle is drawn with a midsegment. The midsegment is labeled 4 x minus 1 and the side of the triangle that is parallel to the midsegment is labeled 30.
30
15
7.75
4 Solve for x.
A triangle is drawn with a midsegment. The midsegment is labeled 4 x minus 1 and the side of the triangle that is parallel to the midsegment is labeled 30.
30
15
7.75
4
Find angle A if mDE is equal to 53° and mBC is equal to 8°
if the difference in the side lengths of two squares is 10 and the sum of the side lengths is 18 what are the side lenghts
I'll upvote everything
Which expression represents "3 more than twice a number"?
3−2n3−2n
2n−32n−3
2n+32n+3
2+n+3
Write the following comparison as a ratio reduced to lowest terms.
10 nickels to 11 dimes
To find the simplified ratio of 10 nickels to 11 dimes, convert the counts into their monetary values, create a ratio, and reduce it. The end result is a simplified ratio of 5:11, as 10 nickels are worth 50 cents and 11 dimes are worth 110 cents.
The question asks for a ratio to be written and reduced to its lowest terms. This involves dividing both quantities by the same number until they cannot be divided further without resulting in a fraction. To write the comparison of 10 nickels to 11 dimes as a ratio reduced to lowest terms, we consider the value of each coin type. A nickel is worth 5 cents, and a dime is worth 10 cents. Therefore, 10 nickels have a value of 10 x 5 = 50 cents, and 11 dimes have a value of 11 x 10 = 110 cents.
Creating a ratio of these values, we get 50:110. Since both numbers are divisible by 10, we can simplify the ratio by dividing each side by 10, which gives us 5:11. This ratio is already in its simplest form, as 5 and 11 have no common divisor other than 1.
The simplified ratio of the value of 10 nickels to 11 dimes is 5:11.
You have 17 coins in pennies, nickels, and dimes in your pocket. The value of the coins is $0.47. There are four times the number of pennies as nickels. How many of each type of coin do you have? Set up the system and solve.
Final answer:
By setting up a system of equations and using the elimination method, we concluded that there are 12 pennies, 3 nickels, and 2 dimes to make up the 17 coins totaling $0.47.
Explanation:
The question asks us to determine how many pennies, nickels, and dimes we have, given that there are a total of 17 coins worth $0.47, with four times as many pennies as nickels. To solve this problem, we can set up a system of equations based on the information given.
Let p be the number of pennies, n be the number of nickels, and d be the number of dimes. Therefore, we have three equations:
p + n + d = 17 (total number of coins)
1p + 5n + 10d = 47 (total value of coins in cents)
p = 4n (four times as many pennies as nickels)
Substituting the third equation into the first and second equations, we get:
4n + n + d = 17
4n + 5n + 10d = 47
Simplify the equations:
5n + d = 17
9n + 10d = 47
Now, we solve this system of equations using substitution or elimination. Let's use the elimination method:
Multiply the first equation by 10 so that when subtracted from the second equation, the d variable will be eliminated: 50n + 10d = 170
Now subtract this from the second equation: (9n + 10d) - (50n + 10d) = 47 - 170
This results in -41n = -123, and after dividing both sides by -41, we get n = 3
Substitute n = 3 into the first simplified equation: 5(3) + d = 17, resulting in d = 17 - 15, so d = 2
Substitute n = 3 into the original third equation to find the number of pennies: p = 4(3), so p = 12
Therefore, we have 12 pennies, 3 nickels, and 2 dimes.
Write 0.4375 as a fraction in simplest form.
Answer: 7/16
Step-by-step explanation:
because if you do long division your answer is
16 ) 7.0000 ( 0.4375
-64
60
-48
120
-112
80
-80
0
wich is is = 0.4375