Given: ∠P ≅ ∠Q and Line Segment RS bisects ∠PQR. Prove: Line segments PR≅QR . Supply the missing statement in Statement 5 of the proof of the the Converse of the Isosceles Triangle Theorem.
Begin with isosceles ∆PRQ with ∠P ≅ ∠Q. Construct Line Segment RS a bisector of ∠PRQ.
A. ∆PRS ≅ ∆PRQ
B. ∆PRS ≅ ∆PRS
C. ∆PRS ≅ ∆SRQ
D. ∆PRS ≅ ∆QRS
Answer:
D
Step-by-step explanation:
Vertices P and Q correspond, vertices R and S correspond to themselves.
By the property of (Angle-Angle-Side)AAS postulates ΔPRS≅QRS
Option (D) is correct.
It is required to find the missing statement in Statement 5 of the proof.
What is congruence in Triangle?Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
Given that:
∠P ≅ ∠Q and Line Segment RS bisects ∠PQR.
In ΔPRS≅QRS ,
∠P≅∠Q (Given)
∠PRS≅∠QRS (Definition of angle bisector)
RS≅RS (reflexive property of congruence)
so,ΔPRS≅QRS (By AAS congruence)
Therefore, by the property of (Angle-Angle-Side)AAS postulates ΔPRS≅QRS
Learn more about the congruence in triangle here:
https://brainly.com/question/27085416
#SPJ5
Your teacher asks the class to evaluate the expression (3³)¹. Your classmate gives an incorrect answer of 81. Evaluate the expression. Then find the likely error. **PLEASE FIND THE ERROR I DON'T NEED THE ANSWER I KNOW ITS 27**
Answer:
see explanation
Step-by-step explanation:
The most likely error is adding the exponents instead of multiplying them, that is
[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex] , then [tex](3^{3}) ^{1}[/tex] = [tex]3^{3(1)}[/tex] = 3³ = 27
However
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] ← the student may have used this definition to obtain 81
Is (-1,2) a solution to the following system of equations? Show and explain why or why not.
f(x)=x^2+3x+4
g(x)=2x+4
Answer:
It is a solution.
Step-by-step explanation:
Plug in (-1,2) to both equations:
Plug in -1 to see if 2 comes out:
f(x)=x^2+3x+4
y=(-1)^2+3(-1)+4
y=1-3+4
y=-2+4
y=2
(yes it works)
g(x)=2x+4
y=2(-1)+4
y=-2+4
y=2
(yes it works)
6+8x/2=5x solve for X
In a class, the ratio of the boys to the girls is 5:3. There are 15 girls in the class
8. Which of the following equation represents the ratio of the number of boys to the number of girls in the class?
A.5/3=×/15
B.5/3=15/×
C.5/15=3/×
D.3/5=×/15
9. How many boys are there in the class?
A. 10 boys
C. 20 boys
B. 15 boys
D. 25 boys
10. How many students are there in the class?
A. 30 students
C. 40 students
B. 35 students
D. 45 students
Answer:
ratio of girls to boy :5:3
Step-by-step explanation:
=5 x /8 x 100
x cancels x
The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT dt equals negative k times the quantity T minus A, where T is the temperature of the coffee, A is the room temperature, and k is a positive constant. If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25°C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes.
74
67
60
42
Answer:
(b) 67
Step-by-step explanation:
A solution to the differential equation describing the temperature according to Newton's Law of Cooling could be written as ...
T = (final temp) + (initial difference)×(decay factor)^t
where the decay factor is the fraction of change during 1 unit of time period t.
__
Here, the initial difference of 100-25 = 75 degrees decays to 90-25 = 65 degrees in 1 minute. So, the units of t are minutes, the decay factor is 65/75, the initial difference is 75 degrees, and the final temperature is 25 degrees. That lets us write the equation as ...
T = 25 +75(65/75)^t
Then for t=4, the temperature is ...
T = 25 +75(13/15)^4 ≈ 67.3 . . . . degrees
After 4 minutes the temperature of the coffee is about 67 degrees.
f(x) = 1?-1.9(x) = x - 2. Find
(a) ( + g)(3)
Answer: f(x)=1-1.9x=x-2
Step-by-step explanation:
Big brain time.
Question 15
7 pts
During a clothing store's Bargain Days, the regular price for T-shirts is discounted by $6. There is a state sales tax of 5%, and the $6 discount is applied before the
sales tax is calculated. A). Write an expression that shows the regular price r of a T-shirt minus the $6 discount. B). Write a rule for the function p(r) that expresses the
final price p of a T-shirt with the discount applied and sales tax added. C). How much would you pay during Bargain Days for a shirt regularly priced at $20.00?
Answer:
A) The expression that shows the regular price minus the discount is r - 6
B) The function is p(r) = 1.05r - 6.3
C) You would pay $14.7 during Bargain Days
Step-by-step explanation:
∵ The regular price is r
∵ The discount on it is 6%
∴ The price after the discount = r - 6
A) The expression that shows the regular price minus the discount is
r - 6
∵ The state sales tax is 5% applied after the discount
∴ The sales tax = 5%(r - 6)
→ Change 5% to decimal y dividing it by 100
∵ 5% = [tex]\frac{5}{100}[/tex] = 0.05
∴ The sales tax = 0.05(r - 6) = 0.05(r) - 0.05(6)
∴ The sales tax = 0.05r - 0.3
∵ p is the price of the T-shirt with discount and sales tax
→ Add the sales tax to the regular price minus the discount
∴ p(r) = r - 6 + 0.05r - 0.3
→ Add the like terms
∴ p(r) = (r + 0.05r) + (-6 - 0.3)
∴ p(r) = 1.05r + (-6.3)
∴ p(r) = 1.05r - 6.3
B) The function is p(r) = 1.05r - 6.3
∵ The regular price of a shirt is $20
→ Substitute r by 20 in the function above to find how much you would
pay during the Bargain Days
∴ p(20) = 1.05(20) - 6.3
∴ p(20) = 21 - 6.3
∴ p(20) = $14.7
C) You would pay $14.7 during Bargain Days
What is nineteen minus twelve divided by six
19 - 12 / 6
Answer:
17
Step-by-step explanation:
Using PEMDAS you divide first and get 2
19-2
then you get 17 as your final answer
solve the equation for x 5x squared - 4x = 6
26. Which integers are greater than -3 and
less than 0
QUICK PLS
A circle with the center C (4, -2) contains the point D (8,1). What is the equation of the line perpendicular to the radius of the circle passing through point C?
Answer:
y = -4x/3 + 10/3
Step-by-step explanation:
We find the slope of CD and get (-2 - 1)/(4 - 8) = -3/-4 = 3/4
The slope of a perpendicular line is the opposite reciprocal of the slope of the line it's perpendicular to, so we get a slope of -4/3.
We can use point-slope form and get (using point C):
y - (-2) = (-4/3)(x - 4) -->
y + 2 = -4x/3 + 16/3 -->
y = -4x/3 + 10/3
**NOTE** I can't see the picture (because of a problem on my computer) so if there is any info given there that isn't given in the text, then my answer will be incorrect.
Plot the point (3, - 2 .
Darren and Jovanne are ata restaurant for dinner. They can choose their meal from three different cuisines Mexican (M). Greek (G) and American
A)
Which organized list represents all possible outcomes for Darren and Jovanne's dinner choices using the format of
(Darren's choice, Jovanne's choice)?
O (M,G),(M,A),(MM),(G,G),(G,A),(G,M),(A,G),(A,A),(A, M)
O (MG). (M,A),(G,A),(G,M),(A,G),(A,M)
O (M,G,A). (M,A,G),(G, M,A),(G, A, M). (A,G,M). (A,M,G)
O (MM). (G,G). (AA)
The sample space for their trial is given by:
(M,G),(M,A),(M,M),(G,G),(G,A),(G,M),(A,G),(A,A),(A, M).
What is the sample space of an experiment?The sample space is the set that contains all possible outcomes for an experiment.
In this problem, for each of the two people, there are three outcomes, hence the cardinality of the sample space is given by:
C = 2³ = 8.
Considering both can choose the same food, and each outcome has two options(Darren's and Jovanne's), the first option is correct.
More can be learned about sample space at https://brainly.com/question/15006554
8.)
To buy your Halloween costume, you borrowed $15.00 from your mom. Then you
borrowed $3.50 from your Dad to buy face paint, and another $4.00 from your
sister for accessories. How much money do you owe altogether?
Answer:
22.50$
give brainiest
Answer:
You Owe $22.50
Step-by-step explanation: All yo do is add up all of the $ That they owe to each person and That is your answer.
Lisa used 14 cup of milk per batch using her muffin recipe. How many cups of milk did she use when she made 6 batches of muffins?
Answer:
1
Step-by-step explanation:
1
They need to park the Mystery Machine. They could
either park in the lot that charges $5 and then $2 an
hour, or they could park using the meter on the street
that charges $3.75 per hour.
Write an equation that describes when the cost is the
same at both locations (the parking lot and on the
street).
Answer:
12 hours in the street=20 hours in the lot
Step-by-step explanation:
Well basically if you're at the street for 12 hours it will add up to 45 dollars. subtract the 5 starting dollars and you get 40. Divide 40 by 2 and you get 20. What does this mean? This means that in 12 hours on the street you can match the same amount of money if you were in the lot for 20 hours.
What is 84, percent of 300?
Answer:
252
Step-by-step explanation:
.84 times 300 = 252
Answer:
252%
Step-by-step explanation:
I did the Khan Academy.
help me please i dont get it
Answer:
Q11 part a
Q12 part b
Step-by-step explanation:
A sheet of notebook paper is four thousandths of an inch thick. What is the thickness, in centimeters, of a 500-sheet stack of notebook paper
Answer:
2 inches thick
Step-by-step explanation:
4/1000*500
Thickness of a 500 sheet stack of notebook paper is 5 cm.
What is Measurement units?
A measurement unit is a standard quality used to express a physical quantity.
Given that;
Thickness of a sheet of notebook paper = 0.004 inch
Now,
1 inch = 2.54 cm
Hence, Thickness of a sheet of notebook paper = 0.004 inch
= 0.004 × 2.54 cm
= 0.01016 cm
= 0.01 cm
So, Thickness of a 500 sheet stack of notebook paper = 500 × 0.01
= 5 cm
Thus, Thickness of a 500-sheet stack of notebook paper is 5 cm.
Learn more about the measurement unit visit:
https://brainly.com/question/174910
#SPJ2
e. What is the value of 60 tens?
Answer:
The answer is 600
Step-by-step explanation:
Because 60×10=600.
Answer:
600
Step-by-step explanation:
60*10=600
I might have misunderstood. If I have, please tell me
The mass of the apples harvested from a particular orchard follows a nearly normal distribution with a mean of 94 grams and a standard deviation of 27 grams. What size sample is needed to get a standard error of 3
The sample size needed to get a standard error of 3 is 81
How to determine the sample size?The given parameters are:
Mean = 94Standard deviation = 27Standard error = 3The standard error is calculated using:
[tex]SE = \frac{\sigma}{\sqrt n}[/tex]
So, we have:
[tex]3= \frac{27}{\sqrt n}[/tex]
Divide both sides by 3
[tex]1= \frac{9}{\sqrt n}[/tex]
Square both sides
1 = 81/n
Multiply both sides by n
n = 81
Hence, the sample size needed to get a standard error of 3 is 81
Read more about standard errors at:
https://brainly.com/question/6851971
plss help mee
Show your work plss not just the answer
If two people share one soda, how much of the soda should each person get?
Answer:
1/2 of the soda:) sure yan
Answer:
sorry i dont know
Step-by-step explanation:
Please help quick. I tried everything (2, 7, 7) (2*7*7) and more.
Answer:
I think it would be 2 * 7 * 7
Step-by-step explanation:
I believe that you can't use squares in factorization.
A t-shirt that was originally priced at $14 is marked down to $10.
About what is the percent decrease?
A. 40%
B. 28.6%
C. 71.4%
D. 140%
Nina can stitch of a dress in 4 hours. If d represents the number of dresses and h represents the number of hours, which equation represents this proportional relationship?
Answer:d=6h
trust bro its right
White 4x+y=8 in slope intercept form
Answer:
y=-4x+8
Step-by-step explanation:
What type of graph is best to use to show changes over time?
A. bar graph
B. line graph
C. histogram
D. circle graph
Answer:
You're answer should be (B) Line graph
Step-by-step explanation:
Answer:
line graph
EXPLANATION
trust me g
Find the value of xxx, yyy, and zzz in the parallelogram below.
Answer:
Step-by-step explanation:
Solve. Use the discount equation
S = R − rR, where S is the sale price, R is the regular price, and r is the discount rate.
An exercise bike is on sale for $320, having been marked down 20% off the regular price. Find the regular price.
Answer:
[tex]\$ 400[/tex].
Step-by-step explanation:
In this question, [tex]S[/tex] (sales price) and [tex]r[/tex] (discount rate) are both given. The unknown is the regular price, [tex]R[/tex].
Rearrange the discount equation to solve for [tex]R[/tex] in terms of [tex]S[/tex] and [tex]r[/tex].
[tex]S = R - r\, R[/tex].
[tex]S = (1 - r)\, R[/tex].
Divide both sides by [tex](1 - r)[/tex]:
[tex]\displaystyle \frac{S}{1 - r} = \frac{(1 - r)\, R}{1 - r}[/tex].
[tex]\begin{aligned}R &= \frac{S}{1 - r}\end{aligned}[/tex].
It is given that [tex]S = 320[/tex]. A mark-down of [tex]20\%[/tex] is equivalent to a discount rate of [tex]r = 20 / 100 = 0.20[/tex]. Substitute in [tex]S[/tex] and [tex]r[/tex] to find the value of [tex]R[/tex]:
[tex]\begin{aligned}R &= \frac{S}{1 - r} \\ &= \frac{320}{1 - 0.2} \\ &= \frac{320}{0.8} \\ &= 400\end{aligned}[/tex].
Thus, the regular price would be [tex]\$ 400[/tex].