In the adjoining figure , APB and AQC are equilateral triangles. Prove that PC = BQ. ( Hint : [tex] \triangle[/tex]APC = [tex] \triangle[/tex]AQB, then PC = BQ)
~Thanks in advance ! ツ
Answer:
See Below.
Step-by-step explanation:
Statements: Reasons:
[tex]\displaystyle 1)\text{ } \Delta APB \text{ and } \Delta AQC \text{ are equilateral triangles}[/tex] Given
[tex]\displaystyle 2) \text{ } m \angle PAB = 60[/tex] Definition of equilateral.
[tex]3)\text{ } m \angle QAC = 60[/tex] Definition of equilateral.
[tex]4)\text{ } m\angle PAB = m\angle QAC[/tex] Substitution
[tex]5)\text{ } m\angle PAC=m\angle PAB+m\angle BAC[/tex] Angle Addition
[tex]\displaystyle 6)\text{ } m\angle QAB=m\angle QAC+m\angle BAC[/tex] Angle Addition
[tex]7)\text{ } m\angle QAB=m\angle PAB+m\angle BAC[/tex] Substitution
[tex]\displaystyle 8)\text{ } m\angle PAC=m\angle QAB[/tex] Substitution
[tex]9)\text{ } PA=BA[/tex] Definition of equilateral
[tex]10)\text{ } AC=AQ[/tex] Definition of equilateral
[tex]\displaystyle 11)\text{ } \Delta PAC \cong \Delta BAQ[/tex] Side-Angle-Side Congruence*
[tex]\displaystyle 12)\text{ } PC=BQ[/tex] CPCTC
* SAS Congruence:
PA = BA
∠PAC = ∠QAB
AC = AQ
7. Tyler works in a shoe store. Tyler earns a commission. He earns 3.5% of the amount he sells. Last
week, he sold $600 worth of shoes. How much was his commission?
2 over 3 multiplied by 15
Answer:
The answer is 10.
Step-by-step explanation:
2/3 times 15 is the same as 2/3 of 15.
2/3 of 15 is 10.
So, the answer is 10.
What is the percent of decrease from 600 to 90 ??
Answer:
85%
Step-by-step explanation:
((600-90)/600) x 100 = 85%
Find the value of x in the kite below.
x = [?]
Enter the number that goes in the green box.
Please helppp
pls help me i will give you brainliest
Answer:
its a linear function
Step-by-step explanation:
Help I’m stuck on this
Did you just say you were stuck step-sis?
Answer:
it is 6,000 diffrence
Step-by-step explanation:
Help me pls!!!
Can you factor: [tex]8x^{3} -1[/tex]
Answer:
(2x - 1) (4x^2 + 2x + 1)
Step-by-step explanation:
brainliest me pls
Answer:
[tex]\boxed{\bold{\left(2x-1\right)\left(4x^2+2x+1\right)}}[/tex]
Explanation:
Apply difference of cubes formula: [tex]\bold{x^3-y^3=\left(x-y\right)\left(x^2+xy+y^2\right)}[/tex]
[tex]\bold{\left(2x\right)^3-1^3=\left(2x-1\right)\left(2^2x^2+2x+1\right)}[/tex]
= [tex]\bold{\left(2x-1\right)\left(2^2x^2+2x+1\right)}[/tex]
2² = 4
[tex]\boxed{\bold{\left(2x-1\right)\left(4x^2+2x+1\right)}}[/tex]
- zyxx
Which expression is equivalent to 8(7m - 9p)?
Answer:
8(7m-9p) = 8(7m) - 8(9p)
= 56m - 72p
Let me know if this helps!
Answer:
56m-72p
Step-by-step explanation:
8(7m-9p) = 8*7p + 8*-9p = 56m-72p
Factor: m*(m+n)-3m*(m+n)^2
Answer:
−m(m+n)(3m+3n−1)
Step-by-step explanation:
25% of a population have pets. What is the probability that the next person you speak to has pets?
Answer: I d k
Step-by-step explanation:
Answer:
25
explanation:
just because
The book rack sold 24 paperbacks on Saturday, 17 of them mysteries. What percent of the books were mysteries?
Answer:
About 71% of the books were mystery books
Step-by-step explanation:
To find the percentage of something you simply divide the amounts. 17 of the 24 books were mystery so to find the percentage of mystery books you do 17 divided by 24
17/24= 0.70833333333
and round it to 71
Stefan made a paper cone with a diameter of 6 inches and height of 12 inches which measurement is closest to the volume of the this cone in cubic inches?
Answer:
Step-by-step explanation:
113 in ^3
What is the equation of the line that has a
slope of 5 and a y-intercept of -1?
Step-by-step explanation:
y= mx+b
where m is the slope , and b is the y intercept
y= 5x -1
-2(4x-1)-7=5
whats the next step in solving this equation
Answer:
Using distributive property is the next step in solving the equation
Step-by-step explanation:
-2(4x-1)-7=5
-8x+2-7=5
Answer:
The next step would be to do distributive property.
Step-by-step explanation:
-2(4x-1)-7=5
-8x + 2 - 7 = 5
-8x - 5 = 5
+5 +5
-8x = 10
/-8 /-8
x= -5/4
or
x = -1 1/4
Hope this helps and I hope u have an Amazing day!!
A certain forest covers an area of 4800 km^2 . Suppose that each year this area decreases by 5.25% . What will the area be after 6 years? Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
the area after 6 years is 3,473 km^2
Step-by-step explanation:
The computation of the area after 6 years is as follows:
= Area × (1 - decreased percentage)^number of years
= 4,800 km^2 × (1 - 5.25%)^6
= 4,800 km^2 × 0.9475^6
= 3,473 km^2
Hence, the area after 6 years is 3,473 km^2
Alfred has 21 boxes of pencils. He is dividing them equally among four students. How many boxes of pencils will each student receive? Write your answer as a decimal.
Answer:
5.25
Step-by-step explanation:
21/4 = 5.25
pls give me brainliest :)
solve the inequality for x
-x+23<2-2(x-8)
Answer:
inequality form: x<-5
Step-by-step explanation:
Can you guys figure out the linear function for this table, please?
Answer:
y = 6x + 10
Step-by-step explanation:
This is because the slope is 6 and the y intercept is 10, therefore the answer is y = 6x + 10
parallelogram
b= 13 ft. 6 in.
h= 10 ft. 3 in.
Answer:
A=19,926in.
or
A=1660.5ft
Step-by-step explanation:
you convert the feet into inches which gives you a base of 162 inches and a height of 123 inches. Next you multiply your base and height and it gives you an Area of 19,926inches but then if you need to convert the inches back into feet by dividing 19,926 by 12. After you do that you should end up with an area of 1660.5 feet.
If an inscribed angle measures 67°, how would you find the intercepted arc?
Multiply the angle measure by two.
Set the angle and arc measures equal.
Divide the angle measure by two.
Answer:
Multiply the angle measure by two.
Step-by-step explanation:
Answer:
you would multiple the angle and measure by two
Determine whether the triangles are congruent by AA., SSS, SAS, or not similar.
Step-by-step explanation:
they are similar by AA .
plz mark my answer as brainlist plzzzz . hope this will be helpful to you.
The membership in the Lego Club decreased from 120 members in August to 82 members in October. What was the percent decrease from August to October?
Type your answer using the % key. Round to the nearest whole percentage if necessary.
Answer:
72% decrease I...guess?
120 members-60 members=50%
-70 should be approx=60%
-80 should be approx=70%
so 80 is around 70%, so I'd say 82 is 72%
I'm most likely wrong but i dunno maybe im right
Step-by-step explanation:
Answer:
32%
Step-by-step explanation:
((120 - 82) / 120) x 100 = 31.66 %
31.66% to the nearest whole percentage is 32%
Please show work and help me please
Answer:
31.4 in
Step-by-step explanation:
the formula for circumference is 2*[tex]\pi[/tex]*radius. Since the diameter (which is the radius multiplied by 2) is labeled we can divide 10 by 2 to get the radius. 10/2 is 5. Since pi is an infinite number, we round it to 3.14. Then, plug in the numbers. The expression will be 2*3.14*5. 2* = 10 and 10 * 3.14 you can just move the decimal so the answer is 31.4.
Rich also has £400 pounds invest 3% compound interest . How many years does he need to invest the money to get at least £475
Answer: 6 years
Step-by-step explanation:
Formula to calculate compound amount: [tex]A=P(1+r)^t[/tex], where P= Principal , r=rate of interest, t= time
Given: P = £400, r = 3% = 0.03 , A= 475
Required equation: [tex]400(1+0.03)^t\geq475[/tex]
[tex]400(1.03)^t\geq475\\\\\Rightarrow\ (1.03)^t\geq\dfrac{475}{400}\\\\\Rightarrow\ (1.03)^t\geq1.1875[/tex]
Taking log on both sides , we get
[tex]t \log 1.03\geq\log1.1875\\\\\Rightarrow\ t(0.0128372)\geq(0.0746336)\\\\\Rightarrow\ t\geq\dfrac{0.0746336}{0.0128372}=5.81385\approx6[/tex]
Hence, he needs to invest the money for 6 years to get atleast £475.
What is the slope for this graph?*
(3,2)
|(1,2)
(-2,1)
(-1,2)
Answer:
the slope is 0
Step-by-step explanation:
Answer:
the answer is 0 .....,..........,..,
a) Simplify
a x b x 8
(1)
b) Simplify
y xyxy
(1)
c) Simplify fully
ex ex exexf
ex ex exfxf
(2)
Total marks: 4
Answer:
a. 8ab
b. y^3
c. e/f
Step-by-step explanation:
a; a * b * 8 = 8ab
b. y * y * y = y^3
c. we cancel out the e and f
e^4/e^3 * f/f^2
= e/f
Can you solve for a, b and c?
20 – 3b = -5
4a + 3b = 17
50 - 2a = 1
Answer:
c = 1 , a = 2, b = 3
Step-by-step explanation:
what's the sum of 15+(-19)
-4
15+-19
15 to 19 is 4
19 is the larger than 15 so since 19 is negative your answer will also be negative
3+2=___
4+2=___
8-8=___
Answer:
1)5
2)6
3)0
Step-by-step explanation:i subtracted