Answers
Answer:
I) Eq(1) reason: sum of segments of a straight line
II) Eq(2) reason: Given PQ = ST & PS = RT
III) Eq(3) reason: sum of segments of a straight line
IV) Eq(4) reason: Same value on right hand sides of eq(2) and eq(3) demands that we must equate their respective left hand sides
V) Eq(5) reason: Usage of collection of like terms and subtraction provided this equation.
Step-by-step explanation:
We are given that;
PS = RT and that PQ = ST
Now, we want to prove that QS = RS.
From the diagram, we can see that from concept of sum of segments of a straight line we can deduce that;
PQ + QS = PS - - - - (eq 1)
Now, from earlier we saw that PQ = ST & PS = RT
Thus putting ST for PQ & PS for RT in eq 1,we have;
ST + QS = RT - - - - (eq 2)
Again, from the line diagram, we can see that from concept of sum of segments of a straight line we can deduce that;
RS + ST = RT - - - - -(eq 3)
From eq(2) & eq(3) we can see that both left hand sides is equal to RT.
Thus, we can equate both left hand sides with each other to give;
ST + QS = RS + ST - - - (eq 4)
Subtracting ST from both sides gives;
ST - ST + QS = RS + ST - ST
This gives;
QS = RS - - - - (eq 5)
Thus;
QS = RS
Proved
Related Questions
Steven bought nuts last week, consisting of 3.37 pounds of cashews, 2.6 pounds of almonds, and peanuts that weighed 7.89 pounds. What is the total weight, in pounds, of the nuts that Steven bought last week?
Answers
Answer:
13.86 pounds
Step-by-step explanation:
3.37 + 2.6 = 5.97
5.97 + 7.89
= 13.86
Hope this helps!!
if given f(x)=2x+5 what is f(-10)
Answers
the function f(x)=-4x+9 has a range given by {1, -3, -7, -15, -19, -23} select the domain values of the function from the list. complete the explanation for how you arrived at your answer. btw this isn’t actually a test it’s assigned as hw but please help
Answers
Let's see what to do buddy....
_________________________________
Remember from now on ,
rang = output
and also Remember ,
output = y = f(x)
So : range = f(x)
So we must put the range number instead of f(x) and solve for x.
Let's do it...
=======================================
[tex]f(x) = 1[/tex]
[tex] - 4x + 9 = 1[/tex]
Both sides minus 9
[tex] - 4x = 1 - 9[/tex]
[tex] - 4x = - 8[/tex]
Negatives simplified
[tex]4x = 8[/tex]
Divided both sides by 4
[tex]x = \frac{8}{4} \\ [/tex]
[tex]x = 2[/tex]
_________________________________
[tex]f(x) = - 3[/tex]
[tex] - 4x + 9 = - 3[/tex]
[tex] - 4x = - 3 - 9[/tex]
[tex] - 4x = - 12[/tex]
[tex]4x = 12[/tex]
[tex]x = \frac{12}{4} \\ [/tex]
[tex]x = 3[/tex]
_________________________________
[tex]f(x) = - 7[/tex]
[tex] - 4x + 9 = - 7[/tex]
[tex] - 4x = - 7 - 9[/tex]
[tex] - 4x = - 16[/tex]
[tex]4x = 16[/tex]
[tex]x = \frac{16}{4} \\ [/tex]
[tex]x = 4[/tex]
_________________________________
[tex]f(x) = - 15[/tex]
[tex] - 4x + 9 = - 15[/tex]
[tex] - 4x = - 15 - 9[/tex]
[tex] - 4x = - 24[/tex]
[tex]4x = 24[/tex]
[tex]x = \frac{24}{4} \\ [/tex]
[tex]x = 6[/tex]
_________________________________
[tex]f(x) = - 19[/tex]
[tex] - 4x + 9 = - 19[/tex]
[tex] - 4x = - 19 - 9[/tex]
[tex] - 4x = - 28[/tex]
[tex]4x = 28[/tex]
[tex]x = \frac{28}{4} \\ [/tex]
[tex]x = 7[/tex]
_________________________________
[tex]f(x) = - 23[/tex]
[tex] - 4x + 9 = - 23[/tex]
[tex] - 4x = - 23 - 9[/tex]
[tex] - 4x = - 32[/tex]
[tex]4x = 32[/tex]
[tex]x = \frac{32}{4} \\ [/tex]
[tex]x = 8[/tex]
=======================================
So the domain values are :
x = { 2 , 3 , 4 , 6 , 7 , 8 }
_________________________________
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
Find the axis of symmetry for this parabola:
y = -4x2 - 8x - 7
Answers
Answer:
Step-by-step explanation:
If we want to find the axis of symmetry of the parabola of [tex]y=-4x^{2} -8x-7,[/tex] we would use the formula of [tex]-\frac{b}{2(a)}[/tex] to find it.
b=-8
a=-4
so the formula would look like this [tex]-\frac{-8}{2(-4)}[/tex], simplify it >>>[tex]-\frac{-8}{-8}[/tex] which is -1
So -1 would be the axis of symmetry
*It would mean a lot to me if you guys gave this post a "THANKS"
solve: What number is 62% of 324? Round to the nearest hundredth.
Answers
Answer:
200.88
Step-by-step explanation:
324 · 0.62 = 200.88
(0.62 is equal to 62%)
Hope I helped :)
Please consider Brainliest :)
62% of 324 is 200 Round to the nearest hundredth.
What is percent?In mathematics,a percent is a number or ratio expressed as a fraction of 100. It is often denoted using percentage sign "%".
Now the given number is 324.
Given percentage is 62% or 0.62.
So for 62% of 324 we have,
62% of 324 = 0.62 x 324
or, 62% of 324 = 200.88
Now to round to the nearest hundredth we have
200.88 ≈ 200 round to the nearest hundredth.
Hence, 62% of 324 is 200 Round to the nearest hundredth
More about percent :
https://brainly.com/question/302226
#SPJ2
Use the figure below to solve for X.
Answers
x=45, we know 2x is 90 because it is a right angle, so we can divide 90 by two, to get 45. Now to substitute, 90+55+(45-10) = 180, therefore, this answer would make logical sense.
Jill reads 6 books per month. The number of books varies directly with the
number of months. How many books does Jill read in a year?
Answers
Hope this helps
what is 8 to the power of 3 minus 9 times 2 divided by 3
Answers
Answer:
506
Step-by-step explanation:
I did mentally
Answer:
506
Step-by-step explanation:
Write it out: [tex]8^{3}[/tex] - 9 × 2 ÷ 3[tex]8^{3} = 512[/tex] Plug 512 in: 512 - 9 × 2 ÷ 3-9 × 2 = -18Plug -18 in: 512 - 18 ÷ 318 ÷ 3 = 6Plug 6 in: 512 - 6512 - 6 = 506I hope this helps!
Parallel drainage pipes are connected with a third pipe. The connector pipe makes a 65 degree angle with a pipe as shown. What is the measure of the angle it makes with the pipe on the other side of the road. Explain.
Answers
65 is an interior alternate angle to the angle next to left of question mark. The line is supplementary so subtract 65 from 180. I’m pretty sure that’s how you solve it(:
21≥4x-15 solve
.....
Answers
Answer:
Inequality Form: x < 9
Interval Notation: (-∞,9)
I hope this helps
if you could, feel free to mark me Brainliest it would be much appreciated :D
Suppose it cost you $78.48 for a 9-month subscription to a streaming video service. Write a proportion that you can use to find the cost in dollars for a 12-month subscription. Then solve.
Answers
Answer:
78.48÷9×12=cost
104.64
Step-by-step explanation:
amount divide by 9 months equals cost per month
take that by 12 to give 12 months sub
Select two fractions equivalent to 3/5
Answers
Answer:
6/10
And 9/15
Step-by-step explanation:
Eric earns $7.50 per hour working at a grocery store. The total amount of money he
earns on a given day is a function of how many hours he works that day?
Answers
Answer: 37.50
Step-by-step explanation: If he works 5 hours A DAY and he earns $7.50 PER HOURS, you just need to multiple
7.50(5)= 37.50
2/3 divided by 2/5
lesson 4 module 2
grade 6
page s.20
Answers
Answer:
1 2/5
Step-by-step explanation:
Flip 2/5 to be 5/2
Multiply.
2/3 ⋅ 2/5 = 10/6
Simplify.
1 2/5
Hope I helped :)
Please consider Brainliest :)
Find the value of x.
Answers
Answer:
that would be 45
Step-by-step explanation:
is the combined savings enough for a charity donation?why?
Answers
Answer:
Combined savings are enough for charity because for charity since it is helping people, any bit of money you have can be enough for charity even if it is $1.00. Anything you have is enough, as long as you give. "Each of you should give what you have decided in your heart to give, not reluctantly or under compulsion, for God loves a cheerful giver" 2 corinthians 9:7.
Please explain how to find 40 x 50 using mental math... xD
Answers
Answer:
Basically, what you do is multiply 4 times 5 ( this only applies when the numbers are in tens so like 10,20,30,40, etc.)
then after this you add the zeros of both numbers.
Step-by-step explanation:
so, this would be 2000
What is the value of x?
Answers
Answer:
The answer is 30 degrees
Step-by-step explanation:
the total of all three angles in a triangle add up to 180.
50+100= 150
so,
180-150= 30
x= 30 degrees
hope this helps!!
Answer:
answer is B 30
Step-by-step explanation:
180 is the total degrees of the whole thing subtract both angels they already give you (100+50) that leaves you with 30
What is the product of the GCF and LCM of 16 and 24?
Answers
Answer:
48
Step-by-step explanation:
16= 2×2×2×2=2^4
(I just put this here because I needed 20 characters so yeah...)
Rebecca’s boss pays her time and a half for overtime work. If her regular wage is $13.50 per hour, what is her overtime rate?
Answers
Answer:
Rebecca's overtime rate is $20.25 per hour
Step-by-step explanation:
Rebecca is paid $13.50 per hour as her regular wage.
Her boss pays her that amount and a half for overtime work.
Half of her regular pay rate is 13.50/2= $6.75
Thus, her overtime rate is:
$13.50 + $6.75 = $20.25
Rebecca's overtime rate is $20.25 per hour
Given g(x) = -X – 1, solve for x when g(x) = 3.
Answers
Answer:
You have 2 values for g(x) and they are set equal to each other. Which means.....
-x-1 = 3
-x = 3+1
-x = 4
x = 4/-1
x = -4
What is the product of (3 + 2i) and (-8 - 41)?
Answers
its 39...............................................because...............................................
The debate team participated in 18 debate it won twice as often as it lost how many times did it win
Answers
There are approximately 1 1/2 kilometers in one mile. Approximately how many kilometers are in 6 miles?
Answers
Write an equation in slope-intercept form for the line that passes through (−2, 3) and is parallel to
the line with the equation 3x + 2y = 6.
Answers
y= (-3x+6)2
For parallel lines, slopes are the same,
y = mx + c
Substitute the values,
3 = (-3/2)(-2) + c
3=3 + c,
c = 0
Thus, the equation is y= -3/2x
Hope it helps :)
Andre’s school day is 63 hours long. He has 8 classes that are 3 hour long.
a. Create an expression to show how much time Andre is not in class during the day.
Answers
Answer:
(8×3)-63
just trust me that the right answer
Someone please help me with this one
Answers
Answer:
its 5
Step-by-step explanation:
got it right on quiz
please I need help
Answers
Answer:
please I need help......gjmtjmgj?hi?tmzdthwyriyotul!tkht
I’ll give Brainly! Jim has ten more dollars than Gail. Together they have at most twenty-seven dollars.
A. Determine the possible amounts of money Gail could have.
B. Sketch the solution on a number line.
Answers
Answer:
see below
Step-by-step explanation:
Let g= amount that gail has
j = g+10
j+g ≤ 27
Substitute the first equation into the inequality
g+g+10 ≤ 27
2g + 10 ≤ 27
Subtract 10 from each side
2g≤ 17
Divide by 2
g≤ 8.5
Answer:
Let g= amount that gail has
j = g+10
j+g ≤ 27
Substitute the first equation into the inequality
g+g+10 ≤ 27
2g + 10 ≤ 27
Subtract 10 from each side
2g≤ 17
Divide by 2
g≤ 8.5
Step-by-step explanation:
Which pair of undefined terms is used to define the term parallel lines?
Answers
Answer:
The answer is A: point and line : )
Answer: point and line
Step-by-step explanation:
