parallel lines, transversal, and algebra really need help
Answer:
1. 58 = 5x-2, 60 = 5x, x = 12
2. 134 = 16x+22, 112 = 16x, x = 7
3. 125 = 7x-1, 126 = 7x, x = 18
4. 133+9x+2 = 180, 9x=45, x=6
5. 8x-77 = 3x+38, 5x = 115, x=23
6. 11x-47 = 6x-2, 5x = 45, x=9
7. 13x-21 = 5x+75, 8x = 96, x=12
8. 5x+3+9x-33 = 180, 14x = 210, x=15
9. 8x-31 = 6x+3, 2x = 34, x=17
5y+35+6(17)+3 = 180, 5y = 40, y = 8
10. 29x-3+15x+7 = 180, 44x = 176, x=4
13y-17+15(4)+7 = 180, 13y = 130, y=10
1. x = 12
2. x = 7
3. x = 18
4. x = 5
5. x = 23
6. x = 9
7. x = 12
8. x = 15
9. x = 17; y = 8
10. x = 4; y = 10
To find the value of each missing variable(s), we would need to apply our knowledge of algebra. However, recall the following rules of angles in parallel lines:
corresponding angles are congruent (i.e. equal to each other)vertically opposite angles are congruent alternate angles are congruent same-side interior angles are supplementary (i.e. sum up to give 180°alternate exterior angles are congruent.Let's solve the given problems as shown below given that line l is parallel to line m:
1. [tex]58 = (5x - 2)[/tex] (corresponding angles)
solve for x
[tex]58 = 5x - 2\\58 + 2 = 5x - 2 +2[/tex] (addition property of equality)
[tex]60 = 5x \\\frac{60}{5} = \frac{5x}{5}[/tex](division property of equality)
[tex]12 = x\\x = 12[/tex]
2. [tex]134 = 16x+22[/tex] (alternate exterior angles)
[tex]\\134 - 22 = 16x +22-22[/tex] (subtraction property of equality)
[tex]134 - 22 = 16x +22-22\\112 = 16x\\\frac{112}{16} = \frac{16x}{16}[/tex](division property of equality)
[tex]7 = x\\x = 7[/tex]
3. [tex]7x - 1 = 125[/tex] (alternate angles)
[tex]7x - 1 + 1 = 125 + 1\\7x = 126\\\frac{7x}{7} = \frac{126}{7} \\x = 18[/tex]
4. [tex](9x+2) + 133 = 180[/tex] (same-side interior angles)
[tex]9x+2 + 133 = 180\\9x + 135 = 180\\9x + 135 - 135 = 180 - 135\\9x = 45\\\frac{9x}{9} = \frac{45}{9} \\x = 5[/tex]
5. [tex]3x+38 = 8x-77[/tex] (alternate exterior angles)
[tex]77 + 38 = 8x - 3x\\115 = 5x\\\frac{115}{5} = \frac{5x}{5} \\23 = x\\x = 23[/tex]
6. [tex]6x-2 = 11x-47[/tex] (corresponding angles)
[tex]6x-2 = 11x-47\\47 - 2 = 11x - 6x\\45 = 5x\\x = 9[/tex]
7. [tex]5x+75 = 13x - 21[/tex] (alternate angles)
[tex]5x+75 = 13x - 21\\21 + 75 = 13x - 5x\\96 = 8x\\12 = x\\x = 12[/tex]
8. [tex](5x+3)+(9x-33)= 180[/tex] (same-side interior angles)
[tex]5x+3+9x-33= 180\\14x - 30 = 180\\14x - 30 + 30 = 180 + 30\\14x = 210\\x = 15[/tex]
9. [tex]8x-31 = 6x+3[/tex] (alternate angles)
[tex]8x - 6x = 31 + 3\\2x = 34\\x = 17[/tex]
Solve for y
[tex](5y + 35) + (6x + 3) = 180[/tex] (same-side interior angles)
[tex]5y + 35 + 6x + 3 = 180\\[/tex]
Plug in the value of x
[tex]5y + 35 + 6(17) + 3 = 180\\5y + 35 + 102 + 3 = 180\\5y + 140 = 180\\5y = 180 - 140\\5y = 40\\y = 8[/tex]
10. [tex](29x-3)+(15x+7) = 180[/tex](supplementary angles)
Solve for y
[tex]13y - 17 = 29x - 3[/tex] (alternate exterior angles)
Plug in the value of x
[tex]13y - 17 = 29(4) - 3\\13y - 17 = 116 - 3\\13y - 17 = 113\\13y = 113 + 17\\13y = 130\\y = 10\\[/tex]
Learn more about parallel lines here:
https://brainly.com/question/16227989
Please help me will be much appreciated <3
Answer:
She earned 300 dollars by selling 100 headbands.
What is it will mark Brainliest
which of these is a composite number? 4 2 6 8
Step-by-step explanation:
4,6 and 8 are composite numbers
and 2 is an prime number
hope it helpful
Answer:
4 , 6 , & 8 are composite numbers
what does x equal and what are the angle measures?? help Asap
all triangles are 180 always. make a equation 2x+x+x+8 then combine like terms so it will be 4x+8 then divide by 4 on bith sides x=2
Find the slope of 6x – 3y = 5
Answer:
slope is 2
Step-by-step explanation:
simplify this equation so that you can get to "y ="
your equation is: 6x - 3y = 5
start by subtracting 6x from both sides: -3y = -6x - 5
then divide both sides by -3 to isolate y: y = 2x - 5/3
so now we can clearly see that the slope is 2, since that is what is right next to x
6th grade math i mark as brainliest
just add you the numbers and you will get the answer
Pls someone help me!
Answer:
When present,outliers will have an effect of the range since one of the outliers will either be highest or lowest number in a given data set and the range is found by finding the difference of the highest and lowest numbers.
What is the cube root of 27x^18?
A)3x^6
B)3x^9
C)9x^6
D)9x^9
Answer:
It’s B
Step-by-step explanation:
just answered question
2 lines intersect to form angles 1 and 2.
Which equation represents the relationship between their measures?
mAngle1 + mAngle2 = 90°
mAngle1 + mAngle2 = 100°
mAngle1 + mAngle2 = 180°
mAngle1 + mAngle2 = 200°
Answer:
mAngle1 + mAngle2 = 180°
Step-by-step explanation:
This is the answer hope it helps
if u had a picture i could give further details
Hope this helped
Answer:
What if I told you I guessed
Step-by-step explanation:
but submitted and got it correct
...
its C:)Solve for z. 2z − 3 = 1
Answer:
z = 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define
2z - 3 = 1
Step 2: Solve for z
Add 3 on both sides: 2z = 4Divide 2 on both sides: z = 2Helpppppp
Find the quotient: -45/5
A. -40
B. -9
C. 9
D. 40
Answer:
B - 9
Step-by-step explanation:
5 x 9 = 45 or 45 divided 5
A rectangle has an area of 135 ft 2 . What is the length, if the width is 9 ft?
Answer:
15 ft
Step-by-step explanation:
A=LxW
135 ft2 =m X 9ft
Divide 135 by 9
& that equals 15ft.
To check your answer, you multiply 15X9 and that equals 135. So the length of the rectangle is 15ft.
someone answer please:)
I think its saying to find out what a means
ANSWER PLEASE 40 POINTS!
Answer: |10 - (-8)|
The absolute value is 18
Step-by-step explanation:
The distance between two numbers is a subtraction equation.
10 - (-8) Subtracting a negative is like adding a positive
10 + 8 = 18
If you look at it as the first negative sign means -1 multiplied by the next negative number, "Remember that a negative times a negative is a positive!"
Answer:
|-10 - (-8)|
Step-by-step explanation:
Distance from 10 to 0: 10Distance from 0 to -8: 8Put them together (with absolute value): |-10 - (-8)|I hope this helps!
The Science Club went on a two-day field trip. The first day the members paid $70 for transportation plus $19 per ticket to the planetarium. The second day they paid $100 for transportation plus $16 per ticket to the geology museum. Write an expression to represent the total cost in dollars for two days for the n members of the club.
Answer:
$170 + $35n
Step-by-step explanation:
Given that:
First day:
Transport fare = $70
Fee per ticket = $19
2nd day:
Transport fare = $100
Fee per ticket = $16
Total cost in dollars for the two days for n members
Number of members = n
First day:
70 + 19n
Second day :
100 + 16n
Totak cost :
(70 + 19n) + (100 + 16n)
70 + 100 + 19n + 16n
170 + 35n
$170 + $35n
holly has $10.00. she saw a purse in a catalog that was marked $14.95 plus 5 sales tax
Answer:Molly won't be able to pay for the purse because $14.95 plus 5 is $19.95 and Molly only has $10.00 so she won't be able to buy the purse.
Step-by-step explanation:
Answer: A. $5.70
Step-by-step explanation:
anybody knows the best way to get rid of a migraine or to make it feel better
it k1lls so bad it's so painful. don't say got to the doctor's cuz there medicine doesn't rlly help
Answer:
The best way to help is to get some water or get some sleep.It is either because you didn't get enough sleep or that you are dehydrated.
Step-by-step explanation:
Answer:
Drink a soda the instant you feel one coming on- sugar and caffeine tend to help.
If you can, try a good chiropractor- they can do adjustments that help with so many things including splitting headaches.
Try an OTC medicine.
sleep, dark, quiet, calm- try not to think too much and stay hydrated. maybe try carbonated water.
try to massage your neck yourself. it could help.
try to use a cold or a hot compress on your head.
Bananas. A tried and true natural headache reliever, bananas have potassium, magnesium, B vitamins, and complex carbohydrates, all components that contribute to headache relief.
The taste and smell of green apples have shown to help dim or lessen the intensity of migraines.
Hot packs and heating pads can relax tense muscles. Warm showers or baths may have a similar effect. Drink a caffeinated beverage. In small amounts, caffeine alone can relieve migraine pain in the early stages or enhance the pain-reducing effects of acetaminophen (Tylenol, others) and aspirin.
Step-by-step explanation:
avoid blue light from screens.
A freezer can be bought on hire purchase by making a desposiy of 15% of the cash price which is $2975 the interest which is 20% of the outstanding balance is charged the amount payable is paid in 12 monthly instalements.Calculate the freezer
Answer: See explanation
Step-by-step explanation:
a. The deposit
= 15% × $2975
= 15/100 × $2975
= 0.15 × $2975
= $446.25
b. The hire purchase price
Outstanding balance = $2975 - $446.25 = $2528.75
20% of outstanding balance
= 20% × $2528.75
= 0.2 × $2528.75
= $505.75
Hire purchase price
= $2975 + $505.75
= $3480.75
c. The difference the hire purchase price and cash price
= $3480.75 - $2975
= $505.75
d. The difference as a percentage of the cash price.
= ($505.75 / $2975) × 100
= 0.17 × 100
= 17%
The graph of f (x) = x + 5 is a vertical translation 5 units
up of the graph of f(x) = x. How can you obtain the graph of
f(x) = x + 5 from the graph of f (x) = x using a horizontal
translation?
Answer:
A horizontal translation of 5 units to the left.
Step-by-step explanation:
Given the parent linear function:
[tex]\displaystyle f(x)=x[/tex]
To shift vertically n units, we can simply add n to our function. Hence:
[tex]f(x)=x+n[/tex]
So, a vertical shift of 5 units up implies that n=5. So:
[tex]f(x)=x+5[/tex]
As given.
However, to shift a linear function horizontally, we substitute our x for (x-n), where n is the horizontal shift. So:
[tex]f(x-n)=(x-n)[/tex]
Where n is the horizontal shift.
For example, if we shift our parent linear function 1 unit to the right, this means that n=1. Therefore, our new function will be:
[tex]f(x-1)=(x-1)[/tex]
Or:
[tex]f(x)=x-1[/tex]
We notice that this is also a vertical shift of 1 unit downwards.
Therefore, we want a number n such that -n=5.
So, n=-5.
Therefore, it we shift our function 5 units to the left, then n=-5.
Then, our function will be:
[tex]f(x-(-5))=(x+5)\text{ or } f(x)=x+5[/tex]
Hence, we can achieve f(x)=x+5 from f(x)=x using a horizontal translation by translating our function 5 units to the left.
What happens to the graph of f(x) when it is multiplied
by a number between 0 and 1?
Answer:
Therefore multiplying x by a number between 0 and 1 creates a horizontal stretch, which looks like a vertical compression. That is, the parabola will be shorter/wideStep-by-step explanation:
Answer:
Therefore multiplying x by a number between 0 and 1 creates a horizontal stretch, which looks like a vertical compression. That is, the parabola will be shorter/wider
Step-by-step explanation:
hope it heped
Treys gas tank is 1/6 full. After he buys 14 gallons of gas, it is 3/4 full. How many gallons can Treys tank hold?
Answer:
Goran's gas tank is 1/6 full. After he buys 14 gallons of gas, it is 3/4 full. How many gallons can Goran's tank hold?"
Let x = gallons to fill the tank
14
multiply by 12
12*3%2F4x = 12*1%2F6x + 12(14)
3(3x) = 2x + 168
9x - 2x = 168
7x = 168
x = 168/7
x = 24 gallons
:
see if that is true
1%2F6*24 + 14 = 18 gallons which is 18/24 = 3/4 of the tank
please help me answer this!! geometry
Answer:
-2x+7(10+18)
Step-by-step explanation:
Hope this helps
What is the square root of 3 to the square root of 2 power times the square root of 3 to the negative square root of 2 power
Answer:
3
Step-by-step explanation:
multiplication rule of exponents is to multiply the bases (sq rt 3) and add the exponents
(sq rt 3)^2 = 3
add exponents and power of 1
The measures of the angles of a triangle are shown in the figure below. Find the
measure of the smallest angle.
(3x-9)°
(x+15)
Answer:
318.6
Step-by-step explanation:
(3x-9) + (x+15) = 180
3x (x+15) -9 (x+15)
4x + 45x - 9x + 6 = 180
40x + 6 = 180
40x = 180 - 6
40x = 174
x = 4.34
(3x-9) = 4.34 * 3x-9 = 4.02
(x+15) = 4.34 + 15 = 19.34
180 - (4.02 + 19.34)
= 180 - 23.36
= 156.64
hope this answer helps!!
The equation f = V + at represents the final velocity of an object, f, with an initial velocity, w, and an acceleration rate,
a, over time, t. Which is an equivalent equation solved for a?
Of-v=a
Of-vra
1
Of+V = a
o+v=a
Answer:
hey
Step-by-step explanation:
the answer is 5
Pls help me ASAP I have other homework to do and I don’t have time for this. It also detects if it’s right or wrong:(
Answer:
y = 25x + 50
Step-by-step explanation:
Greg went to Bed Bath and Beyond to buy Christmas gifts for his family this year. In his first trip he bought 4 candles, 5 wallflowers, and 6 lotions for a total of $123. Greg forgot some people on his list the first time so he makes a second trip and spent $48 to buy 2 candles, 3 wallflowers, and 1 lotion. The price of a lotion is 2 less than 2 times the price of a wallflower. How much does each item cost?
Answer:
Price of Candle: 12.5
Price Wallflower: 5
Price of Lotion: 8
Step-by-step explanation:
Let cost of a candle = [tex]x[/tex]
Let cost of a wallflower = [tex]y[/tex]
Let cost of a lotion = [tex]z[/tex]
Cost of 4 candles = 4[tex]x[/tex]
Cost of 5 wallflowers = 5[tex]y[/tex]
Cost of 6 lotions = 6[tex]z[/tex]
Cost of 2 candles = 2[tex]x[/tex]
Cost of 3 wallflowers = 3[tex]y[/tex]
Cost of 1 lotion = [tex]z[/tex]
As per question statement:
[tex]4x+5y+6z=123 .... (1)\\2x+3y+z=48 ...... (2)\\z=2y-2 ..... (3)[/tex]
Using equation (3) in (1) and (2), the equations get reduced to :
[tex]\Rightarrow 4x+17y = 135 ..... (4)\\\Rightarrow 2x+5y = 50 ..... (5)[/tex]
Multiplying (5) with 2 and subtracting from equation (1):
[tex]7y = 35\\\Rightarrow y = 5[/tex]
By equation (3):
[tex]\Rightarrow z =8[/tex]
By equation (4):
[tex]\Rightarrow x = 12.5[/tex]
Therefore, the answer is:
Price of Candle: 12.5
Price Wallflower: 5
Price of Lotion: 8
Please help me solve this.
Answer:
9
Step-by-step explanation:
13*3=39
48-39=9
Answer:
48-39=9
^
(13 x 3=39)
Sovle for x !!!!!!!!
Answer: A -11
Step-by-step explanation: trust me