Answers
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:
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Related Questions
Which shows the correct expanded form and product of 35 x 3?
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Answer:
(30 x 3) + (5 x 3) = 105
Step-by-step explanation:
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Step-by-step explanation:
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6mx-3nx+my
Step-by-step explanation:
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6mx-3nx+2my-my
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Step-by-step explanation:
There are 4 nickels and 4 dimes in your pocket.You randomly pick a coin out of your pocket and placed it on a counter. Then you randomly pick another coin. The first coin is a nickel and the second coin is a dime. What is the probability
Answers
Answer:
The probability of picking a nickel or a dime is 25%
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
To answer this question, use the following:
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At McCord Middle school, 40 percent of the 500 students ride their bikes or walk home. How many students ride their bikes or walk to school A. 12 B. 80 C. 200 or D. 2,000 it is not D. tho
Answers
Answer:
200
Step-by-step explanation:
C
The solution of 3x - 4 ( x - 2 ) = 0 is ;
Answers
Answer:
8
Step-by-step explanation:
simplify the expression
3x - 4x+8 = 0
put like terms together 3x-4x = -x
-x + 8 = 0
add x on both sides
x = 8
happy holidays :)
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Step-by-step explanation:
STEP 1:
Equation at the end of step 1
(3x - 4)2 = 0
STEP 2:
Solving a Single Variable Equation:
2.1 Solve : (3x-4)2 = 0
(3x-4) 2 represents, in effect, a product of 2 terms which is equal to zero
For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : 3x-4 = 0
Add 4 to both sides of the equation :
3x = 4
Divide both sides of the equation by 3:
x = 4/3 = 1.333
One solution was found :
x = 4/3 = 1.333
please help!!!!
algebra 2
Answers
Answer:
domain: x<2 or x>2
x-intercepts: (3/2, 0), (-3/2, 0)
what’s the percentage help me please
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Answer:
B) 19
Step-by-step explanation:
The first step is to substitute 2 for x into the equation. f(2) = 2(3^2)+1
The second step is to square 3 which equals 9. f(2) = 2(9)+1
The third step is to multiply 2 by 9 which equals 18. f(2) = 18+1
The fourth step is to add 18+1 which equals 19. f(2) = 19
A 5-foot piece of string costs $4.20. What is the price per inch?
Answers
Answer:
$0.035
Step-by-step explanation:
Answer: 0.84 cents per inch
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Answers
Answer:
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Find the simple interest earned for principal of $2,000 at and 8% rate for 5 years.
Answers
Answer:
$2800.00
Step-by-step explanation:
A total accrued amount 800 = principal (P) $2000 + interest (I)
R Rate of interest per year decimal - 0.08
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T time period months or years - 5 years
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A = 2000 (1 + (0.08 x 5)) = 2800
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Given the parallelogram below, find the value of angle 1
Answers
Can someone answer these pls!! I will be glad to have you answer them !! I need this done by tomorrow!
Answers
Answer:
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Step-by-step explanation:
You and two friends buy snacks for a field trip. Using the
information given in the table, determine the price per pound for mixed nuts,
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Answers
Answer:
13.15
Step-by-step explanation:
Which of the following relations describes a function?
OA. {(-3,-4), (-4,-3), (3, 4), (4,3)}
OB. {(3,-1), (3, 1), (4, -1), (4, 1) }
OC. {(3, 3), (3, 4), (4,3), (4,4)}
OD. {(0,0), (0, 3), (3, 0), (3, 3) }
Answers
Answer:
{(-3,-4), (-4,-3), (3, 4), (4,3)}
Step-by-step explanation:
{(-3,-4), (-4,-3), (3, 4), (4,3)}
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Answers
Answer:
Yes, all equilateral triangles are acute.
Step-by-step explanation:
yea
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Answers
Answer:
203.5
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Step-by-step explanation:
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Answer:
the square root of 20 could be between 4 and 5 OR -4 and -5.
Step-by-step explanation:
plus or minus 4 squared is 16 and plus or minus 5 squared is 25. finally, 20 is between 16 and 25.
will give brainliest.
Which of the binomials below is a factor of this trinomial?
3x^2+16x+ 5
A- 3x-5
B. 3x-1
C. 3x+1
D. 3x+5
Answers
Answer:
option c
Step-by-step explanation:
The zeros of 3x+1
3x=-1
x=-⅓
plug in -⅓ into the trinomial. if it gives an answer of 0 then it's a factor
3(-⅓)²+16(-⅓)+5
=0
can someone explain
Answers
Answer:
K = -2
Step-by-step explanation:
K represents the y-intercept, which is where the line crosses the y axis. We can see from the y = -4x -2, that -2 is the y-intercept, because in y = mx + b, b is the y -intercept.
~theLocoCoco
Is the following relation a function?
Answers
Answer:
yes
Step-by-step explanation:
A function is any graph that the x values do not repeat.
You can check this by using this vertical line test
Run your finger or a pencil down a specific vertical (top to bottom) line on the graph, if you can see that it intersects into the graph more than once, then it's not a function.
Ben earns an annual income of $12,800 a year. The income tax he has to pay is 15%. What is the amount of income tax in dollars and cents that the Ben has to pay?
Answers
Answer:
$
1
,
920
Explanation:
Find
15
%
×
12800
15
100
×
12800
1
=
$
1
,
920
Step-by-step explanation:
2x+4y=8 find the slope
Answers
4y = -2x + 8
Divide by 4
Y = -1/2x + 8
The slope is -1/2
Factor the following by completing the square w^4-22w^2+9
Answers
Answer:
(w² - 4w - 3) (w² + 4w - 3)
Step-by-step explanation:
w² + 4w³ - 3w² -4w³ - 16w² + 12w-3w² - 12w + 9
Which number is the additive inverse of -5?
Answers
Answer:
5
Step-by-step explanation:
Because -5 is a negative number and the opposite of negative is positive and 5 is positive.
Final Answer: [tex]5[/tex]
Steps/Reasons/Explanation:
Write down [tex]-5 + x = 0[/tex] because this is our equation with [tex]-5[/tex] plugged in to get an additive inverse. We will have to add [tex]5[/tex] to both sides. This means our additive inverse is positive [tex]5[/tex].
Question: Which number is the additive inverse of [tex]-5[/tex]?
[tex]-5 + x = 0[/tex]
Step 1: Regroup terms.
[tex]x - 5 = 0[/tex]
Step 2: Add [tex]5[/tex] to both sides.
[tex]x = 5[/tex]
~I hope I helped you :)~
Last sunday 1575 people visited the amusement park 56% was adults 16% were teenagers and 28% are children ages 12 and under find the number of adults teenagers and children that visited the park
Answers
Answer:
984 adults
281 teens
492 children
Step-by-step explanation: Multiply the total by the corresponding percentage to find the number. We assume the percentages have been rounded, so some adjustment is needed in the result of the multiplication.
{adults, teens, children} = 1757 × {.56, .16, .28} = {983.92, 281.12, 491.96}
≈ {984, 281, 492}
Answer:
984
492
281
Step-by-step explanation:
hope that helps
What number is 60% of 80?
Input only whole numbers.
Answers
Answer:
[tex]\huge\bf\underline{\underline{\pink{A}\orange{N}\red{S}\green{W}\purple{E}\blue{R}}}[/tex]
[tex] 60\% \: of \: 80 \\ = \frac{60}{100} \times 80 \\ = \frac{4800}{100} = 48[/tex]
[tex]\color{purple}{HOPE}[/tex] [tex]\color{purple}{THIS}[/tex] [tex]\color{purple}{WILL}[/tex] [tex]\color{purple}{HELPS}[/tex] [tex]\color{purple}{YOU}[/tex]
please help with 1-3