transversals angles​

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.

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:

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

Answer:

the expression is: [tex]^{15}P_3=\frac{15!}{(15-3)!}[/tex]

and 2730 different ways are possible.

Step-by-step explanation:

In the given question we have to choose a president, vice

president, and secretary.

Permutations are used when order is important so, as in the given question order is required. We would use permutations

The formula used is: [tex]^nP_r=\frac{n!}{(n-r)!}[/tex] where:

n=total number of objects

r=number of objects selected

In our case: n=15, r=3

Putting values and finding the answer:

[tex]^nP_r\\^{15}P_3=\frac{15!}{(15-3)!} =2730 \ ways[/tex]

So, the expression is: [tex]^{15}P_3=\frac{15!}{(15-3)!}[/tex]

and 2730 different ways are possible.

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

Answer:

x=5.7

Step-by-step explanation:

sin(35=x/10

Answer:

A. 1/5k - 2/3j and -2/3j +1/5k

Step-by-step explanation:

A. 1/5k - 2/3j and -2/3j +1/5k

B. 1/5k - 2/3j and -1/5k +2/3j

There is a change in the signs of each term

1/5k changed to -1/5k

-2/3j changed to +2/3j

Not equivalent

C. 1/5k - 2/3j and 1/5j - 2/3k

There is a change in the variables

1/5k changed to 1/5j

-2/3j changed to -2/3k

D. 1/5k - 2/3j and 2/3j - 1/5k

The is a change in the signs of each term

1/5k changed to -1/5k

-2/3j changed to +2/3j

The only equivalent expression is

A. 1/5k - 2/3j and -2/3j +1/5k

Answer:

-2x+7(10+18)

Step-by-step explanation:

Hope this helps

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:

I hope this helps!

Answer:

40

Step-by-step explanation:

Just use a calculator. I didn´t need to. My brother helped me a little

Answer:

She earned 300 dollars by selling 100 headbands.

Answer:

1) x=10   2) x= -7.25

Step-by-step explanation:

Im not sure

Answer:

7 4/11

Step-by-step explanation:

this is the answer

Answer:

7  4/11

Step-by-step explanation:

81/11= 7  4/11

Answer:

f(-2) = 2

Step-by-step explanation:

Look at the graph and find -2 on the x-axis and see what the y-coordinate is on the line where x is -2. When you do this, you can see that where x is -2, y is 2.

So basically it wants the y-value :)

Answer:

1.25

Step-by-step explanation:

the answer is 1.25. To get that, I found the slope, wrote the equation in point slope form, and then I calculated when the f(x) function hits the line

Thats insane tho!

Whats ur aops class that you take?

Answer:

Slope = 46.000/2.000 = 23.000

x-intercept = 6/23 = 0.26087

y-intercept = -6/1 = -6.00000

Answer:

25561485

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

13*3=39

48-39=9

Answer:

48-39=9

        ^

(13 x 3=39)

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.

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

Answer:

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.

Answer:

40

Step-by-step explanation:

This can be solved by changing the percentage to a decimal number, then multiplying by 160.

0.25×160=40

Answer:

hey

Step-by-step explanation:

the answer is 5

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

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

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%

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

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!!