Determine if the given lines are parallel, perpendicular or neither. line a: 6x - 12y = -24 line b: 3y = 2x + 18

Answer: Alternate exterior angles

Step-by-step explanation:

In the coordinate plane shown we can say that the y-coordinate of point A is 3.

Let us now take the statement one by one and try to find out if they are true or false.

A. True. The y-coordinate for A is 3

B. False. Point D has x-coordinate of 5 and E has 6

C. True The x-coordinate for F is 7

D. True The ordered pair for point G is (8,6)

E. False. Point H names the ordered pair (9,10).

F. false point B is √34 units away from origin

G. True.

The coordinate plane is a two-dimensional surface created by combining two number lines. A single horizontal number line makes up the x-axis. The name of the vertical number line, which is the other number line, is the y-axis. The intersection of the two axes is the origin. The graphing of points, lines, and other objects can be done using the coordinate plane.

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Answer:

0.31

Step-by-step explanation:

√13.7/3.05^2 + 2.6

= 3.7/ 9.3 + 2.6

= 3.7/ 11.9

= 0.31

Answer:

36

Step-by-step explanation:

24 customers dividend into 4 tables

so 24/4 = 6

then 6 customers can sit in 1 table

in case of 6 tables 6×6 =36

36 customers would sit in 6 tables

The total distance climbed by Kristen and her family is 16 meters.

It is given in the question that Kirsten and family climb down to 8 meters below ground level. Then they climb the opposite of 8 meters to return to ground level.

We have to find the total distance climbed by Kristen and her family.

We know that,

Total distance climbed by Kristen and her family = Distance climbed down the cave + distance climbed up the cave to reach ground level

Hence, we can write that,

Total distance climbed by Kristen and her family = 8+8 = 16 meters.

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Answer: y=-47/5

Step-by-step explanation:

Yw

The roots of the function f(x) = [tex]x^2+2x-1[/tex] are

x = [tex]-1+\sqrt{2}[/tex]

x = [tex]-1-\sqrt{2}[/tex]

The function is given f(x)=  [tex]x^2+2x-1[/tex]

The roots of given function will be at f(x) = 0

Substitute the value in the equation

[tex]x^2+2x-1[/tex] =0

Here to find the roots of the function, we have to use the quadratic formula in the given function

Roots of the function = [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

From the given function the values of

a = 1

b = 2

c = -1

Substitute the values in the quadratic formula and find the roots of the function

= [tex]\frac{-2+/-\sqrt{2^2-4(1)(-1)} }{2(1)}[/tex]

= [tex]\frac{-2+/-\sqrt{4+4} }{2}[/tex]

= [tex]\frac{-2+/-2\sqrt{2} }{2}[/tex]

The roots of the given functions are

x = [tex]-1+\sqrt{2}[/tex]

x = [tex]-1-\sqrt{2}[/tex]
Hence, the roots of the function f(x) = [tex]x^2+2x-1[/tex] are

x = [tex]-1+\sqrt{2}[/tex]

x = [tex]-1-\sqrt{2}[/tex]

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Answer:

Kareem takes longer to drive the 25 miles. Kadeen takes 10 minutes longer than Quinn.

Step-by-step explanation:

The formula for time is distance over speed (distance/speed)

Kadeem

distance/speed = 25/50 = 1/2 hour = 30 minutes

Quinn

distance/speed = 25/75 = 1/3 hour = 20 minutes

Answer: y = f (n 1)

Step-by-step explanation:

If we count interest rate = 5%

then if he earned 'y' amount in 1st year then in 2nd year he must earned

= y + 5% of y

== 1.05 y

here, y = f(n 1)

Price of key ring = £1.6

Price of purse = £3.2

The unitary approach is a strategy for problem-solving that involves first identifying the value of a single unit, then multiplying that value to figure out the required value.

Given Data

Vicky makes 8 purses and 9 key rings to sell for charity.

Vicky wants to get a total of exactly £40

Suppose the price of key ring be v

and the price of purses be 2v

£40 = £8(2v) + £9(v)

40 = 16v + 9v

40 = 25v

v = [tex]\frac{40}{25}[/tex]

v = 1.6

Price of key ring = £1.6

Price of purse = £3.2

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Answer:

16/5

Step-by-step explanation:

The direct variation equation (where k is the constant variation):

z = kw

First, we must solve for k:

k = w/z

Plug in -5 and 2:

k = 2/-5 = -2/5

Now plug k into the formula with 8 to solve for z:

z = -2/5 x 8 = 16/5

Answer:

15 pounds

Step-by-step explanation:

Kevin is making potato casserole for a dinner party. He needs 2½ pounds of potatoes per guest. How many pounds of potatoes will he need for 6 guests?

15 pounds

6.5 pounds  

25 pounds

12.5 pounds

2.5lb × 6 guest = 15 pounds

Answer: 15 pounds of potatoes.

Step-by-step explanation:

Kevin will perform basic multiplication to find how many potatoes he needs for all of the guests. Since each person requires 2 1/2 pound of potatoes and there are a total of 6 guests, multiplying these two values will find the pounds of potatoes that are needed for all of the guests.

2 1/2 * 6 = 15 pounds of potatoes

Therefore, Kevin needs 15 pounds of potatoes to make potato casserole for everyone at the dinner party.

The numerical length of GH = 20 units

FH is a line segment.

G is a point on the line segment.

Then G divides the line segment FH into two line segments FG and GH.

We are given the lengths of FH, FG and GH in terms of x.

That is,  FH=4x+8, FG=x and GH=5x

We need to find the numerical length of the line segment GH. We first need to find the x for this.

As G cuts the line segment FH into two parts, the length of the line segment FH is the sum of the lengths of the line segments FG and GH.

That is, FH = FG + GH

⇒ 4x+8 = x +5x

⇒ 4x+8 = 6x

⇒ 2x = 8

⇒ x = 4

So the numerical length of GH = 5x = 5 x 4 = 20 units

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Answer:

x=22

Step-by-step explanation:

Since a straight line is equal to 180 degrees,

(3x+3)+(5x+1) = 180

(3x+3)+(5x+1)-180=0

8x+4-180=0

8x-176=0

8x=176

x=176/8

x=22

Which also means that the first angle is (3(22)+3)=69 degrees

the second angle is (5(22)+1) = 111 degrees

111 + 69 = 180  

Answer:

2; 6

Step-by-step explanation:

for the first shape there are 2 lines of symmetry

TWO

for the hexagon or the regular polygon there are 6 lines of symmetry

SIX

you can find lines of symmetry by drying a line down and seeing if when you fold them they will be exactly the same

Answer: 60 inches in 5 feet

Step-by-step explanation:

5X12=60

one may note that y = 4 is a horizontal line, and a line perpendicular to a horizontal line will be a vertical one, Check the picture below.

The range of elevations is 166 meters.

Find the biggest observed value of a variable (the maximum) and subtract the smallest observed value to determine the range (the minimum). The data points between the distribution's two extremes are not taken into account by the range; just these two values are.

So as mentioned above, given to us are the lowest and highest values

So as the lowest value is 7 meters and the highest value is 173 .

Thus range is equal to 173-7

which is equal to 166.

Thus range is 166 meters.

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Answer:

1.34 units.

Step-by-step explanation:

The line y = 2x - 5 has a slope of 2 so the line passing through the given point will be perpendicular to y= 2x - 5 and will have a slope of -1/2.

Let this line be y = -1/2x + c.

Its passes through (4, 6) so:

6 = -1/2*4 + c

6 = -2 + c

c = 6 + 2 = 8

So, equation of this line is y = -1/2x + 8.

Now we find the point where the 2 lines intersect:

y = 2x - 5

y = -1/2x + 8

2x - 5 = -1/2x + 8

2x + 1/2 x = 5 + 8

(5/2)x = 13

x = 26/5

  = 5.2.

and y = 2(5.2) - 5

          = 5.4.

So, the point of intersection is (5.2, 5.4)

and the distance between the point (4,6) and the line y = 2x - 5

= √((6 - 5.4)^2 + (4-5.2)^2)

= √(0.36 + 1.44)

= √1.8

= 1.34

There is a formula you can use directly to solve this.

The given coordinate pair, (10, -7) is not on the x–axis or the y–axis, but it is in Quadrant IV

A coordinate pair specifies a point on the coordinate plane.

The coordinates of points on the x–axis have a y–coordinate of 0

Therefore, the coordinates of a point that is on the x–axis can be expressed as (x, 0)

Points that are on the y–axis have a x–coordinate of 0, which gives the coordinates of the points located on the y–axis as (0, y)

The coordinates of the given point is (10, -7), therefore, the point is neither on the x or y–axis, but in one of the four quadrants.

The coordinate of points in the first quadrant can be represented generally as (x, y)

Points in the second quadrant have the general form of (-x, y)

The points in the third quadrant can be expressed generally in the form (-x, -y)

The coordinates of points on the fourth quadrant are of the form, (x, -y)

The given point is (10, -7), therefore it is in the fourth quadrant or Quadrant IV

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To withdraw money from the automated teller machine the numeric pattern required to complete the personal ID numbers is 2, 13, 24, 35,46,57,68.

As given in the question,

Using automated teller machine customers at the bank withdraw money

Numeric pattern given for the personal ID numbers is

2, 13, 24, 35

First term 'a'= 2

Common difference between consecutive terms are same

'd'=13 -2                                                  

   =11

It is an arithmetic progression series

nth term = a+ (n-1)d

5th term = 2 +(5-1)11

               =46

6th term =2+(6 -1)11

              =57

7th term= 2+ (7-1)11

             = 68

Therefore, to withdraw money from the automated teller machine the numeric pattern required to complete the personal ID numbers is 2, 13, 24, 35,46,57,68.

The complete question is:

The customers at the bank would like to withdraw money from the automated teller machine. Help them enter their personal ID numbers by completing the numeric patterns. 2, 13, 24, 35, ___, ___, ____.

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Answer:

Terms: x, 4y, 32

variables: x, y

constant: 32

coefficients: 4, 1

Step-by-step explanation:

Hope this helps!

Answer:

(x,y)=(10,11)

Step-by-step explanation:

Drew actually has almost finished the equation. So I'm starting with the left part

[tex]2.5x+ 6= 31[/tex]

Cancel out 6 from both sides and divide both sides 2.5 which leaves us with

[tex]x=\boxed{10}[/tex]

Plug in the value of x into the second equation and simplify

y=-2.10+ 31

[tex]y=\boxed{ 11}[/tex]

An equivalent expression to given expression is 35(3 + m)

In this question, we have been given an expression 105 + 35m

We need to write an equivalent expression of given expression.

To find an equivalent expression we factorize given expression using the distributive property and the greatest common factor.

A common number for 35 and 105 is 35.

105 = 35 × 3

So, we can write given expression as,

105 + 35m

= (35 × 3) + 35m

= 35(3 + m)

Therefore, an equivalent expression to given expression is 35(3 + m)

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The total area of the sandbox is given by 6x^2-11x+5

Width of the sandbox = (x-1)

Length of the sandbox = (6x-5)

Rectangle area in geometry refers to the area that a rectangle occupies on a two-dimensional plane. A quadrilateral, a form of a two-dimensional object with four sides and four vertices, is what a rectangle is. The rectangle's four angles are all right angles or exactly 90 degrees. The rectangle's opposing sides are equal and parallel to one another.

The formula for the area of a rectangle:

Area of rectangle = Length*Width

Substituting the value in the formula we get:

Area of rectangle = (x-1)*(6x-5)

= 6x^2-5x-6x+5

= 6x^2-11x+5

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Answer:

x = 2

Step-by-step explanation:

x + 3 + 1/2 x + 3 +x + 1 = 12  Combine like terms

21/2 x + 7 = 12   Subtract 7 from both sides of the equation

2 1/2 x = 5

Another name for 2 1/2 is [tex]\frac{5}{2}[/tex]        ([tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{1}{2}[/tex])

[tex]\frac{5}{2}[/tex] x = 5  Multiply both sides of the equation by [tex]\frac{2}{5}[/tex]

[tex](\frac{2}{5})[/tex][tex](\frac{5}{2})[/tex]x = [tex]\frac{2}{5}[/tex][tex](\frac{5}{1})[/tex]

x = 2

     To prove this, we need to show that 2 is equal to x.

     Given:

2(x + 5) - 3x = 7x - 6

     Distribute:

2x + 10 - 3x = 7x - 6

     Combine like terms:

-1x + 10 = 7x - 6

     Add 1x to both sides of the equation:

10 = 8x - 6

     Add 6 to both sides of the equation:

16 = 8x

     Divide both sides of the equation by 8:

2 = x

     Reflexive property:

x = 2

       ✓

2(x + 5) - 3x = 7x - 6

x = 2

Answer:

D

Step-by-step explanation:

the sum of the 3 angles in Δ DEF = 180° , that is

∠ D + 90° + 35° = 180°

∠ D + 125° = 180° ( subtract 125° from both sides )

∠ D = 55°

------------------------

using the tangent and cosine ratios in the right triangle

tan35° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{DE}{EF}[/tex] = [tex]\frac{DE}{12}[/tex] ( multiply both sides by 12 )

12 × tan35° = DE , then

DE ≈ 8.40 ( to 2 dec. places )

--------------------------

cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{EF}{DF}[/tex] = [tex]\frac{12}{DF}[/tex] ( multiply both sides by DF )

DF × cos35° = 12 ( divide both sides by cos35° )

DF = [tex]\frac{12}{cos35}[/tex] ≈ 14.65 ( to 2 dec. places )

Answer:

3(2(4)(3)(2.8))

3(24(2.8))

3(67.2)

2016