If the measure of angle 1 is 78 degrees and the measure of angle 3 is (5x-2)degrees, what is the value of x ?

The lines are skew

To make things clearer, rewrite the given lines as follows;

[tex]L_1 : \frac{x}{1} = \frac{y-1}{-1} = \frac{z-2}{3}[/tex]

[tex]L_2 : \frac{x-2}{2} = \frac{y-3}{-2} = \frac{z}{7}[/tex]

(i) Test if the lines are parallel.

Two lines are parallel if the cross product of their directional vectors is equal to the zero vector 0 (which is equal to <0, 0, 0>). For example, if their directional vectors are m and n, then;

m x n = 0

Where;

m, n and 0 are vectors

In the given lines, L₁ and L₂, their directional vectors are given by the denominators of their symmetric equation.

For L₁, the directional vector = <1, -1, 3>

For L₂, the directional vector = <2, -2, 7>

Let

m = <1, -1, 3> =  i - j + 3k

n = <2, -2, 7> = 2i - 2j + 7k

Now, find the cross product of the vectors;

m x n   =   |  i        j        k |

              |  1       -1       3 |

              |  2      -2      7 |

m x n   =  i(-7 + 6) -j(7 - 6) + k(-2 + 2)

m x n   =  i(-1) -j(1) + k(0)

m x n   =  -i -j + 0k

Since the cross product does not give a zero vector, then the lines are not parallel.

(ii) Test if the lines intersect

To do this:

(a) First, we express the lines in parametric form rather than the symmetric form. Therefore

[tex]L_1 : \frac{x}{1} = \frac{y-1}{-1} = \frac{z-2}{3}[/tex]  is equated to say a;

   and

[tex]L_2 : \frac{x-2}{2} = \frac{y-3}{-2} = \frac{z}{7}[/tex] is equated to say b;

We have;

[tex]L_1 : \frac{x}{1} = \frac{y-1}{-1} = \frac{z-2}{3} = a[/tex]

[tex]L_2 : \frac{x-2}{2} = \frac{y-3}{-2} = \frac{z}{7} = b[/tex]

Split the lines into system of three equations in terms of a and b

For L₁

=> [tex]\frac{x}{1}[/tex] = a  which gives x = a

=> [tex]\frac{y-1}{-1}[/tex] = a which gives y = 1 - a

=> [tex]\frac{z-2}{3}[/tex] = a which gives z  = 3a + 2

∴ L₁ has these three equations

x = a                           -------------------------(i)

y = 1 - a                      --------------------------(ii)

z = 3a + 2                  --------------------------(iii)

For L₂

=> [tex]\frac{x-2}{2}[/tex] = b which gives x = 2b + 2

=> [tex]\frac{y-3}{-2}[/tex] = b which gives y = 3 - 2b

=> [tex]\frac{z}{7}[/tex] = b which gives z = 7b

∴ L₂ has these three equations

x = 2b + 2                        --------------(iv)

y = 3 - 2b                         ---------------(v)

z = 7b                              ----------------(vi)

(b) Secondly, we combine the set of equations of the two lines.

Equations of x : (i) and (iv)

a = 2b + 2                  

=> a - 2b = 2                   --------------------------------------(vii)

Equations of y: (ii) and (v)

1 - a = 3 - 2b

=> - a + 2b = 2               --------------------------------------(viii)

Equations of z: (iii) and (vi)

3a + 2 = 7b

=> 3a - 7b = -2               -------------------------------------(ix)

(c) Thirdly, solve equations (vii), (viii) and (ix) simultaneously to find the values of a and b

Add equations (vii) and (viii)

    a - 2b = 2

+

   -a + 2b = 2  

   0  +  0  = 4    

Since 0 + 0 ≠ 4, then the values of s and t cannot be determined from the system of equations due to inconsistency. Therefore, the lines L₁ and L₂ do not intersect.

(iii) Test if the lines are skew

Two lines are said to be skew if they are neither parallel nor intersecting.

Since the lines L₁ and L₂ are neither parallel nor intersecting, the lines are skew.

Answer:

[tex]9x - 10y = - 34 - - - (a) \\ 3x - 4y = - 16 - - - (b) \\ (a) - 3 \times (b) : \\ 0x + 2y = 14 \\ y = 7 \\ 3x - (4 \times 7) = - 16 \\ 3x = 12 \\ x = 4[/tex]

answer: ( 4, 7 )

Hi there!  

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I believe your answer is:  

(4,7)

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Here’s why:  

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Hope this helps you. I apologize if it’s incorrect.  

Answer

1. 4am to 6am and 12 midnight

2. 8am and 10 pm

3. 12 noon and 6pm

4. 10 am 8 pm

5. 2pm

6. 1pm and 4pm

7. 2pm (22C)

8. 4am to 6am and 12 midnight (10 C)

9. 8 am to 1 pm

You need to find the temperature on the y axis, then move right in the same line, and when the line touches the line graph, turn 90 degrees down. Then you get the time.

Please give brainliest if it helps

Answer:

c + (C+2) = 12

Step-by-step explanation:

Assume C is the no of dimes

So there are C+2 no of nickels

Guven that C + (C+ 2) = 12

Answer:

AE=4

EC=4

BF=2.24

FD=2.24

Step-by-step explanation:

here we go honey  

Answer:

0

Step-by-step explanation:

=>sec A cosec A - tan A - cot A

=>(1/sinAcosA)-(sinA/cosA)-(cosA/sinA)

You get the LCM as sinAcosA then it becomes

=>(1-sin^2(A)-cos^2(A)) /sinAcosA [1-sin^2(A)=cos^2(A)]

=>(cos^2(A)-cos^2(A))/sinAcosA

=>0/sinAcosA

=>0

Answer:

the answer is d trust me 0.22

Step-by-step explanation:

Answer:

125

Step-by-step explanation:

Sum of Exterior Angles must add to 360 so

[tex]60 + 70 + 40 + 65 + x = 360[/tex]

[tex]235 + x = 360[/tex]

[tex]x = 125[/tex]

Answer:

B

Step-by-step explanation:

If you do 640/75 that equals 8.5333 etc. That is between 8 and 9!

Hope that helps!

Answer:

25% of 6430 is 1607.5

Step-by-step explanation:

A line with the specific numbers plotted on it, numerical order

Answer:

1- Put the letter A on positive 7

2- Put the letter B on positive 5

3- Put the letter C on 0

4- Put the letter D on negative 4

5- Put the letter E on negative 9

Given equations;

y₁ = 3x - 8               -------------------(i)

y₂ = 0.5x + 7          --------------------(ii)

To fill the table, substitute the values of x into equations (i) and (ii)

=> At x = 0

y₁ = 3(0) - 8 = -8

y₂ = 0.5(0) + 7 = 7

=> At x = 1

y₁ = 3(1) - 8 = -5

y₂ = 0.5(1) + 7 = 7.5

=> At x = 2

y₁ = 3(2) - 8 = -2

y₂ = 0.5(2) + 7 = 8

=> At x = 3

y₁ = 3(3) - 8 = 1

y₂ = 0.5(3) + 7 = 8.5

=> At x = 4

y₁ = 3(4) - 8 = 4

y₂ = 0.5(4) + 7 = 9

=> At x = 5

y₁ = 3(5) - 8 = 7

y₂ = 0.5(5) + 7 = 9.5

=> At x = 6

y₁ = 3(6) - 8 = 10

y₂ = 0.5(6) + 7 = 10

=> At x = 7

y₁ = 3(7) - 8 = 13

y₂ = 0.5(7) + 7 = 10.5

=> At x = 8

y₁ = 3(8) - 8 = 16

y₂ = 0.5(8) + 7 = 11

=> At x = 9

y₁ = 3(9) - 8 = 19

y₂ = 0.5(9) + 7 = 11.5

=> At x = 10

y₁ = 3(10) - 8 = 22

y₂ = 0.5(10) + 7 = 12

The complete table is attached to this response.

(ii) To find the solution of the system of equations using the table, we find the value of x for which y₁ and y₂ are the same.

As shown in the table, that value of x = 6. At this value of x, the values of y₁ and y₂ are both 10.

Answer:

The minimum percentage of stores that sell a gallon of milk for between $3.65 and $4.17 is of 75%.

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

In this question:

We have a mean of $3.91 and a standard deviation of $0.13.

Using Chebyshev's Theorem, what is the minimum percentage of stores that sell a gallon of milk for between $3.65 and $4.17?

3.65 = 3.91 - 2*0.13

4.17 = 3.91 + 2*0.13

Within 2 standard deviations of the mean, so, by the Chebyshev's Theorem, the minimum percentage of stores that sell a gallon of milk for between $3.65 and $4.17 is of 75%.

Given:

Three coins are tossed.

Let the event H represents all Heads and the event K represents at least one Heads.

To find:

a. The probability that the outcome is all heads if at least one coin shows a heads.

b. P(K) = ?

c. P(H∩K) = ?

Solution:

If three coins are tossed, then the total possible outcomes are:

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Total outcomes = 8

Possible outcomes for all Heads = 1

Possible outcomes for at least one Heads = 7

Let the following events:

H = all Heads

K = at least one Heads.

Then,

[tex]H=\{HHH\}[/tex]

[tex]K=\{HHH, HHT, HTH, HTT, THH, THT, TTH\}[/tex]

[tex]H\cap K=\{HHH\}[/tex]

Now,

[tex]P(K)=\dfrac{7}{8}[/tex]

[tex]P(H\cap K)=\dfrac{1}{8}[/tex]

a. The probability that the outcome is all heads if at least one coin shows a heads is:

[tex]P(H|K)=\dfrac{P(H\cap K)}{P(K)}[/tex]

[tex]P(H|K)=\dfrac{\dfrac{1}{8}}{\dfrac{7}{8}}[/tex]

[tex]P(H|K)=\dfrac{1}{7}[/tex]

Therefore, the probability that the outcome is all heads if at least one coin shows a heads is [tex]\dfrac{1}{7}[/tex].

b. [tex]P(K)=\dfrac{7}{8}[/tex]

c. [tex]P(H\cap K)=\dfrac{1}{8}[/tex]

Answer:

[tex]\begin{array}{ccc}{Midpoint} & {Class} & {Frequency} & { 64.5} & {64-65} & {4} & {66.5 } & {66-67} & {4} & {68.5 } & {68-69} & {4} &{70.5 } & {70-71} & {5} & {72.5 } & {72-73} & {10} & {74.5 } & {74-75} & {4}\ \end{array}[/tex]

Using the frequency distribution, I found the mean height to be 70.1129 with a standard deviation of 3.2831

Step-by-step explanation:

Given

[tex]\begin{array}{ccc}{Midpoint} & {Class} & {Frequency} & { } & {64-65} & {4} & { } & {66-67} & {4} & { } & {68-69} & {4} &{ } & {70-71} & {5} & { } & {72-73} & {10} & { } & {74-75} & {4}\ \end{array}[/tex]

Solving (a): Fill the midpoint of each class.

Midpoint (M) is calculated as:

[tex]M = \frac{1}{2}(Lower + Upper)[/tex]

Where

[tex]Lower \to[/tex] Lower class interval

[tex]Upper \to[/tex] Upper class interval

So, we have:

Class 64-65:

[tex]M = \frac{1}{2}(64 + 65) = 64.5[/tex]

Class 66 - 67:

[tex]M = \frac{1}{2}(66 + 67) = 66.5[/tex]

When the computation is completed, the frequency distribution will be:

[tex]\begin{array}{ccc}{Midpoint} & {Class} & {Frequency} & { 64.5} & {64-65} & {4} & {66.5 } & {66-67} & {4} & {68.5 } & {68-69} & {4} &{70.5 } & {70-71} & {5} & {72.5 } & {72-73} & {10} & {74.5 } & {74-75} & {4}\ \end{array}[/tex]

Solving (b): Mean and standard deviation using 1-VarStats

Using 1-VarStats, the solution is:

[tex]\bar x = 70.1129[/tex]

[tex]\sigma = 3.2831[/tex]

See attachment for result of 1-VarStats

Solving (c): Compare the calculated mean to the actual mean

The actual mean is missing from the question, so I will make assumptions in this part

Assume they are close

This means that the selected sample is a reflection of the actual population where the samples are selected.

Assume they are not close

This means that the selected sample does not reflect the actual population where the samples are selected.

Answer:

7480 hours

Step-by-step explanation:

440 - 100 = 340

LCM of 440 and 340

440 = 2 × 2 × 2 × 5 × 11

340 = 2 × 2 × 5 × 17

LCM = 2 × 2 × 2 × 5 × 11 × 17

LCM = 7480

Answer:

-3

Step-by-step explanation:

change in y over the change in x

pick to points and use slope formula

9-3

0-2

that's 6/-2 = -3

Answer:

length = 22

Width = 17

Step-by-step explanation:

78 = 2(w+5) + 2(w)

78 = 2w + 10 + 2w

78 = 4w + 10

68 = 4w

w = 17

l = 17 + 5 = 22

Answer:

it will have 2be 408,99 cent plan so tht u can be able 2 speak the whole month

Answer:

none Geometric mean cannot be calculated for negative values

Step-by-step explanation:

Answer:

10.A

11.A

12.A

Step-by-step explanation:

thank me later

Answer:

3/4

Step-by-step explanation:

f(x)=3•2^x

Let x = -2

f(-2)=3•2^-2

Exponents first  ( We know a^-b = 1/ a^b)

f(-2)=3• 1/2^2

     =3 * 1/4

     = 3/4

Answer: $108.60

Step-by-step explanation:

Initial cost: $95.50

Tip is an additional cost. They want to give a tip of 20%, so they will give additional 20% of the initial cost.

$90.50 + (90.50 * 0.2)

= $90.50 + $18.10

= $108.60

Answer:

[tex]P(Yellow) = \frac{29}{147}[/tex]

Step-by-step explanation:

Given

[tex]Brown = 27\\Purple = 47\\Yellow = 29\\Green = 44[/tex]

Required

[tex]P(Yellow)[/tex] --- next roll to be yellow

This is calculated as:

[tex]P(Yellow) = \frac{Yellow}{Total}[/tex]

So, we have:

[tex]P(Yellow) = \frac{29}{27 + 47 + 29 + 44}[/tex]

[tex]P(Yellow) = \frac{29}{147}[/tex]

Answer:

6 1/6

Step-by-step explanation:

Divide the numerator (19) by the denominator (6)

Write down the whole number result which in this case would be 3

Use the remainder as the new numerator over the denominator. This is the fraction part of the mixed number. which in this case is 1/6

therefore the answer is 6 1/6

Answer:

I think the answer is 200cm^2

Step-by-step explanation:

since the square is divided into eight equal parts

and one shaded part is =25cm^2

multiply the area of the shaded part by the number of equal parts

= 25cm^2 ×8

= 200cm^2

Answer:

first and third option are correct.

Step-by-step explanation:

6(x+3)

=6*x + 6*3

=6x + 18