Given: l || m; ∠1 ∠3

Prove: p || q

Horizontal and parallel lines l and m are intersected by parallel lines p and q. At the intersection of lines l and p, the uppercase left angle is angle 1. At the intersection of lines q and l, the bottom right angle is angle 2. At the intersection of lines q and m, the uppercase left angle is angle 3.

Complete the missing parts of the paragraph proof.



We know that angle 1 is congruent to angle 3 and that line l is parallel to line m because
. We see that is congruent to by the alternate interior angles theorem. Therefore, angle 1 is congruent to angle 2 by the transitive property. So, we can conclude that lines p and q are parallel by the

.

The regular price of the camera is $227.

Given that, the total amount paid=$201.75 and the cost of the memory card=$12.35.

Cost of camera=201.75-12.35=$189.4

A discount is a deduction from the usual price of something. To discount means to deduct an amount from the price.

Discount is given to the camera=20%.

The regular price of the camera=189.4+20% of 189.4

=189.4+0.2×189.4=189.4+37.88=$227.28

The estimation to the nearest the whole number is $227.

Therefore, the regular price of the camera is $227.

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answer

yes do it your self

The simplified expression using  the commutative property is : [tex]\frac{6}{3}[/tex] + [tex]\frac{3}{4}[/tex]

commutative property can be defined as a mathematics attribute that is possessed by a mathematical equation, that enables the objects undergoing addition or multiplication to change position.

In conclusion, The simplified expression using  the commutative property is : [tex]\frac{6}{3}[/tex] + [tex]\frac{3}{4}[/tex]

4/3 + 3/4 + 2/3 =  ( [tex]\frac{4}{3}[/tex] +  [tex]\frac{2}{3}[/tex] ) +  [tex]\frac{3}{4}[/tex]  =   [tex]\frac{6}{3}[/tex] + [tex]\frac{3}{4}[/tex]

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Step-by-step explanation:

calculated the cost of numbers of units usex

Step-by-step explanation:

[tex] = 49[/tex]

[tex] = 7 \times 7[/tex]

[tex] = {7}^{1 + 1} [/tex]

[tex] = {7}^{2} [/tex]

Answer:

(x-2)(4x³+8x²+15x+18)

The area of the water well is [tex]4\pi r^2[/tex]

The radius is given as:

Radius, R = 2r

The area of the water well is calculated using:

[tex]A = \pi R^2[/tex]

This gives

[tex]A = \pi (2r)^2\\\\\\[/tex]

Evaluate the expression

[tex]A = 4\pi r^2[/tex]

Hence, the area of the water well is [tex]4\pi r^2[/tex]

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The height of the target is 29 feet.

The correct option is (D)

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The given table path of the thrown ball,

where x represents the horizontal distance and f(x) represents the height of the ball.

Now,

when x = 1.25 feet horizontally, the height will be maximum.

also, the height of the ball at  distance x = 1.25 feet is

f(1.25) = 29 feet.

Hence, height of the target is 29 feet.

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Answer:

D. 29 feet

Step-by-step explanation:

Answer:

£60

Step-by-step explanation:

70% of original price = £42

100% of original price = £42 * 10/7 = £6 * 10 = £60

Answer:

D

Step-by-step explanation:

the diagonals of a parallelogram bisect each other , then

2 AE = AC ( substitute values )

2(2x - 5) = 22 ( divide both sides by 2 )

2x - 5 = 11 ( add 5 to both sides )

2x = 16 ( divide both sides by 2 )

x = 8

Answer:

  13

Step-by-step explanation:

Perhaps the most straightforward way to find the value of the given function is to first solve the equations for x and y. The results can be substituted into your expression to find the value you want.

__

We notice the y-coefficients are opposites, so we can eliminate the y-variable by adding the equations.

  (2x -y) +(x +y) = (3) +(1)

  3x = 4 . . . . . . simplify

  x = 4/3 . . . . . divide by 3

The value of y can be found from the second equation:

  4/3 +y = 1 . . . . substitute for x

  y = -1/3 . . . . . . subtract 4/3

The value of 8x-7y is found by substituting the x- and y-values into this expression:

  8(4/3) -7(-1/3) = 32/3 +7/3 = 39/3 = 13

The value of 8x-7y is 13.

_____

Additional comment

You can also work out what combination of the two equations will give 8x -7y. That turns out to be 5 times the first minus 2 times the second:

  5(2x -y) -2(x +y) = 5(3) -2(1)

  10x -5y -2x -2y = 15 -2

  8x -7y = 13

__

The coefficients 5 and -2 are found by solving the system of equations ...

  a(2x -y) +b(x +y) ≡ 8x -7y   ⇒   {2a +b = 8, -a +b = -7}

Answer:

D

Step-by-step explanation:

Because.............

Answer:

B.

Step-by-step explanation:

Since all bulbs are connected in series, by opening switch A, you break the series connection, and all bulbs go out.

Step-by-step explanation:

square root 3 divided by

2

The confidence interval is  0.028, 0.872

862 of 1013 randomly selected adults  wear seat belts.

The 95% confidence interval for the proportion of adults who always wear seat belts.

A Confidence Interval is defined as a range of values we are sure our true value lies within it.

A 95% confidence interval is defined as that if we take 100 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value.

= 862/1013 = 0.85

At a 95% confidence interval ,the critical value is [tex]z_{0.025} = 1.96[/tex]

The 95% confidence interval for proportion is

[tex]\widehat p +/- z0.025 * sqrt(\widehat p * (1 - \widehat p)/n)[/tex]

[tex]= 0.85 +/- 1.96 * sqrt(0.85 * (1 - 0.85)/1013)[/tex]

[tex]= 0.85 +/- 0.022[/tex]

= 0.028, 0.872

The sample should use at least 10 successes and 10 failures.

[tex]n * \widehat p = 1013 * 0.85 = 861 > 10[/tex]

[tex]n * (1 - \widehat p) = 1013 * 0.15 = 152 > 10[/tex]

As the sample size is larger, we can use an approximate formula for the standard error.

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The simple interest rate is 9% if the Tk 13000 will be Tk 18850 as profit-principal in 5 years.

It is defined as the interest on based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount of borrowed amount.

We have given:

The principal amount, P = Tk 13000

Final amount A = Tk 18850

Number of years n = 5 years

Rate = r

I = A - P

I = 18850 - 13000 = Tk 5850

I = Pnr

5850 = 13000(5)(r)

r = 0.09

r = 9%

Thus, the simple interest rate is 9% if the Tk 13000 will be Tk 18850 as profit-principal in 5 years.

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Distribute

Add the numbers

Combine like terms

Distribute

3(x + 2) - 9x +5

3x + 6 - 9x + 5

Add the numbers

3x + 6 - 9x + 5

3x + 11 - 9x

Combine like terms

3x + 11 - 9x

6x + 11

Answer:

-104

Step-by-step explanation:

1) Substitute 50 into n.

-2(50) - 4

-100 - 4

-104

Step-by-step explanation:

[tex] = 0,43[/tex]

[tex] = \frac{0,43}{1} [/tex]

[tex] = \frac{0,43}{1} \times \frac{100}{100} [/tex]

[tex] = \frac{43}{100} [/tex]

Answer:

2⁶

Step-by-step explanation:

law of indices states multiplication of powers in and out of bracket 3×2=6

[tex]\text{Let's work out:: 2 to the power of 3 to the power of 2 }\\\text{We can start by raising 2 to the power of 3:: 2*2*2=8, then raising that}\\\text{to the power of 2:: 8*8=64}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\text{The value is 64}[/tex]

The table that matches the equation is:

Time    Calories

-20          -110

-10          -55

-15         - 82.50

-5            -27.50

The correct table would contain values that are multiples of 5.5t

For example:

Total calories burned at 20 seconds : 5.5 x 20 = 110

Total calories burned at 10 seconds : 5.5 x 10 = 55

Total calories burned at 15 seconds : 5.5 x 15 = 82.50

Total calories burned at 5 seconds : 5.5 x 5 = 27.50

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Answer:

The 2nd one

Step-by-step explanation:

its the right one

Answer:

The equation of the graph is   y = -lx - 4l - 1.

Step-by-step explanation:

As the values of y are same before and after (4, -1)

the slope of the graph is change on point (4, -1)

the equation of first line is

y - (-1) = 1 (x -4)

the equation of the second line is:

y - (-1) = -1 (x - 4)

As value of y should remain same in both equations

therefore: y - (-1) = - lx - 4l

y = - lx - 4l -1

The equation of the graph is   y = -lx - 4l - 1.

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Answer:

y= 1/4 x-62+1

Step-by-step explanation:

Answer:

If 11 people use all three facilities, this means:

22 − 11 or 11 are using the gym and the pool but no the track,

29 − 11 or 18 are using the pool and the track but no the gym,

25 − 11 or 14 are using the gym and the track but no the pool.

How many people use the gym only?

130 − (14 + 11 + 11) = 94

How many people use the pool only?

62 − (18 + 11 + 11) = 22

How many people use the track only?

58 − (14 + 11 + 18) = 15

How many people go in for sports?

94 + 22 + 15 + 11 + 14 + 18 + 11 = 185

How many people use exactly one of the facilities?

94 + 22 + 15 = 131

What is the probability that the person uses exactly one of the facilities?

= 131/185 ≈ 0.7081

Step-by-step explanation:

its a bit confusing

Hope It Helps !!!!

Answer:

x(3√6)

Step-by-step explanation:

Radicals:

  Take out a variable or number for every pair of the variable or number  inside the radicals

        [tex]\sf 3\sqrt{6x^2}=3*\sqrt{6*x*x}\\\\[/tex]

                   [tex]\sf = 3x \sqrt{6}[/tex]

The 90% confidence interval for the population mean is 78.1905<x<81.8095

The formula for calculating the confidence interval is expressed as:

CI = x ± z*s/√n

Given the following parameters

mean "x" = 80

z = 1.645

s = 5.5

n = 25

Substitute

CI = 80 ± 1.645*5.5/√25

CI = 80 ± 1.8095

CI = {78.1905, 81.8095}

Hence the 90% confidence interval for the population mean is 78.1905<x<81.8095

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Answer:

30

Step-by-step explanation:

Step-by-step explanation:

[tex] {x}^{2} - 14x - 25 {y}^{2} + 100y = 76[/tex]

Factor by grouping,

[tex]( {x}^{2} - 14x) - (25 {y}^{2} - 100y) = 76[/tex]

Complete the square, with the x variables,

[tex]( {x}^{2} - 14x + 49) - (25 {y}^{2} - 100y) = 125[/tex]

Factor out 25 for the y variables

[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y) = 125[/tex]

Complete the square

[tex]( {x}^{2} - 14x + 49) - 25( {y}^{2} - 4y + 4) = 25[/tex]

Simplify the perfect square trinomial

[tex](x - 7) {}^{2} - 25(y - 2) {}^{2} = 25[/tex]

Make the right side be 1 so divide everything by 25.

[tex] \frac{(x - 7) {}^{2} }{25} - (y - 2) {}^{2} = 1[/tex]

Here our center is (7,2).

Answer:

4J = 52

Step-by-step explanation:

If Jenny's height is J:

4J = 52

Answer:

D, C

Step-by-step explanation:

for part a, there is a negative slope with the graph shifted two units upwards

for part b, if you plug in C, you get an answer that works

Answer:

27

Step-by-step explanation:

i promise :)

Answer:

27π units^2

Step-by-step explanation: