Complete the following statements to prove that ∠IKL and ∠JLD are supplementary angles.

It is given that ∠EIJ ≅ ∠GJI.

Also, ∠EIJ ≅ ∠IKL and ∠GJI ≅ ∠JLK, as they are corresponding angles for parallel lines cut by a transversal.

By the definition of congruent angles, m∠EIJ = m∠GJI, m∠EIJ = m∠IKL, and m∠GJI = m∠JLK.

So, m∠IKL = m∠JLK by the
.

Angle JLK and ∠JLD are supplementary angles by the
, so m∠JLK + m∠JLD = 180°.

By the
, m∠IKL + m∠JLD = 180°.

Therefore, ∠IKL and ∠JLD are supplementary angles by definition.

The Product of 1 5/8, 2, and 3/5 is equal to 39/20, which is simplified completely. The answer is 39/20.

To find the product and simplify completely, you need to perform multiplication and simplify the resulting fraction. Here, we are multiplying the following fractions and mixed numbers:1, 5/8, 2, and 3/5.The first step is to convert the mixed numbers into improper fractions.

We do that by multiplying the whole number by the denominator, and then adding the numerator.For 1 5/8, we get:$$1 \frac{5}{8} = \frac{8}{8} \times 1 + \frac{5}{8} = \frac{13}{8}$$For 2, we get:$$2 = \frac{2}{1} = 2 \times \frac{1}{1} = \frac{2}{1}$$For 3/5, we leave it as is since it's already a fraction.

Now that we have all the numbers as fractions, we can multiply them:$$\frac{13}{8} \times \frac{2}{1} \times \frac{3}{5} = \frac{13 \times 2 \times 3}{8 \times 1 \times 5} = \frac{78}{40}$$

To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 2:$$\frac{78}{40} = \frac{2 \times 39}{2 \times 20} = \frac{39}{20}$$

Therefore, the product of 1 5/8, 2, and 3/5 is equal to 39/20, which is simplified completely. The answer is 39/20.

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The pressure in the can become triple the original value. Option B is correct.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,
From the ideal gas equation, we know that,
pressure is directly proportional to the temperature,
So,
P₁ / P₂ = T₁ / T₂
Where,
P₁ and T₁ are the initial pressure and temperature,
P₂ and T₂ are the final pressure and temperature.

Substitute the values,
P₁ / P₂ = 300 / 900
P₂ = 3P₁

Thus, the pressure in the can become triple the original value. Option B is correct.

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Answer:

X=9

Step-by-step explanation:

10x-30 = 7x-3

10x-7x = -3 + 30

3x = 27

x=9

Answer:

y=1/7x

Step-by-step explanation:

55-48= 7, 2-1=1, 1/7= slope

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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Using a calculator, the value of  csc (203°) is -1.086

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Since csc (203°) = 1/[sin (203°)]

Press 1/ [sin (203°)] and then the equal to button on your calculator. We have:

1/[sin (203°)] = -1.086

Note: If you calculator have "cosec" or "csc" button, you can simply press cosec (203°) or csc (203°) to get the answer.

Thus, the value of  csc (203°) is -1.086

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Answer:

4.5 lb

Step-by-step explanation:

1.5*3 is 4.5

Answer:

x = 65

Step-by-step explanation:

let the number be 'x'.

If 86 is added to a number, the result is 44 less than three times the number. Therefore the equation will be,

=> 86 + x = 3x - 44

Rearranging,

=> x - 3x = -44 - 86

=> -2x = -130

=> x = 130/2

=> x = 65

Answer:

A straight angle changes the direction you are pointing in. A straight angle looks like a straight line. It has an angle measurement of 180 degrees. Straight angles can be composed of several angles, as long as the angles add up to 180 degrees.

Step-by-step explanation:

Answer: Angles on a straight line add up to 180°.

Step-by-step explanation:

Answer:

f(x)=(x+2)(x-7)(x-5)(x-5)

Step-by-step explanation:

With the use of the roots and leading coefficient, you can easily write out the polynomial as I have above.

Answer:

f(x)= (x-7)(x-5)(x-5)((x+2)

Step-by-step explanation:

Edge answer D

Answer a=3f+g/b+x

Step-by-step explanation:

Let's solve for a.

a(x+b)=g+3f

Step 1: Factor out variable a.

a(b+x)=3f+g

Step 2: Divide both sides by b+x.

a(b+x)/b+x=3f+g/b+x

a=3f+g/b+x

The line segment FG represent the volume of water decreases in Katherine's water bottle.

From the given graph, x-axis represents the distance from home (km) and the y-axis represents the volume (L).

The line segment FG represent the volume of water decreases in Katherine's water bottle, the line segment HI represent the volume of water increases in Katherine's water bottle and the line segment KL represents there is no change in water level.

Therefore, the line segment FG represent the volume of water decreases in Katherine's water bottle.

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The three individual terms are:

Let's write the factors,

The common factors are >>>

2 and x

So,

Answer:

b = 4

Step-by-step explanation:

you must divide both sides of the equation by -5 to get b by itself. division cancels out multiplication but also keeps both sides equal

b = -20/-5

b = 4

Answer:

y=3/4x-3/2

Step-by-step explanation:

the equation right now is in standard form (ax+by=c)

Slope intercept form is y=mx+b

3x-4y=6

subtract 3x on both sides

-4y=-3x+6

divide by -4

y=3/4x-6/4

simplify

y=3/4x-3/2

hope this helps :)

Answer:

5m, 606cm, 88m, 499dm, 322km

Step-by-step explanation:

Let's convert everything to meters.

606 cm = 6.06 meters.

88 m = 88 meters.

322 km = 322000 meters.

5 m = 5 meters.

499 dm = 49900 meters.

Thus, in increasing order we have: 5m, 606cm, 88m, 499dm, 322km.

Let me know if this helps!

Answer:  $4,000

Step-by-step explanation:

If the total earnings were $40,000 and the base pay was $10,000, then the commission earned would be $40,000 - $10,000 = $30,000.

Since the commission rate is 40%, we can set up the equation:

40% x Total Sales = Commission Earned

We know that the commission earned is $30,000, and we also know that 15 cars were sold. Therefore, we can solve for the average price of each car:

40% x Total Sales = Commission Earned

40% x (15 x Price per Car) = $30,000

6 x Price per Car = $30,000

Price per Car = $5,000

However, this is just the average price per car. Since the commission is based on the total sales, we need to calculate the actual commission earned on each car:

Commission per Car = 40% x Price per Car

Commission per Car = 40% x $5,000

Commission per Car = $2,000

Therefore, the total earnings of $40,000 divided by the number of cars sold (15) gives the amount earned per car:

Amount earned per Car = Total Earnings / Number of Cars Sold

Amount earned per Car = $40,000 / 15

Amount earned per Car = $4,000

The domain of the function f(x) that has a range of [-2, ∞) is [-2, ∞)

The inverse of a function that maps x into y, maps y into x.

The given coordinates of the points on the radical function, f(x) are; (-3, -2), (1, 0), (6, 1)

To determine the domain of

\( {f}^{ - 1}( x)\)

The graph of the inverse of a function is given by the reflection of the graph of the function across the line y = x

The reflection of the point (x, y) across the line y = x, gives the point (y, x)

The points on the graph of the inverse of the function, f(x), \( {f}^{ - 1} (x)\) are therefore;

\(( - 3, \: - 2) \: \underrightarrow{R_{(y=x)}} \: ( - 2, \: - 3)\)

\(( 1, \: 0) \: \underrightarrow{R_{(y=x)}} \: ( 0, \: 1)\)

( 6, \: 1) \: \underrightarrow{R_{(y=x)}} \: ( 1, \: 6)

The coordinates of the points on the graph of the inverse of the function, f(x) are; (-2, -3), (1, 0), (1, 6)

Given that the coordinate of point (x, y) on the image of the inverse function is (y, x), and that the graph of the function, f(x) starts at the point (-3, -2) and is increasing to infinity, (∞, ∞), such that the range of y–values is [-2, ∞) the inverse function, \( {f}^{ - 1}( x)\), which starts at the point (-2, -3) continues to infinity, has a domain that is the same as the range of f(x), which gives;

The domain of the inverse of the function, \( {f}^{ - 1}( x)\), using interval notation is; [-2, ∞)

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If lines m and n are parallel, then the value of x must be 4.

If lines m and n are parallel, then the measures of the angles in the correspondent quadrants must be the same ones.

Here we can see that the two angles are in the third quadrant, thus, these angles have the same measure. Then we can write this as:

6x² = 96

Now we can solve this for x, we will get:

x² = 96/6

x² = 16

x = √16

x = 4

That is the value of 4.

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Answer:

It's 457152.

Step-by-step explanation:

 4762

x    96

Lay it out like this. Then begin muliplying the bottom right number (6) by each top number. Then once finished, add a 0 below your answer. Then multiply the bottom left number (9) by each top number again. Once that's all finished, add those two answers.

Answer:

Step-by-step explanation:

p = .3

n = 150

p(bar ) = 1 - p = .7

\(\sigma_p=\sqrt\frac{p(1-p) }{n} }\)

\(\sigma_p=\sqrt\frac{.3(1-.3) }{150} }\)

=.037

b )

P ( .2 <p<.4 ) = P [ (.2 - .3) / .037 < z < ( .4 - .3 ) / .037 ]

= P [ (-2.7  < z < +2.7 ]

= .9965-.0035

= .993

c )

P ( .25 <p<.35 ) = P [ (.25 - .3) / .037 < z < ( .35 - .3 ) / .037 ]

= P [ (-1.35  < z < +1.35 ]

= .9115 - .0885

= .823

Answer:

20%

Step-by-step explanation:

100/20 (the number of questions) = 5 (how much each question is worth)

16(the number of questions she got correct) times 5 is 80

She got 80 percent correct

That means that she missed 20 percent

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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Answer:

it's b

Step-by-step explanation:

literally twelve minus m

Answer:

B

Step-by-step explanation:

12 minus m is, 12 - m

Answer:

40 miles

Step-by-step explanation:

100 - 60 = 40. 40%

60 ÷ 30 = 2. 2 miles = 10%

10 * 4 = 40

The taxi can travel a maximum distance of 11 miles if we have at most $10 to spend on the cab ride.

What is distance?

The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line.

The formula for measuring distance between two lines, the total length of all a polygon's sides, the perimeter of a polygon on a coordinate plane, the area of a polygon, and many other things are all found in analytical geometry. For instance, we can use the distance formula to find the lengths of a triangle's sides and decide if it is scalene, isosceles, or equilateral.

It is given that, a taxi charges a flat rate of $1.75 plus an additional fee of $0.75 per mile.

We have to find the maximum distance it could travel at most with $10

Let the maximum distance be x miles.

Thus, the fare would be

$(1.75 + 0.75x) = 10

⇒ 0.75x = 8.25

⇒ x = 8.25/0.75

⇒ x = 11

The taxi can travel a maximum distance of 11 miles if we have at most $10 to spend on the cab ride.

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In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.

1. Begin with the equation 0.2 = 0.

2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.

  This simplifies to 0 = -0.2.

3. Observe that the right side of the equation, -0.2, is a negative number.

4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.

5. Rewrite the equation as 0 = +0.2.

6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.

7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.

8. Simplify the equation to 0 = +0.2.

9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.

10. As a result, the original equation 0.2 = 0 is invalid.

11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.

12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.

To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.

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