Find the measure of z

A. 108
B. 120
C. 135
D. 144

To find a coterminal angle with 153°, we can either add 360° to get 513° or subtract 360° to get -207°, both of which have the same terminal side as 153°.

To find an angle that is coterminal with 153°, we add or subtract multiples of 360° to the original angle. Adding 360° to 153° gives us 513° as one such coterminal angle. Subtracting 360° from 153° provides us with -207° as another coterminal angle. Both of these angles have the same terminal side position as 153° when plotted in standard position on a coordinate system.

Jeff has used 11,000 gallons of water. We find this by subtracting the base charge from the total bill and dividing it by the cost per 1000 gallons.

The water bill that Jeff receives is made up of a base charge of $12.00, plus an additional charge of $1.50 for each 1000 gallons of water used. From the given information, we know that Jeff's bill came to $28.50. To find out how much water Jeff used, we first need to subtract the base charge from the total bill which gives us $16.50. Now we divide this number by the cost per 1000 gallons, which is  $1.50. Therefore, we can say that Jeff used 16.50 ÷ 1.50 = 11 units of water. Since 1 unit refers to 1000 gallons, Jeff has used 11,000 gallons of water.

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Answer: First and third

Step-by-step explanation:

In the given pictures, the first and third picture are representing function  because each input corresponds to exactly one output.

In second and fourth picture one input value corresponds to two output values.

i.e. a corresponds to 25 and 55 and x corresponds to 7 and 5 in output.

Answer:  

translation 3 units down then a reflection across x-axis

Step-by-step explanation:

In the given figure, we can see that Δ ABC is vertically 3 units away from the x axis .

So we translate  Δ ABC by 3 units down and then reflect it across x axis to get ΔDEF.

The correct answer among all the choices is C) Yes; the corresponding sides are proportional. This is the correct answer because the corresponding sides have a similar relationship of 1:5. We can see this relationship when dividing 25 by 5 & dividing 15 by 3, since their both equal to 5, we know the figures are similar. I hope I answered this question to your satisfaction. Have a good day!

Answer:

Yes; the corresponding sides are proportional

Step-by-step explanation:

If two figures are similar, the lengths of their sides are proportional.  This means if we set up a proportion with the sides we are given and cross-multiply, we get a true statement at the end of it.

Using the similarity statement ABCD~EFGH, we will compare AB to EF and BC to FG:

5/3 = 25/15

Cross multiply:

5(15) = 3(25)

75 = 75

We got a true statement, so the sides are proportional.

The price per gallon of gasoline is the cost of one gallon of gasoline which can be obtained by dividing the cost by the number gasoline purchased. Hence, the price per gallon of gasoline ls $1.15

Amount of gasoline purchased = 6 gallons

Total cost = $6.89

The price per gallon of gasoline can be calculated thus :

Price per gallon = $6.89 ÷ 6 = $1.148

Therefore, the price per gallon of gasoline ls $1.15 (rounded to the nearest tenth)

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The correct sequence of transformations that shows that △ABC is similar to △A′B′C′ is:

translation of 2 units left followed by a dilation with respect to the origin by a scale factor of 12.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object.

In this case, we can see that a dilation with respect to the origin by a scale factor of 12 would stretch or shrink the triangle, but would not change the angles.

Therefore, we need to apply a translation first to move the triangle into the correct position.

So, we first translate the triangle 2 units left, which does not change its shape or size, but moves it to a position where it can be more easily compared to the other triangle.

Then, we apply a dilation with respect to the origin by a scale factor of 12, which stretches or shrinks the triangle but does not change its shape.

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Answer:

The average depth of the water will be 0.155 kilometers or 155 meters.

Step-by-step explanation:

The speed at which the tsunami waves travel is [tex]S=356\sqrt{d}[/tex]. Here S is the speed in kilometers per hour and d is the average depth of the water in kilometers.

Now, it is given that the wave travels at the speed of [tex]S=140\rm km/hr[/tex].

So, the average depth of the water will be,

[tex]S=356\sqrt{d}\\140=356\sqrt{d}\\\sqrt{d}=0.393\\d=0.155\rm km[/tex]

Therefore, the average depth of the water will be 0.155 kilometers or 155 meters.

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Answer: c

Step-by-step explanation:

0.155 km

Final answer:

When a transversal intersects parallel lines perpendicularly, all angles formed are right angles (90°). This is due to perpendicular lines creating right angles and the angles at the intersection points being equal in measure because of the corresponding angle postulate.

Explanation:

When a transversal is perpendicular to two parallel lines, all the angles formed measure 90° because of the geometric properties of parallel lines and transversals. A transversal is a line that intersects two or more lines at distinct points. In the case of perpendicular transversals and parallel lines, the angles formed are called right angles.

If we consider two parallel lines, like railway tracks, they never meet and are always the same distance apart, maintaining a 180° straight line angle between them. A transversal that is perpendicular to these lines would intersect at points which lie along the x-axis if we consider the parallel lines to be along this axis. By the definition of perpendicular lines, the angles formed at the intersection points are 90°. As there are two intersection points on each parallel line, and due to the corresponding angle postulate, all four angles formed are equal in measure and hence are all right angles.

This can also be understood by considering vectors in physics, where if two vectors are perpendicular to each other, they form a right triangle, indicating a 90° angle between them. Knowing that parallel lines crossed by a perpendicular transversal produce angles of equal measure, and by the property that perpendicular lines form right angles, we can conclude that all angles formed in the described scenario are indeed 90°.

The tree diagram shows all the possible outcomes for 2 spins C is correct.

We have given that,

The 3 sections of a game spinner are numbered 1 to 3.

We have to determine, which tree diagram shows all the possible outcomes for 2 spins.

There are 3 options the first time and after that,

There are 3 options for each of those.

So it would be C.

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