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jolli1 [7]
3 years ago
10

Given that p || q, what are the reasons that each statement is true?

Mathematics
1 answer:
suter [353]3 years ago
8 0

Answer:

See answers below

Step-by-step explanation:

1) This is the given premise "line p is parallel to line q"

2) Angles 1 and 2 are equal (congruent) because they are vertical opposite angles.

3) Angles 2 and 3 are equal (congruent) because they are alternate angles.

4) Angles 3 and 4 are equal (congruent) because they are vertical opposite angles.

5) Angles 1 and 4 are equal (congruent) because: a) angle 1 is equal to angle 2 being vertical opposite,  b) angle 2 is equal to angle 4 because they are corresponding angles, therefore c) due to transitive property, angle 1 will equal angle 4.

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43.
aleksklad [387]

Answer:

4.12 kg

Step-by-step explanation:

Regular cakes:

1 dozen normal sponge cakes: 264 g plain flour

Vegetarian cakes:

1 dozen cakes: 264 g plain flour

4 eggs are replaced by 4 * 30 g of flour = 120 g flour

total flour for 1 dozen vegetarian cakes = 264 g + 120 g = 384 g

Proportion for regular cakes:

12 cakes to 264 g flour = 100 cakes to x grams flour

12/264 = 100/x

12x = 26400

x = 2200

2200 g flour for 100 regular cakes

Proportion for vegetarian cakes:

12 cakes to 384 g flour = 60 cakes to y grams flour

12/384 = 60/y

12y = 384 * 60

12y = 23040

y = 1920

1920 g flour for 60 vegetarian cakes

Total flour needed:

2200 g + 1920 g = 4120 g

4120 g * 1 kg/(1000 g) = 4.12 kg

Answer: 4.12 kg

4 0
3 years ago
Cindy shoots a bottle rocket straight up into the air such that its height h, in feet, at time t, in seconds, is given by the fu
dezoksy [38]

Answer:

t = [0.493,4.2]

Step-by-step explanation:

The height of the rocket straight up into the air is given by :

h(t)=-16t^2+85t+5

We need to find the interval the rocket be at least 43 feet above the ground.

43\ge -16t^2+85t+5\\\\t\ge 0.493\ and\ t\le 4.82\ s

So, the required interval during which the rocket is at least 43 feet above the ground is [0.493,4.2].

6 0
3 years ago
(2.75 x 107) + (1.23 x 108) simplify
Thepotemich [5.8K]

Answer:

427.09

Step-by-step explanation:

(2.75 x 107) + (1.23 x 108)

294.25 + 132.84 = 427.09

6 0
2 years ago
Evaluate -x - y when x = -12 and y = 2
xz_007 [3.2K]

Answer:

-14

Step-by-step explanation:

subtract

8 0
3 years ago
Read 2 more answers
The height of a vase is 45.7 centimeters when rounded to the nearest tenth of a centimeter. What is the shortest possible height
vlada-n [284]

Answer:

45.650 centimeters

Step-by-step explanation:

The height of a vase is 45.7 centimeters when rounded to the nearest tenth of a centimeter. What is the shortest possible height of the vase? Give your answer to 3 decimal places

Given that :

Height of vase = 45.7 when rounded to the nearest tenth

The shortest possible height of the vase : will be 45.65, this is because, the subsequent digit (hundredth) after the tenth digit is the figure rounded to give a tenth digit of 7

From the we know that the tenth digit before rounding is 7 - 1 = 6

And smallest possible value the hundredth placed digit could have in other to be rounded to 1 is 5.

To three decimal place, the thousandth placed value could take the least possible value in a digit series, which is 0

Hence, the shortest possible height of the vase = 4.650

4 0
2 years ago
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