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LuckyWell [14K]
1 year ago
15

Could I please get help with my last statements reasoning? I have tried multiple reasons but still could not get the reasoning r

ight

Mathematics
1 answer:
alisha [4.7K]1 year ago
3 0

You have the next:

Side AB is congruent with side CD

Side AC is congruent with side AC

Angle BAC is congruent with angle DCA

SAS congruence of triangles: If any two sides and included angle (angle between those sides) of one triangle are equal to corresponding two sides and included angle of second triangle, then the two triangles are condruent by SAS rule

Angle BAC is the included angle of sides AB and AC in triangle ABC

Angle DCA is the included angle of sides CD and AC in triangle CDA

Then,

\Delta ABC\cong\Delta CDAReason: SAS rule

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Bo and Brica are yoga instructors. Between the both of them, they teach 46 yoga classes each week. If Brica teaches 11 fewer tha
PtichkaEL [24]

Bo teaches 19 classes and Brica teaches 27 classes per week

Step-by-step explanation:

Bo and Brica are yoga instructors

  • They teach 46 yoga classes each week
  • Brica teaches 11 fewer than twice as many as Bo

We need to find how many classes each instructor teaches per week

Assume that Bo teaches x classes per week

∵ Bo teaches x classes per week

∵ Brica teaches 11 fewer than twice as many as Bo

∵ Twice means times 2 and 11 fewer is - 11

- Multiply x by 2 and subtract 11 from the product

∴ Brica teaches 2x - 11 classes per week

∵ They teach 46 classes per week

- Add the number of their classes and equate the sum by 46

∴ x + 2x - 11 = 46

- Add the like terms in the left hand side

∴ 3x - 11 = 46

- Add 11 to both sides

∴ 3x = 57

- Divide both sides by 3

∴ x = 19

∵ Bo teaches x classes per week

∴ Bo teaches 19 classes per week

∵ Brica teaches 2x - 11 classes per week

∴ Brica teaches 2(19) - 11 = 27 classes per week

Bo teaches 19 classes and Brica teaches 27 classes per week

Learn more:

You can learn more about the linear equations in brainly.com/question/11306893

#LearnwithBrainly

5 0
3 years ago
Karma's brother was born
torisob [31]

Answer:

Basically just add 12 to the hour that you want

Step-by-step explanation:

I'm honestly not sure what you're asking...

but if it was 13 min after 8pm, then it would be 20:13

if it was 18 min after 8pm, then it would be 20:18

6 0
3 years ago
Using properties of sets show that : a) A ∩ (A’ U B) = A ∩ B b) A ∩ (A U B )’ = Ф
asambeis [7]

Answer:

a) From A ∩ A' = ∅, we have;

A ∩ (A' ∪ B) = A ∩ B

b) From A ∩ (A' ∩ B') = (A ∩ A') ∩ B' and A ∩ A' = ∅, we have;

A ∩ (A ∪ B)' = ∅

Step-by-step explanation:

a) By distributive law of sets, we have;

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

From the complementary law of sets, we have;

A ∩ A' = ∅

Therefore, for A ∩ (A' ∪ B) = A ∩ B, we have

A ∩ (A' ∪ B) = (A ∩ A') ∪ (A ∩ B) (distributive law of sets)

A ∩ A' = ∅ (complementary law of sets)

Therefore;

(A ∩ A') ∪ (A ∩ B) = ∅ ∪ (A ∩ B)  = (A ∩ B) (Addition to zero identity property)

∴  A ∩ (A' ∪ B) = A ∩ B

b) By De Morgan's law

(A ∪ B)' = A' ∩ B'

Therefore, A ∩ (A ∪ B)' = A ∩ (A' ∩ B')

By associative law of sets, we have;

A ∩ (A' ∩ B') = (A ∩ A') ∩ B'

A ∩ A' = ∅ (complementary law of sets)

Therefore, (A ∩ A') ∩ B' = ∅  ∩ B' = ∅

Which gives;

A ∩ (A ∪ B)' = ∅.

4 0
3 years ago
A petrol kiosk p is 12 km due north of another petrol kiosk q. The bearing of a police station r from p is 135 degree and that f
tiny-mole [99]

Answer:

Distance between P and R is 40.15 km.

Step-by-step explanation:

From the picture attached,

Petrol kiosk P is 12 km due North of another petrol kiosk Q.

Bearing of a police station R is 135° from P and 120° from Q.

m∠QPR = 180° - 135° = 45°

m∠PQR = 120°

m∠PRQ = 180° - (m∠QPR +m∠PQR)

             = 180° - (45° + 120°)

             = 180° - 165°

             = 15°

Now we apply sine rule in ΔPQR to measure the distance between P and R.

\frac{\text{sin}(\angle QPR)}{\text{QR}}= \frac{\text{sin}(\angle PQR)}{\text{PR}}=\frac{\text{sin}\angle PRQ}{\text{PQ}}

\frac{\text{sin}(45)}{\text{QR}}= \frac{\text{sin}(120)}{\text{PR}}=\frac{\text{sin}(15)}{\text{12}}

\frac{\text{sin}(120)}{\text{PR}}=\frac{\text{sin}(15)}{\text{12}}

PR = \frac{12\text{sin}(120)}{\text{sin}(15)}

PR = 40.15 km

Therefore, distance between P and R is 40.15 km.

8 0
3 years ago
2 × 10^12 red blood cells have a total mass of 90 grams.
galina1969 [7]

Answer:

2×10¹² cells → 90 g

mass of 1 red blood cell : 90÷(2×10¹²) = 45×10^-12 g = 4.5×10^-11 g

5 0
2 years ago
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