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Tasya [4]
3 years ago
7

Given that D is the midpoint of AB and B is the midpoint of AC which statement must be true a) AD= 1/3AC

Mathematics
1 answer:
garik1379 [7]3 years ago
3 0

Answer:

AD = 1/4AC

Step-by-step explanation:

Given that,

D is the the midpoint of AB

Therefore

AB = AD + DB

Since, D is the midpoint of the AB, therefore AD = DB

AB = AD + AD

AB = 2AD (i)

Similarly, B is the midpoint of AC

Hence,

AC = AB + BC

AC = AB + AB (because B is the midpoint)

AC = 2AB (ii)

By putting the value of AB from equation i to equation ii, we get

AC = 2(2AD)

AC = 4AD

AC/4 = AD

AD = 1/4AC

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Given: △ABC, AB=5sqrt2 <br> m∠A=45°, m∠C=30°<br> Find: BC and AC
Marysya12 [62]

BC is 10 units and AC is 5+5\sqrt{3} units

Step-by-step explanation:

Let us revise the sine rule

In ΔABC:

  • \frac{AB}{sin(C)}=\frac{BC}{sin(A)}=\frac{AC}{sin(B)}
  • AB is opposite to ∠C
  • BC is opposite to ∠A
  • AC is opposite to ∠B

Let us use this rule to solve the problem

In ΔABC:

∵ m∠A = 45°

∵ m∠C = 30°

- The sum of measures of the interior angles of a triangle is 180°

∵ m∠A + m∠B + m∠C = 180

∴ 45 + m∠B + 30 = 180

- Add the like terms

∴ m∠B + 75 = 180

- Subtract 75 from both sides

∴ m∠B = 105°

∵ \frac{AB}{sin(C)}=\frac{BC}{sin(A)}

∵ AB = 5\sqrt{2}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{BC}{sin(45)}

- By using cross multiplication

∴ (BC) × sin(30) = 5\sqrt{2} × sin(45)

∵ sin(30) = 0.5 and sin(45) = \frac{1}{\sqrt{2}}

∴ 0.5 (BC) = 5

- Divide both sides by 0.5

∴ BC = 10 units

∵ \frac{AB}{sin(C)}=\frac{AC}{sin(B)}

- Substitute AB and the 3 angles in the rule above

∴ \frac{5\sqrt{2}}{sin(30)}=\frac{AC}{sin(105)}

- By using cross multiplication

∴ (AC) × sin(30) = 5\sqrt{2} × sin(105)

∵ sin(105) = \frac{\sqrt{6}+\sqrt{2}}{4}

∴ 0.5 (AC) = \frac{5+5\sqrt{3}}{2}

- Divide both sides by 0.5

∴ AC = 5+5\sqrt{3} units

BC is 10 units and AC is 5+5\sqrt{3} units

Learn more:

You can learn more about the sine rule in brainly.com/question/12985572

#LearnwithBrainly

6 0
3 years ago
Matrix A = [6 -12 4 8]. What is matrix X if 1/2x=A?
Step2247 [10]

Answer:

X = \left[\begin{array}{cccc}12&-24&8&16\end{array}\right]

Step-by-step explanation:

A matrix is given by

A = \left[\begin{array}{cccc}6&-12&4&8\end{array}\right]

Now, we have to find the matrix X if \frac{1}{2} X = A

⇒ X = 2A

Now, multiplication of a constant with a matrix means multiplication with that constant with all the terms of the matrix.

So, X = \left[\begin{array}{cccc}6 \times 2&-12 \times 2&4 \times 2&8 \times 2\end{array}\right]

⇒ X = \left[\begin{array}{cccc}12&-24&8&16\end{array}\right] (Answer)

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Answer:

Y = 6 and x=6 are perpendicular because they both measure at a 90 degree angle

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10 + 9 • (−3) 2− (−1 + 8)
Vitek1552 [10]

Answer:

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Step-by-step explanation:

PEMDAS suggests you start with parenthesis

10+9•(-3)2-(7)

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gregori [183]
3,000. You take 15,000 and multiply by .4 to get how much she spent on rent (6,000). They you subtract the rent money from her total pay to get her money that she spent on living expenses, clothes and entertainment in total (9,000). Since she spent her money in six parts (3+2+1), you divide 9,000 by 6 to get 1,500 to get each part. Since for entertainment she has two parts you multiply 1,500 by 2 to get 3,000.
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