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kicyunya [14]
2 years ago
5

If ΔPQR ≅ ΔJKL and ∠P = 35º, then which other angle also equals 35º. a ∠J b ∠K c ∠L d None of these choices are correct.

Mathematics
1 answer:
aivan3 [116]2 years ago
3 0

Answer:

A: Angle J

Step-by-step explanation

If the two triangles are congruent then their corresponding angles are also congruent. This means that angle P is congruent to angle J, angle Q is congruent to angle K and angle R is congruent to angle L. Hope this helps :D

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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
100 POINTS 10 QUESTIONS PLEASE HELP PICTURES BELOW PLEASE SPECIFY WHICH QUESTION YOU ARE ANSWERING
Semenov [28]

Answer:

The answers are \frac{2}{5}, \frac{1}{4}, \frac{1}{10}, \frac{5}{2}, \frac{5}{8}, \frac{4}{1}, \frac{8}{5}, and \frac{10}{1}.

Step-by-step explanation:

Proportions are fractions that can be made by using the given numbers, which in this case are 2, 5, 8, and 20. Let's pair each one with the other three and then simplify if possible.

First, let's begin with 2:

\frac{2}{5} = \frac{2}{5}

\frac{2}{8} = \frac{1}{4}

\frac{2}{20} = \frac{1}{10}

Then, let's do 5:

\frac{5}{2} = \frac{5}{2}

\frac{5}{8} = \frac{5}{8}

\frac{5}{20} = \frac{1}{4}

Note that we already have \frac{1}{4}, so we do not need to include an additional one.

Now, let us do 8:

\frac{8}{2} = \frac{4}{1}

\frac{8}{5} = \frac{8}{5}

\frac{8}{20} = \frac{2}{5}

See how we already have \frac{2}{5}, so we won't have to include that as well.

Finally, let's do 20:

\frac{20}{2} = \frac{10}{1}

\frac{20}{5} = \frac{4}{1}

\frac{20}{8} = \frac{5}{2}

Now see that we already have both \frac{4}{1} and \frac{5}{2}, so we won't have to include both of them, as they are both extras.

Hence, the answers are \frac{2}{5}, \frac{1}{4}, \frac{1}{10}, \frac{5}{2}, \frac{5}{8}, \frac{4}{1}, \frac{8}{5}, and \frac{10}{1}.

<h2><u><em>PLEASE MARK AS BRAINLIEST!!!!!</em></u></h2>
8 0
3 years ago
Read 2 more answers
Convert 40 ounces into pounds. Round your answer to the nearest tenth.
alex41 [277]

Answer:

Step-by-step explanation:

7 0
2 years ago
What is the solution of quadratic system of equations ?
kobusy [5.1K]

Answer:

(- 1, 1) and (- 5, - 35)

Step-by-step explanation:

since both equations express y in terms of x, equate the right sides

x² + 15x + 15 = - x² + 3x + 5 ( subtract - x² + 3x + 5 from both sides )

2x² + 12x + 10 = 0  ( divide all terms by 2 )

x² + 6x + 5 = 0 ← in standard form

(x + 1)(x + 5) = 0 ← in factored form

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x + 5 = 0 ⇒ x = - 5

substitute these values into either of the 2 equations and solve for y

x = - 1 : y = (- 1)² + 15(- 1) + 15 = 1 - 15 + 15 = 1 ⇒ (- 1, 1 )

x = - 5 : y = (- 5)² + 15(- 5) + 15 = 25 - 75 + 15 = - 35 ⇒ (- 5, - 35 )

None of the given options



8 0
3 years ago
A small town of 1,000 people increases its population by 2,000 the grocery store raises its prices to match the new equilibrium
Alexxandr [17]

1. If a shift in demand and/or supply has taken place, identify the change and list the determinant.

Answer:

The answer is below

Step-by-step explanation:

The demand has increased or shifted to the right.

The supply did not change.

The determinant for this situation is the increase in demand

However, with the price increment, the will be an increase in supply.

7 0
2 years ago
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