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3 years ago

Triangle ABC has vertices A(0, 2), B(x, 0), and C(0, -2). Determine the value of x that makes triangle ABC a regular triangle.

Mathematics

1 answer:

Jobisdone [24]3 years ago

5 0

Answer:

$x = \sqrt{12 } = 2 \sqrt{3} \: or \\ x = - \sqrt{12} = - 2 \sqrt{3}$

Step-by-step explanation:

In order for the triangle to be a right one we need every side to be of the same length. see the photo for furyher explanation.

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Angus has $3,000 he want to invest. What interest rate compounded continuously does an account need to offer so that Angus has $

kaheart [24]

Answer:

The interest rate is 7.58%

Step-by-step explanation:

Compound continuous interest can be calculated using the formula:

A = P $e^{rt}$ , where

A is the future value of the investment, including interest

P is the principal investment amount (the initial amount)

r is the interest rate in decimal

t is the time the money is invested for

∵ Angus has $3,000 he want to invest

∴ P = 3000

∵ The interest rate is compounded continuously

∵ Angus has $5,500 in 8 years

∴ A = 5500

∴ t = 8

→ Substitute them in the rule above to find r

∵ 5500 = 3000 $e^{8r}$

→ Divide both sides by 3000

∴ $\frac{11}{6}$ = $e^{8r}$

→ Insert ㏑ in both sides

∵ ㏑( $\frac{11}{6}$ ) = ㏑( $e^{8r}$ )

→ Remember ㏑( $e^{n}$ ) = n

∴ ㏑( $\frac{11}{6}$ ) = 8r

→ Divide both sides by 8

∴ 0.07576697545 = r

→ Multiply it by 100% to change it to a percentage

∴ r = 0.07576697545 × 100%

∴ r = 7.576697545 %

→ Round it to the nearest hundredth

∴ r ≅ 7.58

∴ The interest rate is 7.58%

3 0

3 years ago

Given the following formula , solve for t.

hodyreva [135]

I think it’s c. Not sure though. Pure guess

4 0

3 years ago

If the discrminant of a quadratic equation is 4, which statement describes the roots

ryzh [129]

Hi ^^

Note: This answer is already on brainly, but to save up your time here is the answer (the owner of the answer is listed below).

Owner: timothycarney2004

Rank: Ambitious

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Answer: There are two real roots

Step-by-step explanation: Terms in this set (6) If the discriminant of a quadratic equation is 4, which statement describes the roots? B. There are two real roots.

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Anyways bye! <3

4 0

2 years ago

Three less than a number b is more than 15.

Korolek [52]

Answer:

b-3>15b>18(18 infinity)

Step-by-step explanation:

4 0

3 years ago

In triangle ABC shown below, DE is parallel to AC. The following two-column proof with missing statements and reasons proves tha

lianna [129]

Answer:

The correct option is;

C. 3. ∠BDE ≅∠BAC, Corresponding Angles Postulate 4. ∠B ≅ ∠B Reflexive Property of Equality

Step-by-step explanation:

The two column proof can be written as follows;

Statement, Reason

1. $\overline{DE} \parallel \overline{AC}$ , Given

2. $\overline {AB}$ is a transversal , Conclusion from statement 1.

We note that ∠BDE and ∠BAC are on the same side of the transversal relative to the parallel lines, and are therefore, corresponding angles.

Therefore, we have;

3. ∠BDE ≅∠BAC, Corresponding Angles Postulate

Also

4. ∠B ≅ ∠B, Reflexive Property of Equality

In the two triangles, ΔABC and ΔDBE, we have ∠BDE ≅∠BAC and ∠B ≅ ∠B,

From ∠BDE + ∠B + ∠BED = 180°

∠BAC + ∠B + ∠BCA = 180°

Therefore, ∠BED = ∠BCA Substitution property of equality

Which gives;

5, ΔABC ~ ΔDBE, Angle Angle Similarity Postulate

6. BD/BA = BE/BC, Converse of the Side-Side-Side Similarity Theorem

5 0

3 years ago