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MatroZZZ [7]
3 years ago
9

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 = Pe^{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 = 3000e^{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]

<em>Hi ^^</em>

<u>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).</u>

<em>Owner:  timothycarney2004</em>

<em>Rank: Ambitious</em>

--------------------------------------------------------------------------------------------------------------

<u>Answer:</u><em> There are </em><u>two </u><em>real roots </em>

<em> </em><u>Step-by-step explanation:</u><em> 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.</em>

<em>--------------------------------------------------------------------------------------------------------------</em>

<em />

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
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