Which of the following could be the ratio of the length of the longer leg of a 30 60 90 triangle to the length of its hypotenuse

Answers

Answer 1

Answer: for 30 60 90 triangles, the ratio of the side lengths is
$(1)/(2) : ( √(3) )/(2) :1$
where the first is the shorter leg, the second is the longer leg, and the third is the hypotenuse (the longest side that doesn't form a 90 degree angle)

so the ratio of the longer leg to the hypotenuse is $( √(3) )/(2) :1$
or
$( ( √(3) )/(2) )/(1)$
which equals $( √(3) )/(2)$

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The Spartan Bike Shop has a credit card that they use for business transactions. Their starting amount is 4,500. Create a balance sheet similar to the one created in class which include: Date, Transaction, deposit withdraw and balance

Answers

Answer:

Step-by-step explanation:

Here is a sample balance sheet for the Spartan Bike Shop credit card transactions:

Date | Transaction | Deposit | Withdraw | Balance

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

01/01/2022 | Starting balance | - | - | $4,500

01/15/2022 | Purchase of supplies| - | $500 | $4,000

02/05/2022 | Payment received | $1,000 | - | $5,000

02/20/2022 | Equipment purchase | - | $2,500 | $2,500

03/10/2022 | Refund received | $300 | - | $2,800

In this example:

- The starting balance on 01/01/2022 is $4,500.

- On 01/15/2022, the shop made a purchase of supplies, resulting in a withdrawal of $500 from the credit card account, leaving a balance of $4,000.

- On 02/05/2022, the shop received a payment of $1,000, which was deposited into the credit card account, increasing the balance to $5,000.

- On 02/20/2022, the shop made an equipment purchase, resulting in a withdrawal of $2,500 from the credit card account, leaving a balance of $2,500.

- On 03/10/2022, the shop received a refund of $300, which was deposited into the credit card account, increasing the balance to $2,800.

This balance sheet provides a clear record of the credit card transactions for the Spartan Bike Shop, including the dates, transaction details, deposits, withdrawals, and the resulting balance after each transaction. It helps the shop keep track of their credit card activity and maintain an accurate record of their financial transactions.

What two numbers multiply to 44 and add up to 12?

Answers

This pattern of question is always coming up. Since we can't easily guess, then let us set up simultaneous equation for the statements.

let the two numbers be x and y.

Multiply to 44.    x*y = 44 ..........(a)

Add up to 12. x + y = 12 .........(b)

From (b)

y = 12 - x .......(c)

Substitute (c) into (a)

x*y = 44

x*(12 - x) = 44

12x - x² = 44

-x² + 12x = 44

-x² + 12x - 44 = 0.

Multiply both sides by -1

-1(-x² + 12x - 44) = -1*0

x² - 12x + 44 = 0.

This does not look factorizable, so let us just use quadratic formula

comparing to ax² + bx + c = 0, x² - 12x + 44 = 0, a = 1, b = -12, c = 44

x = (-b + √(b² - 4ac)) /2a   or (-b - √(b² - 4ac)) /2a

x = (-(-12) + √((-12)² - 4*1*44) )/ (2*1)

x = (12 + √(144 - 176) )/ 2

x = (12 + √-32 )/ 2

√-32 = √(-1 *32) = √-1 * √32 = i * √(16 *2) = i*√16 *√2 = i*4*√2 = 4i√2

Where i is a complex number. Note the equation has two values. We shall include the second, that has negative sign before the square root.

x = (12 + √-32 )/ 2 or (12 - √-32 )/ 2

x = (12 + 4i√2 )/ 2 (12 - 4i√2 )/ 2

x = 12/2 + (4i√2)/2 12/2 - (4i√2)/2

x = 6 + 2i√2 or    6 - 2i√2

Recall equation (c):

y = 12 - x, When x = 6 + 2i√2, y = 12 - (6 + 2i√2) = 12 - 6 - 2i√2 = 6 - 2i√2

When x = 6 - 2i√2, y = 12 - (6 - 2i√2) = 12 - 6 + 2i√2 = 6 + 2i√2

x = 6 + 2i√2, y = 6 - 2i√2

x = 6 - 2i√2, y = 6 + 2i√2

Therefore the two numbers that multiply to 44 and add up to 12 are:

6 + 2i√2 and 6 - 2i√2

$xy=44\n x+y=12\n\n xy=44\n x=12-y\n\n (12-y)y=44\n 12y-y^2=44\n y^2-12y+44=0\n y^2-12y+36+8=0\n (y-6)^2=-8$

No solutions in real numbers.

In complex numbers:
$(y-6)^2=-8\n y-6=-√(-8) \vee y-6=√(-8)\n y=6-2\sqrt2 i \vee y=6+2\sqrt2 i\n\n x=12-(6-2\sqrt2i) \vee x=12-(6+2\sqrt2i)\n x=12-6+2\sqrt2i \vee x=12-6-2\sqrt2i\n x=6+2\sqrt2i \vee x=6-2\sqrt2i$

These numbers are $6-2\sqrt2i$ and $6+2\sqrt2i$ .

Richard has 5 markers in a backpack. One of them is black and one is red. Find the probability Richard will reach into the backpack without looking and grab the black marker and then reach in a second time and grab the red marker. Express your answer as a fraction in simplest form.

Answers

!/5x1/5 =2/5

!/5 one possible of the total of 5

Multiply both

PLEASE HELP!!! needs to be answered in sentaces(01.07 HC)

Michael and Derrick each completed a separate proof to show that corresponding angles AKG and ELK are congruent. Who completed the proof incorrectly? Explain.

Line AB is parallel to EF, transversal GJ crosses line AB at K and crosses line EF at L.

Michael's Proof

Statement Justification
1. line AB ∥ line EF with transversal segment GJ 1. Given
2. angle AKG is congruent to angle AKL 2. Vertical Angles Theorem
3. angle BKL is congruent to angle ELK 3. Alternate Interior Angles Theorem
4. angle AKG is congruent to angle ELK 4. Transitive Property

Derrick's Proof

Statement Justification
1. line AB ∥ line EF with transversal segment GJ 1. Given
2. angle AKG is congruent to angle BKL 2. Vertical Angles Theorem
3. angle BKL is congruent to angle ELK 3. Alternate Interior Angles Theorem
4. angle AKG is congruent to angle ELK 4. Transitive Property

Answers

The proof that is completed incorrectly is Michael's proof of the statement "corresponding angles AKG and ELK are congruent."

Both proofs start with the same given information – lines AB and EF are parallel, and transversal segment GJ crosses line AB at point K and crosses line EF at point L. Both proofs also rely on the same theorems – the vertical angles theorem and the alternate interior angles theorem. However, the difference is in the way the two proofs make the jump from the first three statements to the fourth statement.

In Michael's proof, statement number 3 is incorrect. Statement 3 in Michael's proof states that "angle BKL is congruent to angle ELK" based on the alternate interior angles theorem. However, this statement is not true because the interior angle BKL is not formed by the intersection of two straight lines from a point on the line AB and a point on the line EF, which is required for the alternate interior angles theorem to apply.

In contrast, Derrick's proof uses the vertical angles theorem before applying the transitive property in statement 4. The statement "angle AKG is congruent to angle ELK" in Derrick's proof is a result of applying the transitive property to the statement that "angle AKG is congruent to angle BKL" in statement 3 and the statement that "angle BKL is congruent to angle ELK" in statement 2, which are both results of applying the vertical angles theorem. This is a valid proof.

Therefore, Michael's proof is incorrect because of an incorrect application of the alternate interior angles theorem, while Derrick's proof is correct because it uses the vertical angles theorem and applies the transitive property correctly.

How to solve 5(x-3)+2=7?step by step please help me math tutor. Right answer only.