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4 years ago

Solve the following quadratic equations by completing the square. y^2-14y+48=0

Mathematics

1 answer:

NISA [10]4 years ago

5 0

Answer:

y = 6 or 8

Step-by-step explanation:

1. Subtract the constant:

y^2 -14y = -48

2. Add the square of half the y-coefficient:

y^2 -14y +49 = -48 +49

Write as a square, if you like:

(y -7)^2 = 1

3. Take the square root:

y -7 = ±√1 = ±1

4. Add the opposite of the constant on the left:

y = 7 ±1 = 6 or 8

The solution is y = 6 or y = 8.

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Solve 5 tan x = 5√(3) for 0° ≤ x ≤ 180°. a. 60° b. 150° c. 30° d. 120°

ladessa [460]

Answer:

$\boxed{a.\:\:\:60\degree}$

Step-by-step explanation:

The given trigonometric equation is

$5\tan(x)=5\sqrt{3}$ for $0\degree \le x\le 180\degree$ .

We divide through by 5 to get;

$\tan(x)=\sqrt{3}$

We take the inverse tangent of both sides to obtain;

$x=tan^{-1}(\sqrt{3})$

$x=60\degree$

Since the tangent ratio is positive, it means $x$ could also be in the 3rd quadrant. But this is outside the given range.

Therefore the correct answer is A

6 0

4 years ago

Sara has 7/21 yard of ribbon. What is the maximum number of 1/3 yard-long pieces Marilyn can cut from this ribbon?

Darya [45]

Answer:

Step-by-step explanation:

Given parameters:

Length of ribbon = $\frac{7}{21}$ yards

Unknown:

Maximum number of $\frac{1}{3}$ yards that can be cut = ?

Solution:

Maximum number of length that can be cut;

= $\frac{Total length}{maximum number of length}$

Maximum number of length = $\frac{\frac{7}{21} }{\frac{1}{3} }$

Maximum number of length = $\frac{7}{21}$ x $\frac{3}{1}$ = 1

The maximum number of $\frac{1}{3}$ yards that can be cut is 1

4 0

3 years ago

Does anyone know how to do this I’m really confused

Levart [38]

<h3>Given:</h3>

Pentagon

The size of the unknown angle "x"

<h3>Solution:</h3>

The given polygon is a Pentagon so the sum of interior angle will be,

$\large\boxed{Formula: ( n − 2 ) × 180}$

n means the number of sides

Let's substitute the values according to the formula.

$(5-2)×180$

$=540°$

Now, we can find the sum of one interior angle.

$\large\boxed{\frac{sum \: of \: interior \: angles}{n}}$

n means the number of sides.

Let's substitute the values according to the formula.

$x=\frac{540}{5}$

$\large\boxed{x= 108°}$

Therefore, the size of the unknown angle "x" is 108°

4 0

3 years ago

A Parmer spray 3 rows of tomato plants each row with a different type of fertilizer which questions should he look to determine

Virty [35]

Which fertilizer makes the plant grow the fastest?

Which is the slowest?

6 0

4 years ago

8. Which statement is an example of a transitive relationship?

11Alexandr11 [23.1K]

Answer:

Transitive

If x = 2y and 2y = 8, then x = 4.

7 0

3 years ago