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2 years ago

Latisha works x hours each day. Demetrius works 1 more hour each day than Latisha.

1 answer:

3 0

The expressions that can be used to calculate both numbers of hours Demetrius works in 5-day work week is 5(x + 1) and 5x + 5

We are being told that Latisha works x hours each day and Demetrius works 1 more hour each day than Latisha.

So,

Let the amount of works done by Latisha be = x
Then, the amount of works done by Demetrius will be = x + 1

Thus, the both expression that can determine the number of hours Demetrius works in five days is:

= 5(x + 1) and 5x + 5

This is because if we open the bracket from 5(x+1) and multiply each term in the bracket with 5, we end up having 5x + 5.

5 times open paren x plus 1 close paren and 5 x plus 5 is correct.

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Find all solutions

Anton [14]

Answer:

The solutions of the equation are 0 , π

Step-by-step explanation:

* Lets revise some trigonometric identities

- sin² Ф + cos² Ф = 1

- tan² Ф + 1 = sec² Ф

* Lets solve the equation

∵ tan² x sec² x + 2 sec² x - tan² x = 2

- Replace sec² x by tan² x + 1 in the equation

∴ tan² x (tan² x + 1) + 2(tan² x + 1) - tan² x = 2

∴ tan^4 x + tan² x + 2 tan² x + 2 - tan² x = 2 ⇒ add the like terms

∴ tan^4 x + 2 tan² x + 2 = 2 ⇒ subtract 2 from both sides

∴ tan^4 x + 2 tan² x = 0

- Factorize the binomial by taking tan² x as a common factor

∴ tan² x (tan² x + 2) = 0

∴ tan² x = 0

OR

∴ tan² x + 2 = 0

∵ 0 ≤ x < 2π

∵ tan² x = 0 ⇒ take √ for both sides

∴ tan x = 0

∵ tan 0 = 0 , tan π = 0

∴ x = 0

∴ x = π

OR

∵ tan² x + 2 = 0 ⇒ subtract 2 from both sides

∴ tan² x = -2 ⇒ no square root for negative value

∴ tan² x = -2 is refused

∴ The solutions of the equation are 0 , π

4 0

3 years ago

Read 2 more answers

Please Help! Here is the picture question can't be copied.

Ostrovityanka [42]

Answer is B. Becuz (4,096)1/3 equals to 16. And so does (16×16)1/2

4 0

3 years ago

Solve for x <img src="https://tex.z-dn.net/?f=x%20%2B%2015%20%3D%208" id="TexFormula1" title="x + 15 = 8" alt="x + 15 = 8" al

Makovka662 [10]

Answer:

x = -7

Step-by-step explanation:

Subtract 15 from both sides of the equation.

x = 8 -15 = -7

8 0

4 years ago

Solve the quadratic equation x2=25/36. What are the solutions of the equation x2=25/36?

Alinara [238K]

Answer:

x is equal to positive 5/6 and negative 5/6

Step-by-step explanation:

To solve this, you simply need to take the square root of both sides:

$x^2 = \frac{25}{36}\\\sqrt{x^2} = \sqrt{\frac{25}{36}}\\x = \pm \frac{5}{6}$

7 0

3 years ago

Here is a sketch of a curve.

Ugo [173]

Answer:

The turning point of the graph is at (3,-16)

Step-by-step explanation:

The general equation of curve is given as:

y = x² + ax + b

The two point for which the equation satisfies is (0,-7) and (7,0).

Substitute (0,-7) in the general equation:

y = x² + ax + b

-7 = 0² + a(0) + b

b = -7

Substitute (7,0) in the general equation:

y = x² + ax + b

0 = 7² + 7a + b

Where b = -7

0 = 49 + 7a - 7

0 = 42 + 7a

a = -6

The equation of the curve is:

a = -6 and b = -7

y = x² + ax + b

y = x² - 6x - 7

Graph of the equation is attached below.

We can see that the the turning point of the graph is at (3,-16)

5 0

3 years ago