Dylan earns $283 on Monday and he earns $546 on Tuesday. How much total money does Dylan earn?

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

babunello [35]

The 4th one goes with the 1st box
The 2nd one goes with the 2nd box
The last one goes with the 3rd box

3 0

3 years ago

Which is an equation in point slope form of the line that passes through the points (7, 5) and (-4, -1)

emmasim [6.3K]

Answer:

y = (6/11)x + 13/11

Step-by-step explanation:

y = mx + c

m = (-1-5)/(-4-7) = -6/-11 = 6/11

y = (6/11)x + c

When x = 7, y = 5

5 = (6/11)(7) + c

5 = 42/11 + c

c = 5 - 42/11

c = 13/11

y = (6/11)x + 13/11

11y = 6x + 13

5 0

3 years ago

Given α and β are Supplementary. Show the necessary steps.

user100 [1]

Answer:

$\alpha = 108\degree, \: \beta = 72\degree$

Step-by-step explanation:

α and β are Supplementary (given)

$\therefore \alpha + \beta = 180\degree.... (1)$

It is given that:

$\alpha= \frac{3}{2} \beta$

Plugging the value of α in equation (1), we find:

$\frac{3}{2} \beta + \beta = 180\degree$

$\therefore \frac{3+2}{2} \beta = 180\degree$

$\therefore \frac{5}{2} \beta = 180\degree$

$\therefore \beta = 180\degree\times \frac{2}{5}$

$\therefore \beta = 72\degree$

$\implies \alpha= \frac{3}{2} \times 72\degree= 108\degree$

So,

$\alpha = 108\degree, \: \beta = 72\degree$

7 0

2 years ago

What must be added to both sides in 4x² + 24x + 8 = 32 in order to complete the square?

Sergeu [11.5K]

Answer:

16

Step-by-step explanation:

To solve a quadratic equation by using the completing the square method, the coefficient of the square term i.e x² must be one (1).

Therefore, we would have to first make the coefficient of x² to be equal to 1.

4x² + 24x + 8 = 32

We would simplify the equation;

4x² + 24x = 32 - 8

4x² + 24x = 24

Divide all through by 4;

x² + 8x = 24

The value to be added = (8/2)² = 4² = 16

x² + 8x + 16 = 8 + 16

x² + 4x + 4x + 16 = 24

x(x + 4) + 4(x + 4) = 24

(x + 4)² = 24

Taking the square root of both sides;

x + 4 = ± 4.9

x = -4 ± 4.9

x = -4 + 4.9 = 0.9

or

x = -4 - 4.9 = - 8.9

<em>Therefore, 16 must be added to solve the quadratic equation by completing the square method. </em>

6 0

3 years ago

A seat on a Ferris wheel is level with the center of the wheel. The diameter of the wheel is 210 feet (ft). If the wheel

frutty [35]

Answer:

The change in the height of the seat of the Ferris wheel is a reduction in height of approximately 74.25 feet

Step-by-step explanation:

The given information are;

The position of the seat on the Ferris wheel = The center level of the wheel

The diameter of the Ferris wheel = 210 feet

The angle of rotation of the wheel = 45° counterclockwise

The height of a point on the Ferris wheel is given by the relation;

h = A·cos(b·x + c) + d

With regards to the question, we have;

h = The height of the seat of the Ferris wheel

A = The amplitude = 1/2 × The diameter of the wheel = 210/2 = 105 feet

360/b = The period

c = The phase shift = 90°

d = The mid line = 0

For a rotation of 45° counterclockwise or-45° clockwise, we have;

b·x = 45°, therefore;

h = 105 × cos(45° + 90°) + 0 = 105 × cos(135°) + 0

h = 105 × cos(135°) ≈ -74.25 feet

Therefore, the height of the seat of the Ferris wheel reduces by 74.246 feet.

6 0

3 years ago