And work to pleaseeeeeeee

Please Help me with X and Y

Bad White [126]

Answer:

a) x = 69°

b) y = 69°

Step-by-step explanation:

a. Given that AB and CD are parallel lines, therefore:

x = 69° (alternate interior angles are congruent to each other)

b. y + 111° = 180° (consecutive interior angles are supplementary)

y = 180° - 111° (substraction property of equality)

y = 69°

6 0

3 years ago

Which of the following best explains why

Dima020 [189]

We can see values of angles in degrees first

$\frac{5\pi}{6} = \frac{5 \times 180}{6}= \frac{900}{6}$ = 150°

Similarly

$\frac{5\pi}{3} = \frac{5 \times 180}{3}= \frac{900}{3}$ = 300°

Now reference angle means positive acute angle they will have

As we can see in attachment 150° lies in second quadrant so its reference angle will be 180°-150° = 30° from x axis line as shown.

Where as angle 300° lies in fourth quadrant so its reference angle will be 360° - 300° = 60° from x axis as shown. So clearly both reference angles are different . So 1st choice " angles donot have same reference angle" best explains it

Choice (2) and (3) are incorrect as tan is positive only in first and third quadrants and angle 300° is in fourth quadrant.

since angle 150° is in second quadrant and 300° is in fourth quadrant so both will have same negative sign so choice (4) is not correct.

So final ansewr is choice (1) "the angles donot have same reference angle"

8 0

4 years ago

A factory is to be built on a lot measuring 210 ft by 280 ft. A local building code specifies that a lawn of uniform width and e

Tresset [83]

Answer:

Width of lawn = 35 ft

Dimensions of factory = length: 210 ft, width: 140 ft

Step-by-step explanation:

The total area of the lot can be calculated as:

$A_{lot} = 210 * 280\\A_{lot} = 58800 ft^{2}$

Since, the area of factory should be equal to area of lawn:

$A_{lot} = A_{factory} + A_{lawn}\\58800 = 2 A_{factory or lawn}\\\\A_{factory or lawn} = \frac{58800}{2}\\A_{factory or lawn} = 29400 ft^{2}$

Now, let 'x' be the width of lawn, the dimensions of factory can be written as:

$(210-2x)\\(280-2x)\\$

Since, area is equal to length x width:

$(210-2x)*(280-2x) = 29400\\Simplifying:\\210*280 - 210*2x - 2x*280 + 4x^{2} = 29400\\58800 - 420x - 560x +4x^{2} = 29400\\4x^{2} - 980x +58800 = 29400\\4x^{2} - 980x + 29400 = 0\\$

Divide whole equation by 4,

$x^{2} - 245 + 7350 = 0\\$

Solving above quadratic equation, we get,

$x = 210\\x = 35\\$

x = 35 seems realistic width of the lawn.

Now, finding the dimension of factory:

$(210-2x) = 210 - 2(35) = 140 ft\\(280-2x) = 280 - 2(35) = 210ft$

We can also reconfirm the area of factory by multiplying the above two lengths:

140 * 210 = 29400 ft

8 0

3 years ago

Put the functions, with their corresponding intervals, in order from least to greatest according to their average rates of chang

Svetllana [295]

Answer

Step-by-step explanation:

easy

8 0

2 years ago

The illustration below shows the graph of y as a function of x.

Viefleur [7K]

Answer:

1). Increases

2). Slope = 4

3). Slope = -1

4). y = 4 when x = 5

Step-by-step explanation:

1). Initially, as x increases, y also increases. (Linear growth has been shown in the graph initially).

2). Afterward, the slope of the graph of the function is equal to 4 for all x between x = 3 and x = 5.

[Slope of the line passing through two points (3, 0) and (5, 4)

m = \frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}

(x

2

−x

1

)

(y

2

−y

1

)

= \frac{4-0}{5-3}

5−3

4−0

= \frac{4}{1}

1

4

= 4 ]

3). The slope of the graph is equal to -1 for x between x = 5 and x = 9.

[Slope of the line passing through two points (5, 4) and (9, 0),

Slope = \frac{(y_{2}-y_{1})}{(x_{2}-x_{1})}

(x

2

−x

1

)

(y

2

−y

1

)

= \frac{4-0}{5-9}

5−9

4−0

= -\frac{4}{4}

4

= -1 ]

4). The greatest value of y is y = 4, and it occurs when x = 5. (From the given graph)

3 0

3 years ago