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3 years ago

Find the x-intercept of the line:

Mathematics

2 answers:

Dmitry [639]3 years ago

8 0

The X- intercept is (4,0).

frozen [14]3 years ago

6 0

2x+4y=8
-2x -2x
4y=-2x+8
/4 /4 /4
y=-1/2x+2

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An architect wants to draw a rectangle with a diagonal of 15 centimeters. The length of the rectangle is to be 6 centimeters mor

S_A_V [24]

Answer:

She should make a rectangle with dimensions 14.4 cm by 4.2 cm.

Step-by-step explanation:

The diagonal of a rectangle is represented by $\sqrt{length^2+width^2}$ .
Area of rectangle is = length×width
Perimeter of a rectangle = 2(length+width).

Assume x be the width of the rectangle.

The length of the rectangle is to be 6 cm more than twice the width.

The length of the rectangle is= (2x+6) cm

Then the diagonal of the rectangle is $\sqrt{length^2+width^2}$

$=\sqrt{(2x+6)^2+x^2}$

$=\sqrt{4x^2+24x+36+x^2}$

$=\sqrt{5x^2+24x+36}$ cm

According to the problem,

$\sqrt{5x^2+24x+36}=15$

Squaring both sides

$\Rightarrow{5x^2+24x+36}=15^2$

$\Rightarrow{5x^2+24x+36}=225$

$\Rightarrow{5x^2+24x+36-225=0$

$\Rightarrow{5x^2+24x-189=0$

⇒5x²+45x-21x-189=0

⇒5x(x+9)-21(x+9)=0

⇒(x+9)(5x-21)=0

⇒x+9=0 or, 5x-21=0

$\Rightarrow x=-9, \frac{21}5$

⇒x= -9, 4.2

Since the width of a rectangle can not negative.

So, x=4.2 cm

The width of rectangle is = 4.2 cm

The length of the rectangle is =(2×4.2+6)

=14.4 cm

She should make a rectangle with dimensions 14.4 cm by 4.2 cm.

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3 years ago

A point on the terminal side of an acute angle in standard position is (1, 2 √2). Find the cosine value of this angle.

kozerog [31]

Answer:

$cos\theta=1/3$

Step-by-step explanation:

The point at the terminal side of an acute angle is given by $(1, 2\sqrt{2} )$ .

That is,

$x = 1$ and $y= 2\sqrt{2}$ .

Let r be the length of line segment drawn from the origin to the point and is given by the formula:

$r = \sqrt{x^{2} + y^{2}}$

Substituting the values of x and y into r,

$r = \sqrt{1^{2} + (2\sqrt{2} )^{2}}$

$r = \sqrt{1 + 8}$

$r = \sqrt{9}$

Thus, $r=3$

Also, $cos\theta$ is given by:

$cos\theta = x/r\\$

Substituting values of x and r,

$cos\theta = 1/3\\$

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3 years ago