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2 years ago

12

Find the area of the shaded region.

1 answer:

satela [25.4K]2 years ago

4 0

Answer:

16

Step-by-step explanation:

area of big triangle is 36

area of small triangle is 20

area of shaded is 36 - 20=16

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BRIA is a rectangle. AN=5. NR=x-3. please solve for x, NR, and BI

Lena [83]

Answer:

x=8

NR=5 units

BI=10 units

Step-by-step explanation:

In a rectangle BRIA

AN=5 units

NR=x-3

We have to solve for x , NR and BI.

We know that

Diagonals of rectangle bisect to each other.

BI and AR are the diagonals of rectangle BRIA and intersect at point N.

AN=NR

$5=x-3$

$x=5+3=8$

$x=8$

Substitute the value of x

NR=8-3=5

By property of rectangle

BI=AR=AN+NR=5+5=10 unit

BI=10 units

7 0

2 years ago

The graph shows the cost of some taxi journeys<br><br> work out a formula for c in terms of n

Vitek1552 [10]

Answer:

$c=\frac{3}{5}(n)+2.5$

Step-by-step explanation:

see the attached figure to better understand the problem

Let

c -----> the cost of some taxi journeys

n ----> the number of miles

we know that

The graph is a line

The equation of a line in slope intercept form is

$c=m(n)+b$

where

m is the slope

b is the c-intercept (value of c when the value of n is equal to zero)

Observing the graph we have the points

(0,2.5), (5,5.5)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

$m=\frac{c2-c1}{n2-n1}$

substitute the values

$m=\frac{5.5-2.5}{5-0}$

$m=\frac{3}{5}$

we have

$b=2.5$ -----> because the point (0,2.5) is the c-intercept

substitute in the equation of slope-intercept form

$c=\frac{3}{5}(n)+2.5$

4 0

2 years ago

PLEASE HELP ME ON THIS!!!! THIS IS URGENT<br> I need to know if 1-5 if they are congruent or not

ehidna [41]

Answer:

3 and 4 not congruent

Step-by-step explanation:

8 0

2 years ago

I need help with this

netineya [11]

Answer:

1. -9

2. -2

3. -3

4. 2 (positive)

Step-by-step explanation:

positive + negative= positive

negative + positive =negative

positive +positive =positive

negative +negative =negative

hope you like it ( ' - ' )

4 0

2 years ago

Read 2 more answers

Mariulka [41]

Answer:

$A = 74.7^\circ$

$B = 42.5^\circ$

$C = 62.8^\circ$

Step-by-step explanation:

Given

$A = (-1,2) \to (x_1,y_1)$

$B = (2,8) \to (x_2,y_2)$

$C = (4,1) \to (x_3,y_3)$

Required

The measure of each angle

First, we calculate the length of the three sides of the triangle.

This is calculated using distance formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

For AB

$A = (-1,2) \to (x_1,y_1)$

$B = (2,8) \to (x_2,y_2)$

$d = \sqrt{(-1 - 2)^2 + (2 - 8)^2$

$d = \sqrt{(-3)^2 + (-6)^2$

$d = \sqrt{45$

So:

$AB = \sqrt{45$

For BC

$B = (2,8) \to (x_2,y_2)$

$C = (4,1) \to (x_3,y_3)$

$BC = \sqrt{(2 - 4)^2 + (8 - 1)^2$

$BC = \sqrt{(-2)^2 + (7)^2$

$BC = \sqrt{53$

For AC

$A = (-1,2) \to (x_1,y_1)$

$C = (4,1) \to (x_3,y_3)$

$AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2$

$AC = \sqrt{(-5)^2 + (1)^2$

$AC = \sqrt{26$

So, we have:

$AB = \sqrt{45$

$BC = \sqrt{53$

$AC = \sqrt{26$

By representation

$AB \to c$

$BC \to a$

$AC \to b$

So, we have:

$a = \sqrt{53$

$b = \sqrt{26$

$c = \sqrt{45$

By cosine laws, the angles are calculated using:

$a^2 = b^2 + c^2 -2bc \cos A$

$b^2 = a^2 + c^2 -2ac \cos B$

$c^2 = a^2 + b^2 -2ab\ cos C$

$a^2 = b^2 + c^2 -2bc \cos A$

$(\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A$

$53 = 26 +45 - 2 * 34.21 * \cos A$

$53 = 26 +45 - 68.42 * \cos A$

Collect like terms

$53 - 26 -45 = - 68.42 * \cos A$

$-18 = - 68.42 * \cos A$

Solve for $\cos A$

$\cos A =\frac{-18}{-68.42}$

$\cos A =0.2631$

Take arc cos of both sides

$A =\cos^{-1}(0.2631)$

$A = 74.7^\circ$

$b^2 = a^2 + c^2 -2ac \cos B$

$(\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B$

$26 = 53 +45 -97.67 * \cos B$

Collect like terms

$26 - 53 -45= -97.67 * \cos B$

$-72= -97.67 * \cos B$

Solve for $\cos B$

$\cos B = \frac{-72}{-97.67}$

$\cos B = 0.7372$

Take arc cos of both sides

$B = \cos^{-1}(0.7372)$

$B = 42.5^\circ$

For the third angle, we use:

$A + B + C = 180$ --- angles in a triangle

Make C the subject

$C = 180 - A -B$

$C = 180 - 74.7 -42.5$

$C = 62.8^\circ$

8 0

2 years ago