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2 years ago

What is the system of inequalities associated with the following graph?

Mathematics

1 answer:

Xelga [282]2 years ago

7 0

y >= 5x + 3

y >= -x - 3

The system is:

5x - y <= -3

x + y >= -3

Answer: The 4th choice

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Triangle X Y Z is shown. Angle X Y Z is 51 degrees and angle Y Z X is 76 degrees. The length of X Z is 2.6, the length of X Y is

stepan [7]

Answer:

$z=3.2\ units$

Step-by-step explanation:

we know that

In the triangle XYZ

Applying the law of sines

$\frac{2.6}{sin(51^o)}=\frac{z}{sin(76^o)}$

solve for z

$z=\frac{2.6}{sin(51^o)}sin(76^o)$

$z=3.2\ units$

5 0

2 years ago

Read 2 more answers

A circle has diameter of 11cm

dlinn [17]

Since length of diagonal ( $Diagonal= 9.9cm$ ) is less than diameter of circle ( 11 cm ) , Therefore , the square will fit inside the circle without touching the edge of the circle.

<u>Step-by-step explanation:</u>

Here we have , A circle has diameter of 11 cm A square has side length of 7 cm . Use Pythagoras’ Theorem to show that the square will fit inside the circle without touching the edge of the circle . Let's find out:

We know the concept that for any square to fit inside the circle without touching the edge of circle , diagonal of square must be less than diameter of circle . Let's find out length of diagonal by using Pythagoras Theorem :

$Hypotenuse ^2 = Perpendicular^2+Base^2$

For a square , $Perpendicular = base = side$

⇒ $Diagonal^2 = 2(side)^2$

⇒ $Diagonal= \sqrt{2}(side)$

⇒ $Diagonal= \sqrt{2}(7)$

⇒ $Diagonal= 9.9cm$

Since length of diagonal ( $Diagonal= 9.9cm$ ) is less than diameter of circle ( 11 cm ) , Therefore , the square will fit inside the circle without ruching the edge of the circle.

5 0

2 years ago

Quadrilateral $abcd$ is a trapezoid with $ab$ parallel to $cd$. we know $ab = 20$ and $cd = 12$. what is the ratio of the area o

alekssr [168]

Draw a diagram to illustrate the problem as shown below.

The area of triangle acb is
A₁ = (1/2)*20*h = 10h

The area of trapezoid abcd is
A₂ = (1/2)*(20+12)*h = 16h

The ratio A₁/A₂ is
A₁/A₂ = (10h)/(16) = 5/8

Answer:
The ratio of triangle acb to the area of trapezoid abcd is 5/8.