Which of these is equivalent to the given angle? A) 73.6° B) 110° C) 147.3° D) 220°

Which ordered pair is a solution to the following system of inequalities?

PtichkaEL [24]

Answer: (0,-1)

Step-by-step explanation:

Let's start with the first inequality, $y < -x^{2}+x$ . To check which points satisfy this inequality, we can substitute the x- and y-coordinates and see if they satisfy the inequality.

A) $-1 < -0^{2}+0 \longrightarrow -1 < 0 \longrightarrow \text{ True}$
B) $1 < -1^{2}+1 \longrightarrow 1 < 0 \longrightarrow \text{ False}$
C) $-3 < -2^{2}+2 \longrightarrow -3 < -2 \longrightarrow \text{ True}$
D) $-6 < -3^{2}+3 \longrightarrow -6 < -6 \longrightarrow \text{ False}$

Once again, we can repeat this for the second inequality (but this time, we only need to check the points that satisfy the first inequality).

A) $-1 > 0^{2}-4 \longrightarrow -1 > -4 \longrightarrow \text{ True}$
C) $-3 > 2^{2}-4 \longrightarrow -3 > 0 \longrightarrow \text{ False}$

Therefore, the answer is (A) (0, -1).

3 0

2 years ago

What is the solution of y= 1/2x - 1 and y=3x+4

exis [7]

Answer:

(-2,-2)

Step-by-step explanation:

solve by elimination

3 0

3 years ago

The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is

andriy [413]

Answer:0.2

Step-by-step explanation:

A=3

P(A)=P(3)

=0.2

7 0

3 years ago

The height of the above triangle is ?

valentina_108 [34]

A = 1/2 bh
A = 1/2 (9)(5)
A = 45/2
A = 22.5

answer
22.5 cm^2

3 0

3 years ago

If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3

horrorfan [7]

Answer: The correct option is (B) 24 : 25.

Step-by-step explanation: Given that the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2 : 3.

We are to find the ratio of the area of R to the area of S.

Let 2x, 3x be the sides of rectangle R and y be the side of square S.

Then, according to the given information, we have

$\textup{Perimeter of rectangle R}=\textup{Perimeter of square S}\\\\\Rightarrow2(2x+3x)=2(y+y)\\\\\Rightarrow 5x=2y\\\\\Rightarrow \dfrac{x}{y}=\dfrac{2}{5}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Therefore, the ratio of the area of R to the area of S is

$\dfrac{2x\times3x}{y\times y}\\\\\\=\dfrac{5x^2}{y^2}\\\\\\=6\left(\dfrac{x}{y}\right)^2\\\\\\=6\times\left(\dfrac{2}{5}\right)^2~~~~~~~~~~~[\textup{Using equation (i)}]\\\\\\=\dfrac{24}{25}\\\\=24:25.$

Thus, the required ratio of the area of R to the area of S is 24 : 25.

Option (B) is CORRECT.

6 0

3 years ago