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2 years ago

Solve the inequalities for x, and match each solution to its number line graph.

Mathematics

1 answer:

horrorfan [7]2 years ago

3 0

On a number line that represents an inequality, if it has a closed circle the inequality will say or show a greater/ less than or equal to or it will say the number is at least this. The at least means that it could be more than this but it could also be this number.

2 - 3/2(x) greater than or equal to 5 1/2 - This one is the last option

(2 * x) + (-2) greater than or equal to 8 - This one is the first option

7 - (4 * x) greater than 13 - The second one

4 + (3 * x) less than 19 - The third one

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Which equation represents a proportional relationship? A) y = x 8 B) y = 8 x C) y = x 8 + 8 D) y = 8 x + 8

Liula [17]

Answer:

B y=8x

Step-by-step explanation:

A proportional relationship must go through the point x=0, y=0 and be in the form y=kx where x is a constant

A) y = x^8

B) y = 8 x

C) y = x^8 + 8

D) y = 8 x + 8

The only points that is in the form y= kx is option B

C and D do not go through x=0, y=0 and A is not in the form y=kx where k is a constant

6 0

3 years ago

Plot the vertex, focus, and directrix for the parabola represented by this equation. X=-1/12(y-2)^2+1

alukav5142 [94]

The vertex of the parabola is (1, 2), focus of the parabola is (-2, 2), and directrix x = 4.

<h3>What is a parabola?</h3>

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have a parabola equation:

$\rm x = -\dfrac{1}{12}(y-2)^2+1$

The standard form of the parabola:

$\rm x = \dfrac{1}{4(f-h)}(y-k)^2+h$

(h, k) is the vertex of the parabola and (f, k) is the focus.

$\rm x = \dfrac{1}{4(-2-1)}(y-2)^2+1$

h = 1, k =2, and f = -2

The directrix is x = 4

Thus, the vertex of the parabola is (1, 2), focus (-2, 2), and directrix x = 4.

Learn more about the parabola here:

brainly.com/question/8708520

#SPJ1

5 0

2 years ago

Can someone simplify these expressions (c)

creativ13 [48]

Answer:

(10x+5)-(-23-2x)=

10x+5+23+2x

=12x+28

2x+5x^2-(3x+7x^2)=

2x+5x^2-3x-7x^2

= -2x^2-1

8 0

3 years ago

Pls solve the simultaneous equation in the attachment.

siniylev [52]

Answer:

Part a) The solution is the ordered pair (6,10)

Part b) The solutions are the ordered pairs (7,3) and (15,1.4)

Step-by-step explanation:

Part a) we have

$\frac{x}{2}-\frac{y}{5}=1$ ----> equation A

$y-\frac{x}{3}=8$ ----> equation B

Multiply equation A by 10 both sides to remove the fractions

$5x-2y=10$ ----> equation C

isolate the variable y in equation B

$y=\frac{x}{3}+8$ ----> equation D

we have the system of equations

$5x-2y=10$ ----> equation C

$y=\frac{x}{3}+8$ ----> equation D

Solve the system by substitution

substitute equation D in equation C

$5x-2(\frac{x}{3}+8)=10$

solve for x

$5x-\frac{2x}{3}-16=10$

Multiply by 3 both sides

$15x-2x-48=30$

$15x-2x=48+30$

Combine like terms

$13x=78$

$x=6$

<em>Find the value of y</em>

$y=\frac{x}{3}+8$

$y=\frac{6}{3}+8$

$y=10$

The solution is the ordered pair (6,10)

Part b) we have

$xy=21$ ---> equation A

$x+5y=22$ ----> equation B

isolate the variable x in the equation B

$x=22-5y$ ----> equation C

substitute equation C in equation A

$(22-5y)y=21$

solve for y

$22y-5y^2=21$

$5y^2-22y+21=0$

Solve the quadratic equation by graphing

The solutions are y=1.4, y=3

see the attached figure

<em>Find the values of x</em>

For y=1.4

$x=22-5(1.4)=15$

For y=3

$x=22-5(3)=7$

therefore

The solutions are the ordered pairs (7,3) and (15,1.4)

3 0

3 years ago

I NEED HELP FAST WHAT IS 80 + -9 - 5 + 89-66+44-9+87-100+213

kow [346]

Answer:

324 is ya answer!

5 0

3 years ago