Which expression has a negative value?
7 + 3 (negative 4) (2)
Negative 2 Left-bracket 12 divided by (negative 3) Right-bracket
(15 minus 7) minus (9 divided by 3)
Negative 5 Left-bracket 7 + (negative 14) Right-bracket minus 30

A: 7 + 3 (negative 4) (2)

Step-by-step explanation:

Just as a rule of thumb, whenever you multiply or divide one negative number and one positive number, the outcome is always negative. However, whenever you multiply or divide two negative numbers OR two positive numbers, the outcome is always positive.

Now, let's first convert all these words into simple mathematical expressions and then solve them:

A) "7 + 3 (negative 4) (2)" = 7 + 3 * (-4) * 2 = 7 + (-24) = -17

B) "Negative 2 Left-bracket 12 divided by (negative 3) Right-bracket" =

-2 * [12/(-3)] = -2 * (-4) = 8

C) "(15 minus 7) minus (9 divided by 3)" = (15 - 7) - (9/3) = 8 - 3 = 5

D) "Negative 5 Left-bracket 7 + (negative 14) Right-bracket minus 30" =

-5 * [7 + (-14)] - 30 = -5 * (-7) - 30 = 35 - 30 = 5

The only expression that produces a negative value is the first one, A.

Hope this helps!

First one

Step-by-step explanation:

7 + 3 (negative 4) (2)

7 + 3(-4)(2)

7 - 24

= -17

Negative 2 Left-bracket 12 divided by (negative 3) Right-bracket

-2(12/-3)

-2 × -4

8

(15 minus 7) minus (9 divided by 3)

(15 - 7) - (9/3)

8 - 3

5

Negative 5 Left-bracket 7 + (negative 14) Right-bracket minus 30

-5(7 + -14) - 30

-5(-7) - 30

35 - 30

5

1. f(x)=x²+10x+16

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=1(as, a> 0 the parabola is open upward), b=10. by putting the values.

-b/2a = -10/2(1) = -5

f(-b/2a)= f(-5)= (-5)²+10(-5)+16= -9

so, vertex = (-5, -9)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+16, we get point (0,16).

now find x-intercept put y=0 in the above equation. 0= x²+10x+16

x²+10x+16=0 ⇒x²+8x+2x+16=0 ⇒x(x+8)+2(x+8)=0 ⇒(x+8)(x+2)=0 ⇒x=-8 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

2. f(x)=−(x−3)(x+1)

by multiplying the factors, the general form is f(x)= -x²+2x+3.

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=2. by putting the values.

-b/2a = -2/2(-1) = 1

f(-b/2a)= f(1)=-(1)²+2(1)+3= 4

so, vertex = (1, 4)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point (0, 3).

now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.

-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒x=3 , x=-1

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

3. f(x)= −x²+4

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(as, a< 0 the parabola is open downward), b=0. by putting the values.

-b/2a = -0/2(-1) = 0

f(-b/2a)= f(0)= −(0)²+4 =4

so, vertex = (0, 4)

now, find y- intercept put x=0 in the above equation. f(0)= −(0)²+4, we get point (0, 4).

now find x-intercept put y=0 in the above equation. 0= −x²+4

−x²+4=0 ⇒-(x²-4)=0 ⇒ -(x-2)(x+2)=0 ⇒x=2 , x=-2

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

4. f(x)=2x²+16x+30

use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=2(as, a> 0 the parabola is open upward), b=16. by putting the values.

-b/2a = -16/2(2) = -4

f(-b/2a)= f(-4)= 2(-4)²+16(-4)+30 = -2

so, vertex = (-4, -2)

now, find y- intercept put x=0 in the above equation. f(0)= 0+0+30, we get point (0, 30).

now find x-intercept put y=0 in the above equation. 0=2x²+16x+30

2x²+16x+30=0 ⇒2(x²+8x+15)=0 ⇒x²+8x+15=0 ⇒x²+5x+3x+15=0 ⇒x(x+5)+3(x+5)=0 ⇒(x+5)(x+3)=0 ⇒x=-5 , x= -3

from vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. the graph is attached below.

5. y=(x+2)²+4

the general form of parabola is y=a(x-h)²+k , where vertex = (h,k)

if a> 0 parabola is opened upward.

if a< 0 parabola is opened downward.

compare the given equation with general form of parabola.

-h=2 ⇒h=-2

k=4

so, vertex= (-2, 4)

as, a=1 which is greater than 0 so parabola is opened upward and the graph has minimum.

hope this : )

a

step-by-step explanation: