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diamong [38]
3 years ago
13

What integer values satisfy both inequalities? − 2 < x < 3 − 2 ≤ x < 2

Mathematics
1 answer:
NARA [144]3 years ago
6 0

Given:

The inequalities are:

-2

-2\leq x

To find:

The integer values that satisfy both inequalities.

Solution:

We have,

-2

-2\leq x

For -2, the possible integer values are

x=-1,0,1,2          ...(i)

For -2\leq x, the possible integer values are

x=-2,-1,0,1        ...(ii)

The common values of x in (i) and (ii) are

x=-1,0,1

Therefore, the integer values -1, 0 and 1 satisfy both inequalities.

You might be interested in
Given that (x+y+z)(xy+xz+yz)=18 and that x^2(y+z)+y^2(x+z)+z^2(x+y)=6 for real numbers x, y, and z, what is the value of xyz?
worty [1.4K]

Answer:

4

Step-by-step explanation:

(x+y+z)(xy+xz+yz)=18 Equation 1

x^2(y+z)+y^2(x+z)+z^2(x+y)=6 Equation 2

What is the value of xyz where each variable represents a real number?

Let's expand equation 1:

(x+y+z)(xy+xz+yz)=18

x(xy)+x(xz)+x(yz)+y(xy)+y(xz)+y(yz)+z(xy)+z(xz)+z(yz)=18

Simplify each term if can:

x^2y+x^2z+xyz+y^2x+xyz+y^2z+xyz+z^2x+z^2y=18

See if we can factor a little to get some of the left hand side of equation 2:

The first two terms have x^2 and if I factored x^2 from first two terms I would have x^2(y+z) which is the first term of left hand side of equation 2.

So let's see what happens if we gather the terms together that have the same variable squared together.

x^2y+x^2z+y^2x+y^2z+z^2y+z^2x+xyz+xyz+xyz=18

Factor the variable squared terms out of each binomial pairing:

x^2(y+z)+y^2(x+z)+z^2(y+x)+xyz+xyz+xyz=18

Replace the sum of those first three terms with what it equals which is 6 from the equation 2:

6+xyz+xyz+xyz=18

Combine like terms:

6+3xyz=18

Subtract 6 on both sides:

3xyz=12

Divide both sides by 3:

xyz=4

4 0
3 years ago
Let f(x) = x^2 + 6x.
rusak2 [61]

Answer:

(A) The slope of secant line is 18.

(B) The slope of secant line is h+16.

Step-by-step explanation:

(A)

The given function is

f(x)=x^2+6x

At x=3,

f(3)=(3)^2+6(3)=27

At x=9,

f(9)=(9)^2+6(9)=135

The secant line joining (3,27) and (9,135). So, the slope of secant line is

m=\dfrac{y_2-y_1}{x_2-x_1}

m=\dfrac{135-27}{9-3}=18

The slope of secant line is 18.

(B)

The given function is

f(x)=x^2+6x

At x=5,

f(5)=(5)^2+6(5)=55

At x=5+h,

f(5+h)=(5+h)^2+6(5+h)=h^2 + 16 h + 55

The secant line joining (5,55) and (5+h,h^2 + 16 h + 55). So, the slope of secant line is

m=\dfrac{h^2 + 16 h + 55-55}{5+h-5}

m=\dfrac{h^2 + 16 h }{h}

m=h+16

The slope of secant line is h+16.

4 0
3 years ago
Quincy is trying to estimate the height of a tree in his backyard. he measures the tree’s shadow as 12 ft. he stands near the tr
slava [35]
I believe he should add 2ft to the height of the tree as well
3 0
3 years ago
How many solutions does this linear system have?<br> Y=-1/2x +4x+2y=-8
Vadim26 [7]

Answer: theres no solution

7 0
3 years ago
A grocery store sells a bag of 3 oranges for $2.79. How much would it cost for 4 oranges?
Kaylis [27]

Answer:

$3.72

Step-by-step explanation:

Divide $2.79 by 3

$0.93 is the price of one orange

$0.93 times 4 is $3.72

Hope this helps!

3 0
3 years ago
Read 2 more answers
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