Which of the following phrases are equations

Alexandra complete 40 percent of a 50-question assignment.how many questions did she complete?.

Georgia [21]

She answered 20 questions

3 0

3 years ago

Solve the given inequality :

tigry1 [53]

Answer:

x < -5 or x = 1 or 2 < x < 3 or x > 3

Step-by-step explanation:

Given rational inequality:

$\dfrac{(x-1)^2(x-2)^3}{(x^2-5x+6)^2(x+5)}\geq 0$

$\textsf{Factor }(x^2-5x+6):$

$\implies x^2-2x-3x+6$

$\implies x(x-2)-3(x-2)$

$\implies (x-3)(x-2)$

Therefore:

$\dfrac{(x-1)^2(x-2)^3}{(x-3)^2(x-2)^2(x+5)}\geq 0$

Find the roots by solving f(x) = 0 (set the numerator to zero):

$\implies (x-1)^2(x-2)^3=0$

$\implies (x-1)^2=0\implies x=1$

$\implies (x-2)^3=0 \implies x=2$

Find the restrictions by solving f(x) = undefined (set the denominator to zero):

$\implies (x-3)^2(x-2)^2(x+5)=0$

$\implies (x-3)^2=0 \implies x=3$

$\implies (x-2)^2=0 \implies x=2$

$\implies (x+5)=0 \implies x=-5$

Create a sign chart, using closed dots for the roots and open dots for the restrictions (see attached).

Choose a test value for each region, including one to the left of all the critical values and one to the right of all the critical values.

Test values: -6, 0, 1.5, 2.5, 4

For each test value, determine if the function is positive or negative:

$f(-6)=\dfrac{(-6-1)^2(-6-2)^3}{(-6-3)^2(-6-2)^2(-6+5)}=\dfrac{(+)(-)}{(+)(+)(-)}=+$

$f(0)=\dfrac{(0-1)^2(0-2)^3}{(0-3)^2(0-2)^2(0+5)}=\dfrac{(+)(-)}{(+)(+)(+)}=-$

$f(1.5)=\dfrac{(1.5-1)^2(1.5-2)^3}{(1.5-3)^2(1.5-2)^2(1.5+5)}=\dfrac{(+)(-)}{(+)(+)(+)}=-$

$f(2.5)=\dfrac{(2.5-1)^2(2.5-2)^3}{(2.5-3)^2(2.5-2)^2(2.5+5)}=\dfrac{(+)(+)}{(+)(+)(+)}=+$

$f(4)=\dfrac{(4-1)^2(4-2)^3}{(4-3)^2(4-2)^2(4+5)}=\dfrac{(+)(+)}{(+)(+)(+)}=+$

Record the results on the sign chart for each region (see attached).

As we need to find the values for which f(x) ≥ 0, shade the appropriate regions (zero or positive) on the sign chart (see attached).

Therefore, the solution set is:

x < -5 or x = 1 or 2 < x < 3 or x > 3

As interval notation:

$(- \infty,-5) \cup x=1 \cup (2,3) \cup(3,\infty)$

4 0

2 years ago

Find the value of each variable so that the quadrilateral is a parallelogram.

Dmitry [639]

Answer:

x = -2

y = -5

Step-by-step explanation:

Properties of a Parallelogram

Two pairs of opposite sides are parallel.
Two pairs of opposite sides are equal in length.
Two pairs of opposite angles are equal in measure
The diagonals bisect each other.
Adjacent angles are supplementary.
Each diagonal divides the quadrilateral into two congruent triangles.

Each diagonal is divided into two measures expressed with variables. Since diagonals bisect each other:

y + 23 = -4y - 2. And

-2x + 6 = x + 12

Solve the first equation. Adding 4y:

5y + 23 = - 2

Subtracting 23:

5y = -25

Dividing by 5:

y = -5

Solve the second equation. Subtracting x and 6:

-3x = 6

Dividing by -3:

x = -2

Solution:

x = -2

y = -5

4 0

3 years ago

A line has a slope of

padilas [110]

Step 1. The General Equation of a straight line is

Y = Mx + C where

M is the slope and
C is that point on the y axis where the curve cuts that axis (where x = 0)
In this case we are told that M = (3/4)

Our equation is now Y = (3/4)X + C ••• Equ 1

We are told that this curve passes through Point ( x, y ) = ( 8, -1 ).

Substitute these values of x, and y into Equ 1 to find C.

Y = (3/4)X + C or

( -1 ) = ( 3/4 )*( 8 ) + C or

( -1 ) = ( 6 ) + C or

C = ( - 7 )

Therefore the Equation of the Point Slope curve is

Y = ( 3/4 )X - 7

: Hope this helps :)

3 0

3 years ago

Alan needs to drive 400 miles to reach Madison. He is driving at a constant speed of 55 miles per hour. The function y = 400 − 5

lord [1]

Question is not written properly but i think you are looking for the table of given equation y=400-55x. So I will explain about how to get that.

number of hours can't be negative so that means x must be 0 or more.

like x=0,1,2,3,...

we just have to plug these x-values into above equation to find the y-value in order to calculate table.

I will show you calculation for x=2

y=400-55x=400-55*2=400-110=290

so the point in table will be (2,290)

similarly we can find more point and get final table as shown below:

7 0

4 years ago