# What is the value of the discriminant for the quadratic equation –3 = –x2 + 2x? Discriminant = b2 – 4ac –8 4 8 16

QUESTION POSTED AT 14/01/2020 - 03:06 PM

QUESTION POSTED AT 14/01/2020 - 03:06 PM

A= -1; b= 2; c=3

so the answer will be 16

so the answer will be 16

**Step-by-step explanation:**

We are given an algebraic expression as (2x - 8). We have to write the verbal expression for the above expression. Here, x is a variable, 8 is a constant minus is the algebraic operations. 2 is multiplied by the variable x.

A variable is defined as the number which changes. It stores only an integer.

Addition, subtraction, division etc are algebraic operations.

In the given verbal expression, it can be written as "the eight less than twice a number".

**Hence, the correct option is (a) "eight less than twice a number".**

ANSWERED AT 21/01/2020 - 10:48 AM

QUESTION POSTED AT 21/01/2020 - 10:48 AM

1.) Parallel to 10x - 5y = 8 ; (2,4)

10x - 5y = 8

5y = 10x - 8

y = 2x - 8/5

m = 2

y - 4 = 2(x - 2)

y - 4 = 2x - 4

y = 2x

2.) Parallel to 4x + 2y = 5 ; (-3,5)

4x + 2y = 5

2y = -4x + 5

y = -2x - 5/2

m = -2

y - 5 = -2(x + 3)

y - 5 = -2x - 6

y = -2x -1

3.) Parallel to 4x + y = -1 ; (5,0)

4x + y = -1

y = -4x - 1

m = -4

y - 0 = -4(x - 5)

y = -4x + 20

4.) Perpendicular to x - 5y = -10 ; (2,5)

x - 5y = -10

5y = x + 10

y = x/5 - 2

m = -5

y - 5 = -5(x - 2)

y - 5 = -5x + 10

y = -5x + 15

5.) Perpendicular to x - 3y = 9 ; (3,5)

x - 3y = 9

3y = x - 9

y = x/3 - 3

m = -3

y - 5 = -3(x - 3)

y - 5 = -3x + 9

y = -3x + 14

10x - 5y = 8

5y = 10x - 8

y = 2x - 8/5

m = 2

y - 4 = 2(x - 2)

y - 4 = 2x - 4

y = 2x

2.) Parallel to 4x + 2y = 5 ; (-3,5)

4x + 2y = 5

2y = -4x + 5

y = -2x - 5/2

m = -2

y - 5 = -2(x + 3)

y - 5 = -2x - 6

y = -2x -1

3.) Parallel to 4x + y = -1 ; (5,0)

4x + y = -1

y = -4x - 1

m = -4

y - 0 = -4(x - 5)

y = -4x + 20

4.) Perpendicular to x - 5y = -10 ; (2,5)

x - 5y = -10

5y = x + 10

y = x/5 - 2

m = -5

y - 5 = -5(x - 2)

y - 5 = -5x + 10

y = -5x + 15

5.) Perpendicular to x - 3y = 9 ; (3,5)

x - 3y = 9

3y = x - 9

y = x/3 - 3

m = -3

y - 5 = -3(x - 3)

y - 5 = -3x + 9

y = -3x + 14

ANSWERED AT 21/01/2020 - 10:48 AM

QUESTION POSTED AT 21/01/2020 - 10:48 AM

From my research, the question had contained the following choices:

Show that the solution to the system of equations 10x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

Show that the solution to the system of equations 10x – 2y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

Show that the solution to the system of equations 11x – y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

Show that the solution to the system of equations 11x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

Since all of the 2nd second equations of the choices are the same, we will ignore that. What we will do however, is to obtain the 1st equation of each choice and subtract it from the 1st given equation, and see if it is a multiple to the 2nd given equation. To show an example, let us take the equation in choice D:

11x + y = 7

6x – 2y = 3

_________

5x + 3y = 4

As we can see, it is a multiple of the second given equation. Therefore, the correct answer is choice D.

Show that the solution to the system of equations 10x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

Show that the solution to the system of equations 10x – 2y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

Show that the solution to the system of equations 11x – y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

Show that the solution to the system of equations 11x + y = 7 and 5x + 3y = 4 is the same as the solution to the given system of equations

Since all of the 2nd second equations of the choices are the same, we will ignore that. What we will do however, is to obtain the 1st equation of each choice and subtract it from the 1st given equation, and see if it is a multiple to the 2nd given equation. To show an example, let us take the equation in choice D:

11x + y = 7

6x – 2y = 3

_________

5x + 3y = 4

As we can see, it is a multiple of the second given equation. Therefore, the correct answer is choice D.

ANSWERED AT 21/01/2020 - 10:46 AM

QUESTION POSTED AT 21/01/2020 - 10:46 AM

There are a lot of information's that are already given in the question. Based on these information's the answer can be deduced.

1 mile = 1609 meters

Then

70 miles = 1609 * 70 meters

= 112630 meters

again

1 hour = 3600 seconds

3 hours = 3600 * 3 seconds

= 10800 seconds

So

Speed = 112630/10800 meters/second

= 10.4 meters per second.

So the falcon was flying at a speed of 10.4 meters per second.

1 mile = 1609 meters

Then

70 miles = 1609 * 70 meters

= 112630 meters

again

1 hour = 3600 seconds

3 hours = 3600 * 3 seconds

= 10800 seconds

So

Speed = 112630/10800 meters/second

= 10.4 meters per second.

So the falcon was flying at a speed of 10.4 meters per second.

ANSWERED AT 21/01/2020 - 10:46 AM

QUESTION POSTED AT 21/01/2020 - 10:46 AM

A right triangular prism is a solid that has faces that consist of 2 equilateral triangles and 3 congruent rectangles. It is also described to have two parallel faces, and 3 other faces that belong to the same place (and are not parallel to the parallel pair of faces).

ANSWERED AT 21/01/2020 - 10:45 AM

QUESTION POSTED AT 21/01/2020 - 10:45 AM

Given table:

X | Y

-------

1 | 22

2 | 40

3 | 58

4 | 76

As easy way to find out which of the equations in the choices is correct, is to plug in the different values of x, and see which equation gives out the corresponding values of y. Let us try this below:

A. y = 22x

22(1) = 22 || OK

22(2) = 44 || WRONG

B. y = 18x + 4

18(1) + 4 = 22 || OK

18(2) + 4 = 40 || OK

18(3) + 4 = 58 || OK

18(4) + 4 = 76 || OK

Therefore, the correct answer is B.

X | Y

-------

1 | 22

2 | 40

3 | 58

4 | 76

As easy way to find out which of the equations in the choices is correct, is to plug in the different values of x, and see which equation gives out the corresponding values of y. Let us try this below:

A. y = 22x

22(1) = 22 || OK

22(2) = 44 || WRONG

B. y = 18x + 4

18(1) + 4 = 22 || OK

18(2) + 4 = 40 || OK

18(3) + 4 = 58 || OK

18(4) + 4 = 76 || OK

Therefore, the correct answer is B.

ANSWERED AT 21/01/2020 - 10:44 AM

QUESTION POSTED AT 21/01/2020 - 10:44 AM

B 3:7

If there are 6 mops, and 14 mops and brooms, you get 6:14, which simplifies to 3:7.

If there are 6 mops, and 14 mops and brooms, you get 6:14, which simplifies to 3:7.

ANSWERED AT 21/01/2020 - 10:44 AM

QUESTION POSTED AT 21/01/2020 - 10:44 AM

**Answer:**

Correct option is:

**b. 37.5**

**Step-by-step explanation:**

We know that 1 qt=0.25 gal

also 1 min=0.0166 h

2.5 qt/min =

=

=

= 37.5 gal/h

**Hence, Correct option is:**

**b. 37.5**

ANSWERED AT 21/01/2020 - 10:43 AM

QUESTION POSTED AT 21/01/2020 - 10:43 AM

Let x be the certain number and that six time this number may be expressed as 6x. Based on the conditions presented above, the sum of 6x and 8 should be equal to 32. This may be mathematically expressed as,

6x + 8 = 32

Therefore, the answer is fourth choice.

6x + 8 = 32

Therefore, the answer is fourth choice.

ANSWERED AT 21/01/2020 - 10:42 AM

QUESTION POSTED AT 21/01/2020 - 10:42 AM

The given equation is in the point-slope form. The slope can be obtained by simple identification of the parts of the equation. This is shown below:

Given equation:

(y - 3) = -2 (x - 4)

y - y1 = m(x - x1)

Where slope, m = -2

The slope of a line perpendicular to the line CD is the negative reciprocal of the slope of the line CD. Therefore:

Slope = 1/2

Given equation:

(y - 3) = -2 (x - 4)

y - y1 = m(x - x1)

Where slope, m = -2

The slope of a line perpendicular to the line CD is the negative reciprocal of the slope of the line CD. Therefore:

Slope = 1/2

ANSWERED AT 21/01/2020 - 10:42 AM

QUESTION POSTED AT 21/01/2020 - 10:42 AM

the diagonals bisect eachother. 2x+2 = 3x -8
and
4y = 1/2 (32)

x - 8 = 2

x=10

x - 8 = 2

x=10

ANSWERED AT 21/01/2020 - 10:42 AM

QUESTION POSTED AT 21/01/2020 - 10:42 AM

Drawing this solid may be hard. Basing on the given description, a solid with nine vertices and having faces consisting of four triangles, three rectangles and one hexagon (polygon with six sides) would have a number of edges around twelve edges. Hence, letter A.

ANSWERED AT 21/01/2020 - 10:40 AM

QUESTION POSTED AT 21/01/2020 - 10:40 AM

The slope of line XY: m = - 2/3

The slope of a line perpendicular to XY:

m1 =

m 1 =**1.5**

The slope of a line perpendicular to XY:

m1 =

m 1 =

ANSWERED AT 21/01/2020 - 10:39 AM

QUESTION POSTED AT 21/01/2020 - 10:39 AM

Here-

(7.86)(4.6) =36.156

(7.86)(4.6) =36.156

ANSWERED AT 21/01/2020 - 10:38 AM

QUESTION POSTED AT 21/01/2020 - 10:38 AM

To answer the problem, let x be the number of apples Maria picked. By this representation, the number of apples Andre picked is 3x and that Jane picked 6x apples. The sum of all apples picked is 840. The equation that represent the situation is,

x + 3x + 6x = 840 ; x = 84

Andre picked 3x apples. Thus, Andre picked 252 apples.

x + 3x + 6x = 840 ; x = 84

Andre picked 3x apples. Thus, Andre picked 252 apples.

ANSWERED AT 21/01/2020 - 10:37 AM

QUESTION POSTED AT 21/01/2020 - 10:37 AM

Convert first the cost of $98 /yd³ by the conversion factor that 1 yd³ = 27 ft³.

($98 /yd³) (1 yd³ / 27 ft³) = $ 3 17/27/ft³

Let x be the width, the volume of the rectangular portion of the driveway is,

V = (8 ft) (1/3 ft) x = 8x/3 ft³

Using the given total cost of the protion,

C = $58.07 = (8x/3 ft³)($ 3 17/27/ft³)

x = 5.99957 ft

Thus, the answer is d. 6 feet.

($98 /yd³) (1 yd³ / 27 ft³) = $ 3 17/27/ft³

Let x be the width, the volume of the rectangular portion of the driveway is,

V = (8 ft) (1/3 ft) x = 8x/3 ft³

Using the given total cost of the protion,

C = $58.07 = (8x/3 ft³)($ 3 17/27/ft³)

x = 5.99957 ft

Thus, the answer is d. 6 feet.

ANSWERED AT 21/01/2020 - 10:36 AM

QUESTION POSTED AT 21/01/2020 - 10:36 AM

When you

Therefore, the solutions to the original equation (which is the polynomial set to zero) will be the solutions of the simpler equations because they are equivalent.

ANSWERED AT 21/01/2020 - 10:35 AM

QUESTION POSTED AT 21/01/2020 - 10:35 AM

We will use Pythagorean theorem:

x - The direct distance between the lizard and the cactus;

r = 7 - radius of the cactus;

x + 7 - the distance between the lizard and the center of the cactus:

( x + 7 )² = 7² + 8²

( x + 7)² = 49 + 64

( x + 7 )² = 113

x + 7 = √ 113

x + 7 = 10.63

x = 10.63 - 7

**x = 3.63**

Answer: A)

x - The direct distance between the lizard and the cactus;

r = 7 - radius of the cactus;

x + 7 - the distance between the lizard and the center of the cactus:

( x + 7 )² = 7² + 8²

( x + 7)² = 49 + 64

( x + 7 )² = 113

x + 7 = √ 113

x + 7 = 10.63

x = 10.63 - 7

Answer: A)

ANSWERED AT 21/01/2020 - 10:35 AM

QUESTION POSTED AT 21/01/2020 - 10:35 AM

**Answer:**

**Option a is correct**

The parent function y=x^3 is shifted 10 units to the right.

**Step-by-step explanation:**

**Horizontal shift:**

If a parent function y = f(x);

then; the transformation y = f(x+h) is either horizontal right or left.

If h < 0, then the shift is h units right

If h > 0, then the shift is h units left

**As per the statement:**

The transformed function below is obtained from its parent function is:

By definition of horizontal shift:

h = -10 < 0

⇒so the graph is shifted to 10 units right

**Therefore, The parent function y=x^3 is shifted 10 units to the right. **

ANSWERED AT 21/01/2020 - 10:34 AM

QUESTION POSTED AT 21/01/2020 - 10:34 AM

The generic equation of the circle is given by:

Where,

r: radius of the circle

(xo, yo): center of the circle.

The center of the circle in this case is:

The radius of the circle is:

Substituting values we have:

Rewriting the equation we have:

**Answer:**

** The general form of the equation of a circle with center at (a, b) and radius of length m is:**

** **

**option A**

Where,

r: radius of the circle

(xo, yo): center of the circle.

The center of the circle in this case is:

The radius of the circle is:

Substituting values we have:

Rewriting the equation we have:

ANSWERED AT 21/01/2020 - 10:34 AM

QUESTION POSTED AT 21/01/2020 - 10:34 AM

Based on the description, the edges lying on those coordinates can be considered end points to a line. In this scenario, we can apply the midpoint formula to find the coordinates that lies on the vertical symmetry.

Midpoint formula: (x1+x2) / 2 for the x coordinate

(y1+y2) / 2 for the y coordinate

After calculating this, we obtain (-5.5, -4) as our midpoint. Hence the answer is letter A.

Midpoint formula: (x1+x2) / 2 for the x coordinate

(y1+y2) / 2 for the y coordinate

After calculating this, we obtain (-5.5, -4) as our midpoint. Hence the answer is letter A.

ANSWERED AT 21/01/2020 - 10:34 AM

QUESTION POSTED AT 21/01/2020 - 10:34 AM

Forming thw diagram, you have the length of the hypotenuse, and you want to find the height, which is the 'opposite length to the angle'

So using SOHCAHTOA we have:

sin15 = height / 3000

height = 3000 sin 15 height = 776.46m

So, the height of the plane above the ground at this instant is 776.46m

So using SOHCAHTOA we have:

sin15 = height / 3000

height = 3000 sin 15 height = 776.46m

So, the height of the plane above the ground at this instant is 776.46m

ANSWERED AT 21/01/2020 - 10:34 AM

QUESTION POSTED AT 21/01/2020 - 10:34 AM

** Option: B**

B. substitute the coordinates of the ordered pair in both equations to see if it produces a true statement for each.

Solution to the system of linear equations is a set of the ordered pair (x,y) such that it satisfy both the equations and make both the equations true.

We solve the system of linear equations by different methods such as substitution method (In this method we substitute the value of one variable in terms of other variable from one equation into the other to find the value of both the variables which is the solution) , elimination method (In this method by applying some operations such as multiplying a equation by some variable and then subtract or add to the other equation we find the solution set) etc.

ANSWERED AT 21/01/2020 - 10:33 AM

QUESTION POSTED AT 21/01/2020 - 10:33 AM

The correct answer for this question is "b. there are infinite number of solutions."

Following the steps: Make a conjecture about the solution of a system of equations if the result of subtracting one equation from the other is 0 = 0. This will give you an infinite number of solutions.

Following the steps: Make a conjecture about the solution of a system of equations if the result of subtracting one equation from the other is 0 = 0. This will give you an infinite number of solutions.

ANSWERED AT 21/01/2020 - 10:32 AM

QUESTION POSTED AT 21/01/2020 - 10:32 AM

**Answer:**

The same lines

**Step-by-step explanation:**

The same lines will form a dependent system of equations.

This is because when two lines are coincident we have say lines as the same.

If the same line is of the form say

ax+by=c

THis time we can write (x,y) as y = (c-ax)/b

Thus solution would be

ordered pair

Thus dependent solution

But parallel lines do not have solution at all, while intersecting lines have unique solution.

So answer is same lines

ANSWERED AT 21/01/2020 - 10:32 AM

QUESTION POSTED AT 21/01/2020 - 10:32 AM

To determine the maxima and minima of the polynomial, differentiate the given based on x and equate to 0.

C(x) = 400x - 0.2x²

dC(x) / dt = 400 - 0.4 x = 0

The value of x is 1000. This is the value of the maxima. As the value of C(x) continously becomes lesser as the value of x is set higher, the minima is not identified. Substitute x to the original equation,

C(x) = (400)(1000) - 0.2(1000²) = $ 200,000

Thus, the answer is letter B.

C(x) = 400x - 0.2x²

dC(x) / dt = 400 - 0.4 x = 0

The value of x is 1000. This is the value of the maxima. As the value of C(x) continously becomes lesser as the value of x is set higher, the minima is not identified. Substitute x to the original equation,

C(x) = (400)(1000) - 0.2(1000²) = $ 200,000

Thus, the answer is letter B.

ANSWERED AT 21/01/2020 - 10:31 AM

QUESTION POSTED AT 21/01/2020 - 10:31 AM

The answer is ten over nine. 10/9.

ANSWERED AT 21/01/2020 - 10:31 AM

QUESTION POSTED AT 21/01/2020 - 10:31 AM

Guys, the answer is A. for short.

Good luck with the rest of the test, and have a nice day!

ANSWERED AT 21/01/2020 - 10:29 AM

QUESTION POSTED AT 21/01/2020 - 10:29 AM

It is aaaaaaaaaaaaaaaaa

ANSWERED AT 21/01/2020 - 10:29 AM

QUESTION POSTED AT 21/01/2020 - 10:29 AM

If the equation is this:

1.3 x 10^4 kg

Then answer would be:

1.3 x 10^4 kg = 13000 kg

The given is in scientific notation and the answer is already an integer. So, the answer to the questions is 13,000 kg.

1.3 x 10^4 kg

Then answer would be:

1.3 x 10^4 kg = 13000 kg

The given is in scientific notation and the answer is already an integer. So, the answer to the questions is 13,000 kg.

ANSWERED AT 21/01/2020 - 10:28 AM

QUESTION POSTED AT 21/01/2020 - 10:28 AM