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

Answered by admin AT 14/01/2020 - 03:06 PM

A= -1; b= 2; c=3
so the answer will be 16
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Related questions

Which of the following verbal expressions represents the algebraic expression 2x – 8?. A.. eight less than twice a number. B.. the difference between eight and twice a number. C.. twice eight less than a number. D.. twice a number and eight

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.Write the equation of the line parallel to the line 10x - 5y = 8 and passing through the point (2,4).. 2.Write the equation of the line parallel to the line 4x + 2y = 5 and passing through the point (-3,5).. 3.Write the equation of the line parallel to the line 4x + y = -1 and passing through the point (5,0).. 4.Write the equation of the line perpendicular to the line x - 5y = -10 and passing through the point (2,5).. 5.Write the equation of the line perpendicular to the line x - 3y = 9 and passing through the point (3,5).. . a.y = -5x + 15. b.y = 2x. c.y = -3x + 14. d.y = -2x

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

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


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

A system of equations is shown below:. . 6x – 2y = 3->(equation 1). 5x + 3y = 4->(equation 2). . A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations. If equation 2 is multiplied by 1, which of the following steps should the student use for the proof?

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.

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


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

A falcon flew 70 miles in 3 hours. What was the speed of the falcon?. . Given: speed = distance over time; 1 mile = 1609 meters.

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.

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


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

If a solid has faces that consist of 2 equilateral triangles and 3 congruent rectangles, what type of solid is it?

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

To buy concert tickets there is a service charge and a cost per ticket. Write an equation to show the cost for any number of tickets. x y Number of Tickets Cost in Dollars 1 22 2 40 3 58 4 76 A. y = 22x B. y = 18x + 4 C. y = 18x D. y = 4x + 18

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.

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


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

There are 8 brooms and 6 mops in a janitor's closet. What is the ratio of the number of mops to the total number of brooms and mops?. . A: 4/3 . B:3/7 . C:7/3. D:3/4

B 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

Convert the following equation: 2.5 qt/min = ____ gal/h. a. 60 c. 72 . b. 37.5 d. 105 . . . .

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 = 2.5\times \dfrac{1\ qt}{1\ min}

                 = 2.5\times \dfrac{0.25\ gal}{0.0166\ h}

                 =37.5\times \dfrac{1\ gal}{1\ h}

                 = 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

If 6 times a certain number is added to 8, the result is 32.. . Which of the following equations could be used to solve the problem?. . . 6x = 32. 6(x + 8) = 32. 6x = 8 + 32. 6x + 8 = 32

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. 

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


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

The equation of line CD is (y−3) = − 2 (x − 4). What is the slope of a line perpendicular to line CD?. . .

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

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


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

The diagonals of parallelogram ABCD intersect at point E. If DE=2X+2,BE=3X-8 ,CE=4y , and AC=32, solve for x.. . A.. x = 2. B.. x = 10. C.. x = 15. D.. x = 22.

the diagonals bisect eachother. 2x+2 = 3x -8 and 4y = 1/2 (32)
x - 8 = 2
x=10

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


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

A solid has faces that consist of 4 triangles, 3 rectangles, and 1 hexagon. The solid has 9 vertices. How many edges does the solid have?. A.. 12 edges. B.. 15 edges. C.. 18 edges. D.. 21 edges.

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 equation of line XY is (y−3) = negative 2 over 3(x − 4). What is the slope of a line perpendicular to XY?

The slope of line XY: m = - 2/3
The slope of a line perpendicular to XY:
m1 =  \frac{-1}{ \frac{-2}{3} }=  \frac{3}{2}
m 1 = 1.5

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


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

Solve for the following equation: 7.86*4.6=? .

Here-
(7.86)
(4.6)           
=36.156


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


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

Jane , Andre and Maria picked 840 pounds of apples. Andre picked 3 times as many as Maria. Jane picks 2 times as many as Andre. How many pounds did Andre pick..

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. 

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


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

Matt plans to put concrete on a rectangular portion of his driveway. The portion is 8 feet long and 4 inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Matt needs is $58.07. Which of the following is closest to the width of the portion of the driveway on which Matt plans to put concrete?. . [1 foot = 12 inches; 1 yard = 3 feet]. a. 0.5 feet. b. 1.5 feet. c. 3 feet. d. 6 feet

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.

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


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

When you factor using the zero product rule, the solutions to the simpler equations are also the solutions to the original equation.. . A.True. B. False

Answer: TRUE

The zero product rule states that a product of factors is zero if and only if one or more of the factors is zero.

When you factor a polynomial, you break it up into simpler terms multiplied by each other, but such as the result of the multiplication is the original polynomial. Therefore, you simply write the polynomial in an alternative form made of factors.

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

. A lizard needs to stay a safe distance from a cactus. The diameter of the cactus is 14 inches. If the lizard is 8 inches from a point of tangency, find the direct distance between the lizard and the cactus (x). If necessary, round to the hundredths place.. . A.. x = 3.63 in.. B.. x = 4.57 in.. C.. x = 7.26 in.. D.. x = 17.63 in..

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)  

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


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

Describe how the transformed function below is obtained from its parent function. . y=(x-10)^3. . a.The parent function y=x^3 is shifted 10 units to the right. b.The parent function y=x^3 is shifted 10 units to the left.. c.The parent function y=(-x)^3 is strectched vertically by a factor of 10.. d.The parent function y=x^3 is shifted 10 units down.

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 y=x^3  is:

y = (x-10)^3

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

What is the general form of the equation of a circle with center at (a, b) and radius of length m?. A. x2 + y2 − 2ax − 2by + (a2 + b2 − m2) = 0 . . B.x2 + y2 + 2ax + 2by + (a2 + b2 − m2) = 0. C. x2 + y2 − 2ax − 2by + (a + b − m2) = 0. D. x2 + y2 + 2ax + 2by + a2 + b2 = -m2.

The generic equation of the circle is given by:
 (x-xo) ^ 2 + (y-yo) ^ 2 = r ^ 2&#10;
 Where,
 r: radius of the circle
 (xo, yo): center of the circle.
 The center of the circle in this case is:
 (xo, yo): (a, b)&#10;
 The radius of the circle is:
 r = m&#10;
 Substituting values we have:
 (x-a) ^ 2 + (y-b) ^ 2 = m ^ 2&#10;
 Rewriting the equation we have:
 x ^ 2 - 2ax + a ^ 2 + y ^ 2 - 2by + b ^ 2 - m ^ 2 = 0&#10;&#10;x ^ 2 + y ^ 2 - 2ax - 2by + a ^ 2 + b ^ 2 - m ^ 2 = 0
 Answer:
 The general form of the equation of a circle with center at (a, b) and radius of length m is:
 x ^ 2 + y ^ 2 - 2ax - 2by + a ^ 2 + b ^ 2 - m ^ 2 = 0&#10;
 option A

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


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

A figure with vertical line symmetry is placed on the coordinate plane. Given that the points (–8, –4) and (–3, –4) are on the edges of the figure, which of the following points lies on the line of symmetry?. A.(–5.5, –4). B.(–2.5, 0). C.(5.5, 4). D.(11, 8).

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. 

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


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

A plane takes off at an angle of elevation of 15° and travels in a straight line for 3,000 meters. What is the height of the plane above the ground at this instant?

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

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


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

To determine if an ordered pair is a solution to a system of linear equations in two variables, __________.. A.. substitute the coordinates of the ordered pair into either equation to see if it produces a true statement. B.. substitute the coordinates of the ordered pair in both equations to see if it produces a true statement for each. C.. substitute the coordinates of the ordered pair in the first equation to see if it produces a true statement. D.. substitute the coordinates of the ordered pair in the second equation to see if it produces a true statement

Answer:

                    Option: B

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

Step-by-step explanation:

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

Make a conjecture about the solution of a system of equations if the result of subtracting one equation from the other is 0 = 0. . . . . . a. . . . there are no solutions . . . c. . . . cannot determine any solution . . . . . b. . . . there are infinite number of solutions . . . d. . . . the solutions are inverses of each other . @petiteme

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.

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


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

A dependent system of equations is a system with __________.. . the same line. . parallel lines. . intersecting lines and lines that have the same equation. . intersecting lines and lines that have the same slope

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

(x,\frac{c-by}{a}

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

The function C(x) = 400x – 0.2x2 represents the total costs for a company to produce a product, where C is the total cost in dollars and x is the number of units sold. Which statement is true?. A. One thousand units have the minimum cost of $200,000.. B. One thousand units have the maximum cost of $200,000.. C. Two thousand units have the minimum cost of $800,000.. D. Two thousand units have the maximum cost of $800,000..

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. 

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


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

The product of two numbers is 713. The first number is 9 more than the second number. Which equation can be used to find x, the greater number?

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

Solve for the following equation:1.30×104kg=? Express your answer in Integers

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.

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


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