What are the values of a, b, and c in the quadratic equation 0 = 5x – 4x2 – 2? a = 5, b = 4, c = 2 a = 5, b = –4, c = –2 a = –4, b = 5, c = –2 a = 4, b = –5, c = –2

QUESTION POSTED AT 14/01/2020 - 03:08 PM

Answered by admin AT 14/01/2020 - 03:08 PM

Answer : a = -4, b = 5, c = -2

We need to find the values of a, b, and c in the quadratic equation   0 = 5x - 4x^2 - 2

The general form of quadratic equation is   ax^2 + bx + c =0

First we arrange the equation in order. x^2 should come first

  0 = 5x - 4x^2 - 2 can be written as   0 = - 4x^2+ 5x - 2

The coefficient of x^2 is the value of 'a' = -4

The coefficient of x is the value of 'b' = 5

The constant is the value of 'c' = -2

So a = -4, b=5 and c= -2

Post your answer

Related questions

Each trip, a bus drops off more fans at a concert. On the first trip, the bus dropped off 30. On the 14th trip, which was the last one, the bus dropped off 95 fans. How many fans did the bus deliver to the concert in total?. A. 875. B. 813. C. 455. D. 423

This question is talking arithmetic sequence.
The first term (the first drop) = 30 people went down
The last term (14th trip) = 95 people went down

We are asked to get the total number of people delivered to the concert. We can used this formula.
= (1/2) * n * (first + last)
= (1/2) * 14 * (30 + 95)
= 875.

So there are 875 people who went to the concert.

ANSWERED AT 21/01/2020 - 10:49 AM


QUESTION POSTED AT 21/01/2020 - 10:49 AM

What is the sale price of a cell phone that is on sale for 15% off if the regular price is $75?. . . A.$60.00. B.$63.75. C. $64.25. .

The sale price would be 58.75.
If the retail value is $75 with a 15% discount, which the discount is $11.25, it's sale price would be $58.75.

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


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

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

Which of the following is a property of inverse variation?. A.. Two variables exhibit inverse variation if they have a constant ratio.. B.. Two variables exhibit inverse variation if their products always equal the same nonzero constant.. C.. Two variables exhibit inverse variation if, when one variable increases, the other variable increases.. D.. Two variables exhibit inverse variation if, when one variable decreases, the other variable decreases..

Answer:

The property which represents a inverse variation is:

                        Option: B

B.. Two variables exhibit inverse variation if their products always equal the same nonzero constant.

Step-by-step explanation:

Two variables i.e. variable  x and variable y are said to be in inverse variation if there exist a non-zero constant k such that:

                     xy=k

Also, with the increase of one variable the other variable decreases i.e. they vary inversely.

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


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

If you add the digits in a two-digit number and multiply the sum by 7, you get the original number. If you reverse the digits in the two-digit number, the new number is 18 more than the sum of its two digits. What is the original number? A. 42 B. 24 C. 64 D. 46 E. 36

The answer is A. 42

Solution:
Let x= ones digit, y=tens digit

1st condition (original number) : 7(x+y)=10y + x
2nd condition (new number by reversing the digits): 18+x+y=10x+y

simplifying:
1st condition: 6x=3y
2nd condition: x=2
substituting x=2 to 6x=3y
y=4

ANSWERED AT 21/01/2020 - 10:47 AM


QUESTION POSTED AT 21/01/2020 - 10:47 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

The base of S is an elliptical region with boundary curve 9x^2+4y^2=36. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base. Find the volume of the described solid S?

To obtain the equation for an elliptical region, we divide the boundary curve equation by 36, which gives us:

[9x^2 + 4y^2 = 36] / 36

(x^2)/4 + (y^2)/9 = 1

Since the given cross-sections are isosceles right triangles, the hypotenuse is found on the base. Using trigonometric functions, the hypotenuse is found to be 6 * sqrt(1 - (x^2)/4). The cross-sectional area is then found to be  9 (1 - (x^2)/4).

With the cross-section, we integrate it with limits of -2 to 2 in terms of x to find the volume. This is shown below:

 ∫ 
9 (1 - (x^2)/4) dx (-2,2) = 24

Therefore, the volume is 24 units^3.

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


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

The length of a rectangle is four times its width. If the perimeter is at most 130 centimeters, what is the greatest possible value for the width? Write an inequality to model the problem.. A.2w + 2 • (4w) < 130. B.2w + 2 • (4w) > 130. C. 2w + 2 • (4w) ≤ 130. D.2w + 2 • (4w) ≥ 130


Solution.

L = 4w --------The length of a rectangle is four times its width.
2w + 2L ≤ 130 ------- the perimeter is at most 130 centimeters.
Now, if substitute the first equation into the second inequality you will get
2w + 2 • (4w) ≤ 130.

Therefore, the inequality model in C is correct.

Bonus.
If you solve the inequality you will have a final answer w ≤ 13. The greatest value being 13.

Hope it helps,

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


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

An observer on the ground is x meters from the base of the launch pad of a rocket, which is at the same level as the observer. A few seconds after the rocket takes off vertically, the observer sees its tip at an angle of q° from the horizontal. How far above the ground is the tip of the rocket at that instant? Assume that the ground is level.. a) x/ tan q. b) x/sin q. cx tan q. d) x cos q.

This can be solved using trigonometric functions. The distance x serves as one leg of a triangle, and makes an angle q with the hypotenuse. The distance from the tip of the rocket to the ground make up the other leg of the triangle. So solving this:

tan q = y / x

Where: y = distance from the tip of the rocket to the ground

Therefore, y = x tan q

Among the choices, the correct answer is C.

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


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

A school district needs to arrange transportation for at least 360 students for a field trip. The district can use large buses or small buses. The large buses hold 60 students each and have an operating expense of $300 for the day. The small buses hold 45 students each and have an operating expense of $200 for the day. The district only has chaperones for, at most, seven buses. What is the minimum cost for the transportation for the field trip?. A.$1,400. B. $1,600. C.$1,700. D.$1,800

Answer:

$1700

Step-by-step explanation:

Let the number of large buses be x

Let number of small buses be y

Let C be the total cost for the trip

Since w eare given that cost of 1 large bus is 300 and 1 small bus is 200

So, Cost C  = 300 * number of large buses + 200 * number of small buses

So  C = 300 x + 200 y

Constraints are :

Since we are given that large buses can hold 60 students each

So, total students in x buses = 60 x

We are also given that small buses can hold 45 students each.

So, total students in y buses = 45y

Since we are also given that A school district needs to arrange transportation for at least 360 students

So, 60x+45y\geq 360

Number of large busesx\geq 0

Number of small buses y\geq 0

We are also given that The district only has chaperones for, at most, seven buses.

So, x+y\leq 7

Now we graph the constraints and find all the endpoints

Refer the attached Graph

So,End points are (3,4) , (6,0) and (7,0)

Now substitute these points in Cost function to find minimum cost.

with(3,4)

C = 300(3) + 200(4)

C = 1700

with (6,0)

C = 300(6) + 200(0)

C = 1800

With (7,0)

C = 300(7) + 200(0)

C = 2100

Hence the minimum cost is $1700.

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


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

What is the value of the fourth term in a geometric sequence for which a1 = 30 and r = 1/2?.

For a Geometric sequence:
a n = a ( n-1 ) * r
In this case: a 1 = 30
a 2 = 30 * 1/2 = 15
a 3 = 15 * 1/2 = 7.5
a 4 = 7.5 * 1/2 = 3.75 = 3 3/4
Answer: The value of the fourth term is 3.75 or 3 3/4.

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


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

WWhich of the following would not be a correct interpretation of a correlation of r = .90? . a) the variables are inversely related.. b) most of the data points fall very close to a distinct pattern. c) there exists a positive relationship between the variables. d) there exists a strong relationship between the variables. e) all of the above statements are correct

The answer to this question is letter A. the variables are inversely related. This means that if the number is bigger the lesser the prediction which is not the definition of correlation coefficient that has an r = .90. A correlation of r = .90 means a positive relationship between variables.

ANSWERED AT 21/01/2020 - 10:41 AM


QUESTION POSTED AT 21/01/2020 - 10:41 AM

John translated parallelogram ABCD using the rule (x,y)→(x+3, y-2). If angle A is 110° and angle B is 70°, what is the degree measurement of angle A'? . . a.70°. .b. 110°. .c. 40°. . d.180°

This is kind of a trick question. 
Translation is moving an object a certain distance. The original object and its translation have the same shape and size.
Answer: B ) Angle A´ = 110°

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


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

A transversal intersecting two lines creates eight different angles: _____ pairs of corresponding angles, _____ pairs of alternate interior angles,and _____ pairs of alternate exterior angles. . . A).. 2 . . . 2 . . .2. B).. 4 . . . 2 . . . 2. C).. 2 . . . 2 . . . 4. D).. 4 . . . 4 . . . 4

The correct answer among the choices given is option B. A transversal intersecting two lines creates eight different angles: four pairs of corresponding angles, two pairs of alternate interior angles,andtwo pairs of alternate exterior angles. A transversal line is a line that passes through two lines.

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


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

A model rocket is launched vertically with an engine that is ignited at time t = 0. The engine provides an upward acceleration of 30 m/^2 for 2 seconds. Upon reaching its maximum height, the rocket deploys a parachute, and then descends vertically toward the ground. A) Determine the speed of the rocket after the 2s firing of the engine B) What maximum height will the rocket reach? C) At what time after t=0 will the maximum height be reached?

A. For the first questions, it asked for the speed of the rocket when it goes down. A stands for speed so you add the upward speed of 30 then slows down by 10 when it goes down so

a=30+10=40m/s2

B. This refer to speed of the rocket as it goes down so with the formula

V = u +at

V = 40*2 = 80m/s

Then solve for S

S = ut + ½^2

S = 1/2* 40 * 2*2 = 80m

C. At t=0, the rocket is at rest.

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


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