# 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

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

**Answer :**

We need to find the values of a, b, and c in the quadratic equation

The general form of quadratic equation is

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

can be written as

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

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.

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

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.

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

**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

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.

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:

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

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**

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:

substituting x=2 to 6x=3y

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

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

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.

[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

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

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.

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

**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

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,

Number of large buses

Number of small buses

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

So,

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)

with (6,0)

With (7,0)

Hence the minimum cost is $1700.

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

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

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**.

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

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

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

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

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°**

Translation is moving an object a certain distance. The original object and its translation have the same shape and size.

Answer:

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

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

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

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

**Answer:**

the answer is D and B

**Step-by-step explanation:**

APEX

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

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

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

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