WRITE THE EQUATION OF THE CONIC SHOWN BELOW

Answer:

m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Step-by-step explanation:

2m³ - 5m² - 7m = 0 ← factor out common factor m from each term

m(2m² - 5m - 7) = 0

factorise the quadratic 2m² - 5m - 7

consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term

product = 2 × - 7 = - 14 and sum = - 5

the factors are + 2 and - 7

use these factors to split the m- term

2m² + 2m - 7m - 7 ( factor the first/second and third/fourth terms )

2m(m + 1) - 7(m + 1) ← factor out (m + 1) from each term

(m + 1)(2m - 7)

then

2m³ - 5m² - 7m = 0

m(m + 1)(2m - 7) = 0 ← in factored form

equate each factor to zero and solve for m

m = 0

m + 1 = 0 ( subtract 1 from both sides )

m = - 1

2m - 7 = 0 ( add 7 to both sides )

2m = 7 ( divide both sides by 2 )

m = \(\frac{7}{2}\)

solutions are m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Answer:

2 units

Step-by-step explanation:

vertical distance will be the magnitude of the difference in the 'y' coordinates

| -.8 - 1.2| = 2 units

Answer:

We have the magnitude, M, and the angle A.

(The angle is always measured from the +x-axis)

Then we have that:

x = M*cos(A)

y = M*sin(A)

in this case:

M = 9m

A = -80°

x = 9m*cos(-80°) = 1.562

y = 9m*sin(-80) = -8.86m

Now, the component parallel to the x axis is:

x = 9m*cos(-80°) = 1.562 m

And the slope of something parallel to the x-axis is always zero, as this is a constant line.

Answer:

700 and 700

Step-by-step explanation:

Answer:

4x+y=-4

Step-by-step explanation:

Plug in the intercept after the equal sign and multiply the x coordinate by the slope

A variable in mathematics is a number that can change depending on the issue. Several mathematical statements and equations use the generic letters x, y, and z. In other words, a variable is a symbol that stands for an unknowable numeric value. Say that x Plus 5 equals 10. The "x" variable is used here.

The variable "model of car driven" is qualitative because it is an attribute characteristic. Qualitative variables are those that are not numerical in nature but rather represent characteristics or categories that can be observed or measured through attributes. In this case, the model of the car driven is a type of attribute that describes the make and model of the car, such as Honda Civic, Toyota Corolla, etc.

Therefore, option B is the correct answer.

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Optiοn B, "The variable is qualitative because it is an attribute characteristic," is the cοrrect answer.

A qualitative variable is a type οf variable in statistics that describes a characteristic οr quality οf an οbject οr phenοmenοn. It is alsο called a categοrical variable, and it can be nοminal οr οrdinal. Nοminal variables have categοries that have nο inherent οrder, while οrdinal variables have categοries with a natural οrder οr ranking.

The variable "Mοdel οf car driven" is qualitative because it is an attribute characteristic. Qualitative variables are variables that are nοt numerical in nature but are based οn attributes οr characteristics. In this case, the mοdel οf the car driven is a categοrical variable that describes a particular characteristic οf the car, such as its make οr mοdel. This variable cannοt be measured quantitatively οr numerically, but rather it can be categοrized based οn specific attributes οr features.

Therefοre, οptiοn B, "The variable is qualitative because it is an attribute characteristic," is the cοrrect answer.

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Answer:

10

Step-by-step explanation:

The length of segment GH is approximately 2.2

We have,

To find the length of segment GH, we need to calculate the distance between points G(-1, -4) and H(-3, -3).

The distance formula between two points \((x_1, y_1) ~and ~(x_2, y_2)\) in a coordinate plane is given by:

\(d = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}\)

Applying the formula to the coordinates of points G and H, we have:

d = √((-3 - (-1))² + (-3 - (-4))²)

d = √((-3 + 1)² + (-3 + 4)²)

d = √((-2)² + (1)²)

d = √(4 + 1)

d = √(5)

The length of segment GH is the square root of 5, which is approximately 2.24 when rounded to the nearest tenth.

Therefore,

The length of segment GH is approximately 2.2

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Answer:

y = 8 when x = 2

Step-by-step explanation:

y = 4x

Answer:

Given equations are,

5x+2y=−2        (1)

3x−5y=17.4      (2)

Multiply equation (1) by 5 and equation (2) by 2, we get,

5(5x+2y)=5×−2

∴25x+10y=−10          (3)

2(3x−5y)=2×17.4

∴6x−10y=34.8          (4)

Adding equations (3) and (4), we get,

31x=24.8

∴x=

31

24.8

​

Put this value in equation (1), we get,

5(

31

24.8

​

)+2y=−2

∴

31

124

​

+2y=−2

∴2y=−2−

31

124

​

∴2y=

31

−186

​

∴y=

31

−93

​

Step-by-step explanation:

8/21 of the lawn still needs to be mowed.

To compare fractions, we need a common denominator. The least common multiple of 7 and 3 is 21.

Miss Lianto's fraction: (2/7) x (3/3) = 6/21

Son's fraction: (1/3) x (7/7) = 7/21

To calculate how much of the lawn still needs to be mowed, we can subtract the combined fractions mowed from the total:

Combined fractions mowed: 6/21 + 7/21 = 13/21

So, Remaining fraction: 1 - 13/21 = 8/21

Therefore, 8/21 of the lawn still needs to be mowed.

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Answer:

see below

Step-by-step explanation:

Mr. Brown

72 magazines/ 24 students = 3 magazines per student

Mrs. Garcia

98 magazines/ 28 students = 3.5 magazines per student

Mrs. Garcia sold more per student

Answer:

5

Step-by-step explanation:

5 x 3 = 15

n x 4 = 4n

3 + 4 = 7

(5 x 3) + (n x 4) = 5(3 + 4)

15 + 4n = 5*7

15 + 4n = 35

4n = 35 - 15

4n = 20

n = 20/4

n = 5

Hence, the value of missing number (n) is 5.

9

This seems to be an isosceles triangle, which means that 2 sides are equal. In this case, that would be 9.

Answer:

12 square yards

Step-by-step explanation:

The formula for area is A = l x w The length is 4 and the width is 3. Now that you know these values, you can substitute them into the equation and get the actual area as the answer. 3 x 4 = 12, so the answer is 12 square yards.

Answer:

28th

Step-by-step explanation:

There will be  a wednesday in the first week

Wed        2nd Wed

1                    8

2                   9          <===== this is the Wednesday in question

                             Monday would be 2 days earlier at 7th

                                then every 7 days there is another Monday

                                      7   14  21  28  <===== this would be the last one

The solution to 3x + 2(4 + 6x) = 113 is x=7

3x + 2(4 + 6x) = 113

We will multiply the 2 with the brackets

3x+8+12x=13

adding the coefficients os x together

15x+8=113

adding -8 on both the sides

15x=105

dividing both the sides by 15

x=105/15

after division we get

x=7

To check our solution

we first put value of x in our original equation

3x7 + 2(4 + 6x7) = 113

we simplify the equation

21+2(4+42)=113

According to BODMAS we first solve the bracket

21+2(46)=113

now we solve the multiplication part

21+92=113

solving this

113=113

∴ LHS=RHS

Hence the solution is correct.

Therefore, the solution to 3x + 2(4 + 6x) = 113 is x=7

BODMAS is an acronym used to remember the order of precedence for operations. It stands for Brackets of Order(exponents) Division, multiplication, Addition, Subtraction

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Answer:

The range of values of x for which the function is < 0 is:

2<x<3.

Step-by-step explanation:

x²-5x+6<0

First find the critical points:

x^2 - 5x + 6 = 0

(x - 2)(x - 3) = 0.

x = 2, 3.

The critical points are 2 and 3.

Make a table of values:

x                      x<2      2<x<3          x >3

x -2                  < 0          >0             >0

x -3                   <0           <0             >0

(x - 2)(x - 3)       >0          <0             >0

Answer:

Step-by-step explanation:

We assume your intended attendance equation is ...

  A = -1.95x^3 +70.1x^2 -188x +2150

a. For x=0 (corresponding to 1985), the first three terms are 0, so we have ...

  A = 2150 . . . . the initial value of the function

__

b. For x=13 (corresponding to 1985) we have ...

  A = ((-1.95(13) +70.1)(13) -188)(13) +2150 = (44.75(13) -188)(13) +2150

  = 393.75(13) +2150 = 7268.75

Attendance in the year 1998 is modeled to be about 7269.

The probability that both disc are white will be 1/9.

The probability that both disc are red will be 10 /27.

Number of red disc = 6

Number of white disc = 3

Total number of disc = 3 + 6 = 9 disc

The probability that both disc are white will be:

= 3/9 × 2/8

= 6/72

= 1/9

The probability that both disc are red will be:

= 6/9 × 5/9

= 30/81

= 10/27

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Answer:

Step-by-step explanation:

Pythagorean theorem

a²+b²=c²

so

5² + 12² = x²

25 + 144 = x²

169 = x²

x = √169

x = 13

Option B: The domain of the function is the set of all real numbers, Option C: the range of the function is the set of all non-negative real numbers, Option D: the graph has an intercept at (0, 0), and option G: the graph is symmetric with respect to the y-axis are correct statements about the graph.

There are only real numbers in the domain, or collection of x-values. This is so because x holds true for all numbers. The set of all non-negative real numbers is known as the range or set of y-values. This is due to the fact that every value we obtain for y is a positive real number. The graph's x-intercept and y-intercept, also known as the intersection point, are located at (0, 0). Instead of the other way around, the graph increases on the interval x>0 and decreases on the interval x<0. Instead of a maximum, the graph shows a minimum at (0, 0). The graph is symmetric with respect to the y-axis because it may be folded in half along that axis.

As per the question, the function described below is an example of a polynomial function since it is a function of a single independent variable that has been raised to an integer power. Adding terms with a numerical coefficient multiplied by a specific power of the independent variables results in polynomial functions.

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Refer image for the complete question.

The inequality that represents the value of x is (b)  x > 80

from the question, we have the following parameters that can be used in our computation:

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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Answer:

Step-by-step explanation:

But if we are to check carefully we know that c is the y-intercept wherein x=0 and we already had the point so there was no point of calculating it.

Answer:

D

Step-by-step explanation:

It helps to break the pyramid into shapes

triangles:  ((b x h) ÷ 2) x 5

((4 x 8) ÷ 2) x 5= 80in

base: 27.5in

total sa: 27.5 + 80 = 107.5in

Answer:

x = 2

Step-by-step explanation:

Well the diagonals bisect each other.

4x = 8

x = 2

Answer:

x = 2

Step-by-step explanation:

5x = 3x+4

2x = 4

x = 2