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Karolina [17]
3 years ago
9

Write the quadratic equation whose roots are six and -2 and who’s leading coefficient is 3 use the letter X to represent the var

iable
Mathematics
1 answer:
Artist 52 [7]3 years ago
6 0

Answer:

3X^{2} - 12X - 36 = 0

Step-by-step explanation:

6 and - 2 are the only two solutions to the required quadratic equation.

So, if the variable is represented by X then (X - 6) and (X + 2) will be the only two factors of the polynomial function.

Therefore, the equation is  

(X - 6)(X + 2) = 0

⇒ X^{2} - 4X - 12 = 0

If the leading coefficient of the equation is 3 then we can write the equation as 3X^{2} - 12X - 36 = 0 (Answer)

You might be interested in
For five mathematics tests, your scores were 81, 86, 81, 76, 71. what was your average score?
trasher [3.6K]

add them together then divide by 5

81 +86 +81 +76 +71 = 395

395/5 = 79

 your average was 79

7 0
3 years ago
In circle D, angle ADC measures (7x + 2)°. Arc AC
Akimi4 [234]

Answer:

The measure of angle ABC is 36° ⇒ 1st answer

Step-by-step explanation:

Let us revise some important facts in the circle

The measure of the center angle is equal to the measure of its subtended arc

The measure of the inscribed angle is equal to half the measure of the central angle subtended by the same arc

The vertex of a central angle is the center of the circle and its sides are radii in the circle

The vertex of an inscribed angle is a point on the circle, and its sides are chords in the circle

In circle D

∵ D is the center of the circle

∵ A and C lie on the circle

- DA and DC are radii

∴ ∠ADC is a central angle subtended by arc AC

∴ m∠ADC = m of arc AC

∵ m∠ADC = (7x + 2)°

∵ m of arc AC = (8x - 8)°

- Equate them to find x

∴ 8x - 8 = 7x + 2

- subtract 7x from both sides

∴ x - 8 = 2

- Add 8 to both sides

∴ x = 10

Substitute the value of x in the measure of ∠ADC

∵ m∠ADC = 7(10) + 2 = 70 + 2

∴ m∠ADC = 72°

∵ AB and BC are two chords in circle D

∴ ∠ABC is an inscribed angle subtended by arc AC

∵ ∠ADC is a central angle subtended by arc AC

- By using the 2nd fact above

∴ m∠ABC =  m∠ADC

∴ m∠ABC =  × 72

∴ m∠ABC = 36°

7 0
2 years ago
Two isosceles triangles have the same base length. the legs of one of the triangles are twice as long as the legs of the other.
Makovka662 [10]
An isosceles triangle is a type of triangle where 2 sides are equal.

Picture out 2 triangles with the same base length. 
On the first triangle, its legs are twice the length of the legs of the second triangle.

To put it into variables, let:
     B = the same base length of the two triangles
     A = the length of one leg the smaller triangle
    2A = the length of one leg of the bigger triangle

Given:    Perimeter of smaller triangle = 23cm
              Perimeter of bigger triangle = 43cm

Recall the formula for solving the perimeter of a triangle:
      Perimeter = A + B + C
   
where, A, B, and C are the legs of the triangle

Since the triangle involved is an isosceles triangle, therefore, we can say that
        Perimeter = 2A + B     ,   2 legs are equal ( A=C )

Substituting the given perimeter value to the formula. 
   
23cm = 2A + B                    ⇒   equation 1  (smaller triangle)
43cm = 2(2A) + B                ⇒   equation 2  (bigger triangle)

Simplifying equation 2.
                                    43cm = 4A + B
  (rearranging)             B = 43cm - 4A        ⇒ equation 3

Substituting equation 3 to equation 1:
   (equation 1)              23cm = 2A + B
                                    23cm = 2A + (43cm - 4A)
                                    23cm = -2A + 43cm
                                    2A = 43cm - 23cm
                                    2A = 20cm  ⇒   length of the leg of the bigger triangle
                                     A = 10cm   ⇒   length of the leg of the smaller triangle

To solve for the base length, just substitute the value of A to equation 3
     (equation 3)       B = 43cm - 4A
                               B = 43cm - 4(10cm)
                               B = 3 cm

Final Answer:

• For the smaller triangle, the length of the sides are 10cm, 10cm, and 3cm
• For the bigger triangle, the length of the sides are 20cm, 20cm, and 3cm
8 0
3 years ago
Is Tracking Effective? Now that you have read and reviewed the material on cognitive development during adolescence, take your l
Mila [183]

Answer:

Step-by-step explanation:

1. The independent variable in this experiment would be the separation of students into distinct groups based on standardized tests of ability and achievement.

2. To implement the independent variable, the experimenter needs to divide the 100 volunteers into separate groups based on standardized tests of ability and achievements. He must also make sure that each groups’ students’ ability levels are the same. Then they would be given tasks as per their ability level.

3.The dependent variable here would be the academic achievements of the groups formed based on ability.

4. First, the volunteers’ achievement would be tested. Then based on their abilities as per standardized tests, they would be divided into groups of students with similar abilities. Then they would be given tasks as pr their abilities. Finally, their achievements would be measured to see if there is any significant difference in achievement between them before and after the grouping as per ability.

5.

6. Null Hypothesis: There would be no significant difference between the academic achievements in high school students of varying abilities due to separation into distinct groups based on standardized tests of ability and achievement.

Alternative Hypothesis: There would be a significant difference between the academic achievements in high school students of varying abilities due to tracking.

8 0
3 years ago
SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is inter
Rama09 [41]

Answer:

The administrator should sample 968 students.

Step-by-step explanation:

We have to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.88}{2} = 0.06

Now, we have to find z in the Z-table as such z has a p-value of 1 - \alpha.

That is z with a p-value of 1 - 0.06 = 0.94, so Z = 1.555.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

Standard deviation of 300.

This means that n = 300

If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample?

This is n for which M = 15. So

M = z\frac{\sigma}{\sqrt{n}}

15 = 1.555\frac{300}{\sqrt{n}}

15\sqrt{n} = 300*1.555

Dividing both sides by 15

\sqrt{n} = 20*1.555

(\sqrt{n})^2 = (20*1.555)^2

n = 967.2

Rounding up:

The administrator should sample 968 students.

5 0
3 years ago
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