If the quadratic equation has two rational roots,then the discriminant is_____and a perfect square

Answer:

3

Step-by-step explanation:

A simple way to solve this is by substituting, we start with trying 1 for x, 2+6=8, and 1+9=10. Because the two values are different, that means 1 is the incorrect value. We can try 2, 4+6=10, and 2+9=11, once again inequivalent. We finally try 3, and 6+6=12 and 3+9=12 meaning x must be 3

Answer:

hope you can understand

The point divides the line in the respective ratios. The correct matches are done.

When a point lies on the line such that is gets divided into the ratio is said to be the division of line.

The coordinates of point can be find out by the following formula.

x = mx₂ +nx₁ / m+n   and y = my₂ +ny₁ / m+n

For, Point C(-3.6, -3.4) divides in the ratio 2 : 3.

Substituting the values, we get

-3.6 =  2x₂ +3x₁ / 2+3                 and           -3.4 = 2y₂ +3y₁ / 2+3

 2x₂ +3x₁ = -18                           and               2y₂ +3y₁ = -17

The above equations are satisfied by the points A(-2,-1) and B (-6,-7)

For, Point C(4, 1.6) divides in the ratio 3 : 2.

Substituting the values, we get

4 =  3x₂ +2x₁ / 2+3                     and           1.6 = 3y₂ +2y₁ / 2+3

3x₂ +2x₁ = 20                          and               3y₂ +2y₁ = 8

The above equations are not satisfied by any of the points.

For, Point C(3.5, -2.5) divides in the ratio 1 : 7.

Substituting the values, we get

3.5 =  1x₂ +7x₁ / 1+7                     and           1.6 = y₂ +7y₁ /1+7  

x₂ +7x₁ = 28                          and                y₂ +7y₁ = -20

The above equations are not satisfied by any of the points.

For, Point C(8, 9) divides in the ratio 5 : 3.

Substituting the values, we get

8 =  5x₂ +3x₁ /5+3                    and           9 = 5y₂ +3y₁ /5+3  

 5x₂ +3x₁ =64                          and                5y₂ +3y₁ = 72

The above equations are satisfied by the points A (3,4) and B(11, 12).

For, Point C(-2, 5) divides in the ratio 2 : 6.

Substituting the values, we get

-2 =  2x₂ +6x₁ /2+6                    and           5 = 2y₂ +6y₁ /2+6  

 2x₂ +6x₁  =-16                          and                2y₂ +6y₁ = 40

The above equations are satisfied by the points A (-5,2) and B(7,14).

For, Point C(0,1) divides in the ratio 4 : 7.

Substituting the values, we get

0 =  4x₂ +7x₁ /4+7                   and           1= 4y₂ +7y₁ /4+7  

 4x₂ +7x₁  = 0                      and                4y₂ +7y₁ = 11

The above equations are satisfied by the points A (4,-3) and B(-7,8).

Thus, all the equations are joined with their satisfying points.

Learn more about division of line.

https://brainly.com/question/27065786

#SPJ1

Answer:

y = -mx - 13.

Step-by-step explanation:

21-y-mx=34

Add y to both sides

21 - mx = 34 + y

Subtract 34 from both sides

-13 - mx = y

Rearrange:

y = -mx - 13.

Answer:

22 8th graders

Step-by-step explanation:

if 25% of the 88 kids are 8th graders then do this.

88x.25=22

88x.75=66

there are 22 eighth graders

and 66 seventh graders.

Answer:

96

Step-by-step explanation:

Each day is 24 hours.

2 days = 2 × 24 hours = 48 hours

30-minute slot = 0.5-hour slot

48 hours / 0.5 hours = 96

Answer: 96

Answer:

96

Step-by-step explanation:

Factorization of sin²θ + sin²θ cos²θ gives us; 2sin²θ - sin⁴θ

We want to simplify;

sin²θ + sin²θ cos²θ

Let us factorize out sin²θ to get;

sin²θ(1 + cos²θ)

Now, we know that cos²θ = 1 - sin²θ

Thus;

sin²θ(1 + cos²θ) = sin²θ(1 + 1 - sin²θ)

⇒ sin²θ(2 - sin²θ)

⇒ 2sin²θ - sin⁴θ

Read more about Trigonometric functions at; https://brainly.com/question/6904750

#SPJ1

Answer:

Step-by-step explanation:

For part a :

The circumference of the circle is given by the formula 2πr. We are given r so we double r and put it next to pi :

C = 2×π×r = 2×π×8 = 16π

For part b :

The area of a circle is given by the formula πr². We are given r so we square r and put it next to pi :

A = π×r² = π×8² = 64π

For part c :

The area of a square is given by the formula a² where a is the side length. This question requires an extra step as we don't have the length of the square. But we know that the diameter of the circle will be equal to the side of the length. The diameter of a circle is given by the formula   2r : so

D = 2r = 2×8 = 16

So the area of the square will equal :

A = 16² = 256

Hope this helped and brainliest and hearts please.

I'm on my road to genius rank

Answer with a step-by-step explanation:

Let us write answers to the questions using the given Venn diagram

1) 4 students

2) 3 students

3) 3 students

4) Face book ( 7 students are using Face book while only 6 students are using the other social media platform)

- More explanation is attached to the picture -

Two methods Fred could use to solve the equation are

The solution for the function is x ≅ -0.7 OR x ≅ - 3.3

From the question, we are to solve the given quadratic equation

Two methods Fred could use to solve the equation are

The given quadratic function is

f(x) = 4x² + 16x+9

Now, we are to solve f(x) = 0 for x

That is,

4x² + 16x+9 = 0

Using the formula method to solve the equation

[tex]x =\frac{-b \pm \sqrt{b^{2}-4ac } }{2a}[/tex]

In the equation,

a = 4, b = 16, and c = 9

∴ [tex]x =\frac{-16 \pm \sqrt{16^{2}-4(4)(9) } }{2(4)}[/tex]

[tex]x =\frac{-16 \pm \sqrt{256-144 } }{8}[/tex]

[tex]x =\frac{-16 \pm \sqrt{112 } }{8}[/tex]

[tex]x =\frac{-16 \pm 10.58 }{8}[/tex]

[tex]x =\frac{-16+ 10.58 }{8}[/tex] OR [tex]x =\frac{-16- 10.58 }{8}[/tex]

[tex]x =\frac{-5.42 }{8}[/tex] OR [tex]x =\frac{-26.58 }{8}[/tex]

x = -0.6771 OR x = - 3.3229

x ≅ -0.7 OR x ≅ - 3.3

Hence, the solution for the function is x ≅ -0.7 OR x ≅ - 3.3

Learn more on Solving quadratic equations here: https://brainly.com/question/8649555

#SPJ1

Using proportions, it is found that the ordered pair that represents the location of the layover is (3.75, 1.5).

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The flight distance is partitioned in a ratio of 3:1, hence, for both the x and y coordinates, we have that:

L - Nv = 3/4(Ny - Nv)

For the x-coordinate, we have that:

[tex]x + 4 = \frac{3}{4}(5 + 4)[/tex]

[tex]x = \frac{27}{4} - \frac{16}{4}[/tex]

[tex]x = \frac{11}{4}[/tex]

x = 3.75

For the y-coordinate, we have that:

[tex]y = \frac{3}{4}(2)[/tex]

[tex]y = \frac{6}{4}[/tex]

y = 1.5.

The ordered pair that represents the location of the layover is (3.75, 1.5).

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

The residual value will be equal to -1.

A residual is a difference between the observed y-value of a data point and the predicted y-value on a regression line for the x-coordinate of the data point. A residual is positive when the point is above the line, negative when it is below the line, and zero when the observed y-value equals the predicted y-value.

Take, for instance, we have the following data entry:

Observed value = 69.4

Predicted value = 70.4

The residual (r) would be:

Residual value = 69.4 - 70.4 = -1

Therefore the residual value will be -1

Read more about residuals at:

brainly.com/question/7467603

#SPJ1

Answer: x = -1 , y = -1

Using the probability concept, it is found that the correct statements are given as follows:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are eight letters, two of which are vowels and six of which are consonants.

Hence:

E is one out eight letters, hence the probability is drawing the tile with E written on it is 1/8.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Answer:

A, C, E

Step-by-step explanation:

The correct answers are A C E

or if you want to be more specific

A: The number of possible outcomes is 8.

C: P(vowel)=1/4

E: Choosing one letter at random is a simple event.

I got it right on Edge22

Answer:

A.0

Step-by-step explanation:

Vertical angles are angles that are opposite of each other when two lines cross

Hope This Helped

Answer:

108 square units

3 x 4 = 12

3 x 4 = 12

6 x 3 = 18

6 x 3 = 18

6 x 4 = 24

6 x 4 = 24

24(2) + 18(2) + 12(2) = 108 square units

Therefore, the surface area of the rectangular solid below using its net is 108 square units

Answer:

83,752,000

Very positive with this answer

Answer:

83,752,200

Step-by-step explanation:

please give me brainlist

Answer:

[tex]x =\sqrt 2[/tex]

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

Degree of f(x)=3

Degree of g(x)=2

Degree of h(x)=2

Degree of f(g(h(x)))

Option D

Answer:

d) 12

Step-by-step explanation:

Given functions:

[tex]f(x)=6x^3+5x[/tex]

[tex]g(x)=3x^2+5[/tex]

[tex]h(x)=9x^2-8[/tex]

As we are only interested in the degrees of the function, we can eliminate the coefficients of each variable and the constants:

Therefore:

[tex]\begin{aligned}g[h(x)]& =(x^2)^2\\& =x^4\end{aligned}[/tex]

[tex]\begin{aligned}f[g[h(x)]] & = (x^4)^3+x^4\\& = x^{12}+x^4\end{aligned}[/tex]

Therefore, the degree of f[g[h(x)]] is 12

The correct option for the synthetic division is A. 2x³ + 3x² + 9x + 7

Write down the first coefficient without changes and multiply the entry in the left part of the table by the last entry in the result.

Then, add the obtained result to the next coefficient of the dividend, and write the sum. All the coefficients are the coefficients of the quotient, and the last coefficient is the remainder.

Learn more about division on:

https://brainly.com/question/25289437

#SPJ1

Based on the subtraction property of equality: C. Correct. Jen could have also subtracted 100 from both sides and then divide both sides by -1/2.

In order to balance both sides of an equation, we can subtract same value from both sides by subtracting a value from both sides based on the subtraction property of equality. Same applies to other operations.

To balance both sides of the equation, 100 needs to be subtracted from the equation given. This means Jen was correct.

If she also divide both sides by -1/2, she would get same result as when she multiplies both sides by -2.

The correct description of the accuracy of her work is: C. Correct. Jen could have also subtracted 100 from both sides and then divide both sides by -1/2.

Learn more about subtraction property of equality on:

https://brainly.com/question/1601404

#SPJ1

Step-by-step explanation:

due to the principle of identical angles on parallel lines when intersected by an inclined line, x is equal to the angle at B on the other side of AB.

in other words it is the supplementary angle to 150° at B.

that means together they are 180°. that is because the sum of all angles around a single point on one side of a line is 180° (because that line can be seen as the diameter of a circle, the point as the center of that circle, and one side of the diameter is a half-circle, which represents 180°).

so,

x = 180 - 150 = 30°

now, for the same principle,

x + y = 70

y = 70 - x = 70 - 30 = 40°

Answer:

The answer would be 14 cm

[tex]V = \frac{4pi(1.5)^3}{3}[/tex]

[tex]4.5pi = 14.3[/tex]

(pi = π)

Your welcome :)

Answer:

14 cm

Step-by-step explanation:

THE SIMPLE ANSWER

Answer:

circle graph and bar graph

Step-by-step explanation:

they visualize because they are not simply just words, they make colorful graphs

[tex] \frac{ - 9 + a}{15} > 1 \\ \\ - 9 + a > 1 \times 15 \\ - 9 + a > 15 \\ a - 9 + 9 > 15 + 9 \\ a > 24[/tex]

Fractions are written as a ratio of two integers. The total number of cars owned is 154000 cars

Fractions are written as a ratio of two integers.

Given the following

Total cars = 112,420 cars

If Seventy three percent of a town’s population own cars, then;

73% of x = 112,420

where x is the total population

0.73x = 112,420

x = 112,420/0.73

x = 154000

Hence the total number of cars owned is 154000 cars

Learn more on percentages here: https://brainly.com/question/24304697

#SPJ1

Answer:

3rd one

Step-by-step explanation:

it is the only one with a function and a straight line

Andy's equation is incorrect and the correct equation of the line is y + 2= 3/4(x - 3)

The given parameters are:

Slope, m = 3/4

Point, (x,y) = (3,-2)

The equation of the line is calculated using:

y - y1 = m(x - x1)

Substitute the known parameters

y + 2= 3/4(x - 3)

From the question;

Andy's equation is y + 2 = 3/4(x - 9/4)

The above equation is different from the actual equation y + 2= 3/4(x - 3)

Hence, Andy's equation is incorrect and the correct equation of the line is y + 2= 3/4(x - 3)

Read more about linear equations at:

https://brainly.com/question/1884491

#SPJ1