Find the value of x in each case:

Answer:

it should be p=14,x=16,12

The roots of the equations are 2 and 6.

The equation of the form ax² + bx +c is known as a quadratic equation.

Given that, the quadratic equation is x² - (4 + p)x + 12= 0.

Let the roots of the quadratic equation be a and b.

If the coefficient of x² is 1 in a quadratic equation, then the coefficient of x is equal to the sum of the roots and the constant term is equal to the product of the roots.

Therefore,

a + b = -(4 + p)    (1)

ab = 12                (2)

Given that, one root is three times the other, so, let a = 3b and substitute it into equation (2)

3b(b) = 12

3b² = 12

b² = 4

b = 2

Therefore, the value of a is:

a= 3(2)

a = 6

Hence, the roots of the equations are 2 and 6.

Learn more about the quadratic equations:

https://brainly.com/question/17177510

#SPJ2

Answer:

y = -[tex]\frac{1}{3}[/tex] + 4

Step-by-step explanation:

first of all we know the slope of the equation which is 3x. then we know that we are supposed to write an equation that is perpendicular to y = 3x + 3. so since it is supposed to be perpendicular we have to make the current slope opposite.

so slope for our new equation will be -[tex]\frac{1}{3}[/tex]x.

now since we know our slope we use point-slope form and plug everything in.

point-slope form: y1-y=m(x1-x)

plug it in:

y - 2 = -[tex]\frac{1}{3}[/tex] (x - 6)

= y - 2 = -[tex]\frac{1}{3}[/tex]x +2

= y = -[tex]\frac{1}{3}[/tex] + 4

Answer:

what

Step-by-step explanation:

why would you even need to know this

Answer:

4 Kilometers

Step-by-step explanation:

if 2 centimeters = 1 kilometer than 8 centimeters = 4 kilometers

the answer is 9 feet

cuz 12-3=9

Answer: (4,9)

Step-by-step explanation: We assume a straight line, so y=mx+b.

We can determine slope, m: Change in x is (6-5)=1. Change in y is (1-(-4)) = 5 Slope is (Change in y)/(Change in x) = 5/1, or 5

y=5x+b

Find b for (6,1)

1 = 5*6 + b

b = -29

y = 5x-29

Since A is (6,1) and m is (5,-4) we can calculate y for x=4 (point B)

y = 5(4)-29

y = -9

B is (4,-9)

Answer:

4x+12

I think that's it............

Answer:

Step-by-step explanation:

The answer is A. to set aside land for animals as more people moved west

Answer:

Your image is too lite to see

Answer:

I wrote the answers in the screenshot

9514 1404 393

Answer:

  Yes, Yolanda bought enough

Step-by-step explanation:

a. Read and understand the question, including what is given and what is asked for. Here, we have ...

  Given: mixed nuts $6.75 per pound, $21.60 spent on mixed nuts; dried fruit $4.25 per pound, $11.90 spent on dried fruit.

  Find: is the total weight of purchased mixed nuts and dried fruit at least 6 pounds?

__

b. Select appropriate relations to create a path from what is given to what is asked for. Here, we have ...

  weight = cost/(cost per pound)

  total weight = weight of mixed nuts + weight of dried fruit

__

c. Use the relations with the given information to come to a conclusion that will answer the question.

  weight of mixed nuts = $21.60/($6.75/lb) = 3.2 lb

  weight of dried fruit = $11.90/($4.25/lb) = 2.8 lb

  total weight = (3.2 lb) +(2.8 lb) = 6.0 lb

Yolanda wanted to buy a total of 6 pounds for the party, and she bought 6 pounds. Yolanda bought enough for the party.

Assuming the given number is in base 2, we have

111.01₂ = 2² + 2¹ + 2⁰ + 2⁻²

111.01₂ = 4 + 2 + 1 + 0.25

111.01₂ = 7.25

1.3 Is that the answer you looking for

Answer:

2.06

Step-by-step explanation:

Temperature

the temperature in Sitka 2 hours after midnight is :

= 29.7°F + (2 × 1.23°F)

= 29.7°F + 2.46°F

= 32.16°F

So, the temperature in Sitka 2 hours after midnight is 32.16°F

#LearnWithEXO

Answer:

Step-by-step explanation:

After 2 hours the temperature is:

Answer: Ma'am It says that 39-14=25 is the example problem

Answer:

it would be 23

Step-by-step explanation:

5-3=2

5-8=3

12-8=4

17-12=5

23-17=6

Answer:

5.00

Step-by-step explanation:

The direct distance between Buckingham Palace and St. Paul's Cathedral is 5 kilometers.

Given the coordinates of Buckingham Palace as (-2, 2) and St. Paul's Cathedral as (-2, -3).

To find the direct distance between two points on a grid, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula in a 2-dimensional Cartesian plane is:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

We can calculate the distance between them as follows:

x₁ = -2, y₁ = 2 (Coordinates of Buckingham Palace)

x₂ = -2, y₂ = -3 (Coordinates of St. Paul's Cathedral)

Distance = √((-2 - (-2))² + (-3 - 2)²)

= √(0² + (-5)²)

= √(0 + 25)

= √25

= 5 kilometers

So, the distance is 5 kilometers.

To learn more about the distance between two points;

https://brainly.com/question/24485622

#SPJ3

Answer:

For question 3 its definitely 5^15 and I searched 4 so I thinks its 71 or 161? sorry I don't know angles but 3 is correct

Answer:

[tex] {5}^{4 + 8 + 3} = {5}^{15} \\ \\ 90 - 19 = 71[/tex]

Answer:

I think its A

Step-by-step explanation:

Answer:

1. 5

2. 1.29

3. 9.90

Step-by-step explanation:

They are buying 5 of each thing, so multiply it by 5.

The diced tomatoes cost $1.29.

When you solve the equation, you get 9.9. Convert that to money, and you have $9.90

Answer:

15 cubic units

Step-by-step explanation:

If you add up the blocks you get 15

Answer:

31, 114 and 35

Step-by-step explanation:

I set up the equation as such:

(3x + 21) + (x + 4) + x = 180

then I combined like terms:

5x + 25 = 180

And then solving for x I get:

5x = 155

x = 31

And then plugged the solved x value into the terms to give:

(3(31) + 21) = 114

(31 + 4) = 35

alongside the found angle of 31.

Answer:

[tex]31^{\circ}, 35^{\circ}, 114^{\circ}[/tex]

Step-by-step explanation:

Let the first angle be [tex]x[/tex]. Then, the second angle is [tex](x+4)^{\circ}[/tex] and the third angle is [tex](3x+21)^{\circ}[/tex].

We know that the sum of the angles in a triangle will always be [tex]180^{\circ}[/tex]. So, we want to solve the equation for x: [tex](x)+(x+4)+(3x+21)=180[/tex].

Combining like terms on the left side gives [tex]5x+25=180[/tex].

Subtracting [tex]25[/tex] from both sides gives [tex]5x=155[/tex].

Dividing both sides by [tex]5[/tex] gives [tex]x=31[/tex].

So, the first angle is [tex]31^{\circ}[/tex].

The second angle is [tex]x+4=31+4=35[/tex], so the second angle is [tex]35^{\circ}[/tex].

The third angle is [tex]3x+21=3(31)+21=93+21=114[/tex], so the third angle is [tex]114^{\circ}[/tex].

So, the angles are [tex]\boxed{31^{\circ}, 35^{\circ}, 114^{\circ}}[/tex] and we're done!

The check that these angles work is left as an exercise to the reader.

Step-by-step explanation:

yes 1 / 3..it is a fraction

Answer:

Its A

Step-by-step explanation:

Answer:

A. 4

Step-by-step explanation:

#1 p(x)=(x-3)*(x-5)*(x-1)=x3-9x2+23x-15

You try the next one...a fractional root would look like (x-3/2)

Using the Factor Theorem, it is found that an example of a polynomial of degree at least 3 where one or more of the roots are fractions is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In this problem:

Hence:

[tex]f(x) = (x - x_1)(x - x_2)(x - x_3)[/tex]

[tex]f(x) = (x - 1)(x - 2)\left(x - \frac{1}{2}\right)[/tex]

[tex]f(x) = (x^2 - 3x + 2)\left(x - \frac{1}{2}\right)[/tex]

[tex]f(x) = x^3 - \frac{7}{2}x^2 + \frac{1}{2}x - 1[/tex]

To learn more about the Factor Theorem, you can take a look at https://brainly.com/question/24380382

Answer:

x+2y=2 x-2y=-2. It has infinitely many solutions. It has no solution. It has one solution