What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of .

3x - y - 7 = 0
x - 3y + 7 = 0
x - 3y - 7 = 0

Answer: B. 29° & 61°

Step-by-step explanation:

The concentration of hydrogen ions ([H+]) in the solution with a pH of 2.45 is approximately 0.00355 moles per liter (M).

The process you described is correct for finding the concentration of hydrogen ions ([H+]) from a given pH value using the formula [H+] = 10^(-pH).

Here's how you would calculate the [H+] concentration for a solution with a pH of 2.45:

a) Take the negative of the pH value:

-log(2.45) = -0.389

b) Now, use your calculator and calculate 10 raised to the power of the negative pH value:

10^(-0.389) ≈ 0.00355

So, the concentration of hydrogen ions ([H+]) in the solution with a pH of 2.45 is approximately 0.00355 moles per liter (M).

for such more question on hydrogen ions

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Gabriel and his sister's expression mean the same; However, the information available is not sufficient to determine if they are correct or not.

According to the question;

Upon computation; we find out that the expressions supplied by Gabriel and his sister are the same.

However, we must note that the information available is not sufficient to determine if both parties are correct or not.

Ultimately, if Gabriel is correct, then his sister is too and if otherwise, she is not correct too.

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well $30 is 185.02 in turkish lira.

Answer:

Step-by-step explanation:

The given equation is

[tex]sin(40\°)=\frac{b}{20}[/tex]

Where [tex]b[/tex] represents the length of the segment AC, according to the given graph.

To find [tex]b[/tex] we just need to isolate it in the given equation,

[tex]b=20sin(40\°)[/tex]

Then, we know that [tex]sin(40\°) \approx 0.64[/tex], so

[tex]b=20(0.64)=12.9cm[/tex]

Therefore, the length of segment AC is 12.9 centimeters, rounded to the nearest tenth.

Answer:

B

Step-by-step explanation:

edge 2021

Answer:

To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game.

Step-by-step explanation:

0.5 miles

The jogger's movement can be represented as a right-angled triangle, where the legs of the triangle represent the distances traveled west and south, and the hypotenuse is the direct distance from the starting point to the finishing point. To solve for the distance the jogger traveled south, we need to use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is expressed as c2 = a2 + b2.

Using the Pythagorean theorem:

1.32 = 1.22 + b2

Therefore:

b2 = 1.32 - 1.22

b2 = 1.69 - 1.44

b2 = 0.25

b = [tex]\sqrt{0.25}[/tex]

b = 0.5 mi

So, the jogger traveled 0.5 miles south.

Answer:

10 pints

Step-by-step explanation:

There are 8 pints in a gallon, so ...

(1.25 gal) × (8 pt/gal) = 10 pt

Step-by-step explanation:

Given expression [tex]\frac{1}{x} -\frac{2}{x^2+x}[/tex].

Let is factor second denominator [tex]x^2+x[/tex] first.

Factoring out GCF x we get

[tex]x^2+x= x(x+1)[/tex]

Rewriting the equation

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

Now, we need to find the lowest common denominator of x and x(x+1).

The lowest common denominator of x and x(x+1) is x(x+1).

So, we need to multiply first fraction by (x+1) in top and bottom to get lowest common denominator  x(x+1) under first fraction.

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

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

We got denominators same.

Therefore, subtracting numerators, we get

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

[tex]\frac{x-1}{x(x+1)}[/tex].

Therefore, simplified form is [tex]\frac{x-1}{x(x+1)}[/tex].

To form a quadratic equation, let α and β be the two roots.

Let us assume that the required equation be ax22 + bx + c = 0 (a ≠ 0).

According to the problem, roots of this equation are α and β.

Therefore,

α + β = - baba and αβ = caca.

Now, ax22 + bx + c = 0

⇒ x22 + babax + caca = 0 (Since, a ≠ 0)

⇒ x22 - (α + β)x + αβ = 0, [Since, α + β = -baba and αβ = caca]

⇒ x22 - (sum of the roots)x + product of the roots = 0

⇒ x22 - Sx + P = 0, where S = sum of the roots and P = product of the roots ............... (i)

Formula (i) is used for the formation of a quadratic equation when its roots are given.

Given the roots: (-1+-i)

where; i=sqrt(-1)

Thus, the answer is (2x)

You can also do checking to verify if x^2+2x+2 will have roots equal to (-1+-i)

Answer:

Option A.

Step-by-step explanation:

To determine an appropriate model of the data each data should satisfy the expression.

For function 1. f(x) = -x² + 4x

Now for each point

f(0) = 0 , f(1) = 3, f(3) = 3 and f(4) = 0

therefore the given points lie on the function.

For option 2

f(0) = 0, f(1) = -3, f(2) = -4, f(3) = -3 and f(4) = 0

Therefore points do not lie on the function.

For Option 3.

f(0) = -1, f(1) = 2, f(2) = 3, f(3) = 2 and f(4) = -1

Therefore the points do not satisfy the expression.

For option 4.

f(0) = 1, f(1) = -2, f(2) = -3, f(3) = -2 and f(4) = 1

Therefore, the points do not satisfy the expression.

Option A. is the correct option.