If a line has a slope of 3 and contains the point (-1, 4), what is its equation in point-slope form?
A. y+1=3(x-4)
B. y-1=3(x-4)
C. y-4=3(x-1)
D. y-4=3(x+1)

The trigonometric value relations are solved and

a) cos 45° = √2/2

b) tan 30° = √3/3

c) sin 60° = √3/2

Given data ,

Let the trigonometric relations be represented as A

Now , the value of A is

a)

cos x = √2/2

On simplifying , we get

cos x = 1/√2

Taking inverse on both sides , we get

x = cos⁻¹ ( 1/√2 )

x = 45°

b)

tan x = √3/3

On simplifying , we get

tan x = 1/√3

Taking inverse on both sides , we get

x = tan⁻¹ ( 1/√3 )

x = 30°

c)

sin x = √3/2

Taking inverse , we get

x = 60°

Hence , the trigonometric relations are solved

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Step-by-step explanation:

70 ÷ 3 = 23  1/3

The average score of the spelling test is 90.6%

To find the average score of the test, we need to add up all the scores and divide by the total number of students. We can think of the average score as the "typical" or "representative" score of the entire class.

First, let's add up all the scores:

2(100) + 9(95) + 10(90) + 3(80) + 1(70) = 200 + 855 + 900 + 240 + 70 = 2265

Next, we divide by the total number of students:

Average score = (2 + 9 + 10 + 3 + 1) / 25 * 100% = 25 / 25 * 100% = 90.6%

Therefore, the average score of the spelling test is 90.6% when rounded to one decimal place.

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Answer:

A is the correct answer.

Angle 2 is an exterior angle of the triangle because Angles 2 and 3 are supplementary angles.

Answer:

5 pints

Step-by-step explanation:

every 2 cups is 1 pint

10 Divide by 2 is 5

4 cups = 2 pints

6 cups = 3 pints

8 cups = 4 pints

10 cups = 5 pints

The correct congruency for prove that ΔPQR ≅  ΔRSP is,

⇒ SAS

We have to given that;

In the figure below,

∠PQR ≅ ∠ RSP

And, both equal 90 degrees.

Now, In ΔPQR and ΔRSP;

∠PQR ≅ ∠ RSP

PR = RP

PS = QR

Thus, By SAS congruency theorem,

ΔPQR ≅  ΔRSP

So, The correct congruency for prove that ΔPQR ≅  ΔRSP is,

⇒ SAS

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Answer:

y = (-2/3)x + 5

Step-by-step explanation:

To write the equation of a line, we need to find its slope and y-intercept using the given points.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:slope = (y2 - y1) / (x2 - x1)

Using the points (-3,7) and (9,-1), we can find the slope as:slope = (-1 - 7) / (9 - (-3))

     = -8 / 12

     = -2/3

Now that we have the slope, we can use the point-slope form of the equation of a line to find the y-intercept. The point-slope form of the equation of a line passing through a point (x1, y1) with slope m is:y - y1 = m(x - x1)

Using the point (-3,7) and the slope we just found (-2/3), we get:y - 7 = (-2/3)(x - (-3))

Simplifying this equation, we get:y - 7 = (-2/3)x - 2

y = (-2/3)x + 5

Answer: F(x) = (-5/6) x + 13/42

Step-by-step explanation: The provided points are (x1, y1) = (2/7, 3/7) and (x2, y2) = (-1/7, 11/14) respectively.

The following formula can be used to determine the slope of the line connecting the two points:

m = (y2 - y1)/(x2 - x1)

m = (11/14 - 3/7)/(-1/7 - 2/7)

m = (5/14)/(-3/7)

m = -5/6

In order to construct the equation of the line, we can now utilize the point-slope form:

y - y1 = m(x - x1)

The result of substituting the values of m, x1, and y1 is:

y - 3/7 = (-5/6)(x - 2/7).

The solution is, Option B.) one culture will have always 50 more bacteria than the other.

We have,

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.

Given:

We have,

The population, P, of bacteria in a culture can be calculated at any time, t, using the equation P= a(2).

In the equation, the initial number of bacteria is a.

The initial number of bacteria in two different cultures were 100 and 125.

so, in one cultures population, P, of bacteria is = 100(2)

                                                                             = 200

in the other cultures population, P, of bacteria is = 125(2)

                                                                             = 250

so, we get,

the two populations compare over time = 250 - 200

                                                                   = 50

Hence, The solution is, Option B.) one culture will have always 50 more bacteria than the other.

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The requried it will take 98.8 years for the account balance to reach 1 million dollars.

(a) The formula for compound interest is:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

In this case, P = $500, r = 0.0425, n = 1 (compounded annually), and we want to find the function for A as a function of t. Therefore, the equation is:

[tex]A = 500(1 + 0.0425/1)^{(1t)}\\A = 500(1.0425)^t[/tex]

(b) To find the amount of time it takes for the account balance to reach 1 million, we need to solve for t in the equation:

[tex]1,000,000 = 500(1.0425)^t[/tex]

t ≈ 98.8 years

Therefore, it will take approximately 98.8 years for the account balance to reach 1 million dollars.

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