"Write two equations: one parallel, one perpendicular to (5,-2) y= 1/5x-3
Write in the form y=mx±b,y=mx±b (first the parallel, then the perpendicular)"

Answer:

B: 9

Step-by-step explanation:

We know

Caleb took 24 photos at the zoo. 3/8 of his photos are of giraffes.

How many of Caleb’s photos are of giraffes?

We Take

24 x 3/8 = 9 photos

So, 9 of Caleb's photos are of giraffes.

Answer:

well the answer should be -1.8

but I'm guessing A

Answer:

\(-\frac{9}{10}\) \(or\) \(-0.9\) \(or\) \(C\)

Step-by-step explanation:

\(\frac{2}{4}\div\frac{-5}{9}\) = \(?\)

\(\frac{2}{4}\) = \(0.5\)

\(\frac{-5}{9}\) = \(-0.555555555556\)

\(0.5\div-0.555555555556\) = \(-0.899999999999\) = \(-0.9\)

\(So\), \(the\) \(answer\) \(is\) \(C\).

\(This\) \(is\) \(because\) \(A\) \(is\) \(\frac{-9}{10}\) \(instead\) \(of\) \(-\frac{9}{10}\).

Hope this helps! <3

The features related to vectors are listed below:

Case A: u' = (- 4√41 / 41, - 5√41/ 41)

Case B: Tip coordinantes of vector v: (x, y) = (10, 10)

Case C: r = 11.402

In this question we must determine three features related to vectors: (a) unit vector, (b) the definition of a vector based on the coordinates of its base and its tip, (c) The magnitude of a resulting vector.

Case A - Unit vector

Unit vectors are vectors with magnitude 1, for the case of vector u we have the following definition:

u' = u / ||u||

Where:

Please notice that the magnitude of the vector is determined by Pythagorean theorem:

r = √[(Δx)² + (Δy)²]

Where:

Thus, the unit vector of u is:

u' = (- 4, - 5) / √[(- 4)² + (- 5)²]

u' = (- 4, - 5) / √41

u' = (- 4 / √41, - 5 / √41)

u' = (- 4√41 / 41, - 5√41/ 41)

Case B - Definition of a vector

This can be found easily by vector subtraction:

v = Tip coordinates - Base coordinates

(3, 4) = (x, y) - (7, 6)

(x, y) = (3, 4) + (7, 6)

(x, y) = (10, 10)

Case C - Magnitude of a vector

The magnitude is found by means of Pyhtagorean theorem:

r = √[(- 4 - 3)² + (- 5 - 4)²]

r = √[(- 7)² + (- 9)²]

r = 11.402

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Answer:

1000000 = 10⁶

Step-by-step explanation:

There are 6 zeroes in 1000000, so to convert it to its standard form we must take 6 as the exponent = 10⁶

Answer:

12.5

Step-by-step explanation:

In a rectangle, the two diagonals are equal length, so MK = JL = 2x + 9

Note MK = 2 * MN, so

2x + 9 = 2 * (3x + 1)

expand:

2x + 9 = 6x + 2

Solve:

9 - 2 = 6x - 2x

4x = 7

x = 7/4

MK = JL = 2x + 9 = 2 * 7/4 + 9 = 7/2 + 9 = 3.5 + 9 = 12.5

An explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.

What is the explicit description of a null space matrix?

To find an explicit description of the null space of matrix A, we can find a spanning set of vectors that span the null space.

The null space of matrix A, denoted Nul A, is the set of all vectors x that satisfy the equation Ax = 0. In other words, the null space consists of all vectors that are mapped to the zero vector by the matrix A.

To find a spanning set for Nul A, we can use the following steps:

Row reduces the matrix A to a reduced row-echelon form using elementary row operations.

Identify the free variables in the row-reduced matrix.

For each free variable, create a vector with a 1 in the position corresponding to the free variable and 0's in all other positions.

The set of vectors created in step 3 form a spanning set for Nul A.

For example, consider the matrix A = [1, 2, 3, 0; 0, 0, 1, 0]. To find a spanning set for Nul A, we can row reduce the matrix to reduced row-echelon form:

[1, 2, 3, 0] -> [1, 2, 3, 0]

[0, 0, 1, 0] -> [0, 0, 1, 0]

The matrix is already in reduced row-echelon form, so there are no more elementary row operations to perform. The free variables in this matrix are the third and fourth columns, which correspond to the variables x3 and x4, respectively. Therefore, we can create the following vectors:

x3 = [0, 0, 1, 0]

x4 = [0, 0, 0, 1]

These vectors form a spanning set for Nul A, as they are linearly independent and span the null space.

Hence, an explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.

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The total distance covered is 15000 m. The total time taken is 5220 seconds and the speed is 2.87 m/s.

We know that speed has to do with the ratio of the distance that has been covered to the time taken. The speed is a scalar quantity and as such we do not consider the direction hence we would not consider that going back in the opposite direction. The total distance can be obtained algebraically.

The total distance that the student travelled can be obtained from;

5000 m + 5000 m + 5000 m

= 15000 m

The total time taken in seconds = 1800 seconds + 1800 seconds + 1620 seconds

= 5220 second

Speed = Distance/ Time

= 15000 m/5220 second

= 2.87 m/s

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The values of the complex expressions are ✓(x - iy) = a - ib and x² + y² =  (a + ib)²(a - ib)²

From the question, we have the following parameters that can be used in our computation:

✓(x + iy) = a + ib

Changing the signs, we have

✓(x - iy) = a - ib

Multiply both expressions

This gives

✓(x + iy) * ✓(x - iy) =  (a + ib)(a - ib)

Square both sides

So, we have

(x + iy) * (x - iy) =  (a + ib)²(a - ib)²

This gives

x² + y² =  (a + ib)²(a - ib)²

Hence, the values of ✓(x - iy) is a - ib and x² + y² is  (a + ib)²(a - ib)²

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As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.

In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;

As x → -1⁻, f(x) → ∞.

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Answer:

\(\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}\)

Step-by-step explanation:

We want to find the equation of the line tangent to the graph of:

\(\displaystyle y=\sin^{-1}\left(\frac{x}{5}\right)\text{ at } x=\frac{5}{2}\)

So, we will find the derivative of our equation first. Applying the chain rule, we acquire that:

\(\displaystyle y^\prime=\frac{1}{\sqrt{1-\left(\dfrac{x}{5}\right)^2}}\cdot\frac{1}{5}\)

Simplify:

\(\displaystyle y^\prime=\frac{1}{5\sqrt{1-\dfrac{x^2}{25}}}\)

We can factor out the denominator within the square root:

\(\displaystyle y^\prime =\frac{1}{5\sqrt{\dfrac{1}{25}\big(25-x^2)}}\)

Simplify:

\(\displaystyle y^\prime=\frac{1}{\sqrt{25-x^2}}\)

So, we can find the slope of the tangent line at x = 5/2. By substitution:

\(\displaystyle y^\prime=\frac{1}{\sqrt{25-(5/2)^2}}\)

Evaluate:

\(\displaystyle y^\prime=\frac{1}{\sqrt{75/4}}=\frac{1}{\dfrac{5\sqrt{3}}{2}}=\frac{2\sqrt{3}}{15}\)

We will also need the point at x = 5/2. Using our original equation, we acquire that:

\(\displaystyle y=\sin^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{6}\)

So, the point is (5/2, π/6).

Finally, by using the point-slope form, we can write:

\(\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}\left(x-\frac{5}{2}\right)\)

Distribute:

\(\displaystyle y-\frac{\pi}{6}=\frac{2\sqrt{3}}{15}x+\frac{-\sqrt{3}}{3}\)

Isolate. Hence, our equation is:

\(\displaystyle y=\frac{2\sqrt{3}}{15}x+\frac{\pi-2\sqrt{3}}{6}\)

After answering the presented question, we can conclude that expressions Therefore, the population of the rural city in 2030 is approximately 11,014.18.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the expression 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

To approximate the population in 2030, we need to find the value of P(t) when t = 44, since 2030 is 44 years after 1986.

Using the given exponential growth model, we have:

\(P(t) = 3400^(0.0371t)\\P(44) = 3400^(0.0371*44)\\P(44) = 3400^1.6334\\P(44) = 11014.18\\\)

Therefore, the population of the rural city in 2030 is approximately 11,014.18.

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Based on the principle of prudence, Theo should record the transaction, Sarah shouldn't, Jacob should, Jerry shouldn't, and JSL Inc. should record the transaction in the company accounts based on the principle of prudence.

1. Theo estimates that he might have to incur additional expenses for the purchase of raw materials next month.

  - Should record the transaction: It is prudent to anticipate and record potential expenses to reflect a more accurate financial position.

2. Sarah estimates that the market value price of the office building has risen by $50,000.

  - Shouldn't record the transaction: The principle of prudence suggests that gains should only be recorded when they are realized, not based on estimated market value changes.

3. Jacob bought goods for the business on credit.

  - Should record the transaction: Purchasing goods on credit should be recorded to accurately reflect liabilities and the financial position.

4. Jerry buys fuel for his personal car.

  - Shouldn't record the transaction: Personal expenses should not be recorded in the company accounts as they are unrelated to the business.

5. JSL Inc. bought stocks of another company.

  - Should record the transaction: Buying stocks of another company should be recorded as an investment to reflect the company's financial holdings.

Note: It's important to consider specific accounting regulations and policies that may vary depending on the jurisdiction and the nature of the business.

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To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

Jenelle put $13,000 in Fund A mutual fund and $ 4,000 in Fund B mutual fund.

Step-by-step explanation:

As soon as Jenelle invested $ 17000 in two mutual funds: Fund A, which earned a 4% profit during the first year; and Fund B, which suffered a 1.5% loss, if she received a total of $ 460 profit, to know how much had she invested in each mutual fund, the following calculation must be done:

17000 x 0.04 - 0 x 0.015 = 680

15000 x 0.04 - 2000 x 0.015 = 570

13000 x 0.04 - 4000 x 0.015 = 460

Therefore, Jenelle put $ 13,000 in Fund A mutual fund and $ 4,000 in Fund B mutual fund.

Answer:

81 degrees

This is an acute angle since it’s less then 90 degrees

Step-by-step explanation:

All three angles of a triangle always equal 180 degrees

180-(78+31)

180-109

81 degrees

Hopes this helps please mark brainliest

Answer:

it is roughly 15.3 laps (i rounded 1.6666666666667 to 1.7) i'll explain

Step-by-step explanation:

ratio of laps to minutes: 9:12,

20/12 = 1.6666666666667 rounded to 1.7

9 x 1.7 = 15.3

sorry that i had to round and that it is a little off, hoped i helped you tho

Answer:

To find the value that makes the equation (x-4)^2 = 7 true, we need to take the square root of both sides of the equation, remembering to include both the positive and negative square roots:

(x-4) = ±√7

Adding 4 to both sides of the equation:

x = 4 ± √7

Therefore, the two values that make the equation (x-4)^2 = 7 true are:

x = 4 + √7

and

x = 4 - √7

Note that both of these values are irrational numbers, since √7 is irrational.

(Please could you kindly mark my answer as brainliest you could also follow me so that you could easily reach out to me for any other questions)

The value that makes the equation (x-4)² = 7 true is x = 5.

What is quadratic equation?

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0, where a, b, and c ≠ 0.

Expanding the left-hand side of the equation gives:

(x - 4)² = (x - 4)(x - 4) = x² - 8x + 16

So the equation (x - 4)² = 7 becomes:

x² - 8x + 16 = 7

Subtracting 7 from both sides gives:

x² - 8x + 9 = 0

We can factor this quadratic equation as:

(x - 1)(x - 9) = 0

Therefore, the solutions to the equation are x = 1 and x = 9.

So the values that make the equation (x-4)² = 7 true are x = 1 + 4 = 5 and x = 9 - 4 = 5.

Therefore, the value that makes the equation (x-4)² = 7 true is x = 5.

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The value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

Let's simplify the expression step by step:

Recall the values of trigonometric functions for common angles:

cos(60°) = 1/2

sin(30°) = 1/2

tan(60°) = √(3)

cot(45°) = 1

sec(30°) = 2

Substitute the values into the expression:

\(2(cos^4 60 + sin^4 30) - (tan^2 60 + cot^2 45) + 3sec^2 30\)

= \(2((1/2)^4 + (1/2)^4) - (\sqrt{(3)^2 + 1^2} ) + 3(2^2)\)

= 2(1/16 + 1/16) - (3 + 1) + 3*4

= 2(1/8) - 4 + 12

= 1/4 - 4 + 12

= -15/4 + 12

= -15/4 + 48/4

= 33/4

Therefore, the value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

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Answer:

\(x\sqrt[7]{x^{2} }\) (D)

Step-by-step explanation:

Given: \(x^{\frac{9}{7} }\)

To find: Simplify the given expression

Solution: Simplyfying, we get,

\(x^{\frac{9}{7} } =x^{\frac{7}{7} +\frac{2}{7} }\)

\(=x^{1} *x^{\frac{2}{7} } \\=x*x^{\frac{2}{7} } \\=x=\sqrt[7]{x^{2} }\)

Therefore, \(x\frac{9}{7}\) can be written as \(x\sqrt[7]{x^{2} }\)

Answer:

B=G/m-2q, m\(\neq\)2q

Step-by-step explanation:

G=mB-2qB

mB-2qB=G

(m-2q)B+G

B=g/m-2q,m2q\(\neq\)  0

B=G/m-2q, m\(\neq\)2q

A zero has the same meaning as the vertex.

The point where two lines meet forming an angle or set of angles is referred to as a vertex. This can also be called a point of origin especially when considering the axis of a Cartesian coordinate.

The vertex can be taken as zero since it is referred to as the point of origin. This is different to the axis of symmetry; as the axis of symmetry is one that splits a given plotted points i.e. a graph into two equal parts.

Thus, a zero has the same meaning as the vertex.

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The length of the pool is 5 meters

From the question, we have the following parameters that can be used in our computation:

The length of the pool is calculated as

Length = Surface area / Width

substitute the known values in the above equation, so, we have the following representation

Length = 20/ 4

EValuate

Length = 5

Hence, the length is 5 meters

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Answer:

x = \(\frac{5u+4y}{2-6z}\)

Step-by-step explanation:

2(x - 2y) = 6xz + 5u ← distribute parenthesis on left side

2x - 4y = 6xz + 5u ( add 4y to both sides )

2x = 6xz + 5u + 4y ( subtract 6xz from both sides )

2x - 6xz = 5u + 4y ← factor out x from each term on the left side

x(2 - 6z) = 5u + 4y ← divide both sides by (2 - 6z)

x = \(\frac{5u+4y}{2-6z}\)

a. Assuming no additional restrictions, there are  800 possible three-digit area codes.

b. Considering ERCs, there are  80 ERCs.

c. For the seven digits after the area code, there are \(8 \times 10^6 = 8,000,000\)  possible seven-digit phone numbers.

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers is 800 \(\times\) 8,000,000 = 6,400,000,000.

a. For three-digit area codes, the first digit cannot be 0 or 1.

Assuming no additional restrictions, there are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining two digits (0-9). Therefore, the total number of three-digit area codes possible under this plan is \(8 \times 10 \times 10 = 800.\)

b. For an ERC (Easily Recognizable Code), the second and third digits of the area code must be the same, and the first digit cannot be 0 or 1. There are 8 possibilities for the first digit (2-9) and 10 possibilities for the third digit (0-9).

Since the second digit must be the same as the third digit, there is only 1 possibility.

Therefore, the total number of ERCs is \(8 \times 1 \times 10 = 80.\)

c. For the seven digits after the area code, the first digit of the three-digit local prefix cannot be 0 or 1.

There are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining six digits (0-9).

Therefore, the total number of seven-digit phone numbers possible is 8 * \(10\times 10 \times 10 \times 10 \times 10 \times 10 = 8,000,000.\)

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers can be calculated by multiplying the number of possibilities for each digit position.

For the area code (part a), there are 800 possibilities.

For the seven digits after the area code (part c), there are 8,000,000 possibilities.

Therefore, the total number of ten-digit phone numbers possible is 800 * 8,000,000 = 6,400,000,000.

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The unknown number, represented by the variable b, is 1/2, which satisfies the equation "Five more than the product of a number and 8 equals 9."

To solve the equation "Five more than the product of a number and 8 equals 9" using the variable b for the unknown number, we can express this statement as an equation:

8b + 5 = 9

To solve for b, we need to isolate the variable on one side of the equation. Let's simplify the equation step by step:

Subtract 5 from both sides to get rid of the constant term:

8b + 5 - 5 = 9 - 5

8b = 4

Divide both sides of the equation by 8 to solve for b:

8b/8 = 4/8

b = 1/2

Therefore, the solution to the equation is b = 1/2. This means that when we substitute b = 1/2 into the equation, the equation will hold true:

8(1/2) + 5 = 9

4 + 5 = 9

Both sides of the equation are equal, confirming that b = 1/2 is the solution.

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As per the given equation of the least squares regression line y=10+0.9x the score of Carla's final exam is 95.5.

As given in the question,

Given equation of the least squares regression line is :

y = 10 + 0.9x

Where 'y' shows the predicted final exam score

And 'x' represents the score of the first exam.

Carla's first exam score is equal to 95

Then predicted value 'y' of the Carla's final exam score is given by :

y = 10 + ( 0.9 ) × 95

⇒ y = 10 + 85.5

⇒ y = 95.5

Therefore, the predicted final score of Carla's as per the given least squares regression line is equal to 95.5.

The above question is incomplete, the complete question is :

In a statistics course a linear regression equation was computed to predict the final exam score from the score

on the first test. The equation of the least-squares regression line was y=10+0.9x where y represents the predicted final exam score and x is the score on the first exam.

Carla scored 95 on the first test. What is the predicted value of the Carla's score on the final exam?

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Answer:

7pi/9

Step-by-step explanation:

subtract 360 from 500 as many times as you can

number left should be converted to radians

500 - 360 = 140

140 * (pi/180) =

140Pi/180 =

simplify by dividing by 20 top & bottom

7Pi/9

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