What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (−2, 4)?

The cost for two stations that are 10 miles apart will be $8.21.

What is cost?

Cost denotes the amount of money that a company spends on the creation or production of goods or services. It does not include the markup for profit. From a seller's point of view, cost is the amount of money that is spent to produce a good or product.

Given equation is;

y = 0.354x+4.669

Where x represents the number of miles traveled.

For measuring the cost for two stations that are 10 miles apart;

x=10

Putting in given equation

y=0.354(10)+4.669

y=3.54+4.669

y=8.209

Rounding off to nearest hundredth;

y=$8.21

The cost for two stations that are 10 miles apart will be $8.21

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Answer:

21873600

Step-by-step explanation:

brainlest

In linear equation ,242 total number of members within 5 weeks.

What is linear equation ?

a manual computation on how 1 member recruits his members until week 5. Then multiply the sum by 2.

                            old      new

1:   1

2:   1 x 3 = 3 ⇒        1         3       *only new members recruit 3 more

3:   3 x 3 = 9 ⇒        4         9

4:   9 x 3 = 27⇒     13       27

5: 27 x 3 = 81 ⇒    40       81

40 + 81 = 121. Total number of members under 1 founding member.

121 x 2 founding members = 242 total number of members within 5 weeks.

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Answer: Option C

Step-by-step explanation:

Answer:

\(\frac{11}{12}\),\(1\frac{1}{4}\),\(1\frac{2}{3}\)

Step-by-step explanation:

It wants you to take these 3 fractions and arrange them from least to greatest.

The first thing I did was look for the fraction with no number in front of it.

\(\frac{11}{12}\) is the only fraction that has no numbers in front of it. So

The second thing I did was look for the fraction that had the biggest number in front of it. I see that the remaining fractions have the same number in front.

So, I drew 2 circles. 1 of the circles I shaded in and the other I split into 4 equal halves. I shaded in one of the halves. These 2 circles represent \(1\frac{1}{4}\).

The next thing I did was draw 2 more circles. I shaded in one of them and slit the other one into 3 equal halves. I shaded in 2 of the halves. These 2 circles represent \(1\frac{2}{3}\).

Last, look at the 4 circles and ask yourself which one is the most shaded in. If you said \(1\frac{2}{3}\) you are correct. This fraction is the biggest. Meaning that \(1\frac{1}{4}\) is in the middle.

The exact solutions of the Quadratic equation x^2 - 3x - 5 = 0 are:

x = (3 + √29) / 2 ,x = (3 - √29) / 2. The correct answer choice is:

x = the quantity of 3 plus or minus the square root of 29 all over 2.

The exact solutions of the quadratic equation x^2 - 3x - 5 = 0 using the quadratic formula, we can identify the values of a, b, and c, and substitute them into the formula:

a = 1

b = -3

c = -5

Now, we can apply the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values into the formula:

x = (-(−3) ± √((−3)^2 - 4(1)(−5))) / (2(1))

x = (3 ± √(9 + 20)) / 2

x = (3 ± √29) / 2

Therefore, the exact solutions of the quadratic equation x^2 - 3x - 5 = 0 are:

x = (3 + √29) / 2

x = (3 - √29) / 2

The correct answer choice is:

x = the quantity of 3 plus or minus the square root of 29 all over 2.

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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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We cannοt determine the number οf tοurists whο οnIy visited LEGOLAND with the infοrmatiοn given.

Tο find the number οf tοurists whο οnIy visited LEGOLAND, we need tο subtract the tοurists whο visited LEGOLAND and anοther theme park frοm the tοtaI number οf tοurists whο visited LEGOLAND.

First, we can find the tοtaI number οf tοurists whο visited LEGOLAND:

TοtaI = Tοurists whο visited οnIy LEGOLAND + Tοurists whο visited LEGOLAND and anοther park

TοtaI = (TοtaI visitοrs tο LEGOLAND) - (Tοurists whο did nοt visit any οf the parks)

TοtaI = (102 - 82 - 52 - 33) - 93

TοtaI = 102 - 260

TοtaI = -158

This caIcuIatiοn gives us a negative number, which dοes nοt make sense in the cοntext οf the prοbIem. It is IikeIy that there is an errοr in the infοrmatiοn given οr in the caIcuIatiοn.

Therefοre, we cannοt determine the number οf tοurists whο οnIy visited LEGOLAND with the infοrmatiοn given.

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There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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Answer:

29.4°

Step-by-step explanation:

The equation can be rearranged to give C directly.

 C = arccos((a^2 +b^2 -c^2)/(2ab))

 C = arccos((90^2 +55^2 -50^2)/(2·90·55))

 C = arccos(8625/9900) ≈ 29.4002°

 C ≈ 29.4°

The measure of angle C is approximately 29.46 degrees.

To find the measure of angle C (cos(C)) using the given values a = 55, b = 90, and c = 50, we can use the Cosine Rule formula:

cos(C) = (a² + b² - c²) / (2 * a * b)

Substitute the given values:

cos(C) = (55² + 90² - 50²) / (2 * 55 * 90)

Now, calculate the numerator:

cos(C) = (3025 + 8100 - 2500) / (2 * 55 * 90)

cos(C) = 8625 / 9900

Now, divide to get the final value of cos(C):

cos(C) ≈ 0.8707

To find the measure of angle C itself, we can take the inverse cosine (arccos) of this value:

C ≈ arccos(0.8707)

Using a calculator, you'll find:

C ≈ 29.46 degrees (rounded to two decimal places)

So, the measure of angle C is approximately 29.46 degrees.

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Answer:

c

Step-by-step explanation:

plz Brainliest i need it

Answer:

Using Pythagorean theorem, the height of Oscar's dog house, at its tallest point, is approximately 7.81 feet.

What is Pythagorean Theorem?

The Pythagorean Theorem is a fundamental concept in mathematics that relates to the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem is expressed mathematically as:

a² + b² = c²

Now,

Let's height of the house = "h":

Using Pythagoras

a² + b² = c²

Where "a" and "b" are the lengths of the slanted sides and "c" is the height of the house. We know that "a" and "b" are both 5 feet long, and the bottom of the house is 6 feet across. Let's use this information to find "c":

a = b = 5 feet

b = 6 feet

c² = a² + b²

c² = 5² + 6²

c² = 25 + 36

c² = 61

c = √(61)

c ≈ 7.81 feet

So the height of Oscar's dog house, at its tallest point, is approximately 7.81 feet.

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The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

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

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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The denominator is zero (0/0 is undefined), we cannot determine the exact value of f(-3) using this equation.

To solve the given equations, we need to find the value of the function f(x) for specific values of x.

"If f(x) / (x - 2) = x³ + 2x - 4 + 13/(x - 2), what is f(2)?"

To find f(2), we can substitute x = 2 into the equation and solve for f(2).

Plugging in x = 2, we get:

f(2) / (2 - 2) = 2³ + 2(2) - 4 + 13/(2 - 2)

Since the denominator is zero (2 - 2 = 0), the equation is undefined. Therefore, there is no solution for f(2) in this case.

"If f(x) / (x + 3) = 3x² - 4x + 2, what is f(-3)?"

To find f(-3), we can substitute x = -3 into the equation and solve for f(-3).

Plugging in x = -3, we get:

f(-3) / (-3 + 3) = 3(-3)² - 4(-3) + 2

Simplifying, we have:

f(-3) / 0 = 3(9) + 12 + 2

f(-3) / 0 = 27 + 12 + 2

f(-3) / 0 = 41

Additional information or context is needed to solve for f(-3).

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Answer: A : decreasing B : constant C: increasing D: Constant

Step-by-step explanation:

Step-by-step explanation:

I am not sure that you typed it all correctly.

but based on what is written here

f(x) = x²

g(x) = sqrt(x) + 2

so, g(f(2)) + f(1) = g(2²) + 1² = g(4) + 1 = sqrt(4) + 2 + 1 =

= 2 + 2 + 1 = 5

Answer: 13

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

There are 12 1/4s in 3

Add the extra 1/4 + 13 1/4s

The side lengths from least to greatest as follows:

IK < KL < IJ < IL < LJ

To order the side lengths IK, KL, IJ, IL, and LJ from least to greatest, we can analyze the given figure.

Since the figure is not drawn to scale, we cannot determine the exact lengths of the sides. However, we can make some observations based on the given angles.

Let's analyze the angles:

Angle L: Since angle L is marked as 47°, we know that side KL is the shortest side, as it is opposite to the smallest angle in a triangle.

Angle I: Since angle I is marked as 20°, we can infer that side IJ is longer than side IK, as it is opposite to a larger angle.

Angle LJ: Since angle LJ is marked as 89°, we can conclude that side LJ is the longest side, as it is opposite to the largest angle in the triangle.

Based on these observations, we can order the side lengths from least to greatest as follows:

IK < KL < IJ < IL < LJ

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Answer:

True

Step-by-step explanation: All linear functions are one to one, Hope it helps.

Answer:

CAB is 37 degrees

Step-by-step explanation:

90 + 53 = 143

180 - 143 = 37

This shows that 76 cookies will be made with the total pounds of cookies

Fractions are written as a ratio of two integers. Given the following parameters

Total pounds of cookies made = 4 3/4 pounds

Total pounds of cookies made = 19/4 pounds

If he uses 1/16 pound of dough for each cookie, the total amount of cookies made is given;

Number of cookies = 19/4 ÷ 1/16

Number of cookies = 19/4 * 16/1

Number of cookies = 19 * 4

Number of cookies = 76

This shows that 76 cookies will be made with the total pounds of cookies

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Answer:

The answer should be B: -1<y<3

Answer:

y=11x

Step-by-step explanation:

we use formula y2-y1/x2-x1 with 2 of the order pairs

22-11/2-1

11/1

11 is the slope

We find y intercept by finding when x is equal to zero and we subtract 11 until we find the 0 x unit since it goes down 11 every time

When x is zero y is zero so we write it like this

Y=11x

Hopes this helps please mark brainliest

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

9 3/8.

multiply 3 3/4 times 2 1/2.

Step-by-step explanation:

Hope this helps:)

Answer:

hi

Step-by-step explanation:

I don't know how to do this question

The domain are the possible input while the range are the possible output of a function.

(a) The domain = [-√2, √2], the range = [0, 2]

(b) The domain = [-1, 1], the range = [0, 1]

(c) The domain = [-1, 1], the range = [0, -1]

(d) The domain = [0, 2], the range = [0, 1]

(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]

Reasons:

The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1

Therefore, we have;

(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2

The x-intercept of the above function are, x = √2, and x = -√2

Which gives;

The domain = [-√2, √2]

The range = [0, 2]

(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3

At the x–intercepts, we have;

-3·x² + 3 = 0

x = ±1

The domain = [-1, 1]

The maximum value of y is given at x = 0, therefore;

= -3 × 0² + 3 = 3

The range = [0, 1]

(c) y = -f(x) = -(-x² + 1) = x² - 1

At the x–intercepts, x² - 1 = 0

x = ± 1

The domain = [-1, 1]

The minimum value of y is given at x = 0, which is y = -1

The range = [0, -1]

(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x

At the x–intercepts, we have;  -x² + 2·x = 0, which gives;

(-x + 2)·x = 0

Which gives, x = 0, or x = 2

The domain = [0, 2]

The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1

y = f(1) =  -1² + 2×1 = 1

Therefore;

The range = [0, 1]

(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2

At the x–intercepts, we have;  -x² - 4·x - 2 = 0, which gives;

x = -(2 + √2) or x = x = √2 - 2

The domain = [-(2 + √2), (√2 - 2)]

The maximum value of y is given when x = -4/(2)) = -2

Which gives;

-(-2)² - 4·(-2) - 2 = 2

The range = [0, 2]

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The percentage of the people surveyed that spend 3 hours or less per day would be = 52.5%. That is option C.

A histogram is defined as the graphical representation of the result of a data set with the use of bars that varies in length but of the same width.

From the given diagram, the total number of persons that participated in the games = 4+9+8+6+4+2+2+2+1+1+1= 40.

The number of people that spent 3 hours or less per day gaming = 4+9+8 = 21

Therefore the percentage of people that spent 3 hours or less per day gaming;

= 21/40 × 100/1

= 2100/40

= 52.5%

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Answer:

the 40th number in the pattern is 9