Use substitution. What is the solution of the system of equations?

\large y=\frac{1}{2}x+2 and \large 2y=x+4

The merchant uses Selling Price = Cost + $3.00 to determine the selling price.

Addition is a process of combining two or more numbers.

A merchant adds $3.00 to his cost to determine his selling price.

The cost is denoted by c.

The selling price is given by f(c).

As there is given add in the sentence, it means we have to use the addition rule.

Selling price is the sum of cost plus three

Selling Price = Cost + $3.00

So the table becomes as below

c 1, 2, 3, 4, 5,

f(c) 4, 5, 6, 7, 8,

Hence, the merchant uses Selling Price = Cost + $3.00 to determine the selling price.

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Answer:

A=50 B=50 too C=180

The cardinality of a set refers to the number of elements in the set. If the set X has cardinality 16 and the set Y has cardinality 24, then the number of elements in set X is 16 and the number of elements in set Y is 2.

If their intersection has cardinality 21, then the number of elements that both sets have in common is 21.To determine the number of elements contained in the union of X and Y, we need to subtract the number of elements in their intersection from the sum of the cardinalities of X and Y. That is,

|X U Y| = |X| + |Y| - |X ∩ Y| = 16 + 24 - 21 = 19

Therefore, the union of X and Y contains 19 elements.

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The inverse function of p(x) = 50x - 400 is p⁻¹(x) = x/50 + 8.

Given the function in the question;

p(x) = 50x - 400

To determine the inverse, replace p(x) with y.

p(x) = 50x - 400

y = 50x - 400

Now, interchange the variables y and x.

x = 50y - 400

Solve for y

Add 400 to both sides

x + 400 = 50y - 400 + 400

x + 400 = 50y

Reorder the equation

50y = x + 400

Divide both sides by 50

50y/50 = x/50 + 400/50

y = x/50 + 400/50

y = x/50 + 8

Replace y with p⁻¹(x)

p⁻¹(x) = x/50 + 8.

Therefore, the inverse is  x/50 + 8.

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According to square root and multiplication, the simplified answer is 126.54.

Rewriting the equation first to perform multiplication and simplify the equation -

Equation = (5✓3 + ✓15) × (3✓5 + ✓15)

Firstly multiplying the possibile entities in the equation

Equation = 15✓15 + 5✓3×✓15 + 3✓5×✓15 + 15

Keep the value of ✓3 and ✓15 in the equation

✓15 = 3.9

✓3 = 1.7

Equation = 15×3.9 + 5×1.7×3.9 + 3×1.7×3.9 + 15

Performing multiplication on Right Hand Side of the equation

Equation = 58.5 + 33.15 + 19.89 + 15

Performing addition on Right Hand Side of the equation

Equation = 126.54

Thus, the simplified form of equation is 126.54.

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The  Probability of (3 or even) = 3/4

Probability is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one

From the question;

The p(3) = 1/4

The P(even) = 2/4 =1/2

P(3 or even) = 1/4 + 1/2

P(3 or even) = 6/8

Reducing to the lowest terms

P(3 or even) = 3/4

Hence, 3/4 is the Probability of (3 or even) of picking a card at random

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There are 39 nickel coins in the jar.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given a coin jar contains a combination of nickels and quarters,

let the number of nickels be x,

number of quarters be y,

total coins = 60

x + y = 60

y = 60 - x.........(1)

and total coins in the jar worth = $7.20

we know the value of a nickel coin = $0.05

value of quarters coin = $0.25

so, 0.05x + 0.25y = 7.20

substitute the value from equation 1

0.05x + 0.25(60 - x) = 7.20

0.05x + 15 - 0.25x = 7.20

-0.2x = 7.20 - 15

x = 7.8/0.2

x = 39

Hence there are 39 nickel coins.

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The length of the tunnel is approximately 205.6 meters to the nearest tenth.

What is Pythagoras Theorem?

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle. The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

       a²+b²=c²

Here's one way to find the length of the tunnel:

1) Draw a diagram to represent the situation

2) Draw the perpendiculars from the surveyor to each entrance, and label the height of the triangle formed by each entrance and the surveyor as h1 and h2, respectively

3) Use trigonometry to find h1 and h2:

h1 = 243 * sin(47) = 160.1

h2 = 186 * sin(27) = 105.8

4) Find the horizontal distance between the two entrances, which is the length of the tunnel, by using the Pythagorean theorem:

[tex]d = \sqrt{(h1^2 + h2^2) }\\\\ d = \sqrt{(160.1^2 + 105.8^2)}\\\\ d = 205.6[/tex]

So, The length of the tunnel is approximately 205.6 meters to the nearest tenth.

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Answer:

Step-by-step explanation:

First find the hyp..

6^2 + 20^2 = x^2

x = 20.88

Using x, we now know the extra height missing from the original tree height, so we add 6 to find the original.

20.88 + 6 = 26.88ft

The tree was 26.88 feet tall before the storm.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

We have Perpendicular = 6 feet

and, base = 20 feet

Using Pythagoras theorem we get

H² = P² + B²

H² = 6²+ 20²

H²= 36+400

H² = 436

H = 20.88 feet

thus, the height of the tree = 20.88 + 6 = 26.88 feet

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Therefore, the distance covered by a passenger vehicle during one turn of the wheel is roughly 471.2 feet (rounded to the nearest tenth).

The ratio of a circle's circumference to width serves as the basis for the traditional meaning of Pi (). The diameter or extent of a circular is its circumference. A straight line connecting a spot on one point of the circular to a point at the other end, going through the middle, is the diameter.

The following algorithm determines a circle's circumference:

C = πd

where d is the diameter of the circle. In this case, the diameter of the Ferris wheel is 150 ft, so its circumference is:

C = π(150) ≈ 471.2 ft

This indicates that a full rotation of the Ferris wheel is equal to a passenger vehicle moving about 471.2 feet.

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The original price of the pair of jeans is

equals to the $120.

Jodi wants to buy a pair of jeans.

The purchase price of pair of jeans on sale = $90

Discount on price of jeans = 75%

Let the original price of pair of jeans be equal to "$y". As we know, percentage is an important concept of mathematics. It is a number calculated by dividing the part of number to the whole number, then resultant multiply by 100. It's symbol is %. The formula is % = (part/whole )x100

Here, it is said that the price of pair of jeans, $90, is only 75% of the original price. So, we can write it as the following way 75% of y = 90

=> (75/100) of y = 90

=> (75/100) x y = 90

=> y = 90x 100/75

=> y = 9000/75

=> y = 120

Hence, required value of y is $120.

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Answer:

75 over 100

Step-by-step explanation:

To find the probability of "no blue," we need to find the probability of drawing two white marbles. The probability of drawing a white marble in one draw is 5/7. So, the probability of drawing two white marbles is (5/7) * (5/7) = 25/49.

Therefore, the probability of "no blue" is 25/49 = 25/100 = 25%.

So, the answer is D. 75 over 100.

Answer: 27/100 or twenty-seven over one hundred

Step-by-step explanation:

We are trying to find the outcome that does not contain blue. The only one that does not contain blue is (White, White) (27)

Therefore 27/100 is the right answer because it does not have any blue.

The freezing point is normally distributed with mean of 0 degrees celsius and a standard deviation of 1 degree celsius. The probability of getting a score between -1.5 and 2.5 is 0.9332.

To find the probability of getting a score between -1.5 and 2.5, we need to find the area under the normal distribution curve for this range using a z-score table.

First, we need to convert the range into standard units, which is done by subtracting the mean and dividing by the standard deviation:

z1 = ( -1.5 - 0 ) / 1 = -1.5

z2 = ( 2.5 - 0 ) / 1 = 2.5

Next, we look up the z-scores in a z-score table to find the area under the normal curve:

P(-1.5 < Z < 2.5) = 0.9332

This means that the probability of getting a score between -1.5 and 2.5 is 0.9332 or 93.32%.

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After answering the provided question, we can conclude that Option A (QR = SP) and Option B (QP = SR) by themselves are insufficient to demonstrate that PORS is a parallelogram. Option D (ZOPR = ZSRP).

In Euclidean geometry, a parallelogram is a simple quadrilateral with two sets of side lengths. A parallelogram is a type of quadrilateral in which both sets of opposite corners are similar and equal. Parallelograms are classified into four types, three of which are unique. The four different shapes are parallelograms, squares, geometric shapes, and rhombuses. A quadrilateral is a parallelogram when it has two sets of equal spacing. The opposing sides and angles of a parallelogram are both the same length. The interior angles on each side of the solid line are also angles. The total number of interior angles is 360.

Option C: The fact that V is the midpoint of PR suffices to demonstrate that PORS is a parallelogram.

We know that PV = VR because V is the midpoint of PR. Furthermore, because QR = SP (as shown in the drawing), we can conclude that triangles QRP.

We can deduce from this congruence that angle QRP is congruent to angle SPR, which means that angle POR is congruent to angle PSR (because they are corresponding angles). Angle OPS is also congruent with angle ORP (because they are corresponding angles).

Option A (QR = SP) and Option B (QP = SR) by themselves are insufficient to demonstrate that PORS is a parallelogram. Option D (ZOPR = ZSRP).

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Answer:

28, 36, 40

Step-by-step explanation:

Add up the numbers in the ratio, giving us 26. Perimeter divided by 26 equals 4. Then, four times each of the numbers in the ratio gives you the lengths

The answer is :

a. If each car has space for four passengers, then the equation states how many passengers (p) may be transported by n cars:

p = 4n

where n is the number of automobiles and p is the total number of passengers.

b. By using n = 78 instead of n, we can solve for the number of passengers that could fit in 78 cars as follows:

p = 4n

p = 4(78)\sp = 312

Hence, 78 automobiles could accommodate 312 passengers.

c. By rearranging the equation, we can determine how many cars would be required to fit 78 passengers:

p = 4n\sn = p/4

When we enter p = 78 into this equation, we obtain:

n = 78/4\sn = 19.5

We would need to round up to the nearest whole number of cars, which is 20, as the number of cars must be a whole number. Hence, 20 automobiles would be required to accommodate 78 individuals.

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Expression is; 29 - x = 16 an expression to represent this situation.

Where in mathematics is an expression?

An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

                               Term is a mathematical concept that refers to a constant, a single variable, or a mixture of variables and constants along with multiplication or division. Example of an algebraic expression: 3x + 9; 5x + 10

We are told that at lunchtime, it was 29 degrees Celsius and that by sunset, the temperature had dropped to 16 degrees Celsius.

Let the drop be x.

Thus;

29 - x = 16

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The complete question is -

On Tuesday at lunchtime, it was 29 degrees Celsius. By sunset, the temperature had dropped to 16 degrees Celsius. Please write an expression for the situation, and draw a number line diagram.

The figure which is made by placing a triangle on the small side of a rectangle has a area of 95 in.²

According to question, there is a figure made by placing a triangle with a height of 4 inches on the small side of a rectangle that measures 5 inches by 17 inches.

Small side of rectangle is 5 inches, on which triangle is placed so it becomes the base of triangle.

Area of rectangle = length × breadth

Area of rectangle = 17 × 5

so, area of rectangle is 85 in.²

Now calculate the area of triangle

Area of triangle = [tex]\frac{1}{2}[/tex] × base × height

Area of triangle = [tex]\frac{1}{2}[/tex] × 5 × 4

so, area of triangle is 10 in.²

Area of the whole figure = Area of rectangle + Area of triangle

Area of the whole figure = 85 + 10 = 95 in.²

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The probability of rolling 5 distinct values in 5 rolls is equal to the value:

5/162.

Every one of the 5! = 120 distinct occurrences represents a different combination of the digits 1,...,5. Each of these events has a

[tex]\frac{1}{6}[/tex]*[tex]\frac{1}{6}[/tex]*[tex]\frac{1}{6}[/tex]*[tex]\frac{1}{6}[/tex]*[tex]\frac{1}{3}[/tex] percent probability of occurring.

So let's begin. the sides 1, 2, 3, 4, 5, 5A, and 5B. There are 6^5 potential side combinations that might occur in five rolls. You must see either 5A or 5B precisely once in addition to each of the numbers 1, 2, 3, and 4 exactly once in order to have five unique sides in five rolls. That is, you must see each of the following numbers precisely once: 1, 2, 3, 4, and 5A. You must also see each of the following numbers exactly once: 1, 2, 3, 4, and 5B. Each of these two types of sequences has five distinct variations.

P(1)=P(2)=P(3)=P(4)=16, P(5)=1/3, and for each of the 120 distinct occurrences given above and P(1)=P(2)=P(3)=P(4)=1, P(2)=P(3)=P(4)=1,

P In light of this, the chance of the event you describe is

120×1/6×1/6×1/6×1/6×1/3=120/6^4*(3)=5/162 is the probability.

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The value of x in triangle HJK is 5 √2, So correct option is (A). The value of x in triangle ABC is 25√3, So correct option is (H).

The Pythagorean Theorem is a fundamental theorem in mathematics that relates the lengths of the sides of a right triangle. It states that in any 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. Mathematically, the Pythagorean Theorem can be expressed as:

a² + b² = c²

where "a" and "b" are the lengths of the two sides of the right triangle and "c" is the length of the hypotenuse.

The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. It is a widely used theorem in mathematics and has numerous applications in many fields, including geometry, trigonometry, engineering, physics, and computer graphics.

For example, in geometry, the Pythagorean Theorem can be used to find the distance between two points in two-dimensional space. In trigonometry, it can be used to find the sine, cosine, and tangent of an angle. In physics, it can be used to calculate the force required to accelerate an object, or to determine the velocity of an object at a given time.

Overall, the Pythagorean Theorem is an important theorem that provides a simple and elegant solution to many problems involving right triangles and is widely used in mathematics and science.

9. To find the value of x in triangle HJK, we can use the Pythagorean theorem. Let's call JK = x.

HK² + JK² = KH²

Since Angle HKJ is 60 degrees and Angle KHJ is 90 degrees, we can use the trigonometric ratios to find the length of HK:

HK = JK × tan 60 = JK / √3

Substituting this into the equation above, we get:

JK² / 3 + JK² = 5²

Expanding and solving for JK, we find that:

JK = 5 √2

So, the answer is (a) 5√2.

10. To find x in triangle ABC, we can use similar methods as in question 9. Let's call BC = x. Then, by the Pythagorean theorem, we have:

AC² + BC² = AB²

Since Angle BAC is 60 degrees and Angle ABC is 90 degrees, we can use the trigonometric ratios to find the length of AB:

AB = AC / √3

Substituting this into the equation above, we get:

AC² + BC² = (AC / √3)²

Expanding and solving for BC, we find that:

BC = AC * √3 / 2 = 50 × √3 / 2 = 25√3

So, the answer is (H) 25√3

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Answer:2 i think im not sure

Step-by-step explanation:

The car travels 70.83 meters in 3 seconds.

To find the distance the car travels in 3 seconds, we first need to convert its speed from kilometres per hour to meters per second.

1 hour = 3600 seconds

1 kilometer = 1000 meters

So, 85 km/hr = 85 x 1000/3600 m/s = 23.61 m/s

Now we can use this speed to find the distance the car travels in 3 seconds:

distance = speed x time

distance = 23.61 m/s x 3 s = 70.83 m

So the car travels 70.83 meters in 3 seconds.

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--The given question is incorrect; the correct question is

"A car is driving at 85 kilometres per hour. How far, in meters, does it travel in 3 seconds?"--

The exact value of the given trigonometry expression is 16/65

Given the following trigonometry expressions

Cos (x + y)

sin x = 5/13 and:

sin y = 4/5

We need to find the exact value of cos(x+y)

According to the trigonometry identity

cos(x+y) = cosxcosy - sinxsiny

If sinx = 5/13, then cosx = 12/13. Also, if siny = 4/5, then cosy = 3/5

Substitute to have:

cos(x+y) = 12/13(3/5) - 5/13(4/5)

cos(x+y) = 36/65 - 20/65

cos(x+y) = 16/65

Hence the exact value of cos(x+y) is 16/65

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Answer:

50 grams

Step-by-step explanation:

Answer:

there is no question. but these are two of the same lines with different Y-intercepts.

Answer: ez question, the answer is F = 200, and V = 8

Step-by-step explanation:

The probability of randomly selecting an individual in this community who has red hair or is​ left-handed is 0.23

The probability of an event refers to the likelihood of the event occurring, expressed as a number between 0 and 1.

In other words, the probability of the union of two events can be expressed as follows:

P(A or B) = P(A) + P(B) - P(A and B)

Where A represents the event of having red hair, B represents the event of being left-handed, and P(A and B) represents the probability of the intersection of the two events. In this case, P(A) = 0.08 and P(B) = 0.15.

Therefore, to find the probability of a randomly selected individual in this community who has red hair or is left-handed, we would need to know the probability of the intersection of the two events, P(A and B).

This would allow us to subtract it from the sum of the individual probabilities, P(A) + P(B), to find the total probability of having red hair or being left-handed.

=> P(A) + P(B) = 0.08 + 0.15 = 0.23

In conclusion, to find the probability of having red hair or being left-handed in this community, we would need to know the probability of the intersection of the two events, P(A and B).

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The value of y is 45.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Given that, water level rises 15 centimeters every 7 minutes.

Water level in 7 minutes = 15 cm

Water level in 1 minute = 15/7 cm

So the rate of change of the water rising is 15/7 cm per minute.

That is the point is (1, 15/7).

Let x represent the time and y represent the rise of water.

You have to calculate y of the point (21, y).

Water level rise in 21 minutes = 21 × (15/7) = 45 cm

Value of y is 45.

Slope of a line with two points (x, y) and (x', y') is,

Slope = (y' - y) / (x' - x)

We have slope = 15/7 since it is a proportional relationship.

Take the points (1, 15/7) and (21, y).

(y - 15/7) / (21 - 1) = 15/7

(y - 15/7) / 20 = 15/7

(7y - 15) / (20 × 7) = 15/7

7y - 15 = 15/7 × (20 × 7)

7y - 15 = 300

7y = 315

y = 45

Using slope, it is justified.

Hence the value of y is 45.

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Step-by-step explanation:

The general solution of the differential equation can be found as follows:

dQ/dx = k/x^2

Integrating both sides, we get:

Q = k * ln|x| + C

where C is the constant of integration.