Which ordered pair is a solution to the system of linear equations -4x+y=8 and x-5y=17

The perimeter of triangle RST is B) 56.25 units. Therefore, the correct answer is B) 56.25 units.

The perimeter of a triangle is the sum of the lengths of its sides.

Since triangle XYZ is similar to triangle RST, the ratio of the corresponding sides of the two triangles is the same.

Therefore, we can set up the following proportion:

XY / XZ = RS / RT

Substituting the known values, we get:

15 / 4 = RS / RT

Multiplying both sides by RT, we get:

15 = RS * RT

We also know that the sum of the angles in a triangle is 180 degrees. Therefore, we can set up the following equation:

90 + ∠RST + ∠SRT = 180

Substituting the fact that triangle XYZ is similar to triangle RST, we get:

90 + ∠XYZ + ∠XZY = 180

Substituting the known values, we get:

90 + 30 + 60 = 180

Therefore, ∠RST = 60 degrees.

Now that we know the lengths of two sides of triangle RST and the measure of one angle, we can use the law of cosines to find the length of the third side:

RT^2 = RS^2 + ST^2 - 2 * RS * ST * cos(∠RST)

Substituting the known values, we get:

RT^2 = 15^2 + ST^2 - 2 * 15 * ST * cos(60 degrees)

Simplifying, we get:

RT^2 = 225 + ST^2 - 15ST

We also know that the perimeter of triangle RST is equal to the sum of the lengths of its sides:

Perimeter = RS + RT + ST

Substituting the fact that triangle XYZ is similar to triangle RST, we get:

Perimeter = 15 + RT + ST

Now that we know the length of RT and the fact that the perimeter of triangle RST is equal to the sum of the lengths of its sides, we can substitute these values into the equation for the perimeter to find the length of the third side, ST:

Perimeter = 15 + RT + ST

ST = Perimeter - 15 - RT

ST = 56.25 - 15 - 37.5

ST = 3.75

Therefore, the perimeter of triangle RST is:

Perimeter = RS + RT + ST

Perimeter = 15 + 37.5 + 3.75

Perimeter = 56.25

Therefore, the correct answer is B) 56.25 units.

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Question

Triangle XYZ is similar to triangle RST.

Side lengths:

XY = 15 units

XZ = 4 units

YZ = 6 units

Angle measures:

∠X = 90°

What is the perimeter of triangle RST?

A) 45 units

B) 56.25 units

C) 37.5 units

D) 15 units

The first angle measures 39 degrees, the second angle measures 78 degrees, and the third angle measures 63 degrees.

The sum of the angle measures of any triangle is always 180 degrees. Let's denote the measure of the first angle as 'x'. According to the given information, the second angle measures twice the first angle, which means it is 2x. Lastly, the third angle measures 15 degrees less than the second angle, so it is 2x - 15.

To find the angle measures of the triangle, we need to set up an equation and solve for 'x'. The sum of all three angles is 180 degrees, so we have the equation: x + 2x + (2x - 15) = 180. Simplifying this equation gives us 5x - 15 = 180. Adding 15 to both sides and then dividing by 5, we get x = 39.

Therefore, the first angle measures 39 degrees, the second angle measures 2x = 2(39) = 78 degrees, and the third angle measures 2x - 15 = 2(39) - 15 = 63 degrees.

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The probability of drawing a blue crayon first and then a green crayon is 2/21.

To find the probability of drawing a blue crayon first and then a green crayon, we need to consider the total number of crayons and the number of blue and green crayons in the bag.

There are a total of 7 crayons in the bag (2 red + 4 blue + 1 green).

The probability of drawing a blue crayon first is 4/7 because there are 4 blue crayons out of the total 7 crayons.

After drawing a blue crayon, there are 6 crayons left in the bag (1 blue + 2 red + 1 green + 2 blue). The probability of drawing a green crayon second is 1/6 because there is only 1 green crayon left out of the 6 crayons.

Therefore, P(blue, then green) = (4/7) * (1/6) = 4/42 = 2/21.

The probability of selecting a blue crayon followed by a green crayon from the bag is 1/10.5.

The probability of selecting a blue crayon and then a green crayon from a bag containing 2 red crayons, 4 blue crayons, and 1 green crayon is calculated by multiplying the probability of each individual event. The probability of drawing a blue crayon first is 4 divided by the total number of crayons, which is 7 (4/7). After drawing a blue crayon, it is kept out of the bag, reducing the total number of crayons to 6. The probability of then drawing a green crayon is 1 divided by the remaining total, which is 6 (1/6). Multiplying these probabilities together gives us the compound probability: (4/7) × (1/6), which equals 4/42 or 1/10.5 after simplification.

To minimize the amount of material needed for the sides of the sandbox, the sandbox should be square-shaped, with each side measuring 4 feet, resulting in a perimeter of 16 feet, which is the smallest perimeter for a 16-square-foot area.

The student is tasked with designing a rectangular sandbox such that the bottom has an area of 16 square feet and the dimensions of the sandbox require the least material for the sides. To achieve the least amount of material for the sides, we aim for a shape that has the smallest possible perimeter while maintaining the given area. This is achieved with a square-shaped sandbox.

Since the area is 16 square feet, we calculate the side length of the square by finding the square root of 16, which is 4 feet. Therefore, each side of the sandbox should be 4 feet long. This shape will have a perimeter of 16 feet (4 sides * 4 feet), which is the smallest perimeter possible for a rectangular shape with an area of 16 square feet.

In conclusion, the dimensions of the sandbox that will require the least amount of material for the sides are 4 feet by 4 feet.

Answer:

1. The correct answer choice is C $132.

2. The correct answer choice is B -$13.05

Step-by-step explanation:

1. 12 x 4 = 48.

180 - 48 = 132

2. -65.25/5 = -13.05

Yes, I know this is already answer.

Also, I took the test :)

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The sofa at (4, 3) and the bed at (7, 5) are within the 5-meter range of good WiFi coverage from the router at (2, 5), whereas the desk at (6, 1) is outside this range.

The WiFi router is located at point (2, 5), and the radius of good coverage is within 5 meters. Let's use the distance formula d = √{(x_2 - x_1)^2 + (y_2 - y_1)^2} to calculate the distance to each location:

The sofa at (4, 3): d =√{(4 - 2)^2 + (3 - 5)^2} = √{4 + 4} = √{8} ≈ 2.83 meters

The bed at (7, 5): d = √{(7 - 2)^2 + (5 - 5)^2} = √{25 + 0} = √{25} = 5 meters

The desk at (6, 1): d = √{(6 - 2)^2 + (1 - 5)^2} = √{16 + 16} = √{32} ≈5.66  meters

Locations A (The sofa) and B (The bed) are within the 5-meter range of good coverage. Location C (The desk) is outside the 5-meter range.

Answer: 8/3g cm

Step-by-step explanation:

Perimeter of a square = distance round the square

Since 1 side = 2/3g cm

A square has 4 side and all sides are equal

so each of the 4 side of the square is 2/3 g cm

Therefore perimeter = 2/3g cm + 2/3g cm+ 2/3g cm + 2/3g cm

Perimeter = 8/3g cm

Answer:

1/8

Step-by-step explanation:

You need to find P not 4p so you divide 4p by 4 to get P and by doing this you have to divide the other side too. so now you got 4p/4 = 1/2/4 which = p=1/8

Option (C) The expression that has a value less than 32 is 32  times 3 / 4, which equals 24. The other expressions result in values greater than 32.

The student has asked which expression has a value less than 32. To compare the given expressions, we should evaluate them:

32  times 4 / 3 is greater than 32 since 4/3 is greater than 1.

32  times 3 / 4 is 32 multiplied by a fraction less than 1, so this will be less than 32. Multiplying 32 by 3 gives us 96, and dividing 96 by 4 yields 24.

32  times 3 / 4 or 24 is mentioned twice, and it remains less than 32.

32  times 5 / 2 is greater than 32 because 5/2 is more than 2.

Therefore, both instances of 32  times 3 / 4 (or 24) represent the expression that has a value less than 32.

The solution is 3/2

The product of the numbers is given by the equation A = ( 3/4 ) x 2 and the value of A = 3/2 or A = 1.5

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be p

The value of p = 3/2

Let the second number be q

The value of q = 2

Now , the equation will be

A = first number x second number

Substituting the values in the equation , we get

A = ( 3/4 ) x 2

On simplifying the equation , we get

A = ( 3 x 2 ) / 4

A = 3/2

A = 1.5

Therefore , the value of A is 3/2

Hence , the value of the equation is 3/2

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After divide, the quotient of 1.2 divided by 251.2 is 0.004777.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

⇒ 1.2 divided by 251.2

Solve this as;

⇒ 1.2 ÷ 251.2

⇒ 0.004777

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