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
a _____is a know size or amount that helps you understand another size or amount
Understanding size through known quantities in mathematics and utilizing conversion factors for unit conversions.
Size is a known size or amount that helps understand another size or amount. It is a visual variable conducive for quantitative attributes in various fields, such as mathematics and science.
In mathematics, known quantities can be used to determine unknown quantities through approximations and comparisons, such as estimating lengths or measurements based on familiar values.
Conversion factors are numbers that relate different units of measure for the same quantity, enabling easy conversions between units.
How would I solve the following: 328=(5-6x)
which is a true statement about 7 and 14
how is 1/2 plus 1/4 solved differently than 1/2 plus 1/3?
plz help fast?????
What is 983.491 rounded to the nearest whole number?
Brian irons 2/9 of his shirt in 3 3/5 minutes. At this rate, how much of his shirt does he iron each minute?
Brian irons 1/16 of his shirt per minute.
Explanation:The question is about determining the rate at which Brian irons his shirts per minute. Given the fact that Brian irons 2/9 of his shirt in 3 3/5 minutes, we first convert 3 3/5 into an improper fraction, giving us 18/5 minutes. Dividing the fraction of the shirt he irons, 2/9, by the time it takes, 18/5, we get the fraction of the shirt Brian irons per minute.
To find this, we multiply 2/9 by the reciprocal of 18/5, which is 5/18, resulting in (2/9)*(5/18) = 10/162 shirts per minute. Simplifying this fraction, we find Brian irons approximately 0.062 shirts or about 1/16 of his shirt per minute.
This is an example of using rates and fractions in a real-world context to solve problems. Understanding how to manipulate and simplify fractions is crucial for solving these real-world math problems.
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find a fraction equivalent to 8/4 when added together it equals 84
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weekly salary is $900. Suppose Salesmen A and B have the same number of sales and earn the same amount in Week 4 of this month. How many sales must they both have had?
Answer:
a0 - 0
a1 - 300
a2 - 900
a3 - 65
a4 - 340
a5 - 900
a6 - 650
a7 - 700
a8 - 900
Step-by-step explanation:
there you go
Based on the amount that both Salesmen A and B earn per sale, the number of sales they both had was 12 sales.
How many sales did Salesmen A and B have?Salesman A gets $65 per sale and Saleman B gets $300 and $40 per sale.
Assuming the number of sales to take them both to the same amount is x, the relevant formulas would be:
65x = 300 + 40x
Solving gives:
65x - 40x = 300
25x = 300
x = 300 / 25
= 12 sales
The amount that both of them earned is:
= 65 x 12
= $780
= 300 + 40 x 12
= $780
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A color called "passion purple" is made by mixing 5oz of red paint with 9 oz of blue paint. What percent of passion purple is blue paint? (Round to the nearest percent)
Approximately 64% of the passion purple is blue paint, calculated by dividing the amount of blue paint by the total amount of paint and multiplying by 100%.
Explanation:To determine what percent of passion purple is blue paint, we calculate the ratio of the amount of blue paint to the total amount of paint used to make the color. We have 9 oz of blue paint and a total of 5 oz red paint plus 9 oz blue paint, which equals 14 oz of paint in total. The percentage of blue paint is therefore (9 oz blue paint / 14 oz total paint) × 100%.
Calculating this, we get:
(9 oz / 14 oz) × 100% = 0.642857 × 100% ≈ 64.29%After rounding to the nearest percent, approximately 64% of the passion purple paint is blue paint.
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a line contains the points (4,2) and (0,-1). what is the equation of the line. a) y=2x -6
b)y= 3/4x -1
c) y= 1/4x + 1
d) y= 4/3x - 10/3
The equation of the line passing through the points (4,2) and (0,-1) is y = -3/4x + 5.
Explanation:To find the equation of a line passing through two points, we need to find the slope and the y-intercept.
The formula for finding the slope is: m = (y2 - y1) / (x2 - x1)
Using the points (4, 2) and (0, -1):
x1 = 4, y1 = 2x2 = 0, y2 = -1Substituting these values into the formula, we get: m = (-1 - 2) / (0 - 4) = 3 / -4 = -3/4
The slope of the line is -3/4.
Next, we can use the slope-intercept form of the equation of a line, which is: y = mx + b
Using one point and the slope, we can solve for the y-intercept, b.
x = 4, y = 2, m = -3/4Substituting these values into the slope-intercept form, we get: 2 = (-3/4)(4) + b
Simplifying this equation, we find: 2 = -3 + b
Adding 3 to both sides, we get: b = 5
Therefore, the equation of the line is: y = -3/4x + 5
John is building a rectangular puppy kennel up against his house using 31 feet of fencing. The side against the house does not need a fence and the side parallel to his house needs to be 15 feet long. Write an equation that models the situation and solve for the length of one of the shorter sides that extend out from the house.
Each of the shorter sides extended out from the house is 8 feet long.
Explanation:So John, needs to make a 3 sided fence. He has 31 feet of fencing to do this with and the single side parallel to the house is 15 feet.
We can write the equation for this problem as:
31=2s+15
Where 31 is the total amount of fencing John has to use, 15 is the one side where the length is given, s is the length of each of the other two sides and because there are two sides we multiply s by 2
Solving this equation gives:
31−15=2s+15−15
16=2s+0
16=2s
162=2s2
8=s
Gerain is practicing his free throws at basketball practice he attempts 20 free throws and makes 13 baskets what percent of his attempts were baskets
5x88x9x7x3x9x10x31x47=
What is 30,000 written in scientific notation?
A.
3.0 × 10–5
B.
3.0 × 10–4
C.
3.0 × 104
D.
3.0 × 105
what's does y equal to x=3-3y
what is 42.4% as a fraction in simplest form and as a decimal
2 fourth common denominator
How do you solve a/6=15/2?
The table shows revenue R (in millions of dollars) of a company when it spends A (in millions of dollars) in advertising.
a. Write a linear function that relates the revenue to the advertising cost.
b. What is the revenue of the company when it spends $10 million on advertising?
(Table is attached below)
Julie made a 3 ft. Long submarine sandwich. She is going to cut it into 5 equal length pieces. How long will each piece be?
What is the value of a? 0.0482 − (−0.0091)= a
Haley drove 328 miles in 4 hours. At this rate, how far could she drive for 10 hours?
Unit rate ___________ miles per hour
Miles in 10 hour__________
the height of the triangle shown can be found using the expression 48 divide by b ,where b is the base of the triangle what is the height of the triangle
Answer:
6
Step-by-step explanation:
b is 8ft and 48 divided by 8 is 6
@gamerbrehyt2 What is the solution set of -9x ≤ 27?
x ≤ -3
x ≥ -3
x ≤ 3
x ≥ 3
Answer:
X_>-3
Hope this helps!!!!
3) The City of Oz has to repaint its cylinder-shaped water tower. Only the top and sides need to be painted. If the water tower has a height of 60 feet and a radius of 20 feet, how many square feet must be painted? A) 400π ft2 Eliminate B) 2400π ft2 C) 2800π ft2 D) 4400π ft2
Answer:
The answer is C 2800 ft2.
Step-by-step explanation:
I just took a quiz and that was the answer. I honestly don't know why.
Final answer:
To find the area to be painted on the cylinder-shaped water tower, we sum the areas of the top and sides. The water tower has a height of 60 feet and a radius of 20 feet, resulting in a total area of 2800π ft^2 to paint.
Explanation:
The City of Oz needs to repaint its cylinder-shaped water tower. To calculate the total surface area to be painted, which consists of the top (a circle) and the sides (a rectangle wrapped around), we use the formulas for the area of a circle and the lateral surface area of a cylinder:
Area of the top (circle) = πr²
Lateral surface area (sides) = 2πrh
The water tower has a height of 60 feet and a radius of 20 feet.
Area to paint = Area of the top + Lateral surface area = π(20 ft)² + 2π(20 ft)(60 ft) = 400π ft² + 2400π ft² = 2800π ft².
Therefore, the correct answer is C) 2800π ft².
How do work 3x-2y=3 and 5x-5y=10
suppose Mina and two of her friends go to the movies.write an expression that could be used to find the total cost for them to go to the movies and buy one of each item.
The required expression represents the total cost for them to go to the movies and buy one of each item is y = 2[a + x].
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
The question seems to be incomplete,
Let the cost of the item be 'a' the cost of the movie be x, and the total cost be y,
According to the question,
y = 2[a + x]
Thus, the required expression represents the total cost for them to go to the movies and buy one of each item as y = 2[a + x].
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how many times can 15 go into 21 BTW DIVIDING
what compatible number can you use to estimate 803÷86
PLZ help with 6th math homework!