Trisha's observation that three copies of a certain triangle can be arranged to form a straight line suggests that each interior angle of the triangle measures 60 degrees. This is because a straight line measures 180 degrees, which implies that the sum of the three angles is 180 degrees. Therefore, each angle must measure 60 degrees.
Explanation:In this case, Trisha was able to arrange three copies of the triangle in such a way that their angles form a straight line. That straight line, or 180 degrees, is, in fact, the sum of all interior angles in a triangle. Hence, it can be inferred that the sum of the angles of each triangle she had must be 60 degrees, implying that each triangle is an equilateral triangle. Therefore the correct answer is: a. each interior angle of the triangle must measure 60*.
Step-by-step explanation: If you consider a straight line, it measures 180 degrees. If Trisha's three triangles are forming such a line, it implies that the three angles are combining to give 180 degrees. Assuming each angle is the same (because they are copies of the same triangle), then each angle in the triangle is 60 degrees (since 180/3 = 60).
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Which triangles are congruent by ASA
Answer:
Option B. ΔABC ≅ ΔFGH
Step-by-step explanation:
In the given picture if we compare ΔFGH and ΔABC
side FG = BC
and AB = GH
and angle between them are equal
∠FGH = ∠ABC
Therefore SAS property of congruence is true for these triangles.
Option B. ΔABC ≅ ΔFGH
It takes a boat going upstream 11 hours and 9 hours downstream. What is the speed of The boat if the current is 2mph
what number when increased by 75% of itself will equal to 80?
[tex] p\%=\dfrac{p}{100}\to 75\%=\dfrac{75}{100}=0.75\\\\n-the\ number\\\\the\ equation:\\\\n+0.75n=80\\\\1.75n=80\ \ \ \ |:1.75\\\\n=\dfrac{80\cdot100}{1.75\cdot100}\\\\n=\dfrac{8000}{175}\\\\n=\dfrac{8000:25}{175:25}\\\\n=\dfrac{320}{7}\\\\n=45\dfrac{5}{7} [/tex]
#22 #24 and #26 HELP
The front flap of a tent is shaped like an isosceles triangle. The base of the triangle is 16 feet and the height of the triangle is 6 feet. What is the length of the congruent sides of the triangle?
The equation h(t) = − 16t^2 + 19t + 110 gives the height of a rock, in feet, t seconds after it is thrown from a cliff.
What is the initial velocity when the rock is thrown?
Help I can’t find the area
combine terms 12a+26b-(4b+16a)
The school is 625 meters far from Alex house. It took him 15 minutes to go from home to school, and run back to home in 10 minutes. What was Alex's average speed?
20 POINTS TWO QUESTIONS AND I WILL MARK BRAINLIEST THANK YOU SO MUCH!!!!!
Image 1. Below are two parallel lines with a third line intersecting them. What is the measure of angle x?
Image 2. Below are two parallel lines with a third line intersecting them. What is the measure of angle x?
Simplify the expression. (2x^2y)^3
Answer:
8x6y3 3 and six put at top between y and and threeSure, I'd be happy to show you how to simplify this expression. Here are the steps:
1. In this expression, we have three numbers that are being multiplied together, 2, x^2, and y, and the entire product is raised to the power of 3.
2. Let's take each part of the product individually and raise them to the power of 3.
For the first part, 2 raised to the power of 3: this gives us 8, since 2 * 2 * 2 equals 8.
3. The next part is [tex]x^2[/tex] raised to the power of 3. When raising a power to another power, we multiply the powers together. Therefore, (x^2)^3 becomes x^(2*3), which can be simplified to x^6.
4. Finally, y raised to the power of 3 remains as y^3.
5. So, when we put together all three parts, we obtain the simplified expression, and (2x^2y)^3 simplifies to 8x^6y^3.
So, the simplified expression for (2x^2y) ^3 is 8x^6y^3.
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what does x equal? ......
A total of 907 people went to a fishing tournament. Of these people 627 arrived before noon.Alina estimates that fewer than 300 people arrived in the afternoon. How did she estimate?
In a bag, there are cards each with one of the numbers {1, 2, 3, 4, 5} written on them. Kenneth reaches into the bag, selects a card, and then replaces it. He repeats this 16 times with the following results.
Number on selected card 1 2 3 4 5
Frequency 5 3 2 4 2
What is the relative frequency that Kenneth selects the card with 4 written on it? Enter your answer in the box.
[]%
Anne plans to increase the prices of all the items in her store by 5%. To the nearest cent, how much will the artist save if the artist buys a canvas and a frame that each measure 24 by 36 inches before the price increase goes into effect
Answer:
Step-by-step explanation:
Let the cost of canvas be $x per sq inches.
Measurement of the canvas bought by the artist is
24 × 36 inches
Area of canvas = 24×36= 864 sq inches
Cost of canvas = 864x
New cost of canvas =x+5% of x
=x+0.05x
=1.05x
New Cost of canvas = 907.20x
Increase in price=907.20x-864x=43.2x
Percentage = [tex]\frac{43.2x}{864x}*100[/tex]
= 5%
Hence artist is going save 5% of cost by buying sheet today.
What is the slope that passes through the pair of points? (-1, 4), (3, 12)
A. -2
B. 2
C. 4
D. -4
PLEASE HELPPPPPPPPPPPPPPP
Pierce used the proportion y/x=7/2 when deriving the equation of a line with similar triangles.select 2 that apply and explain
a.the slope of line is 0
b.the slope of line is 2/7
c.the slope of line is 7/2
d. the y int is 0
e.the y int is 2/7 f the y int is 7/2 and again explain plz
The proportion y/x = 7/2 indicates that the slope of the line is 7/2. Without additional information, we cannot determine the y-intercept from this proportion.
Explanation:Pierce used the proportion y/x = 7/2 when deriving the equation of a line with similar triangles. This proportion suggests that for every 2 units of increase in x, y increases by 7 units. Therefore, the slope of the line, which is the ratio of the change in y (rise) to the change in x (run), would be 7/2. Thus, the correct answer is (c) the slope of the line is 7/2.
Because the question does not provide a specific point on the line, we cannot determine the exact y-intercept from the information given. However, since the proportion does not indicate any specific y-intercept value, we cannot conclude that it is 0, 2/7, or 7/2 without additional information. We only know the relationship between y and x given by the slope.
Is my answer correct or incorrect? Explain please. Thank you
A new, trendy department store is experiencing exponential growth across America. The chain began in 2004 when it opened 16 stores in Texas. Since then, it has grown by 35% in new store openings each year. Create an exponential function below to show the number of stores each year, x, since 2004.
It takes typically $27 to fill up your tank up with gas. You have allotted no more than $108 on gasoline for your trip. A) Write and B) solve an inequality to find out how many times you will get to fill up your tank up witj gas.
Final answer:
The student can fill up their gas tank up to 4 times within their $108 budget for gasoline. The inequality used to determine this is 27n ≤ 108, solved by dividing both sides by 27.
Explanation:
To solve the student's question regarding how many times they can fill up their gas tank within a $108 budget, we need to set up an inequality and solve it. Let's define the variable n as the number of times they can fill up their tank.
Step A: Write the Inequality
Since it costs $27 to fill up one tank, and the student has budgeted no more than $108 for gas, the inequality will be:
27n ≤ 108
Step B: Solve the Inequality
To find out how many times the student can fill up the tank, we divide both sides of the inequality by 27:
n ≤ [tex]\frac{108}{ 27}[/tex]
n ≤ 4
Therefore, the student can fill up their gas tank up to 4 times within their budget.
find the interquartile range for the data set: 10,3,8,6,9,12,13
Answer:
The interquartile range would be 6.
Step-by-step explanation:
3, 6, 8, 9, 10, 12, 13,
Median: 9
Lower quartile (Q1): 6
Upper quartile (Q2): 12
(IQR) Interquartile Range: 12 - 6 = 6
The interquartile range for the data set is, 6
We have to given that,
The data set is,
⇒ 10,3,8,6,9,12,13
We can arrange data set in ascending order,
⇒ 3, 6, 8, 9, 10, 12, 13
Hence, First quartile (Q₁) = 6
Second quartile (Q₃) = 12
Hence, The interquartile range for the data set is,
Interquartile range = 12 - 6
Interquartile range = 6
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ow do I put circumference, diameter, and pi into a formula
Find the mean and median of these data: 2,5,9,11,17,19
A pizza corner offers a choice of 2 types of pizza bases and 8 types of pizza toppings. How many different single topping pizzas can a customer order?
Since there are 6 faces on a die, there is a 1/6 chance of rolling a die and getting a 5.
What is 1 over 10 as a percentage?
Answer:
10% or .1 or .10
Step-by-step explanation:
Please someone help!!! The sides of the base of a square right prism are 16 cm each and the height of the prism is 10 cm. what is the surface area of this prism?
Answer:
C
Step-by-step explanation:
Among the expressions, two of them have the same result. Which are they?
a. -25+18+9+(-15)–(-13)
b. (-40)÷(-2)×15-100
c. (-7)×(-5)–(-37)–72
People help me, my account is going wrong!
A full punch bowl holds 4 gallons of punch , if each glass holds 4 ounces of punch,how many glasses can be filled from a full punch bowl?