An isosceles triangle has base angles that each measure 32°. Which equation can be used to find z, the measure of the third angle of this isosceles triangle in degrees?
Responses
A 64 + 2z = 18064 + 2 z = 180
B 64 + z = 18064 + z = 180
C 32 + 2z = 18032 + 2 z = 180
D 32 + z = 18032 + z = 180
The sum of the angles in a triangle is always 180 degrees. Since it is given that the base angles each measure 32 degrees, the third angle can be found by subtracting the sum of the base angles from 180 degrees.
Therefore, the correct equation to find z, the measure of the third angle, is:
32 + 32 + z = 180
This simplifies to:
64 + z = 180
So the correct equation is:
A) 64 + 2z = 180
A city tour bus charges a $10 service fee plus $10.50 per hour for the tour.
Which equation can be used to find h, the number of hours the tour lasted, if the total cost for each person was $41.50?
Responses
A 41.50 = 10h + 10.5041.50 = 10 h + 10.50
B 41.50 = 10x - 10.50h41.50 = 10x - 10.50 h
C 41.50 = 10 + 10.50h 41.50 = 10 + 10.50 h
D 41.50 = 10h - 10.50
The total cost for each person is composed of a fixed service fee of $10 and an additional charge per hour of $10.50.
Let h be the number of hours the tour lasted.
The equation that represents the total cost for each person is:
Total cost = Service fee + (Hourly rate * Number of hours)
41.50 = 10 + (10.50 * h)
Therefore, the correct equation is:
C) 41.50 = 10 + 10.50h
Which situation is best represented by the following equation?
45w + 123.95 = 753.95
Responses
A Kristen paid $753.95 to join a gym. She paid a $45 registration fee and pays $123.95 for each month of her membership. What is w, the number of months that she had the membership? Kristen paid $753.95 to join a gym. She paid a $45 registration fee and pays $123.95 for each month of her membership. What is w , the number of months that she had the membership?
B Kristen and her brother paid $753.95 to join a gym. Kristen paid a $123.95 each month of her membership, and her brother paid $45 for each month of her membership. What is w, the number of months that Kristen and her brother had the membership? Kristen and her brother paid $753.95 to join a gym. Kristen paid a $123.95 each month of her membership, and her brother paid $45 for each month of her membership. What is w , the number of months that Kristen and her brother had the membership?
C Kristen paid $753.95 to join a gym. She paid a $123.95 for each month that she was enrolled at the gym after using a coupon that gave her $45 off for each month of his membership. What is w, the number of months that she had the membership?Kristen paid $753.95 to join a gym. She paid a $123.95 for each month that she was enrolled at the gym after using a coupon that gave her $45 off for each month of his membership. What is w , the number of months that she had the membership?
D Kristen paid $753.95 to join a gym. She paid a $123.95 registration fee and pays $45 for each month of her membership. What is w, the number of months that she had the membership?
A) Kristen paid $753.95 to join a gym. She paid a $45 registration fee and pays $123.95 for each month of her membership. What is w, the number of months that she had the membership?
Jax is using the spinner shown for a probability experiment. The outcomes of his first 32 spins are in the table.
Spinner Probability Experiment
Type of Number Number of Outcomes
Odd 20
Even 12
Based on the information in the table, in how many out of the next 80 spins will the spinner land on an odd number?
Based on the information in the table, the spinner landed on an odd number 20 out of the first 32 spins.
To find the number of spins out of the next 80 spins that the spinner will land on an odd number, we can set up a proportion:
Odd outcomes / Total outcomes = Odd outcomes in next spins / Total spins
20 / 32 = x / 80
Cross-multiplying, we get:
32x = 1600
Dividing both sides by 32, we find:
x = 50
Therefore, the spinner will land on an odd number in 50 out of the next 80 spins.
Use the number line to represent the solution to 2.4x−6>−13.2
.
Select the ray. Move the point on the ray to the correct place on the number line.
To represent the solution to the inequality 2.4x - 6 > -13.2 on a number line, follow these steps:
Step 1: Start by graphing the number -6 on the number line. Place a point at -6.
Step 2: Determine the direction of the inequality. Since we have a greater than sign, the arrow on the number line will point to the right.
Step 3: Determine the interval of the solution. To do this, we need to find the value of x that satisfies the inequality. First, add 6 to both sides of the inequality:
2.4x > -13.2 + 6
2.4x > -7.2
Divide both sides of the inequality by 2.4 to solve for x:
x > -7.2 / 2.4
x > -3
Step 4: Mark the point -3 on the number line, and draw an arrow pointing to the right. This represents the solution to the inequality 2.4x - 6 > -13.2.
I unfortunately cannot directly interact with a graph or number line as an AI text-based model, so you will have to imagine or physically draw the number line and follow the above steps to represent the solution correctly.
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