Question 1 A)(6 points) To solve the equation 5x3=−1355x3=−135, you would first use the operation of by to get the equation x3=−27x3=−27. You would then use the inverse operation of x3x3, which is taking the of both sides. That leaves us solution(s) for x. The solution(s): x = Question 2 A)Put the steps in order for solving the equation: x2+4=53x2+4=53 (1 point) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Step 1 Step 2 Step 3 Take the square root of both sidesDivide by 4 on both sidesDivide by 2 on both sidesSubtract 4 from both sidesSimplify - you get two rational solutionsAdd 4 to both sidesSimplify - you get two irrational solutions Question 3 A) Find the length of the red line segment in the coordinate plane. Which of the following statements are true: (1 point) Responses The length is 40 units; find the sum of the x and y coordinates and square root the answer. The length is 40 units; find the sum of the x and y coordinates and square root the answer. The length is 130; find the difference between the x and y coordinates and square it. The length is 130; find the difference between the x and y coordinates and square it. The length is 260−−−√260; find the difference of the x coordinates and the difference of the y coordinates and subtract those differences. The length is square root of 260 ; find the difference of the x coordinates and the difference of the y coordinates and subtract those differences. The length is 40−−√40units; find the sum of the vertical and horizontal distances squared and then take the square root. The length is square root of 40 units; find the sum of the vertical and horizontal distances squared and then take the square root. Question 4 A) Sidney is traveling from the grocery store to the bank. There are two possible routes she can take, marked yellow and green in the diagram. Which statement is true? (1 point) Responses The green path is 2 miles shorter than the yellow path. The green path is 2 miles shorter than the yellow path. The green path is half the distance of the shorter path. The green path is half the distance of the shorter path. The yellow path is double the distance of the green path. The yellow path is double the distance of the green path. The yellow path and green path are the same distance. The yellow path and green path are the same distance. Question 5 A) If you have a 24 foot ladder that is leaning against the building and touching the ground 6 feet from the building. How high up the building is the top of the ladder? (1 point) Responses 62+b2=24262+b2=242; 23.24 ft 6 squared plus b squared is equal to 24 squared ; 23.24 ft a2+242=62a2+242=62; 23.24 ft A squared plus 24 squared is equal to 6 squared ; 23.24 ft 62+b2=24262+b2=242; 24.7 ft 6 squared plus b squared is equal to 24 squared ; 24.7 ft 242+62=c2242+62=c2; 24.7 ft 24 squared plus 6 squared is equal to c squared ; 24.7 ft Question 6 A) How far is it from the lighthouse to the ship horizontally if the lighthouse is 20 ft tall and shines a beam to the ship 25 ft long? Also, which statement is correct? (1 point) Responses x = 15 ft; the distance from the top of the lighthouse to the ship must be the longest distance x = 15 ft; the distance from the top of the lighthouse to the ship must be the longest distance x = 15 ft; the distance from the lighthouse to the ship must be the shortest distance x = 15 ft; the distance from the lighthouse to the ship must be the shortest distance x = approximately 24.5 yards; from the top of the lighthouse to the boat must be the shortest distance x = approximately 24.5 yards; from the top of the lighthouse to the boat must be the shortest distance x = 225 feet; the distance from the lighthouse to the ship must be the longest distance x = 225 feet; the distance from the lighthouse to the ship must be the longest distance Question 7 A)Which of these triangles is a right triangle?(1 point) Responses u u Question 8 A) Looking at the right triangle, choose all of the statements that are true. (3 points) Responses Right triangles must have the side across from the 90 degree angle as the longest side. Right triangles must have the side across from the 90 degree angle as the longest side. Right triangles have the pattern that the sum of the two shorter sides = the longest side. Right triangles have the pattern that the sum of the two shorter sides = the longest side. Right triangles have interior angles that add to equal 180 degrees. Right triangles have interior angles that add to equal 180 degrees. Right triangles have side lengths that always follow a2+b2=c2a2+b2=c2Right triangles have side lengths that always follow A squared plus b squared is equal to c squared Right triangles have interior angles that are all acute angles. Right triangles have interior angles that are all acute angles. Right triangles have side lengths that are always rational numbers. Right triangles have side lengths that are always rational numbers. Question 9 A) This picture shows a proof of the Pythagorean theorem because (1 point) Responses a < b < c, so the Pythagorean theorem holds true. a < b < c, so the Pythagorean theorem holds true. a = b = c, so the Pythagorean theorem holds true. a = b = c, so the Pythagorean theorem holds true. The four yellow triangles are congruent in both large squares and the large squares are congruent, so c2=a2+b2c2=a2+b2The four yellow triangles are congruent in both large squares and the large squares are congruent, so c squared is equal to A squared plus b squared The yellow triangles fill up the large squares just enough to have a small square in each figure. The yellow triangles fill up the large squares just enough to have a small square in each figure. Question 10 A)Jimmy ran 40 meters west from home and then turned north to jog 15 meters. Jimmy ran 55 meters, but could have arrived at the same point by jogging in a straight line. How many meters could he have jogged using a straight line distance?(1 point) Responses 42.7m 42.7m 15 m 15 m 912.5 m 912.5 m 8 m

Question

Question 1 A)(6 points) To solve the equation 5x3=−1355x3=−135, you would first use the operation of by to get the equation x3=−27x3=−27. You would then use the inverse operation of x3x3, which is taking the of both sides. That leaves us solution(s) for x. The solution(s): x = Question 2 A)Put the steps in order for solving the equation: x2+4=53x2+4=53 (1 point) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Step 1 Step 2 Step 3 Take the square root of both sidesDivide by 4 on both sidesDivide by 2 on both sidesSubtract 4 from both sidesSimplify - you get two rational solutionsAdd 4 to both sidesSimplify - you get two irrational solutions Question 3 A) Find the length of the red line segment in the coordinate plane. Which of the following statements are true: (1 point) Responses The length is 40 units; find the sum of the x and y coordinates and square root the answer. The length is 40 units; find the sum of the x and y coordinates and square root the answer. The length is 130; find the difference between the x and y coordinates and square it. The length is 130; find the difference between the x and y coordinates and square it. The length is 260−−−√260; find the difference of the x coordinates and the difference of the y coordinates and subtract those differences. The length is square root of 260 ; find the difference of the x coordinates and the difference of the y coordinates and subtract those differences. The length is 40−−√40units; find the sum of the vertical and horizontal distances squared and then take the square root. The length is square root of 40 units; find the sum of the vertical and horizontal distances squared and then take the square root. Question 4 A) Sidney is traveling from the grocery store to the bank. There are two possible routes she can take, marked yellow and green in the diagram. Which statement is true? (1 point) Responses The green path is 2 miles shorter than the yellow path. The green path is 2 miles shorter than the yellow path. The green path is half the distance of the shorter path. The green path is half the distance of the shorter path. The yellow path is double the distance of the green path. The yellow path is double the distance of the green path. The yellow path and green path are the same distance. The yellow path and green path are the same distance. Question 5 A) If you have a 24 foot ladder that is leaning against the building and touching the ground 6 feet from the building. How high up the building is the top of the ladder? (1 point) Responses 62+b2=24262+b2=242; 23.24 ft 6 squared plus b squared is equal to 24 squared ; 23.24 ft a2+242=62a2+242=62; 23.24 ft A squared plus 24 squared is equal to 6 squared ; 23.24 ft 62+b2=24262+b2=242; 24.7 ft 6 squared plus b squared is equal to 24 squared ; 24.7 ft 242+62=c2242+62=c2; 24.7 ft 24 squared plus 6 squared is equal to c squared ; 24.7 ft Question 6 A) How far is it from the lighthouse to the ship horizontally if the lighthouse is 20 ft tall and shines a beam to the ship 25 ft long? Also, which statement is correct? (1 point) Responses x = 15 ft; the distance from the top of the lighthouse to the ship must be the longest distance x = 15 ft; the distance from the top of the lighthouse to the ship must be the longest distance x = 15 ft; the distance from the lighthouse to the ship must be the shortest distance x = 15 ft; the distance from the lighthouse to the ship must be the shortest distance x = approximately 24.5 yards; from the top of the lighthouse to the boat must be the shortest distance x = approximately 24.5 yards; from the top of the lighthouse to the boat must be the shortest distance x = 225 feet; the distance from the lighthouse to the ship must be the longest distance x = 225 feet; the distance from the lighthouse to the ship must be the longest distance Question 7 A)Which of these triangles is a right triangle?(1 point) Responses u u Question 8 A) Looking at the right triangle, choose all of the statements that are true. (3 points) Responses Right triangles must have the side across from the 90 degree angle as the longest side. Right triangles must have the side across from the 90 degree angle as the longest side. Right triangles have the pattern that the sum of the two shorter sides = the longest side. Right triangles have the pattern that the sum of the two shorter sides = the longest side. Right triangles have interior angles that add to equal 180 degrees. Right triangles have interior angles that add to equal 180 degrees. Right triangles have side lengths that always follow a2+b2=c2a2+b2=c2Right triangles have side lengths that always follow A squared plus b squared is equal to c squared Right triangles have interior angles that are all acute angles. Right triangles have interior angles that are all acute angles. Right triangles have side lengths that are always rational numbers. Right triangles have side lengths that are always rational numbers. Question 9 A) This picture shows a proof of the Pythagorean theorem because (1 point) Responses a < b < c, so the Pythagorean theorem holds true. a < b < c, so the Pythagorean theorem holds true. a = b = c, so the Pythagorean theorem holds true. a = b = c, so the Pythagorean theorem holds true. The four yellow triangles are congruent in both large squares and the large squares are congruent, so c2=a2+b2c2=a2+b2The four yellow triangles are congruent in both large squares and the large squares are congruent, so c squared is equal to A squared plus b squared The yellow triangles fill up the large squares just enough to have a small square in each figure. The yellow triangles fill up the large squares just enough to have a small square in each figure. Question 10 A)Jimmy ran 40 meters west from home and then turned north to jog 15 meters. Jimmy ran 55 meters, but could have arrived at the same point by jogging in a straight line. How many meters could he have jogged using a straight line distance?(1 point) Responses 42.7m 42.7m 15 m 15 m 912.5 m 912.5 m 8 m

Answer 1

Question 1:

Solution(s): x = -3

Question 2:
Step 1: Subtract 4 from both sides
Step 2: Divide by 3 on both sides
Step 3: Take the square root of both sides

Question 3:
The length is 40 units; find the sum of the x and y coordinates and square root the answer.

Question 4:
The yellow path and green path are the same distance.

Question 5:
6 squared plus b squared is equal to 24 squared ; 23.24 ft

Question 6:
x = 15 ft; the distance from the lighthouse to the ship must be the shortest distance

Question 7:
Triangle u

Question 8:
Right triangles must have the side across from the 90 degree angle as the longest side.
Right triangles have the pattern that the sum of the two shorter sides = the longest side.
Right triangles have interior angles that add to equal 180 degrees.

Question 9:
The four yellow triangles are congruent in both large squares and the large squares are congruent, so c squared is equal to A squared plus b squared

Question 10:
42.7m