5.Jack participated in a 6 day bike marathon of 430 kilometers. He biked 90 kilometers on each of the first 4 days and y kilometers on the fifth day. Which equation can be used to find b, the number of kilometers Jack biked on the sixth day?
A.b=430-90+(4xy)
B.b=430-4+(90xy)
C.b=430-(90x4)-y
D.b=430-(90xy)-4
C
6.Which statement about polygons is false?
A.If all the angles of a triangle are congruent then the measure of each angle is 90 degrees
B.If a traingle has a right angle then both of the other angles are acute
C.If a figure is a rectangle then the sum of the measures of 4 angles is 360 degrees
D.If a quadrilateral has exactly 2 obtuse angles then each of the other angles is an acute angle
A
The circumference of a circular garden is 40 feet. Which expression best represents the radius of the garden?
A.40/pi
B.40xpi
C.40/2pi
D.40x2pi
pi=3
C
All are right.
To solve the first question, we need to set up an equation to find the number of kilometers Jack biked on the sixth day. We know that Jack biked 90 kilometers on each of the first 4 days, totaling 90 * 4 = 360 kilometers. Additionally, we know that the total distance biked over 6 days is 430 kilometers. Therefore, the number of kilometers Jack biked on the sixth day (b) can be found by subtracting the total distance of the first 4 days (360 kilometers) and the distance biked on the fifth day (y) from the total distance of 430 kilometers.
The equation that represents this is:
b = 430 - 360 - y
Simplifying this equation, we get:
b = 70 - y
Therefore, option C, b = 430 - (90 * 4) - y, is the correct equation.
To solve the second question, we need to determine which statement about polygons is false. Let's evaluate each statement:
A. If all the angles of a triangle are congruent, then the measure of each angle is 90 degrees. This statement is false because if all the angles of a triangle are congruent, they must be equal, but not necessarily 90 degrees.
B. If a triangle has a right angle, then both of the other angles are acute. This statement is true because a right angle has a measure of 90 degrees, and the sum of angles in a triangle is always 180 degrees. Therefore, the other two angles must be acute.
C. If a figure is a rectangle, then the sum of the measures of 4 angles is 360 degrees. This statement is true because a rectangle has four right angles, and each right angle measures 90 degrees. Therefore, the sum of the measures of the four angles is 4 * 90 = 360 degrees.
D. If a quadrilateral has exactly 2 obtuse angles, then each of the other angles is an acute angle. This statement is true because in a quadrilateral, the sum of all angles is 360 degrees. If there are two obtuse angles, their sum will be more than 180 degrees, meaning the sum of the other two angles must be less than 180 degrees, making them acute angles.
Therefore, the false statement is A. If all the angles of a triangle are congruent, then the measure of each angle is 90 degrees.
To solve the third question, we need to find the expression that represents the radius of a circular garden given its circumference of 40 feet. The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
We are given the circumference as 40 feet, so we can set up the equation as follows:
40 = 2πr
Since we are given that π is equal to 3, we can substitute it in the equation:
40 = 2 * 3 * r
Simplifying further, we get:
40 = 6r
To isolate the radius, we divide both sides of the equation by 6:
40/6 = r
Simplifying this, we get:
r = 20/3
This means the radius of the circular garden is 20/3 feet.
Among the provided options, the expression that best represents the radius of the garden is C. 40/2π, because it simplifies to 20/3 when π is replaced with 3.