Let x represent the number.
Use the given conditions to write an equation.
Solve the equation and find the number.
Four less than six times a number is the same as eight times the number. Find the number.
Question 18 options:
A)
(1/2)
B)
- (1/2)
C)
-2
D)
2
Let x represent the number.
The equation can be written as 6x - 4 = 8x.
Solving for x:
Subtracting 6x from both sides:
-4 = 2x
Dividing both sides by 2:
-2 = x
The number is -2. The answer is option C) -2.
Find the volume of the solid.
Use (22/7) for π.
14 in. 20 in.
Question 19 options:
A)
12320 cu in.
B)
616 cu in.
C)
154 cu in.
D)
3080 cu in.
To find the volume of the solid, we need to multiply the length, width, and height of the solid.
The length of the solid is 14 inches, the width is 20 inches, and the height is also 20 inches.
Volume = length * width * height
Volume = 14 in * 20 in * 20 in
Using the calculator or long multiplication:
Volume = 5600 cu in
The correct option is not listed among the choices.
Find the mode or modes.
The weights (in ounces) of 14 different apples are shown below.
table ( (5.0 5.5 4.6 6.9 4.1 5.0 5.5)(5.7 6.0 6.9 5.0 4.8 6.9 4.4) )
Question 20 options:
A)
5.0
B)
5.0, 6.9
C)
5.5, 6.9
D)
None
To find the mode or modes, we need to determine the values that occur most frequently in the dataset.
Looking at the dataset, we can identify that the values 5.0 and 6.9 both occur three times, which is the greatest frequency. Therefore, the modes of the dataset are 5.0 and 6.9.
The correct option is B) 5.0, 6.9.
Suppose ABC is a right triangle with sides of length a, b, and c and right angle at C.
Find the exact value of the indicated trigonometric function.
You may need to use the Pythagorean theorem to find the unknown side length.
Rationalize the denominator if necessary.
Find cos A when a = 9 and b = 7.
Question 21 options:
A)
(square root of (130)/7)
B)
(9square root of (130)/130)
C)
(7square root of (130)/130)
D)
(square root of (130)/9)
To find cos A, we need to use the ratios of sides in the right triangle.
In the given triangle ABC, the side opposite angle A is a and the hypotenuse is c. The cosine function is defined as the adjacent side divided by the hypotenuse.
Using the Pythagorean theorem, we can find the length of the missing side: c² = a² + b²
c² = 9² + 7²
c² = 81 + 49
c² = 130
Taking the square root of both sides:
c = √130
Now we can find cos A:
cos A = a / c
cos A = 9 / √130
To rationalize the denominator, we multiply both numerator and denominator by √130:
cos A = (9√130) / (√130 * √130)
cos A = (9√130) / 130
The correct option is C) (7√130 / 130).
Solve the problem.
3x + 12
∠1 and ∠2 are complementary angles.
What are the measures of the two angles?
Question 22 options:
A)
∠1 = 19.5°, ∠2 = 70.5°
B)
∠1 = 26°, ∠2 = 90°
C)
∠1 = 22.5°, ∠2 = 79.5°
D)
∠1 = 42°, ∠2 = 138°
Complementary angles are angles that add up to 90 degrees.
Let ∠1 represent one angle and ∠2 represent the other angle.
We can set up the equation:
∠1 + ∠2 = 90
To find the measures of the angles, we need more information or an equation relating the angles to each other. The expression 3x + 12 does not provide any such equation or information.
Therefore, we cannot determine the measures of the two angles with the given information. The correct option is D) Cannot be determined.