16. Solve y = log3243.
A. y = 0 C. y = 5
B. y = 3 D. y = 243
3. Which of the equations below describes the graph shown here?
A. y = x – 2 C. y = –x + 2
B. y = x + 2 D. y = –x – 2
11. If the triangles in the following figure are proportional, what is the length of side b?
A. 32.4 C. 40
B. 36 D. 45
18. Solve log660 – log630.
A. log630 C. log62
B. 5 D. 2
16.C
3.C
11.B
18.C
can you check it for me please?
#16 and #18 are correct
though I must say the typesetting needs work
The others, no idea. No diagrams or graphs here.
i appreciate this
To solve the given questions, let's go through each of them one by one:
16. Solve y = log3243.
To find the value of y, we need to determine the inverse function of the logarithm with base 3. The inverse function undoes the logarithm operation, so it's equivalent to raising the base to the power of y. In this case, the inverse function would be 3^y = 243. Now we can solve for y. Taking the logarithm base 3 on both sides, we have log3(3^y) = log3(243). The left side simplifies to y, resulting in y = 5. Hence, the correct answer is C. y = 5.
3. Which of the equations below describes the graph shown here?
To determine the equation of the graph, we need to find the slope and y-intercept. From the graph, we can observe that the line has a slope of 1 (since it goes up by 1 unit for every unit in the positive x-direction) and a y-intercept of -2 (since it intersects the y-axis at -2). Therefore, the equation of the graph is y = x - 2. So the correct answer is A. y = x - 2.
11. If the triangles in the following figure are proportional, what is the length of side b?
To solve for the length of side b, we can set up a ratio between the corresponding sides of the two triangles. Since triangle ABC is similar to triangle XYZ, we have the ratio of corresponding side lengths as AB/XY = BC/YZ. Substituting the given values, we have 8/12 = b/30. Cross-multiplying gives us 12b = 8 * 30, which simplifies to 12b = 240. Dividing both sides by 12, we get b = 20. Thus, the length of side b is 20. So the correct answer is B. 20.
18. Solve log660 – log630.
To solve this logarithmic expression, we can use the logarithmic rules. According to the subtraction rule of logarithms, log(a) - log(b) = log(a/b). Applying this rule to the given expression, we can rewrite it as log(660/630). Evaluating the numerator and the denominator, 660/630 simplifies to 11/10. Hence, the expression becomes log(11/10). In logarithmic notation, this means log base 10 of 11/10. Since log base 10 of 11/10 is equal to 0.0413927 (approximately), the correct answer is C. log62.
Therefore, the correct answers are:
16. C. y = 5
3. C. y = x - 2
11. B. 20
18. C. log62