Josie took a long multiple-choice, end-of-year vocabulary test. the ratio of the number of problems josie got incorrect to the number of problems she got correct is 2: 9.
a. if josie missed 8 questions, how many did she get correct? draw a tape diagram to demonstrate how you found the answer.
b. if josie missed 20 questions, how many did she get correct? draw a tape diagram to demonstrate how you found the answer.
c. what ratios can we say are equivalent to 2: 9?
d. come up with another possible ratio of the number josie got incorrect to the number she got correct.
e. how did you find the numbers?
f. describe how to create equivalent ratios.

A. Josie got 36 correct answers.

B. Josie got 90 correct answers.

C. 8:36 and 20:90

D.6:27, 12:54, 30:135, among others.

e. Multiply both numbers on the ratio by the same constant integer, thereby ensuring that the resulting numbers form a ratio equivalent to the original.

Step-by-step explanation:

Very well, so the statement is that Josie got 2 problems incorrect for every 9 that she got correct. First the ask how many questions she got correct given that she missed 8 question. First, we divide the 8 question she missed by 2. Now have 4 pairs of questions that Josie missed and for every pair that she failed; Josie got 9 questions correctly. Therefore, we multiply 4 pairs of incorrect questions times 9 correct questions. So, if Josie had 8 incorrect questions, she also had 36 correct answers on her test.

In the case that Josie missed 20 questions, we divide them by two again in order to obtain the number of pairs that Josie missed. Now have 10 pairs of questions that Josie missed and for every pair that she failed; Josie got 9 questions correctly. Therefore, we multiply 10 pairs of incorrect questions times 9 correct questions. So, if Josie had 8 incorrect questions, she also had 90 correct answers on her test.

With the information we collected, we can affirm that the ratios 8:36 and 20:90 are equivalents to the original 2:9 that was stated. Other examples of equivalents ratios could be 6:27, 12/54, 30:135, among many others.

To find the equivalent ratios what we need to do is find common multiples of the numbers that conform the ratio. To do so, we can multiply both numbers by the same constant integer, thereby ensuring that the resulting numbers form a ratio equivalent to the original.

Have a nice day! :D

"standard form:

3x2 + 14x − 10 = 0

solutions based on quadratic formula:

x1   = −14 − √ 142 − 4×3×(−10) /   2×3   = −14 − 2 × √ 79 /   6   ≈ −5.296

x2   = −14 + √ 142 − 4×3×(−10) /   2×3   = −14 + 2 × √ 79 /   6   ≈ 0.629