1. What is the first step to solve the inequality X^2+4x-12>0
A. Test several possible values of x to see wherex^2+4x−12is positive and where it is negative.
B. Factor the quadratic expression on the left side of the quadratic inequality.
C. Change the sign of the inequality.
D. Isolate the x-terms.
2. Solve the quadratic inequality(x−2)(x−4)>0
A. x<2
B. x>4
C. 2<x<4
D. 2<x<4
3. Solve for x in the quadratic inequality x^2+9x+18<0.
A. x<−6 and x>−3
B. x<−6 or x>−3
C. x>−6
D. −6<x<−3
4. Solve for x. x^2−81>0
A. x<−9 or x>9
B. x<−9
C. −9<x<9
D. x>9
5. A rectangular pen for a pet is 8 feet longer than it is wide. Give possible values for the width, W, of the pen if its area must be greater than 209 square feet.
A. The width of the pen must be greater than 11 feet.
B. The width of the pen must range from 11 feet to 19 feet, inclusive.
C. The width of the pen must be greater than 19 feet.
D. The width of the pen must be less than −19 feet.
1. B. Factor the quadratic expression on the left side of the quadratic inequality.
2. D. 2<x<4
3. A. x<−6 and x>−3
4. A. x<−9 or x>9
5. A. The width of the pen must be greater than 11 feet.
1. Which choice best explains the reason for the use of graphics to aid comprehension when writing informative or explanatory texts?
A. Graphics can be used when a reader has likely encountered the topic of a text before.
B. Graphics can be used when information is difficult to express in words.
C. Graphics can be used when the information in a text is likely to interest the reader.
D. Graphics can be used when it would be hard to use audio or video to provide the information.
2. Which of the following is an example of an objective tone in explanatory writing?
A. a personal, firsthand account of one traveler’s visit to Yellowstone National Park
B. a blog recounting how one writer’s time in Yellowstone National Park made for a transformative experience
C. a persuasive text that asks readers to donate funds to support the wolf population in Yellowstone National Park
D. a neutral and factual text informing readers about the role of the wolf population in Yellowstone National Park
3. Which of these are characteristics of a formal style when writing an explanatory text? Select the three correct answers.(2 points)
A. Slang
B. Contractions
C. personal pronouns
D. advanced vocabulary
E. standard textbook English
F. complex syntax
1. B. Graphics can be used when information is difficult to express in words.
2. D. a neutral and factual text informing readers about the role of the wolf population in Yellowstone National Park
3. D. advanced vocabulary, E. standard textbook English, F. complex syntax
1. Drag each phrase or sentence to the correct location to show whether it is vague or precise.(2 points)
Vague
precise.
We almost purchased a vacation-style home last year
He limped the entire way home
I put butter on the toast
two rivers meet in a town
Vague:
- We almost purchased a vacation-style home last year
- I put butter on the toast
Precise:
- He limped the entire way home
- Two rivers meet in a town
1. B. Factor the quadratic expression on the left side of the quadratic inequality.
To solve the inequality x^2 + 4x - 12 > 0, we first factor the quadratic expression:
(x - 2)(x + 6) > 0
2. D. 2<x<4
To solve the quadratic inequality (x - 2)(x - 4) > 0, we use the concept of zero-product property.
The inequality is satisfied when either both factors are positive or both factors are negative.
By setting each factor to zero and solving, we find that x = 2 and x = 4 are the critical points.
Plotting them on a number line, we can see that the intervals (2, 4) and (4, ∞) satisfy the inequality.
3. A. x<−6 and x>−3
To solve the quadratic inequality x^2 + 9x + 18 < 0, we can factor the quadratic expression:
(x + 3)(x + 6) < 0
Setting each factor to zero, we find that x = -3 and x = -6 are the critical points.
Plotting them on a number line, we can see that the interval (-6, -3) satisfies the inequality.
4. A. x<−9 or x>9
To solve the inequality x^2 - 81 > 0, we can factor it:
(x + 9)(x - 9) > 0
Setting each factor to zero, we find that x = -9 and x = 9 are the critical points.
Plotting them on a number line, we can see that the intervals (-∞, -9) and (9, ∞) satisfy the inequality.
5. C. The width of the pen must be greater than 19 feet.
Let's assume the width of the pen is W. According to the given information, the length is 8 feet longer than the width, so the length is W + 8.
The area of the pen is given by the formula: Area = width * length
So, the area of the pen will be: W * (W + 8)
We need to find the values of W that make the area greater than 209.
Therefore, the width of the pen must be greater than 19 feet.
1. The first step to solve the inequality X^2+4x-12>0 is to factor the quadratic expression on the left side of the inequality. This can be done by finding two numbers that multiply to give -12 and add to give 4. In this case, the numbers are 6 and -2, so the factored form is (x+6)(x-2)>0.
2. To solve the quadratic inequality (x−2)(x−4)>0, you need to analyze the signs of the factors. Since the inequality is greater than zero, you are looking for the values of x for which either both factors are positive or both factors are negative. From the factor (x−2)(x−4), you find that x>4 satisfies the condition. Hence, the answer is x>4.
3. To solve the quadratic inequality x^2+9x+18<0, you can use the fact that the quadratic expression factors into (x+3)(x+6)<0. The inequality is less than zero, so you need to find the values of x for which one factor is positive and the other factor is negative. In this case, it happens when -6<x<-3. Thus, the answer is -6<x<-3.
4. To solve the inequality x^2−81>0, you should factor the quadratic expression by using the difference of squares formula, which gives (x+9)(x-9)>0. Since the inequality is greater than zero, you want either both factors to be positive or both factors to be negative. By analyzing the signs, x<-9 or x>9 satisfies the condition. Thus, the answer is x<-9 or x>9.
5. For the rectangular pen with width W, given that it is 8 feet longer than its width, the length L would be W+8. The area of the pen is given by the product of the length and the width, which is L*W. The inequality states that the area must be greater than 209 square feet, so L*W>209. Substitute L=W+8 into the inequality: (W+8)*W>209. Solve this inequality to get the range of possible values for W. Option B states that the width of the pen must range from 11 feet to 19 feet, inclusive. Thus, the answer is B.