If x represents the width of a rectangle and length is four less than three times the width, which of the following expressions represents the length of the rectangle in terms of x?
A. 4-3x
B. 3-4x
C. 4x-3
D. 3x-4
To form an equation from the word problem, first break the given statement into smaller statements.
First, we are given the width of the rectangle as x. We are told, the length is three times width. Mathematically, this means
Length=3*width=3*x=3x
Again, the length is 4 less than 3 times width of the rectangle. Thus, the length of rectangle in terms of width becomes:
Length =3x-4
This is the required equation.
Therefore, the Correct Answer is D.
More Questions on TEAS 7 Math
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Q #1: Which of the following is the length of the unknown leg of a right triangle that has one leg length of 8 feet and a hypotenuse of 12 feet? (Round to the nearest tenth.)
A. 40 feet
B. 4 feet
C. 14.4 feet
D. 8.9 feet
Answer Explanation
The length of the unknown side of the rectangle can be found by using the Pythagoras theorem. We label the triangle from the given data as shown below
Let the unknown length be x.
Applying the Pythagoras theorem, the value of x is found as:
The unknown length of the triangle is approximately 8.9 feet.
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Q #2: A teacher has asked all the students in the class which days of the week they get up after 8 a.m. Which of the following is the best way to display the frequency of each day of the week?
A. Histogram
B. Scatterplot
C. Pie graph
D. Bar graph
Answer Explanation
The best way to display the frequency of each day of the week when students get up after 8 a.m. is by using a bar graph. Bar graphs are well-suited for representing categorical data, where each day of the week is a separate category, and the height of each bar corresponds to the count or frequency of students waking up late on that specific day.
Note: Histograms, on the other hand, are more appropriate for visualizing continuous or numerical data and are not ideal for categorical data like days of the week. Histograms are useful for understanding the distribution of data, identifying patterns, and assessing the shape of the data distribution, such as whether it's normally distributed, skewed, or has multiple modes.
As you can see below, the Histogram is used to depict a pattern/continuous/range data. While a bar graph does just fine even with discrete data.
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Q #3: If a box of 35 syringes costs $560.00, which of the following is the cost of two syringes?
A. $15.00
B. $16.00
C. $32.00
D. $8.00
Answer Explanation
the question requires we find the cost of two syringes.
If we let x be the cost of two syringes, then we set up a proportion equation with cost as numerator and number of syringes as denominator. The proportion equation becomes
Cross-multiply to solve for x
Rearranging the above
Divide both sides by 35
The cost of 2 syringes is $32.
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Q #4: Which of the following is the greatest value?
A. 34÷96
B. 3/8
C. 0.372
D. 37%
Answer Explanation
we are asked to find the largest value from the options given. To solve this problem, we need to convert all the given values into fraction. Then find the least common denominator for all fractions, which we will use to multiply each fraction and make a comparison.
34÷96=
3/8=3/8
0.372=372/1000
37%=37/100
Now, we need to find the least common denominator of 48, 8, 1000, and 100, which is 6000. We multiply each fraction by 6000 as follows:
17/48*6000=2125
3/8*6000=2250
372/1000*6000=2232
37/100*6000=2220
From the above calculations, arranging the fraction from the largest to the smallest in order is: 3/8, 372/1000,37/100, and 17/48. Thus, the greatest value is 3/8.
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Q #5: A bucket can hold 3 L. How many ml can the bucket hold?
A. 3000 mL
B. 300 mL
C. 30 mL
D. 0.003 mL
Answer Explanation
to change L to mL we use the following options of interconversions:
Or
Since we are needed to change L to mL, use the second option.
Thus, a bucket can hold 3000 mL which is equal to 3 L.
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Q #6: Which of the following statements is true about the graph?
A. The Chargers points per game decreased between seasons eight times between 1996 and 2015
B. The Chargers scored their lowest number of points per game in 1999-2000 season
C. The Chargers scored their greatest number of points per game in the 2008-09 season
D. None of the above
Answer Explanation
To find the true statement we need to analyze the given statements.
For statement 1: the points per game decreased five times between 1996 and 2015. So, the statement is false.
For statement 2: the lowest points scored per game was in 1998-99 season. So, the statement is false.
For statement 3: 2008-09 was the season the chargers scored the greatest number of points per game. So, this statement is true.
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Q #7: How many feet are in 6 yards?
A. 9ft
B. 18 ft
C. 36 ft
D. 2 ft
Answer Explanation
here we use the US customary system to convert between yards and feet. We use the conversion 1 yard =3 feet. Then, 6 yards to ft is found as
Thus, 6 yards is equal to 18 ft.
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Q #8: Which of the following values is the greatest?
A. 9/2
B. 4.4
C. 10/3
D. 4.25
Answer Explanation
The initial step is to convert the decimal numbers into fractions.
4.4 becomes 44/10
4.25 becomes 425/100
Thus, the set of fractions is 9/2, 44/10, 10/3, 425/100. The least common denominator for 2, 10, 3, and 100 is 300, which we use to compare each options given.
9/2*300=1350
44/10*300=1320
10/3*300=1000
425/100*300=1275
From the above, 1350 is the greatest value which corresponds to 9/2. Thus, 9/2 is the greatest value of all the choices given.
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Q #9: The scatter plot below shows the relationship between the number of hours a student listens to music and the student’s test scores. Which of the following types of correlation is shown on the scatter plot?
A. Positive
B. Positive and negative
C. No correlation
D. Negative
Answer Explanation
scatter plots can of three types: positive, negative and no correlation. A positive correlation scatter plot shows that as one variable increase, the other variable increases. A positive correlation can be visually depicted below.
In a negative correlation, the change in one variable is inversely proportional to another variable. That is, as one variable increases, the other variable decreases as shown below.
The third type of scatter plot is a no-correlation scatter plot. In this type of plot, there is no defined relationship between one variable and another one as in the curve below.
If we look at the relationship between the time the student listens to music and his test score, it is evident that no relationship exists between the two variables. Thus, this is a type of no correlation scatter plot.
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Q #10: Lana has $60. She spends 80% of the money. She then invests the remaining amount and earns a profit of 80%. How much money does she now have?
A. $21.60
B. $86.40
C. $9.60
D. $60
Answer Explanation
we are needed to find the amount Lana is left with after spending and investing the rest using the given information.
Amount Lana spends = 80% of $60= 80/100 * 60 = $48
Amount left to invest = $(60-48) = $12
Lana is left with $12, which she invests and earns a profit of 80%.
Profit earned = 80% of $12 = 80/100 * 12 = $9.20
So, Lana will have $12 + $9.20 = $21.60
