The average number of siblings for the group is 1.3.
We must compute the total number of siblings and divide it by the total number of children in the group to determine the average number of siblings for the group.
There are a total of: siblings in the bunch.
3 + 8 + 9 = 20 (1 sibling times 3 children) + (2 siblings times 4 children) + (3 siblings times 3 children)
The total number of kids in the group is: 5 + 3 + 4 + 3 = 15
As a result, the group as a whole has an average of:
20/15 = 1.33 (rounded to the nearest tenth) (rounded to the nearest tenth)
So, the group as a whole has 1.3 siblings on average.
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I will mark you brainiest!
One of the sides of a rectangle has the length of 7. Which of the following points, when paired with (6, 5), will make a side equal to this length?
A) (7, 5)
B) (6, 12)
C) (6, 7)
D) (12, 5)
Answer:its b 6,12
Step-by-step explanation:
Jordan is on a road trip across the country with their family. In one day of traveling, they drove a total of 666.9 miles. Assume the same distance is driven each day of the trip and that the road trip consists of 7 days of traveling. Estimate the total number of miles Jordan will drive.
We estimate that Jordan will drive a distance of approximately 4668.3 miles during the entire 7-day road trip.
What is distance?Distance and displacement are two key words in mechanics that, although having similar sounds, have distinct definitions and meanings. How much of an object's path is covered by a moving object is measured in terms of distance. Whereas "How much route is covered by the item in a specific direction" is measured by displacement, The main distinction between distance and displacement is therefore that the former is a scalar quantity while the latter is a vector quantity.
Given that, the distance travelled is 666.9 miles.
The same distance is travelled for 7 days thus,
distance = Distance per day x Number of days
distance = 666.9 miles/day x 7 days
distance = 4668.3 miles
Hence, we estimate that Jordan will drive approximately 4668.3 miles during the entire 7-day road trip.
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ABCD is a kite, so
�
�
‾
AC
⊥
⊥
�
�
‾
DB
and
�
�
=
�
�
DE=EB. Calculate the length of
�
�
‾
AC
, to the nearest tenth of a centimeter
The length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.
How to solveApplying the Pythagorean Theorem, the length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.
From the information given, we know the following:
DE = EB = 4cmAD = 5 cmCD = 7 cmTriangles AED and CED are right-angled triangles
Thus:
AC = AE + CE
Find AE and CE using the Pythagorean Theorem , where c if the hypotenuse of the right triangle.
Length of AE:
AE = [tex]\sqrt{5^2 -4^2}[/tex]
AE= [tex]\sqrt{9}[/tex]
AE= 3
Length of CE:
CE = [tex]\sqrt{7^2 -4^2}[/tex]
CE= [tex]\sqrt{33}[/tex]
CE= 5.7
Length of AC:
AC = AE + CE
Put the values together:
AC = 3 + 5.7
= 8.7cm
Therefore, the length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.
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find the real cube root of the perfect cube
Answer:
-3/2
Step-by-step explanation:
cubed roots of -27 is -3
cubed root of 8 is 2
Given the two lines l and m are parallel in the figure, name the following:
Answer:
Option B
3&5, 4&6
Step-by-step explanation:
An interior angle is an angle inside a shape
What are the foci of the graph x^2/40-y^2/81=1
Answer:
Step-by-step explanation:
(y^2)/1600-(x^2)/81=1. y21600−x281=1 y 2 1600 - x 2
Answer: y21600x281=1 y 2 1600 - x 2
Step-by-step explanation: for sure chfjjgffjfj ;)
Find the area of the regular polygon below.
The area of the regular polygon which is given above would be = 64.5 cm². That is option D.
How to calculate the area of the regular polygon?To calculate the area of the given regular polygon will require the use of this formula such as:
Area = 1/2(a×p)
where;
a = length of an apothem = 4.3 cm
p = perimeter = 6×5 = 30cm
Area = 1/2 ( 4.3×30)
= 129/2
= 64.5 cm²
Therefore, in conclusion the area of the regular polygon which is a hexagon with 6 sides would be = 64.5 cm².
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You have realised that instead of reducing your car's short-term insurance ium as its book value decreases, your insurer has actually increased the premium % per year "to keep up with inflation". If your premium started off at R450 per month. have you paid in total after 2 years?
To calculate the total amount paid over two years, we first need to determine the annual premium increase percentage. Let's assume the insurer increases the premium by 5% per year to keep up with inflation.
After the first year, the new premium would be:
R450 + (5% of R450) = R472.50 per month
After the second year, the new premium would be:
R472.50 + (5% of R472.50) = R496.13 per month
To calculate the total amount paid over two years, we can use the following formula:
Total amount paid = (monthly premium x 12 months x number of years)
= (R450 x 12 x 2) + (R472.50 x 12 x 1) + (R496.13 x 12 x 1)
= R10,800 + R5,670 + R5,953.56
= R22,423.56
Therefore, you would have paid a total of R22,423.56 over two years.
suppose 2 bakers make 30 loaves of bread in 1 hr. how many hours would 3,5,6,and 15 bakers need to make 30 loaves
Answer:
Therefore, 3 bakers can make 30 loaves of bread in 2 hours.
Therefore, 5 bakers can make 30 loaves of bread in 2 hours.
Therefore, 6 bakers can make 30 loaves of bread in 1.25 hours.
Therefore, 15 bakers can make 30 loaves of bread in 2 hours.
Step-by-step explanation:
In the number of bakers, it would take 2 hours to make 30 loaves of bread.
What is proportion?A proportion is an equation in which two ratios are set equal to each other.
Let h be the number of hours needed for a given number of bakers to make 30 loaves. Then we have:
2 bakers can make 30 loaves in 1 hour, so 1 baker can make 15 loaves in 1 hour.
Therefore:
3 bakers can make 45 loaves in h hours, so 45/3 = 15 loaves can be made in 1 hour. Thus, 3 bakers can make 30 loaves in 2 hours.
5 bakers can make 75 loaves in h hours, so 75/5 = 15 loaves can be made in 1 hour. Thus, 5 bakers can make 30 loaves in 2 hours.
6 bakers can make 90 loaves in h hours, so 90/6 = 15 loaves can be made in 1 hour. Thus, 6 bakers can make 30 loaves in 2 hours.
15 bakers can make 225 loaves in h hours, so 225/15 = 15 loaves can be made in 1 hour. Thus, 15 bakers can make 30 loaves in 2 hours.
Therefore, regardless of the number of bakers, it would take 2 hours to make 30 loaves of bread.
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What is
2+3(3x9)
Someone pls explain this to me
Answer:
83
Step-by-step explanation:
The expression follows the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction, in that order.
First, simplify what is inside the parentheses: 3 x 9 = 27
Next, multiply 3 by 27: 3 x 27 = 81
Finally, add 2 to 81: 2 + 81 = 83
Therefore, the expression 2+3(3x9) equals 83.
The result of this expression is 83
Basic rules for expressionsTo solve them we have to start from the inside to out, that is, parentheses, brackets...
And proceed to signal resolution:
[tex]\begin{array}{l}\sf 2+3\tiny\text{$\times$}(3\times9)\\\sf 2+3\tiny\text{$\times$}(27)\\\sf 2+81\\\bf 83\end{array}[/tex]
We get the result 83
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Use the drawing tool to sketch the graph and label its parts.
The standard equation of a conic section with its center or vertex at the origin is x² = 4ay.
The graph of this conic section is a parabola that opens upward with with its vertex at the origin (0, 0).
What is a conic section?In Euclidean geometry, a conic section can be defined as a curve that is generated as the intersection of the surface of a right circular cone with a plane.
In Mathematics, the standard equation of a conic section is represented or modeled by the following mathematical equation:
(x - h)²/a² - (y - k)²/b² = 1
Where:
y and x represent the point.a, h, b, k represent a constant term.Based on the information provided about the vertex at (0, 0), the foci would be at (0, a) and the directrix would be represented by a horizontal line at y = -a. Therefore, the required equation of a conic section in standard form is given by:
x² = 4ay.
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Here is the problem.
a) The speed at which the car gets maximum gas mileage is given as follows: 48 miles per hour.
b) The max gas mileage is given as follows: 29.5 miles per gallon.
How to obtain the maximum gas mileage?The gas mileage is modeled as a function of the velocity x according to the quadratic function presented as follows:
m(x) = -0.028x² + 2.688x - 35.012.
The coefficients are given as follows:
a = -0.028, b = 2.688, c = -35.012.
The leading coefficient a is negative, hence the vertex represents the point at which the maximum mileage is obtained.
The velocity is given as follows:
x = -b/2a
x = -2.688/[2(-0.028)]
x = 48 miles per hour.
The max gas mileage is obtained as follows:
m(48) = -0.028(48)² + 2.688(48) - 35.012.
m(48) = 29.5 miles per gallon.
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Which shape is given below?
A) a rectangle
B) a rhombus
C) a kite
D) a trapezoid
pls help with number 5 a through d
The surface area of the following solids is:
a.54cm².
b. 43.32cm².
c. 21.2cm².
d. The figures b and c are smaller than a.
Explain surface area?In contrast to the lateral surface area, which is used to determine the area occupied by the shape's curved surface, the total surface area takes into account all faces of the 3D shape, including both flat and curved surfaces.
The area around the bases is not included. One 3D shape called a sphere has just one round surface and no flat base.
In the given question,
In the 1st figure,
Total surface area = Total surface area of 6 squares.
= 6 × 3²
= 54cm².
In the 2nd figure,
Total surface area = Total surface area of 2 triangles + Total surface area of 3 squares + Total surface area of larger triangle.
= 2 × 1/2 × 3 × 3 + 3 × 3² + 1/2 × 3.96 × 3.7
= 9 + 27 + 7.32
= 43.32cm².
In the 3rd figure,
Total surface area = Total surface area of 4 triangles
= 1/2 × 3 × 3 + 1/2 × 3 × 3 + 1/2 × 4.2 × 3.7 + 1/2 × 3 × 3
= 9 + 7.77 + 4.5
= 21.2cm².
Hence, the figures b and c are smaller than the figure a.
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15 ) Ian throws a ball up in the air and lets it fall to the ground.
The height of the ball, h(t), is modeled by the equation
h(t) = -16t² + 6t+ 3, with h(t) measured in feet, and time, t,
measured in seconds. The number 3 in h(t) represents
(1) the maximum height of the ball
(2) the height from which the ball is thrown
(3) the number of seconds it takes for the ball to reach the ground
(4) the number of seconds it takes for the ball to reach its maximum
height
The number 3 in the equation h(t) = -16t² + 6t+ 3 represents option 2 - the height from which the ball is thrown.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The equation h(t) = -16t² + 6t+ 3 gives the height of the ball as a function of time.
The constant term in this equation is 3, which represents the initial height of the ball when it is thrown.
Therefore, the correct answer is (2) the height from which the ball is thrown.
Option (1) cannot be correct, because the maximum height of the ball occurs when the derivative of h(t) is zero, which is not necessarily equal to the constant term in the equation.
Option (3) cannot be correct, because the ball reaches the ground when h(t) = 0, which requires solving a quadratic equation.
Option (4) cannot be correct, because the time it takes for the ball to reach its maximum height is given by the formula t = -b/2a, where a and b are the coefficients of the quadratic equation, and it does not depend on the constant term.
Therefore, option 2 is the correct answer.
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Solve four-sixths minus three-twelfths equals blank.
one-sixth
five-twelfths
seven-twelfths
thirty-six seventy-seconds
Question 4(Multiple Choice Worth 2 points)
(05.04 LC)
Solve seven-eighths minus nine-sixteenths equals blank.
two-sixteenths
two-eighths
five-sixteenths
sixteen thirty-seconds
Question 5(Multiple Choice Worth 2 points)
(05.04 LC)
Solve two-fifths minus one-seventh equals blank.
one-fifth
one-seventh
nine thirty-fifths
three-twelfths
By answering the presented question, we may conclude that As a result, fraction the answer is nine thirty-fifths.
what is fraction?A whole can be represented by any number of equal sections or fractions. In standard English, fractions represent the number of units of a specific size. 8, 3/4. A whole contains fractions. In mathematics, numbers are stated as the ratio of the numerator to the denominator. Each of these is an integer in simple fractions. A fraction exists in the numerator or denominator of a complex fraction. True fractions have numerators that are smaller than their denominators. A fraction is a sum that represents a piece of a total. You may assess it by dividing it up into smaller chunks. Half of a whole number or object, for example, is represented as 12.
We can simplify both fractions to have a common denominator of 12 for the first problem:
Four-sixths = Eighteenths
Three-twelfths + three-twelfths = three-twelfths
As a result, the phrase becomes: 8/12 - 3/12 = 5/12
As a result, the answer is five-twelfths.
For the second case, we may reduce both fractions again such that they have a common denominator of 16:
Seventy-eighths = fourteenteenths
Nineteenths + nineteenths = nineteenths
As a result, the equation becomes: 14/16 - 9/16 = 5/16.
As a result, the answer is five-sixteenths.
We can simplify both fractions to obtain a common denominator of 35 for the third problem:
Two-fifths = 14-thirty-fifths
One-seventh Equals thirty-fifths
As a result, the phrase becomes: 14/35 - 5/35 = 9/35
As a result, the answer is nine thirty-fifths.
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22. A small coffee company claims to include 11 ounces of coffee in every bag of ground coffee it produces. Out of a random sample of 250 bags, 50 of the bags contain only 10.9 ounces. Which inferences from the results of the random sample are reasonable? Choose all that are correct.
A. It can be inferred that 5% of the bags from a second random sample will contain more than 11 ounces.
B. It is likely that a second random sample of bags will show a much lower percentage of bags with only 10.9 ounces.
C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.
D. It is likely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.
E. It is unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces.
The inferences from the results of the random sample that are reasonable is: C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.
Which inferences from the results of the random sample are reasonable?From the sample of 250 bags, we know that 50 of them contain only 10.9 ounces of coffee. Let's calculate the percentage of bags in the sample that contain less than 11 ounces:
50/250 = 0.2 = 20%
Now let's consider each inference:
A. It cannot be inferred that 5% of the bags from a second random sample will contain more than 11 ounces. The sample only provides information about the bags in the sample, not the entire population.
B. It is possible that a second random sample of bags will show a lower percentage of bags with only 10.9 ounces, but it cannot be concluded with certainty based on the given information.
C. It is reasonable to estimate that the percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%. This is because out of a sample of 250 bags, 50 bags contained 10.9 ounces, which is 20% of the sample.
D. It is not necessarily likely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces. The sample provides information about the bags in the sample, not the entire population.
E. It is not necessarily unlikely that the company's claim is true because 20% of the bags in the sample contain 10.9 ounces. The sample provides information about the bags in the sample, not the entire population.
Therefore, the correct inferences from the given information are C. The percentage of all bags produced that contain less than 11 ounces is likely to fall between 15% and 25%.
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Please solve these 2 problems for me
The value of the perimeter:
1. 97. 3 units
2. 27. 8 units
How to determine the perimeter of the shapesThe formula for the perimeter of a triangle is expressed as;
P = a + b + c
Given that;
P is the perimeter of the trianglea, b and c are the length of the sidesFrom the diagram shown, we have that;
Using the tangent identity;
tan 44 = BC/29
find the value and cross multiply
BC = 28. 00
Also, AC ²= 29² + 28²
AC = √1625 = 40. 3
Then, the perimeter = 29 + 28. 00 + 40. 3 = 97. 3 units
For the second diagram;
Note that the perimeter of a rectangle is expressed as 2(length + width)
Substitute the values
Perimeter =2 ( 4 + 3) = 14 units
For triangle;
sin 45 = 4/t
cross multiply
t = 5. 7 units
To determine the adjacent side;
5.7² - 4² = x²
32. 5 - 16 = a²
a = √16. 49
a = 4. 1
Then, the perimeter = perimeter of rectangle + perimeter of triangle
= 14 + 13. 8
= 27. 8 units
Note that no specific unit was given as thus, we used 'units' as the measuring scale.
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PLEASE HELP !! I WILL GIVE BRAINLIEST ANDDD 100 POINTS ! :)
Step-by-step explanation:
Interchange just means to switch really. The first 3 will stay the same be cause they are the same numbers.
The last one will be (2,8) because that's (8,2) but with the numbers switched
Find x correct to 2 decimal places.
Answer:
216.49
Step-by-step explanation:
you have two right triangles, for the left one
[tex]tan(64)=\frac{113}{a}[/tex]
[tex]a=\frac{113}{tan(64)}[/tex]
for the one on the right
[tex]tan(35)=\frac{113}{b}[/tex]
[tex]b=\frac{113}{tan(35)}[/tex]
The total value of X is the sum
[tex]\frac{113}{tan(35)} +\frac{113}{tan(64)}=216.4945073[/tex]
so 216.4945073
find the root of -3x^{3\:}-21x^2+72x+540=0
can someone hel-p me
Round 0.652 to the nearest tenth
Pls help
Answer:
0.7
Step-by-step explanation:
Answer: 0.7
Step-by-step explanation: The tenths place in decimals is the number directly to the right of the decimal. the 5 next to the six is greater than or equal to 5 meaning you can round up the 6 to a 7.
The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year.
A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils.
A box plot uses a number line from 2 to 52 with tick marks every one unit. The box extends from 8 to 26 on the number line. A line in the box is at 16. The lines outside the box end at 5 and 50. The graph is titled Mrs. Cheng's Class, and the line is labeled Number Of Pencils.
Which class lost fewer pencils overall based on the data displayed?
Mrs. Cheng's class; it has a narrow spread in the data
Mr. Johnson's class; it has a wide spread in the data
Mrs. Cheng's class; it has a smaller median value 16 pencils
Mr. Johnson's class; it has a smaller median of 11 pencils
Answer: Based on the data displayed, Mrs. Cheng's class lost fewer pencils overall as it has a smaller spread in the data compared to Mr. Johnson's class. The box plot of Mrs. Cheng's class has a smaller spread, with a larger interquartile range and smaller range compared to Mr. Johnson's class, indicating that the data is more concentrated and consistent. Additionally, the median value of Mrs. Cheng's class is higher than Mr. Johnson's class, indicating that half of the students in Mrs. Cheng's class lost fewer pencils than half of the students in Mr. Johnson's class. Therefore, the correct answer is "Mrs. Cheng's class; it has a narrow spread in the data".
Step-by-step explanation:
Which is the best first step when solving the following system of equations?
x + y = 3. 4 x minus y = 7.
Multiply the first equation by 4.
Add the first equation to the second equation.
Multiply the second equation by Negative 1.
Subtract the second equation from the first equation.
Mark this and return
On solving the provided question, we can say that Hence, the solution to the system of equations is x = 19/8 and y = 5/8.
What is equation?A math equation is a technique that links two statements and utilises the equals sign (=) to express equivalence. In algebra, an equation is a mathematical statement that proves the equivalence of two mathematical expressions. For example, in the computation 3x + 5 = 14, the equal sign inserts a gap between the numbers 3x + 5 and 14. A mathematical formula may be used to explain the link between the two phrases written on either side of a letter. The logo and the programme are usually the same. For example, 2x - 4 equals 2.
4x + 4y = 12 is obtained by multiplying the first equation by four.
To remove y, combine the first and second equations: (4x + 4y) + (4x - y) = 12 + 7, which simplifies to 8x = 19.
Divide both sides of the equation by 8 to find x: x = 19/8.
To find y, plug the value of x into either equation: y = 3 - x = 3 - 19/8 = 5/8.
Hence, the solution to the system of equations is x = 19/8 and y = 5/8.
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The table below shows data for a class's midterm and final exam. Use the table to answer the following questions.
What is the 5 number summary for the class's Midterm Exam?
Minimum
Lower Quartile
Median
Upper Quartile
Maximum
The five-number summary of the class, determined by the results of the final test, is:
Minimum = 60
Lower quartile = 71.5.
Median = 85.
Upper Quartile = 94.
Maximum = 98
What is median?The median, a measure of the center of gravity, reflects the center of value in the collection when values are sorted in either ascending or descending order. The value that distinguishes the lower 50% of the information from the upper 50% of the data is, in other words, the value.
The lowest score is 60, which is the minimum. The highest score, 98, will serve as the maximum.
The formula: can be used to determine the lower quartile.
= (Second score + Third score) / 2
= (65 + 78) / 2
= 71.5.
The upper quartile is:
= (Third to last score + Second to last score) / 2
= (93 + 95) / 2
= 94
The median is:
= (5th score + 6th score) / 2
= (82 + 88) / 2
= 85
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GIFTS Joel has $96 to spend on at least 9 gifts for the holidays. He plans to buy puzzles that cost $8 or games that cost $12. How many of each can he buy? Part A Create a system of inequalities that represents the constraints in the problem. Let x be the number of puzzles Joel can buy and y be the number of games Joel can buy. Can Joel buy 2 games and 6 puzzles and satisfy the constraints?
Joel cannot buy 2 games and 6 puzzles and satisfy the constraints was solved by using inequality.
The total cost of x puzzles and y games must be less than or equal to $96, which gives us the first inequality: 8x + 12y ≤ 96
The second inequality: x + y ≥ 9.
What is inequality function?An inequality is a mathematical statement that compares two quantities or expressions and shows the relationship between them using one of the following symbols: <, >, ≤, or ≥. For example, "x > 5" is an inequality that states that x is greater than 5.
In the given question,
Part A:
Let x be the number of puzzles Joel can buy and y be the number of games Joel can buy.
The total cost of x puzzles and y games must be less than or equal to $96, which gives us the first inequality: 8x + 12y ≤ 96
Joel needs to buy at least 9 gifts, which means that the total number of gifts must be greater than or equal to 9. Since x represents the number of puzzles and y represents the number of games, the total number of gifts is x + y. This gives us the second inequality: x + y ≥ 9
We also know that Joel can only buy puzzles or games, not both. Therefore, x and y must be either both integers or both half-integers (such as 1.5 or 2.5), but they cannot be mixed. This gives us the third inequality:
x, y are both integers or both half-integers
Part B:
To see if Joel can buy 2 games and 6 puzzles and satisfy the constraints, we can substitute x = 6 and y = 2 into the inequalities:
8x + 12y ≤ 96
8(6) + 12(2) ≤ 96
72 ≤ 96
This inequality is true, so the first constraint is satisfied.
x + y ≥ 9
6 + 2 ≥ 9
8 ≥ 9
This inequality is not true, so the second constraint is not satisfied. Therefore, Joel cannot buy 2 games and 6 puzzles and satisfy the constraints.
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A coin purse contains five 10-peso coins, three 5-peso coins, and nine 1-peso coins. If a coin is randomly picked from the purse, find the probability that it is.
a. not a 10-peso coin.
b. a 5-peso coin.
a. The probability that it is not a 10-peso coin is [tex]\frac{12}{17}[/tex].
b. The probability that it is a 5-peso coin is [tex]\frac{3}{17}[/tex] .
What is probability?
The mathematical notion of probability is used to determine the likelihood of an event. It is only helpful for estimating the likelihood that an event will happen. A scale from 0 to 1, where 0 denotes impossibility and 1 denotes a specific occurrence.
We are given that a purse contains five 10-peso coins, three 5-peso coins, and nine 1-peso coins.
Total coins = 5 + 3 + 9 = 17
a. Probability of getting a 10 peso coin is
P (A) = [tex]\frac{5}{17}[/tex]
Probability of not getting a 10 peso coin is
⇒Probability = 1 - P (A)
⇒Probability = 1 - [tex]\frac{5}{17}[/tex]
⇒Probability = [tex]\frac{12}{17}[/tex]
b. Probability of getting a 5 peso coin is [tex]\frac{3}{17}[/tex] .
Hence, the required probabilities have been obtained.
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the length of a rectangle is 5 inches more than twice a number. The width is 4 inches less than the same number. If the area of the rectangle is 15, find the number
Answer: 5
Step-by-step explanation:
A = Lw (area of rectangle is length times width)
A = 15 (Area is 15)
L = 2x + 5 (length is 2 times a number plus another 5)
w = x - 4 (width is 4 less than that number
Plug in the values:
15 = (2x + 5)(x - 4)
FOIL
15 = 2x2 - 8x + 5x - 20
simplify:
15 = 2x2 - 3x - 20
Subtract 15
0 = 2x2 - 3x - 35
Factor out the quadratic. We know that one number has to be 7 and the other 5 so that they multiply together to make 35, and that one of them has to be negative so that it's actually -35.
That means we have m * n = -35
We also need it set up so that so that 2m + n = -3:
2 * -5 + 7 = -3
0 = (2x + 7)(x - 5)
So:
0 = 2x + 7, or 0 = x - 5
x = -7/2 or 5
We cannot have a negative length, so x = 5
Check:
15 = (2 * 5 + 5) (5 - 4)
15 = 15 * 1
15 = 15
Eli has a trophy case that is 4 3/5 feet by 2 feet by 3 1/2feet. What is the volume of Eli’s trophy case?
The volume of Eli's trophy case is 64.4 cubic feet.
Eli's trophy case's length, breadth, and height must be multiplied to determine its volume. The case has the following measurements:
Length = 4 3/5 feet
Width = 2 feet
Height = 3 1/2 feet
We can sum the improper fractions after converting the mixed integers to fractions to arrive at:
Length = 4 3/5 feet = (5*4 + 3)/5 = 23/5 feet
Height = 3 1/2 feet = (2*3 + 1)/2 = 7/2 feet
Now that we have the volume, we can multiply the length, width, and height:
Volume equals length, width, and height
= (23/5) feet x 2 feet x (7/2) feet
= (23 x 2 x 7)/(5 x 2) cubic feet
= (644/10) cubic feet
= 64.4 cubic feet
Eli's trophy case therefore has a 64.4 cubic foot volume.
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