Use the Pythagorean theorem:
70^2 = 42^2 + width^2
4900 = 1764 + width ^2
Subtract 1764 from both sides
3136 = width^2
Take the square root of both sides
Width = 56 inches
The volume (in cubic inches) of a shipping box is modeled by V =2x³ -19x² +39x, where x is the length (in inches). Determine the values of x for which the model makes sense.
Answer:
The values of x for which the model is 0 ≤ x ≤ 3
Step-by-step explanation:
The given function for the volume of the shipping box is given as follows;
V = 2·x³ - 19·x² + 39·x
The function will make sense when V ≥ 0, which is given as follows
When V = 0, x = 0
Which gives;
0 = 2·x³ - 19·x² + 39·x
0 = 2·x² - 19·x + 39
0 = x² - 9.5·x + 19.5
From an hint obtained by plotting the function, we have;
0 = (x - 3)·(x - 6.5)
We check for the local maximum as follows;
dV/dx = d(2·x³ - 19·x² + 39·x)/dx = 0
6·x² - 38·x + 39 = 0
x² - 19/3·x + 6.5 = 0
x = (19/3 ±√((19/3)² - 4 × 1 × 6.5))/2
∴ x = 1.288, or 5.045
At x = 1.288, we have;
V = 2·1.288³ - 19·1.288² + 39·1.288 ≈ 22.99
V ≈ 22.99 in.³
When x = 5.045, we have;
V = 2·5.045³ - 19·5.045² + 39·5.045≈ -30.023
Therefore;
V > 0 for 0 < x < 3 and V < 0 for 3 < x < 6.5
The values of x for which the model makes sense and V ≥ 0 is 0 ≤ x ≤ 3.
The values of x for which the model makes sense are 13/2 and 3
The equation that represents the volume of the box is given as:
[tex]V =2x\³ -19x\² +39x[/tex]
Factor out x from the above equation
[tex]V =x(2x^2 -19x +39)[/tex]
Expand the above equation, as follows
[tex]V =x(2x^2 -6x - 13x +39)[/tex]
Factorize the above equation
[tex]V =x(2x(x -3) - 13(x -3))[/tex]
Factor out x - 3
[tex]V =x(2x -13)(x -3)[/tex]
Equate to 0
[tex]x(2x -13)(x -3) = 0[/tex]
Solve for x
[tex]x = 0[/tex] or [tex]x = 13/2[/tex] or [tex]x = 3[/tex]
The value of x cannot be 0.
Hence, the values of x for which the model makes sense are 13/2 and 3
Read more about volumes at:
https://brainly.com/question/1972490
Brady, Dana, Elijah, and Gianna took part in the school play. Before the start of the play, they each guessed the number of people who would come to see the play. Brady guessed 292 people, Dana guessed 325 people, Elijah guessed 340 people, and Gianna guessed 371 people. It turned out that Dana's guess was the closest, Elijah's guess was the second closest, and Brady's guess was the farthest from the actual number. What is the actual number of people who came to see the play?
Answer:
332
Step-by-step explanation:
Since Dana had the closest guess with 325 people and Elijah had the second closest guess with 340 people we know that the actual number of guests is close to these values. Since Brady had the farthest guess then that means that the actual number of guests is higher than 325 and lower than 340. Therefore the actual number of guests can only be 332 as it is between Dana and Elijah's guesses but still favoring Dana, and also being farthest from Brady's guess.
What is the product of (7/8) (-16) (-7) (-1/14) ?
O A. -7
O B. -9/16
O C. -1/7
O D 23/12
Answer:
-7
Step-by-step explanation:
Answer:
hello guys ^_^ its -7 and if it is wrong don't be afraid to tell me
~your friendly austrailian~
In their last game, the school football team scored an equal number of points in each of the first three quarters, then 14points in the fourth quarter. If they scored 44 points in all, how many points did they score in the first quarter?
Answer:
10 points
Step-by-step explanation:
Points scored in each of the first 3 quarter = x
Total points scored in the first 3 quarter = x + x + x
= 3x
Points scored in the fourth quarter = 14
Total points scored = 44 point
Total points scored = Total points scored in the first 3 quarter + Points scored in the fourth quarter
44 = 3x + 14
Subtract 14 from both sides
44 = 3x + 14
44 - 14 = 3x + 14 - 14
30 = 3x
Divide both sides by 3
x = 30/3
= 10
x = 10 points
Points scored in each of the first 3 quarter = x = 10 points
The school football team scored 10 points points in the first quarter
can some one help me
Answer:
84 grams and 5 ounces
Step-by-step explanation:
because one ounce equals 28 grams, that means 3 ounces = 3 * 28 = 84
because 28 grams equals 1 ounce, 140 grams = 140 / 28 = 5 ounces
Find the volume of the rectangular prism.
9 m
3
m
12
3 m
7 m
Answer:
[tex]189 {m}^{3} [/tex]
Step-by-step explanation:
[tex]9 \times 3 \times 7 \\ = 189 {m}^{3} [/tex]
[tex]3 \times 9 \times 7 \\ = 189 {m}^{3} [/tex]
(For #8 -9) Choose ONE of the application problems below and solve it using a system of 2 equations.
Remember - word problem, word answer.
8. The high school FFA is selling fruit. Together, Kay and Ayan sell a total of 25 boxes. Kay sells 13 less than Ayan.
How many boxes does each girl sell?
Define your variables:
X =
Y =
boxes.
boxes, and Ayan sold
Kay sold
Answer:
Kay sold 6 boxes and Ayan sold 19 boxes
Step-by-step explanation:
Let x be the number of boxes sold by Kay and
Let y be the number of boxes sold by Ayan
Then according to given statements, the equations will be:
[tex]x+y = 25\ \ \ Eqn\ 1\\x = y-13\ \ \ Eqn\ 2[/tex]
Putting x = y-13 in equation 1
[tex]y-13+y = 25\\2y-13=25\\2y=25+13\\2y = 38\\\frac{2y}{2} = \frac{38}{2}\\y = 19[/tex]
Putting y = 19 in equation 2
[tex]x = 19-13 = 6[/tex]
So we get x=6 and y=19
Hence,
Kay sold 6 boxes and Ayan sold 19 boxes
The length of the base of an isosceles triangle is x. The length of a leg is 4x -3. The perimeter of the triangle is 66. Find x
Answer:
x = 8
Step-by-step explanation:
Since the triangle is isosceles then the 2 legs are congruent.
Given the perimeter is 66, then sum the 3 sides and equate to 66, that is
x + 4x - 3 + 4x - 3 = 66 , that is
9x - 6 = 66 ( add 6 to both sides )
9x = 72 ( divide both sides by 9 )
x = 8
in which place is the 7 in the following number: 1,243.7294 *
It is in tenths place.
Hope it helps
A cylindrical well has a radius of 8 feet and a height of 13 feet. What is the volume of the well? Use 3.14 for pi. Round your answer to the nearest hundredth
Answer:
using pi *r^2 *h
volume = 2614.14 cubic ft
Answer:
2612.48 ft3
Step-by-step Explanation:
i got it right on the quiz
Write an equation in slope-intercept form of the line that passes through the points.
Answer:
y = 1/4x + 1
Step-by-step explanation:
.
Every day, you buy your lunch for $4 at school. How much money will you spend if you buy your lunch from Monday through Friday for three weeks?
$70
$40
$65
$60
Answer:
$60
Step-by-step explanation:
Solve for x. X + 47 = -23
X=
Answer:
x=-70
Step-by-step explanation:
x+47=-23
-47 -47
_______________
x=-70
Hope this helps :D
Answer:
X=70
Step-by-step explanation:
Which equation represents a line which is perpendicular to the line y = 5x - 8?
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The 2nd one or either the last one, I suggest the last one hope this helps!!
Systems of equations with different slopes and different y-intercepts have one solution?
Step-by-step explanation:
The systems of linear equations can have:
1. No solution: When the lines have the same slope but different y-intercept. This means that the lines are parallel and never intersect, therefore, the system of equations has no solution.
2. One solution: When the lines have different slopes and intersect at one point in the plane. The point of intersection will be the solution of the system
3. Infinitely many solutions: When the lines have the same slope and the y-intercepts are equal. This means that the equations represents the same line and there are infinite number of solution.
Therefore, based on the explained above, the conclusion is: Systems of equations with different slopes and different y-intercepts never have more than one solution.
Which is the most accurate way to estimate 34% of 19?
Answer: first one
Step-by-step explanation: 34% of 19 is 6.46 and 1/3*18=18/3=6 so its the closest out of the others
What is p to the power of 3?
Answer:
In mathematics, a power of three is a number of the form 3n where n is an integer, that is, the result of exponentiation with number three as the base and integer n as the exponent.
Find the percent increase. Round to the nearest percent.
From 76 books to 131 books
The percent increase is _____%
Answer:
I think it's a 72.36% increase
Step-by-step explanation:
I'm not completely sure but that's what the calculator I used said..
Answer:
3
Step-by-step explanation:
Find the amount of change.
Amount of change = Greater Value − Lesser Value
= 131 − 127 Substitute values.
= 4 Subtract.
Find the percent increase. Round to the nearest percent.
Percent Change =
Amount of Change
Original Amount
=
4
131
Substitute values.
≈ 0.03 Divide and round to the nearest hundredth.
= 3% Write as a percent.
The percent decrease is 3%.
pls press the heart if this was helpful
f(x)=-3x • G(x) = x +7
Answer:
-3x^2 - 21x
Step-by-step explanation:
This question is representing multiplying two functions :
We are finding f(x) * g(x)
We know that f(x) is -3x and g(x) is x + 7, therefore :
(-3x)(x + 7)
Follow FOIL :
First :
(-3x)(x)
-3x^2
Outer :
(-3x)(7)
-21x
Therefore the answer is :
-3x^2 - 21x
Given the equation 4x + 2y = 9, which equation below would cause an inconsistent-independent system? (2 points)
Answer: 2x+y=-6
Step-by-step explanation:
What is the answer???
Answer:
Step-by-step explanation:
An altitude is a line segment that meets the side opposite the vertex at right angles. The line also has to go through the vertex.
The only line that does both those things is DE.
please help!!!!!!!!!!!
Answer:
x= 40
Step-by-step explanation:
The reason this is so is because a straight line's degree is always 180. And 4(40)-20=140 and 180-40=140. This is how you would work out the right side. This gives you your answer.
Answer:
40
Step-by-step explanation:
[tex]x + 4x - 20 = 180 \\ 5x = 180 + 20 \\ x = 200 \div 5 \\ x = 40[/tex]
please mark as brainliest
Mary puts 3 red marbles, 3 blue marbles, 4 green marbles, and 10 yellow marbles into a bag. Mary then picks one marble out of the bag. What is the probability of picking a yellow marble?
Can someone please explain ASA triangle congruence? I will give brainliest.
Answer:
This is easier to explain with pictures, but I'll try here. The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
The number or expression inside a radical symbol
Answer:
radicand
Step-by-step explanation:
List three different examples of rational numbers
Answer:
5, 1.75, .001, and -0.1
Step-by-step explanation:
Number As a Fraction Rational?
5 5/1 Yes
1.75 7/4 Yes
.001 1/1000 Yes
−0.1 −1/10 Yes
Hope this Helps (✿◡‿◡)
P.S I got this off the internet.
What number will be output by the console.log command on line 5?a 10 b 25 c 30 d 35
Answer:
c 30 bc oki
Step-by-step explanation:
Answer:
It’s 35
Step-by-step explanation:
I took the test before…fixx
The function p(x) = −2000x2 + 18000x − 15000 models the monthly profit P of a smoothie company, where x represents the price per smoothie. Identify the price range that will generate a monthly profit of at least $25,000.
Answer: between $4 and $5; inclusive
guys FAST I ONLY HAVE 10MINS Raquel estimated 304,900,000,000 as 3 × 108. What error did she make?
Answer:
The 108 it should be more
Step-by-step explanation:
Answer:she forgot the decimal
Step-by-step explanation