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:
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Evaluate: 3x^2 + y when x=1 and y=-3 *
Answer:
0
Step-by-step explanation:
x=1 and y=-3
so 3x^2 + y = 3*1^2 + (-3)
= 3* 1 -3
=0
c. A share of stock XYZ went from $40 a to $42 & What was the dollar gain for the
stock XYZ?
Answer:
$2 was the dollar gain for the stock XYZ
A line passes through the points (1, –6) and (4, 3). What is the y-intercept of this line?
Answer:
-6 i think
Step-by-step explanation:
Answer:
the y intercept is 3
Step-by-step explanation:
Look at the image below
Choose the correct statement!
Answer:
the lines are not parallel because they have different slopes
Step-by-step explanation:
Answer:
it is either a or c i hope that helps a little:)
factor the expression below
-r -8
Answer:
-(r+8)
Step-by-step explanation:
find the area of the regular polygon
Answer:
433.4
Step-by-step explanation:
Height will be (14/2)/tan36 which is 9.63, then area for one triangle is 1/2*hb which is .5*9.63*7 is 43.34, times 10 you get 433.4
Please help will Mark Brainily and please help me with showing work
Answer:
a=15
Step-by-step explanation:
Pythagorean Theorum says that a²+b²=c², so if we square b and c, subtract b² from c², and then square root that answer, it will equal a.
a²+8²=17²
8²=64
17²=225
225-64=225
√225=15
A rectangle has a length of (x + 4) centimeters and a width of 2/4 x centimeters. If the
perimeter is 35 centimeters, what is the length of the rectangle?
A: 3cm
B: 9cm
C: 13cm
D: 7cm
Answer:
C: 13cm
Step-by-step explanation:
Given;
length of the rectangle, L = (x + 4) cm
width of the rectangle, W = [tex]\frac{2}{4}x[/tex] cm
perimeter of the rectangle, P = 35 cm
The perimeter of a rectangle is given as;
P = 2(L + W)
Substitute the givens;
[tex]35 = 2[(x+ 4) + \frac{2x}{4} ]\\\\35 = 2[\frac{6x}{4} +4]\\\\35 = 3x+8\\\\3x = 27\\\\x = \frac{27}{3}\\\\x = 9[/tex]
Then, L = (x + 4) cm
L = (9 + 4) cm
L = 13 cm
Therefore, the length of the rectangle is 13 cm
Kristi gets $10 a week from her parents if she washes the dishes after dinner every night. Kristi has saved up $30 over the last few weeks from her allowance. She wants to continue saving her allowance until she has enough money to buy the $7o bike she saw at the store last week. Assuming Kristi receives her allowance every week, write an equation that shows how many more weeks Kristi has to save her allowance to buy the bike, where w is the number of weeks. You can solve the equation to check your answer.
Answer:
10w = 70-40
Step-by-step explanation:
To get to $70, Kristi has to work 10w. She has already earned $30 and needs to earn the remaining in 10w. Thus,
10w = 70-30
10w = 40
w = 4
She needs to work for 4 more weeks to buy the bike.
im dumb could somebody help me pleaseeeeeee
Answer:
1. (6-2)
2.40/4
3. 10-4
Step-by-step explanation:
Dont trust me but I think it
A spinner is divided into many sections of equal size. Some sections are red, some are blue, and the remaining are green. The probability of the arrow landing on a section colored red is 9 over 20 . The probability of the arrow landing on a section colored blue is 6 over 20 . What is the probability of the arrow landing on a green-colored section? (1 point)
Group of answer choices
15 over 20
11 over 20
6 over 20
5 over 20
Answer:
11 over 20
Step-by-step explanation:
Answer: 5/20
Step-by-step explanation:
9/20+6/20=15/20
20/20-15/20=5/20
The perimeter of a rectangular field is 318 yards. If the width of the field is 62 yards, what is its length?
Answer:
2 * Length + 2 * width = 318
2 L = 318 - 2 * 62
2 L = 194
Length = 97 Yards
Step-by-step explanation:
Which number(s) below belong to the solution set of the equation? Check all
that apply.
x + 12 = 13
D A. 13
B. 312
O C. 14
O D.O
O E. 1
F. 25
Answer:
E
Step-by-step explanation: 1+12=13
write an exponential equation for the graph.
Answer:
Step-by-step explanation:
Exponential equations can be written as
[tex]y = ab^x\\[/tex]
in this case,
a = 5000 (the starting amount)
we just have to find b
[tex]10000 = 5000b^4\\20000 = 5000b^8\\\\b^4 = 2\\b^8 = 4\\\\\\b = \sqrt[4]{2}[/tex]
[tex]y = 5000(\sqrt[4]{2})^x[/tex]
Which statement about 8 x 9/9
is true?
A) The product will be greater than 8.
B) The product will be less than 1. C) The product will be equal to 8. D) The product will be less than 8.
Answer:
C
Step-by-step explanation:
9/9 is just 1. Therefore, 8*1 is 8. C is correct
(3x^4-12x^3-5x^2-18+8) (x+4)
Answer:
=3x^5−53x^3−20x^2−10x−40
Step-By-Step explanation:
=(3x^4+−12x^3+−5x^2+−18+8)(x+4)
=(3x^4)(x)+(3x^4)(4)+(−12x^3)(x)+(−12x^3)(4)+(−5x^2)(x)+(−5x^2)(4)+(−18)(x)+(−18)(4)+(8)(x)+(8)(4)
=3x^5+12x^4−12x^4−48x^3−5x^3−20x^2−18x−72+8x+32
=3x^5−53x^3−20x^2−10x−40
Evaluate each expression: –23 + (–12) + 3
Answer:
14
Step-by-step explanation:
Find the area of this trapezoid. The Bases are 8
inches and 2.2 inches. The height is 4 inches.
Answer:
20.4 in²Step-by-step explanation:
Area formula
A = 1/2(b1 + b2)hA = 1/2(8 + 2.2)*4 = 10.2*2 = 20.4 in²Use the properties of exponents to simplify: 3^0 ≠ 1 True False
Answer:
True
Step-by-step explanation:
Bcuz, some thing's power 0is 1
According to the zero power rule of exponents, 3^0 = 1. The statement 3^0 ≠ 1 is FALSE.
What is the Zero Power Rule of Exponents?The zero power rule is a property of exponents which simply states that whatever base that is raised to the power of zero would always be equal to one, i.e., x^0 = 1.
We are given that 3^0 ≠ 1. Based on the zero power rule of exponents, this is FALSE because 3^0 = 1.
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Joseph drove from Kentucky to Louisiana. It took 35 gallons of gas for him to get there. Gas costs $2.09 per gallon. How much money did Joseph spend on gas?
- 1/2 - 2/3v = 4/5 please help
Answer:
v = - [tex]\frac{39}{20}[/tex]
Step-by-step explanation:
Given
- [tex]\frac{1}{2}[/tex] - [tex]\frac{2}{3}[/tex] v = [tex]\frac{4}{5}[/tex]
Multiply through by 30 ( the LCM of 2, 3 and 5 )
- 15 - 20v = 24 ( add 15 to both sides )
- 20v = 39 ( divide both sides by - 20 )
v = - [tex]\frac{39}{20}[/tex]
Answer:
[tex]v=-\frac{39}{20}[/tex]
Step-by-step explanation:
Given the expression
[tex]-\frac{1}{2}-\frac{2}{3}v=\frac{4}{5}[/tex]
Add 1/2 to both sides
[tex]-\frac{1}{2}-\frac{2}{3}v+\frac{1}{2}=\frac{4}{5}+\frac{1}{2}[/tex]
[tex]-\frac{2}{3}v=\frac{13}{10}[/tex]
Multiply both sides by 3
[tex]3\left(-\frac{2}{3}v\right)=\frac{13\cdot \:3}{10}[/tex]
[tex]-2v=\frac{39}{10}[/tex]
Divide both sides by -2
[tex]\frac{-2v}{-2}=\frac{\frac{39}{10}}{-2}[/tex]
[tex]v=-\frac{39}{20}[/tex]
Therefore,
[tex]v=-\frac{39}{20}[/tex]
(a) A square has a perimeter of 12 cm. What is the length of each side?
(b) A square has an area of 36 m². What is the length of each side?
Answer:
P = 4 c
12 = 4 c
3 = c
Step-by-step explanation:
Hope this helps.
I need help on this
Answer:
No they or not
Step-by-step explanation:
The first on is 60 and the second one is 40
special right triangles
Answer:
what is that a question or...
Answer:
what?? if your talking about the angle of one, that would be 90 degrees.
A drawer contains 6 pink gloves and 5 yellow gloves. What is the probability that you select two pink gloves if you reach in the drawer and randomly grab two gloves without replacement?
1/11
1/30
2/11
3/11
1/15
Answer:
[tex]\dfrac{3}{11}[/tex]
Step-by-step explanation:
Given that:
A drawer contains 6 pink and 5 yellow gloves.
Two gloves are randomly drawn without replacement.
To find:
The probability that the two gloves drawn are both pink.
Solution:
First of all, let us have a look at the formula for Probability of an event E:
Formula for probability of an event E can be observed as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Here, number of favorable cases are to draw 2 pink gloves out of 6, which is equal to:
[tex]_6C_2 = \dfrac{6\times 5}{2} = 15[/tex]
Here, Total number of cases are to draw 2 gloves out of 11, which is equal to:
[tex]_{11}C_2 = \dfrac{11\times 10}{2} = 55[/tex]
Now, the required probability is:
[tex]P(2\ pink\ gloves) = \dfrac{15}{55}\\\Rightarrow P(2\ pink\ gloves) = \dfrac{3}{11}[/tex]
Therefore, the answer is:
[tex]\dfrac{3}{11}[/tex]
What is the product of 1/2x1/8
Answer:
1/16
Step-by-step explanation:
Which expression shows the amount of tax on a t shirt that cost x dollars, if tax is 7%
Answer:
2nd option: 0.07
Step-by-step explanation:
100% in decimal form is 1.00. S0, 7 is really 0.07. Hope this helps. Mark brainliest if it does!
The expression which represents the amount of tax on a t-shirt that cost x dollars, if tax is 7% is 0.07x.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is just like the amount of that value but between 1 to 100 and it is very useful to predict for example if you say 678 then we have to know about the full number also but if you say 80% then it becomes clear.
Given that,
Cost of t-shirt = x dollars
Tax is 7% which means tax is 7% of the cost of the t-shirt
7% of x ⇒ 7/100 × x = 0.007x
Hence "The expression which represents the amount of tax on a t-shirt that cost x dollars, if tax is 7% is 0.07x".
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In one grade of 150 students, the ratio of boys to girls is 2 : 3.
How many boys are in that grade?
Answer:
60 boys are in the grade.
Step-by-step explanation: Since there are 150 students, we can divide that number by the combined ratio, which in this case is 5. Dividing 150 by 5 would yield 30 students. We can use this information to multiply the given number of boys in the ratio by 30, which would produce 60.
4+a cuz I don’t get this
Answer:
This isn't a question lol
Put the question in the replies to this answer and I'll gladly answer it for you.
Step-by-step explanation:
May I have brainliest please? :)
please help it's urgent.
Answer:
It is the second triangle.
Step-by-step explanation:
This is because the area of the square is given as 25^2 as the perpendicular, 144^2 as the base, and the hypotenuse is 169^2.
Length of the perpendicular = 5^2 (Because 25^2 / 5^2)
Length of the base = 12^2
Length of the hypotenuse = 13^2
So, the Pythagoras theorem is,
=> [tex]H^{2} = P^{2} + B^{2}[/tex]
=> [tex]13^{2} =12^{2} +5^{2}[/tex]
This is true, because, 13*13 = 12*12 + 5*5
=> 169 = 144 + 25
=> 169 = 169
If my answer helped, kindly mark me as the brainliest!!
Thanks!!