Answer:
For a rectangular solid with:
width = w
length = l
height = h
The volume is equal to:
V = w*l*h
in this case we know that:
width = w.
"length of 7 more than the width"
l = w + 7.
"a height that is equivalent to 15 decreased by 3 times the width."
h = 15 - 3*w
Then the volume will be:
V = w*l*h = w*(w + 7)*(15 - 3w) = (w^2 + 7*w)*(15 - 3*w)
V = ( -3*w^3 + 15*w^2 + 105*w - 21*w^2)
V = (-3*w^3 - 6*w^2 + 105*w)
Now, the maximum volume will be for the value of w such that:
V'(w) = 0.
and:
V''(W) < 0
Where:
dV/dw = V'(w).
dV'/dw = V''(w)
Then first we need to differentiate the equation for the volume.
V'(w) = dV/dw = ( 3*(-3*w^2) + 2*(-6*w) + 105)
V'(w) = -9*w^2 - 12*w + 105.
Then we need to find the solution for:
-9*w^2 - 12*w + 105 = 0.
We can use the Bhaskara formula, and we will get:
[tex]w = \frac{+12 +-\sqrt{(-12)^2 - 4*(-9)*105} }{2*-9} = \frac{+12 +- 62.6}{-18}[/tex]
Then the two solutions are:
w₁ = (+12 - 62.6)/(-18) = 2.81
w₂ = (+12 + 62.6)/(-18) = -15.5
But we can not have a negative width, so we can just discard the second solution.
Now let's check the second condition for the maximum, we must have:
V''(2.81) < 0.
V'' = dV'/dw = 2*(-9*w) - 12 = -18*w - 12
V''(2.81) = -18*2.81 - 12 = -62.58 < 0 .
Then the volume is maximized when w = 2.81, and the maximum volume will be:
V(2.81) = (-3*(2.81)^3 - 6*(2.81)^2 + 105*2.81) = 180.1
Mr. Turner bought 12 pounds of carrots to make some cakes. The recipe calls for 3/4 pound of carrots for each cake. How many cakes can Mr. Turner make?
A package of 4 pairs of insulated gloves costs $25.96 What is the unit price of the pairs of gloves?
Answer:
Step-by-step explanation:
25.96/4 = 6.49
Answer:
$6.49 per pair of gloves
Step-by-step explanation:
$25.96 / 4 pairs of gloves = $6.49 per pair of gloves
PLEASE HELP 20 PTS i need it quick!
Answer:
B. 6 + 0.2x
Step-by-step explanation:
One fifth = 1/5 = 0.2One fifth of x = 0.2xSum of 6 and one fifth of x = 6 + 0.2xI hope this helps!
Answer:
I think it is C
Step-by-step explanation:
if I am wrong I am soooo sorry
Rewrite the equation in Ax+By=C form. Use integers for A, B, and C. y=1/5x-6
Answer:
C I think
Step-by-step explanation:
Which statements are true about triangle ABC and its translated image, A'B'C'? Select two options.
> The rule for the translation can be written as T–5, 3(x, y).
>The rule for the translation can be written as T3, –5(x, y).
>The rule for the translation can be written as
(x, y) → (x + 3, y – 3).
>The rule for the translation can be written as
(x, y) → (x – 3, y – 3).
>Triangle ABC has been translated 3 units to the right and 5 units down.
Answer:
Option (2) and Option (5)
Step-by-step explanation:
Blue triangle ABC has been translated to form the image triangle A'B'C' (in red).
Let take a point A of ΔABC,
Coordinates of point A → (-1, 3)
Coordinates of point A' → (2, -2)
Rule for the translation will be,
A(-1, 3) → A'(2, -2)
A(-1, 3) → A'(-1 + 3, 3 - 5)
A(x, y) → A'(x + 3, y - 5)
[tex]T_{3, -5}(x, y)[/tex]
ΔABC has been translated 3 units to the right and 5 units down.
Therefore, Option (2) and Option (5) will be the correct options.
Answer:
B and E
Step-by-step explanation:
What is 38 percent of 22
(In percentage) :)
Answer:
6.6%
Step-by-step explanation:
30% of 22 is 6.6%
Feel free to give brainliest.
Have an awesome day!
Answer:
I think it is 172.73
Step-by-step explanation:
I am so sorry if i am wrong
Identify whether each set of ordered pairs is a function or is not a function.
Answer:
Step-by-step explanation:
To be a function, the x or first number of the pairs can not duplicate. It needs to pass the vertical line test.
A. not a function
B. function
C. function
D. not a function
E. not a function
Three friends said their heights were 5 and start fraction 13 over 30 end fraction feet, 5 and one-sixth feet, and 5 and start fraction 68 over 90 end fraction feet. Put the heights of the friends in order from least to greatest. A. 5 and start fraction 68 over 90 end fraction < 5 and start fraction 13 over 30 end fraction < 5 and one-sixth B. 5 and start fraction 13 over 30 end fraction <5 and one-sixth <5 and start fraction 68 over 90 end fraction C. 5 and one-sixth <5 and start fraction 68 over 90 end fraction < 5 and start fraction 13 over 30 end fraction D. 5 and one-sixth <5 and start fraction 13 over 30 end fraction< 5 and start fraction 68 over 90 end fraction
Answer:
[tex]5\frac{1}{6} < 5\frac{13}{30} < 5\frac{68}{90}[/tex]
Step-by-step explanation:
Represent the friends with A, B and C
[tex]A = 5\frac{13}{30}[/tex]
[tex]B = 5\frac{1}{6}[/tex]
[tex]C = 5\frac{68}{90}[/tex]
Required
Order from least to highest
First, we convert the given parameters to decimal
[tex]A = 5\frac{13}{30}[/tex]
[tex]A = 5 + \frac{13}{30}[/tex]
[tex]A = 5 + 0.43[/tex]
[tex]A = 5.43[/tex]
[tex]B = 5\frac{1}{6}[/tex]
[tex]B = 5 + \frac{1}{6}[/tex]
[tex]B = 5 + 0.17[/tex]
[tex]B = 5.17[/tex]
[tex]C = 5\frac{68}{90}[/tex]
[tex]C = 5 + \frac{68}{90}[/tex]
[tex]C = 5 + 0.76[/tex]
[tex]C = 5.76[/tex]
So, we have:
[tex]A = 5.43[/tex] [tex]B = 5.17[/tex] [tex]C = 5.76[/tex]
Order from least to greatest
[tex]B = 5.17[/tex] [tex]A = 5.43[/tex] [tex]C = 5.76[/tex]
Replace them with the original values
[tex]B = 5\frac{1}{6}[/tex] [tex]A = 5\frac{13}{30}[/tex] [tex]C = 5\frac{68}{90}[/tex]
Hence, the correct order is:
[tex]5\frac{1}{6} < 5\frac{13}{30} < 5\frac{68}{90}[/tex]
Answer:
The answer is 5235 5521 2356
Step-by-step explanation:
Pls help will give brainlest answer
Answer:
220
Step-by-step explanation:
because i divided 1,760 by 8 i needed to find how many penguin dives in 2 minutes Hope this Helps!
pretty easy! help pls!
Answer:
ok C
Step-by-step explanation:
6 ( − 2.1 x − 2 ) + ( 7 x + 5 )
Answer: −5.6x −7
Step-by-step explanation:
in the diagram <4 = <40 °. Find the measure of <3 = (?)°
Answer:
∠3=140°
Step-by-step explanation:
∠4 = 40°
∠3 + ∠4 = 180° (co-exterior angles are equal)
∠3 + 40° = 180°
∠3 = 180° - 40°
∠3 = 140°
[tex]or^{}[/tex]
∠2 = ∠4 = 40° (corresponding angles)
∠3 + ∠2 = 180° (linear pair)
∠3 + 40° = 180°
∠3 = 180° - 40°
∠3 = 140°
hope you understood
The interest on an investment varies directly as the rate of interest. If the interest is $43 when the interest rate is 4%, find the interest when the rate is 8%.
9514 1404 393
Answer:
$86
Step-by-step explanation:
Since the interest varies directly, doubling the rate will double the interest.
The interest is $86 when the rate is 8%.
Plz help. Write an equation of the line
y=mx+b format
Solve 126 = 14x
*Only enter the number for what x = in the box*
Answer:
x = 9
Step-by-step explanation:
divide both sides by 14
Answer: x = 9.
Step-by-step explanation: Step 1: Flip the equation.
14x=126
Step 2: Divide both sides by 14.
14x /14
=
126 /14
x=9
Write the equation of a line with a slope of 3 and a y-intercept of 4. Do not use spaces in your response
Answer:
y=3x+4
Step-by-step explanation:
it's in slope intercept form
Five less than the product of a number and -8 is -77
Answer:
9
Step-by-step explanation:
-77+5=-72
-72 divided by -8 = 9
Amaya is reviewing her checking account statement from the bank. Her starting balance and transactions are listed.
Starting balance of $97.13
Spent $63.27 at Food Lion
Deposit from work of $415.80
Lunch at Tropical Smoothie for $12.85
Withdrawal of cash at the ATM of $60.00
If reconciled, her bank statement and personal records should have current balance of $
Answer:
376.81
Step-by-step explanation: 376.81
If the measure of angle 3 is equal to (2x + 6)° and x = 7, which statements are true? Check all that apply.
3 lines intersect to form 6 angles. From top left, clockwise, the angles are 1 (90 degrees), 2, 3, 4, 5, 6.
The measure of angle 6 is 20°.
The measure of angle 5 is 70°.
The measure of angle 2 is 80°.
Angles 2 and 5 are complementary.
Angles 5 and 6 are supplementary.
Angles 1 and 4 are supplementary.
Answer:
The answers are
A. The measure of angle 6 is 20"
B. The measure of angle 5 is 70"
F. Angles 1 and 4 are supplementary
Hope this Helps!
Answer:
1,2,6
Step-by-step explanation:
ON EDGE.2020
the slope of the line whose equation is x+y=6
what is 0.371 as a decimal
Answer:
It is in a decimal.
In a fraction it’s 371/1000
In a percentage 37.1%
9514 1404 393
Answer:
0.371
Step-by-step explanation:
A decimal number is a string of digits in the range 0-9, with an optional single decimal point (period) somewhere in the string. Usually, leading zeros are not shown, except one leading zero ahead of a decimal point to help reduce errors in transcription.
The number you show, 0.371, is a decimal number.
The local newspaper has letters to the editor from 80 people. If this number represents 4percent of the newspaper's readers, how many does the newspaper have?
Answer:
2000 newspaper readers
Step-by-step explanation:
Let the total number did newspaper readers the local news paper has be represented by x
Therefore,
4% of x = 80 people
Hence,
4/100 × x = 80
4x/100 = 80
Cross Multiply
4x = 100 × 80
4x = 8000
x = 8000/4
x = 2000 people
Therefore, the number of people the newspaper has is 2000 newspaper readers
A trapezoid has verities A(-5, 4), B(-3, 2) C(-7, -2) and D(-7, 2). It is transformed according to the rule
Suppose you want to prove the converse of the Pythagorean Theorem by drawing two triangles. If
one of the triangles has side lengths of m, n, and p, such that m² + n2 = pº what should
be the lengths of the sides that form a 90-degree angle in the second triangle?
А
m and n
B
m and p
С
n and p
D
p and p
Answer:
a
Step-by-step explanation:
The sides of the right angle that form 90° will be 'm' and 'n'. Then the correct option is A.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
"In the event that the square of a side is equivalent to the amount of the square of the other different sides, then triangle should be correct point triangle".
The Pythagoras theorem formula is given as
H² = P² + B²
Assume you need to demonstrate the opposite of the Pythagorean Hypothesis by drawing two triangles.
If one of the triangles has side lengths of m, n, and p, such that m² + n² = p².
Then the sides of the right angle form 90° will be 'm' and 'n'. Then the correct option is A.
More about the Pythagoras theorem link is given below.
https://brainly.com/question/343682
#SPJ2
Find the two number who sum is 13 and whose product is 40
Answer:
A = 8 and B = 5
Brainly pls
Step-by-step explanation:
whats the answer? help lol
Properties of isosceles triangle
Answer:
Had two congruent sides
Has congruent base angles
Without graphing, determine whether the function represents exponential growth or exponential decay. Then find the y-intercept.
A. Exponential growth; 4
B. Exponential decay; 4
C. Exponential growth; 0
D. Exponential decay; 5
I will give brainliest to the correct answer!
Answer:
Exponential decay; 4
Step-by-step explanation:
This represents exponential decay, because the number which is being raised to the power x is less than one. This means that as x increases, y decreases.
The y-intercept occurs when x is equal to zero. When x = 0, we have [tex]y = 4(5/6)^0 = 4(1) = 4[/tex], so the y-intercept is 4.
Answer:
Now you can give the other person brainliest
Given the function f(x) = x^2, which of the following represents a vertical shift of 3 units up?
9514 1404 393
Answer:
f(x) = x² +3
Step-by-step explanation:
The transformation
g(x) = a·f((x -c)/b) +d
represents a vertical expansion by a factor of 'a', a horizontal expansion by a factor of 'b' (before the horizontal shift), a horizontal (right) shift by 'c' units, and an upward shift by 'd' units.
You want only an upward shift of 3, so ...
g(x) = f(x) +3
For f(x) = x^2, the shifted function is ...
f(x) = x^2 +3
__
Other choices are ...
b. (x -3)^2 = right shift by 3
c. 3x^2 = vertical expansion by a factor of 3
d. (x +3)^2 = left shift by 3
8 women and 12 girls can paint a large mural in ten hours. 6 women and 8 girls paint it in 14 hours. Find the time it takes 1 woman to paint it alone
Answer:
280 hours
Step-by-step explanation: