Therefore the minimum cost of a rectangular box of volume is x = 4.641588834 cents.
What is the volume of cuboid?A cuboid is a six-faced solid known as a hexahedron in geometry. Four-sided quadrilaterals make up its faces. A cuboid is a hexahedron, a solid with six faces, and the word "cuboid" means "like a cube" in the sense that a cuboid can become a cube by changing the length of its edges or the angle between its faces and edges. Four-sided quadrilaterals make up its faces. A cuboid can be made to look more like a cube by varying the lengths of its edges or the angles between its faces and edges. A cuboid's volume is equal to the sum of its length, breadth, and height. The opposite faces of a cuboid on a rectangular cuboid are equal, and all the angles are at right angles.
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What is the quotient when (x+3) is divided into the polynomial 2x^2+x-15
The value of the quotient of the polynomials is 2x - 1
How to determine the quotient of the polynomials?The polynomials are given as
2x² + x - 15
x + 3
Where
Dividend = 2x² + x - 15
Divisor = x + 3
The quotient of the polynomials is calculated as
Quotient = Dividend/Divisor
Substitute the known values in the above equation
So, we have
Quotient = (2x² + x - 15)/(x + 3)
Factorize the numerator
Quotient = (x + 3)(2x - 1)/(x + 3)
Cancel out the common factors
Quotient = 2x - 1
Hence, the quotient is 2x - 1
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Describe the Method and Operation
Given that
[tex]\begin{gathered} (\frac{5n^6}{m^{-3}n^2})^2 \\ \text{According to the law of indies,} \\ (\frac{a}{b})^2\text{ = }\frac{(a)^2}{(b)^2} \\ (\frac{5n^6}{m^{-3}n^2})\text{ = }\frac{(5n^6)^2}{(m^{-3}n^2)^2} \\ \text{According to the law of indicies again,} \\ (a^x)^y=a^{x\cdot y} \\ =\text{ }\frac{(5n^{6\text{ x 2}})}{(m^{-3\cdot2}n^{2\cdot2})} \\ =\text{ }\frac{5n^{12}}{(m^{-6}n^4)} \\ \text{According to the law of indices} \\ x^{-1}\text{ = }\frac{1}{x} \\ =5^{}n^{12}\cdot n^{-4}\cdot m^6 \\ =5n^{12\text{ - 4}}m^6 \\ =5n^8m^6 \end{gathered}[/tex]Prove that the opposite angles of a parallelogram are equal.
The opposite angles of a parallelogram are equal.
x + y = a+ b
Let's consider a quadrilateral ABCD which is a parallelogram with AC as its diagonal.
We know, in parallelograms opposites' sides are parallel.
So, AB∥DC and AD∥BC
Since AB is parallel to DC and AC is the transversal.
By alternate angles,
∠BAC = ∠DCA
y = a -----------------(1)
Similarly, AD is parallel to BC and AC is the transversal.
The alternate angles,
∠DAC = ∠BCA
x = b -----------------(2)
Adding equations ( 1 ) and ( 2 ),
∠BAC + ∠DAC = ∠DCA + ∠BCA
∠BAD = ∠DCB
x + y = a + b
Similarly, we can prove, ∠ADC=∠ABC
Hence proved, opposite sites of a parallelogram are equal.
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is 1/8 a rational number? explain your reasoning
The number given as 1/8 is a rational number
How to determine the true statement?The number is given as
Number = 1/8
As a general rule, a rational number is represented as
Rational number = Numerator/Denominator
This in other words means that
A rational number can be represented as a fraction of two integers
In this case, we have
Numerator = 1
Denominator = 8
This means that the given number is 1 rational number
This is because it can be represented as a fraction of two integers
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If you buy 40 m of timber at a cost of $200, what is the cost per metre?
Answer: a meter of timber is 5$
Answer:
Rs5
Step-by-step explanation:
40m =Rs 200
Therefore, 1m = 200/40
= Rs 5
f(x) = -7x - 1 f()= -8
f(x) = -7x - 1
f()= -8
-7x - 1 = -8
-7x - 1 + 1 = -8 + 1
-7x = -7
-7x/-7 = -7/-7
Apple Melon recipe calls for two 2 1/2 cups of watermelon, 3/4 cups of cantaloupe been one and 1/2 tablespoons of honey. what amount of ingredients is needed for 10 and 15?
The amount of ingredients needed for 10 apple melon recipe is 25 cups of watermelon, 7.5 cup of cantaloupe and 15 cup of honey, and for 15 is 37.5 cups of watermelon, 11.25 cup of cantaloupe and 22.5 cup of honey.
What do you mean by recipe?
A recipe contains the list of ingredients and set of instructions that tells us how to cook any particular dish.
As given in the question, for one recipe, we need
2 & 1/2 cups of watermelon, 3/4 cup of cantaloupe and 1 &1/2 cup of honey.
We can also say it as:
2.5 cups of watermelon, 0.75 cup of cantaloupe and 1.5 cup of honey.
In order to the amount of ingredients for 10 we need to multiply each ingredient with 10.
so it will become,
25 cups of watermelon, 7.5 cup of cantaloupe and 15 cup of honey.
Similarly, In order to the amount of ingredients for 15 we need to multiply each ingredient with 15.
so it will become, 37.5 cups of watermelon, 11.25 cup of cantaloupe and 22.5 cup of honey.
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When you flip a biased coin the probability of getting a tail is 0.75.
How many times would you expect to get tails if you flip the coin 240 times?
Answer:
180
Step-by-step explanation:
It's 180 because 75% of 240 is 180.
PLEASE HELP I WILL GIVE BRAINLIEST TO WHOEVER IS CORRECT :)
Answer:
its c
Step-by-step explanation:
not sure how to explain it
estimate the square root of 7 to the nearest whole number.
The frequency table shows the scores from rolling a dice.
Score
1
2
3
4
5
6
Work out the range.
Frequency
8
4
5
5
7
8
Answer:
I don't know
Step-by-step explanation:
There is none
the edge of a cube was found to be 30 cm with a possible error in measurement of .1 cm. use differentials to estimate the percentage error (to the nearest hundredth) in computing (a) the volume of the cube and (b) the surface area of the cube.
a) The volume of the cube is 27,271 cubic centimeter
b) The surface area of the cube is 5,400
Well the edge is 30 cm +- 0.1 cm
Volume will be side cubed, so max estimate for volume is (30.1)^3, and minimum (29.9)^3
So percentage error = [(30.1)^3 - 30^3/ / 30^3 x 100 = 1,00 %
Surface area is 6 x side squared
So max estimate for area is 6 x 30.1^2,
minimum 6 x 29.9 ^ 2
So percentage error = (6 x 30.1^2 - 6 x 30^2) / (6 x 30^2) x 100 = 0.67 %
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a. Graph f(x)=left brace7x−12if x≤3x2if x>3b. Find f(1) and f(5).c. State the domain of the function.
Given:
The function is,
[tex]\begin{gathered} f(x)=7x-12,\text{ x}\leq3 \\ =x^2,x>3 \end{gathered}[/tex]a) The graph of the given function us,
Answer: option B)
b) f(1) and f(5) is,
[tex]\begin{gathered} \text{For x=1,} \\ f(x)=7x-12\text{ , if x}\leq3 \\ f(1)=7(1)-12=-5 \\ \text{For x=5,} \\ f(x)=x^2,\text{ if x>3} \\ f(5)=5^2=25 \end{gathered}[/tex]Answer:
[tex]\begin{gathered} f(1)=-5 \\ f(5)=25 \end{gathered}[/tex]c) the domain of the function is,
[tex]undefined[/tex][tex][(1 + \frac{1}{2})}^{2} -2[/tex]
The value of the expression as in the task content is; 1/4.
What is the value of the expression given in the task content?It follows from the task content that the value of the expression is to be determined.
Hence, since the expression whose value is required to be determined is ; (1 + (1/2))² - 2.
It follows from PEMDAS guidelines that the parentheses be solved first so that we have;
(3/2)² - 2........After solving the parentheses.
Next, the exponent should be solved as follows;
= (9/4) - 2.
And finally, by solving the subtraction; we have;
= 1/4 = 0.25.
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There were 6 gallons of water in Shivani's bathtub. Then 0.64 gallons drained out. How much water is left in the bathtub?
Answer: 5.36 gallons
Step-by-step explanation:
0.64 gallons [liquid] are equal to 0.16907 litre
6 - 0.64 = 5.36
Please help me i can't seem to get it
Answers:
Horizontal lineGraph rises and is steeperGraph falls and is steeperGraph rises and is less steepGraph falls and is less steep=======================================================
Explanation:
Think of a roller coaster. A sharp drop is where we have a very steep decline. The steeper the line, the more rapid the drop.
The same can be said for when the graph increases as well.
Horizontal portions of the graph are when the elevator isn't moving. The x value (time) is always moving forward of course, but the y value (height of the elevator) is not changing.
f(x) = -8x + 20; 5 – 2[f(-1)]
The value of the function at the given value of x = -1 is 5 - 2[f(-1)] = -51
How to evaluate the function at the given value?The equation of the function is given as
f(x) = -8x + 20
The function to calculate is given as
5 - 2[f(-1)]
So, we start by calculating the value of the function at x = -1
This is represented as 'f(-1)
So, we have the following equation
f(-1) = -8(-1) + 20
Evaluate the product
So, we have the following equation
f(-1) = 8 + 20
Evaluate the sum
So, we have the following equation
f(-1) = 28
Substitute f(-1) = 28 in the expression 5 - 2[f(-1)]
So, we have
5 - 2[f(-1)] = 5 - 2 x 28
Evaluate the product
5 - 2[f(-1)] = 5 - 56
Evaluate the difference
5 - 2[f(-1)] = -51
Hence, the value is -51
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5) Find the value of y.
(21y-1)
(4x+23) (9x-38)
The value of y in the expression (21y-1)=(4x+23)(9x-38) is (103x - 875)/21.
According to the given question
We have a linear equation in two variables
(21y - 1) = (4x + 23)(9x -38)
For finding the value of y solve the above equation by adding and subtracting the like terms.
So, 21y - 1 = 4x(9x -38) + 23 (9x -38)
⇒ 21y - 1 = 48x - 152x + 207x - 874
⇒ 21y - 1 = 103x - 874
⇒ 21y = 103x - 874 + 1
⇒ 21y = 103x - 875
⇒ y = [tex]\frac{103x - 875 }{21}[/tex]
Hence, the value of y in the expression (21y-1)=(4x+23)(9x-38) is [tex]\frac{103x - 875 }{21}[/tex]
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PLEASE HELP ME SOMEONE THAT'S GOOD WITH MATH? BC I CANT UNDERSTAND THIS QUESTION
Question 3
Let f(x) = 4^x and g(x) = 4^x + 1 - 3.
Which transformations are needed to transform the graph of f(x) to the graph of g(x)?
Select EACH correct answer.
A. Horizontal translation 1 units right.
B. Horizontal translation 3 units right.
C. Vertical translation 3 units down.
D. Vertical translation 1 unit down.
E. Horizontal translation 1 unit left.
F. Vertical translation 3 units up.
We can see that function g(x) is a translation of one unit to the left and 3 units downwards of f(x), thus, the correct options are:
C and E.
What transformations are applied to the function f(x)?Here we have the two functions:
f(x)
g(x) = 4^(x + 1) - 3
And we know that g(x) is a translation of f(x)
Remember that the translations works as follows:
Vertical translation of N units:
g(x) = f(x) + N
If N > 0, the translation is upwards.
If N < 0, the translation is downwards.
Horizontall translation of N units:
g(x) = f(x) + N
If N > 0, the translation is to the left
If N < 0, the translation is to the right.
In this case, we can write g(x) as:
g(x) = f(x + 1) - 3 = 4^(x + 1) - 3
So we will have a translation of one unit to the left and 3 units downwards.
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Answer all the questions for brainliest all info you need is in the photo please help asap
Total of 10 and $ total of $0.85. The place value denotes a word, whereas the total value denotes a figure. In mathematics, ten numbers are known as symbols or digits.
What is meant by Summation?The sum of the digit and its place value is the total value. Example 1: In the number 58439, what is the place value of digit 4? As a result, digit 4's place value is Hundreds. Market capitalization is the value of a company as determined by the stock market. It is defined as the sum of all outstanding shares' market values. Multiply the number of outstanding shares by the current market value of one share to calculate a company's market cap.
Therefore,
a # total of 10
a $ total of $0.85
· Since we have 2 unknowns, we need to set up a System of 2 Equations.
· A System of 2 Equations helps us solve a situation with 2 Unknowns.
Let's set up our 2 equations for # and $.
· For the # equation:
Let n = # of nickels
Let d = # of dimes
So, n + d = 10
· For the $ equation, we have to assign a "value" to each of the coins:
A nickel is worth 5 cents or $0.05
A dime is worth 10 cents or $0.10
· They told us we have 5 cents, a specific # of times + 10 cents, a certain # of times, that = $0.85
So, $0.05n + $0.10d
= $0.85
To solve this, we have to have just 1 unknown, meaning just 1 variable.
· We represent one of the variables in terms of the other. But, which one?
· Well, since they are asking for # of dimes, let's define a nickel in the duration of a dime.
· Let's apply this in the simpler # equation:
So, n + d = 10
becomes n = 10 - d
· So now, in our $ equation, we can just replace "n" with "10 - d", and then solve for d, which is the # of dimes!
$0.05n + $0.10d = $0.85
$0.05(10-d) + $0.10d = $0.85
$0.5 - $0.05d + $0.10d = $0.85
$0.50 + $0.05d = $0.85
$0.05d = $0.35
d = 7
Check this with the # equation:
n + d = 10
n + 7 = 10
n = 3
Does that make sense? Let's see:
3 nickels + 7 dimes = $0.85 ?
3($0.05) + 7($0.10) = $0.85
$0.15 + $0.70 = $0.85
$0.85 = $0.85
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ABC is a triangle.
ADC is a straight line with BD perpendicular to AC.
AB = 8 cm
BC = 12 cm
Angle ABD = 60.
Calculate the length of DC.
Give your answer to 3 significant figures
The length of segment DC is given by the law of sines and trigonometric ratios as approximately 11.3 cm
What is the law of sines?The law of sines states that in a triangle, the ratio of the sine of an interior angle of a triangle to the length of the side opposite the angle is constant.
The given parameters are;
The figure ABC is a triangle
The figure ADC is a straight line segment
Segment BD is perpendicular to segment AC
The length of segment AB = 8 cm
Length of segment BC = 12 cm
The measure
[tex] \angle ABD = 60^{ \circ} [/tex]
Required;
The length of segment DC
Solution;
[tex] \angle ADB = 90^{ \circ} [/tex]
Definition of segment BD being perpendicular to segment AC
[tex] \angle BAC = 90^{ \circ} - 60^{ \circ} = 30^{ \circ}[/tex]
Using the law of sines, we have;
[tex]AD = AB × sin( \angle ABD) [/tex]
A vertex of the triangle from the question is point B
Which gives;
AD = 8 × sin(60°) = 4•√3
Similarly, from the law of sines, we have;
[tex]\displaystyle{\frac{BC}{sin ( \angle BAC)} = \frac{AB}{sin ( \angle BCA)} } [/tex]
Which gives;
[tex] \displaystyle{\frac{12}{sin ( 30^{ \circ})} = \frac{8}{sin ( \angle BCA)} } [/tex]
[tex] \displaystyle{ sin ( \angle BCA) = \frac{sin ( 30^{ \circ}) \times 8}{12}= \frac{1}{3} }[/tex]
[tex] \displaystyle{ \angle BCA = arcsine \left(\frac{1}{3}\right) }[/tex]
[tex] \displaystyle{DC= 12 \times cos\left(arcsine \left(\frac{1}{3}\right)\right) = 8\cdot \sqrt{2}}[/tex]
Therefore, DC = 8•√2 ≈ 11.3
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Mia has 12 boxes of chocolate chip cookies and 24 boxes of sugar cookies. Each box of chocolate chip cookies has 36 cookies. Each box of sugar cookies has 84 cookies. Mia says she has about 1,800 cookies in all. Is her answer reasonable? Explain.
Yes, because (12 x 20) + (40 x 80) = 3,400
Yes, because (12 x 80) + (40 x 40) = 2,560
No, because (12 x 40) + (20 x 80) = 2,080
No, because (12 x 80) + (20 x 40) = 1,760
Answer:
The answer given by Mia is not reasonable cause, when we sum up the data given by her we will conclude that the expression should be like (12*36) + (24*84) = 1800.
Step-by-step explanation:
Mia has 12 boxes of chocolate chip cookies and 24 boxes of sugar cookies.
Each box of chocolate chip cookies has 36 cookies.
Each box of sugar cookies has 84 cookies.
So, the total number of chocolate chips cookies will be = 12 * 36 ----(i)
And the total number of sugar cookies will be = 24 * 84 -----(ii)
As Mia says she has about 1,800 cookies in all.
So, we can write (i) and (ii) combined as,
(12*36) + (24*84) = 1800
The answer given by Mia is not reasonable cause, when we sum up the data given by her we will conclude that the expression should be like (12*36) + (24*84) = 1800.
Explanation: No, her answer is not reasonable.
Step by Step solution:
According to the given information, Mia has 12 boxes of chocolate chip cookies and 24 boxes of sugar cookies.
Now, each box of chocolate chip cookies has 36 cookies which means she has (36 × 12) = 432 chocolate chip cookies in total, using the unitary method.
Also, each box of sugar cookies has 84 cookies which means she has (84 × 24) = 1008 sugar cookies in total, using the unitary method.
Mia will then have with her in total of [(36 × 12) + (84 × 24)] = 1440 cookies.
It is an incorrect fact that Mia says that she has about 1800 cookies in total.
Hence, Mia has 1440 cookies in total.
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Given m<7=107 and m<4= (8x+1) what is the value of x?
The value of x comes out to be 9.
Here, we are given that m∠7 = 107 and m∠4 = (8x+1)
From the figure given below, we can see that angle 7 and angle 6 are vertically opposite angles. Thus-
angle 7 = angle 6
measure of angle 6 = 107°
Now, angle 6 and angle 4 are opposite interior angles and the sum of opposite interior angles is equal to 180. Thus-
m∠4 + m∠6 = 180
8x + 1 + 107 = 180
8x + 108 = 180
8x = 180 - 108
8x = 72
x = 72/8
x = 9
Thus, the value of x comes out to be 9.
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Your question was incomplete. Check for the missing figure below.
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 8 people took the trip. She was able to purchase coach tickets for $250
and first class tickets for $1250. She used her total budget for airfare for the trip, which was $8000. How many first class tickets did she buy? How many coach tickets did she buy?
Sarah buys 6 tickets for first class and 2 for coach class, finding by using properties of linear equation.
What is linear equation in one variable?
A linear equation which has only one variable is called linear equation in one variable.
Let assume,
Sarah has number of first-class tickets = x
then Sarah has number of coach tickets = 8-x
(Because total tickets she has are 8)
given that
The coach tickets price = $250
The first-class tickets price =$1250
so, from above
[tex]\begin{array}{l}1250 \mathrm{x}+250(8-\mathrm{x})=8000 \\1250 x+250(8)-250(x)=8000 \\1250 x+2000-250 x=8000 \\1250 x-250 x=8000-2000 \\1000 x=6000 \\x=\frac{6000}{1000} \\x=6\end{array}[/tex]
Therefore, Sarah buys 6 tickets for first class and 2 for coach class.
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Rachael had an average score of 88 on 7 equally-weighted tests. Her teacher decided to drop the lowest test grade. Rachael's average forthe 6 remaining tests is now 91. What was Rachael's lowest test score before her teacher removed that score?
Let:
x = Rachael's lowest test score
y = average score of the other tests
Rachael had an average score of 88 on 7 equally-weighted tests. so:
[tex]88=\frac{x+y}{7}[/tex]Her teacher decided to drop the lowest test grade. Rachael's average for
the 6 remaining tests is now 91. so:
[tex]\begin{gathered} 91=\frac{y}{6} \\ so\colon \\ y=6\cdot91 \\ y=546 \end{gathered}[/tex]Replace the valuel of y into the first equation:
[tex]88=\frac{x+546}{7}[/tex]solve for x:
[tex]\begin{gathered} 88\cdot7=x+546 \\ 616=x+546 \\ x=616-546 \\ x=70 \end{gathered}[/tex]Hey can somebody help me with this math homework you have to solve it step by step so can anybody help?
symkiiiussksznzznzznzbswwy
-4t=20 what does t equal
Answer:
divide -4 from 20 so t is -5
Step-by-step explanation:
Answer:
t=-5
Step-by-step explanation:
divide both sides by -4 now we have t=-5
On Monday, 473 students went on a trip to the zoo. All 8 buses were filled, and 9 students had to travel in
cars. How many students were in each bus?
Answer:
58.
Step-by-step explanation:
The number of students who travelled by bus = 473 - 9 = 464.
So, the number of students in each bus = 464/8
= 58.
PLS HELP 30 POINTS IF YOU ANSWER THIS! AND BARIN LIST. PRETTY SIMPLE.
• Jackie made a mistake when he _________.
• The Triangle Congruence Postulate or Theorem that is easiest for me to use is ____ because _____.
• The Triangle Congruence Postulate or Theorem that is the most difficult for me to use is ____ because _____.
By HL theorem we can conclude that both the triangles are congruent
ΔAED ≅ ΔBEC
What is HL theorem?HL theorem: The Hypotenuse-Leg (HL) Triangle Congruence Theorem is a special case that allows you to show that two right triangles are congruent. If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
Jackie made a mistake by determining ΔADE is congruent to ΔCBE
we can't conclude it directly because the angles at D and B may be different
∠E=90° and given that hypotenuse of both the triangles are congruent
AD≅CB and leg of the two triangles are congruent AE≅BE
then by HL theorem we can conclude that both the triangles are congruent
ΔAED ≅ ΔBEC
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The Hypotenuse-Leg (HL) Triangle Congruence Theorem is a special case that allows you to show that two right triangles are congruent. If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
Jackie made a mistake by determining ΔADE is congruent to ΔCBE
we can't conclude it directly because the angles at D and B may be different
∠E=90° and given that hypotenuse of both the triangles are congruent
AD≅CB and leg of the two triangles are congruent AE≅BE
Then by HL theorem we can conclude that both the triangles are congruent
ΔAED ≅ ΔBEC
What’s the range of 4x+5?
Answer:261
Step-by-step explanation:
4x4x4x4=4x4=16\16x4=64x4=256\256+5=261
