Answer:
w = -3/8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define Equation
-6(w + 2) = w - 9 + 3(3w + 1)
Step 2: Solve for w
Distribute: -6w - 12 = w - 9 + 9w + 3Combine like terms: -6w - 12 = 10w - 6Add 6w to both sides: -12 = 16w - 6Isolate w term: -6 = 16wIsolate w: -3/8 = wRewrite: w = -3/8I REALLY REALLY NEED HELP. I WILL MARK BRAINLIEST FOR THE BEST ANSWER!!! Question: What are the dimensions of a box with minimal surface area that has a volume of 64000 cm^3? AND REMEMBER, PLEASE SHOW ALL WORK NECESSARY. THANKS.
God Bless :)
9514 1404 393
Answer:
40 cm × 40 cm × 40 cm
Step-by-step explanation:
Since this is in the high-school math forum, we assume that you're not intended to use calculus to determine the answer. All three dimensions are open for variation, so we'll try to use some logic to determine a reasonable solution.
The dimensions of a box are interchangeable with respect to their effect on surface area. You can see this in the area formula:
A = 2(LW +LH +WH)
That is, no particular dimension makes more or less contribution to surface area than any other. This suggests that the minimum area will be obtained when each dimension is equal to the others. That is, a cube has the minimum surface area for a given volume.
The volume of a cube in terms of its edge dimension s is ...
V = s³
So, the edge dimension is ...
s = ∛V = ∛(64000 cm³) = 40 cm
The dimensions of the box are 40 cm × 40 cm × 40 cm.
_____
Calculus method of Lagrange Multipliers
We want to minimize A=2(LW +WH +LH) subject to the constraint that LWH = 64000. We can write the Lagrangian as ...
L = 2(LW +WH +LH) +λ(LWH -64000)
We want to set all of the partial derivatives of L to zero.
dL/dL = 0 = 2(W+H) +λWH
dL/dW = 0 = 2(L+H) +λLH
dL/dH = 0 = 2(L+W) +λLW
dL/dλ = 0 = LWH -64000
Solving the first two equations for λ and setting the results equal, we have ...
-2(W+H)/(WH) = λ = -2(L+H)/(LH)
Multiplying by H/(-2) gives ...
1 +H/W = 1 +H/L ⇒ W = L
Similarly, solving the 2nd and 3rd equations for λ and setting the results equal, we have ...
-2(L+H)/(LH) = λ = -2(L+W)/(LW)
1 +L/H = 1 +L/W ⇒ H = W
So, now we know that L = W = H, which is the assumption we started with in our "logical" answer.
Answer:
Step-by-step explanation:
By the arithmetic-geometric mean inequality, surface area of any rectangular parallelpiped satisfies
2(xy+yz+zx)≥2(3)(x2y2z2−−−−−−√3)=6V23.
On the other hand, a cube with side lengths V13 has surface area
2(V13V13+V13V13+V13V13)=6V23.
Hence the cube does indeed have minimum surface area
Explain how to multiply decimals by powers of 10. Use 8.653 x 10000 as an example, to show how the multiplication is done.
Answer:
We move the decimal point to the right by a number of digit places equal to the power of 10.
Step-by-step explanation:
If we want to multiply a decimal by a power of 10, we move the decimal point to the right by a number of digit places which is the power of the number ten or the number of zeros which are present in the multiplying number 10. If we do not have a digit after the last digit, we put zeros to complete the number of digits until, we have the number of digit places added after the decimal point which are equal to the power of 10.
Using the example given above
8.653 x 10000, we have four zeros. So, in index form it is
8.653 x 10⁴
Since we have the number 10 raised to the power of four or having 4 zeros, we move the decimal point 4 places to the right.
So, 8.653 x 10000 = 8.653 x 10⁴ = 86530
Three lines of crops in a garden form a triangular shape. Strawberries are planted in a 10 ft line and green beans are planted in an 18 ft line. If the third side, a line of pumpkins, makes an 68 degree angle with the strawberries, determine the length of the pumpkins.
Answer:
[tex]p = 19.18[/tex]
Step-by-step explanation:
This question is illustrated using the attachment and will be solved using cosine formula
[tex]a^2 = b^2 + c^2 - 2bcCosA[/tex]
Let the strawberry side be s, the Green beans be b and the pumpkins be p.
The cosine formula in this case is:
[tex]g^2 = s^2 + p^2 - 2spCosG[/tex]
Where
[tex]s = 10[/tex]
[tex]g = 18[/tex]
[tex]<G =68[/tex]
The equation becomes
[tex]18^2 = 10^2 + p^2 - 2 * 10 * p * Cos\ 68[/tex]
[tex]324 = 100 + p^2 - 20 * p * 0.375[/tex]
[tex]324 = 100 + p^2 - 7.5p[/tex]
Collect Like Terms
[tex]p^2 - 7.5p + 100 - 324 = 0[/tex]
[tex]p^2 - 7.5p - 224 = 0[/tex]
Using quadratic formula:
[tex]p = \frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
Where
[tex]a = 1[/tex]
[tex]b = -7.5[/tex]
[tex]c = -224[/tex]
[tex]p = \frac{-(-7.5)\±\sqrt{(-7.5)^2-4*1*-224}}{2*1}[/tex]
[tex]p = \frac{7.5\±\sqrt{56.25+896}}{2}[/tex]
[tex]p = \frac{7.5\±\sqrt{952.25}}{2}[/tex]
[tex]p = \frac{7.5\± 30.86}{2}[/tex]
[tex]p = \frac{7.5 + 30.86}{2}[/tex] or [tex]p = \frac{7.5 - 30.86}{2}[/tex]
[tex]p = \frac{38.36}{2}[/tex] or [tex]p = \frac{-23.36}{2}[/tex]
[tex]p = 19.18[/tex] or [tex]p = -11.68[/tex]
But length can not be negative.
So:
[tex]p = 19.18[/tex]
pls help ill mark brainliest
Answer:
The answer is B. No only Zack will finish.
Step-by-step explanation:
which one of these are not true?
A) Dilations make images bigger.
B) Dilations make images smaller.
C) Dilations do not change the size of the pre-image.
D) A dilated image has different angle measurements than the pre-image.
E) A dilated image has the same angle measurements as the pre-image.
Answer:
D is the answer, the angles remain the same
Step-by-step explanation:
will mark brainliest
Answer:
It would be b
Step-by-step explanation:
Answer:
Answer choice 3
Step-by-step explanation:
Se tienen 224 plumas de color negro y 420 de color rojo. Se quiere ponerlas en cajas iguales, de tal manera que cada caja tenga plumas de un sólo color. ¿Cuántas plumas se deben poner en cada caja para que se utilice el menor número posible de cajas? ¿Cuántas cajas se necesitan?
Answer:
La cantidad de plumas que se deben poner en cada caja para que se utilice el menor número posible de cajas es 28.
Requieres 8 cajas con plumas de color negro y 15 cajas con plumas de color rojo, necesitando 23 cajas en total.
Step-by-step explanation:
El divisor común es un número que es divisor a la vez de dos o más números, es decir, es un divisor común a esos números.
Por lo que se denomina máximo común divisor o M.C.D al mayor número que divide exactamente a dos o más números a la vez. En otras palabras, el Máximo Común Divisor es el mayor de los divisores comunes de varios números.
Para calcular el M.C.D, se descompone cada uno de ellos en factores primos. El M.C.D. es el resultado de multiplicar los factores que se repitan en todas las descomposiciones, afectados por el menor exponente.
En este caso, los números 224 y 420 se descomponen en:
224= 2⁵*7
420= 2²*3*5*7
Entonces, el M.C.D entre 224 y 420 es calculado como 2²*7, que da como resultado 28. Esto indica que la cantidad de plumas que se deben poner en cada caja para que se utilice el menor número posible de cajas es 28.
Para el calculo de cantidad de cajas que se necesitan, primero es necesario saber cuántas cajas de cada color de plumas se necesitan. Para eso, debes dividir la cantidad de plumas que tienes por la cantidad de cajas por las que debes repartirlo:
224 plumas negras÷ 28= 8
420 plumas rojas÷ 28= 15
Por lo que requieres 8 cajas con plumas de color negro y 15 cajas con plumas de color rojo, necesitando 23 (8+15) cajas en total.
Help me y'all plz and thank you
Answer:
1. 3
2. 20
3. 240
4. 1600
Answer: 1863
Step-by-step explanation:
Monika has 67 stamps in her collection. To expand the collection, she is planning to buy some books of stamps that have 14 stamps each. All of the books cost the same. Monika is not sure yet about the number of books of stamps she wants to buy, but she has enough money to buy up to 5 of them. Write a function to describe how many stamps Monika can have. Let x represent the number of books of stamps Monika buys. Find a reasonable domain and range for the function.
A) f(x) = 67x + 14
D: (1,2,3,4); R: (81, 95, 109, 123, 137)
B) f(x) = 14x + 67
D: (0, 1, 2, 3, 4, 5); R: (67, 81, 95, 109, 123, 137)
C) f(x) = 67x + 14
D: (5); R: (137)
D) f(x) = 14x + 67
D: (0, 1, 2, 3, 4); R: (67, 81, 95, 109, 123)
Answer:
A
Step-by-step explanation:
It gave us 5 domains and 5 ranges :)
A function is represented by the values in the table.
Are these linear or nonlinear? (2,4) (4,8) (5,10) (7,14) (8,16) will mark brainliest
Answer:
These are linear. These values can all match the function y = 2x.
Angelo is training for a long-distance bicycle ride. He travels 15 miles each hour. How many hours will it take him to ride 210 miles?
Answer:
210 divided by 15=14
thats your answer
Step-by-step explanation:
HELLO I AM NEW WHAT IS X + Y IF X IS 12 AND Y IS 81 THANK YOU
Answer:
93
Step-by-step explanation:
Because if you start with X + Y
and
X= 12
Y = 81
you would do
12 + 81
witch is 93
2. Simplify 5/7 +12v6-10v7-5/6 (1 point)
O 5V14-7N12
O 5v7-7N6
O 7V12-5v14
O 7V6-5v7
A
Step-by-step explanation:
combine like terms and simplefiy
Hamza bought 8 gallons of brown paint to paint his kitchen and dining room. Unfortunately, when Hamza started painting, he thought the paint was too dark for his house, so he wanted to make it lighter. The store manager would not let Hamza return the paint but did inform him that if he used 1/4 of a gallon of white paint mixed with 2 gallons of brown paint, he would get the shade of brown he desired. If Hamza decided to take this approach, how many gallons of white paint would Hamza have to buy to lighten the 8 gallons of brown paint?
Answer:
1 gallon of white paint
Step-by-step explanation:
correct me if im wrong
Darwin's coach recorded that he had bowled 250 points out of 300 in a bowling tournament. However, the official
scoreboard showed that Darwin actually bowled 225 points out of 300
Find f(x) = g(x) given that f(x) = x - 8 and g(x) =- 3x2 + 4x - 1
Step-by-step explanation:
x-8= -3x²+4x-1
3x²+x-4x=-1+8
3x²-3x=7
3x²-3x-7=0
x²-x-3.5=0
Delta = -1²-(4)(1)(-3.5)
+1+14=15
x1=-1- sqrt(15) /2(1) =2.43
x2=-1+sqrt(15)/2(1) =-1.93
I don't think it is right but i tried my best
3x2 = 6x - 3
O (1)
O (-1,0)
O (-1,1)
O (-1)
Answer:
I THINK ITS THE 3RD ONE
Step-by-step explanation:
Lillian wants to purchase a new camper. She needs to borrow $6000 for 2 years. Lillian will have a 3.5% interest rate. How much interest will be earned? Hint: Use this formula: Interest = Prt
Answer:
$420 interest will be earned.
Step-by-step explanation:
The answer is 420 because 3.5% of 6000 is 210 and 210 multiplied by 2 is 420
P.S Can I have brainliest?
which relationship between x and y in the equation shows a proportional relationship
A. y=3x
B. y=x-2
C. y=5x+3
D. y=5 (x+3)
Answer:
The equation y = 3x shows a proportional relationship between x and y
Step-by-step explanation:
The proportional relationship is represented graphically by a line passes through the origin point The equation of the proportional relationship is y = m xLet us solve the question
Substitute x by 0 to find the value of y, if y = 0, then the line represents this equation passes through the origin point, then the equation shows a proportional relationship
∵ y = 3x
∵ x = 0
∴ y = 3(0)
∴ y = 0
→ That means the line that represents the equation passes through
the origin point
∴ The equation y = 3x shows a proportional relationship between x and y
f (x) = x2 + 6x +12
How do you find the inverse?
If a car travels 300 miles on 15 gallons of gas, how far can it travel on 90 gallons?
Answer:
1800
Step-by-step explanation:
because 15 goes into 90 6 times and 300 times 6 is 1800
Answer:
1800 miles
Step-by-step explanation:
300 miles on 15 gallons
90/15=6
6 times 300=1800
Which fraction is equivalent to StartFraction 2 Over 6 EndFraction?
(im to lazy ) : )
Answer:
1/3
Step-by-step explanation:
2/6
divide both by 2 because they're both even
2/2=1 6/2=3
1/3
A circle has a radius of 7cm. Which of these is closest to its circumference?
Answer:
You didn't list the answers but it's 43.98 so close to 44 I'm guessing
Step-by-step explanation:
circumference=2*pi*r
2*3.14*7=about 44
Answer:
Approximately 22 or 7πcm
Step-by-step explanation:
The ratio between the circumference of a circle and its diameter is π. We commonly write c=2πr, using the radius instead and doubling.
In the given example, we are told that the diameter is
7 cm. So using the common approximation π≈[tex]\frac{22}{7}[/tex] we find that the circumference is approximate:
[tex]\frac{22}{7} * 7cm= 22 cm[/tex]
please help am smol brain
Answer:
A
Step-by-step explanation:
In the proof, it says that MO is congruent to MO, <PMO is congruent to <NMO, and <POM is congruent to <NOM. We can locate these angles and side to find that these congruent angles surround the side. Therefore, the congruent relation is ASA (angle-side-angle) postulate
Answer:
a. ASA Postulate
Step-by-step explanation:
The proof is using an angle, a side, and an angle, in that order, to prove two triangles congruent, so the missing reason in ASA Postulate.
Answer: a. ASA Postulate
Even when mixed, elements and molecules still keep their unique properties. Explain why.
Mixing is a physical reaction, which does not change any chemical properties of elements and molecules because it does not change the number of protons.
It is the number of protons that determine the unique properties of each element (hence why the periodic table sorts elements by increasing the number of protons).
How may cups are in 3 gallons
Sin^3A.cos A + Cos^ 3 A = Cos A
Answer:
One root is 90 degrees or π/2 radians.
Drawing a graph we get all the roots:
nπ and π(n - 1/2)
Step-by-step explanation:
Sin^3A.cos A + Cos^ 3 A = Cos A
Divide through by cos A
sin^3A + cos^2A = 1
sin^3 A = 1 - cos^2 A
sin^3 A = sin^2 A
sin A = 1
So one root is A = 90 degrees or π/2 radians.
Checking this result:
(sin 90^3 * cos 90 + (cos 90)^3 = 1 * 0 + 0 = 0
cos 90 = 0
So this is correct..
IM BEING TIMED HELPP!!!!!!
Jada is buying 4 stamps that cost $0.49 each. How can rounding be used to estimate the total cost of the stamps? Since each stamp is about $0.50, the total cost is approximately 4 +0.5 = $4.50. 0 Since she is buying about 10 stamps, the total cost is approximately 10 × 0.49 = $4.90. Since each stamp is about $0.50, the total cost is approximately 4 x 0.5 = $2.00. O Since she is buying about 10 stamps, the total cost is approximately 10 + 0.49 = $10.49.
Answer:
ummm maybe $4.90, i don't really know how to incorporate rounding in this
which of the following are equivalent to the decimal 1.6
Solve the inequality for n in the equation
14 < n - 3
