Find the axis of symmetry and the vertex of the graph of y=3x^2+2x

The dimension of the box of the greatest volume that can be constructed in this way is 12x12x3 and the volume is 432.

Let x be the side of the square to remove. Then the volume of the box is:

V(x) = (18 - 2x)² * x = 324x - 72x² + 4x³

To find the maximum volume, differentiate and set it to 0:

V'(x) = 324 - 144x + 12x²

0 = x² - 12x + 27

0 = (x - 9)(x - 3)

x = 3 or 9

When x = 3,

V"(x) =-144+24x

V"(3) =-144+72=-72<0

so volume is maximum at x=3

Therefore the box is 12x12x3 and the volume is 432.

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Answer: 3/4 is 75%

Step-by-step explanation: Since his fav number is 36 the half of 36 is 18 bc 18 + 18 is 36

Answer:

ur right its A

Step-by-step explanation:

Answer:

22.97

Step-by-step explanation:

17 divided by pi is 5.41

5.41 divided by 2 is 2.075

r^2(pi)

is 2.075 x 2.075 x 3.41 is 22.97

Answer:

Michelle walks 1 4 hour every day of the week (Monday through Sunday). Sandra walks 2 4 hour per day, but only on weekdays (Monday through Friday). Both Michelle and Sandra continue their routines for 9 weeks. Calculate who walked the most over this 9 week period, and calculate how much more time this person walked than the other person. Be sure to show how you calculated each person's total walking time as a mixed fraction, and show how you calculated how much more time was walked by either Michelle or Sandra as a mixed fraction. this is a word problom

Answer:

people are not doing it it's because that it's multiplying mixed numbers by whole numbers and we don't really need to do that

Step-by-step explanation:

Answer:

yea

Step-by-step explanation:

I think you meant to say

[tex]\ln(x+y) = 4xy[/tex]

and not "4 times y" on the right side (which would lead to a complex value for y when x = 0). Note that when x = 0, the equation reduces to ln(y) = 0, so that y = 1.

Implicitly differentiating both sides with respect to x, taking y = y(x), and solving for dy/dx gives

[tex]\dfrac{1+\frac{dy}{dx}}{x+y} = 4y + 4x\dfrac{dy}{dx}[/tex]

[tex]\implies \dfrac{dy}{dx} = \dfrac{4xy+4y^2-1}{1-4x^2-4xy}[/tex]

Note that when x = 0 and y = 1, we have dy/dx = 3.

Differentiate both sides again with respect to x :

[tex]\dfrac{d^2y}{dx^2} = \dfrac{(1-4x^2-4xy)\left(4y+4x\frac{dy}{dx}+8y\frac{dy}{dx}\right)-(4xy+4y^2-1)\left(-8x-4y-4x\frac{dy}{dx}\right)}{(1-4x^2-4xy)^2}[/tex]

No need to simplify; just plug in x = 0, y = 1, and dy/dx = 3 to get

[tex]\dfrac{d^2y}{dx^2} \bigg|_{x=0} = \boxed{40}[/tex]

Answer:

A = $1,742.75

A = P + I

Where

P is the principal (1,500.00)

I is the interest (242.75)

Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 1.5/100

r = 0.015 rate per year,

Then solve the equation for A

[tex]A = Pe^{rt}\\A = 1,500.00(2.71828)^{(0.015)(10)}\\A = $1,742.75[/tex]

Summary:

The total amount with compound interest on a principal of $1,500.00 at a rate of 1.5% per year compounded continuously over 10 years is $1,742.75.

Step-by-step explanation:

[tex]13 - 4y = 1 - y(opposite \: angles \: of \: a \: parallelogram \: are \: equal) \\ 13 - 4y = 1 - y \\ - 4y + y = 1 - 13 \\ - 3y = - 12 \\ y = \frac{ - 12}{ - 3} \\ y = 4 \\ \\ 7x - 3 = 6x + 3(opposite \: angles \: of \: a \: parallelogram \: are \: equal) \\ 7x - 3 = 6x + 3 \\ 7x - 6x = 3 + 3 \\ x = 6 \\ x = 6 \: \: \: \: \: y = 4[/tex]

Answer:

4 5/6 quarts or 4.83 quarts

Step-by-step explanation:

5 1/2 quart pot has an equal value to 11/2 quart pot

it is filled with 2/3 quarts of water

Therefore, the quarts of water the pot can hold is;

11/2 - 2/3

LCM = 6

11/2 - 2/3 ÷ 6

33 - 4 ÷ 6

29/6

:. 29/6 quarts(4 5/6 quarts or 4.83 quarts) of water is the amount needed to fill the 5 1/2 quart pot

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve for x ~

[tex]\qquad \sf  \dashrightarrow \:4x - 16 = 64[/tex]

[tex]\qquad \sf  \dashrightarrow \:4(x - 4) = 64[/tex]

[tex]\qquad \sf  \dashrightarrow \:(x - 4) = 64 \div 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:x - 4 = 16[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 16 + 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:x =20[/tex]

[tex] \boxed{ \bf \huge \: Answer \: }[/tex]

[tex] \: \: [/tex]

[tex] \sf \large \: 4x - 16 = 64[/tex]

[tex] \: \: [/tex]

[tex] \sf \large \: 4x = 64 + 16[/tex]

[tex] \: \: [/tex]

[tex] \sf \large \: 4x = 40[/tex]

[tex] \: [/tex]

[tex] \sf \large \: x = \cancel \frac{80}{4} [/tex]

[tex] \: \: [/tex]

[tex] \sf \large x = 20[/tex]

[tex] \: \: [/tex]

Hope It's Helps uh Miss<3"

Answer:

[tex]4 \cot {}^{2} (45) - 3 \tan {}^{2} (60) + 2 \sec {}^{2} (60) = 3 \\ [/tex]

[tex]LHS = 4 \cot {}^{2} (45) - 3 \tan {}^{2} (60) + 2 \sec {}^{2} (60) \\[/tex]

let us first take a look at the values of the trigonometric ratios given in the question so that we get quite clear about what is to be done.

here ,

[tex] \cot(45) = 1 \\ \\ \tan(60) = \sqrt{3} \\ \\ \sec(60) = 2[/tex]

now ,

we just have to plug in the values considering certain other things given in the question and we're done!

so let's start ~

[tex]4(1) {}^{2} - 3( \sqrt{3} ) {}^{2} + 2(2) {}^{2} \\ \\ \dashrightarrow \: 4(1) - 3(3) + 2(4) \\ \\ \dashrightarrow \: 4 - 9 + 8 \\\\ \dashrightarrow \: 12 - 9 \\ \\\dashrightarrow \: 3 = RHS[/tex]

hence , proved ~

hope helpful :D

Answer:

they are 3 1/10 units away from each other

Step-by-step explanation:

11 3/10 - 9 2/10

3 1/10

Answer:

Let's first try to find the angle supplementary to measure 141°.

(Supplementary angles are two angles that add up together to equal 180°).

Set up an equation;

141 + x(unknown angle measure) = 180°

Solve for x:-

141 + x = 180

-141        -141

x = 39°.

Now that we've found one of the interior angles measure to this triangle, we will use this value to figure out the angle measure next to 'x'.

If we think of the line (highlighted in the picture I attached to this), extended, we can kind of make out of this line as a transversal cutting into the two parallel lines(L & M).

Furthermore, the measured angle 39°, is an alternate interior angle with the missing angle next to 'x'(highlighted with yellow in my picture).

And, alternate interior angles are congruent(meaning they measure the same degree).

Therefore, we can infer that the missing angle next to 'x' is also 39°.

Now that we've found one angle measure and another angle(given) next to x, we can see that angle x and those two angle measures (48° and 39°) combined are supplementary!

So now that we know that angles 48° and 39° are supplementary with x, we can find the value of x by finding it's supplement value!

Arrange an equation;

(48 + 39) + x = 180°

Simplify and solve for x:-

87 + x = 180

-87        -87

x = 93°, hence ∠X = 93°.

Answer:

it is the same because slope is a measure of steepness.

Step-by-step explanation:

(0,1) (2,4)

4-1/2-0=3/2

slope=3/2

Tip: Go to the internet and put the topic you are focused more on that you posted in Brainly

Step-by-step explanation:

Try it to give you some help

Answer:

the answer is 3 :))

Step-by-step explanation:

9/3= 3

Answer:

16,667

Step-by-step explanation:

13,925 + 2,742 = 16,667

Answer:

Bonjour

Step-by-step explanation:

Reese : 13 925

Manny : 2 742 de plus que Reese donc 13 925 + 2 742

13 925 + 2 742 = 16 667

Manny a marqué 16 667 points.

Answer:

O = 15

Step-by-step explanation:

.mean ' is the average

(12 + 16 + O + 14 + 8) / 5 = 13

50 + O = 65

O = 15

[tex]"20cm"[/tex]

[tex]Area\ of\ rq=a^2[/tex]

[tex]a=\sqrt{200}=10\bullet \sqrt{2}[/tex]

[tex]d\ iargul=\sqrt{2}9[/tex]

             [tex]=10\times \sqrt{2}\times \sqrt{2}[/tex]

             [tex]=20cm[/tex]

I hope this helps you

:)

Answer:

Use the geometric sequence formula since you are multiplying each town's villagers by the amount your teacher gave you.

Step-by-step explanation:

Plug in the parts of the formula from the numbers given in the question, then you can calculate the number of villagers needed for the 15th town.

Answer:

35.375 Villagers Live in the 15th village

Step-by-step explanation:

Brennan can use the Geometric Sequence formula to predict the number of villagers in the 15th town.

(work attached)

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

[tex]\qquad \tt \dashrightarrow \:x - \dfrac{1}{2} \geqslant 43 [/tex]

[tex]\qquad \tt \dashrightarrow \:x \geqslant43 + \dfrac{1}{2} [/tex]

[tex]\qquad \tt \dashrightarrow \:x \geqslant \dfrac{86 + 1}{2} [/tex]

[tex]\qquad \tt \dashrightarrow \:x \geqslant \dfrac{87}{2} [/tex]

hope this helps Belinda aunty ~

Step-by-step explanation:

please mark me as brainlest

Answer:

I hope it helped you

Step-by-step explanation:

Pls refer the given attachment

so let's say the equation is y = ax² + bx + c, where a,b,c are constants.

we know that f(3) = 5, or namely when x = 3 , y = 5.

we also know that f'(3) = 6, or namely the slope at the point (3,5) is 6.

we also know that at (3,5) the 2nd derivative is 4, so a positive number simply tell us its concavity, is up, so is a parabola opening upwards.

[tex]y=ax^2+bx+c\implies \left. \cfrac{dy}{dx}=2ax+b \right|_{x=3}~~ = ~~ 6\implies 6=2ax+b \\\\\\ 6=2a(\stackrel{x}{3})+b\implies 6=6a+b\implies 6-6a=b\implies \boxed{6(1-a)=b} \\\\[-0.35em] ~\dotfill\\\\ \left. \cfrac{d^2y}{dx^2}=2a \right|_{x=3}~~ = ~~4\implies 2a=4\implies a=\cfrac{4}{2}\implies \boxed{a=2}~\hfill \boxed{-6=b} \\\\[-0.35em] ~\dotfill[/tex]

[tex]y=2x^2-6x+c\qquad \begin{cases} x=3\\ y = 5 \end{cases}\implies 5=2(3)^2-6(3)+c\implies \boxed{5=c} \\\\\\ y=2x^2-6x+5~\hfill y(2)=2(2)^2-6(2)+5\implies \blacktriangleright y(2)=1 \blacktriangleleft[/tex]

Step-by-step explanation:

[tex] 2 \frac{1}{3} \times \frac{3}{4} \\

[/tex]2 1/3 = 7/3

[tex] \frac{7}{3} \times \frac{3}{4} \\ [/tex]

21/12 = 7/4

Answer:

10,000 is the total amount of.money that was distributed

Check the picture below, so the circle looks more or less like so, with a radius of 9.

[tex]\textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=9 \end{cases}\implies C=2\pi (9)\implies C\approx 57[/tex]

Answer: c

Step-by-step explanation: The cube represents the earth, the octahedron represents the air, the tetrahedron represents the fire, the icosahedron represents the water, and the dodecahedron represents the universe

The name of the platonic solid shown is hexahedron.

Tetrahedron - A tetrahedron, also referred to as a triangle pyramid, is a polyhedron with four triangular faces, six straight edges, and four vertex corners in geometry.

Hexahedron - Any polyhedron with six faces is called a hexahedron.

Octahedron - An octahedron is a polyhedron with eight faces in geometry.

Dodecahedron - In geometry, a dodecahedron or duo decahedron is any polyhedron with twelve flat faces.

The figure given in the question has clearly six flat faces and hence according to the definitions it is a hexahedron.

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The complete question is attached.

The required length of the rectangle is 12/5 feet and the width is 9/5 feet.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let's denote the length of the rectangle as L and the width as W.

From the problem statement, we know that:

3L = 4W (equation 1)

We also know that the perimeter P is given by:

P = 2L + 2W = 8 2/5 feet

Multiplying both sides by 5 to get rid of the fraction, we get:

10L + 10W = 42

Dividing by 2, we get:

5L + 5W = 21 (equation 2)

Now we can use equations 1 and 2 to solve for L and W.

First, we can substitute equation 1 into equation 2 to get an equation in terms of W:

5L + 15L/4 = 21

Multiplying both sides by 4, we get:

20L + 15L = 84

35L = 84

L = 84/35 = 12/5 feet

Now we can substitute the value of L into equation 1 to get the value of W:

3L = 4W

3(12/5) = 4W

W = 9/5 feet

Therefore, the length of the rectangle is 12/5 feet and the width is 9/5 feet.

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