Which division problem does the diagram below best illustrate?

A diagram with 5 ovals containing 7 squares.
30 divided by 5 = 6

The quadratic functions are: f(x) = 0.03x² for Design A and g(x) = 0.024x² for Design B.

A quadratic function is a type of polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants and x is the variable. In a quadratic function, the highest power of the variable is 2.

The graph of a quadratic function is a parabola, which is a U-shaped curve that opens either upwards or downwards depending on the sign of the coefficient a. If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards. The vertex of the parabola, which is the point where the curve changes direction, is given by the coordinates (-b/2a, f(-b/2a)).

Quadratic functions have a wide range of applications in various fields such as physics, engineering, economics, and finance. For example, they can be used to model the motion of projectiles, the trajectory of a rocket, the shape of a bridge arch, the optimization of business profits, and the behavior of financial markets.

Let's assume that each side of the cube has a length of x inches. Then, the surface area of the cube is 6x² square inches.

a. For Design A with a cost of $0.005 per square inch, the total cardboard cost can be calculated using the quadratic function:

f(x) = 0.005(6x²) = 0.03x²

b. For Design B with a cost of $0.004 per square inch, the total cardboard cost can be calculated using the quadratic function:

g(x) = 0.004(6x²) = 0.024x²

Therefore, the quadratic functions are:

f(x) = 0.03x² for Design A

g(x) = 0.024x² for Design B

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The complete question is:

\(\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o\)

Make sure your calculator is in Degree mode.

Answer:

5/14

Step-by-step explanation:

1\(\frac{3}{4}\) = 7/4

4\(\frac{9}{10}\) = 49/10

\(\frac{7}{4}\) / \(\frac{49}{10}\)

\(\frac{7}{4}\) x \(\frac{10}{49}\) = \(\frac{70}{196}\)

or

\(\frac{1}{2}\) x \(\frac{5}{7}\) = \(\frac{5}{14}\)

Answer:

e

Step-by-step explanation:

e

Answer:

d = 5

Step-by-step explanation:

(d-5)² = 0

Using the algebraic identity (a-b)² = a² + b² - 2(a)(b)

d² + 25 - 10d = 0

d² - 10d + 25 = 0

d² - 5d - 5d + 25 = 0

d(d-5) -5(d-5) = 0

(d-5)(d-5)

d = 5

Answer:

(0.0706, 0.1294)

Step-by-step explanation:

Confidence interval of a proportion is:

CI = p ± CV × SE

where p is the proportion,

CV is the critical value (z score or t score),

and SE is the standard error.

The sample is large enough to estimate as normal.  For 95% confidence level, CV = z = 1.96.

Standard error for a proportion is:

SE = √(pq/n)

SE = √(0.1 × 0.9 / 400)

SE = 0.015

The confidence interval is:

CI = 0.1 ± (1.96)(0.015)

CI = (0.0706, 0.1294)

Round as needed.

Answer:

set of all real numbers

Step-by-step explanation:

Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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The equation for a parallel street that passes through (−2,4) is y = 4x + 12

Since the two streets are parallel and the first street passes through (4, 7) and (3, 3), we need to find its slope of the line passing through the points.

So, slope m = (y₂ - y₁)/(x₂ - x₁) where

Substituting the values of the variables into the equation, we have

m = (y₂ - y₁)/(x₂ - x₁)

m = (3 - 7)/(3 - 4)

m = -4/-1

m = 4

Since both streets are parallel, their slopes are equal. So, the slope of the second street is m = 4.

Now, since the second street passes through the point (-2, 4), the equation of the second street is given by the equation of a line in slope form

m = (y - y₃)/(x - x₃) where

So, susbstituting the values of the variables into the equation, we have

m = (y - y₃)/(x - x₃)

4 = (y - 4)/(x - (-2))

4 = (y - 4)/(x + 2)

y - 4 = 4(x + 2)

y - 4 = 4x + 8

y = 4x + 8 + 4

y = 4x + 12

So, the equation for a parallel street that passes through (−2,4) is y = 4x + 12

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Answer:

32.0

Step-by-step explanation:

i really can't explain it but comment if need more help

and can u take better picture

\(Question\)

Alice skates 2/5 mile in 1/5 hour. Elizabeth skates 2/3 mile in 2/9 hour. How far did elisabeth escape in in 1 hour?

Answer:

The Correct Answer is \(\frac{8}{9}\)

Complete the multiplication and the equation becomes

\(\frac{2}{9}\) +\(\frac{2}{3}\) = ?

The two fractions now have like denominators so you can add the numerators.

\(\frac{2+6}{9}\) = \(\frac{8}{9}\)

Therefore, The Answer Is \(\frac{8}{9}\)

Hope this helps!

\(xXxAnimexXx\)

Answer:

1031p + £20 , I dont understand what the p stands for but that is it

Step-by-step explanation:

- remove 100 free minutes from 140 from Jim's usage, youre left with 40 minutes at a rate of 9p each minute. 40 x 9 = 360

- remove 200 free texts from 261, youre left with 61 texts at a rate of 11p per text, 61 x 11 = 671

671 + 360 = 1031

1031 + 20

20 for the monthly charge

Answer:

311.3 feet

Step-by-step explanation:

1 yard = 3 feet

Therefore, 103.76 yards = 311.28 feet (by multiplying 103.76 by 3)

Rounding to the nearest tenth gives us 311.3 feet.

Answer:

5(x+4)(x+1)

Step-by-step explanation:

The equation of line passing through (-4, -16) and (5, 2) are y = 2x – 8, y - 2 = 2(x - 5) and y + 16 = 2(x + 4)

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

The standard form for linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The equation of line passing through (5, 2) and (-4, -16) is:

y - 2 = [(-16-2)/(-4-5)](x - 5)

y - 2 = 2(x - 5)

y = 2x - 8

y + 16 = 2(x + 4)

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Answer:

here you go I hope this helps:)

Answer:

∴surface area = 384 unit^2

Step-by-step explanation:

volume =512 unit^3

formula for cube volume is a^3 where a is the length and we know all the length in cube is similar

a^3 = 512

a=8

∴a = 8

∴surface area of cube formula : 6a^2

6 * ( 8 )^2

384 unit^2

hope this helps and appreciate if u mark this as brainliest answer

Answer:

Step-by-step explanation:

Volume of cube = 512 cubic units

Side³ = 512

\(Side =\sqrt[3]{512}=\sqrt[3]{8*8*8}\\\\\\Side = 8 \ unit\)

Surface area of cube = 6a² = 6*8*8 = 384 square units

Yes, the proof of congruence of two triangles ∆ABC ≅ ∆GHF is possible.

The convergence method which proves this congruence is SSS(side-side-side) congruence.

We have given the sketch of two triangles as seen above. We have to prove ∆ABC ≅ ∆GHF

Now , AB = √(-7+7)² + 5² = 5 in triangle ABC and FG = 5 in triangle FGH,

so, AB ≅ FG

Because AC = 3 in triangle ABC and FH = 3 in triangle FGH,

so, AC ≅ FH

To find the lengths of BC and GH , we can use distance formula.

Length of BC :

BC = √[(x₂ - x₁)² + (y₂ - y₁)²]

(x₁, y₁) = B(-7, 0) and (x₂, y₂) = C(-4, 5).

BC = √[(-4 + 7)² + (5 - 0)²]

= √[32 + 52]

= √[9 + 25]

= √34

Length of GH :

GH = √[(x₂ - x₁)² + (y₂ - y₁)²]

(x₁, y₁) = G(1, 2) and (x₂, y₂) = H(6, 5).

GH = √[(6 - 1)² + (5 - 2)²]

= √[52 + 32]

= √[25 + 9]

= √34

Conclusion :because BC = √34 and GH = √34,

=>BC ≅ GH

All the three sides of one triangle is congruent to the corresponding sides of other triangle.

By SSS congruence postulate,

ΔABC ≅ ΔFGH

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Answer:

ghjug,yhfgugug kuul

Step-by-step explanation:

Let x be the time (in hours) it takes Meredith to edit a textbook alone. We know that Phil takes 4x hours to edit a textbook alone, since he takes four times as long as Meredith.

We also know that it takes them 16 hours to edit a textbook together. We can use this information to set up the equation:

x + 4x = 16

5x = 16

x = 16/5

So it takes Meredith 16/5 hours to edit a textbook alone.

We know that Phil takes 4x to edit a textbook alone, so we can substitute in the value we found for x to find his time:

4x = 4(16/5) = 16/5 * 4 = 64/5

So it takes Phil 64/5 hours to edit a textbook alone.

Step-by-step explanation:

agile is the answer I'm pretty sure

Answer:

Levers work to move the body in a ____________ motion.

projectile

stable

balanced

agile

According to the table, the rate of change of the function is of -3.

The rate of change of a function is given by the change in the output y divided by the change in the input x.

In this problem, when x changes by 3, y changes by -9, hence:

\(m = \frac{-9}{3} = -3\)

The rate of change of the function is of -3.

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The length of BD is 18.5 units.

In the given right triangle ABC, with altitude BD drawn to hypotenuse AC, we are given the lengths AD = 22 and DC = 15. We need to find the length of BD.

Let's consider triangle ABD. Since BD is the altitude, it divides the right triangle ABC into two smaller right triangles: ABD and CBD.

In triangle ABD, we have the following sides:

AB = AD = 22 (given)

BD = ?

Now, let's consider triangle CBD. In this triangle, we have the following sides:

BC = DC = 15 (given)

BD = ?

Since triangles ABD and CBD share the same base BD, and their heights are the same (BD), we can say that the areas of these triangles are equal.

The area of triangle ABD can be calculated as:

Area(ABD) = (1/2) * AB * BD

Similarly, the area of triangle CBD can be calculated as:

Area(CBD) = (1/2) * BC * BD

Since the areas of ABD and CBD are equal, we can equate their expressions:

(1/2) * AB * BD = (1/2) * BC * BD

We can cancel out the common factor (1/2) and solve for BD:

AB * BD = BC * BD

Dividing both sides of the equation by BD (assuming BD ≠ 0), we get:

AB = BC

In triangle ABC, the lengths AB and BC are equal, which implies that triangle ABC is an isosceles right triangle. In an isosceles right triangle, the leg's length are congruent, so AB = BC = AD = DC.

BD is equal to half of the hypotenuse AC:

BD = (1/2) * AC

Substituting the given values, we have:

BD = (1/2) * (AD + DC) = (1/2) * (22 + 15) = (1/2) * 37 = 18.5

Therefore, the length of BD is 18.5 units.

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Answer:

45

Step-by-step explanation:

In an inverse variation situation, we have mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant.

So in this case: x*y is a constant

since x=9 and y=5 so

xy = 45

the constant of variation is 45

For inverse function, we usually write it as \(y = \dfrac{45}{x}\)

The required solution of the value of the constant of variation is 45.

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases.

Given:

for an Inverse variation, y=5 when x=9

According to given question we have

Relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant.

x×y  =constant

x×y  =k

Where k is a constant.

By put the value of

y=5 when x=9.

k= 9×5

k=45

Therefore, the required solution of the value of the constant of variation is 45.

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Answer:

m ≥ –6

Step-by-step explanation:

m+5 ≥ –1

subtract 5 from both sides

m ≥ -6

Answer:

Step-by-step explanation:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)

Lets look at the derivative part:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)

\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)

Substituting in eq(1), we have:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)

Answer:

\(f(x)=0.2\,(x-2)^2+1\)

Option "B" as per the list of possible answers

Step-by-step explanation:

Notice that the parabola has a minimum at the point (2, 1), therefore first look at which of the options gives you  \(f(2) = 1\). You would be able then the discard the last two functions listed (they render "-1" (not 1) for x = 2.

Now to decide between the first and the second option, notice that the first option has a negative coefficient (-0.2) multiplying the perfect square \((x-2)^2\) which means that the branches of such parabolic function would be pointing down. So you discard the first option, and now the only one left is the second option:

\(f(x)=0.2\,(x-2)^2+1\)

which you can check briefly by evaluating a couple of easy points  (like what values you get for x = 0, and at x = 4, and confirm it is the correct option.

slope= 1/4

y intercept= -5