Franklin used the polynomial expression x(x−3)(x+4) to model the volume of a rectangular prism. What is the length of the shortest side of this prism? A x B x−3 C x2−3x D x3+x2−12x

Answer:

(5,-3) in the 4th quadrant

Step-by-step explanation:

Step-by-step explanation:

here's the answer to your question

Answer:

[tex]\frac{1}{a^{\frac{-5}{6} } }[/tex]

OAmalOHopeO

Answer:

the third option - they are perpendicular to each other.

Step-by-step explanation:

for a perpendicular slope we need to exchange the x and y values (remember, a slope is the ratio of y/x) and flip the sign.

and that is exactly what happened here.

Answer: Choice A

2(2L + L)  = 42

=================================================

Explanation:

The length is L, which is some placeholder for a positive number.

The width is twice as much as this, so it's 2L

The perimeter is found by adding up the four sides (two of which are L, the other two are 2L)

So we have L+L+2L+2L = 2(2L+L) representing the perimeter.

Or we could use this formula

P = 2(L+W)

where L and W are the length and width respectively.

Either way, we end up with 2(2L + L) = 42

Answer:

42 = 2( l+2l)

Step-by-step explanation:

width = 2 length

Perimeter = 2 (l+w)

42 = 2( l+2l)

Divide each side by 2

42/2 = 2 (3l) /2

21 = 3l

Divide by 3

21/3 = 3l/3

7 = l

The length is 7

width is 2*l = 2*7 = 14

Answer:

polygon is 15 side

Step-by-step explanation:

Here sum of interior angels is 2340 degrees. Therefore, the polygon is 15 side

Answer:

54piecm^3

Step-by-step explanation:

pie x radius ^2 x h

= v

pie x 9

= 9pie x 6

= 54pie

Answer:

32:3/4

33:4/3

34:40

35:48

Answer:

5.1 cm

Step-by-step explanation:

(Probable) Question;

Given a circle with center O and radius 2.4 cm. P is a point on the tangent that touches the circle at point Q, such that the length of the tangent from P to Q is 4.5 cm. Find the length of OP

The given parameters are;

The radius of the circle with enter at O, [tex]\overline{OQ}[/tex] = 2.4 cm

The length of the tangent from P to the circle at point Q, [tex]\overline{PQ}[/tex] = 4.5 cm

The length of OP = Required

By Pythagoras's theorem, we have;

[tex]\overline{OP}[/tex]² = [tex]\overline{OQ}[/tex]² + [tex]\overline{PQ}[/tex]²

∴ [tex]\overline{OP}[/tex]² = 2.4² + 4.5² = 26.01

[tex]\overline{OP}[/tex] = √26.01 = 5.1

The length of OP = 5.1 cm

Answer:

-6

Step-by-step explanation:

2n can be the smallest integer, and 2n + 18 will be the largest integer.

The sum of this, divided by two, will result in the average/mean.

(2n + 2n + 18)/2 = 3

Multiply each side by 2:

(2n + 2n + 18)/2 ⋅ 2 = 3 ⋅ 2

2n + 2n + 18  =  6

Combine the like terms:

4n + 18 = 6

Subtract 18 from both sides:

4n + 18 - 18 = 6 - 18

4n = -12

Divide each side by 4:

4n/4 = -12/4

n = -3

Since we decided to go by 2n:

2n = 2(-3) = -6

Answer: The correct answer is in the first option.

Step-by-step explanation:

Equation of an Ellipse

[tex]\dfrac{x^{2} }{a^{2} } +\dfrac{y^{2} }{b^{2} } =1\\\\25x^{2} - 150x + 9y^{2} = 0\\\\\text {Let's \: perform \: the \: transformations:}\\\\\dfrac{25x^{2} }{25 \cdot 9} -\dfrac{150x}{25 \cdot 9} +\dfrac{9y^{2} }{25 \cdot 9} =0\\\\\dfrac{x^{2} }{3^{2} } -\dfrac{6x}{3^{2} } +\dfrac{y^{2} }{5^{2} } =0\\\\\dfrac{x^{2} -6x}{3^{2} } +\dfrac{y^{2} }{5^{2} } +\dfrac{3^{2} }{3^{2} } -\dfrac{3^{2} }{3^{2} } =0\\\\\dfrac{x^{2} -6x+3^{2} }{3^{2} } +\dfrac{y^{2} }{5^{2} } =\dfrac{3^{2} }{3^{2} }[/tex]

[tex]\dfrac{(x-3)^{2} }{3^{2} } +\dfrac{y^{2} }{5^{2} } =1[/tex]

Answer:

x=12

Step-by-step explanation:

x/4 + 17 =20

Subtract 17 from each side

x/4 +17-17 =20-17

x/4 = 3

Multiply each side by 4

x/4 *4 = 3*4

x =12

Answer:

The formula to determine the area of the circle.

Step-by-step explanation:

↔

Answer:

254m

Step-by-step explanation:

The setup will be in form of a right triangle. Hence;

The angle of elevation = 64degrees

distance from herself to the base of the castle = 124 meters (Adjacent)

Required

Height of the castle (Opposite)

Using the SOH CAH TOA identity

Tan theta = opp/adj

Tan 64 = H/124

H = 124tan64

H = 124(2.05030)

H = 254.23

H ≈ 254m

Hence the height of the castle to the nearest whole meters is 254metres

Answer:

The width is 5 cm

Step-by-step explanation:

The perimeter of a rectangle is

P = 2(l+w)

Substitute what we know

24 = 2(7+w)

Divide each side by 2

24/2 = 2/2(7+w)

12 = 7+w

Subtract 7 from each side

12-7 = 7+w-7

5 =w

The width is 5 cm

The formula for perimeter = 2 x length  + 2 x width

Fill in the known dimensions:

24 = 2 x 7 + 2 x width

Simplify:

24 = 14  + 2 x width

Subtract 14 from both sides:

10 = 2 x width

Divide both sides by 2:

Width = 5 cm

Answer: Width = 5 cm.

Step-by-step explanation:

1 . when we collect like terms we only focus on the variables and the power of the variable I f exist so in this question the answer is 8x^2 because both have the same variable and same power or exponent.

2. one term is monomial

two terms is binomial

3. b

4. -9

5. c

Answer: C

Step-by-step explanation:

To find the surface area of a cone, you use the formula [tex]A=\pi r(r+\sqrt{h^2+r^2} )[/tex]. Since we are already given the height and radius, all we have to do is plug in the values and solve.

[tex]A=9\pi (9+\sqrt{41^2+9^2} )[/tex]       [solve inside of square root]

[tex]A=9\pi (9+\sqrt{1762} )[/tex]             [parenthesis]

[tex]A=9\pi (50.976 )[/tex]                   [multiply]

[tex]A=458[/tex]

Therefore, the closest answer is C.

Answer:

see explanation

Step-by-step explanation:

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

The graph of g(x) is the graph of f(x) shifted up by 4 units

Answer: 23, 27,29

Those im absolutely positive about.

Im not sure abt the rest

Step-by-step explanation:

Answer:

the polygon above has 6 sides . It is a hexagon with 6 obtuse angles interior angles equal to 720° .

Answer:

the polygon above has 6 sides . It is a hexagon with 6 obtuse angles interior angles equal to 720° .

Step-by-step explanation:

Answer:

ewfwefwfewfwfwe

Step-by-step explanation:

Answer:

A is the correct one

cause according to function rule the vertical line should cut only on a one point to be function

as here we can see that vertical line cuts here at two point

Answer:

w ≈ 33.9 in

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

w² + w² = 48²

2w² = 2304 ( divide both sides by 2 )

w² = 1152 ( take the square root of both sides )

w = [tex]\sqrt{1152}[/tex] ≈ 33.9 in ( to the nearest tenth )

Answer:

1. not continuous, as the function definitions deliver different function values at x=1 when approaching this x from the left and from the right side.

2.

2 = a + b

3.

0 = 2a + b

4.

a = -2

b = 4

Step-by-step explanation:

the function is continuous at a specific point or value of x, if the f(x) = y functional value is the same coming from the left and the right side at that point.

1. that means that for x=1

3 - x = ax² + bx

so,

3 - 1 = a×1² + b×1 = a + b

2 = a + b

we have to use a=2 and b=3

2 = 2 + 3 = 5

2 is not equal 5, so the assumed equality is false, so the function is not continuous there.

2. point 1 gave us already the working relationship between a and b.

2 = a + b

only if that is true, is the function continuous at x=1.

3. now for x=2

5x - 10 = ax² + bx

5×2 - 10 = a×2² + b×2 = 4a + 2b

10 - 10 = 4a + 2b

0 = 4a + 2b

0 = 2a + b

4. to find a and b to be continuous at both locations x=1 and x=2 both expressions in a and b must apply.

so, they establish a system of 2 equations with 2 variables.

2 = a + b

0 = 2a + b

a = 2 - b

0 = 2×(2-b) + b = 4 - 2b + b = 4 - b

b = 4

therefore

a = 2 - 4 = -2

5. I cannot draw a graph here.

just use now the function

3 - x, x < 1

‐2x² +4x, 1 <= x < 2

5x - 10, x >= 2

Answer:

$6778.36

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Compounded Interest Rate Formula: [tex]\displaystyle A = P(1 + \frac{r}{n})^{nt}[/tex]

Step-by-step explanation:

Step 1: Define

Identify variables

P = 6000

r = 5% = 0.05

n = 1

t = 2.5

Step 2: Find Interest

Answer:

6=n

Step-by-step explanation:

Hi there!

We are given this equation:

3(n+4)=5n

And we need to solve it for n

To do that, we need to isolate n on one side

But we need to open up the parentheses on the left side by doing the distributive property

Multiply both n and 4 by 3

3n+12=5n

Now subtract 3n from both sides to remove it from the left side

12=2n

Divide both sides by 2 to change the coefficient on n from 2 to 1

6=n

n is now isolated on one side

Hope this helps!

Answer:

n=6

Step-by-step explanation:

Using the distributive property, we distribute 3 to n and 4. In case if you don't know what that means, it means we multiply 3 to the variables inside the parentheses. So we get (3×n)+(3×4)=5n, and we simplify it so we get 3n+12=5n. Now, we can subtract 3n from both sides and get 12=2n, and divide 2 from both sides and get n=6.

Presumably, ln⁵(x) is the same as (ln(x))⁵ (as opposed to a quintuply-nested logarithm, log(log(log(log(log(x)))))).

Then substituting u = ln(x) and du = dx/x gives

[tex]\displaystyle\int\frac{\mathrm dx}{x\ln^5(x)} = \int\frac{\mathrm du}{u^5} = -\frac1{4u^4}+C = \boxed{-\frac1{4\ln^4(x)}+C}[/tex]

Answer:

It will take him 10 minutes to jog 1 mile.

Step-by-step explanation:

can i have brianliest please

Answer:

Answer is 90 ways

Step-by-step explanation:

You multiply the members (30) by the number of positions (3) to get your answer

Answer:

A' (9,4)

B' (8,-1)

C' (5,1)

Answered by GAUTHMATH

Answer:

A' = 9,4

B' = 8,-1

C' = 5,1

Step-by-step explanation: