Assuming that no denominator equals zero, which is equivalent to? r^2-r-6/(r-2)(r-3)​

Answer:

Hi,

Step-by-step explanation:

directrix: x=-8

focus=(8,0)

[tex]x=\dfrac{(y-0)^2}{2*(8+8)}+\dfrac{8-8}{2}\\\\\boxed{x=\dfrac{y^2}{32}}[/tex]

Answer:

i think its just water bro

BE and CD are parallel, so the triangles ABE and ACD are similar. Then the following relation holds:

AE/AD = AB/AC

10/(10 + 8) = x/(x + 6)

Solve for x :

10 (x + 6) = x (10 + 8)

10x + 60 = 18x

8x = 60

x = 60/8 = 7/5

Answer:

remainder = 4

Step-by-step explanation:

using the remainder theorem

when f(x) is divided by (x - a) then the remainder is f(a)

so when f(x) is divided by (x - 7) the remainder is f(7) , that is

f(7) = 7³ - 13(7)² + 40(7) + 18

      = 343 - 13(49) + 280 + 18

      = 343 - 637 + 298

      = 4

Hence, the remainder is [tex]4[/tex].

What is the remainder value?

The remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient.

Applying the remainder theorem

In general when [tex]f(x)[/tex] is divided by [tex](x - a)[/tex] then the remainder is [tex]f(a)[/tex].

So, here when [tex]f(x)[/tex]  is divided by [tex](x - 7)[/tex]  the remainder is [tex]f(7)[/tex], that is

[tex]f(7)=7^3-13(7)^3+40(7)+18\\=343-13(49)+280+18\\=343-637+298\\=4[/tex]

Hence, the remainder is [tex]4[/tex].

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The answers to the options are:

This inequality is known tp imply that the normal body temperature is taken (subtracted) from the minimum and maximum body temperature.

Note that in case A, the The inequality that represent the temperatures  is less than sign.

In case b, it is an open interval because it means that in -40°F to -140°F , it is not equal to as that is the reason that  the gas cannot stay liquid.

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Answer:

3 Hours

Step-by-step explanation:

Plumber A.

Initial fee: $45

Per Hour: $60

Plumber B.

Full rate: $225

To determine the number of hours it will take for both plumbers to charge the same amount you have to start with $45.

Then add 60$ every hour.

$45 + $60 = $105

$105 + $60 = $165

$165 + $60 = $225

Therefore, it takes 3 hours for them to charge the same rate.

Hi Student!

Looking at the problem, we are given a variable with a coefficient that is to the power of 4.  We are asked to write the same expression but without exponents which means that we need to factor out the exponents to each of the items inside of the parenthesis.

Expand the expression

Simplify the expression

Therefore, the final answer for writing the expression [tex](9m)^4[/tex] without exponents would be [tex]6561m^4[/tex] after expanding the expression.

Answer:2x

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

using Pythagorean theory.

equate it to the hypotenus.

thus- hyp sq=adjacent sq +opposite sq

Answer:

probably it

Step-by-step explanation:

First, get the area of the rectangle then subtract the triangle, the result will be the shaded area:

area rec = 18 * 11

area rec = 198 cm²

small side of tri = 11 - 5

small side of tri = 6 cm

area tri = (height * width) / 2

area tri = (6 * 18) / 2

area tri = 108 / 2

area tri = 54 cm²

area shaded = 198 - 54

area shaded = 144 cm²

The probability can be calculated as given because there are a total of 52 cards.

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Total number of card = 52

Number of king of heart = 1

P(getting a king of hearts) = 1/52

P(getting a spade) = 13/52 = 1/4

P (getting a 5 or a club) = (16/52) = 4/13

P(getting a 5 or a 7) = 4/52 + 4/52 = 8/52 = 2/13

P(getting a card which is not a spade) = 1 - 1/4 = 3/4

P(getting 11 of clubs) = 1/52

Thus, the probability can be calculated as given because there are a total of 52 cards.

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Answer:

1. 1

2. 51

3. 7

4. 9

Step-by-step explanation:

hope i helped

Answer:

Step-by-step explanation:

3(1) + 4(3) + 9 = 0

3 + 12 + 9 = 0

24 ≈ 0                                                                                                                                                                                                                                                                                                                                                                              

Answer:

-7/8

Step-by-step explanation:

Quadratic formula is ax^2 + bx + c

In this case, x = -b/2a, which is -7/(2(4)) = -7/8

Answer:

x = - [tex]\frac{7}{8}[/tex]

Step-by-step explanation:

given a quadratic in standard form

f(x) = ax² + bx + c (a ≠ 0 )

then the equation of the axis of symmetry is

x = - [tex]\frac{b}{2a}[/tex]

f(x) = 4x² + 7x + 6 ← is in standard form

with a = 4 and b = 7

then equation of axis of symmetry is

x = - [tex]\frac{7}{2(4)}[/tex] = - [tex]\frac{7}{8}[/tex]

1 hour = 60 minutes

Distance travelled in 60 minutes = 50 km

Distance travelled in 1 minute = 50/60

Distance travelled in 30 minutes = 50/60×30

50/60×30 = 25 km

OR

A car travelled 50 km in 60 minutes. For 30 minutes, half the distance that is 25 km.

Answer:

She would need at least 11 buses leaving 17 spare seats.

Step-by-step explanation:

171+22+13= 206

206/20= 10.3

10.3 = 11

The solution to this system of equations is infinitely many solutions

The system of equations is given as:

-5.9x  -3.7y = -2.1.

5.9x + 3.7y = 2.1.

Add both equations to eliminate a variable

-5.9x + 5.9x - 3.7y + 3.7y = -2.1 + 2.1

Evaluate

0 +0 = 0

Evaluate the sum of zeros

0 = 0

Both sides of the equations are the same

Hence, the solution to this system of equations is infinitely many solutions

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Answer:

Option C is correct. The system of linear equation -5.9x - 3.7y =  -2.1 and 5.9x +3.7y = 2.1 have infinitely many solutions.

What is system of linear equation?

The system of linear equations is "a set of two or more linear equations or   variables is called system of linear equation".

What is infinitely many solutions?

An equation has infinitely many solutions only if "the two lines are coincident and having the same y-intercept".

According to the question,

The system of linear equation,

-5.9 x - 3.7y = -2.1            →  (1)

5.9 x + 3.7y = 2.1              →  (2)

The equation (1) is same as the equation (2) only the difference equation (1) is multiplied by (-1). Both equation give the same line. To check if above equations have same y-intercept, the equation can be written in slope intercept form y = m x +c where 'm' is the slope of the line, 'c' is the 'y-intercept'.

y = - (5.9/3.7) x + 2.1   [From equation (1)]

y = -(5.9/3.7) x + 2.1      [From equation (2)]

The both equation have same y-intercept. Therefore, the system of linear equations have infinitely many solution.

Hence, the system of linear equation -5.9x - 3.7y =  -2.1 and 5.9x +3.7y = 2.1 have infinitely many solutions.  

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Step-by-step explanation:

Answer: 8

Step-by-step explanation:

The discriminant is [tex]b^2-4ac[/tex]

in the equation:

[tex]-x^2+4x-2[/tex]

A = -1, B = 4, C = -2

plug into equation

[tex]4^2-4(-1)(-2)[/tex]

[tex]16-8[/tex]

⇒ [tex]8[/tex]

Answer:

3,600 x (1.0375) ^ 1

Step-by-step explanation:

Compund interest formula.

IA * (r + 1) ^t

IA = Initial amount; r = rate (as decimal); t = time (in years)

IA = 3600

r = .0375

t = 1 (2008-2009)

3,600 x (1.0375)^1

-- Gage Millar, Algebra 1/2 Tutor, (Pending Pre-Calc Tutor)

Answer:

  (d)  48 yd³

Step-by-step explanation:

The net shown is of a rectangular prism. To find its volume, we need to know its dimensions. The volume will be the product of those dimensions.

__

The area of a rectangle is given by the formula ...

  A = LW

So, if we know one of the dimensions, we can find the other from ...

  W = A/L . . . . . divide by L

For the right-most rectangle, the area is 24 yd², and its length is given as 6 yd. Then the other dimension of that rectangle is ...

  W = 24 yd²/(6 yd) = 4 yd

__

For the left-most rectangle, the area is 12 yd², so its width is ...

  W = 12 yd²/(6 yd) = 2 yd

__

Now we know the dimensions of the cuboid are 6 yd by 4 yd by 2 yd. Its volume is ...

  V = LWH = (6 yd)(4 yd)(2 yd) = 48 yd³

The volume of the solid figure is 48 yd³.

The volume of the solid figure is 48 cubic yd if the length, width, and height of the solid figure are 6, 4, and 2 yd respectively option fourth is correct.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape. It is also called a cuboid.

We have a net of the solid figure shown in the picture.

From the figure, the face has 24 square yards area and one side length is given, we can calculate the width of this face:

24 = 6×w

w = 4 yd

From the face that has 8 square yards area, we can calculate the height of the solid net:

8 = 4h

h = 2 yd

Volume of the solid net = 6×4×2 = 48 cubic yd

Thus, the volume of the solid figure is 48 cubic yd if the length, width, and height of the solid figure are 6, 4, and 2 yd respectively.

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Answer:

[tex]y = 3\left(x-\dfrac{3}{2}\right)^2+\dfrac{41}{4}[/tex]

Step-by-step explanation:

Given equation:

[tex]y = 3x^2 - 9x + 17[/tex]

Factor out 3 from the first 2 terms:

[tex]y = 3(x^2 - 3x) + 17[/tex]

Divide the coefficient of x by 2 and square it:  (-3 ÷ 2)² = 9/4

Add this inside the parentheses and subtract the distributed value of it outside the parentheses:

[tex]y = 3\left(x^2 - 3x+\dfrac{9}{4}\right) + 17-\dfrac{27}{4}[/tex]

Factor the parentheses and combine the constants:

[tex]y = 3\left(x-\dfrac{3}{2}\right)^2+\dfrac{41}{4}[/tex]

4618 mega liters of water, in 7 years, will be used annually.

Interest is the outlay you pay to borrow money. Interest is often deliberated as an annual percentage of a loan amount.

here, we have,

I=PRT/100

=6740×10/100×7

=674×1×7

=4618

the nearest hundredth is a 4618 this is the answer.

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Answer:

13,134.35 megaliters

Step-by-step explanation:

Plug in 6,740 megaliters for the initial amount, 0.1 for the rate of increase, and 7 years for the time elapsed.

y

= a(1+r)t

y

= 6,740(1+0.1)7 Plug in values

y

= 6,740(1.1)7 Add

y

= 6,740(1.94871…) Simplify

y

= 13,134.35325… Multiply

Round to the nearest hundredth.

13,134.35325… → 13,134.35

To the nearest hundredth, Rockport will use 13,134.35 megaliters of water annually.

Answer:

1,728

Step-by-step explanation:

v = a³

v = 12³

v = 1,728 in³

The line passes through the origin and if it has a constant of variation of 3, so it represents a direct variation , Option A is the correct answer.

When a quantity increases and the other quantity also increases , then those two quantities are said to be in direct variation.

It is asked in the question that which option depicts whether On a coordinate plane, a line goes through points (0, 0) and (1, 3) , represents a direct variation

As it is mentioned in the question that the line passes through the origin and if it has a constant of variation of 3, so it represents a direct variation.

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Answer:

a

Step-by-step explanation:

Answer:

43.8

When you round look at the number after the one your rounding up to. If its greater than 5 round up. If its lower than 5 keep it the same number

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y= \stackrel{\stackrel{m}{\downarrow }}{4}x+6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is 4 and passes through (1 , 6)

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{4}(x-\stackrel{x_1}{1})[/tex]

[tex]y-6=4x-4\implies y=4x\underset{\stackrel{\uparrow }{b}}{+2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

The correct matching of each amount in the situation with the expression that represents it is:

Given that:

We have the situations and expressions that need to be matched such that:

Therefore, considering the situation,

The correct matching is given as:

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Answer:

Circumference = 2 x pi x r

Radius, r = 7/2

Circumference = 2 x 22/7 x 7/2

                         = 22 cm

Answer:

21.99

Step-by-step explanation:

2 times pi times radius