The ratio of dogs to cats at the animal shelter is 4:5. if there are 20 cats, how many dogs are there?

Answer:

[tex]3(x - 2) (x^2 + 3x + 6)\\[/tex]

Step-by-step explanation:

Firstly, divide all parts of the equation by 3:

[tex]3x^3 + 3x^2-36[/tex]

[tex]3(x^3 + x^2-12)[/tex]

Now focus on the equation:

[tex]x^3 + x^2-12[/tex]

We know that the equation can be factored using x so we know that (x +- unknown) is the factor. We need to find the easiest way to factor this, lets find the factors of 12:

1 12

2 6

3 4

1 and 12 won't work so let's try 2 and 6, initially start as a negative 2:

[tex]\frac{ x^3 + x^2 - 12}{x - 2}[/tex] = [tex]x^2 + 3x + 6[/tex]

We can confirm this is simplified by multiplying together:

[tex](x - 2) (x^2 + 3x + 6)[/tex]

[tex]x* x^2 = x^3\\x * 3x = 3x^2\\x * 6 = 6x\\-2 * x^2 = -2x^2\\-2 * 3x = 6x\\-2 * 6 = -12[/tex]

= [tex]x^3 + x^2 - 12[/tex]

Meaning it is simplified.

Now, put the equations together:

[tex]3(x - 2) (x^2 + 3x + 6)\\[/tex]

Hope this helps!

Evaluate the derivative of f(x) at x = 1. I'll use the limit definition:

[tex]\displaystyle \lim_{x\to1} \frac{f(x)-f(1)}{x-1} = \lim_{x\to1} \frac{6x^2-x^3-5}{x-1} = \lim_{x\to1}(-x^2+5x+5) = 9[/tex]

Then using the point-slope formula, the equation of the tangent line to f(x) at the point (1, 5) is

y - 5 = 9 (x - 1)

y = 9x - 4

The equation of "tangent-line" to the curve "y = 6x² - x³" at the point (1, 5) is : y = 9x - 4.

To find the derivative of the function f(x) = 6x² - x³, we differentiate each term with respect to x:

f(x) = 6x² - x³,

f'(x) = d/dx (6x²) - d/dx (x³),

f'(x) = 12x - 3x²,

Now, we need to find f'(1), which means evaluating derivative at x = 1;

f'(1) = 12(1) - 3(1)²,

f'(1) = 12 - 3,

f'(1) = 9,

The slope of tangent-line at point (1, 5) is given by f'(1), which is 9;

Using the point-slope form of equation of line (y - y₁ = m(x - x₁)), where m = slope and (x₁, y₁) is the given point (1, 5);

⇒ y - 5 = 9(x - 1),

Simplify the equation:

⇒ y - 5 = 9x - 9,

⇒ y = 9x - 4,

Therefore, the required equation of tangent-line is y = 9x - 4.

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Answer:

9 x 23.79 = $214.11

Answer:

32

Step-by-step explanation:

36-4

Use Pythagorean theorem

Answer:

B=4

Step-by-step explanation:

Answer:

[tex] - \frac{1}{3} [/tex]

Step-by-step explanation:

[tex] - 3.7 = - 5.4x - 5.5 \\ - 3.7 + 5.5 = - 5.4x \\ 1.8 = - 5.4x \\ \ - \frac{1.8}{5.4} = x = - \frac{1}{3} [/tex]

Answer:

Happy birthday to you

Nobody like you

U look like a an animal go back to the zoo

Step-by-step explanation:

HINDI PO NAKATAWA

Answer:

75 marks

Step-by-step explanation:

one question worth 3 marks

so 25×3=75

Answer:

Isn't it 8000 cubic cm sorry if it's wrong

Answer:

x + 5 + 5x + 10 + 2y = 6x + 2y + 15

Step-by-step explanation:

Group like terms

= x + 5x + 2y + 5 + 10  

Add the number 5 + 10 = 15  

= x + 5x + 2y + 15

Add similar elements x + 5x = 6x  

= 6x + 2y + 15

Have a good day :)

Answer:

b and c are parallel lines

Step-by-step explanation:

Parallel lines have equal slopes

The product of the slopes of perpendicular lines = - 1

Calculate the slopes m of the lines using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, 7 ) and (x₂, y₂ ) = (1, 1 )

[tex]m_{b}[/tex] = [tex]\frac{1-7}{1-6}[/tex] = [tex]\frac{-6}{-5}[/tex] = [tex]\frac{6}{5}[/tex]

Repeat with (x₁, y₁ ) = (7, 10 ) and (x₂, y₂ ) = (2, 4 )

[tex]m_{c}[/tex] = [tex]\frac{4-10}{2-7}[/tex] = [tex]\frac{-6}{-5}[/tex] = [tex]\frac{6}{5}[/tex]

Since slope are equal then line b and line c are parallel lines

Answer:

Step-by-step explanation:

Slope = (change in y)/ (change in x)

          = (13 - 3)/(1 - (-1))

           = (13 - 3)/(1 + 1)

           = 10/2

           = 5

Answer:

50.4

Step-by-step explanation:

38.12 + 12.24 = 50.36

6 is near 10

50.36 = 50.4

YOUR INPUT:

[tex]T-Re^{x}[/tex]

FIRST DERIVATIVE:

 [tex]\frac{d}{dx} [T-Re^{x} ]\\=\frac{d}{dx} [T]-R*\frac{d}{dx} [e^{x} ]\\=0-Re^{x} \\=-Re^{x}[/tex]

Root/zero found at:

[tex]x=ln(\frac{T}{R} )[/tex]

Answer:

=2x+4

Step-by-step explanation:

Let's simplify step-by-step.

5x+4−3x

=5x+4+−3x

Combine Like Terms:

=5x+4+−3x

=(5x+−3x)+(4)

=2x+4

Answer:

2x+4...

Step-by-step explanation:

Hopefully it helps

Answer:

[tex]y=\displaystyle\frac{1}{2} x+\displaystyle \frac{5}{2}[/tex]

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.

Perpendicular lines always have slopes that are negative reciprocals (ex. 1/2 and -2, 3/4 and -4/3)

Determine the slope (m):

[tex]y = 1 -2x[/tex]

Rearrange into slope-intercept form:

[tex]y = -2x+1[/tex]

Now, we can identify clearly that the slope is -2. Because perpendicular lines always have slopes that are negative reciprocals, a perpendicular line would have a slope of [tex]\displaystyle\frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=\displaystyle\frac{1}{2} x+b[/tex]

Determine the y-intercept (b):

[tex]y=\displaystyle\frac{1}{2} x+b[/tex]

Plug in the given point (1,3) and solve for b:

[tex]3=\displaystyle\frac{1}{2} *1+b\\\\b=\displaystyle \frac{5}{2}[/tex]

Therefore, the y-intercept is [tex]\displaystyle \frac{5}{2}[/tex]. Plug this back into [tex]y=\displaystyle\frac{1}{2} x+b[/tex]:

[tex]y=\displaystyle\frac{1}{2} x+\displaystyle \frac{5}{2}[/tex]

I hope this helps!

Answer:

260 Meters Below the Surface

Step-by-step explanation:

"Dove 450 meters" = - 450

"Climbed 270 meters" = +270

"Dove 80 meters more" = - 80

-450+270-80

-180-80

-180+(-80)

-260 or 260 Meters Below the Surface

9514 1404 393

Answer:

  3.5 hours

Step-by-step explanation:

The separation distance is increasing at the rate of 20 mph + 60 mph = 80 mph. It will be 280 miles after ...

  time = distance/rate

  time = (280 mi)/(80 mi/h) = 3.5 h

The two cars will be 280 miles apart after 3 1/2 hours.

Cost  $425.00

Markup  200 %

Revenue  $1,275

Profit  $850

To find markup percentage, businesses use the markup percentage formula:

Markup Percentage = (Markup / Cost) x 100% Determine markup. Markup is the difference between selling price and cost:

Markup = Selling Price - Cost. Divide markup by cost. ...

Markup Percentage = (Markup / Cost) Convert to a percentage.

Answer is:

a=4, b=6 c=5

Answer:

$44.04

Step-by-step explanation:

let 3 be the number of people and 14.68 the person owes

3*14.68 = 44.04

Using the normal distribution, we have that:

a) The sketch of the situation is given at the end of this answer.

b) The probability is:

[tex]P(2.8 \leq X \leq 7) = 0.8284[/tex]

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Item a:

The part between 2.8 and 7 years is shaded on the sketch given at the end of this answer.

Item b:

The probability is the p-value of Z when X = 7 subtracted by the p-value of Z when X = 2.8, thus:

X = 7:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{7 - 4.1}{1.3}[/tex]

[tex]Z = 2.23[/tex]

[tex]Z = 2.23[/tex] has a p-value of 0.9871.

X = 2.8:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.8 - 4.1}{1.3}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a p-value of 0.1587.

0.9871 - 0.1587 = 0.8284, thus:

[tex]P(2.8 \leq X \leq 7) = 0.8284[/tex]

A similar problem is given at https://brainly.com/question/25151638

Answer:

16 = 16

Step-by-step explanation:

Cross multiplying is when you multiply the numerator and denominator of two fractions.

So, it would be 4 × 4 = 8 × 2 or 16 = 16. This is essentially proving they are equal to one another.

Hope this helps.

Answer:

Step-by-step explanation:

Similar triangles given:

The ratio of corresponding sides:

Answer:

1/2

hope this helps

Answer:

1/2

Step-by-step explanation:

7/18   is close to 1/2

9514 1404 393

Answer:

  D. 5 < x < 9

Step-by-step explanation:

The third side cannot be any shorter than the difference of the other two sides: 7 -2 = 5. It cannot be any longer than the sum of the other two sides: 7+2 = 9. It cannot be equal to either of those values. So, we must have ...

  5 < x < 9

Answer:

1/36

Step-by-step explanation:

So what you have to do is take all the numbers on the dice. Getting a 4 would be a 1 in 6 (1/6) chance, but then you take the risk of rolling again and trying to get another 4. Nothing changes with the amount of sides, so it would just be another 1/6 change to get the 4. Then, you have to multiply the two changes together. SO 1/6 x 1/6 = 1/36. It is a 1/36 chance to role a 4 on both roles.

The probability of an event is a number between  [tex]0[/tex] and [tex]1[/tex]. Hence, the probability of showing a [tex]4[/tex] on both the rolls is [tex]\frac{1}{36}[/tex].

What is probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between  [tex]0[/tex] and [tex]1[/tex].

The probability of the first throw  [tex]4[/tex] is [tex]\frac{1}{6}[/tex].

And on the second throw is [tex]\frac{1}{6}[/tex].

For both, the throws probability [tex]4[/tex] would be

[tex]\frac{1}{6}[/tex]×[tex]\frac{1}{6}[/tex][tex]=\frac{1}{36}[/tex]

Hence, the probability of showing a [tex]4[/tex] on both the rolls is [tex]\frac{1}{36}[/tex].

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Answer:

EZ answer 9+10=21

Step-by-step explanation: