Write the equation of the line that passes through (–1, 5) and has a slope of 3 in point-slope form.

The difference is [tex]\( \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \)[/tex].

To subtract the two rational expressions [tex]\( \frac{5x}{x^2-x-6} \) and \( \frac{4}{x^2+4x+4} \)[/tex], we need to find a common denominator.

First, factor the denominators:

1. x²-x-6 = (x-3)(x+2)

2. x²+4x+4 = (x+2)²

The common denominator will be (x-3)(x+2)(x+2).

Now, rewrite the expressions with the common denominator:

1. [tex]\( \frac{5x}{(x-3)(x+2)} \)[/tex]

2. [tex]\( \frac{4}{(x+2)^2} \)[/tex]

To subtract, the numerators remain the same, so the expression becomes:

[tex]\[ \frac{5x}{(x-3)(x+2)} - \frac{4}{(x+2)^2} \][/tex]

To combine the fractions, we need to rewrite the first fraction with the common denominator:

[tex]\[ \frac{5x(x+2)}{(x-3)(x+2)(x+2)} - \frac{4(x-3)}{(x-3)(x+2)(x+2)} \][/tex]

Now, we can subtract the fractions:

[tex]\[ \frac{5x(x+2) - 4(x-3)}{(x-3)(x+2)(x+2)} \\\[ = \frac{5x^2 + 10x - 4x + 12}{(x-3)(x+2)(x+2)} \\\[ = \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \][/tex]

So, the difference is [tex]\( \frac{5x^2 + 6x + 12}{(x-3)(x+2)(x+2)} \)[/tex].

To find the difference between the two rational expressions, we first need to factorize the denominators and simplify where possible. Let's break it down step by step:

1. Factorize the denominators:

[tex]\(x^2 - x - 6 = (x - 3)(x + 2)\) \(x^2 + 4x + 4 = (x + 2)^2\)[/tex]

2. We rewrite the expressions with common denominators:

  [tex]\(\frac{5x}{(x - 3)(x + 2)} - \frac{4}{(x + 2)^2}\)[/tex]

3.  To simplify these, we need a common denominator, The least common denominator is [tex]\((x - 3)(x + 2)^2\).[/tex], so to get it, we multiply (x + 2) with Expression 1 and  (x - 3) with Expression 2 on both numerator and denominator. We get:

  [tex]\(\frac{5x(x + 2)}{(x - 3)(x + 2)^2} - \frac{4(x - 3)}{(x - 3)(x + 2)^2}\)[/tex]

4. We combine the fractions:

[tex]\(\frac{5x(x + 2) - 4(x - 3)}{(x - 3)(x + 2)^2}\)[/tex]

  [tex]\(= \frac{5x^2 + 10x - 4x + 12}{(x - 3)(x + 2)^2}\) \(= \frac{5x^2 + 6x + 12}{(x - 3)(x + 2)^2}\)[/tex]

So, the difference between the two rational expressions is [tex]\(\frac{5x^2 + 6x + 12}{(x - 3)(x + 2)^2}\).[/tex]

About 2 hours

(About 2 hours and 25 minutes exactly)

I added minutes anyways

260 divided by 95 = 2 Remainder 25

                                 Hrs                  Mins

D. Shifted 4 units left and 2 units down

The answer to your problem is d.

Answer:

Center: (0,0)

Radius: [tex]r=\sqrt{10}[/tex]

Step-by-step explanation:

The given circle has equation

[tex]10x^2+10y^2=100[/tex]

In order to complete the square, we must make sure the coefficient of the quadratic terms are unity.

We divide through by 10 to obtain;

[tex]x^2+y^2=10[/tex]

The coefficient of the linear terms of both variables are zero.

Therefore the equation can be rewritten as;

[tex](x-0)^2+(y-0)^2=10[/tex]

Comparing to [tex](x-h)^2+(y-k)^2=r^2[/tex]

We have (h,k)=(0,0) to the center of the circle and [tex]r=\sqrt{10}[/tex] to be the radius of the circle.

Answer:

Equation: x²  + y² = 10

center = (0, 0)

  radius = √10

Step-by-step explanation:

The general equation of a circle is ;

(x - a)²  + (y - b)² = r²

Where (a, b) is the coordinate of the center of the circle, and r is its radius.

Where the center is (0,0), the equation becomes,

x²  + y² = r²

In our case we have;

10x² + 10y² = 100

dividing both side by ten,

x²  + y² = 10

∴ center = (0, 0)

  radius = √10

Martha walked for 0.67 hours.

Here's how we can calculate it:

Total time spent hiking:

12:30 AM - 11:30 PM = 1 hour (since 12:30 AM is midnight and the same as 00:30 AM)

Convert hours to minutes: 1 hour * 60 minutes/hour = 60 minutes

Time spent running:

Subtract the walking time from the total time: 60 minutes - 20 minutes = 40 minutes

Convert running time to hours:

Divide minutes by minutes per hour: 40 minutes / 60 minutes/hour = 0.67 hours

Therefore, Martha walked for 0.67 hours.

Question

If Martha went on a hiking trip at 11:30 PM, and walked for 20 minutes, and ran the rest, and came back at 12:30 AM, how many hours did Martha WALK?

The equation x + y = 10 represents a linear relationship that spans all real numbers in both x and y directions. Thus, the domain and the range for this function are both all real numbers.

The equation for the set F is x + y = 10, which is a straight line on a graph. This line extends infinitely in both directions, meaning that there is no restriction on the possible values of x (the domain) and y (the range). Therefore, the correct answer for both domain and range would be 'All Real Numbers'.

To visualize this, imagine you plug in any number for x and solve the equation for y. Similarly, you can do the same, guessing a y-value and solving for x. No matter the number chosen, there will always be a corresponding number on the other side, whether positive, negative, or zero.

Remember that a domain is the set of all inputs (or 'x' values) that a function can accept, and a range is the set of all possible outputs (or 'y' values) that the function can produce. In this example, the function can handle and generate all real numbers, so its domain and range are all real numbers.

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Answer:

D

Step-by-step explanation:

The surface area of the rectangular prism is the sum of all the 6 faces.

Area = 2 (3*3.4) = 20.4

Area = 2 (3*4.1) = 24.6

Area = 2 (3.4*4.1) = 27.88

Thus, Surface Area = 20.4 + 24.6 + 27.88 = 72.88 ft ^2

Answer:

The correct answer option is D. 72.88 ft^2.

Step-by-step explanation:

We are given a diagram of a rectangular prism with width 3 ft, length 3.4 ft and height 4.1 ft and we are to find its surface area.

We know that the surface area of a rectangular prism is given by:

[tex]2(wl \times hl \times hw)[/tex]

So substituting the given values in the above formula to get:

Surface area of rectangular prism = [tex]2[(3 \times 3.4) + (4.1 \times 3.4) + (4.1 \times 3)][/tex] = 72.88 ft^2

The number of students not eating salads and sandwiches are 9

According to the BODMAS rule, the brackets have to be solved first followed by powers or roots (i.e. of), then Division, Multiplication, Addition, and at the end Subtraction. Solving any expression is considered correct only if the BODMAS rule or the PEMDAS rule is followed to solve it.

Given here: 3/8 of the students in the cafeteria eat salads and 1/4 of the students eat sandwiches.

∴3/8×24+1/4×24=9+6

                          =15

Thus the number of students eating lunches other than salads or sandwiches are 24-15=9

Hence, The number of students not eating salads and sandwiches are 9

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Answer:

The volume of a rectangular prism is [tex]28\frac{7}{8}\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

[tex]V=BHL[/tex]

Convert the given dimensions to an improper fractions

[tex]B=3\frac{1}{2}\ cm=\frac{3*2+1}{2}=\frac{7}{2}\ cm[/tex]

[tex]H=1\frac{1}{2}\ cm=\frac{1*2+1}{2}=\frac{3}{2}\ cm[/tex]

[tex]L=5\frac{1}{2}\ cm=\frac{5*2+1}{2}=\frac{11}{2}\ cm[/tex]

substitute in the formula

[tex]V=(\frac{7}{2})(\frac{3}{2})(\frac{11}{2})=\frac{231}{8}\ cm^{3}[/tex]

Convert to mixed number

[tex]\frac{231}{8}=\frac{224}{8}+\frac{7}{8}=28\frac{7}{8}\ cm^{3}[/tex]

Answer:

t = 1

Step-by-step explanation:

Formula

i = prt

Givens

P = 500

i = 25

r = 5% = 5/100

t = ?

Solution

25 = 500 * 5/100 * t       Cancel out 100 on the right

25 = 5*5*t                        Combine the right

25 = 25 * t                       Divide by 25

25/25 = 25*t/25              

t = 1

Answer:   " 1 year . "

_________________________________________________

Step-by-step explanation:

_________________________________________________

Use the formula/equation:

        I = Prt ;   that is;  " I = P × r × t "  ;

in which:  

" Interest (in dollars) =

     Principal amount ("P" ; in dollars) * r ["rate"]   *  time ("t", in years) ]  ;

Note: the rate, "r" ; refers to the interest rate.

We wish to solve for the "time, "t" .

_________________________________________________

 I = Prt ;

_________________________________________________

Let us isolate "t" one one side of the equation;

    by rearranging the formula;

We know:  I = Prt   ;

Divide each side of the equation by "Pr" :

I/ (Pr) = [ (Prt) / (Pr) ]  ;

to get:

I / (Pr) = t ;

↔  t = I (P * r ) ;

Now, plug in our given values, and solve for "t" ; time, in years.

Given:  P = 500 (dollars) ;

            I  = 25 (dollars) ;  

           r = 5% ;  Note, for the purposes of this formula; we write this as a "decimal" ;

           r = 5% = 5/100 = 0.05 ;

_________________________________________________

 t  =  I / (P * r)  ;

t = 25  / (500 * 0.05) ;

t =  25 / (25) ;

t = 1  yrs.

_________________________________________________

Hope this helps!

 Best wishes in your academic pursuits

        — and within the "Brainly" community, as well!

_________________________________________________

Answer:

6

Step-by-step explanation:

Given equation is [tex]f(x)= x(x+1)^2 (2x-3)(x+2)^2[/tex].

Now we need to find about what is the degree of the give function.

We know that degree of polynomial function is the highest exponent of the variable (x).

So we can either expand the whole equation or count the degree of each factor then add those to get the degree of the given function.

Second choice will be easier.

Degree of [tex]x[/tex] = 1

Degree of [tex](x+1)^2[/tex] = 2

Degree of [tex](2x-3)[/tex] = 1

Degree of [tex](x+2)^2[/tex] = 2

Hence degree of the given polynomial function = 1+2+1+2=6

Answer:

Step-by-step explanation:

[tex]\dfrac{5^{11}}{5^x}=5^4\qquad\text{multiply both sides by}\ 5^x\\\\5^{11}=5^4\cdot5^x\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\5^{11}=5^{4+x}\iff11=4+x\qquad\text{subtract 4 from both sides}\\\\11-4=4-4+x\\\\7=x\to x=7[/tex]

Answer: OPTION B

Step-by-step explanation:

 Use the following formula:

[tex]SA=\frac{pl}{2}+B[/tex]

Where p is the perimeter of the base, l is the slant height and B is the area of the base.

The perimeter is:

[tex]p=6*s=6*3m=18m[/tex]

Where s is the lenght of a side.

The slant height is given:

[tex]l=6,2m[/tex]

The area of the base is:

[tex]B=\frac{3\sqrt{3}s^2}{2}=\frac{3\sqrt{3}(3m)^2}{2}=23.382m^2[/tex]

Where s is the length of a side.

Substitute values. Then, the result is:

[tex]SA=\frac{(18m)(6.2m)}{2}+23.382m^2=79.18m^2[/tex]

Answer:

The correct answer option is B. 79.18 m^2.

Step-by-step explanation:

We are given a diagram of a regular hexagonal pyramid with height 5.6 m, slant height 6.2 m and base edge length 3m.

We know that the surface area of a regular hexagonal pyramid is given by:

[tex]\frac{PI}{2} +B[/tex]

where P = perimeter of the base, I = slant height and B = base area.

Perimeter of base = [tex]3 \times 6[/tex] = 18 m^2

Base area (area of hexagon) = [tex]\frac{3\sqrt{3} }{2} a^2[/tex] =  [tex]\frac{3\sqrt{3} }{2} 3^2[/tex] = 23.38 m^2

Surface area of hexagonal pyramid = [tex]\frac{18 \times 6.2}{2} +23.38[/tex] = 79.18 m^2

Answer:

26 is the answer

Step-by-step explanation:

well, in the election, the losing candidate received 10200 votes, and we know that's 30% of the whole votes cast, le's say the whole amount is "x" or namely 100%.

B)

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 10200&30\\ x&100 \end{array}\implies \cfrac{10200}{x}=\cfrac{30}{100}\implies \cfrac{10200}{x}=\cfrac{3}{10} \\\\\\ 102000=3x\implies \cfrac{102000}{3}=x\implies 34000=x[/tex]

A)

Dorian's 3060 is really 30% of 10200, however, the losing candidate received 30% of the total votes cast, and that is 10200, so Dorian mistakenly is using 30% of the 30% received by the losing candidate as point of reference for her total.

Final answer:

Dorian's claim is incorrect because dividing 10,200 votes by 30% (or 0.30) gives 34,000 votes, which is the correct total number of votes cast in the mayoral election. Therefore, the calculation shows that the total votes are much higher than Dorian's claim of 3,060 votes.

Explanation:

A. Dorian's claim that the total number of votes cast in the mayoral election was 3,060 is not reasonable because if the losing candidate received 10,200 votes which represented 30%, then the total votes should be much higher than 3,060. To find the total, you would divide the number of votes the candidate received by the percentage they represent.

B. To find the total number of votes cast in the mayoral election, you would set up the equation 10,200 = 0.30 * Total Votes. Dividing 10,200 by 0.30 gives the total number of votes cast, which is 34,000.

Equation: Total Votes = 10,200 votes / 0.30 = 34,000 votes

Answer: the answer is D

Step-by-step explanation: there is 8 different strands of outcomes

Answer: D, or 8.

Step-by-step explanation: The first part is a pretty simple win or lose diagram.

That's two possibilities.

The next choice has both Win, both Lose, Lose-Win, or Win-Lose.

That's four possibilities.

The next and last choice is the following: All Win, All Lose, Win-Win-Lose, Lose-Lose-Win, Lose-Win-Win, Win-Lose-Lose, Win-Lose-Win, and Lose-Win-Lose. That leaves a total of 8 combinations.

Answer:

(x-3)²

Step-by-step explanation:

x²-6x+9

x² can be written as (x)²

9 can be written as 3²

(x)²-6x +(3)

we can break 6x as 2(3)(x)

by using square formula

(a+b)²= a²-2ab+b²

Putting all the values back in expression we get

(x)²-2(3)(x)+(3)²

by closing formula we get

(x-3)²

Answer:

(x-3)2

Step-by-step explanation:

i took the test

Answer:

It is the famous Pythagorean theorem which is this equation:

a^2 + b^2 = c^2,

where a and b are the legs and c is the hypotenuse.

Answer:

Pythagorean theorem

Step-by-step explanation:

Answer:

so A = 45degrees because tan^-1(1) = 45 and c = 30 because the half triangle is a 30-60-90 triangle so d = 105

Since its a 30-60-90 triangle and you know that one of the sides is 6, you can now infer that the rest of the sides are 8, and 10.

Also using the 6 side you can use a 3-4-5 triangle by dividing 6 by 4 wich equals 1.5 then multiply that by 3 to get the other sides by using Pythagorean therom. so the sides are 10, 7.5 and 12.5 witch gives you the bas and since area = 1/2bh area= 1/2(12.5 times 6)= 37.5

A = 37.5

milk went up to a $1.20

Answer:

The rate of change in price is

$0.2 per year

Step-by-step explanation:

This problem bothers on rates

Given data

Initial price of milk = $2.7

Final price of milk = $3. 5

Time duration = 4 years

Hence the rate of the change of price can be estimated as follows

= Δ in price/Δin time

= (Final price - initial price)/4

=3.5-2.7/4

=0.8/4

=$0.2 per year

Your answer is D. 2 seconds because her distance from the floor is consistent. Every push-up is 2 seconds apart, therefore it’s D.

Answer:

Answer: 572

Step-by-step explanation:

Answer:

23°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

3x + 1 +2x - 3 + 9x = 180 ( simplify left side )

14x - 2 = 180 ( add 2 to both sides )

14x = 182 ( divide both sides by 14 )

x = 13

The 3 angles are

3x + 1 = (3 × 13) + 1 = 39 + 1 = 40°

2x - 3 = (2 × 13) - 3 = 26 - 3 = 23° ← smallest angle

9x = 9 × 13 = 117°

To solve divide both sides by 4 to cancel out the 4 on the x side to get x alone. Then just do -10/4. That gives you 2.5 so (X=2.5). Hope I helped and have a great day and night

Answer:

-5/2

Step-by-step explanation:

We start with 4x = -10 and want to solve this for x.

We divide both sides by 4 (which isolates x), obtaining:

x = -10/4

and then we reduce this to x = -5/2.

Answer:

b

Step-by-step explanation:

Answer:

4.422, 4.769, 4.904

Step-by-step explanation:

Answer:

LEAST: 4.422

AVERAGE: 4.769

GREATEST: 4.904

I HOPE THIS HELPED !!

Unfilled circle on 3, filled circle on 0, line connecting the circles.

•—————o

0 3

The values of x that have the absolute value less than 3 are plotted in the figure attached.

The number line should be represented in the straight line that have the zero point in the middle, having the positive and negative numbers that should be listed on the other side.

Given that to plot all values of x that have the absolute value less than 3,

It can be written as |x| ≤ 3

We can say that,

The values of x that have the absolute value greater than 3 are -3 and 3. It should be located into the equal intervals.

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➷ It would be y + 23

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

The algebraic expression for 23 more than y is y + 23

An algebraic expression usually shows the relationship between a variable and a whole number with its arithmetic operations.

In the given question,

Now when y is more than 23, we have the algebraic expression for 23 more than y as:

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Answer:

No, because the median test score decreased 5 points.

Step-by-step explanation:

The middle line is is the median so, if the pre-test is 60 and the post-test is 55 then there is a 5 point difference.

Answer:

-61

Step-by-step explanation:

-42-34=-76= -61