What is the equation of a line that passes through the point (-4, 3) and has a slope of 1/2 ?

A
y=xm −5 1/2

B
y=12x −2 1/2

C
y=1/x m +1

D
y= 1/2x+5

There will be 12 slices of pizza left over, which can be expressed as 3/2 or 1 1/2 slices in fraction form.

To find out how much pizza will be left over, we need to calculate the total number of slices available and subtract the number of slices consumed by the players.

Given that there are six pizzas and each pizza has eight slices, the total number of slices available is 6 pizzas * 8 slices/pizza = 48 slices.

Since there are 36 players on the team, and each player has one slice, the total number of slices consumed is 36 slices.

To determine the remaining slices, we subtract the consumed slices from the total available slices: 48 slices - 36 slices = 12 slices.

Therefore, there will be 12 slices of pizza left over.

To express this as a fraction, we can write it as 12/1, which simplifies to 12. This means there will be 12 whole slices of pizza left over.

If you would like to express it as a fraction in its simplest form, you can write it as 12/8. By dividing both the numerator and denominator by their greatest common divisor, which is 4, we get 3/2. So, in fraction form, there will be 3/2 or 1 1/2 slices of pizza left over.

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The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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Answer:

The first tank contains

486 gal - (4 gal/week) t

gal of water after t weeks.

Similarly, the second tank contains

648 gal - (7 gal/week) t

gal of water.

The tanks hold the same amount of water when these two amounts are equal:

486 gal - (4 gal/week) t = 648 gal - (7 gal/week) t

(7 gal/week) t - (4 gal/week) t = 648 gal - 486 gal

(3 gal/week) t = 162 gal

t = (162 gal) / (3 gal/week)

t = 54 weeks

Step-by-step explanation:

Answer:

-33/6

Step-by-step explanation:

20+6x+20 = 22-3(5)

40+6x = 7

6x = -33

x = -33/6

9514 1404 393

Answer:

  k = 10

Step-by-step explanation:

The exterior angle is equal to the sum of the remote interior angles.

  115° = (4k +5)° +(6k +10)°

  115 = 10k +15 . . . . . . . . . . . divide by °, simplify

  100 = 10k . . . . . . . . . . . . subtract 15

  10 = k . . . . . . . . . . . . . . divide by 10

Total amount after three years

=  $8.360  

Explanation:

Given -

Principal amount  

p  = $.8,000

Rate of interest  

r  =  1.5%

Duration  

n  =  3 years

Total amount after three years = Principal amount + Interest amount

Total amount after three years

=  p +  (pnr)  = 8000  +  (8000×1.5100×3)  =  8000  +  360  =  $8.360

Total amount after three years

=  $8.360

Answer:

$8.360

Step-by-step explanation:

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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Answer:

False

Step-by-step explanation:

from *millermoldwarp*

"Events are called dependent when the probability of an event depends on the occurrence of another. When event A depends on event B, the probability that A occurs, given that B has occurred, is different from the probability that A occurs only ."

hopes this helps

Answer:false

Step-by-step explanation:

Answer: \(4m^{6}\)

Step-by-step explanation:

\(\frac{8.4m^{9} n^{5} }{2.1m^{3}n^{5}}\)

Dividing exponents is the same as subtracting the exponents, so

\(\frac{m^{9}}{m^{3}} =m^{9-3}=m^{6}\)

\(\frac{n^{5}}{n^{5}} =n^{5-5}=n^{0}=1\)

So now our equation looks like

\(\frac{8.4m^{6}}{2.1}\)

Now we can divide the numbers

8.4/2.1 = 4

So your final answer is \(4m^{6}\)

Answer:

Step-by-step explanation:

You want the reciprocal function of f(x) = 5x² +13x -6 and the equations of its vertical asymptotes. You also want the graph of f(x) = ((x +4)(x -5))/(x² +2x-8) along with its domain, range, and intervals of positive, negative, increase, and decrease.

The reciprocal function will be ...

 1/f(x) = 1/(5x² +13x -6)

Its vertical asymptotes will be found where f(x) = 0. Those values of x are nicely found by factoring the function.

  f(x) = 5x² +13x -6 = (5x +15)(5x -2)/5 = (x +3)(5x -2)

The product of factors will be zero when one of the factors is zero.

  x +3 = 0   ⇒   x = -3

  5x -2 = 0   ⇒   x = 2/5

The equations of the vertical asymptotes are x = -3 and x = 2/5.

The function can be simplified by factoring the denominator anc cancelling common factors:

  \(f(x)=\dfrac{(x+4)(x-5)}{x^2+2x-8}=\dfrac{(x+4)(x-5)}{(x+4)(x-2)}=\dfrac{x-5}{x-2}\quad x\ne -4\)

The function changes sign where the factors are zero, at x = 2 and x = 5. It is approaches the horizontal asymptote y = 1 for large positive or negative values of x, and is increasing everywhere it is defined. There is a vertical asymptote at x = 2, and a "hole" at x = -4 where the numerator and denominator factors canceled, but the function remains undefined. The function can take on any value except those at the horizontal asymptote and the "hole".

Domain, Increasing

The function is increasing everywhere it is defined, so the "increasing" intervals and the domain are the same:

  (-∞, -4) ∪ (-4, 2) ∪ (2, ∞) . . . .  . domain, intervals of increase

The function has no intervals of decrease.

Negative, Positive, Range

The function is positive everywhere it is defined, except for the interval between sign changes.

  negative: (2, 5)

  positive: (-∞, -4) ∪ (-4, 2) ∪ (5, ∞)

  range: (-∞, 1) ∪ (1, 1.5) ∪ (1.5, ∞)

Answer:

D

Step-by-step explanation:

as x → 2 , the denominator is x - 2 = 2 - 2 = 0

this makes f(x) undefined

to overcome this , factor the numerator , that is

f(x) = \(\frac{x^2+x-6}{x-2}\) = \(\frac{(x+3)(x-2)}{x-2}\) ( cancel x - 2 on numerator/ denominator )

f(x) = x + 3

then as x → 2

f(2) → 2 + 3 → 5

Answer:

186000km in 6 hours

Step-by-step explanation:

Multiply the 2 numbers please put brainliest

Answer:

1.86 x 10⁵km

Step-by-step explanation:

31000 km in one hour x 6 hours = 186,000km/6 h

Answer:

? = 77°

Step-by-step explanation:

the 3 angles in a triangle sum to 180° , that is

? + 35° + 68° = 180°

? + 103° = 180° ( subtract 103° from both sides )

? = 77°

Answer:77

Step-by-step explanation:

180-103=77

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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Answer:

L x W (original)

(L+3) x w     (one dimension changed)

(L+3)(W+3)   (both dimensions changed)  

Step-by-step explanation:

Rectangle when one dimension increase 3 units, area will change from original (L and w are its two sides)

L x W to (L+3) x w

If both dimension increase 3 units, the area will become

(L+3)(W+3)

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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Answer:

8x-6y

Step-by-step explanation:

(3x-2y)+(5x-4y)

put like terms together

(3x+5x)+(-2y-4y)

add together

8x           -6y

put together

8x-6y

Answer:

C(M) = 0.65*M + 22.55

Step-by-step explanation:

We know that the cost to rent and drive for M miles is given by:

S(M) = 0.40*M + 17.75

And the insurance, also a function of M, is given by:

I(M) = 0.25*M + 4.80

We want to find the equation of the total cost for a rental that includes insurance.

This would be just the sum of the two above functions:

C(M) = S(M) + I(M)

C(M) = (0.40*M + 17.75) + (0.25*M + 4.80)

Now we just need to simplify this:

Taking M as a common factor, we get:

C(M) = (0.40 + 0.25)*M + 17.75 + 4.80

C(M) = 0.65*M + 22.55

Then the total cost equation, as a function of M, is given by:

C(M) = 0.65*M + 22.55

Answer:(-(3x^(3)-x-1))/((x^(2)+1)^(2))

Answer:

a

Step-by-step explanation:

Both the exponential and logarithmic functions tend to infinity.

A. The solution to the system of equations is x = 1/2, y = -1.

B. The solution to the system of equations is x = 1/2, y = -1.

C. The solution to the system of equations is x = 215/81, y = -175/81.

D. The solution to the system of equations is x = 215/81, y = -175/81.

A. To solve the system of linear equations:

3x - y = -11 ... (1)

-x + y = 5 ... (2)

Add equations (1) and (2) to eliminate y:

2x = -6

x = -3

Substitute x = -3 into equation (2) to solve for y:

-(-3) + y = 5

y = 8

Therefore, the solution to the system of equations is x = -3, y = 8.

To check the solution, substitute x = -3 and y = 8 into both equations and verify that they are true:

3(-3) - 8 = -11

-(-3) + 8 = 5

Both equations are true, so the solution is correct.

B. To solve the system of linear equations:

-2y + 3 = 4x + 2 ... (1)

6x + 4y = 1 ... (2)

Simplify equation (1) by subtracting 3 from both sides and dividing by 4:

-2y = 4x - 1

y = -2x + 1/2

Substitute y = -2x + 1/2 into equation (2) and solve for x:

6x + 4(-2x + 1/2) = 1

-2x + 2 = 1

-2x = -1

x = 1/2

Substitute x = 1/2 into equation (1) to solve for y:

-2y + 3 = 4(1/2) + 2

-2y + 3 = 5

-2y = 2

y = -1

Therefore, the solution to the system of equations is x = 1/2, y = -1.

To check the solution, substitute x = 1/2 and y = -1 into both equations and verify that they are true:

-2(-1) + 3 = 4(1/2) + 2

6(1/2) + 4(-1) = 1

Both equations are true, so the solution is correct.

C. To solve the system of linear equations:

32y - x = -25 ... (1)

5x = 100 + x - 8y ... (2)

Simplify equation (2) by combining like terms:

4x + 8y = 100

Divide both sides of equation (1) by -1:

x - 32y = 25

Add equations (1) and (2) to eliminate x:

5x - 32y = 75

Substitute the simplified equation (2) into the above equation to solve for y:

5(4x + 8y) - 32y = 75

20x + 8y = 75

y = (75 - 20x)/8

Substitute the above value of y into equation (1) to solve for x:

32[(75 - 20x)/8] - x = -25

240 - 80x - x = -25

-81x = -215

x = 215/81

Substitute x = 215/81 into the equation for y:

y = (75 - 20(215/81))/8

y = -175/81

Therefore, the solution to the system of equations is x = 215/81,

y = -175/81.

To check the solution, substitute x = 215/81 and y = -175/81 into both equations.

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Answer:

The graph of g(x) = |x - h| + k is a translation of h units horizontally and k units vertically of the graph of f(x) = | x |.

Hope this helps.

Answer:

H units horizontally, k units vertically

Step-by-step explanation:

Answer:

Step-by-step explanation:

Perimeter of a rectangular wall P = 2L+2W

L is the length of the wall

W is the width

Given

P = 148feet

If the width is two more than seven times the length, this is represented as

W = 7L+2

Substitute W = 7L+2 into the formula above

P = 2L + 2(7L+2)

P = 2L +14L+4

P == 16L+4

148 = 16L+4

16L = 148-4

16L = 144

L = 144/16

L = 9

To get the width

W = 7L+2

W = 7(9)+2

W = 63+2

W = 65feet

Hence the width of the rectangular wall is 65feet

Answer:

If you get tax you should know the details of the what the tax is FOR

Step-by-step explanation:

Not enough details in question

Answer:

Step-by-step explanation:

Since the person earns over $30,000, they will be charged 20% on $30,000 plus 40% on ($47,000−$30,000)=$17,000. Hence the total amount of tax that they'd need to pay under the proposal is

Total Income Tax=$30,000×20%+$17,000×40%=$30,000×20100+$17,000×40100=$6,000+$6,800=$12,800.

55-15=40

40÷10=4

There is one adult and 4 children going to the movies

Answer:

8

Step-by-step explanation:

let x be the number , then

\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )

3x = 108 ( divide both sides by 3 )

x = 36

the number is 36, so

\(\frac{2}{9}\) × 36 = 2 × 4 = 8

The two ninths of the number is 8

We know that Three quarters of a number is  \(\frac{3}{4}\)  times of a number

Hence we will assume the number x ,

                     \(\frac{3}{4} of x = 27\)

                     \(x = 27 X \frac{4}{3}\)

                       \(x = 36\)

Now as we know the number is 36

Therefore , the two ninths of the number assumed as y

We will multiply the number 36 by 2 and then divide by 9

Hence,

                           \(y = 36 X \frac{2}{9}\)

                               \(y = 8\)

Thus, the two ninths of the number 36  is 8                            

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Answer:

Y=-6+2x

Step-by-step explanation:

So Since the tivne equation is 6x-3y=18, Isolate y Because we’re finding the variable y not x

So First subtract 6x on both sides (it doesn’t have to be the same number when subtracting like what they taught you in middle school, but you can’t combine those two since their different terms)

-3y=18-6x

Now divide -3 on both sodes to isolate Y

y=18-6x/-3

Simplify

y=-6+2x

If it’s not then i would need x the variable.

The solution to the questions are:

From the question, we have the following parameters that can be used in our computation:

Length = 350 - 2x

Width = x

The area of a rectangle is the product of its dimensions

So, we have

Area = Length x Width

Substitute the known values in the above equation, so, we have the following representation

A = (350 - 2x) * x

Evaluate

A = 350x - 2x²

Differentiate and set to 0

350 - 4x = 0

So, we have

4x = 350

Divide by 4

x = 87.5

Recall that

Length = 350 - 2x

So, we have

Length = 350 - 2 x 87.5

Evaluate

Length = 175

The area is then calculated as

Area = Length x Width

So, we have

Area = 175 x 87.5

Evaluate

Area = 15312.5 square meters

Hence, the area is 15312.5 square meters

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Answer:

hey

Step-by-step explanation: