Which is a better buy?

2-cup carton of pineapple juice for $1.04

Or

2-quart carton of pineapple juice for $6.24

Answer:

(-2,-4)

Step-by-step explanation:

in this exercise I have the formula of the parable expressed as:

[tex]y=ax^{2} +bx+c[/tex]

I can write it in its "vertex form"

[tex]y=a(x-d)^{2} +e[/tex] being (d,e) the coordinates of the vertex of said parabola.

by clearing the equation I can see that [tex]d=\frac{-b}{2a}[/tex] so I substitute[tex]d=-\frac{4}{2*1} =-2[/tex]

Now taking d as the value for the x axis of the vertex coordinate, I substitute d in x, in the initial equation

[tex]y=x^{2} +4x =(-2)^{2}+4(-2)=4-8=-4[/tex]

So finally, I have the coordinates of the vertex of the parabola are (-2,-4)

Done

Answer:

(-2, 0), (-3, 0), and (5, 0)

Step-by-step explanation:

The x-intercept is found when y = 0.

So, we have to find x when (x + 2)(x + 3)(x - 5) = 0

We can do that by pulling apart all parts, because if one part = 0, the whole thing will have to be too (multiplication property of identity).

1. When x + 2 = 0, x = -2

2. When x + 3 = 0, x = -3

3. When x - 5 = 0, x = 5

That gives us (-2, 0), (-3, 0), and (5, 0)

Answer:

Step-by-step explanation:

x-intercepts are for

(x + 2)(x + 3)(x - 5) = 0

The product is equal to 0 if one of the factors is equal to 0.

Therefore

x + 2 = 0 or x + 3 = 0 or x - 5 = 9

x + 2 = 0     subtract 2 from both sides

x = -2

x + 3 = 0        subtract 3 from both sides

x = -3

x - 5 = 0              add 5 to both sides

x = 5

Answer: OPTION D

Step-by-step explanation:

To complete the table, you need to substitute the values of "x" given in the table into the quadratic equation [tex]y=x^{2}-x-6[/tex] to obtain the corresponding value of "y".

Then:

When [tex]x=-5[/tex] :

[tex]y=(-5)^{2}-(-5)-6[/tex]

[tex]y=24[/tex]

When [tex]x=-3[/tex] :

[tex]y=(-3)^{2}-(-3)-6[/tex]

[tex]y=6[/tex]

When [tex]x=-1[/tex] :

[tex]y=(-1)^{2}-(-1)-6[/tex]

[tex]y=-4[/tex]

When [tex]x=2[/tex] :

[tex]y=(2)^{2}-(2)-6[/tex]

[tex]y=-4[/tex]

Answer:

Linear Function

[tex]y=4x+18[/tex]

Step-by-step explanation:

Let

x----> the time in hours

y----> the total inches of snow on the ground

we know that

The function that best model this situation is the linear function

so

[tex]y=mx+b[/tex]

In this problem

[tex]m=4\frac{in}{h}[/tex]

[tex]b=18\ in[/tex] ----> the y-intercept

substitute

[tex]y=4x+18[/tex]

Answer:

Linear decreasing function best model this situation and the required function is

f(x)=4x+18

Step-by-step explanation:

It is given that a ski resort has 18 inches of snow on the ground. The snow is falling at a rate of 4 inches per hour.

If a function has constant rate of change, then the it is a linear function.

It the given case the rate of change is constant so linear function best model this situation.

The slope intercept form of linear function is

[tex]f(x)=mx+b[/tex]           ... (1)

where, m is slope and b is y-intercept or initial value.

Ski resort has 18 inches of snow on the ground it means initial value is 18.

The snow is falling at a rate of 4 inches per hour. So, m=4.

Substitute m=4 and b=18 in equation (1).

[tex]f(x)=4x+18[/tex]

Therefore the required function is f(x)=4x+18.

Explanation:

1. The set of points 5 cm from the nearest point on a circle of radius 2 cm will be a circle with a radius 5 cm larger: a circle with a radius of 7 cm.

__

2. The set of points 6 in from the nearest point on a line will be a cylindrical shell 12 inches in diameter centered on the line.

If AB is a line segment, then the shell will have hollow hemispherical ends of radius 6 inches about the end points.

Answer:

The distance between points P1 = (4,2) and P2=(8,5)  is 5.

Step-by-step explanation:

Let P1 = (4,2) and P2=(8,5)

The distance between two points can be found using formula:

[tex]d(P,Q), \sqrt{(x_{2}-x_{1})^2+ (y_{2}-y_{1})^2}[/tex]

where x₁ = 4 , x₂=8, y₁= 2 and y₂ = 5

Putting values in the formula

[tex]=\sqrt{(8-4)^2+(5-2)^2} \\=\sqrt{(4)^2+(3)^2} \\=\sqrt{16+9} \\=\sqrt{25} \\=5[/tex]

So, the distance between points P1 = (4,2) and P2=(8,5)  is 5.

Final answer:

The distance between the points (4,2) and (8,5) can be found using the Pythagorean Theorem. After calculating the squares of the differences in the x and y coordinates and adding them, the square root of the sum gives a distance of 5 units.

Explanation:

The distance between two points in a two-dimensional plane can be calculated using the Pythagorean Theorem. The coordinates of the points provided are (4, 2) and (8, 5). To find the distance, we calculate the difference in the x-coordinates and the difference in the y-coordinates, and then square both values before adding them together. This gives us the distance squared.

The formula is as follows:

d² = (x2 - x1)² + (y2 - y1)²

In this scenario:

d² = (8 - 4)² + (5 - 2)²

d² = (4)² + (3)²

d² = 16 + 9

d² = 25

Finally, we take the square root of the distance squared to get the distance:

d = √25

d = 5

The distance between the points (4,2) and (8,5) is 5 units.

For this problem you must do Pythagorean theorem:

[tex]a^{2} + b^{2} =c^{2}[/tex]

In this example 10ft is c and 7ft is a (or it could be b, and you'll be solving for a instead of b. It's the same thing, since a and b are both legs)

Plug what you know into the equation:

[tex]7^{2} +b^{2} = 10^{2}[/tex]

49 +b^{2} = 100

Bring 49 to the right side by subtracting it:

b^{2} = 51

Now you still must isolate b. The opposite of squaring is taking the square root so take the square root of both sides to cancel it from the left side:

[tex]b =\sqrt{51}[/tex]

b = 7.1414

b ≈ 7 ft

Hope this helped!

Answer:

a =4   b=8 c=-8

y-value of vertex =

ah^2 + bh + c

where h = -b/2a

h= -8/8 =-1

y-value of vertex =

4(-1)^2 + 8*-1 -8

4 -8 -8

y value of vertex = -12

Step-by-step explanation:

Answer:

the first year 8

the second 16

the third 24

hope this helps

give me a five star plz

Answer:

11

Step-by-step explanation:

The x-value -4 is less than 3, so use the first formula for f:  x^2 - 5.

Then f(-4) = (-4)^2 - 5 = 11

3/14

When you multiply two negative numbers together, the negatives cancel each other out and you get a positive answer. So, you can just forget about the negative signs. This leaves us with 1/6 * 9/7.

To multiply a fraction, multiply the numerators together and multiply the denominators together. So, multiply 1 * 9 to get 9, and multiply 6 * 7 to get 42. This means the answer is 9/42.

However, the numerator and denominator share a factor, and that is 3. So, you can divide the numerator and the denominator each by 3 to simplify the fraction to 3/14.

The equation represented by the tape diagram is: 2x + 3 = 5x

This can be solved by subtracting 2x from both sides: 3 = 3x

Dividing both sides by 3 gives the solution: x = 1

Therefore, the equation to solve is: 2x + 3 = 5x

The tape diagram represents the following equation:

2x + 3 = 5x

This can be solved by subtracting 2x from both sides:

2x + 3 - 2x = 5x - 2x

3 = 3x

Dividing both sides by 3 gives the solution:

x = 3 / 3

x = 1

Therefore, the equation to solve is:

2x + 3 = 5x

The solution is:

x = 1

The  equation to solve m is  2/3 = 1/4 + m.

The equation you wrote, 2/3 = 1/4 + m, is indeed correct based on the tape diagram you described.

Here's how to solve it:

Combine fractions:

Get both fractions on the same side of the equation. Subtract 1/4 from both sides:

m = 2/3 - 1/4

Find a common denominator:

The smallest common denominator for 3 and 4 is 12.

Multiply both sides by 12:

12m = 8 - 3

Solve for m: Combine like terms and simplify:

12m = 5

m = 5/12

Therefore, the value of m is 5/12.

If the decimal expansion of pi would end, then it would have to be a rational number, ie pi could be written as a fraction pi = p/q with integers p and q. There are many proofs that this is not the case, but they are all a bit complicated

Pi is an irrational and transcendental number, meaning it never terminates or repeats. Its non-ending and non-repeating nature is reflected in its definition as the ratio of a circle's circumference to its diameter. Pi's transcendence ensures it cannot be expressed by any algebraic equation with rational coefficients.

Understanding the Nature of Pi ( 3.141592653589793237...)

Pi ( 3.14159...) is known to be a non-terminating, non-repeating decimal, which classifies it as an irrational number. This means that no matter how many digits you calculate, Pi will never repeat in a pattern nor end. The number has been calculated to trillions of digits without any repeating pattern emerging.

The non-ending nature of Pi arises from its definition as the ratio of a circle's circumference to its diameter. This ratio is the same for all circles, but it can never be expressed exactly by a fraction or a finite decimal.

Moreover, Ferdinand von Lindemann's proof that Pi is a transcendental number further solidifies that it cannot be the solution of any algebraic equation with rational coefficients, making Pi an essentially complex and infinite entity in mathematics.

Answer:

Step-by-step explanation:

The first question is true. In order for a relation to be a function, it has to have only one x value for every y value. y = 3x - 5 is a straight line, so it doesn't share any x values with any y values. In other words, each x value in that graph will not be "used" more than once. Also, the function will pass the vertical line test. this means that if you draw a perfectly vertical line through the function ANYWHERE it will only go through the function at a single point.

The second question is false. There are several different types of functions that come to mind right away, besides a straight line. There's a parabola, which opens up like a "u" (at least the positive one does!), an absolute value function, a cubic function, an exponential function, a log function...

Hope that helps!

Answer:

90

Step-by-step explanation:

sa- is 113.04 i think

[tex]\bf \textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} r=6 \end{cases}\implies SA=4\pi (6)^2 \\\\\\ SA=144\pi \implies SA\approx 452.39 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} r=6 \end{cases}\implies V=\cfrac{4\pi (6)^3}{3} \\\\\\ V=288\pi \implies V\approx 907.78[/tex]

Hey there! :)

Given the coordinates (1, 4) & (3, 10), we must find the slope, y-intercept, and standard form.

Keep in mind that in order to find the slope, we must use the slope formula, which is : [tex]m = \frac{y_{2-y_{1} } }{x_{2}-x_{1}  }[/tex]

(1, 4) is our first set of coordinates while (3, 10) is our second set. Meaning that for 1 = x1, 4 = y1 while 3=x2, 10 = y2

Using this information, simply plug into our slope formula.

m = (10-4) / (3-1)

Simplify/

m = 6/2 --> 3

Therefore, our slope is 3.

Now, use the point-slope form to figure out what the y-intercept is.

y - y1 = m(x - x1)

Plug in using the above coordinates and our slope, which is 3.

y - 4 = 3(x - 1)

Simplify!

y - 4 = 3x - 3

Add 4 to both sides.

y = 3x + 1

This means that 1 is our y-intercept.

This is also our equation in standard form.

Hope this helped! :)

if we take 72 as the 100%, what is 27 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 72&100\\ 27&x \end{array}\implies \cfrac{72}{27}=\cfrac{100}{x}\implies \cfrac{8}{3}=\cfrac{100}{x}\implies 8x=300 \\\\\\ x=\cfrac{300}{8}\implies x=\cfrac{75}{2}\implies x=37.5[/tex]

To calculate the percentage, divide the part (27) by the whole (72) and multiply by 100, resulting in 37.5%.

Percentage is a way of expressing a portion or fraction of a whole as a value out of 100. It is commonly used to compare relative quantities, represents proportions, or express the relationship between a part and a whole.

The term "percent" comes from the Latin phrase "per centum," which means "per hundred." It signifies that percentages are calculated on a scale of 100.

In practical terms, a percentage represents a fraction of a whole, where the whole is equal to 100%. It allows us to easily compare different quantities and understand their relative sizes or proportions.

To calculate a percentage, you typically divide the part (the specific quantity you want to express as a percentage) by the whole (the total or reference quantity) and then multiply by 100 to obtain the value as a percentage.

To calculate the percentage, you can divide the given number (27) by the total number (72) and then multiply the result by 100. So, to find out what percent 27 is of 72:

(27 ÷ 72) × 100 ≈ 37.5%

Therefore, 27 is approximately 37.5% of 72.

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N = 3 - Y

- You isolate the variable by dividing each side by factors that don't contain any variables what so ever.

- Ouma

Answer:

n = 3 - p

Step-by-step explanation:

Given

14n + 6p - 8n = 18 ← simplify left side

6n + 6p = 18 ( subtract 6p from both sides )

6n = 18 - 6p ( divide both sides by 6 )

n = [tex]\frac{18-6p}{6}[/tex] = [tex]\frac{18}{6}[/tex] - [tex]\frac{6p}{6}[/tex] = 3 - p

Answer:

Step-by-step explanation:

The total number of students is 350 + 50 + 225 + 375 = 1000.

There are 225 students in band only, as well as 50 students in both band and choir.  So there are 275 students in band out of the total of 1000, or 27.5%.

There are 350 students in choir only, as well as 50 students in both choir and band.  So there are 400 students in choir, 50 of whom are also in band.  So the probability is 50/400, or 12.5%.

The probabilities are not the same.

Since the probabilities are not the same, the probability of being in band is affected by whether or not the student is in choir.  So the events are not independent.

The answer is Perpendicular and parallel lines have their line extending in one direction only

Answer:

Perpendicular and parallel lines have their lines extending in one direction only.

Step-by-step explanation:

Just solve.

[tex](17-k)^3\\k=12 \\ \\ (17-12)^3 \\ \\ (5)^3 \\ \\ 125\\[/tex]

[tex]\\\\(5+2n)^5 \\ n=-2 \\ \\ (5+2(-2))^5 \\ \\ (5-4)^5 \\ \\ (1)^5 \\ \\ 1[/tex]

Answer:

$11,480

Step-by-step explanation:

1,400 x 0.9 = 1,260

1,260 x 8 = 10,080

1,400 + 10,080 = 11,480

Answer:

8y+12

Step-by-step explanation:

Answer: x = 4.69/ x = (squareroot) 22

Quadratic Equation: 17 - x² = -5

Subtract 17 from both sides

17 - x² - 17 = -5 - 17

Simplify

-x² = -22

Divide both sides by -1

-x² / -1  =  -22 / -1

Simplify

x² = 22

x = (squareroot) 22 or

x = 4.69

The solutions to the equation are x= √ 22 and x= -√ 22.

The Solving Quadratic Equation given is 17-x²=-5.

First, let's rearrange this equation in a form ax²+bx+c=0.

When rearranged, it reads as: x² - 22 = 0. Here, a=1, b=0, c=-22.

The solutions or the roots of this quadratic equation can be calculated using the quadratic formula -b ± √b² - 4ac/2a.

Substituting the values into the formula gives -0 ± √(0 - 4(1)(-22))/2(1), simplifying this gives x = ± √ 22.

Therefore, the solutions to the equation are x= √ 22 and x= -√ 22.

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The probable question may be:

Solve the following quadratic equation for all values of x in simplest form !! Please answer this !!

17-x^2=-5

since AC=1/2AB=6 THEREFORE C is the midpoint ofAB

Step-by-step explanation:

Given : AB = 12 , AC = 6

To prove = AB = 2 × AC (C is mid point of AB)

Solution:

AB = 12...[1]

AC = 6.....[2]

[1] ÷ [2]

[tex]\frac{AB}{AC}=\frac{12}{6}[/tex]

[tex]\frac{AB}{AC}=\frac{2}{1}[/tex]

[tex]AB=2\times AC[/tex] (hence, proved)

The answer will be c

Answer is a) because you cut parallel with the base

The quotient of 7 and 1/5 is calculated by multiplying 7 by the reciprocal of 1/5, which is 5. This yields the result 35.

To compute the division of integers and fractions, we generally 'multiply by the reciprocal'. The reciprocal of a fraction is obtained by reversing the numerator and denominator.

In this case, you are asked to obtain the quotient of 7 and 1/5. The reciprocal of 1/5 is 5/1, or simply 5. Thus, we manipulate the problem from division to multiplication:

7 ÷ (1/5) = 7 * 5 = 35.

So, the quotient of 7 and 1/5 is 35.

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Answer:

The building is [tex]116\ m[/tex] high

Step-by-step explanation:

we know that

Using proportion

Let

x-----> the height of the building

[tex]\frac{2}{6}=\frac{x}{348}\\ \\x=2*348/6\\ \\x=116\ m[/tex]

Answer:

400cm2

Step-by-step explanation:

20 • 20 = 400

The answer is 400 cm squared.

Hope this helps!

If it does then I would appreciate it if you could make me brainliest.