Gabriella and her children went into a grocery store and where they sell apples for $1 each and mangos for $0.50 each. Gabriella has $15 to spend and must buy at least 19 apples and mangos altogether. If Gabriella decided to buy 13 mangos, determine the maximum number of apples that she could buy.

To create a consistent and independent system of equations with the solution (-1, -4), we generate two linear equations: 2x - 3y = 10 and 5x + 4y = -21, both of which are satisfied by the given solution.

To construct an independent and consistent system of equations that has the solution (-1, -4), we can create two distinct linear equations where the point (-1, -4) satisfies both.

As an example, we choose two arbitrary linear equations, ensuring that they are not multiples of each other, and that they are satisfied by x = -1 and y = -4.

The general form of a linear equation is Ax + By = C.

For our first equation, we could have 2x - 3y = 2(-1) - 3(-4) = 10. To ensure the second equation is not a multiple of the first, we could choose 5x + 4y = 5(-1) + 4(-4) = -21.

The system of equations would then be:

Answer:

X/18=6/4

Step-by-step explanation:

4hrs=6 logs

18hrs=x

4x=18×6

Which can also be written as

[tex] \frac{x}{18 } = \frac{6}{4} [/tex]

Answer:

40

Step-by-step explanation:

(6 + 2i)(6 – 2i) = 36 – 4i²

= 36 + 4 = 40

(C) 40.

[tex]6+2i\\(6+2i)(6+2i)=36-4i^{2} \\36+4+40\\=40[/tex]

`Therefore, the correct option is (C) 40.

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Answer:

      [tex]\dfrac{1}{15}[/tex]

Explanation:

The number of different ways in which the two armadillos would be at the ends of the row is 2:

                      [tex]P(2,2)=\dfrac{2!}{(2-2)!}=\dfrac{2}{0!}=2[/tex]

The number of different combinations in which two of the three aardvarks can sit at the ends of the row is P(3,2):

          [tex]P(3,2)=\dfrac{3!}{(3-2)!}=\dfrac{3\times 2\times 1}{1}=6[/tex]

Therefore, there are 2 + 6 = 8 different ways in which the two animlas on the ends of the row were both armadillos or both aardvarks.

Now calculate the total number of different ways in which the animals can sit. It is P(5,5):

        [tex]P(5,5)=\dfrac{5!}{(5-5)!}=5!=5\times 4\times 3\times 2\times 1=120[/tex]

Thus, the probability that the two animals on the ends of the row were both armadillos or both aardvarks is equal to the number of favorable outputs divided by the total number of possible outputs:

      [tex]Probability=\dfrac{8}{120}=\dfrac{1}{15}[/tex]

Answer:

2/5

Step-by-step explanation:

2/5 1 1 1  1/4

A R R R A

2/20 or 1/10 is the odds that there will be an armadillo both ends

3/5 1 1 1 1/2

R A A R R

3/10 are the odds that there will be an aardvark on both ends and so you then have to add the two to get 4/10 or 2/5 which is the answer

Answer:

Cylinder: Radius: 6 in, height: 6 in

Step-by-step explanation:

See the attached image for a visual explanation!

Answer:

.25mm a week

Step-by-step explanation:

There are 52 weeks in a year.

13/52=.25

If Toenails grow about 13 millimeters per year as a result .25 millimeters will grow in one week.

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

We'll apply division by Splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.

It is given that Toenails grow about 13 millimeters per year.

As we know there are 52 weeks in a year.

Toenails growth in one  week is obtained by dividing the growth per year by the total number of weeks,

= 13/52

=.25

Thus, if Toenails grow about 13 millimeters per year as a result .25 millimeters will grow in one week.

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Answer:

I think it is the third:

6 + 4 n = 18

7% at 6 years would best fit their payment option as they would then be paying $238.69 monthly and that is under the $250

Answer: 12 weeks

Step-by-step explanation:

125-65=60

60/5=12

Given:

ABC is a right triangle and AC = BC

The length of AB is [tex]AB=12\sqrt{2}[/tex]

We need to determine the length of each of the legs.

Length of AC and BC:

Let the length of AC and BC be x.

The length of AC and BC can be determined using the Pythagorean theorem.

Thus, we have;

[tex]AB^2=AC^2+CB^2[/tex]

Substituting the values, we have;

[tex](12\sqrt{2})^2=x^2+x^2[/tex]

Simplifying, we get;

[tex]288=2x^2[/tex]

Dividing both sides by 2, we get;

[tex]144=x^2[/tex]

Taking square root on both sides, we get;

[tex]12=x[/tex]

Thus, the length of each legs is 12 units.

Hence, the length of AC and BC are 12 units each.

Answer:

AC= 18 units for khan academy

Step-by-step explanation:

Answer:

it repeating not terminating

Step-by-step explanation:

this is because after 3 numbers behind the decimal

and if the number keeps going it's repeating

Answer:

The correct answer is the basket ball is 54.87 times bigger in volume than the tennis ball.

Step-by-step explanation:

The diameter of a basketball is approximately given to be 9.5 inches.

The radius of the basket ball is given by [tex]\frac{9.5}{2}[/tex] = 4.75 inches.

The volume of the basket ball is given by = [tex]\frac{4}{3}[/tex] × π × [tex]radius^{3}[/tex] = 449.1012 cubic inches.

The diameter of a tennis ball is approximately given to be 2.5 inches.

The radius of the tennis ball is [tex]\frac{2.5}{2}[/tex] = 1.25 inches.

The volume of the tennis ball is given by = [tex]\frac{4}{3}[/tex] × π × [tex]radius^{3}[/tex] = 8.1845 cubic inches.

Ratio between the volume of the basketball and tennis is given by [tex]\frac{449.1011}{8.1845}[/tex] = 54.87.

Thus the volume of the basket ball is 54.87 times greater than the volume of the tennis ball.

Final answer:

To find how many times greater the volume of a basketball is than a tennis ball, calculate the volumes using the sphere volume formula and divide the basketball's volume by the tennis ball's volume, which yields approximately 54.86 times greater.

Explanation:

To determine how many times greater the volume of a basketball is compared to a tennis ball, we start by calculating the volume of each using the formula for the volume of a sphere, V = 4/3 π r3, where r is the radius of the sphere. The radius is half the diameter, so for the basketball, r = 9.5 inches / 2 = 4.75 inches, and for the tennis ball, r = 2.5 inches / 2 = 1.25 inches.

The volume of the basketball is approximately
Vbb = 4/3 π (4.75)3 = 448.74 cubic inches. The volume of the tennis ball is approximately
Vtb = 4/3 π (1.25)3 = 8.18 cubic inches.

To find out how many times greater the volume of the basketball is, we divide the volume of the basketball by the volume of the tennis ball:
448.74 cubic inches / 8.18 cubic inches ≈ 54.86. Therefore, the volume of a basketball is approximately 54.86 times greater than that of a tennis ball.

Answer:

where are the answer choices?

Step-by-step explanation:

Answer:

It is 3^-4

Step-by-step explanation:

-6+2=-4

Answer:

In a circle, interior angles that are not inscribed or central can be found using the formula < = larger arc + smaller arc / 2. So, in order to find <2, the formula would be <2 = 147 + 133 / 2, so 140.

Answer:

m < 2 is 140

Step-by-step explanation:

Answer:

x = 17/5

Step-by-step explanation:

Plug in 2y + 3 as x in the second equation and solve for y to get 1/5

Then plug in y into the first equation and solve for x to get 17/5

Answer:

Step-by-step explanation:

x=2y+3

3x=7-4y

Rearrange the numbers so they compare,

x=2y+3

3x=-4y+7

Multiply the first equation by 2 (this is so the variable with y matches in both equations)

2x=4y+6

3x=-4y+7

Add the two equations together

2x=4y+6

+

3x=-4y+7

5x=13

Divide both sides by 5 to isolate x

x=13/5

Simply the equation

x=2 3/5

Answer:

6 yards.

Step-by-step explanation:

You can find this answer by using the Pythagorean theorem. Because c in the equation will always stand for the hypotenuse, the longest side, it's easier to fill in the blanks with the stuff given to you.

In this case, 1.1^2 + a^2 = 6.1^2

If you simplify, the answer should be 6 yards.

Answer:

[tex]\frac{169\pi }{180}[/tex]

Step-by-step explanation:

To convert from degree measure to radian measure

radian = degree × [tex]\frac{\pi }{180}[/tex], thus

radian measure = 169 × [tex]\frac{\pi }{180}[/tex] = [tex]\frac{169\pi }{180}[/tex]

Considering it's surface area, it is found that [tex]48\pi \text{ft}^2[/tex] of vinyl was used to make the exercise ball.

The surface area of a cylinder of radius r and height h is given by:

[tex]S = 2\pi r(r + h)[/tex]

In this problem, we have that r = 3 ft and h = 5 ft, hence the surface area in ft² is given by:

[tex]S = 2\pi r(r + h) = 2\pi \times 3(3 + 5) = 48\pi[/tex]

Hence, [tex]48\pi \text{ft}^2[/tex] of vinyl was used to make the exercise ball.

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Answer:

x=4.36

this is rounded

Step-by-step explanation:

a^2 + b^2 = c^2

A^2 + 9^2 = 10^2

a^2 + 81 = 100

Then subtract 81 from each side

a^2 = 19

then you have to square root 19 and you get

x=4.3588989

Brainliest?

Answer:

The equation of the ellipse is [tex]\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1[/tex]

Step-by-step explanation:

The standard form of the equation of an ellipse with center (0 , 0) is

[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex] , where

∵ The ellipse is centered at the origin

∴ The center of it is (0 , 0)

∵ It has foci at (± 8 , 0)

- The coordinates of the foci are (± c , 0)

∴ c = ±8

∵ It has Vertices at (± 17 , 0)

- The coordinates of the vertices are (± a , 0)

∴ a = ±17

∵ c² = a² - b²

- Substitute the values of c and a to find b

∴ (8)² = (17)² - b²

∴ 64 = 289 - b²

- Add b² to both sides

∴ b² + 64 = 289

- Subtract 64 from both sides

∴ b² = 225

- Take √  for both sides

∴ b = ± 15

∵ The equation of the ellipse is [tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1[/tex]

- Substitute the values of a and b in it

∴ [tex]\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1[/tex] ⇒ [tex]\frac{x^{2}}{289}+\frac{y^{2}}{225}=1[/tex]  

∴ The equation of the ellipse is [tex]\frac{x^{2}}{(17)^{2}}+\frac{y^{2}}{(15)^{2}}=1[/tex]

The standard form equation for this ellipse is (x²/17²) + (y²/15²) = 1.

To find the equation of an ellipse centered at the origin with foci at (±8,0) and vertices at (±17,0), we need to follow these steps:

Determine the values of 'a' and 'c': The vertices give us the value of 'a', which is the distance from the center to a vertex. Here, a = 17.

The foci give us the value of 'c', which is the distance from the center to a focus. Here, c = 8.

Using the relationship c² = a² - b², we can calculate 'b'.

c² = a² - b²

8² = 17² - b²

64 = 289 - b²

b² = 225

b = 15

So, the standard form of the equation of the ellipse is: (x²/17²) + (y²/15²) = 1

Answer:

  x^2 +y^2 -8x +4y +11 = 0

Step-by-step explanation:

The center of the given circle is located at (x, y) = (4, -2). Its radius is 3.

You know this because the center is halfway between the vertical and horizontal extremes, and the radius is half the difference of those extremes. You can determine this by counting squares, or "by eye," or by working with the coordinates of the extreme points.

For example, the horizontal extremes are (1, -2) and (7, -2). The diameter is the difference of the x-values: 7 -1 = 6, so the radius is 6/2 = 3. The x-coordinate of the center is (1+7)/2 = 4.

__

The standard form of the equation of a circle is ...

  (x -h)^2 + (y -k)^2 = r^2

where (h, k) is the center, and r is the radius.

For this circle with center (4, -2) and radius 3, the standard form equation is ...

  (x -4)^2 + (y +2)^2 = 9

General form has the parentheses removed and the polynomial written in descending powers of the variables:

  x^2 -8x +16 +y^2 +4y +4 = 9

  x^2 +y^2 -8x +4y +11 = 0

Answer:

20

Step-by-step explanation:

If she has 68 lollipops, and she had 8 remaining, we should subtract the two.

68 - 8 = 60

So now we know she gave away 60 lollipops in total.

We know she gave 3 to each of her friends, so we would divide 60 by 3.

60/3 = 20

So she has 20 friends.

Answer: it will take pipe c 7.2 hours to fill the pool.

Step-by-step explanation:

Let t represent the number of hours it will take pipe c to fill the pool alone. It means that the rate at which pipe c fills the pool per hour is 1/t

Pipe b can fill a pool in 9 hours. It means that the number of hours it takes pipe b to fill the pool alone per hour is 1/9

By working together, they would work simultaneously and their individual rates are additive. When pipes b & c are both open, the pool can be filled in 4 hours. It means that the rate at which both pipes fill the pool per hour is 1/4. Therefore,

1/t + 1/9 = 1/4

(9 + t)/9t = 1/4

Cross multiplying, it becomes

4(9 + t) = 9t

36 + 4t = 9t

9t - 4t = 36

5t = 36

t = 36/5

t = 7.2 hours

Answer:

discriminant

Step-by-step explanation:

Discriminant is the expression under the radical in a quadratic equation formula that indicates the nature of the solutions real or complex, rational or irrational , single or double root in other words

A discriminant can be said to be used to indicate the nature of the result that a quadratic equation when solved will yield and this can be : rational or irrational , complex or real, single or double roots. and it also indicates by how many  it would be  

Answer:

  p = (-1/5000)x +11

Step-by-step explanation:

We are given two points (x, p) as (5000, 10) and (15000, 8). Using the two-point form of the equation of a line, we can find the equation to be ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1 . . . . . 2-point form

  p = (8 -10)/(15000 -5000)(x -5000) +10

  p = -2/10000(x -5000) +10

  p = -x/5000 +11 . . . . . linear demand function

Final answer:

A student asked how to find the demand function for a baseball team's ticket prices based on attendance. By finding the slope between two given points and using the point-slope form, the demand function is determined to be p = $11 - 0.0002x.

Explanation:

To find the demand function that relates the price p of baseball tickets to the average attendance x, we can use the two given points (x, p) = (5,000, $10) and (15,000, $8) and assume the relationship is linear. We can express the demand function as p = mx + b, where m is the slope and b is the y-intercept.

First, find the slope m:

m = (p2 - p1) / (x2 - x1)

m = ($8 - $10) / (15,000 - 5,000)

m = -$2 / 10,000 = -0.0002

Next, we'll use the slope and one of the points to find b, the y-intercept. Plugging into the point-slope form:

p - p1 = m(x - x1)

$10 - p = -0.0002(5,000 - x)

$10 - p = -1 + 0.0002x

p = $11 - 0.0002x

The demand function is p = $11 - 0.0002x.

Final answer:

To simplify the expression, distribute the 5 to both terms inside the parentheses, combine like terms, and obtain the simplified expression 2x^2 + 23.

Explanation:

To simplify the expression 7x2 + 3 - 5(x2 - 4), we can distribute the 5 to both terms inside the parentheses:

7x2 + 3 - 5x2 + 20

Combining like terms:

2x2 + 23

So, the simplified expression is 2x2 + 23.

Answer:

30cm

Step-by-step explanation:

150*0.2=30cm, 20% of 150 is 30cm.

Answer:

$651.46‬

Step-by-step explanation:

$596.95 * 9.25% = 55.21

$596.25 + 55.21 =651.46‬

Answer:

B

Step-by-step explanation

a squared plus b squared equals c squared.

16 plus 144 equal 160.

now square 160