Each bottle of lemonade costs the local soccer team $0.75 they have $437.25 in their treasury to buy as many bottles of lemonade as possible to sell for a profit at their soccer games. How many bottles can they afford to buy.

Replace x in the second equation with the value of x from the first one.

x = -3y

x + y = -6

-3y + y = -6

Simplify:

-2y = -6

Divide both sides by -2:

y = -6 / -2

y = 3

Now replace Y with 3 in one of the equations to solve for x:

x = -3y = -3(3) = -9

X = -9, Y = 3

(-9,3)

Answer:

$70,201.38

Step-by-step explanation:

To determine the principal amount, we can use the formula:

[tex]P=\dfrac{A}{(1+\frac{r}{n})^{nt}}[/tex]

A = $200,000

r = 7% or 0.07

t = 15 years

n = 12

Now let's substitute our values.

[tex]P=\dfrac{200,000}{(1+\frac{0.07}{12})^{12(15)}}[/tex]

[tex]P=\dfrac{200,000}{(1.00583333333)^{12(15)}}[/tex]

[tex]P=70,201.38[/tex]

So the principal needed to get 200,000 in 15 years is $70,201.38.

Answer:

D

Step-by-step explanation:

Answer:

The correct answer options are D and E.

Step-by-step explanation:

We are to determine whether which of the given data sets in the answer options are continuous.

For this, we need to know what a continuous data set is.

A data set which have no definite end to its value but keep on continuing.

Here, the data sets given in A, B and C have definite starting and ending points.

While D and E are continuous sets as its values are continuing.

Answer:

9 hours.

Step-by-step explanation:

Average rate = distance / time

=  871 / 13

=  67 mph

So the time to travel 603 miles

=  distance / rate

= 603 / 67

=  9 hours.

Answer:

C. y = -4x +10

Step-by-step explanation:

Equation of a line is found by the formula y = mx +b

Where m is the slope and b is the y intercept

we see that y-intercept is given as 10, so b = 10 and we plug in the coordinate (2,2) into the equation to find the slope (m). We plug in x = 2 and y = 2. Shown below:

[tex]y=mx+b\\2=m(2)+10\\2=2m+10\\2-10=2m\\-8=2m\\m=\frac{-8}{2}\\m=-4[/tex]

We know the value of m to be -4 and b to be 10, thus we can write the equation as:

[tex]y=-4x+10[/tex]

Answer choice C is right.

Answer:

c. y = -4x + 10

Step-by-step explanation:

y = mx + b where b = y -intercept = 10

so

y = mx + 10

Plug in (2,2) to find slope m

2 = 2m + 10

2m = -8

m = -4

Slope m = -4

Equation

y = -4x + 10

Answer:  BCDA

Step-by-step explanation:

[tex]\dfrac{1}{\sqrt[4]{3x^3y^5}}\\\\\\\text{Since it is a 4th root, you need 4 on the "inside" to make 1 on the "outside"}\\=\dfrac{1}{y\sqrt[4]{3x^3y}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{1}{y\sqrt[4]{3x^3y}}\bigg(\dfrac{\sqrt[4]{3^3xy^3} }{\sqrt[4]{3^3xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{\sqrt[4]{3^3xy^3} }{y(3xy)}\\\\\\\boxed{=\dfrac{\sqrt[4]{3^3xy^3} }{3xy^2}}\quad Option\ B[/tex]

[tex]\dfrac{3}{\sqrt[4]{3^3x^{11}y^{13}}}\\\\\\\text{Since it is a 4th root, you need 4 on the "inside" to make 1 on the "outside"}\\=\dfrac{3}{x^2y^3\sqrt[4]{3^3x^3y}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{3}{x^2y^3\sqrt[4]{3^3x^3y}}\bigg(\dfrac{\sqrt[4]{3xy^3} }{\sqrt[4]{3xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{3\sqrt[4]{3xy^3} }{x^2y^3(3xy)}\\\\\\\boxed{=\dfrac{\sqrt[4]{3xy^3} }{x^3y^4}}\quad Option\ C[/tex]

[tex]\dfrac{2}{\sqrt[6]{2x^7y^5}}\\\\\\\text{Since it is a 6th root, you need 6 on the "inside" to make 1 on the "outside"}\\=\dfrac{2}{x\sqrt[6]{2xy^5}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{2}{x\sqrt[6]{2xy^5}}\bigg(\dfrac{\sqrt[6]{2^5x^5y} }{\sqrt[6]{2^5x^5y}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{2\sqrt[6]{32x^5y} }{x(2xy)}\\\\\\\boxed{=\dfrac{\sqrt[6]{32x^5y} }{x^2y}}\quad Option\ D[/tex]

[tex]\dfrac{4}{\sqrt[6]{2^5x^5y^9}}\\\\\\\text{Since it is a 6th root, you need 6 on the "inside" to make 1 on the "outside"}\\=\dfrac{4}{y\sqrt[6]{2^5x^5y^3}}\\\\\\\text{Rationalize the denominator by multiplying so there are 4 on the "inside"}\\=\dfrac{4}{y\sqrt[6]{2^5x^5y^3}}\bigg(\dfrac{\sqrt[6]{2xy^3}}{\sqrt[6]{2xy^3}}\bigg)\\\\\\\text{Simplify}\\=\dfrac{4\sqrt[6]{2xy^3} }{y(2xy)}\\\\\\\boxed{=\dfrac{2\sqrt[6]{2xy^3} }{xy^2}}\quad Option\ A[/tex]

Answer:

[tex]\frac{1}{2} (x+5)\leq 10[/tex]

Step-by-step explanation:

Half the sum of (1/2 * ) a number and five (x + 5) is a maximum of 10 (less than or equal to).

Answer:[tex]\frac{x+5}{2}\leq 10[/tex]

Step-by-step explanation:

The salary of the real estate broker = $18,000

Commission earned on total sales = 4% or 0.04

Total income earnings = $55,000

Let the total sales be = x

Equation becomes :

[tex]18000+0.04x=55000[/tex]

[tex]0.04x=55000-18000[/tex]

[tex]0.04x=37000[/tex]

[tex]x=925000[/tex]

Hence, the real estate broker must sell $925,000 worth of real estate to earn $55,000.

To earn $55,000 total, the real estate broker must sell $925,000 in total.

To find out how much the real estate broker must sell to earn $55,000 total, we need to consider both her base salary and her commission. Let's set up an equation to solve for the total sales needed:

$18,000 + 0.04x = $55,000

Subtracting $18,000 from both sides gives:

0.04x = $37,000

Dividing both sides by 0.04 gives:

x = $925,000

Therefore, the real estate broker must sell $925,000 in total to earn $55,000.

https://brainly.com/question/4818219

#SPJ3

The cost of painting a wall varies jointly with the length and width of the wall, represented by the formula C = k * l * w, where C is the cost, k is the cost per unit area, l is the length, and w is the width.

The cost of painting a wall varies directly with its area. The area of a rectangular wall is found by multiplying its length (l) by its width (w), giving the formula A = l * w for the area. If C represents the cost of painting, and k is the cost per unit area, then the cost formula can be written as C = k * A, which simplifies to C = k * l * w. This means the cost varies jointly with the length and width of the wall, as both dimensions contribute to the total area. Therefore, the cost does not vary directly with l or w alone, but with their product.

Answer:

C. F(X) = (X - 3)⁴

Step-by-step explanation:

Hope this helps you.

The graph of F (x) will be;

⇒ F (x) = (x - 3)⁴

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The function G (x) is,

⇒ G (x) = x⁴

And, The function of G (x) is shown in figure.

And, It is shifted 3 units to the right.

Now,

Here, The function G (x) is,

⇒ G (x) = x⁴

Since, The function of G (x) is shown in figure.

And, It is shifted 3 units to the right.

So, The function of F(x) become;

⇒ F (x) = (x - 3)⁴

Learn more about the translation visit:

https://brainly.com/question/1046778

#SPJ2

Answer:

Step-by-step explanation:

The last one

I hope I helped you.

Polygons are closed figures based on a plane that are characterized by their sides and angles. Without an image or description of the polygon, it's impossible to identify the specific polygon indicated.

In mathematics, polygons are divided based on many factors such as the number of sides, length of sides, angle measures, etc. However, without the image or description of the polygon, I can't definitively tell what polygon you're referring to. For example, a polygon could be anything from a triangle (3 sides) to a decagon (10 sides). Remember, a polygon is basically a closed figure formed by three or more sides in a plane.

https://brainly.com/question/34047098

#SPJ2

Answer:

[tex]y=\frac{\sqrt{x} -8}{-2}[/tex]

Step-by-step explanation:

To find an inverse, switch x and y values in the equation. Then solve for y.

[tex]F(x) = (8-2x)^2\\x = (8-2y)^2\\\sqrt{x} = 8 - 2y\\\sqrt{x} -8 = -2y\\\frac{\sqrt{x} -8}{-2} =y[/tex]

Answer:

7.125 feet

Step-by-step explanation:

1. convert both fractions to decimals by dividing numerator by denominator

    10 1/2 = 10.5

    3 3/8 = 3.375

2. Subtract 10.5-3.375 = 7.125 feet left

Answer:

7.125 ft

Step-by-step explanation:

an equation for a circle has formula

(x-m)² + (y-n)² = r²

where (m,n) is its center

and r is its radius

so, the equation has center (4,3) and radius 4

the equation is derived from the pythagorean theorem

Answer:

D

Step-by-step explanation:

We need to graph both  [tex]6^x[/tex]  and  [tex]3^x[/tex]  and figure out the x-value at which the graph of  [tex]6^x[/tex] is LESS THAN that of the graph of [tex]3^x[/tex].

The attached picture shows the graph of  [tex]6^x[/tex] in BLUE and the graph of  [tex]3^x[/tex] in RED.

We need to find x-value where the BLUE graph is "BELOW" the RED graph. We can see that this occurs when x < 0.

Thus the correct answer is  D

Answer:

d = 50 in.

Step-by-step explanation:

A = Pi*r^2

625Pi = Pi*r^2

625 = r^2

r = 25 in

Diamenter = 2(radius=

d = 50 in

Best regards

Answer:

The shape includes a curve.

Step-by-step explanation:

A polygon consists of joined straight lines - no curves.

Rewrite y^4 as (y^2)^2

(y^2)^2 + 14y^2 +49

Rewrite 49 as 7^2

(y^2)^2 + 14y^2 +7^2

Factor using the perfect square rule.

Final answer: (y^2 + 7)^2

The factorization of given expression  [tex]y^{4}[/tex] + 14y² + 49 is a perfect square which is equal to (y² + 7)².

What is factorization ?

The factorization of algebraic expressions is the process of identifying two or more expressions whose product is the given expression.

The given expression is [tex]y^{4}[/tex] + 14y² + 49.

Before factorization if we look at the given expression we can find out that it is a form of perfect square which is :

A² + B² + 2AB.

Let's convert the given expression in the perfect square form. This will be equal to :

(y²)² + (7)² + 2 × y² × 7

We know that the expansion A² + B² + 2AB is equal to (A+B)².

Here ; A = y² and B = 7.

So , the factorization of given expression  [tex]y^{4}[/tex] + 14y² + 49 is equal to :

(y² + 7)²

Therefore , the factorization of given expression  [tex]y^{4}[/tex] + 14y² + 49 is a perfect square which is equal to (y² + 7)².

Learn more about factorization here :

https://brainly.com/question/25829061

#SPJ2

Answer:

3c=36

c = 12

Step-by-step explanation:

We have 36 sugar flowers

We put 3 on each cupcake

The number of cupcakes times the number of flowers per cupcake equals the total flowers

3*c = 36

Divide each side by 3

3c/3 = 36/3

c = 12

Answer:

12 cupcakes

Step-by-step explanation:

3 sugar flowers on each (1) cupcake

36 sugar flowers on c cupcakes

3c = 36 * 1

3c = 36

 c = 36/3

 c = 12 cupcakes

Answer:

the answer is D

Step-by-step explanation:

Answer:

[tex]18\ pieces[/tex]

Step-by-step explanation:

step 1

Divide each large candy bar into thirds

so

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

Now for each large candy bar you have 3 pieces of [tex]\frac{1}{3}[/tex]

step 2

Find the total number of candy bars pieces by proportion

[tex]\frac{1}{3}\frac{bar}{pieces} =\frac{6}{x}\frac{bar}{pieces}\\ \\x=6*3\\ \\x=18\ pieces[/tex]

Final answer:

To determine the total number of candy bar pieces after splitting 6 large bars into thirds, you multiply 6 by 3 resulting in 18 pieces.

Explanation:

The student's question is about dividing candy bars into thirds. If you start with 6 large candy bars and want to split each one into thirds, you end up with 6 groups of 3 pieces. To find the total number of candy bar pieces, you multiply the number of candy bars by the number of pieces you want to make from each bar, which is:

6 bars × 3 pieces per bar = 18 pieces.

Therefore, after splitting all the large candy bars into thirds, you will have a total of 18 candy bar pieces.

Answer:

6

Step-by-step explanation:

volume is (lwh) since youre trying to find the height just multiply the 2 and 4 together to get 8. Then divide 8 by 48 to get your height.

Answer:

Yes, the right angle is angle C.

Step-by-step explanation:

The given triangle has vertices at A(–2, 3), B(–3, –6), and C(2, –1).

Recall the slope formula;

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

The slope of the line going through AC is

[tex]m_{AC}=\frac{-1-3}{2--2}=-1[/tex]

The slope of the line going through BC s

[tex]m_{AC}=\frac{-1--6}{2--3}=1[/tex]

The product of the slopes of AC and BC is [tex]-1\times1=-1[/tex]

This means line AC is perpendicular to BC at C.

Hence the triangle ABC is right angled at C.

Answer:

Yes, the right angle is angle C.

Step-by-step explanation:

Answer:

15. 4.9 cm

17. 6.63 cm

Step-by-step explanation:

15. A perpendicular bisector is a segment which divides another in half. Since JH is 9.8 then each of the two segments it divides into is 4.9.

17. The segments within the circle form a right angle. Triangle CRS as a right triangle must follow the Pythagorean theorem which says the square of each leg adds to the square of the hypotenuse.

a² + b² = c²

Here a is unknown, b = 10 and c = 12.

a² + 10² = 12²

a² + 100 = 144

a² = 44

a = √44 = 6.63

Answer:

The series is convergent ⇒ answer (a)

Step-by-step explanation:

* The series is 3/2 + 9/8 + 27/32 + ........

- It is a geometric series with:

- first term a = 3/2 and common ratio r = 9/8 ÷ 3/2 = 3/4

* The difference between the convergent and divergent

  in the geometric series is :

- If the geometric series is given by  sum  = a + a r + a r² + a r³ + ...

* Where a is the first term and r is the common ratio

* If |r| < 1 then the following geometric series converges to a / (1 - r).  

- Where a/1 - r is the sum to infinity

* The proof is:

∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number

∴ r^n approach to zero

∴ S = a(1 - 0)/(1 - r) = a/(1 - r)

∴ S∞ = a/1 - r

* If |r| ≥ 1 then the above geometric series diverges

∵ r = 3/4

∴ r < 1

∴ The series is convergent

Answer:

I would think the answer would be 35

Step-by-step explanation:

Step 1: Round your answer to 2 decimal places.

Step2: Divide or Multiply your answer you got by 2.

cos42= 35/y

y=35/cos42

y= 47.10

is the answer

Answer: [tex]m=-\frac{8}{7}[/tex]

Step-by-step explanation:

To calculate  the slope of the line that has the coordinates given in the problem you must use the formula shown below:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Given the points (-3, 6) (4,-2), when you substitute them into the eequation shown above, you obtain that the slope is the following:

[tex]m=\frac{-2-6}{4-(-3)}\\m=-\frac{8}{7}[/tex]

Answer:

[tex] - \frac { 8 } { 7 } [/tex]

Step-by-step explanation:

We are given the following two points on a line and we are to find the slope of this line:

(-3, 6) and (4,-2)

We know the formula of the slope is given by:

[tex] \frac { y_2 - y_1 } { x_2 - x_1 } [/tex]

Substituting the given coordinates in the above formula to get:

Slope = [tex] \frac { - 2 - 6 } { 4 - - 3 } = - \frac { 8 } { 7 } [/tex]

Answer:

[tex]\large\boxed{V=\dfrac{1600\pi}{3}\ cm^3}[/tex]

Step-by-step explanation:

The formula of a volume of a cone:

[tex]V=\dfrac{1}{3}\pi r^2H[/tex]

r - radius

H - height

We have r = 10cm and H = 16cm. Substitute:

[tex]V=\dfrac{1}{3}\pi(10^2)(16)=\dfrac{1}{3}\pi(100)(16)=\dfrac{1600\pi}{3}\ cm^3[/tex]

Answer:

The percentage is [tex]130\%[/tex]

Step-by-step explanation:

Let

x-----> the number

we have

[tex]\frac{13}{10}x=1.3x[/tex]

To find the percentage multiply by 100

[tex]1.3*100=130\%[/tex]

Answer:

none

Step-by-step explanation:

y = -4x^2 +3x-2

To find the x intercepts, let y =0

0 = -4x^2 +3x-2

Using the discriminant

a=-4, b=3  c=-2

b^2 -4ac

3^2 -4(-4)(-2)

9 -32

-23

Since this is negative all the roots are complex, so it has no real roots

none