Solve the system of equations.
4x - 9y - 2 = 0
12x - 5y + 38 = 0
x =
y =

We know that

• Gemma's dinner cost $5 more than her cousin's.

• Their combined bill was under $25.

Based on the given information, we express the following

Where G is Gemma and C is her Cousin.

Hence, the inequality that represents this situation is

Answer:

$18.5

Step-by-step explanation:

6 divided by 3 = 2

27 divided by 2 = 18.5

In this scenario, the researcher is interested in studying the population of men in a particular village. This group of men represents the population of interest for the study. The relevant population data would consist of the height measurements of all the men in the village. The population parameter of interest to the researcher is the average height of the men in the village.

By determining this population parameter, the researcher can gain insight into the central tendency of the height distribution for men in the village. This information can be used to make informed decisions or draw conclusions about the population of interest.

To obtain an accurate estimate of the population parameter, the researcher would need to collect a representative sample of height measurements from the men in the village and calculate the sample mean. The sample mean could then be used to estimate the population parameter with a certain degree of confidence.

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Answer:

3x-y=15 should be the answer

Answer:

The answer simplified would be:

-4y^2+3y+5

If you combine the like terms, you will get this answer.

You have to add 8y^2 to -12y^2 and you get -4y^2.

Hope this helps you! :)

Using a trigonometric relation we will see that the height is  8.62m

On the diagram we can see a right triangle, where we know one of the angles and the adjacent cathetus and we want to find the opposite cathetus.

Then we can use the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing the values that we know we will get:

tan(72°) = n/2.8m

2.8m*tan(72°) =n = 8.62m

That is the height.

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Answer:

the unit cost per rubber tile is $$$$$$$$$$$$$6

Step-by-step explanation:

..

Answer:

The Answer Is: 33.846153846154

round to the digit needed

Step-by-step explanation:

Answer:

the absolute value is 7.

Step-by-step explanation:

the absolute value is just the number, so you take away the negative

Answer:

slope = - \(\frac{2}{3}\)

Step-by-step explanation:

Parallel lines have equal slopes

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (9, 6) and (x₂, y₂ ) = (3, 10)

m = \(\frac{10-6}{3-9}\) = \(\frac{4}{-6}\) = - \(\frac{2}{3}\) ← slope of parallel line

Answer:

Step-by-step explanation:

Y2-Y1÷X2-X1=slope

10-6÷3-9=M

4÷-6=M

Slope =0.67

Answer:

100 kids.

Step-by-step explanation:

First you add 240+260=500

Then you take 1/5 of 500 which is 100.

Hope this helps!

Answer:As it is given that, a cylinder has radius 3 inches and height 5 inches and we are to find the volume of the cylinder, also a extra information is given that is a cone has the same radius and height.

We know,

Where,

r is the radius of the cylinder.

h is the height of the cylinder.

Here, we will take the value of π as 3.14 approximately .

Now, we will substitute the given values in the formula :

Note :

Answer might be different if we take the value of π as 22/7 .

Step-by-step explanation:

Answer:

volume of cylinder= πr²h

22. ×4²×5

7

22 × 16×5

7

251.43 inches³

volume of cone=1 × πr²×h

3

1×22×4²×5

3. 7

83.81 inches ³

well, the midpoint of segment AB is the center of the circle, so

\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 -2}{2}~~~ ,~~~ \cfrac{ 9 +1}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 10 }{2} \right)\implies \stackrel{center}{(2~~,~~5)}\)

now since we know AB is the diameter, so half that distance AB is its radius, so

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{6}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}\)

\(AB=\sqrt{(~~6 - (-2)~~)^2 + (~~9 - 1~~)^2} \implies AB=\sqrt{(6 +2)^2 + (9 -1)^2} \\\\\\ AB=\sqrt{( 8 )^2 + ( 8 )^2} \implies AB=\sqrt{ 64 + 64 } \implies AB=\sqrt{ 128 } \\\\\\ AB=8\sqrt{2}\hspace{5em}\stackrel{\textit{half that is the radius}}{\cfrac{8\sqrt{2}}{2}\implies 4\sqrt{2}\implies \sqrt{32}} \\\\[-0.35em] ~\dotfill\)

\(\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{2}{h}~~,~~\underset{5}{k})}\qquad \stackrel{radius}{\underset{\sqrt{32}}{r}} \\\\\\ (x-2)^2~~ + ~~(y-5)^2~~ = ~~(\sqrt{32})^2\implies {\large \begin{array}{llll} (x-2)^2~ + ~(y-5)^2~ = ~32 \end{array}}\)

The speed of the glider when it reaches the bottom of the track is determined as 4.24 m/s.

The speed of the glider at the bottom of the track is calculated by applying the third kinematic equation as shown below.

v² = u² + 2as

where;

The glider is assumed to start from rest, thus the initial velocity, u = 0.

v² = 0 + 2as

v = √2as

Substitute the given values, and solve for the speed at the bottom track as follows;

v = √ (2 x 1.19 x 7.55 )

v = 4.24 m/s

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The complete question is below:

The glider is released at a distance 1.19 m from the bottom of the track. Use the acceleration value you obtained in Part C to calculate the speed of the glider when it reaches the bottom of the track. "

(if the acceleration is part C is found  to be7.55 m/s²)

In summary, the critical points in increasing order are:

x1 = -2

x2 = 0

x3 = 2

To find the critical points of the function f(x) = x^4 - 8x^2, we need to find the values of x where the derivative of f(x) is equal to zero or undefined.

First, let's find the derivative of f(x) with respect to x:

f'(x) = 4x^3 - 16x

To find the critical points, we set the derivative equal to zero and solve for x:

4x^3 - 16x = 0

Factoring out 4x, we have:

4x(x^2 - 4) = 0

Setting each factor equal to zero, we get:

4x = 0 --> x = 0

x^2 - 4 = 0 --> x^2 = 4 --> x = ±2

So, the critical points are:

x1 = -2

x2 = 0

x3 = 2

To determine the nature of these critical points, we can use the second derivative test or examine the behavior of the function around each critical point.

Taking the second derivative of f(x):

f''(x) = 12x^2 - 16

Now we can evaluate the second derivative at each critical point:

f''(-2) = 12(-2)^2 - 16 = 48 - 16 = 32

f''(0) = 12(0)^2 - 16 = -16

f''(2) = 12(2)^2 - 16 = 48 - 16 = 32

Since f''(-2) and f''(2) are both positive, the function has a local minimum at x = -2 and x = 2. Since f''(0) is negative, the function has a local maximum at x = 0.

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Answer:

$33.00 for 22 bottles of water and 1.50 for each bottle.

Step-by-step explanation:

The amount for energy bar for 22 players=22x2=44

The amount for the water=77-44=33

The amount for each bottle=33 divided by 22=$1.50

Answer:

C.6

Step-by-step explanation:

The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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Answer:

B on E2020

Step-by-step explanation: ok

Answer:

1. ∠YZX = 37°

2. ∠YXZ = 53°

3. XZ = 30 meters

Step-by-step explanation:

1. To solve for an unknown angle, we need to utilize the inverse of a trigonometric function.

⭐What are the inverses of the trigonometric functions?

To know which inverse of the trigonometric functions we use, we have to see the type of side lengths we are given (opposite, adjacent, or hypotenuse)

We are given side length XY, which is opposite of ∠YZX, and we are given side length YZ, which is adjacent to ∠YZX. Therefore, we will use \(tan^-1 (opposite/adjacent) =\)

Substitute the values we are given into the function:

\(tan^-1 (18/24) =\)

Compute this equation using a scientific calculator. I recommend using the Desmos Scientific Calculator:

\(= 37\)

∴ ∠YZX = 37°

2. We already know 2 angles (∠YZX = 37°, and ∠ZYX = 90°) Therefore, to find ∠YXZ, we have to utilize the triangle sum theorem.

⭐ What is the triangle sum theorem?

Substitute the angles we know already (∠YZX and ∠ZYX), and solve for ∠YXZ.

\(< YZX + < ZYX + < YXZ = 180\)

\(37 + 90 + YXZ = 180\)

\(127 + YXZ = 180\)

\(< YXZ = 53\)

∴ ∠YXZ = 53°

3. We already know 2 side lengths (ZY = 24 meters, and XY = 18). Therefore, to find XZ, we have to utilize the Pythagoras' theorem.

⭐ What is the Pythagoras' theorem?

Substitute the values of the side lengths into the formula:

\((XZ)^2 = (XY)^2 + (ZY)^2\)

\((XZ)^2 = 18^2 + 24^2\)

Solve for XZ:

\((XZ)^2 = 324 + 576\)

\((XZ)^2 = 900\)

\(\sqrt{(XZ)^2} = \sqrt{900}\)

\(XZ = 30\)

∴ XZ = 30 meters

Answer:

the answer should be negative one and one-fourth, negative one -half

Step-by-step explanation:

hope this helps

Answer:

15 is the product.

Step-by-step explanation:

when you multiply, the answer is called the product.

The product of two given numbers is 15.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

The given equation is 5×3=15.

The product of 5 and 3 is 15

Now, 5×3=15

15=15

LHS=RHS

Therefore, the product of two given numbers is 15.

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Answer:

Concept: Rectangular Figures

Given data:

The upper end length of the trapezoid is: a=6 cm

The lower end length of the trapezoid is: b=10 cm

The height of the trapezoid is: h=15 cm

The expression to calculate the area of the trapezoid is,

Substitute vall known values in the above expression.

Thus, the area of the trapizoid is 120 square centi meter.

The Maclaurin series for cos(x) is given by:

cos(x) = Σ (-1)^n * (x^(2n)) / (2n)!, for n = 0 to ∞

Now, we need to find the Maclaurin series for f(x) = 12x * cos(12x). We can substitute x with 12x in the Maclaurin series for cos(x):

cos(12x) = Σ (-1)^n * (12x)^(2n) / (2n)!, for n = 0 to ∞

Now, multiply the series by 12x:

f(x) = 12x * cos(12x) = 12x * Σ (-1)^n * (12x)^(2n) / (2n)!, for n = 0 to ∞

Simplify the expression:

f(x) = Σ (-1)^n * 12^(2n + 1) * x^(2n + 1) / (2n)!, for n = 0 to ∞

This is the Maclaurin series for the given function f(x) = 12x * cos(12x).

You should be concise and not provide extraneous amounts of detail. You should not ignore any typos or irrelevant parts of the question. Here is the solution to the given problem.Student question: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = 12X COS 12x cos(12)Step 1:We are required to find the Maclaurin series for a function involving cos(x). Let's recall the Maclaurin series for cos(x).cos(x) = Σ(-1)^(n)/(2n)!  (n=0)The same equality would be true for any variable, and in particular for u = x^2.x^2/2! = 1/2!x^4/4! = 1/4! x^6/6! = 1/6!Therefore, the Maclaurin series for cos(x^2) isx^4nΣ(-1)^(n)/n!(2n)!  (n=0)Step 2:Now we can use this to find the Maclaurin series of the given function, treating the term 12x as a constant and using the rule can=canf(x) = 12x cos(12x cos(1+2)) = 12x cos((12x)cos(1+2))= 12xΣ(-1)^(n)/(2n)! [12x cos(1+2)]^(2n) =Σ(-1)^(n)/(2n)!  (24nx)^(2n) =Σ(-1)^(n)/(2n)!  24^(2n) x^(4n+1) (n=0)Therefore, the required Maclaurin series of the given function is Σ(-1)^(n)/(2n)!  24^(2n) x^(4n+1) (n=0).

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Answer:

27

Step-by-step explanation:

Discount is 0.354838, Discount percentage is 35.4838 %.

According to the question

A shop item is marked down from r 6.20 to r 4.

A discount is an amount that is subtracted from the regular price of an item.

Based on the given conditions

= \(\frac{6.2-4}{6.2}\)

Solving 6.2 - 4, we get 2.2

= 2.2/6.2

Discount = 11/31 = 0.354838

Percentage discount is a discount that is given to a product or service that is given as an amount per hundred. For example, a percentage discount of 20% would mean that an item that originally cost $100 would now cost $80.

Discount percentage = \(\frac{11}{31}\) × 100

= 35.4838 %

Hence,

Discount is 0.354838, Discount percentage is 35.4838 %.

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Answer:

B. 35°

Step-by-step explanation:

m<4 = x + 20

m<8 = 2x + 5

✔️First, find the value of x:

m<4 = m<8 (corresponding angles are equal)

Substitute

x + 20 = 2x + 5

Collect like terms

x - 2x = -20 + 5

-x = -15

Divide both sides by -1

x = 15

✔️Find m<8:

m<8 = 2x + 5

Plug in the value of x

m<8 = 2(15) + 5

m<8 = 30 + 5

m<8 = 35°