How many ways are there to choose 4 books from a collection of 11 books? Hint... does order matter? Type your answer...

After factoring out, 4(5x+3y) simplifies to 20x + 12y.

The act of replacing a complex mathematical expression with a simpler equivalent is known as simplification (usually shorter).

An equivalent fraction is one in which the numerator and denominator are both divisible by the same non-zero number. If a fraction's numerator and denominator are both divisible by a number greater than 1, the fraction can be reduced to an equivalent fraction by reducing both its numerator and its denominator.

To simplify 4(5x+3y), we can use the distributive property of multiplication over addition:

4(5x + 3y) = 4(5x) + 4(3y)

Simplifying the multiplication:

4(5x + 3y) = 20x + 12y

Therefore, 4(5x+3y) simplifies to 20x + 12y.

Learn more about Simplification

https://brainly.com/question/2804192

#SPJ1

The property illustrated in "√2+√8 is a real number" is the closure property of addition,

The property illustrated in the given statement is the closure property of addition, which states that the sum of two real numbers is also a real number.

The closure property of addition states that the sum of any two real numbers is also a real number. In the given statement, √2 and √8 are both real numbers, and therefore their sum √2+√8 is also a real number.

This property applies to all real numbers, and it is an important property of the number system. which states that the sum of two real numbers is also a real number.

Learn more about property at https://brainly.com/question/28252812

#SPJ11

Since the park is isosceles trapezoid-shaped, the two sides, AB and CD, that make up the parallel sides of the trapezoid are of equal length.

An isosceles triangle is a type of triangle with two sides of equal length. It has two equal angles opposite of the two equal sides, and the third angle is usually different. Isosceles triangles are named after the Greek term isoskelēs, which means “equal legs”. They are very common in geometry and are used in many applications, including architecture and engineering.

We can then use the midpoints of the adjacent sides of the trapezoid, E and F, to form a rhombus. Since the rhombus is formed from the midpoints of the two parallel sides, we know that the two sides AE and CF of the rhombus are of equal length. Similarly, the two sides BE and FD of the rhombus are also equal in length. This means that the trail, if constructed in the shape of the rhombus, will have all sides of equal length, satisfying the criteria set by the Parks Commission.

To learn more about isosceles
https://brainly.com/question/29793403
#SPJ1

Answer: (0, 2)

Step-by-step explanation:

The solution of a system of equations is where the lines intersect at.

We will use substitution to solve the system.

Equations:

y = 1/2x + 2

y = -1/5x + 2

Set both equations to equal each other:

1/2x + 2 = -1/5x + 2

Simplify:

7/10x = 0

x = 0

Plug 0 back in:

y = 1/2(0) + 2

y = 0 + 2

y = 2

The solution is (0, 2)

(This can also be seen by looking at the graph)

Hope this helps!

The radius of this circle corresponds to the radius of the circle whose answer is x2 + y2 = 9, where the circle's centre is on the x-axis.

In mathematics, a circle is a geometric figure made up of all the points in a sphere that are equally spaced from the circle's centre. The radius of the circle is the distance measured from any location on the circle to its centre. The width of a circle is the distance across the circle that passes through its centre, and the circumference of a circle is the distance around the circle. The equations of circles in the coordinate plane can be used to characterise them. The equation for a circle with centre (h,k) and radius r has the following conventional form:

(x - h)² + (y - k) (y - k)² = r² where (x,y) are any location on the circle's coordinates.

given

We can begin by completing the cube to rewrite the equation in standard form:

x2 - 2x + y2 = 8

(x - 1)2 + y2 = 9

We can see from this standard shape that the circle's centre is (1, 0), which is located on the x-axis. This circular has a radius of √9 units, or 3 units. Thus, the following assertions are true:

The circular has a radius of three units.

The x-axis is where the circle's middle is located.

The radius of this circle corresponds to the radius of the circle whose answer is x2 + y2 = 9, where the circle's centre is on the x-axis.

To know more about circle visit:

https://brainly.com/question/29142813

#SPJ1

Answer: They shared 40 grapes for Tommy and 48 grapes for Kim

Step-by-step explanation:

Let's assume that the initial number of grapes they shared is 5x for Tommy and 6x for Kim.

After Tommy eats half of his grapes, he will have 5x/2 grapes left.

Kim eats 4 more grapes than Tommy, so she will have 5x/2 + 4 grapes.

To find the total number of grapes they have after eating, we can add them together:

5x/2 + 4 + 5x/2 = 11x/2 + 4

Since they now have the same number of grapes, we can set this equal to the initial total number of grapes they shared:

5x + 6x = 11x

11x = 11x/2 + 4

Multiplying both sides by 2:

22x = 11x + 8

Subtracting 11x from both sides:

11x = 8

Dividing by 11:

x = 8/11

So the initial number of grapes they shared is:

5x + 6x = 11x = 11(8/11) = 8

Therefore, they shared 40 grapes (5x) for Tommy and 48 grapes (6x) for Kim at the beginning.

Answer:   35+63

The only way to label the expression without changing our numbers is 35+63. We still get the sum of 98 and the same numbers are being used, they are just in a different order.

I hope this helped and Good Luck <3!!!

In interval notation, the solution of the inequality is (25, ∞).

To solve the inequality x(x-7) < x^2 - 5x - 50, we can rearrange the terms and factor the quadratic expression:
x^2 - 7x < x^2 - 5x - 50
-2x < -50
x > 25

In interval notation, the solution is (25, ∞).

So, the answer is (25, ∞).

For more such questions on Inequality.

https://brainly.com/question/30228778#

#SPJ11

Answer: 26

Step-by-step explanation:

65x40%

calculate 65x0.4

    Please give me brainliest

Angle, when two straight lines or rays intersect at a single endpoint,  then an angle is created.

The exterior angle of a triangle equals the sum of opposite interior angles. The angle between any side of a shape and a line that extends from the next side is known as the exterior angle.

∠XYZ  = ∠YWX + ∠WXY

10x - 5   = 3x + 17 + 3x + 2

10x - 5 = 6x + 19

10x - 6x  = 24

4x  = 24

x = 6

∠WXY =  3x + 2

= 3*6 + 2

= 20°

To learn more about angle, visit :

https://brainly.com/question/1309590

#SPJ1

Answer:

1 trillion times larger

Step-by-step explanation:

One kilogram (kg) is equal to 1,000,000,000,000 (1 trillion) nanograms (ng).

Therefore, one kilogram is 1 trillion times larger than one nanogram.

The solution to the inequality is x <= 50. This means that any value of x less than or equal to 50 will satisfy the inequality.

To solve the inequality 100 - 3x >= -50, we want to find the values of x that satisfy this inequality.

Makayla solved the equation 100 - 3x = -50 and got x = 50. This equation is not the same as the inequality we want to solve, but we can check whether Makayla's solution is a valid solution to the inequality.

Substituting x = 50 into the inequality, we get:

100 - 3x >= -50

100 - 3(50) >= -50

100 - 150 >= -50

-50 >= -50

This is a true statement, so x = 50 is a valid solution to the inequality.

However, we also need to check whether there are any other values of x that satisfy the inequality. We can do this by rearranging the inequality to isolate x:

100 - 3x >= -50

100 + 50 >= 3x

150 >= 3x

50 >= x

Therefore, the solution to the inequality is calculated to x <= 50.

Learn more about inequality :

https://brainly.com/question/28418048

#SPJ4

The distance between the landing pads is approximately 12.82 miles.

A straight line is the shortest distance between two points in a two-dimensional space. It is a one-dimensional geometric object that extends infinitely in both directions.

Let's label the distance between the helicopter and Pad A as "x" and the distance between the helicopter and Pad B as "y". Also, let's label the distance between Pad A and Pad B as "d".

We can start by using the tangent function to find the height of the helicopter above Pad A:

tan(46) = h / x

h = x tan(46)

Similarly, we can find the height of the helicopter above Pad B:

tan(16) = h / (x + d)

h = (x + d) tan(16)

Since the helicopter is flying at a constant height, we can equate the two expressions for h and solve for d:

x tan(46) = (x + d) tan(16)

xtan(46) = xtan(16) + dtan(16)

d = x(tan(46) - tan(16)) / tan(16)

Substituting x = 5 miles and the values for the tangent functions, we get:

d = 5 (0.9851 - 0.2760) / 0.2760

d = 5 (0.7091) / 0.2760

d = 12.82 miles

Therefore, the distance between the landing pads is approximately 12.82 miles.

To learn more about straight line from given link:

https://brainly.com/question/29223887

#SPJ1

The area of the triangle is approximately 6.696 square feet.

What is Area of Triangle?

The area of a triangle is the amount of space enclosed by the three sides of the triangle

To find the area of a triangle with two sides and the included angle, we can use the following formula:

Area = (1/2) x a x b x sin(C)

where "a" and "b" are the lengths of the two sides and "C" is the angle between them.

Substituting the given values, we get:

Area = (1/2) x 3.2 ft x 4.7 ft x sin(62 degrees)

Using a calculator, we can evaluate sin(62 degrees) to be approximately 0.88.

So, Area = (1/2) x 3.2 ft x 4.7 ft x 0.88

= 6.696 ft²

Therefore, the area of the triangle is approximately 6.696 square feet.

To learn more about Area of Triangle from the given link

https://brainly.com/question/17335144

#SPJ1

Answer:

The answer is 6.64 ft^2

Step-by-step explanation:

After 11 days, the concentration is 42.4 g/L.

The recursive formula for Cn can be written as Cn = Cn-1 + 0.14Cn-1. This formula shows that the concentration after n days is equal to the concentration after n-1 days plus 14% of the concentration after n-1 days.

To find the salt concentration after 11 days, we can use the recursive formula and plug in the values for C0 and n.

C0 = 10 g/L

C1 = C0 + 0.14C0 = 10 + 0.14(10) = 11.4 g/L

C2 = C1 + 0.14C1 = 11.4 + 0.14(11.4) = 13 g/L

C3 = C2 + 0.14C2 = 13 + 0.14(13) = 14.8 g/L

C4 = C3 + 0.14C3 = 14.8 + 0.14(14.8) = 16.9 g/L

C5 = C4 + 0.14C4 = 16.9 + 0.14(16.9) = 19.3 g/L

C6 = C5 + 0.14C5 = 19.3 + 0.14(19.3) = 22 g/L

C7 = C6 + 0.14C6 = 22 + 0.14(22) = 25.1 g/L

C8 = C7 + 0.14C7 = 25.1 + 0.14(25.1) = 28.6 g/L

C9 = C8 + 0.14C8 = 28.6 + 0.14(28.6) = 32.6 g/L

C10 = C9 + 0.14C9 = 32.6 + 0.14(32.6) = 37.2 g/L

C11 = C10 + 0.14C10 = 37.2 + 0.14(37.2) = 42.4 g/L

Learn more about The Concentration: https://brainly.com/question/10725862

#SPJ11

$$x = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}.$$

To compute the least squared error solution to \( A x=b \), we will use the formula \(x = (A^T A)^{-1} A^T b\).

In this case, \(A = \begin{bmatrix} 4 & 1 \\ 5 & 1 \\ 6 & 1 \end{bmatrix}\), so \(A^T = \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix}\). Therefore, we have that

$$(A^T A)^{-1} A^T b = \left(\begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} \begin{bmatrix} 4 & 1 \\ 5 & 1 \\ 6 & 1 \end{bmatrix}\right)^{-1} \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} b$$

From here, we can compute the inverse of the matrix \(A^T A\) to get

$$(A^T A)^{-1} = \frac{1}{21}\begin{bmatrix} -1 & 2 \\ 2 & -1 \end{bmatrix}$$

Substituting this into the equation above and multiplying through, we get

$$x = \frac{1}{21}\begin{bmatrix} -1 & 2 \\ 2 & -1 \end{bmatrix} \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} b = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}$$

Therefore, the least squared error solution to \( A x=b \) is $$x = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}.$$

  Learn more about least squared error

  brainly.com/question/30176124

  #SPJ11

Answer:

x = 3.92699081 + 7.85398163n where n is an integer

As per the given digit value, 10 times the value of the 7 in 637.739 is 7.

To understand this problem, we need to understand the concept of place value. In our base-10 number system, each digit in a number has a specific value based on its position, or place, in the number. The rightmost digit represents the ones place, the next digit to the left represents the tens place, the next represents the hundreds place, and so on.

In the number 637.739, the digit in the tenths place is 7. This means that the 7 represents 7 tenths, or 0.7. We can see this by writing the number in expanded form:

6 hundreds + 3 tens + 7 tenths + 7 hundredths + 3 thousandths + 9 ten-thousandths

So, if we want to find 10 times the value of the digit in the tenths place (which is 7), we need to multiply 0.7 by 10:

0.7 x 10 = 7

To know more about digit here

https://brainly.com/question/30142622

#SPJ4

Answer:

5 (3x+2)

Step-by-step explanation:

Hope this helps! :)

The factored form is 2y(x - y) - 11x.

Factored form of a polynomial is when the polynomial is written as a product of its factors. Each factor is either a polynomial or a number. Factored form is useful for identifying the zeros of a polynomial and for solving polynomial equations.

To simplify the given expression, we need to combine like terms and factor if possible.

First, let's combine the like terms:

x^2 + 3xy - 4y^2 - 6x + 3y - x^2 - xy + 2y^2 - 5x - 3y

= 2xy - 2y^2 - 11x

Next, let's see if we can factor the expression:

2xy - 2y^2 - 11x

= 2y(x - y) - 11x

Since we cannot factor any further, the simplified expression in factored form is:

2y(x - y) - 11x

To know more about factored form click on below link:

https://brainly.com/question/29065045#

#SPJ11

Therefore, the distance from the center of the circle to the crossing point of the two strings is 40sqrt(2) cm, or approximately 56.57 cm to two decimal places.

The Pythagorean theorem can be used to calculate the distance between the circle's centre and where the two strings cross. Let A and B represent the spots where the threads converge, with O serving as the circle's centre. Next, we have:

OA2 plus OB2 equals AB2.

The circle's radius being equal to half the separation between the two strings, we get:

The equation OA = OB = sqrt((560/2)2 + (640/2)2) (156800)

And because the circle's diameter is twice its radius, we get the following equation: AB = 2 * radius = 2 * 360 = 720.

Now that we have the values, we can calculate:

2 * (156800) = AB2 => 2 * (156800) = 7202 => 313600 = 518400 - 2 * OA2 => OA2 = 102400 / 2 => OA = sqrt(51200) => OA = 40sqrt (2)

Learn more about Decimal here:

brainly.com/question/29765582

#SPJ1

Answer:

y=2-2x

so y=2x+2--£8;£++£

Answer: y=−2x + 2

Step-by-step explanation:

Subtract 2x from both sides of the equation.

y= 2 − 2x

Reorder 2 and −2x.

y= −2x + 2

Answer: Your welcome!

Step-by-step explanation:

Part A: 2x^2 + 3x^2 - 4 + 3xy + 6 + 6 = 7x^2 - 4xy + 6

Part B: 0 = 7x^2 - 4xy + 6 - (2x^2 + 3x^2 - 4 + 3xy + 6 + 6)

= 0 = 5x^2 - 4xy

A) The expression that represents the amount of canned food collected by the three friends is [tex]5x^2 + 3xy + 2[/tex].

B) The expression that represents the number of cans the friends still need to collect to meet their goal is [tex]2x^2 - 7xy + 4[/tex].

Given: Number of cans collected

Jessa: 2x²

Tyree: 3x² - 4

Ben: 3xy + 6

Goal : [tex](7x^2 - 4xy + 6)[/tex]

A) The total amount collected:

Total = Jessa + Tyree + Ben

         = [tex]2x^2 + (3x^2 - 4) + (3xy + 6)[/tex]

         = [tex]2x^2 + 3x^2 - 4 + 3xy + 6[/tex]

         = [tex](2x^2 + 3x^2 + 3xy) + (-4 + 6)[/tex]

         = [tex]5x^2 + 3xy + 2[/tex]

Therefore, the expression is [tex]5x^2 + 3xy + 2[/tex].

B) The number of cans the friends still need to collect to meet their goal is

Cans still needed = Goal - Total

                              [tex]= (7x^2 - 4xy + 6) - (5x^2 + 3xy + 2)[/tex]

                              [tex]= 7x^2 - 4xy + 6 - 5x^2 - 3xy - 2[/tex]

                              [tex]= (7x^2 - 5x^2) + (-4xy - 3xy) + (6 - 2)[/tex]

                              [tex]= 2x^2 - 7xy + 4[/tex]

Therefore, the expression is [tex]2x^2 - 7xy + 4[/tex].

Learn more about Expression here:

https://brainly.com/question/34132400

#SPJ4

Answer:

60

Step-by-step explanation:

Answer:

The area of the triangle is 60 unit²

Step-by-step explanation:

We know that the area of a triangle is :

[tex]A= \frac{1}{2}(Base \times Height)[/tex]

Since Base = 12 unit and Height = 10 unit

So

[tex]A= \frac{1}{2}(12\times 10)=60\\[/tex]

Hence the area of this triangle is = 60 unit²

The Answers are:

            6. HCF is equal to 2

            7. HCF is equal to 2

            8. HCF is equal to 1

            9. HCF is equal to 2

            10. HCF is equal to 49

Highest Common Factor is the full form for this term. The highest factor that may divide two integers evenly is known as the HCF of two numbers. HCF can be assessed using two or more numbers. 

To find the HCF of the following:

HCF of (26, 32):

2      | 26, 32

| 13, 16

HCF is equal to 2.

HCF of (32, 58)

2 | 32, 58

| 16, 29

HCF is equal to 2.

HCF of (25, 37)

No common divisor except 1.

HCF is equal to 1.

HCF of (158, 200)

2 | 158, 200

| 79, 100

HCF is equal to 2.

HCF of (49, 98)

49 | 49, 98

| 1, 2

HCF is equal to 49.

Hence, 6. HCF is equal to 2

            7. HCF is equal to 2

            8. HCF is equal to 1

            9. HCF is equal to 2

            10. HCF is equal to 49

To learn more about HCF, click:

brainly.com/question/29114178

#SPJ1

The percent increase in pipe footage sales is approximately 7%.

To find the percent increase in pipe footage sales, use the formula:

[(New Value - Old Value)/Old Value] × 100.

In this case, the new value is the amount of pipe sold in September (2,558 feet) and the old value is the amount of pipe sold in August (2,390 feet). Plugging these values into the formula, we get:

[(2,558 - 2,390)/2,390] × 100 = [168/2,390] × 100 = 0.0703 × 100 = 7.03%

Therefore, the correct answer is 7%, which is option A. The percent increase in pipe footage sales from August to September is 7%.

Learn more about percent increase here: https://brainly.com/question/11360390.

#SPJ11

m - (8 - 3m)

m - 8 + 3m

m + 3m - 8

4m - 8

Answer:

Step-by-step explanation:

m-(8-3m)

m-8 + 3m

=m+3m-8

=4m-8

Answer:

$948.34

Step-by-step explanation:

35% = .35

.35 x $2299

= $804.65

That is the total before the sales tax and after the sale.

6.25% = .0625

.0625 x $2299

= $143.69, and because that is 6.25% of the total, it must be added onto that as tax.

That means the total is $804.65 + $143.69

= $948.34

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

put the value of x = 4

[tex] \: [/tex]

[tex] \sf \: f( 4 )*g( 4 ) = 3(4)²*( 4 - 8 ) \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3×16*(-4) \\ \sf \: \: \: \: \: \: \: \: \: \: \: = 48*( -4 ) \\ \: \: \: \: \underline{ \sf \red{ \: = -192 \: }}[/tex]

[tex] \: [/tex]

hope it helps! :)

(fo)(fog)(x) = 7x^(2)-6x+1

(gof)(x) = 7x^(2)+8x

Domain is a real number.

The first step in finding (fo)(fog)(x) and (gof)(x) is to substitute the functions into each other. For (fo)(fog)(x), we will substitute g(x) into f(x) for x:

(fog)(x) = f(g(x))

= f(7x^(2)-6x-1)

= (7x^(2)-6x-1) + 1

= 7x^(2)-6x

Now we will substitute (fog)(x) into f(x) for x:

(fo)(fog)(x) = f((fog)(x))

= f(7x^(2)-6x)

= (7x^(2)-6x) + 1

= 7x^(2)-6x+1

For (gof)(x), we will substitute f(x) into g(x) for x:

(gof)(x) = g(f(x))

= g(x+1) = 7(x+1)^(2)-6(x+1)-1

= 7x^(2)+14x+7-6x-6-1

= 7x^(2)+8x

The domain of each function is the set of all real numbers, since there are no restrictions on the values of x. Therefore, the domain of (fo)(fog)(x) and (gof)(x) is all real numbers.

Learn more about domain and functions here:

https://brainly.com/question/23909581#

#SPJ11