2(4+3(x-5))
Answer: 6x-22


-3(9-2(k+3)+5k)

Answer: -9k-9

Explain how you get the answer

The number of solutions to an equation x₁ + x₂ + x₃ + x₄ = 17 are 1140

Consider given equation x₁ + x₂ + x₃ + x₄  = 17,

where x₁ , x₂ , x₃ and x₄ are non-negative integers.

As we know x₁ is the number of ones before the first zero, x₂ the number of ones between the first and the second zero, x₃ the number of ones between the second and the third zero, and x₄ is the number of ones after the third zero.

This means, there is a 1-1 correspondence between the solutions and reorderings of 17 ones and 3 zeros.

So, the number of solutions to given equation would be,

n = ²⁰C₃

Using combination formula [tex]^nC_r=\frac{n!}{r!\times(n-r)!}[/tex],

²⁰C₃ = 20! / (3! × (20 - 3)!)

²⁰C₃ = 1140

So, n = 1140

The possible number of solutions = 1140

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The complete question is:

How many solutions are there to the equation x₁ + x₂ + x₃ + x₄ = 17 where x₁ , x₂ , x₃ and x₄  are nonnegative integers?.

Answer:

Below

Step-by-step explanation:

The answer can be found by   11/5 * 325

 here is how this comes about

    ratios

  325 is to 5 hours as 'd' is to 11 hours

325/5 = d/11     Multiply both sides by ' 11 '

11/5  * 325 = d     ( the equation above )

d = 715 miles

Answer:

8x+42=27

8x=-15

x=-1.875

Step-by-step explanation:

Answer: [tex]16x^2-102x+77[/tex]

Step-by-step explanation:

1) distribute

[tex](-8x+7)(4x+2)\\-32x^2-16x+28x+14\\-32x^2+12x+14[/tex]

2) distribute

[tex](-8x+7)(6x-9)\\-48x^2+72x+42x-63\\-48x^2+114x-63[/tex]

3) solve

[tex](-32x^2+12x+14)-(-48x^2+114x-63)\\(-32x^2+12x+14)+(48x^2-114x+63)\\16x^2-102x+77[/tex]

The simplified exponential expression 3^10×37^9/9^12 as a single power of 3 is given as follows:

3^70.

The exponential expression for this problem is defined as follows:

[tex]\frac{3^{10} \times (3^7)^{12}}{9^{12}}[/tex]

Applying the power of power rule, we have that:

(3^7)^12 = 3^(7 x 12) = 84.

When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:

3^10 x 3^84 = 3^94.

For the denominator, we have that:

9^12 = (3²)^12 = 3^24.

When two terms with the same base and different exponents are divided, we keep the base and subtracted the exponents, hence:

3^94/3^24 = 3^(94 - 24) = 3^70.

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Answer:

(f∘g)(x) = 2x + 12

Step-by-step explanation:

(f∘g)(x) =

f(g(x)) =

2(g(x)) + 4 =  ==> substitute g(x) for x in f(x) = 2x + 4

2(x + 4) + 4 =  ==> substitute x + 4 for g(x)

2x + 2*4 + 4 =  ==> use distribution property on x and 4

2x + 8 + 4 = ==> simplify

(f∘g)(x) = 2x + 12

Answer:

$488.33 monthly savings

Step-by-step explanation:

Parent payment 30% of $21,800 is $6,540.

Subtract all payment from total cost.

21,800−6,540−5,600−3,800=5,680.

Split this into monthly payment by dividing 5,680 by 12 months.

5,680÷12= $488.33

Answer:

3.05yx - 6y

Step-by-step explanation:

​y(3.05x−3.75​)−2.25y

3.05yx -3.75y - 2.25y

3.05yx - 6y

A quadratic equation has the generic form ax2 + bx + c = 0. Thus, the roots are hypothetical, meaning that they have two false roots.

The equation's nature of roots indicates whether it contains rational, irrational, or fictitious roots. Imaginary roots and unreal roots are synonyms.

Having just second-order terms, the quadratic form is a unique nonlinear function (either the square of a variable or the product of two variables).

2x2 - 3x + 5 = 0

a = 2 , b = -3, c = 5

b2 - 4ac = (- 3)2 - 4 (2) (5) (5)

= 9 - 40

= - 31

b2 - 4ac < 0

Therefore, the equation lacks any true roots.

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Full Question = Find the nature of the roots of the quadratic equations. If the real root exist, find them:

i) 2x2 - 3x + 5 = 0

Answer:

Step-by-step explanation:

We can write this out as an equation and let x represent the number:

7x-5=0

Adding five on both sides gives us: 7x=5

Therefore, x=5/7

According to the question A line has a slope of -3 and includes the points (9, 4) and (8, t) then the value of t is 7

Typically, a line's slope provides information about the steepness and direction of the line. Finding the difference between the coordinates of the locations will allow you to quickly compute the slope of a straight line connecting two points, (x1,y1) and (x2,y2). The letter "m" is typically used to signify slope.

tan θ = Δy/Δx

the solution is -

Considering a line with a slope of -3 and also the point (9, 4), we could use the point-slope form of either a line to find the equation of a line:

y - 4 = -3(x - 9)

y = -3x + 27 + 4

y = -3x + 31

We are given some other point on the line (8, t) we can try substituting it in the equation above:

t = -3(8) + 31

t = -24 + 31

t = 7

And hence, the value of the t is 7.

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A. The work done is 300 ft-lbs when a 100 lb rock is lifted to a height of 3 ft.

To calculate the work done, we can use the formula: Work = force x distance x cos(Ф).In this case, the force is the force of gravity acting on the rock, which can be calculated using the formula:

force = m * g

where m is the mass of the rock and g is the acceleration due to gravity (32.17 ft/s^2).

force = 100 lb * 32.17 ft/s^2 = 3,217 ft-lbs

The distance is the height to which the rock is lifted, which is 3 ft.

The angle of the rock to the vertical is 90 degrees, so cos(90) = 0.

So,

Work = force x distance x cos(theta) = 3,217 ft-lbs * 3 ft * 0 = 300 ft-lbs

So, the work done is 300 ft-lbs.

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Answer:

37500

Step-by-step explanation:

40%=$15,000

100%=?

100%×$15,000/40%

$1,500,000/40

=37500

A function argument is a value supplied to achieve the Range function's outcome. This is often alluded to as a latent variable.

This is an optional argument that determines the sequence's point of reference. The default assumption is 0.

A mathematical function includes one or much more arguments in the form of the independent variables that are specified in the definition and can also include parameters.

This is a necessary argument that determines the sequence's final chapter location.

This is an optional argument that specifies the adjustment between both sequence members. The default mode is 1.

A domain of the sum of two or multivalued argument values is considered to be the domain of a function with two or more variables.

A cyclical function's argument is angular. A hyperbolic perspective is the input of a hyper equation.

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Equations of degree one and having two variables are known as linear equations in two variables. It is of the form, ax +by +c = 0, where a, b and c are real numbers, and both a and b not equal to zero.

Equations of the form a x +b y = 0; where a and b are real numbers, and a ,b ≠ 0, is also linear equations in two variable.

Since the solution of linear equation in two variable is a pair of numbers (x,y), we can represent the solutions in a coordinate plane.

To draw graph , we need to find some points

y =-3x

for  y =-3x ,lets substitute value and check,

x=0

then y =0

x=1

then y =-3

x=2

then y =-6

x=3

then y =-9

x=-1

then y =3

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Since 1 and 3 are vertical angles, the graphic demonstrates that m1 = 90. They have identical measurements, therefore m3 = 90. 1 and 2 are additional.

A circle is formed when every point in the plane that is a specific distance apart from another point does so (center). Thus, it is a curve made up of points that are separated from one another by a set distance while moving in the plane. It is also rotationally symmetric about the center at all angles. A circle is a closed, two-dimensional object where each pair of points in the plane is equally separated from the "center." A specular symmetry line is made by drawing a line through the circle. It is also rotationally symmetric about the center at all angles.

given

when measured with a protractor, points to 100°, crossing 90°. As a result, the angle has a 100° measurement.

Since 1 and 3 are vertical angles, the graphic demonstrates that m1 = 90. They have identical measurements, therefore m3 = 90. 1 and 2 are additional.

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When solving an inequality:

In arithmetic, an inequality is a relation that makes a non-equal assessment between two numbers or other mathematical expressions. it is used most usually to evaluate numbers on the range line by using their size.

In mathematics, a dating between two expressions or values that aren't identical to every other is called 'inequality. ' So, a loss of balance consequences in inequality. The three facets and three angles proportion an important relationship. In arithmetic, the term “inequality” represents the that means “not equal”. allow us to bear in mind a simple example if the expressions in the equations are not the same, we can say it is inequality.

Whilst two actual numbers or algebraic expressions are represented with symbols like <, > or ≤, ≥ they can be called an inequality. as an example, 3x<20, or 4x+y>12. which means Of The Symbols used in Inequalities: The image < manner 'less than' and ≤ means much less than or same to.

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Answer:18

Step-by-step explanation: Using the order of operations (PEMDAS), you would first perform any calculations inside of parentheses, then exponents, then multiplication and division from left to right, and finally, addition and subtraction from left to right.

9 + 15 / 5 x 3

= 9 + 3 x 3

= 9 + 9

= 18

So the answer would be 18.

[tex]\huge\text{Hey there!}[/tex]

[tex]\frak{\text{A}ssuming. . .}[/tex]

[tex]\mathsf{4.8x = 2.4}[/tex]

[tex]\frak{\mathsf{DIVIDE}\ 4.8\ to\ both\ sides}[/tex]

[tex]\mathsf{\dfrac{4.8x}{4.8} = \dfrac{2.4}{4.8}}[/tex]

[tex]\frak{\mathsf{Simplify} \ it}[/tex]

[tex]\mathsf{x = \dfrac{2.4}{4.8}}[/tex]

[tex]\mathsf{x = 0.5}[/tex]

[tex]\huge\boxed{\frak{T}}\huge\textsf{herefore your answer should be:}}[/tex]

[tex]\huge\boxed{\mathsf{x = 0.5}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

There are several ways to find the measure of an angle in a triangle, depending on the information given about the triangle and the angles. Some common methods include:

Using the angles in a triangle sum to 180 degrees: If you know the measures of two angles in a triangle, you can use the fact that the angles in a triangle sum to 180 degrees to find the measure of the third angle.

Using the Pythagorean theorem: If you have a right triangle, you can use the Pythagorean theorem to find the measure of the right angle (90 degrees)

Using the Law of Cosines: If you know the measures of two angles and the lengths of all three sides of a triangle, you can use the law of cosines to find the measure of the third angle.

Using trigonometry: If you know the lengths of two sides of a triangle and the measure of one angle, you can use trigonometry to find the measure of the other angles.

It is important to note that in order to find the measure of an angle you need to know at least one angle and the values of the sides of the triangle or two angles.

log x is strictly increasing in interval (0, ∞).

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as For x > 0 , a > 0, and a ≠1,y= loga x if and only if x = ay .Then the function is given by f(x) = loga x .The base of the logarithm is a. This can be read it as log base a of x. The most 2 common bases used in logarithmic functions are base 10 and base e

The given function is f(x)= logx.

f'(x)=derivative of f= 1/x.

clearly ,1/x>0

hence the function is strictly increasing.

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Substitution is a method for solving systems of equations by substituting the values from one equation into the other. To use substitution to determine if an ordered pair is the solution to a system of equations, first solve one of the equations for either x or y.

Then substitute this value into the other equation, and solve for the other variable. If the ordered pair you obtain is also found in both equations, then it is a solution to the system.

Take the equation set as an example.

2x + y = 5

3x – y = 1

To use substitution to determine if (2, 3) is a solution to this system, first solve one of the equations for either x or y:

2x + y = 5  ⇒ y = 5 – 2x

Add this value to the other equation after that:

3x – (5 – 2x) = 1  

⇒  5x = 6  

⇒ x = 6/5

Finally, substitute 6/5 back into either equation to find y:

2(6/5) + y = 5  

⇒ 12/5 + y = 5  

⇒  y = 10/5  

⇒  y = 2

Since (6/5, 2) is found in both equations, it is a solution to the system.

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Answer:

400!

Simple Step-by-step explanation:

40x10

=400

Sorry for being late <3

Answer:

x = -3

y = 5

Step-by-step explanation:

3x + 2y = 1

5x + 4y = 5 ​

First, we multiply the first equation by -2

-6x -4y = -2

5x + 4y = 5

-x = 3

x = -3

Now put -3 back in for x and solve for y

3(-3) + 2y = 1

-9 + 2y = 1

2y = 10

y = 5

Let's check

3(-3) + 2(5) = 1

-9 + 10 = 1

1 = 1

So,  x = -3 & y = 5 is the correct answer.

32.56 is the expected weight for a bluegill fish that is 11 inches long.

Equation: What is it?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party. Multiple terms, operators, and variables are not required on each side of an equation. Without them, one can still create an equation, such as 5 + 10 = 15. There are no variables in the equation below.

given expression:

In(Weight) = -5.28 + 3.44 In(Length)

So, we have to find 11 inches then

In(weight) = -5.28 + 3.44 x 11

               = -5.28 + 37.84

               = 32.56

Hence, 32.56 is the expected weight for a bluegill fish that is 11 inches long.

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The type of function always has an inverse is one to one.

In math function is referred as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Here we need to identify the type of the function always has an inverse.

As we all know that in each and every function has an inverse, here we have also know that but not every inverse will be a function.

Where as the inverse may fail the vertical line test.

Here we have identified that if the original function is a one-to-one function then its inverse will be a function.

Finally in a one-to-one function not only passes the vertical line test, then it also passes a horizontal line test.

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Lana has 5 apples and her friend has 10 times as many as her So her friend will have 50 apples.

Here times mean The symbol is used in mathematics to represent the multiplication operation and the resultant product. It is sometimes referred to as the time sign or the dimension sign.

So if Lana has 5 apples

her friend has 10 times as many as her

By using the unitary method

The unitary approach is a methodology for problem-solving that involves first determining the value of a single unit and then determining the necessary value by multiplying the single unit value.

The unitary method's formula is to get the value of a single unit and then multiply that value by the number of units to obtain the required value.

5 time 10

50 apples

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The exponent or power that must be added to a base to produce a particular number is called the logarithm.

Indicated by the letter log n, the later class of logarithms, those with base 10, are referred to as common or Briggsian logarithms.

Logarithms, which were developed in the 17th century to expedite calculations, significantly decreased the amount of time needed to multiply integers with numerous digits. For more than 300 years, they served as the foundation for numerical labor, but the development of mechanical adding machines in the late 19th century and computers in the 20th century made them obsolete for large-scale calculations.

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