Solve each equation by factoring. Check your answers.
x²+9 x+20=0

Taking into account the definition of a system of linear equations, you little brother has 6 dimes.

A system of linear equations is a set of equations that have more than one unknown, appearing in several of the equations but necessarily in all of them. The equations relate the unknowns to each other.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. In other words, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know that:

The system of equations to be solved is

[tex]\left \{ {{d+n=42} \atop {0.1d + 0.05n=3}} \right.[/tex]

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "n" from the first equation:

n= 42 -d

Replacing this expression in the second equation obtained:

0.1d + 0.05×(42 - d)= 3

Solving:

0.1d + 0.05×42 - 0.05d= 3

0.1d + 2.1 - 0.05d= 3

0.15d + 2.1=3

0.15d= 3 -2.1

0.15d= 0.9

d= 0.9÷0.15

d= 6

Finally, you little brother has 6 dimes.

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Answer:

I am not sure but I think its is $1.13

There are 12 cups inside a 3-quart container

Step-by-step explanation:

Answer:

This equation has one solution I believe if you substitute the variable 68.3375

Step-by-step explanation:

According to the question, the solution for the equation [tex]ln(x)=2[/tex]  is [tex]e^{2}[/tex]. And the procedure for the given equation is as follows:

Expression: [tex]ln(x)=2[/tex]

Removing logarithmic function from the equation, equate it to exponential. Therefore, the expression can be re-written as:

                                  [tex]ln(x)=2\\(x)=e^{2}[/tex]

Therefore, the solution for the equation is :[tex]x=e^{2}[/tex].

What is logarithmic function?

In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.

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The measure of the angles m∠JKL = (10x + 5)° and m∠PLK = (12x - 1)° are 25 degrees and 23 degrees respectively.

Parallel segments are defined as lines on a plane that never meets.

The properties of parallel segments include:

Given the angles;

We can see that the two angles are vertically opposite angles and thus equal.

Then,

m∠JKL  = m∠PLK

substitute the values

10x + 5 = 12x - 1

collect like terms

10x - 12x = -1 - 5

-2x = - 6

Make 'x' the subject of formula

x = 3

But:

m∠JKL = (10x + 5)° = 10(2) + 5 = 25°

m∠PLK = (12x - 1)° = 12(2) - 1 = 23°

Thus, the measure of the angles m∠JKL = (10x + 5)° and m∠PLK = (12x - 1)° are 25 degrees and 23 degrees respectively.

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Answer:

8.3333333 square & root of 25

Step-by-step explanation:

Answer:

1/20 = 5%

Hope this helps with your question :)

Step-by-step explanation:

1. Multiply numerator and denominator by 5 to get 100 in the denominator.

1/20 = 5/100

2. A number over 100 means it is that number on top of 100.

5/100 = 5% out of 100%

3. So final answer is 5%

=================================================

Explanation:

First let's find the nth term denoted as [tex]a_n[/tex]

[tex]a_n = a_1 + d(n-1) \ \text{ ... formula for arithmetic sequences}\\\\a_n = 20 + (-5)(n-1) \\\\a_n = 20 -5n+5 \\\\a_n = -5n+25 \\\\[/tex]

Now we can find the 18th term by plugging in n = 18

[tex]a_n = -5n+25 \\\\a_{18} = -5(18)+25 \\\\a_{18} = -90+25 \\\\a_{18} = \boldsymbol{-65} \\\\[/tex]

Answer:

-65

The 18th term in the sequence is -65.

Step-by-step explanation:

an=a1+(n-1)d

d=-5

a1=20

n=18

a18=20+(18-1)(-5)

Simplify.

a18=20+(17)(-5)

a18=20-85

a18=-65

The 18th term in the sequence is -65.

Hope this helps!

Please mark as brainliest if correct!

The time taken by Sonia to mow 2.5 acres of land with push mower is 3.125 hours .

According to the question we have been given that

    Time taken by push mower to mow 1 acre land = 1.25 hours

     Time taken by Gas mower to mow 1 acre land = 35 minutes

We need to find how many hours Sonia take to mow 2.5 acre of land with push mower.

To find this we will use unitary method. That is

                    1 acre = 1.25 hours

                    2.5 acre = 1.25*2.5 hours

                                 = 3.125 hours.

Hence the time taken by Sonia to mow 2.5 acres of land with push mower is 3.125 hours .

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Since in the image above angle 3 is 79 degrees, angle 11 is also equal to 79 degrees based on the vertical angles theorem.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

The vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are generally formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

In Geometry, when two (2) parallel lines are cut by a transversal, the interior angles that are formed on the same side of the transversal are supplementary angles, which makes:

Angle 3 = Angle 14

Angle 14 = Angle 9

Angle 3 ≅ Angle 9 (Congruent angles or supplements of the same angle)

By applying the vertical angles theorem, we have:

Angle 9 ≅ Angle 11 = 79 degrees.

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Answer:

3

Step-by-step explanation:

11 = 3x+2
9 = 3x
x = 3

The value of e³/₂ is 4.4758

e in here is considered as Euler's number. Euler's number is a numerical constant which is often used in mathematical calculations. the value of e can be taken into consideration as 2.71828.

The given expression e⁽³÷²⁾ can also be written as √e³. First the cube of e is calculated which is then followed by finding the square root of the calculated value.e⁽³÷²⁾ = √e³. The value of e³ when calculated is 2.7182 x 2.7182 x 2.7182 = 20.0855

Now taking the square root of the calculated value is √20.0855 is 4.4816

Therefore the value of e⁽³÷²⁾ up to four decimal places is 4.4816

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The coefficient in this question represents the cost for the gigabytes over her plan.

A coefficient is a number that is multiplied by a variable. In this question, the coefficient is 10 and the variable is x. 10 here represents the the cost for the gigabytes over her plan.

10x represents the variable cost. Variable cost is the cost that increases with the number of gigabyte used. Fixed cost is the cost that does not change with the gigabyte used. It remains constant regardless of the level of gigabyte used.  Total cost is the sum of the fixed cost and the variable cost. The fixed cost is the cost of her normal plan.

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1) The earthquake at New Madrid was of greater intensity than earthquake at San Francisco.

2) The earthquake at New Madrid was of lesser intensity than earthquake at Valdivia.

3) The earthquake at New Madrid was of greater intensity than earthquake at  Charlottesville.

4) The earthquake at New Madrid was of greater intensity than earthquake at  Kobe.

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The question is incomplete. The complete question is

In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below.

1. magnitude 7.7 in San Francisco, California, in 1906

2. magnitude 9.5 in Valdivia, Chile, in 1960

3. magnitude 3.2 in Charlottesville, in 2001

4. magnitude 6.9 in Kobe, Japan, in 1995

Using given algebraic equation, Keelan collected 431 tokens.

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

At least one variable and one operation must be present in an algebraic expression (addition, subtraction, multiplication, division). One such algebraic statement is 2(x + 8y).

You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic statement. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we may substitute those values for the original variables before evaluating the expression.

Given,

p=20x+75

p = 8695

8695 = 20x + 75

x = 8695 - 75 / 20

x = 431

Therefore Keelan collected 431 tokens.

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The three positive integers are 34, 35, 36

Three positive integers are given as (x-1),x and (x+1)

Sum of these three integers are 105,

As we know the total sum of the three positive integers, we can get the value by adding the three integers to the sum value.

Thus,

(x-1) + x + (x+1) = 105

x - 1 + x + x + 1 = 105

3x + 0 = 105

3x = 105

x = 105/3

x = 35

Then, the integers are (35 - 1) , 35 , (35 + 1)

Therefore, the three positive integers are 34, 35, 36

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The sides of angle 4 will be side CD and side DG.

We are given a ray diagram.

We need to tell the sides or the rays of the angle 4.

an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes.

Here, angle 4 has the sides as CD and DG.

Therefore, the sides of angle 4 will be side CD and side DG.

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Answer:477.47 revolutions

Step-by-step explanation:

The perimeter of the polygon is 12.

The perimeter of a closed figure is the sum of the lengths of its outermost sides. It is the sum of the lengths of a polygon's sides. All sides add up to the perimeter.

The distance between the two points A(x, y) and B(x₁, y₁ ).

AB = √ [ (x₁ - x)² + (y₁ - y)² ]

Consider the vertices U ( -1, 4), V (3, 4), W (3, 1).

Then,

UV = √ [ ( 3 +1)² + (4 - 4)² ] = √4² = 4

VW = √ [ ( 3 - 3)² + ( 1 - 4)² ] = √(- 3)² = 3

UW = √ [ ( 3 + 1)² + ( 1 - 4)² ] = √ [ ( 4)² + (-3)² ] = √ [ 16 + 9 ] = √25 = 5

Then the perimeter of the polygon will be:

perimeter = UV + VW + UW

perimeter = 4 + 3 + 5 = 12

Hence, the perimeter of the polygon is 12.

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Answer: The answer is B

Answer: 225

Step-by-step explanation:

I may not be right but I’m taking that ascends is basically adding up the height so 150+75=225

The answer of the logarithmic form is -2 .

We have given an equation [tex]log_2\frac{1}{4}[/tex]   ..... (1)

Applying the property of logarithm which is given by [tex]log_xy=\frac{log_ay}{loh_ax}[/tex]  in equation (1) ,we get

     [tex]log_2\frac{1}{4}=\frac{log\frac{1}{4} }{log2}[/tex]                      ..(2)

[tex]log\frac{1}{4}[/tex] can be written as [tex]log1-log4[/tex] using property [tex]log\frac{a}{b} =loga-logb[/tex] whereas [tex]log1=0[/tex]

Then , the equation (2) becomes

       [tex]log_2\frac{1}{4}=\frac{log1-log4 }{log2}\\\\log_2\frac{1}{4}=\frac{0-log4 }{log2}\\\\log_2\frac{1}{4}=\frac{-log4 }{log2}[/tex]

[tex]log4[/tex] can be written as [tex]log2^2[/tex]

The equation (2) becomes

                    [tex]log_2\frac{1}{4}=\frac{-log2^2 }{log2}[/tex]                

   using property [tex]loga^b=bloga[/tex]

           [tex]log_2\frac{1}{4}=\frac{-2log2 }{log2}\\log_2\frac{1}{4}=-2[/tex]

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Answer: There is none

Step-by-step explanation:

Answer:

[tex] {1.4 \times 10}^{3} | [/tex]

Step-by-step explanation:

*winks and runs off ;)*

Probability of at least one boy and one girl = [tex]\frac{3}{4}[/tex]

The probability of no of boys = 1/2 ×1/2×1/2= 1/8

The probability of no of girls = 1/2×1/2×1/2= 1/8

Now we have to find the probability of at least one girls

Probability of one boy and one girl = 1 - (1/8 + 1/8)

                                                           = 1 - 1/4

                                                           = 3/4

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The point of discontinuity for y= x²-x-2 / 3 x²-7 x+2 is x= 1/3 and x= 2.

What is discontinuous function?

Mathematics, functions, and applications all place a premium on continuous functions. But not every function is continuous. A function is said to have a discontinuity there if it is not continuous at that point in its domain.

Given,

y = x²-x-2 / 3 x²-7 x+2

It can be expressed in the form of -

⇒ y = (x-2) (x+1) / (3x-1) (x-2)

The function will be undefined if the denominator will be 0

⇒ 3x-1 = 0

⇒ x = 1/3

⇒ x-2 = 0

⇒x = 2

So, we can conclude that the given function will be having points of discontinuity as x = 2, 1/3

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Check the picture below, that one shows the imperial units, however is pretty much the same curve for a metric one, namely using metres, so the maximum point is at the vertex y-coordinate.

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-4.9}t^2\stackrel{\stackrel{b}{\downarrow }}{+229}t\stackrel{\stackrel{c}{\downarrow }}{+234} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 229}{2(-4.9)}~~~~ ,~~~~ 234-\cfrac{ (229)^2}{4(-4.9)}\right) \implies \left( - \cfrac{ 229 }{ -9.8 }~~,~~234 - \cfrac{ 52441 }{ -19.6 } \right) \\\\\\ \left(\cfrac{1145}{49}~~,~~ 234+\cfrac{262205}{98} \right)\qquad \approx\qquad (\stackrel{seconds}{23.37}~~,~~\underset{\bigtriangleup}{\stackrel{meters}{2909.56}})[/tex]

The solution to the equation 3 - 1/2d = 3/2d + 4 - d is d = -7

The expression is given as

3 - 1/2d = 3/2d + 4 - d.

Multiply through the expression by 2

So, we have

6 - d = 3d + 8 - 2d

Evaluate the like terms

6 - d = d + 8

Evaluate the like terms

2d = -14

Divide by 2

d = -7

Hence, the solution to the equation 3 - 1/2d = 3/2d + 4 - d is d = -7

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