At which points are the functions y = f(x) and y = g(x) equal? What are the x-values of the solution?

The slope of the equation 3x + 4y = -12 is -3/4

Slope in math is defined as the ratio of the amount that y increases as x increases some amount

Here we have given the equation 3x + 4y = -12.

As we all know that the general form of the equation of the line is written as,

y = mx + c

here m refers the slope of the line and c refers the y intercept of the line.

Now, we have to convert the given equation into the general form then it can be look like the following,

=> 4y = -12 - 3x

=> y = -12/4 - 3x/4

It can be rewritten as,

=> y = -3x/4 - 12/4

Then the resulting slope is -3/4.

Complete Question:

What is the slope of the equation 3x + 4y = -12?

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The solutions of the system are x = 1, y = 2 and z = -1.

And we solve the system with the help of Jordan-canonical form.

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the numbers.

Given:

A system of equations,

x + y - 2z = 5

-x + 2y + z = 2

2x + 3y - z = 9

In the matrix form;

[tex]\left[\begin{array}{ccc}1&1&-2\\-1&2&1\\2&3&-1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}5\\2\\9\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}1&1&-2\\0&0&-10/3\\0&1&3\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}5\\10/3\\-1\end{array}\right][/tex]

That means,

x = 1, y = 2 and z = -1.

Therefore, the solutions of the system are x = 1, y = 2 and z = -1.

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The credit utilization ratio would be 11.7%.

What is credit utilization?

The credit utilization ratio is a measure of how much of a person's credit limit is being used. It is calculated by dividing the total credit card balances by the total credit limit.

In Mary's case, the total credit card balances are $150 + $200 = $350

The total credit limit is $2000 + $1000 = $3000

To find the credit utilization ratio, we divide the total credit card balances by the total credit limit:

$350 / $3000 = 0.117 or 11.7%.

Hence, the credit utilization ratio would be 11.7%.

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The nth partial sum of a geometric sequence can be calculated using the first term a1 and common ratio r as follows: Sn=a1(1−rn)1−r. The infinite sum of a geometric sequence can be calculated if the common ratio is a fraction between −1 and 1 (that is |r|<1) as follows: S∞=a11−r.

In arithmetic, a chain is an enumerated series of gadgets in which repetitions are allowed and order matters. Like a hard and fast, it consists of contributors (additionally referred to as elements, or terms). The quantity of elements (possibly endless) is called the duration of the series.

Unlike a fixed, the same factors can appear a couple of times at distinct positions in a chain, and unlike a fixed, the order does be counted. formally, a chain can be described as a function from herbal numbers (the positions of elements inside the collection) to the factors at each position. The belief of a sequence may be generalized to a listed family, defined as a character from an arbitrary index set.

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The product is 3x * 4x^(3/2) = 12x^(5/2)

How to do the product of root?

When multiplying two terms with the same base and different exponents, you can add their exponents.

For example, √(a^m) * √(a^n) = √(a^m * a^n) = √(a^(m+n)) = a^((m+n)/2)

The product of 3√(x^2) * 4√(x^3) is equal to:

12x^(5/2)

This is because when you multiply two terms with the same base, you can add their exponents:

3√(x^2) * 4√(x^3) = (3*4)√(x^(2+3/2)) = 12x^(5/2)

This is because

√(x^2) = x^(2/2) = x

√(x^3) = x^(3/2) = x^(3/2)

so we can write 3root x^2 = 3x and 4root x^3 = 4x^(3/2)

Hence, the product is 3x * 4x^(3/2) = 12x^(5/2)

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Therefore , the solution of the given problem of inequality comes out to be 13 and 17 is the number of hikers.

In mathematics, an inequality is a linear connection or a collection of numbers even when there is no equal sign. Equity always comes after equilibrium. When two numbers are not equal, inequality exists. Between equality and inequality, there exist differences. The most common symbol was chosen because when parameters aren't the same or comparable (). Values can be compared using a variety of disparities, no matter how few or numerous they are.

Here,

Given :

a) The minimum number of hikers

who walks between 8 miles and 19 miles :

=> 8 < x < 19

=> 7 +6

=> 13

b) The maximum number of hikers

who walks between 8 miles and 19 miles :

=> 8 < x < 19

=> 7+6+4

=> 17

Therefore , the solution of the given problem of inequality comes out to be 13 and 17 is the number of hikers.

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The way to change improper fractions to mixed numbers for kids is solved by using the division operation.

In math the term called fraction is defined as a part of a whole number, and a way to split up a number into equal parts

Here we need to identify the way to change improper fractions to mixed numbers for kids.

As from the definition of fraction we have identified that the way to solve the improper fraction into mixed fraction is written as follows:

Here we have to convert an improper fraction to a mixed number,

Then we have to work out how many whole numbers there are by dividing the numerator by the denominator.

And then we have to make the remainder the new numerator and leave the denominator as it was.

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Answer:

c)31

Step-by-step explanation:

The goal of this exercise is to determine the total savings by paying the debt early at

�

)

a)

19

19th payments

�

)

b)

25

25th payments and

�

)

c)

31

31st payments.

There are two methods of indirect proof:

Proof of the contrapositive and proof by contradiction.

Now, According to the question:

Let's know:

An indirect proof, also called a proof by contradiction, is a roundabout way of proving that a theory is true. When we use the indirect proof method, we assume the opposite of our theory to be true. In other words, we assume our theory is false.

Hence, There are two methods of indirect proof:

Proof of the contrapositive and proof by contradiction.

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The fuel efficiency of the first car was 40.72 miles per gallon and the fuel efficiency of the second car was 14.28 miles per gallon.

The problem can be solved by using a system of equations.

We can call the fuel efficiency of the first car x and the fuel efficiency of the second car y.

From the problem, we know:

x + y = 55 (the combined fuel efficiency of the two cars is 55 miles per gallon)

We can also use the information about the amount of gas consumed and the distance has driven to set up another equation:

(30 gallons) * (x miles per gallon) + (40 gallons) * (y miles per gallon) = 1850 miles

Now we have a system of two equations with two variables (x and y):

x + y = 55

(30)x + (40)y = 1850

We can solve this system of equations using any method of solving such as substitution or elimination.

x = 55 - y

and substitute it in the second equation

(30)(55-y) + (40)y = 1850

1650 - 30y + 40y = 1850

-14y = -200

y = 14.28

x = 55 - 14.28 = 40.72

So the fuel efficiency of the first car was 40.72 miles per gallon and the fuel efficiency of the second car was 14.28 miles per gallon.

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This means that the solution to the equation x is 6.

An equation is a mathematical statement that expresses the relationship between two values. It typically consists of an equal sign (=) and two expressions that are related to each other. Equations are used to describe how one value depends on another, or how two values are related to each other.

To solve this equation, use the Quadratic Formula,
which states that for an equation of the form ax2 + bx + c = 0,
the solution is x = [-b ± √(b2 - 4ac)] / 2a.
Plugging in the given equation,
we have a = 5, b = -3, and c = 45.
This means that the solution to the equation is x = [-(-3) ± √((-3)2 - 4*5*45)] / 2*5, or x = 6.

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The cost of one cookie is 1. This value can be determine from the eliminate methods or substitution methods.

As per data given is a two different formula of pizza and cookie, we can determine it by elimination methods or substitution methods. Let do it by elimination methods. As per formula given are first buy 3 pizza + 2 cookie =  6.50 and the second buy 1 pizza + 1 cookie = 2.50. The calculation will be:

3 pizza + 2 cookie =  6.50

1 pizza + 1 cookie = 2.50     multiply with 3 because we want eliminate pizza

3 pizza + 2 cookie =  6.50

3 pizza + 3 cookie = 7.50       -

0 pizza - 1 cookie = - 1

1 cookie = 1

Hence the price of one cookie will cost you 1.

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The formula which represents the solution of the given equations; 13x = 6y for variable, x is; x = 6y / 13.

It follows from the task content that the solution of the given equation for variable, x is to be determined.

Since the given equation is; 13x = 6y.

It follows that the equation can be solved as follows;

13x = 6y

Divide both sides of the equation by 13 so that we have;

x = 6y / 13.

Ultimately, the formula for x is; x = 6y / 13.

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Erika should use the coupon which gives her a discount of 15% as it will bring down the cost of the cooler to $106.25.

Given,

          The initial cost of the cooler = $125

Erika has two options: (i) 15% off coupon

                                     (ii) $15 off coupon

Cost of the cooler that Erika gets from option (i):

                                [tex]= 125 - \frac{15}{100} * 125\\= 125 - 18.75\\= 106.25\\[/tex]

Cooler costs $106.25 to Erika from option (i).

Cost of the cooler that Erika gets from option (ii):

                                [tex]= 125 -15\\=110[/tex]

Cooler costs $110 to Erika from option (ii).

We can clearly see, $106.25 < $110

Therefore, Erika should use the coupon which gives her a discount of 15%.

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The result of addition and subtraction is

The directions to solve these problems are to round each fraction to the nearest whole number and then add or subtract. We have to round each fraction into the nearest whole number.

1. 5 (2/3) - 1 (1/4) = (5 + 1) - 1 = 6 - 1 = 5

2. 8 (5/12) + 31 (1/6) = 8 + 31 = 39

3. 3 (1/4) + 3 (3/5) = 3 + (3 + 1) = 3 + 4 = 7

4. 9 (1/10) - 6 (7/10) = 9 - (6 + 1) = 9 - 7 = 2

5. 7 (5/8) + 2 (1/7) = (7 + 1) + 2 = 8 + 2 = 10

6. 20 (9/11) - 18 (3/10) = (20 + 1) - 18 = 21 - 18 = 3

7. 10 (3/7) + 22 (2/9) = 10 + 22 = 32

8. 1 (5/6) + 5 (1/6) = (1 + 1) + 5 = 2 + 5 = 7

9. 113 (1/13) + 86 (9/11) = 113 + (86 + 1) = 113 + 87 = 200

10. 65 (17/20) + 19 (3/25) = (65 + 1) + 19 = 66 + 19 = 85

11. 71 (41/50) + 25 (5/24) = (71 + 1) + 25 = 72 + 25 = 97

12. 12 (13/15) + 18 (2/5) = (12 + 1) + 18 = 13 + 18 = 31

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The zeros of the given function y = x²-4 are 2 and -2.

The zeros of a function are defined as the values of the variable of the function such that the function equals 0.

Given is a function, y = x²-4

To find the zeros, equate the function to 0,

x²-4 = 0

x² = 4

x = ±2

Hence, the zeros of the function are 2 and -2.

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Answer:

  28.5 m/s

Step-by-step explanation:

Given that power is 1400 W when speed is 25 m/s, and power is proportional to the square of speed, you want the speed when the power is 1820 W.

Since power is proportional to the square of speed, the ratio of speed squared to power is a constant:

  s²/P = 25²/1400 = x²/1820

where x is the unknown speed.

We can find the value of x by multiplying by 1820 and taking the square root:

  x² = 25²(1820/1400)

  x = 25√(1820/1400) = 25√1.3 ≈ 28.5 . . . . m/s

The speed is 28.5 m/s when the power is 1820 watts.

Multiply the hypotenuse of triangle by sinθ to determine the length of the side opposite the angle (θ). Alternatively, to obtain the side next to the angle, multiply the hypotenuse by cos(θ).

Scalene triangles are typically described as triangles with no two sides that are equal. Isosceles triangles are those triangles whose two sides are equal. An equilateral triangle is one with equal lengths on each of its three sides. Clearly, all equilateral triangles are isosceles, but not the opposite.

The side across from the right angle is always the hypotenuse of a right triangle. The opposite and neighboring sides are the other two sides.  

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It is linear if and only if the coefficients of y (the dependent variable) and all order derivatives of y are functions of t or constant terms.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

It is linear if and only if all order derivatives of y (the dependent variable) are functions of t or constant terms.

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Answer:

65° or 115°

Step-by-step explanation:

there is no picture but if

mEDB looks like mCDB then its 65°

but if they dont look alike then

180-65=115

straight line is 180°

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The questions 18, 19, and 20 have the values of x for the bisected angle to be 6, 15, and 8 respectively.

If line UW bisects m∠TUV then;

m∠TUW = m∠WUV

13x - 5 = 7x + 31

13x - 7x = 31 + 5 {collect like terms}

6x = 36

x = 36/6 {divide through by 6}

x = 6

If line MO bisects m∠PMN then;

2(m∠OMN) = m∠PMN

2(2x + 7) = 74 {divide through by 2}

2x + 7 = 37

x = (37 - 7)/2 {make x the subject}

x = 15

If line EF bisects m∠CEB then;

m∠FEB = m∠CEF

10x - 3 = 7x + 21

10x - 7x = 21 + 3 {collect like terms}

3x = 24

x = 24/3 {divide through by 3}

x = 8

Therefore 6, 15, and 8 are the values of x for questions 18, 19, and 20 respectively for the bisected angles.

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Answer:

I think its two

Step-by-step explanation:

If I am wrong sorry

Answer:To find the unit rate in chapters per hour, we need to divide the number of chapters read by the amount of time it took to read them.

6 3/4 chapters / 1 7/8 hours = (64+3)/(18+7) chapters/hours

= (25/8) chapters/hours

To simplify this fraction, you can divide both the numerator and denominator by their greatest common factor which is 1.

25/8 chapters/hours = (25/8) chapters/hours

So the unit rate in chapters per hour is 25/8 chapters per hour.

Step-by-step explanation:

1 in 3 angle of slope in degree is 18.435°.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located.

The inverse tangent function is called arctangent, often known as arctan or tan-1. Tangent only has a limited domain for its inverse function.

So to find the 1 in 3 angle we have to put the value 1/3 in arctan function

∴ arctan (1/3) = 18.43494882° ≈ 18.435.

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In an experiment, there is a H 0.08 probability that a player will move both two and five spaces during a game.

Player movement during a turn is determined by a spinner. It displays the outcomes of 10 spins.The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities. chances in multiples.

A (1): the probability that a particular occurrence will take place. (2): the proportion of the number of outcomes in a comprehensive set of equally likely options that result in a specific event to the total number of conceivable outcomes. How likely something is to occur is known as its probability. when we are unsure of how an event will turn out.

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=> 999 is not a perfect cube.

Because cube root of 999 is 3 [tex]\sqrt[3]{37}[/tex] .

Now, According to the question:

A cube number is the result when a number has been multiplied by itself twice. The symbol for cubed is 3. For example, 8 is a cube number because it's 2 x 2 x 2 (2 multiplied by itself twice); this is also written as [tex]2^3[/tex] (“two cubed”).

It is the real solution of the equation [tex]x^3[/tex] = 999.

The cube root of 999 is expressed as [tex]\sqrt[3]{999}[/tex] or 3 [tex]\sqrt[3]{37}[/tex] in the radical form and as[tex](999)^\frac{1}{3}[/tex] or [tex](999)^0^.^3^3[/tex] in the exponent form.

The prime factorization of 999 is 3 × 3 × 3 × 37, hence, the cube root of 999 in its lowest radical form is expressed as 3 [tex]\sqrt[3]{37}[/tex].

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Mandy will catch up Rita at 0.5 hour after they start walking.

As per data given are Mandy start = 1, Rita start = 2, Mandy speed = 5 and Rita speed = 2. Based on this explanation we can determine the formula for Mandy time to catch up Rita as follow

s1 = s2

Rita start + Rita speed x t = Mandy start + Mandy speed x t

2 +3 x t = 1 + 5 x t

2 + 3t = 1 + 5t

2 - 1 = 5t - 3t

1 =  2t

t = 0.5 h

Hence, Mandi will catch up with Rita at 0.5h after start.

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