6y+8x-3x
I need help this is for homework

The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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Required polynomial of lowest degree with zeros of multiplicity of 2 for (5/6) and multiplicity of 1 for (-1/6) and f(0) = -25 is given by :

f(x) = - ( 216x³ -324x² + 90x + 25 ).

As given in the question,

Given condition for required polynomial is given by :

Zeros of ( 5 / 6) with multiplicity 2 means zeros repeats two times we get,

= ( 6x - 5 )²  

Zeros of (- 1/ 6) with multiplicity 1 means only once

= 6x + 1

Required polynomial is :

f(x) = a  ( 6x - 5 )²  ( 6x + 1 )  __(1)

Now, f(0) = -25

Now substitute x = 0 we get,

f(0) = a [ 6(0) - 5 ]² ×  [ 6(0) + 1 ]

⇒ -25 = a ( -5)² ×  (1)

⇒ -25 = a (25)

⇒ a = -1

Substitute value of a in (1) we get,

f(x) = - ( 6x - 5 )²  ( 6x + 1 )

Open the parenthesis we get,

f(x) = - [ ( 36x² -60x + 25)( 6x + 1) ]

⇒ f(x) = - ( 216x³ -324x² + 90x + 25 )

Therefore, required polynomial of lowest degree with zeros of multiplicity of 2 for (5/6) and multiplicity of 1 for (-1/6) and f(0) = -25 is given by : f(x) = - ( 216x³ -324x² + 90x + 25 ).

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Hi there!

Answer:

2.5/5

Step By Step Explanation:

Given function:

Therefore, 2 3/15 rounded to the nearest half is 2.5/5.

Answer:

2

Step-by-step explanation:

:)

\(y = -3x + 27\)

Step-by-step explanation:

A parallel line will have the same slope as the given line so we can write the slope-intercept form of the equation as

\(y = -3x + b\)

Since the other line goes through the point (9, 0), we can use this to solve for b:

\(0 = -3(9) + b \Rightarrow b = 27\)

Therefore, the equation of the parallel line that goes through (9, 0) is

\(y = -3x + 27\)

Charisse needs to stain an area of 174 square feet.

The total surface area of the shed's walls that needs to be stained is the sum of the areas of the four walls, minus the area of the front door.

The area of one wall is 8 feet × 6 feet = 48 square feet.

Since there are 4 walls, the total area of all walls is 48 square feet × 4 = 192 square feet.

The area of the front door is 3 feet  × 6 feet = 18 square feet

Now we can subtract the area of the door from the total area of all walls:

192 square feet - 18 square feet = 174 square feet

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Answer:

Step-by-step explanation:

9.05737

The length of the radius of the cone to the nearest foot is 5 feet.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, The surface area of a cone is 216π sq units and the height of the cone is  (5/3) times of the radius.

∴ h = (5/3)r and we know l = √(h² + r²) ⇒ l = √{(25/9)r² + r²} ⇒ l = √{(34/9)r²}.

∴ πrl = 216π.

√{(34/9)r³ = 216.

1.9r³ = 216.

r³ = 113.7.

r = 4.8 feet Or 5 feet.

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The simplified form of the function f(x)=1/2(27) 2x/3 can be expressed as f(x) = (27/2) (2x/3).

Functions are one of the fundamental building blocks of mathematics and are used to describe and analyze relationships between different variables.

The function f(x)=1/2(27) 2x/3 can be simplified by factoring out the common factor of 1/2 and 27.

Thus, the simplified form of the function can be expressed as

f(x) = (27/2) (2x/3).

This function is a polynomial function with degree 1, which means that it is a linear function. The degree of a function is the highest power of the variable in the equation.

The key aspects of this function can be identified by looking at the constant values in the equation.

The constant value 27/2 is the y-intercept, which is the point at which the line crosses the y-axis.

This means that the y-value of the function at x = 0 is 27/2.

The constant value 2/3 is the gradient, which is the slope of the line. This means that for every increase in the x-value, the y-value will increase by 2/3.

This function can be represented graphically as a straight line with a y-intercept of 27/2 and a slope of 2/3.

The graph of this function will pass through the point (0, 27/2) and will have a positive slope of 2/3. This means that the graph will move up and to the right, with each increase in the x-value resulting in an increase of 2/3 in the y-value.

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Answer:

Step-by-step explanation:

(30*48)/100 = 14.40

48 - 14.40 = $ 33.60

48 + 33.60 = $ 81.60

The simplified expression for ( x - y ) ( x - y ) ( x - y ) is x³ - x²y - xy² + y³.

To simplify ( x - y ) ( x - y ) ( x - y ), we can expand the expression using the distributive property of multiplication. We can also simplify the expression by combining like terms.

In using the distributive property of multiplication, we multiply each term in the first set of parentheses by each term in the second set of parentheses. This gives us:( x - y ) ( x - y ) ( x - y ) = ( x(x - y) - y(x - y) ) ( x - y )= ( x² - xy - xy + y² ) ( x - y )= ( x² - 2xy + y² ) ( x - y )

Now we can further simplify the expression by combining like terms. We can use the difference of squares formula to simplify the second set of parentheses.( x² - 2xy + y² ) ( x - y ) = ( x - y ) ( x - y )²= ( x - y ) ( x² - 2xy + y² )= x³ - x²y - 2xy² + xy² - xy² + y³= x³ - x²y - xy² + y³

Therefore, the simplified expression is x³ - x²y - xy² + y³.

Summary: To simplify ( x - y ) ( x - y ) ( x - y ), we expand the expression using the distributive property of multiplication. We simplify the expression by combining like terms. We use the difference of squares formula to simplify the second set of parentheses. Finally, we simplify the expression further by combining like terms. The simplified expression is x³ - x²y - xy² + y³.

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Answer:

Multiply to remove the fraction, then set it equal to 0 and solve.

Exact Form: x = −124/5

Decimal Form: x = −24.8

Mixed Number Form: x = −24 4/5

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The linear function that describes the distance (in miles) is therefore y = 65x + 80

We have to find the slope and the intercept in other to get the linear function

The data points are:

(1, 145) and (3, 275).

m = (y2 - y1) / (x2 - x1)

fixing the data points we have

m = (275 - 145) / (3 - 1)

= 130 / 2

= 65

y = mx + b

(1, 145):

145 = 65(1) + b

b = 145 - 65

= 80

y intercept is 80

The linear function is therefore y = 65x + 80

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114 is 95% of 120

100% of 120 is 120, therefore 95 percent of 120 equals 114. To learn how to solve 114 is 95 percent of what number, see the step-by-step instructions below.

114 is 95 Percent of What Number?

Formula = Number x 100

Percent = 114 x 100

95 = 120

The following shows the steps to derive this formula and find out 95% of the number is 114.

Step 1: If 95% of a number is 114, then what is 100% of that number? Set up the equation.

114

95% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

95Y = 114 x 100

95Y = 11400

Y = 11400

100 = 120

The range of the data is 30, and the interquartile range (IQR) is 15.

To create a box plot using the given data, we first need to determine the five-number summary, which includes the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value.

From the given data, we can determine the five-number summary as follows:

Minimum: 60

Q1: 70

Median (Q2): 80

Q3: 85

Maximum: 90

Now, let's create a box plot using this information:

```

  |         |         |         |         |

60 |––––––––|––––––––|         |

  |         |         |         |         |

70 |––––––––|––––––––|––––––––|––––––––|

  |         |         |         |         |

80 |––––––––|––––––––|––––––––|––––––––|

  |         |         |         |         |

90 |––––––––|––––––––|         |

  |         |         |         |         |

  ------------------------------------

    60       70        80        90

```

In the box plot, the line within the box represents the median (Q2), the box represents the interquartile range (IQR) from Q1 to Q3, and the lines extending from the box (whiskers) represent the minimum and maximum values. Any data points falling outside the whiskers would be considered outliers.

The range can be calculated as the difference between the maximum and minimum values:

Range = Maximum - Minimum = 90 - 60 = 30

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1):

IQR = Q3 - Q1 = 85 - 70 = 15

Therefore, the range of the data is 30, and the interquartile range (IQR) is 15.

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Answer:

1. Sine A = 3/5

2. Cos A = 4/5

3. Tan A = 3/4

4. Sine B = 4/5

5. Cos B = 3/5

6. Tan B = 4/3

Step-by-step explanation:

1. Determination of Sine A

Opposite = 3 in

Hypothenus = 5 in

Sine A =?

Sine A = opposite / Hypothenus

Sine A = 3/5

2. Determination of Cos A

Adjacent = 4 in

Hypothenus = 5 in

Cos A =?

Cos A = Adjacent / Hypothenus

Cos A = 4/5

3. Determination of Tan A

Opposite = 3 in

Adjacent = 4 in

Tan A =?

Tan A = opposite / Adjacent

Tan A = 3/4

4. Determination of Sine B

Opposite = 4 in

Hypothenus = 5 in

Sine B =?

Sine B = Opposite / Hypothenus

Sine B = 4/5

5. Determination of Cos B

Adjacent = 3 in

Hypothenus = 5 in

Cos B =?

Cos B = Adjacent / Hypothenus

Cos B = 3/5

6. Determination of Tan B

Opposite = 4 in

Adjacent = 3 in

Tan B =?

Tan B = opposite / Adjacent

Tan B = 4/3

SOLUTION

x + 15 = 36

You collect like terms by taking 15 to meet 36. When 15 crosses the = sign it becomes -15.

x = 36 - 15

x = 21

Step-by-step explanation:

put x = -6 in the equation.

= -6 ( -6). + 7 =. 36 + 7 = 43

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The line which is passing through the point on the graph (2,7) and with vertex (0,3) having equation is    \(x^{2}\) -y +3 = 0

The polynomial equations of degree two in one variable of type f(x) = ax^2 + bx + c = 0 and with a, b, c are R and a \(\neq\) 0,  are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f(x).

The general equation of the quadratic equation if (h, k) is the vertex and (x, y) is a point on the curve is given by  

y = \(a(x-h)^{2} + k\) ......eqn 1

In the situation where a must be determined at position (h, k) and (x, y)

In the above question, it is given that,

vertex is (h,k) = (0,3) and the point on the graph is (x,y) = (2,7)

Now we'll put the points in the general equation of the quadratic equation to get the desired equation

y = \(a(x-h)^{2} + k\)

y = \(a(x-0)^{2}\) + 3 .....eqn 1

Now putting the value of (x,y)

7 = \(a(2-0)^{2}\) + 3

7 = 4a + 3

4a = 4

a = 1

putting the value of a in the equation 1, we get

y = \(1(x-0)^{2}\) + 3

y = \(x^{2}\) + 3

\(x^{2}\) -y +3 = 0

Hence, the equation of the line passing through a point on the graph (2,7) with the vertex (0,3) is  \(x^{2}\)  -y +3 = 0

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The probability that the sum of the numbers on the dice will be a square number is 1/6.

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.

We can first make a list of every conceivable result when rolling two dice in order to determine the likelihood that the sum of the numbers on the two dice will be a square number:

\((1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6\))

\((2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)\)

\((3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)\)

\((4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)\)

\((5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)\)

\((6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)\)

The sums can then be listed, and the square numbers can be identified:

2, 3, 4, 5, 6, 7

3, 4, 5, 6, 7, 8

4, 5, 6, 7, 8, 9

5, 6, 7, 8, 9, 10

6, 7, 8, 9, 10, 11

7, 8, 9, 10, 11, 12

The likelihood that the sum of the numbers on the dice will be a square number is 6 out of a total of 36 potential outcomes.

P(square sum) = 6/36 = 1/6.

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Answer:

The answer is 270000....

Answer:

Step-by-step explanation:

e

Part a: The probability for the appearance of two science majors:85/1985.

Part b: The probability for the appearance of science major and an engineering major: 75/979.

Probability = favourable outcome/total outcome

For the stated question;

The number of students in various stream are-

Part a: The probability for the appearance of two science majors:

P(science majors) = P(science) × P(science)

P(science majors) = 20/89 × 19/88

P(science majors) = 85/1985

Part b: The probability for the appearance of science major and an engineering major:

P(E and S) = P(science major) × P(engineering major)

P(E and S) = 20/89 × 30/88

P(E and S) = 75/979

Thus, the probability for the appearance of science major and an engineering major is 75/979.

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Answer:

4 1/2

Step-by-step explanation:Because 2x2 =4 and 2x1/4 = 1/2 so it is 4 1/2

Answer:

The sum will be close to 1/4

Step-by-step explanation:

1/8+1/6 is 7/24, and 1/4th of that is 6/24, so it is very close.

Answer: The sum will be close to 1/4

Step-by-step explanation:

You can start by making the fractions have the same denominator, (8*6) which gets you 48

You then want to use the butterfly method, so 1/8 becomes 6/48 and 1/6 becomes 8/48. You then add these up to 14/48.

12/48 is 1/4, and 14/48 is close to 12/48, thus making the answer the first option.

37.5w + 155.95 = 455.95; where w = 8; signifies the number of weeks required to babysit the business in order to purchase the gaming chair.

A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. For instance, in English, an equation is any properly stated formula that consists of two expressions linked by the equals sign, whereas in French, an equation is described as containing one or more variables. To solve a variable equation, identify the values of the variables that cause the equality to hold true. The answer is known as the values of the variables that must satisfy the equality.

Equations can be categorized as identities or conditional equations.

w = (455.95-155.95)/(37.50)

=300/37.50

=8

So, number of weeks = 8

As a result, w = 8 and 37.5w + 155.95 = 455.95 is the solution.

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Answer:

Equation: 2w + 2(2w) = 12

width = 2

length = 4

Step-by-step explanation:

Width is w

Length is 2 * width = 2w

Perimeter is 2w + 2l

Substitute 2w for L.

Perimeter is now 2w + 2(2w) = 12

Distribute the 2 to the parentheses.

2w + 4w = 12

Combine Like terms

6w = 12

Divide by 6 to solve for w.

w = 2

If w = 2, then the length = 4.

Answer:

you su ck hah lol

Step-by-step explanation:

ez