tbe ages of jerry mile and rawl total 80 years jerry is twice as old as mile and mile is three times as old as rawl how old is jerry????​

hope this helps you

Answer:

\(x^4-12x^3+54x^2-108x+81\)

Step-by-step explanation:

We have been given the following binomial expansion for (a + b)⁴:

\(\boxed{(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4}\)

To use this to expand and simplify (x - 3)⁴, first identity the values of a and b:

Substitute the values of a and b into the expansion, and simplify:

\(\begin{aligned}(x-3)^4&=x^4+4x^3(-3)+6x^2(-3)^2+4x(-3)^3+(-3)^4\\\\&=x^4+4x^3(-3)+6x^2(9)+4x(-27)+81\\\\&=x^4-12x^3+54x^2-108x+81\end{aligned}\)

Answer:

To find the length of AB, we can use the property that two tangents to a circle from the same external point are equal. This means that AB = AD. Substituting the given values, we get:

8x = x + 9

Solving for x, we get:

x = 1.5

Therefore, AB = 8x = 8(1.5) = 12.

To check our answer, we can use the Pythagorean theorem on triangle ABD, since AB is perpendicular to BD at the point of tangency. We have:

AB^2 + BD^2 = AD^2

Substituting the values, we get:

12^2 + BD^2 = (1.5 + 9)^2

Simplifying, we get:

BD^2 = 56.25

Taking the square root of both sides, we get:

BD = 7.5

Hence, the length of AB is 12 and the length of BD is 7.5.

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Answer:

19.6 in²

Step-by-step explanation:

area of circle = π r²

= π (3 1/2)²

= π (5/2)²

= π 25/4

= 22/7 x 25/4

= 275/14

=19.6 in²

We can Identify the Valid Equivalance values if the option c) 29,30,31 student clears the exam.

The values that the system or component being tested need to be able to accept are known as valid partitions. The "Valid Equivalence Partition" is the name given to this partition. The values that the component or system under test should reject are known as invalid partitions. The "Invalid Equivalence Partition" is the name of this partition.

For the purpose of the student passing the exam, the values of marks that they can obtain that are equal to or higher than the minimum required marks to pass the exam, which is 24 marks, are regarded real equivalency values. In this case, 29, 30, 31, and all mark values higher than 31 are valid equivalence values.

The appropriate selections are (c), 29, 30, and 31.

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Answer:

You have to multiply the 2 by whatever is in the parenthesis and of course it's a negative two remember that if you are solving it

Step-by-step explanation:

So that you simplify the equation when solving it

Answer: To divide fractions, you have to multiply by the reciprocal.

Step-by-step explanation:

We were given two points to find the equation of the line, these are (4,3) and (5,5).

We need to find the point-slope form, which can be writen as follow:

Where (y1,x1) is one point on the line and "m" is the slope of the line. We first need to find the slope:

Where (y1,x1) and (x2,y2) are the two known points. We can find the slope by applying the two points given to us:

We can know write the expression of the line:

Answer:-(-1,026/3

Step-by-step explanation:

The fraction equivalent to the number A = 0.555... is A = 5/9

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fraction be represented as A

Now , the value of A is

A = 0.555555..

Here , the value of A is 0.555 and the number 5 is repeating

So , the simplified form of the fraction A is given by

A = 5/9

On simplifying the value of A , we get

A = 0.55555...

Hence , the fraction is A = 5/9

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The value of n is 8.

Binomial theorem is the method of expanding an expression consisting of two terms raised to any power.

Using the expansion of Binomial theorem, we can write,

(2 + 3x)ⁿ = ⁿC₀ (2)ⁿ (3x)⁰ + ⁿC₁ (2)ⁿ⁻¹ (3x)¹ + ⁿC₂ (2)ⁿ⁻² (3x)² + ⁿC₃ (2)ⁿ⁻³ (3x)³ + ⁿC₄ (2)ⁿ⁻⁴ (3x)⁴ + .............

Coefficient of x³ is  ⁿC₃ (2)ⁿ⁻³ (3)³ and the coefficient of x⁴ is ⁿC₄ (2)ⁿ⁻⁴ (3)⁴.

Ratio of these coefficients is 8 : 15.

[ⁿC₃ (2)ⁿ⁻³ (3)³] / [ⁿC₄ (2)ⁿ⁻⁴ (3)⁴] = 8 / 15

Simplifying,

(4 × 2) / [(n - 3) 3] = 8/15

8 / 3n - 9 = 8 /15

Equating, we have,

3n - 9 = 15

3n = 24

n = 8

Hence the value of n is 8.

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The equation of the line passing through the two points (4,2) and (-3,1) is 7y-x-10=0

Equation of a line is an algebraic form of showing the set of points, which together forms a line in a coordinate system.

Given the line passes through the points (4,2) and (-3,1)

Here, x1=4, y1=2, x2=-3, y2=1

So, the slope of the line (m)= \(\frac{y2-y1}{x2-x1}\\\)=\(\frac{1-2}{-3-4}\\\)=\(\frac{1}{7}\)

Now we know, the equation of the line is given as,

y-y1=m(x-x1)

Putting the value of y1 and x1 in the equation we get,

y-2=\(\frac{1}{7}\)(x-4)

7y-14=x-4

7y-x-10=0

Hence the equation of the line that passes through the two points (4,2) and (-3,1) is 7y-x-10=0.

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The value of f(-7) from the graoh is 1/128

Exponential function typically refers to the positive-valued function of a real variable, although it can be extended to complex numbers or generalized to other mathematical objects like matrices.

From the given graph, we need to determine then value f(-7). The function f(-7), is the equivalent value on the y-axis if the value of x is -7.

The standard exponential equation is y = ab^x

Using the coordinate points (0, 1) and (-2, 4), the resulting equations are:

1 = ab^0

4 = ab^-2

From equation 1, a = 1

4 = b^-2

b^2 = 1/4

b = 1/2

The exponential function will be y = (1/2)^x

f(-7) = (1/2)^-7
f(-7) = 1/128

Hence the resulting value of f(-7) is 1/128

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In linear algebra, we have learnt that the product of two matrices is only if the number of columns in the first matrix is equal to the number of rows in the second matrix.

Given matrices A and B, the following products are defined:

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_____ The given question is incomplete, the complete question is given below:-

let the matrices a and b.

find each of the following  products and Justify them

Answer:

1/6

Step-by-step explanation:

First you make the denominator on the fractions the same

3 * 2 = 6

Multiply the number the same for the numerator

3 * 1 = 3

so the fraction is 3/6 since 3/6 = 1/2

4/6 - 3/6 = 1/6

she has 1/6 pipe left

The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1)(x - 2)

We have to given that;

Expression is,

⇒ [x /(x² - x - 2)]  + [ (x - 1) / (x - 2) ]

We can simplify as;

⇒ [x / (x² - x - 2)]  + [(x - 1) / (x - 2)]

⇒ [x / (x² - 2x + x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / [ x (x - 2) + 1(x - 2)] + [(x - 1) / (x - 2)]

⇒ [x / (x - 1) (x - 2)] + [(x - 1) / (x - 2)]

⇒ [1/(x - 2)] [ x/(x - 1) + (x - 1) ]

⇒ [1 / (x - 2)]  × [ x + (x - 1)²] / (x - 1)

⇒ [x + (x - 1)² ] / [(x - 1) (x - 2)]

⇒ (x + x² - 2x + 1) / (x - 1) (x - 2)

⇒ (x² - x + 1) / (x - 1) (x - 2)

Hence, The solution of sum of expression is,

⇒ (x² - x + 1) / (x - 1) (x - 2)

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We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.

What is banquet?

A banquet is a large formal meal that usually involves multiple courses and is served to a group of people on special occasions such as weddings, awards ceremonies, or fundraising events. Banquets often include speeches, presentations, and entertainment, and are typically held in a large venue such as a hotel ballroom, banquet hall, or conference center. Banquets can be hosted for a variety of purposes, such as to honor a special guest, celebrate an achievement, or raise money for a charitable cause.

To create a graph showing the solution region of the system of inequalities representing the constraints of the situation, we can use custom relationships to define the variables and constraints.

Let's define the variables:

Let x be the number of adult guests.

Let y be the number of student guests.

Now, let's write the system of inequalities representing the constraints of the situation:

The total number of guests cannot exceed 125: x + y ≤ 125

The cost of hosting the banquet cannot exceed $3375: 45x + 15y ≤ 3375

To graph this system of inequalities, we can plot the boundary lines of each inequality and shade the region that satisfies all the constraints.

The boundary lines of each inequality are:

x + y = 125 (the line that connects the points (0, 125) and (125, 0))

45x + 15y = 3375 (the line that connects the points (0, 225) and (75, 0))

To find the viable combinations of guests that satisfy all the constraints, we need to shade the region that is below the line x + y = 125 and to the left of the line 45x + 15y = 3375.

The resulting graph should look like this:

The point where the two lines intersect, (75, 50), represents the maximum number of adult guests (75) and the maximum number of student guests (50) that can be invited to the banquet while staying within the budget and venue capacity. Any point within the shaded region represents a viable combination of guests.

We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.

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Answer:

Distributive property of multiplication

Step-by-step explanation:

The distributive property of multiplication is basically distributing the terms outside the bracket to all the terms inside the bracket. In this case, 4 is multiplied to 5a as well as 3.

Answer:

Let's start by assigning a variable to Susan's present age. Let's call it "x".

According to the problem, in seven years, Susan will be "x + 7" years old.

Three years ago, Susan was "x - 3" years old.

The problem tells us that Susan will be 2 times as old in seven years as she was 3 years ago. So we can set up the following equation:

x + 7 = 2(x - 3)

Now we can solve for x:

x + 7 = 2x - 6

x = 13

Therefore, Susan's present age is 13 years old.

Let's assume Susan's present age is "x" years. According to the information provided, "Susan will be 2 times old in seven years as she was 3 years ago."

Seven years from now, Susan's age would be x + 7, and three years ago, her age would have been x - 3. According to the given statement, her age in seven years will be two times her age three years ago:

x + 7 = 2(x - 3)

Let's solve this equation to find Susan's present age:

x + 7 = 2x - 6

Subtracting x from both sides:

7 = x - 6

Adding 6 to both sides:

13 = x

Therefore, Susan's present age is 13 years.

That's correct. The rate in the portion formula can be expressed as a decimal, fraction, or percentage, depending on the context and what is most convenient for the problem being solved.

How do you calculate ratio and proportion? Ans: The ratio formula is written as a: b a/b for any two numbers. Contrarily, the percentage formula is written as a:b::c:da:b::c:da:b=cd.

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 1 out of 4 are boys, and 3/ 4 are girls.

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Part a: The shaded area of the figure's polynomial expression: 16x + 30.

B) The larger rectangle has a surface area of 96 Sq in.

D) The smaller rectangle has a surface area of 18 Sq in.

By combining numbers and variables with the help of arithmetic operations like addition, subtraction, multiplied, division, and exponentiation, polynomials are algebraic expressions.

A polynomial can be made by adding or removing terms. Applications ranging from engineering and sciences to business can benefit greatly from polynomials

For question:

Dimensions are-

Complete region:

Non shaded rectangle:

Part A: The shaded area of the figure's polynomial expression is as follows:

Area = Length * width(complete)   -  Length * width(smaller)

Area = (2x + 6)(x + 5) - 2x(x)

Area = 2x² + 16x + 30 - 2x²

Area = 16x + 30

Find x-

Given shaded area = 78 sq. in

78 = 16x + 30

16x = 48

x = 3

B) The larger rectangle has a surface area of ___Sq in.

Area of larger rectangle = (2x + 6)(x + 5)

 = (2*3 + 6)(3 + 5)

= 12*8

= 96 Sq in.

D) The smaller rectangle has a surface area of __Sq in.

Area of smaller rectangle = 2x (x)

= 2*3*3

= 18 Sq in

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Answer:

\( (x_1 =2, y_1 = 6), (x_2 = 2, y_2 = 4)\)

\( m =\frac{y_2 -y_1}{x_2 -x_1}\)

And replacing we got:

\( m=\frac{4-6}{8-3}= -\frac{2}{5}\)

And for this case we can use the first point to find the intercept like this:

\( 6 = -\frac{2}{5}(3) +b\)

And solving we got:

\( b = 6 +\frac{6}{5}= \frac{36}{5}\)

And then the line equation would be given by:

\( y = -\frac{2}{5}x +\frac{36}{5}\)

Step-by-step explanation:

For this case we have the following two points given:

\( (x_1 =2, y_1 = 6), (x_2 = 2, y_2 = 4)\)

And for this case we want an equation for a line with the two points given by:

\( y = mx+b\)

Wher m is the slope and b the y intercept. We can find the slope with this formula:

\( m =\frac{y_2 -y_1}{x_2 -x_1}\)

And replacing we got:

\( m=\frac{4-6}{8-3}= -\frac{2}{5}\)

And for this case we can use the first point to find the intercept like this:

\( 6 = -\frac{2}{5}(3) +b\)

And solving we got:

\( b = 6 +\frac{6}{5}= \frac{36}{5}\)

And then the line equation would be given by:

\( y = -\frac{2}{5}x +\frac{36}{5}\)

Answer:20 m/s

Step-by-step explanation:

Answer:

20 m/s

Step-by-step explanation:

700 ÷ 35 = 20 m/s

Answer:

a) The rate of change associated with the volume of the box is 54 cubic meters per second, b) The rate of change associated with the surface area of the box is 18 square meters per second, c) The rate of change of the length of the diagonal is -1 meters per second.

Step-by-step explanation:

a) Given that box is a parallelepiped, the volume of the parallelepiped, measured in cubic meters, is represented by this formula:

\(V = w \cdot h \cdot l\)

Where:

\(w\) - Width, measured in meters.

\(h\) - Height, measured in meters.

\(l\) - Length, measured in meters.

The rate of change in the volume of the box, measured in cubic meters per second, is deducted by deriving the volume function in terms of time:

\(\dot V = h\cdot l \cdot \dot w + w\cdot l \cdot \dot h + w\cdot h \cdot \dot l\)

Where \(\dot w\), \(\dot h\) and \(\dot l\) are the rates of change related to the width, height and length, measured in meters per second.

Given that \(w = 6\,m\), \(h = 6\,m\), \(l = 3\,m\), \(\dot w =3\,\frac{m}{s}\), \(\dot h = -6\,\frac{m}{s}\) and \(\dot l = 3\,\frac{m}{s}\), the rate of change in the volume of the box is:

\(\dot V = (6\,m)\cdot (3\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot (3\,m)\cdot \left(-6\,\frac{m}{s} \right)+(6\,m)\cdot (6\,m)\cdot \left(3\,\frac{m}{s}\right)\)

\(\dot V = 54\,\frac{m^{3}}{s}\)

The rate of change associated with the volume of the box is 54 cubic meters per second.

b) The surface area of the parallelepiped, measured in square meters, is represented by this model:

\(A_{s} = 2\cdot (w\cdot l + l\cdot h + w\cdot h)\)

The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time:

\(\dot A_{s} = 2\cdot (l+h)\cdot \dot w + 2\cdot (w+h)\cdot \dot l + 2\cdot (w+l)\cdot \dot h\)

Given that \(w = 6\,m\), \(h = 6\,m\), \(l = 3\,m\), \(\dot w =3\,\frac{m}{s}\), \(\dot h = -6\,\frac{m}{s}\) and \(\dot l = 3\,\frac{m}{s}\), the rate of change in the surface area of the box is:

\(\dot A_{s} = 2\cdot (6\,m + 3\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m+6\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m + 3\,m)\cdot \left(-6\,\frac{m}{s} \right)\)

\(\dot A_{s} = 18\,\frac{m^{2}}{s}\)

The rate of change associated with the surface area of the box is 18 square meters per second.

c) The length of the diagonal, measured in meters, is represented by the following Pythagorean identity:

\(r^{2} = w^{2}+h^{2}+l^{2}\)

The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time before simplification:

\(2\cdot r \cdot \dot r = 2\cdot w \cdot \dot w + 2\cdot h \cdot \dot h + 2\cdot l \cdot \dot l\)

\(r\cdot \dot r = w\cdot \dot w + h\cdot \dot h + l\cdot \dot l\)

\(\dot r = \frac{w\cdot \dot w + h \cdot \dot h + l \cdot \dot l}{\sqrt{w^{2}+h^{2}+l^{2}}}\)

Given that \(w = 6\,m\), \(h = 6\,m\), \(l = 3\,m\), \(\dot w =3\,\frac{m}{s}\), \(\dot h = -6\,\frac{m}{s}\) and \(\dot l = 3\,\frac{m}{s}\), the rate of change in the length of the diagonal of the box is:

\(\dot r = \frac{(6\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot \left(-6\,\frac{m}{s} \right)+(3\,m)\cdot \left(3\,\frac{m}{s} \right)}{\sqrt{(6\,m)^{2}+(6\,m)^{2}+(3\,m)^{2}}}\)

\(\dot r = -1\,\frac{m}{s}\)

The rate of change of the length of the diagonal is -1 meters per second.

Answer:

\(1\frac{3}{5}\) meter is the difference in depths of locations diver dove.

Step-by-step explanation:

Answer:

Please check the complete explanation below.

Step-by-step explanation:

We know that the slope-intercept form of the line equation

\(y = mx+b\)

where m is the slope and b is the y-intercept

                                       ANALYZING TABLE 1

Part A)

Given table 1

x           0            1              2            3

y           1             3              5            7

From table 1, the y-intercept can be determined by setting  x=0 and checking the corresponding y-value.

so at x = 0, y = 1

Thus, the y-intercept is (0, 1).

From the graph, it is clear that the line W has a y-intercept (0, 1).

Therefore, table 1 represents the line W.

Part B)

Taking two points (0, 1) and (1, 3) to find the slope using the formula

m = (y₂-y₁) / (x₂-x₁)

m = 3-1 / 1-0 = 2/1 = 2

now substituting m = 2, and b = 1 in the slope-intercept form

y = mx+b

y = 2x+1

Thus, table 1 represents the line W with the equation line y = 2x+1

                                  ANALYZING TABLE 2

Part A)

Given table 2

x           0            1              2            3

y           0             3             6            9

From table 2, the y-intercept can be determined by setting  x=0 and checking the corresponding y-value.

so at x = 0, y = 0

Thus, the y-intercept (0, 0).

From the graph, it is clear that line F has a y-intercept (0, 0).

Therefore, table 2 represents the line F.

Part B)

Taking two points (0, 0) and (1, 3) to find the slope using the formula

m = (y₂-y₁) / (x₂-x₁)

m = 3-0 / 1-0 = 3/1 = 3

now substituting m = 3, and b = 0 in the slope-intercept form

y = mx+b

y = 3x+0

y = 3x

Thus, table 2 represents the line F with the equation y = 3x

                                    ANALYZING TABLE 3

Part A)

Given table 1

x           0            1              2            3

y           2             3             4            5

From table 3, the y-intercept can be determined by setting  x=0 and checking the corresponding y-value.

so at x = 0, y = 0

Thus, the y-intercept (0, 2).

From the graph, it is clear that line N has a y-intercept (0, 2).

Therefore, table 3 represents line N.

Part B)

Taking two points (0, 2) and (1, 3) to find the slope using the formula

m = (y₂-y₁) / (x₂-x₁)

m = 3-2 / 1-0 = 1/1 = 1

now substituting m = 1, and b = 2 in the slope-intercept form

y = mx+b

y = (1)x+2

y = x+2

Thus, table 2 represents the line N with the equation y = x+2

The calculated measure of the angle D is (c) 32 degrees

From the question, we have the following parameters that can be used in our computation:

The triangles ABC and DEF

The triangles are similar triangles

This means that the corresponding angles are equal

Given that

A = 32 degrees

And the corresponding angle is D

We have

D = 32 degrees

Hence, the measure of the angle is (c) 32 degrees

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