m is directly proportional to r squared. when r=2 m=14. work out the value of m when r=12

Answer:

Step-by-step explanation:

Adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85 is 7 years

Let the ages be x and x + 2 since they're consecutive odd integers.

We want to find Adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85. This will be illustrated as:

x² + 4(x + 2) = 85

x² + 4x + 8 = 85

Collect like terms

x² + 4x + 8 - 85

x² + 4x - 77 = 0

x² + 11x - 7x - 77 = 0

x(x + 12) - 7(x + 11) = 0

x - 7 = 0

x = 0 + 7

Therefore, the age is 7 years.

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The value of the expression y³ = 1 is y = 1.

Expression:

An expression also known as algebraic expression consisting of variables, numbers and an arithmetic operation between them.

Given,

Here we have the expression y³ = 1.

Now, we need to find the value of y.

While we looking into the expression, when we have to find the value of y then we have to move the cube vale to the other side.

When we move the cube to the other side then it will be the cube root of the number.

While we simplify the cube root of the number then we get the result.

Therefore,

y³ = 1

Move the cube to the other side,

y = ∛1

We know that,

∛1 = 1

So, the value of y = 1.

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Answer: h(x)=-15

Step-by-step explanation: First: We plug in h(6) for x. Gives us -2(6)-3. When we solve -12-3. -15.

Answer:

h(6) = 9

Step-by-step explanation:

h(x) = 2x – 3,

Let x = 6

h(6) = 2*6 -3

      = 12 -3

      = 9

The x-intercept of the equation is: (8, 0)

The y-intercept is of the equation is: (0, -2)

The x-intercept is the point on the x-axis where the line cuts across the x-axis, while the y-intercept is the point on the y-axis that the graph intercepts.

The value of the x-intercept is the value of x when the value of y is equal to zero, while the y-intercept of a graph is the value of y when the value of x is zero.

Given the equation of the linear graph as, x - 4y = 8, to find the x-intercept, substitute y = 0 into the equation:

x - 4(0) = 8

Solve for x:

x - 0 = 8

x = 8

The x-intercept is: 8.

(8, 0)

To find the y-intercept, substitute x = 0 into the equation, x - 4y = 8 and solve for the value of y:

0 - 4y = 8

-4y = 8

-4y/-4 = 8/-4

y = -2

The y-intercept is: -2.

(0, -2)

The graph for x - 4y = 8 is shown in the attachment.

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Answer:

80

Step-by-step explanation:

Use trial and error until you find a common multiple.

The woodworker should make atmost 4 rocking kitchen chair and 3 simple kitchen chair to maximize the profit under given conditions of 192 woodworking hours and 21 painting hours.

Profit maximization is a process that businesses go through to make sure the best levels of output and prices are realized in order to maximize their returns. The company modifies important variables like sale price, production costs, and output levels in order to achieve its profit objectives.

inequality, A mathematical statement expressing an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to etc.

Given,

Time needed to woodwork a rocking kitchen chair= 30 hours

Time needed to paint a rocking kitchen chair=3 hours

Time needed to woodwork a simple kitchen chair= 24 hours

Time needed to paint a simple kitchen chair=3 hours

Maximum time given by worker= 192 hours for woodwork and 21 hours to paint

Let x and y be the maximum number of chairs created by woodworker of both the types.

so the system of inequality would be,

30x+24y<192      ......(1)

3x+3y<21             ......(2)

To find x and y,

multiply the (2) by 10

30x+30y<210

subtract (1) from (2)

30x+24y-(30x+30y)<192-210

-6y<-18

y<3

3x+3y<21

3x+3*3<21

3x<12

x<4

By this, he can make maximum 4 rocking and 3 simple kitchen chair to earn the maximum profit.

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In linear equation, Number of members in liberal party = 32 * 77 = 2464

What does the term "linear equation" mean?

A mathematical function where the variables only occur in the first degree, where the constants are multiplied, and where the only possible combinations are addition and subtraction.

45% Of liberals switch to the conservative party

total number of eligible votes in the country =7700

Number of members change to liberal to conservative  = 45% of 7700

                                                         = 45/100 * 7700

                                                          = 45 * 77 = 3465

32% of conservative  switch to the liberals party  = 32 % of 7700

                                                      = 32/100 * 7700

Number of members in liberal party = 32 * 77 = 2464

An equilibrium in campain contributions one for the each party among the set of contribution to the party.

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The complete question is -

in a certain county there are two political parties, liberal and conservative. it has been observed that between elections a fixed percentage, 45% of liberals switch to the conservative party and a fixed percentage, 32% of conservatives switch to the liberal party. the other voters remain in the same party. assume that there are altogether 7700 eligible voters in the county. Find the equilibrium Values for the system if any?

Answer:

The answer is 3, but here’s how I got that answer.

Step-by-step explanation:

As we know the trifle recipe requires 1 ½ cups of sugar, and the chocolate cake requires double the amount of sugar.

You have two options.

Multiply 1½ by 2

1½ x 2 = 3

———————————

Or add 1½ + 1½

1½ + 1½ = 3

———————————-

Wasn’t sure what you were asking for with this this question, but hope it helped.

Answer: 3

Step-by-step explanation:

Since the trifle cake uses 1 ½ cups of sugar and the chocolate twice as much sugar as the trifle cake you should multiply 1 ½ x 2 which would equal 3. So, 3 cups of sugar should go into the cake. (This is my first answer to a question so I'm sorry if I'm confusing)

The number of tapes cut is 3 pieces.

He has a roll of tape that is 4 1/2 yard long.

He cuts the tape into pieces that are each 3/2 yard long.

Therefore, the number of roll of tape cut can be calculated as follows:

Initial length of the tape in yard = 4 1 / 2 = 9 / 2 yards

Length of the tape cut in yard = 3  /2 yards

Hence,

number of tape cut = 9 / 2 ÷ 3 / 2

number of tape cut =  9 / 2 × 2 / 3

number of tape cut = 9 / 3

number of tape cut =  3 pieces

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By evaluating the linear equation in t = 5 seconds, we will see that the distance traveled is 271.93 feet.

Here we know that the line that defines the distance traveled by the ball (y) as a function of time (t) is:

y = 3.98 + 53.59*t

Now we want to predict the distance traveled y the ball if it travels for 5 seconds, so we just need to evaluate the above linear equation in t = 5.

So we will get:

y = 3.98 + 53.59*5  = 271.93

So we conclude that the distance traveled in that time is 271.93 feet.

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Answer: 271.93 feet

Step-by-step explanation:

I took the test

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{10}}} \implies \cfrac{ 5 }{ -2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{5}{2}}(x-\stackrel{x_1}{10}) \\\\\\ y-3=-\cfrac{5}{2}x+25\implies {\Large \begin{array}{llll} y=-\cfrac{5}{2}x+28 \end{array}}[/tex]

Answer:

ABC =146.5

ACB=67

ACD=127

CAB=146.5

Step-by-step explanation:

ABD=127

ACD=127

BCD=60 ( Being equilateral triangle)

60+x=127

x=67

ACB=67

CAB=CBA=y (let)

y+y+ACB = 360 ( Sum of int angles of triangle)

2y+67=360

2y=293

y=146.5

CAB=146.5

ABC=146.5

James took 97 minutes to clean his house. there were 12 rooms in the house, and it took him the same amount of time to clean each room. time  left after he finished cleaning is 4 hour 36 minutes

James took 97 minutes to clean his house.

there were 12 rooms in the house,

and it took him the same amount of time to clean each room

how much time did he have left after he finished cleaning?

one room clean =97 minutes

12 room clean = 97*12 amount of minutes

                        = 1164 minutes

                       = 19hour 24 minutes

James took 19 hour 24 minutes to clean 12 room

amount of time left = 24 hour - 19 hour 24 minutes

             = 4 hour 36 minutes

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Answer:

22 cups in total

Step-by-step explanation:

In order to solve this problem we need to know how much money Mimi makes by just selling 1 cup of lemonade. We can find this by dividing

38/19 = 2

Now that we know how much money Mimi makes by just selling 1 cup of lemonade, we can use this to find how many cups she needs to sell in total to earn $44. We can use this equation

2x = 44 (x = cups of lemonade)

Now we solve for x

2x =44

/2    /2

x = 22

So Mimi needs to sell 22 cups in total to earn $44 dollars. Hope this helps :)

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

Bonus: she need to sell 3 more cups lol incase you need to know

Answer:

Step 3, she forgot to square half of the middle term before adding it to both

sides.

Step-by-step explanation:

yw

We will see that the slope of function B is 2, and the slope of function A is 1. This means that the correct equation is:

Slope of function B = 2*Slope of Function A

First, a general linear equation is:

y = a*x + b

Where a is the slope and b the y-intercept.

Here the function A is:

f(x) = x - 9

Then the slope is equal to 1.

We know that function B is a line that passes through (-1, -3) and (2, 3)

Then the slope is:

s = (3 + 3)/(2 + 1) = 6/3 = 2

So the slope of function B is 2, and the slope of function A is 1. Then the equation is:

Slope of function B = 2*Slope of Function A

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The absolute value inequality represents the difference between the rope lengths cut and the specifications are | x - 10 | ≤ 0.5.

Modulus value always outputs a positive value irrespective of the input value sign.

Julian needed to cut ropes for her school project and their length should be 10 inches long with a difference of 0.5 inches.

∴ The maximum allowable length of the rope should be (10 + 0.5) = 10.5 inches and the minimum allowable length of the rope should be

(10 -0.5) = 9.5 inches.

The absolute value of inequality that represents this condition is,

| x - 10 | ≤ 0.5.

x - 10 ≤ 0.5.

x ≤ 10.5, And

- ( x - 10) ≤ 0.5.

-x + 10 ≤ 0.5.

- x ≤ - 9.5.    ( think of moving the terms on either side to make x positive).

x ≥ 9.5.

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By probability , An average rate of one mutation per 12,400 A.A geneticist is examining a strand of DNA .

Describe probability using an example?

Suppose that, in a strand f DNA ,mutations occur randomly and independently of other mutations .

at an average rate of one mutation per 12,400 A.A geneticist is examining a strand of DNA .

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The angle pairs can be classified as follows

∠1 and ∠5       →  Alternate exterior angles

∠2 and ∠10    →  Corresponding angles

∠10 and ∠14   →  Alternate interior angles  

∠6 and ∠7      →  Consecutive interior angles

∠5 and ∠12    →  Consecutive interior angles

∠3 and ∠13    →  Alternate exterior angles

From the question, we are to classify each of the angle pairs as corresponding, alternate interior, alternate exterior, or consecutive interior angles.

Considering the given diagram, and applying the appropriate angle theorems, we can write that

∠1 and ∠5 are alternate exterior angles

∠2 and ∠10 are corresponding angles

∠10 and ∠14 are alternate interior angles  

∠6 and ∠7 are consecutive interior angles

∠5 and ∠12 are consecutive interior angles

∠3 and ∠13 are alternate exterior angles

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The most appropriate choice for matrix will be given by-

The position number of all the matrix entries are

[tex]a_{11} = 0\\a_{12} = -1\\a_{13} = 3\\a_{14} = 5\\a_{15} = -2\\a_{21} = 7\\a_{22} = -8\\a_{23} = 6\\a_{24} = -4\\a_{25} = -9\\a_{31} = 1\\a_{32} = 2\\a_{33} = -3\\a_{34} = -5\\a_{35} = 8[/tex]

What is a matrix?

Any arrangement of numbers in the form of rows and columns are called matrix. The numbers inside a matrix is known as elements of the matrix.

The position number of a matrix entry is denoted by [tex]a_{mn}[/tex] where m denotes the row position and n denotes the column position.

We can do addition, subtraction, multiplication on matrix but two matrices cannot be divided.

Here,

The position number of a matrix entry is denoted by [tex]a_{mn}[/tex] where m denotes the row position and n denotes the column position.

The given matrix is

[tex]\left[\begin{array}{ccccc}0 & -1 & 3 & 5 & -2\\7&-8&6&-4&9\\1&2&-3&-5&8\end{array}\right][/tex]

The position numbers of all the matrix entries are given below

[tex]a_{11} = 0\\a_{12} = -1\\a_{13} = 3\\a_{14} = 5\\a_{15} = -2\\a_{21} = 7\\a_{22} = -8\\a_{23} = 6\\a_{24} = -4\\a_{25} = -9\\a_{31} = 1\\a_{32} = 2\\a_{33} = -3\\a_{34} = -5\\a_{35} = 8[/tex]

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They have not a proportional relationship.

The equation that represents a proportional relationship, or a line, is y = k x , where is the constant of proportionality. Use k = y x from either a table or a graph to find k and create the equation. Proportional relationships can be represented by tables, graphs and equations.

From table 1.

temperature ( ∘ C)                    temperature ( ∘ F)

20                                                           68

4                                                              39.2

175                                                           347

converted by using equation   F=[tex]\frac{9}{5}[/tex]C+32

From table 2.

length (in)                                    length (cm)

10                                                             25.4

8                                                               20.32

[tex]3\frac{1}{2}[/tex]                                                              8.89

Converted by using equation c = 2.54n where c represent length (in cm) and n represent length in inches.

Now,

we will check the proportionality by [tex]\frac{c}{F}[/tex]  if all the values of this ratio is same for the tables then they are showing proportionality .

From the table they are not showing proportionality.

Hence, They have not a proportional relationship
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The product of factor 83.5 with 0.01 will be 0.835

What are mathematics operations?

• A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.

• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.

Here, the given statement is :

The product of a factor and 0.1 is 8.35

Let the factor be a then :

a x 0.1 = 8.35

a = 8.35/0.1

a = 83.5

The factor is 83.5

Now, the product of this with 0.01 will be :

83.5 x 0.01 = 0.835

Therefore, The product of factor 83.5 with 0.01 will be 0.835

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The domain of the given function is (-∞,5) and the range is (5,∞).

All the independent variable, x, for which y is defined, is the domain and range of a function. Every possible value of the dependent variable y comes within a function's range.

From the graph, we can see that x varies from -∞ to -5

So, the domain is the interval of (-∞,-5)

The function of f(x) varies from (5,∞)

So, the range is (5,∞).

Therefore, the domain of the given function is (-∞,-5) and the range is (5,∞).

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The lowest score that Keiko is trying to score to get in the "ryo" range is , the inequality to represent this story is (x+85+57+78)/4 > 70  .

In the question ,

it is given that

Keiko need to score average above 70 to get in the ryo range

let x be the marks that Keiko scores in the next test ,

so, the average = (x+85+57+78)/4

According to the question

Average > 70

Substituting the value of average , the inequality becomes

(x+85+57+78)/4 > 70

x+85+57+78 > 280

x+220 > 280

x > 280-220

x > 60

the lowest score that Keiko should get is greater than 60 .

When the inequality x > 60 , will be graphed then the limit will be an open circle as equal to sign is not included in the inequality .

as when the numbers increases , it move towards right side

So, When the inequality is graphed, the line will have an arrow pointing towards the right .

Therefore , the lowest score that Keiko is trying to score to get in the "ryo" range is , the inequality to represent this story is  greater than 60 ,

the inequality to represent this story is (x+85+57+78)/4 > 70 ,

the limit of graph will be open circle and arrow will be pointing towards right .

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Answer:

8

Step-by-step explanation:

Let the number be “X"

Solution:

4 + (X/2) = 8

(X/2) = 8-4

(X/2) = 4

X = 4×2

X = 8

THEREFORE THE ANSWER IS “8”

Answer:

This is a simultaneous equation.

Step-by-step explanation:

let the first number be x and second be y

Lets make an equation first:

3x-y = 8 .....(1)

x+y = 12........(2)

Solve by elimination.

Dass

3x+x= 8+12

4x=20

x=5

find y

x+y=12

5+y=12

y=12-5

y= 7

Therefore the two numbers are 5 and 7

Rising or growing steadily and quickly: a city in exponential expansion. noun. Mathematics the value of the constant e raised to the power of a given expression, represented as the exponential of 3x, e3x. something that is positive and raised in power.

In the biological sciences, exponential functions are frequently employed to simulate the evolution of a certain quantity over time, such as population number. Experimental data graphs are often created with the quantity on the y-axis and the time on the x-axis.

The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour. After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.

The values of f(x) and g(x) in the table for various values of f(x) = 9x + 7 and g(x) = 5x

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Answer:

9+9b

Step-by-step explanation:

Answer:

9 +9b

Step-by-step explanation:

     Like terms are terms that have same variable with same power.

2b and 7b are like terms.

7 and 2 are like terms (constants).

7 + 2b + 7b + 2 = 7 + 2 + 2b +7b

                           = 9 + 9b

Okay, here we have this:

Considering the provided information, we are going to calculate the speed at which he runs, so we obtain the following:

So we have the following equation:

Distance Traveled Walking + Distance Traveled Running = Total Distance

Distance Traveled Walking + Distance Traveled Running = 20 miles

And taking into account that speed is equal to distance over time, if we take speed to which runs as x we have:

((x/2) mi/h * 2h) + (x mi/h* 1.5h) = 20 miles

x mi+ 1.5x mi= 20 mi

2.5x mi=20mi

x = 20mi/2.5mi

x=8

Finally we obtain that he runs at 8 miles per hour.