Evaluate the function for the given value of x.
f(x) = 7x - 6, f(-2)

The amount James have left after paying his debt in his profit is $32.50.

Blake, James and Staunton invested $9,000, $7,000, and $6,000, respectively. Their profits were to be divided according to the ratio of their investments.

James uses his share of the firm's profit of $825 to pay a personal debt of $230. The amount of money James have left can be calculated as follows;

The ratio of the investment is 9000: 7000 : 6000(9:7:6)

Hence,

James share of profit = 7 / 22 × 825

James share of profit = 5775 / 22

James share of profit = 262.5 dollars

Therefore,

amount he has left after paying his debt = 262.5 - 230

amount he has left after paying his debt = 32.50 dollars

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The cost of 1kg of carrot is $3.1 and 1kg radish is 1.6.

A set of two or more first-degree equations with two or more connected unknowns is known as a system of linear equations.

A system of equations is solved by determining the value of each unknown until the system's equations are all satisfied. That is, it is necessary to find the values of the unknowns so that, when substituted, they will produce the suggested solution in both equations.

Let x=cost of carrot

y= cost of radishes

1.5x+4y=14.80

2x+3y=12.50

Simultaneously solving gives

x=3.1

y=1.6

The cost of 1kg of carrot is $3.1 and 1kg radish is 1.6.

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The approximate length of the apothem is 10.86 feet.

For a regular polygon, the apothem is the perpendicular line drawn from the center to the midpoint of any of its sides.

The formula to find the apothem given its perimeter is:

a = P / (2n tan (180 / n))

where a = length of the apothem

P = perimeter

n = number of sides of the polygon

Plug in the values and solve for the apothem.

a = P / (2n tan (180 / n))

a = 72 feet / (2)(8)(tan (180 / 8))

a = 10.86 feet

Therefore, the approximate length of the apothem is 10.86 feet.

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Answer: 73

Step-by-step explanation:

4 x 5 = 20

93 - 20 = 73

The remainder when X 3x² 2x 1 is divided by x 1 is 2, the last coefficient.

To find the remainder when dividing X 3x² 2x 1 by x 1, we can use the division algorithm. This algorithm states that the remainder is equal to the dividend minus the product of the divisor and the quotient.

To find the quotient, we can use synthetic division, which is a shortcut method that allows us to divide polynomials without needing to use the traditional long division method.

In this case, the divisor is x 1, so we write down x 1 and the coefficients of X 3x² 2x 1 in order from the highest degree to the lowest degree, which is 3x² 2x 1. We then divide the first coefficient, 3, by the divisor, 1, and write this result, 3, as the first number in the quotient.

We then multiply 3 by the divisor, 1, and subtract this from the dividend. The result of this subtraction is 3x² 2x, so we repeat this process until we reach the last coefficient, which is the remainder. In this case, the last coefficient is 2, so this is the remainder when dividing X 3x² 2x 1 by x 1. Therefore, the remainder is 2.

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The volume of the pool, if The depth of the pool is 10 feet, is 1040 cubic feet.

The capacity occupied by a three-dimensional solid shape is known as volume. It is difficult to visualize in any shape, yet it may be compared among shapes. For instance, a compass box has a larger volume than an eraser placed inside of it.

Given:

The depth of the pool is 10 feet,

Calculate the volume of the pool as shown below,

The volume of the pool = the Volume of a rectangular prism with dimensions 20ft. × 10ft. × 4ft. + volume of a rectangular prism has dimensions: 6ft. × 4ft. × 10ft.

The volume of the pool =  20 × 10 × 4 +  6 × 4 × 10

The volume of the pool = 200 × 4 + 24 × 10

The volume of the pool = 800 + 240

The volume of the pool = 1040

Thus, the volume of the pool is 1040 ft³.

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The required percentages are

There is no association between passing the exam and completing the exam review

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

The table of values

The required percentage can be calculated as

Percentage = (Pass the exam and complete the review)/Complete the review)

Using the table of values, we have

Percentage = 55%/65%

Evaluate

Percentage = 85%

Here, the required percentage can be calculated as

Percentage = (Pass the exam and did not complete the review)/Did not complete the review)

Using the table of values, we have

Percentage = 20%/35%

Evaluate

Percentage = 57%

From (a) and (b), we can see that

These percentages are above 50% and they represent opposite entities

This means that there is no association

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These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.

the triangle's circle's center. It is the point where the "perpendicular bisectors," or lines parallel to the centre of both sides, cross.

The intersection of any two perpendicular bisectors of any two triangle sides is known as the circumcenter of a triangle ABC.

The equation y=1 is the perpendicular bisector of sides B(3,0) and C(3,2). Because AB's midpoint is at 3,1 and its slope is unknown. The perpendicular bisector has zero slope. The equation for such a line is y=y1.

The equation for the perpendicular bisector of A(0,0) and B is also x=1.5 (3,0). The reason is that AB has a midpoint of zero slope and (1.5,0). The perpendicular bisector's slope won't be clearly defined. The equation for such a line is x=x1.

These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.

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Answer:

-8p^12q^7+9p^2q^7

Step-by-step explanation:

Use pemdas

multiply -2p^5q^6 ⋅ 4p^7q

to get -8p^12q^7

add that with the first term

Step-by-step explanation:

(1 - 2)/(a + 6)= -1/9

-1/a + 6 = -1/9

-a - 6 = -9

-a = -3

a = 3

The solutions to the equation are

log₃ ( 81 ) = 4

2ˣ = 1/32 , the value of x = -5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

A = log₃ ( 81 ) be equation (1)

On simplifying the equation , we get

logₐ ( aᵇ ) = b

From the equation , we get

A = log₃ ( 81 ) = log₃ ( 3⁴ )

So , log₃ ( 3⁴ ) = 4

Therefore , the value of the equation is A = 4

b)

2ˣ = 1/32   be equation (1)

On simplifying the equation , we get

32 = 2⁵

So , 1/32 = ( 1/2⁵ )

( 1/2⁵ ) = 2⁻⁵

Substituting the values in the equation , we get

2ˣ = 2⁻⁵

Therefore , the value of x = -5

Hence , the equations are solved

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On solving the provide question we can say that - the equation, 40 = 10t - 5t^2 = > t^2 - 2t - 8 = 0

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

u+ 10m/s , a = -10 and s = -40m

-40 = 10t - 5t^2

t^2 - 2t - 8 = 0

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Answer:

18°

Step-by-step explanation:

We know that, sum of the angles in a straight line are added up to 180°.

Accordingly,

[tex]x - 6 + 8x + 24 = 180[/tex]

Combine like terms.

[tex]9x + 18 =180[/tex]

Subtract 18 from both sides.

[tex]9x = 180 - 18 \\ 9x = 162[/tex]

Divide both sides by 9.

[tex]x = 18 \degree[/tex]

Answer:

x = 18

Step-by-step explanation:

The given angles are,

→ x - 6

→ 8x + 24

We generally know that,

→ Sum of angles in straight line is 180°.

Forming the equation,

→ (8x + 24) + (x - 6) = 180

Now required value of x will be,

→ (8x + 24) + (x - 6) = 180

→ 8x + 24 + x - 6 = 180

→ (8x + x) + (24 - 6) = 180

→ 9x + 18 = 180

→ 9x = 180 - 18

→ 9x = 162

→ x = 162 ÷ 9

→ [ x = 18 ]

Therefore, the value of x is 18.

The straight-line distance and the shortest distance between point X and point Y will be 2,260 m and 2,361.78, respectively.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The distance between streets is around 80 m and the distance between avenues is around 260 m, as shown below.

The straight-line distance between point X and point Y will be given as,

⇒ (24 - 15) x 260 + (9 - 5) x 80

⇒ 2,340 + 320

⇒ 2,260 m

The shortest distance along the roads to get from point X to point Y will be given as,

D² = (2,340)² + (320)²

D² = 5,475,600 + 102,400

D² = 5,578,000

D = 2,361.78 meters

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The complete question is attached below.

Iterations are required to sort the array 10 23 14 35 17 15 16 using selection sort = 5

The selection sort algorithm sorts an array by repeatedly finding the minimum element (considering ascending order) from the unsorted part and putting it at the beginning.

The algorithm maintains two subarrays in a given array.

The subarray which already sorted.

The remaining subarray was unsorted.

In every iteration of the selection sort, the minimum element (considering ascending order) from the unsorted subarray is picked and moved to the beginning of unsorted subarray.

After every iteration sorted subarray size increase by one and unsorted subarray size decrease by one.

After N (size of array) iteration we will get sorted array.

Lets consider the following array as an example: array[] ={10 23 14 35 17 15 16}

{64, 25, 12, 22, 11}

First pass:

For the first position in the sorted array, the whole array is traversed from index 0 to 6 sequentially. The first position where 10 is stored presently, after traversing whole array it is clear that 10 is the lowest value.

  10      23       14      35       17      15         16

Thus, replace10 with 10. After one iteration 10, which happens to be the least value in the array, tends to appear in the first position of the sorted list.

10      23       14      35       17      15         16

Second Pass:

For the second position, where 23 is present, again traverse the rest of the array in a sequential manner.

 10      23       14      35       17      15         16

After traversing, we found that 14 is the second lowest value in the array and it should appear at the second place in the array, thus swap these values.

  10      14       23      35       17      15         16

Third Pass:

Now, for third place, where 23 is present again traverse the rest of the array and find the third least value present in the array.

  10      14       23      35       17      15         16

While traversing, 15 came out to be the third least value and it should appear at the third place in the array, thus swap 15 with element present at third position.

   10      14       15      35       17      23         16

Fourth pass:

Now, for fourth place, where 35 is present again traverse the rest of the array and find the fourth least value present in the array.

 10      14       15      35       17      23         16

While traversing, 16 came out to be the fourth least value and it should appear at the fourth place in the array, thus swap 16 with element present at fourth position.

10      14       15      16       17      23         35

Fifth Pass:

At last the largest value present in the array automatically get placed at the last position in the array

The resulted array is the sorted array.

 10      14       15      16       17      23         35

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The unknown multiplier is 6, and the new values for the ingredients are: Flour: 6 cups, Sugar: 4 cups and Baking Soda: 6 teaspoons.

Ingredients are the components used in the production of food or other products.

To find the unknown multiplier in #2, we need to set up an equation with the original recipe and the new recipe.
Original Recipe: Flour: 3 cups, Sugar: 2 cups, Baking Soda: 1 teaspoon

New Recipe: Flour: 6 cups, Sugar: 4 cups, Baking Soda: x teaspoons

We can set up the equation 3/6 = 2/4 = 1/x.
To solve this equation, we can multiply each side of the equation by 6.
3 = 2 × 6 = 4 × 6 = x
Therefore, the unknown multiplier is 6, and the new values for the ingredients are: Flour: 6 cups, Sugar: 4 cups and Baking Soda: 6 teaspoons.

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1. x = (x1+x2)/2

2 .The ratio of DE:AB is DE/AB = √((x2-x1)^2 + (y2-y1)^2) / √((x2-x1)^2 + (y2-y1)^2)

What is the Midpoint?

The midpoint of a line segment is the point that is exactly in the middle of the line segment. It is equidistant from both endpoints of the line segment. It is represented by the coordinates (x, y), where x and y are the averages of the x-coordinates and y-coordinates of the endpoints of the line segment, respectively.

1. To solve for x, we can use the midpoint formula and the fact that D is the midpoint of AC.

The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.

let A(x1,y1) and C(x2,y2) be the coordinates of points A and C respectively

then D(x,y) is the midpoint of AC

x = (x1+x2)/2 and y = (y1+y2)/2

Since we know that AD = 28 and DC = 22, we can use the distance formula to find the coordinates of A and C.

The distance formula states that the distance between two points (x1, y1) and (x2, y2) is √((x2-x1)^2 + (y2-y1)^2)

so we have:

√((x2-x1)^2 + (y2-y1)^2) = √((x2-x1)^2 + (y2-y1)^2) =28

√((x2-x1)^2 + (y2-y1)^2) = √((x2-x1)^2 + (y2-y1)^2) =22

square both equations and we have:

(x2-x1)^2 + (y2-y1)^2 = 28^2

(x2-x1)^2 + (y2-y1)^2 = 22^2

2. To determine the ratio of DE:AB we can use the fact that E is the midpoint of BC.

let B(x1,y1) and C(x2,y2) be the coordinates of points B and C respectively

then E(x,y) is the midpoint of BC

x = (x1+x2)/2 and y = (y1+y2)/2

Since we know that BE = 8x + 3 and EC = 5x + 7.5, we can use the distance formula to find the coordinates of B and C and then find the ratio.

Hence, The ratio of DE:AB is DE/AB = √((x2-x1)^2 + (y2-y1)^2) / √((x2-x1)^2 + (y2-y1)^2)

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The number of games that the team played today is; 15 games

Let me name of each player be A, B, C, D, E, F.

Now, let's start counting number of matches played by each team one after the other.

1. Player A will play with B, C, D, E, F. So number of matches played by team A is equal to 5.

2. Player B will play with C, D, E & F.( Players B & A have already played match with each other. So we won't count it again.) Thus, number of matches played by player B is equal to 4.

3. Player C will play with D, E, F & as it has already played with B & A, we will not count it again. So, number of matches played by player C is equal to 3.

4. Player D is left to play with E & F as it has already played with rest of the team. So, number of matches played by Player D is equal to 2

5. Player E & F will play with each other;

Add total number of matches played from above which is equal to;

5 + 4 + 3 + 2 + 1 = 15

From here, further matches to be played will be based on how many teams will qualify for next round.

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Answer:

34

Step-by-step explanation:

Each number is added to by a doubling sequence

4, 4+2=6, 6+4=10, 10+8=18, 18+16=34, 34+32=66

Answer:

9

Step-by-step explanation:

if you search it up you get the answer your looking for

Life expectancy in the U.S. is steadily increasing due to medical advancements and the increased awareness of maintaining a healthy lifestyle.  0.126 x + 76.74 less-than-or-equal-to 85.  Option A

Generally,  Based on an organism's birth year, present age, and other demographic parameters like sex, life expectancy is a statistical assessment of the typical amount of time that it is predicted to live. Life expectancy at birth, which has two definitions, is the most often used metric.

This inequality states that the life expectancy of women, modeled by the function W(x), is at least 85.

The less-than-or-equal-to symbol is used because the inequality is asking for the minimum birth year required to achieve a life expectancy of at least 85, which means that the value of the function can be equal to 85 as well as greater than 85.

The correct answer is A: 0.126 x + 76.74 less-than-or-equal-to 85.

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The array depicted displays the division represented by the equation

20 ÷ 5 = 4

Division is one of the four basic mathematical operators other include

addition

subtraction and

multiplication

Multiplication is the inverse or opposite of division, this means that when reverting the process of division we et to multiplication

In the array the number to be divided is the counting the whole small boxes which is 20.

Division is used to group the numbers in groups of 4 showing 5 divisions in group of four

This may also be 4 divisions in group of 5

Mathematically this written as

20 / 5 = 4

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For a Hexagonal Prism , the Surface Area can be calculated by using the formula [tex]3sh+3\sqrt{3}s^{2}[/tex] , and the volume can be calculated by using the formula [tex]\frac{3\sqrt{3}s^{2}}{2} \times s^{2} h[/tex]  .

What is a Hexagonal Prism ?

The hexagonal prism is defined as the prism that has  a hexagonal base and top. hexagonal prism is a 3D shape and that has 8 faces, 18 edges, and 12 vertices. As it has 8 faces it can also called as Octahedron.

The formula to calculate the Surface Area of the hexagonal prism is written as : [tex]3sh+3\sqrt{3}s^{2}[/tex] ;

The formula to calculate the Volume of hexagonal prism is written as : [tex]\frac{3\sqrt{3}s^{2}}{2} \times s^{2} h[/tex] ;

where h = is the height of hexagonal prism , and

s = is the side of the hexagonal base .

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To solve this equation, you would need to isolate the logarithm on one side of the equation.

What is a logarithm in simple terms?

A logarithm is the power to which a number must be increased in order to get some other number (see Section 3 of this Math Review for more about exponents) (see Section 3 of this Math Review for more about exponents). For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2, or log 100 = 2.

You can start by using the property of logarithms that states that log(a*b) = log(a) + log(b).

So, you can split the left side of the equation into two logarithms: log(3x²) + log(1 + 4/3x) = log(2x²) + log(1 + 6/x)

Now, you could use the property log(a^b) = b*log(a) to simplify the equation further.

So, you will have: 2log(x) + log(1 + 4/3x) = 2log(x) + log(1 + 6/x)

Then by using log(1+x) ≈ x, you can simplify the equation further to 2log(x) + 4/3x ≈ 2log(x) + 6/x.

Now it's clear that the equation is not true and can't be solved.

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To make 40 meters long shadow, building should have 10 stories.

In arithmetic, the multiplication of two numbers represents the repeated addition of one number with respect to another. These numbers can be whole numbers, natural numbers, integers, fractions, etc. If m is multiplied by n, then it means either m is added to itself ‘n’ number of times or vice versa.

Given,

Stories of building 24 meters long shadow  = 6

Stories making 1 meter long shadow = 6/24

Stories in building making 40 meters long shadow = 6/24 × 40

                                                         = 240 / 24

Stories in 40 meters long building = 10

Hence, 10 stories tall building will make shadow length of 40 meters.

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Answer:

15

Step-by-step explanation:

I took the test and got it right

After solving, the perimeter of △lmn is 8 + √10.

In the given question, we have to find the perimeter of △lmn.

The graph of the given question is given below:

From the graph we can see that N(-1, 4), L(2, 4) and M(-2, 1)

Before finding the perimeter we have to find the length of the line.

We can find the length of the line using the formula

L = √[{x(2)-x(1)}^2+{y(2)-y(1)}^2]

We firstly find the length of line NL.

x(1) = -1, y(1) = 4, x(2) = 2 and y(2) = 4

L(NL) = √[(2-(-1))^2+(4-4)^2]

L(NL) = √[(2+1)^2+0^2]

L(NL) = √[(3)^2+0]

L(NL) = 3

Now we find the length of line LM.

x(1) = 2, y(1) = 4, x(2) = -2 and y(2) = 1

L(LM) = √[(-2-2)^2+(1-4)^2]

L(LM) = √[(-4)^2+(-3)^2]

L(LM) = √[16+9]

L(LM) = √25

L(LM) = 5

Now we find the length of line MN.

x(1) = -2, y(1) = 1, x(2) = -1 and y(2) = 4

L(MN) = √[(-1-(-2))^2+(4-1)^2]

L(MN) = √[(-1+2)^2+(3)^2]

L(MN) = √[(1)^2+9]

L(MN) = √[1+9]

L(MN) = √10

Now we finding the perimeter of △lmn

Perimeter of △lmn = length of NL + length of LM + length of MN

Perimeter of △lmn = 3 + 5 + √10

Perimeter of △lmn = 8 + √10

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The perimeter is equal to the sum of the lengths of its three sides. We added 8 units, 9 units, and 10 units to get a total of 27 units, which is the perimeter of △lmn.

The perimeter of a triangle is the sum of the lengths of its three sides. To calculate the perimeter of △lmn, we must first identify the lengths of the three sides. Let's say the length of side lm is 8 units, side mn is 9 units, and side ln is 10 units. We can now use the formula for the perimeter of a triangle to calculate the perimeter of △lmn:

Perimeter of △lmn = 8 + 9 + 10

Perimeter of △lmn = 27 units

To calculate the perimeter of △lmn, we first identified the lengths of its three sides. Then, we used the formula for the perimeter of a triangle, which states that the perimeter is equal to the sum of the lengths of its three sides. We added 8 units, 9 units, and 10 units to get a total of 27 units, which is the perimeter of △lmn.

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The solution is

a) The total area of the rectangular grass area is 9600 feet²

b) The number of bags required is 9.6 bags

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangular grass area be = A

Now , the equation will be

The length of the rectangular grass portion = 120 feet

The width of the rectangular grass portion = 80 feet

The area of the rectangular grass portion = Length x Width

Substituting the values in the equation , we get

The area of the rectangular grass portion A = 80 x 120

The area of the rectangular grass portion A = 9600 feet²

Now , each bag of the grass seed covers 1000 feet²

So , the number of bags required for the entire area = area of the rectangular grass portion A / each bag of the grass seed covers 1000 feet²

On simplifying the equation , we get

The number of bags required for the entire area = 9600 / 1000

The number of bags required for the entire area = 9.6 bags

Therefore , the number of bags required is 9.6 bags

Hence , the total area of the rectangular grass area is 9600 feet²

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