one positive number is 8 more than twice another. if their product is 1242, find the numbers?

x = 32

Step-by-step explanation:

[tex]{ \tt{p(x) = \frac{x + 7}{3} }}[/tex]

If p(x) = 13, then

[tex]{ \tt{13 = \frac{x + 7}{3}}} [/tex]

[tex]{ \tt{13 \times 3 = x + 7}}[/tex]

[tex]{ \tt{39 = x + 7}}[/tex]

[tex]{ \tt{39 - 7 = x}}[/tex]

[tex]{ \red{ \boxed{ \blue{ \sf{x = 32}}}}}[/tex]

Answer:

Classification - Right Scalene

Perimeter - 30ft

Area - 30ft

Step-by-step explanation:

Classification - There's a right angle, and 3 unequal sides.

Perimeter - 5 + 13 + 12 = 30

Area = 5*12=60, 60/2 = 30

The composition f(4) has a value of -27

The definition of the functions is given as

f(x) = -2x^2 + 5

Rewrite the above function properly

So, we have the following representation

f(x) = -2x² + 5

To find the function f(4), we set the value of x in the equation f(x) = -2x² + 5

This is represented by

Calculate f(x), when x = 4

Substitute 4 for x in the equation f(x) = -2x² + 5

So, we have the following equation

f(4) = -2(4)² + 5

Evaluate the exponents

This gives

f(4) = -2 * 16 + 5

Evaluate the products

This gives

f(4) = -32 + 5

Evaluate the sum

f(4) = -27

Hence, the value of the function is -27

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There can be 2184 ways in which three posts can be selected using permutation.

What is permutation?

An arrangement of things in a specific order is referred to as a permutation. In this arrangement, the components or components of sets are arranged in a linear or sequential order.

Main Body:

Total members =14

total posts =3

As one person can not hold more than 1 post ,

total ways are = ¹⁴P₃

Therefore total ways = 14!/11!  

                                   = (14*13*12*11!)/11!

                                   = 14*13*12

                                   = 2184 ways

Hence answer is 2184 ways to select 3 members out of 14.

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Answer:

20 units

Step-by-step explanation:

we find the side lengths by looking at the coordinates and just counting up

Sides are 6,4,6,4

So we just add

6+4+6+4

10+10

20

Hopes this helps please mark brainliest

Answer: Your answer is 20 units, because the height is 6 units, and the length is 4 units, so we then multiply by 2 for both numbers, then add them together, having a sum of 20 units.

Hope that helps.

The probability expression when converted from odd's expression is 8/17

From the question, we have the following odd parameters

Odd = 8 to 9

To start with, we need to express the odd as ratio

So, we have the following representation

Odds ratio = 8 : 9

Solving further, we need to express the ratio as fraction

So, we have the following representation

Odds fraction = 8/9

To convert the above odd's expression to probability expression, we make use of the following equation

This is represented as

P = Odds/(Odds + 1)

Substitute the known values in the above equation

So, we have the following equation

P = (8/9)/(8/9 + 1)

Evaluate the sum

This gives

P = (8/9)/(17/9)

Express the quotient as product

P = (8/9) * (9/17)

Evaluate

P = 8/17

Hence, the probability is 8/17

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Answer:

(simplify 26³)

26³ = 17,576

= 17,576 + 5 = 3³+57

(simplify 3³)

3³ = 27

= 17,581 = 27+57

= 17,581 ≠ 84

The solution to the equation using graph is x= -0.62 or x = 1.62.

What is equation?

A mathematical equation may be a formula that uses the equals sign to represent the equality of two expressions.

Main Body:

For [tex]-x^{2} +y = 1[/tex]

We make y the subject to obtain

[tex]y = x^{2} +1[/tex]

We can easily graph this function, because we just have to transform the graph [tex]y = x^{2}[/tex] of  by shifting the intercept up to 1.

As for the straight line, -x +y = 2

We find the intercepts as follows,

When y = 0 , x = -2

When x = 0 , y = 2

We plot the points (-2,0)  and (0,2).

We now draw the two graphs on the same graph sheet. The intersection of the two graphs gives the solution to be

x= -0.62 or  x= 1.62

See graph

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60% of the fruit punch is orange juice.

In this question, we have been given 3/5 of a fruit punch is orange juice.

We need to find the percentage of the fruit punch is orange juice.

3/5 of a fruit punch is orange juice, means 3 of 5 fruit punch is orange juice.

Using the percentage formula,

3/5 * 100

= 0.6 * 100

= 60%

Therefore, 60% of the fruit punch is orange juice.

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For the given ratio of orange juice , the percentage of the orange juice from the given fruit juice is equal to 60%.

As given in the question,

Ratio of orange juice in the given fruit juice = 3/5

From the given ratio it indicates out of 5 fruits 3 are orange

Percentage of fruit punch is orange juice in the given juice is equal to

= ( 3 / 5 ) × 100

= ( 3 × 100 ) / 5

= 300 / 5

= 60%

60% of the fruit punch is orange juice.

Therefore,  for the given ratio of orange juice , the percentage of the orange juice from the given fruit juice is equal to 60%.

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The expression [tex](\frac{1}{4^{-3 } } )^{-2}[/tex] is less than 1.

The sign to change to make the expression greater than 1 is changing the sign of the exponential value which will make the new expression as

[tex](\frac{1}{4^{-3 } } )^{2}[/tex]

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).

In other words, an algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.)

Therefore, let's simplify the expression to know if it's equals to 1, greater than 1 or less than 1.

[tex](\frac{1}{4^{-3 } } )^{-2}[/tex]

using law of indices,

[tex](\frac{1}{4^{-3 } } )^{-2}[/tex] = 1 × [tex](4^{-3} )^{2}[/tex]

4⁻⁶  = 1 / 4⁶ = 1 / 4096

Hence,

1 / 4096 = 0.00024414062

Therefore,  the value is less than 1.

Let's change one sign to make the expression greater than 1.

Therefore, the expression will be [tex](\frac{1}{4^{-3 } } )^{2}[/tex]

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Answer:

58%

Step-by-step explanation:

35/60=0.58333=58/100=58%

24.

[tex](6x+3y)-\frac{z^{2}}{(2x)}[/tex]

[tex](6(3)+3(4))-\frac{(6)^{2}}{(2(3))}[/tex]

a) Solve parenthesis.

[tex](18+12)-\frac{(6)^{2}}{6}\\ \\30-\frac{(6)^{2}}{6}[/tex]

b) Solve the exponent.

[tex]30-\frac{36}{6}[/tex]

c) Divide.

[tex]30-6[/tex]

d) Subtract.

[tex]24.[/tex]

The rate of acceleration of a bicycle. if it went from a complete stop to 15 meters per second in 5 seconds is

acceleration is solved using the formula

a = (v - u) / t

definition of variables

final velocity = v

initial velocity = u

time taken  = t

form the question we have that

v = 15 meters per seconds

u = 0 (bicycle went from complete stop)

t = 5 seconds

a = (15 - 0) / 5

a = 15 /5

a = 3 meters per seconds squared

The bicycle is travelling at an acceleration of 3 meters per seconds squared

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Answer:

y=8 x=-19.5

Step-by-step explanation:

Start from the bottom equation and work your way upSolve the fourth equation for w-5w=-15-5w/(-5)=-15/(-5)w = 3 Then use that value of w to plug into the third equation. Notice we're going backwards or up the chain of equations. After w is replaced, solve for zz+w = 2z+3 = 2z+3-3 = 2-3z = -1 Now use z = -1 and w = 3 to plug into the second equation. Solve for y-2y-12z-4w = -16-2y-12(-1)-4(3) = -16-2y+12-12 = -16-2y = -16-2y/(-2) = -16/(-2)y = 8 

Use y = 8, z = -1, w = 3 to plug into the first equation. Solve for x:

2x+4y+z+3w=12x+4(8)+(-1)+3(3)=12x+32-1+9=12x+40=12x+40-40=1-402x=-392x/2=-39/2x = -39/2 The value of x as a fraction is x = -39/2The value of x in decimal form is x = -19.5 

The derivative of the function f(x) = Sin⁻¹(3x) is f'(x) = 3/√(1-9x²)  , the correct option is (c) .

In the question ,

a function is given as

f(x) = Sin⁻¹(3x) , we need to find the derivative .

we know that the derivative of Sin⁻¹(x) is equal to 1/√(1 - x²) .

So , on differentiating both sides with respect to "x" .

we get

f'(x) = d/dx (Sin⁻¹(3x))

= 1/√1-(3x)² ×  d/dx (3x)

= 1/√(1 - 9x²) × 3

On simplifying further ,

we get

= 3/√(1 - 9x²)

Therefore ,the derivative of the function is 3/√(1-9x²)  , the correct option is (c) .

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Answer:

The distance between two points on a 2D coordinate plane can be found using the following distance formula. d = √ (x2 - x1)2 + (y2 - y1)2. where (x 1, y 1) and (x 2, y 2) are the coordinates

Step-by-step explanation:

The domain of the function is [ - 6 , ∞ ]

A radical function is the one provided.

It should be noted that a radical function can only be specified for values that will result in the radicand being larger than or equal to zero.

As a result, either the radicand of the provided function must be larger than or equal to zero, or:

Thus we can write it as

x + 6 ≥ 0

subtract 6 from both LHS and RHS

x + 6 - 6 ≥ 0 - 6

x ≥ - 6

Therefore the domain of the function is [ - 6 , ∞ ]

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Answer:

see explanation

Step-by-step explanation:

(a)

parallel line segments are indicated by arrows on the segments pointing in the same direction.

from the diagram EA and DC are parallel lines.

(b)

equal lines are indicated by a dash through the lines.

from the diagram AB and BC are equal.

(c)

perpendicular lines are at right angles (90° ) to each other, usually indicated by a small box between them.

from the diagram AE and CD are perpendicular to DE

Answer:

5

Step-by-step explanation:

:)

Answer:5

Step-by-step explanation:|-10|-|-5|

                                             10-5

                                              5

Answer:

two times x plus two

Step-by-step explanation:

The quotient will be x² + 5x + 2 and the remainder will be 1.

Synthetic division method is a method used to divide polynomials. It is used to divide polynomial with a linear factor whose leading coefficient is 1.

We will factorize x³ + 7x² + 12x + 5 by x + 2 using synthetic division method.

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Answer:

  f(x) = x² -2x -35

Step-by-step explanation:

You want a quadratic function that has zeros 7 and -5.

Each zero (p) gives rise to a factor (x-p). The zeros 7 and -5 mean the quadratic has factors (x-7) and (x-(-5)).

  f(x) = (x -7)(x +5)

  f(x) = x² -2x -35

__

Additional comment

You may notice that the coefficient of the linear term is the opposite of the sum of the zeros. The constant term is the product of the zeros. Knowing this, we can write the quadratic without any concern for the factors.

  sum: 7-5 = 2

  product: (7)(-5) = -35

  quadratic: f(x) = x² -2x -35

The percentage of shaded grid is 45% and the number of squares is 5.

a. Percentage of shaded grid

The total number of shaded and unshaded grid is 20 while the total number of shaded area is 9 now let find the percentage of the shaded grid.

Percentage of shaded grid = Shaded grid /Total grid

Percentage of shaded grid = 9/20 × 100

Percentage of shaded grid = 45%

b. Number of squares to be shaded

Number of squares = 20 grid × (70% - 45%)

Number of squares = 20 grid × 25%

Number of squares =  5 squares

Therefore the percentage is 45% .

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Answer: x = -135.59

Step-by-step explanation:

20 = 0.694(x + 150)(2)

Step 1: Simplify both sides of the equation.

20 = 0.694 (x + 150)(2)

20 = 1.388x + 208.2 (use the distributive property)

20 = 1.388x + 208.2

Step 2: Flip the equation.

1.388x + 208.2 = 20

Step 3: Subtract 208.2 from both sides of the equation.

1.388x + 208.2 − 208.2 = 20 − 208.2

1.388x = −188.2

Step 4: Divide both sides by 1.388.

1.388x/1.388 = −188.2/1.388

x = −135.590778

Optional: Simplify

x = -135.59

Tthe length of PQ and QR.​ is 6 and 8 m

Area of rectangular field ABCD is = 4m x 6m = 24m2

Area of rectangular field PQRS (ABCD with uniform path) = (4 + x)(6 + x)

= 24 + 4x + 6x + x²

48 = 24 + 10x + x²

x² + 10x - 24 = 0

x² + 12x - 2x - 24

x(x + 12) - 2(x + 12)

(x - 2)(x + 12) = 0

x - 2 = 0

x = 2

PQ = 4 + 2 = 6

QR = 6 + 2 = 8

Therefore,  the length of PQ and QR.​ is 6 and 8 m

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By using addition, subtraction, multiplication and division of integers,

it can be calculated that

There are 3 groups of 9 and 21 groups of 10

What is addition, subtraction, multiplication and division of integers?

Addition of integers is used to find the sum total of two or more integers.

Subtraction of integers is used find the difference between two integers.

Repeated addition is called multiplication. Multiplication is used to find the product of two or more integers.

Division is the process in which the value of single unit can be calculated from the value of multiple unit

The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.

There is a well known formula for division

Divisor x Quotient + Remainder = Dividend.

Here, addition, subtraction, multiplication and division of integers will be used

Total number of boys = 121

Total number of girls = 116

Total number of students = 121 + 116 = 237

Now,

The leader first makes groups of nine students each and then assigns any remaining students to make some groups of 10 students

So the group of 9 is to be made in such a way that on multiplying the number by 9, unit digit of 7 is obtained

So the number is 3 as 9 [tex]\times[/tex] 3 = 27

Remaining number of students = 237 - 21 = 210

They will enter into a group of 10

Number of group of 10 = 210[tex]\div[/tex] 10 = 21

There are 3 groups of 9 and 21 groups of 10

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The value of x is -1 for equation -4x = -x + 3

Two or more expressions with an Equal sign is called as Equation.

The given equation is -4x = -x + 3

In the given equation minus four times of x equal to minus x plus three

x is the variable

Plus and minus are operators

-4x = -x + 3

Take the variables to one sides

Add +x on both sides

-4x+x=-x+x+3

-3x=3

Divide both sides by -3

x=-1

Hence, the value of x is -1 for equation -4x = -x + 3

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The elements of AUB is {6, 7, 8, 9, 11} when A = {6,7,8,11} and B = {7,6,7,9}.

According to the question,

We have the following information:

A = {6,7,8,11} and B = {7,6,7,9}

Now, we know that the elements of AUB means that all the elements which are there in both sets but the elements are not supposed to be repeated.

(Please that AUB can also be found using Venn diagram and questions are asked where the question has to be solved by making Venn diagram and representing all the elements in it.)

So, we have the following expression:

AUB = {6,7,8,9,11}

(Now, note that numbers however repeated in sets are not repeated here.)

Hence, the elements of AUB is {6, 7, 8, 9, 11} when A = {6,7,8,11} and B = {7,6,7,9}.

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