Question 8 (1 point)
Solve the equation. Check for extraneous solutions.
7|14-8x|= 2x + 2;

Answer: Yes

Step-by-step explanation:

A repeating decimal can be a rational number.

Rational

Rational and irrational numbers are 2 of the broadest categories within real numbers.

Writing the Number as a Fraction

Rational numbers are defined as numbers that can be written as simple fractions. Simple fractions have integers for the numerator and denominator. This means neither the numerator nor denominator is a fraction or decimal. The number above is 0.25 repeated. When 2 digits are repeated you can place that number over 99 to create an equivalent fraction.

Since this number can be written as a fraction, it must be a rational number.

Bar Notation

Additionally, repeated decimals are always rational. In the example above, the digits .25 are repeated. If you don't want to write it as a fraction, you can use bar notation. Bar notation helps to shorten repeated decimals and show that they are rational. In this notation, you place a bar over the digits that are repeated.

Answer:

It is not a function because the number 1 repeats twice (If the numbers in the domain repeat then it is not a function)

Answer:   The three angle bisectors of a triangle intersect at a single point. The point of concurrency of the angle bisectors is called the incenter. The three altitudes of a triangle are concurrent.

Step-by-step explanation:

The page number of left page is 213

The page number of right page is 214.

Given,

The left and right page numbers of an open book are two consecutive integers.

We can take:

The left page number = n

The right page number = n + 1

The sum of the page numbers = 427

That is,

n + (n + 1) = 427

We can solve this equation:

n + (n + 1) = 427

2n + 1 = 427

2n = 427 -1

2n = 426

n = 426/2

n = 213

n + 1 = 213 + 1 = 214.

Therefore,

The left page number is 213 and right page number is 214.

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Answer:

A=2

B=-1

Step-by-step explanation:

a=(23−25)⋅ (4−5)=2

b=(97−123)/(18+8)=−1

Answer:

21/12

Step-by-step explanation:

1 3/4 in improper form is 7/4

7 is not 9 more than 4 so its another equivalent

7/4 × 2/2 = 14/8

That isn't 9 more than the denominator either

7/4 × 3/3 = 21/12

21 - 12 = 9 so 21 is greater than 12 by 9.

The solution for the variable a in the fraction equation given as 1/12a - 1/2 = -1/8 is 9/2

The fraction equation is given as

1/12a - 1/2 = -1/8

Add 1/2 to both sides of the equation

So, we have

1/12a = 1/2 - 1/8

Take LCM and evaluate the sum

1/12a = (4 - 1)/8

Evaluate the difference

1/12a = 3/8

Multiply both sides of the equation by 12

So, we have

a = 9/2

Hence, the solution for the variable a in the fraction equation given as 1/12a - 1/2 = -1/8 is 9/2

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The height of the building is 240.34m

Since we are given t=√2h/g

By Squaring both sides we get simplifies equation as t²=2h/g

We are given the value of t as 7 and value of g as 9.81

Putting these values in the simplified equation we get

h=49×9.81/2

h=240.34m

Hence the height of the building is 240.34m

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Answer:

Step-by-step explanation:

a:) Solve for b:

a = b/c^2

a = b/c^2 is equivalent to b/c^2 = a:

b/c^2 = a

Multiply both sides by c^2:

Answer: b = a c^2 = Dark Green

part 2) a = b/c^2 where a = 1/8, c = 4

b = 2

____________________________________________

b:) Solve for v:

-v + m = k

Subtract m from both sides:

-v = -m + k

Multiply both sides by -1:

Answer: v = m - k = Light blue

part 2) m - v = k where k = -7, m = -2

v = 5

__________________________________________

c:) Solve for q:

p/q = r/s

Take the reciprocal of both sides:

q/p = s/r

Multiply both sides by p:

Answer: q = (p s)/r = yellow

part 2) p/q = r/s where p = 14, r = -7, s = -4

q = 8

Answer: I hope this is what your looking for....

12-86+2^2 = 0

w=6

w=2

Step-by-step explanation:

Answer: w = 6,2

Step-by-step explanation:

No extraneous solution to the equation.

The equation is

[tex](2x + 3)^{1/2}[/tex] - 7 = 0

To find whether the equation has an extraneous solution, first we have to find the value of x.

[tex](2x + 3)^{1/2}[/tex] = 7

Squaring both sides, we get

2x + 3 = 49

2x = 46

x = 23

Now put the value of x in the equation,

[tex](2 * 23 + 3)^{1/2}[/tex] - 7 = 0

[tex](46 + 3)^{1/2}[/tex] - 7 = 0

[tex]49^{1/2}[/tex] - 7 = 0

7 - 7 = 0

0=0

Therefore we get that there is no extraneous solution to the equation, x= 23 is the solution of the equation.

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The correct answer is [a]. As value of the x increases the value

According to this function, the value of f(x) grows closer to a constant as the value of x rises.

A relationship between a group of the inputs and one output each is referred to as a function.

The function specified is;

[tex]f(x)= (\frac{1}{5})^{x}-2[/tex]

According to this function, value of f(x) travels in the direction of a constant as the value of x rises.

(-2,00) is function's domain.

The y-intercept of function is at (0,-2).

The performance is the deteriorating.

As a result, statement that this function advances toward a constant value as x rises is accurate.

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The equation of the ellipse, circle, and parabola will be written as (x + 9)² / 4 + (y - 1)² / 16 = 1, (x + 4)² + (y - 3)² = 40, and y = - (x + 3)²/ 4 + 1, respectively.

Equation A is transformed as,

16x² + 4y² + 96x - 8y + 84 = 0

16(x² + 6x + 9 - 9) + 4(y² - y + 1 - 1) + 84 = 0

16(x + 9) - 144 + 4(y - 1)² - 4 + 84 = 0

16(x + 9)² + 4(y - 1)² = 64

(x + 9)² / 4 + (y - 1)² / 16 = 1

This is the equation of the ellipse.

Equation B is transformed as,

x² + y² + 8x - 6y - 15 = 0

x² + 8x + 16 + y² - 6y + 9 - 15 = 16 + 9

(x + 4)² + (y - 3)² = 40

This is the equation of the circle.

Equation C is transformed as,

x² + 6x + 4y + 5 = 0

x² + 6x + 9 - 9 + 4y + 5 = 0

y = - (x + 3)²/ 4 + 1

This is the equation of the parabola.

The graph of the function is given below.

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Step-by-step explanation:

[tex]7x < 67 - 32 \\ 7x < 35 \\ \frac{7x}{7} < \frac{35}{7} \\ x < 5[/tex]

On combining the radicals 3[tex]\sqrt{2}[/tex] and -5[tex]\sqrt{2}[/tex] we get the answer

- 2[tex]\sqrt{2}[/tex].[tex]\sqrt{2}[/tex]

Square Root : The root of a number in math is a number that when multiplied by itself produces the original number. For example, the square root of 49 is 7 because 7×7=49. In this case, because 7 is multiplied by itself twice to produce 49, we call 7 the square root of 49.

Given are the two radicals 3[tex]\sqrt{2}[/tex] and -5[tex]\sqrt{2}[/tex]

Explanation:

Subtracting both the numbers, we get

= 3[tex]\sqrt{2}[/tex] + (- 5[tex]\sqrt{2}[/tex])

opening brackets, we get

= 3[tex]\sqrt{2}[/tex] - 5[tex]\sqrt{2}[/tex]

Taking common [tex]\sqrt{2}[/tex] from both the digits, we get

= ( 3 - 5 )  [tex]\sqrt{2}[/tex]

On subtracting, we get

= - 2[tex]\sqrt{2}[/tex]

Therefore, on combining the radicals 3[tex]\sqrt{2}[/tex] and -5[tex]\sqrt{2}[/tex] we get the answer

- 2[tex]\sqrt{2}[/tex].

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first off let's recall that 4³ = 64, and that i⁴ = 1, so

[tex]i^{64}\implies i^{4^3}\implies i^{4\cdot 4\cdot 4}\implies i^{4\cdot 16}\implies (i^4)^{16}\implies (1)^{16}\implies \text{\LARGE 1}[/tex]

Answer:

39:2 (simplified)

Step-by-step explanation:

books : students

351 : 18

(divide by 9)

39 : 2

Transformation of y= b*x into y = 5x + 3 will take place by vertical dilation by a scale factor of  5 and vertical translation of 3 units.

A parent function is the simplest form of a particular family of functions. A family of operations is a group of tasks with the same highest degree and therefore the same graph shape.

Function transformations "move" "resize" or "mirror" the graph of the parent function.

Mathematically speaking, the transformation of the function y = f(x) is usually y = a f(b(x + c)) + d. where a, b, c, and d are arbitrary real numbers representing transformations. Note that all outer numbers (outside the brackets) represent vertical translations, and all inner numbers represent horizontal translations. Addition and subtraction are translations, and multiplication and division are dilations. Every time a minus sign is multiplied it means  it is a reflection here,  'a' stands for vertical stretch, 'b' stands for horizontal stretch, 'c' stands for horizontal movement, 'd' stands for vertical movement

We have given two functions y=b x  and y = 5x + 3 which means that first, y  changes into 5x  i.e., vertical dilation by a scale factor of 5 and it changes to y = 5x + 3 i.e.., vertical translation of 3 units.

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Answer: you take 4.50 multiply it by 4 for the chaperons and the teacher then multiply 4.50 by how many students there are then add those two together and there is your answer

Step-by-step explanation:

A graph can help us find solutions to two-variable equations through the point of intersection.

The appropriate steps will be:

Draw a graph for each side, or component, of the equation and check to see where the curves intersect, or are equal, to solve an equation graphically.

The answers to the equation are the x values of these places.

Plotting the graph of each equation allows us to clearly understand the solution. The point of intersection of the two lines is where the solution, which is an ordered pair that satisfies both equations, occurs on both lines.

Therefore, a graph can help us find solutions to two-variable equations through the point of intersection.

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Answer: A

explain: because 17 = 35

Answer:

7

Step-by-step explanation:

7x(92+7) = 693

(7x92) = 644

(7x92) +

(7x7) = 49

644 + 49 = 693

The solution for the trigonometric expression 2sin²θ = -sinθ are θ = 0, π, 2π/3, 7π/6, and 11π/6 which are lies between 0 ≤ θ<2π.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

It is given that:

The trigonometric expression is:

2 sin²θ = -sinθ where 0 ≤ θ< 2π

2 sin²θ + sinθ = 0

sinθ(2sinθ + 1) = 0

sinθ = 0    or   sinθ = -1/2

θ = 0, π  or  θ = 2π/3, 7π/6, 11π/6

θ = 0, π, 2π/3, 7π/6, and 11π/6

Thus, the solution for the trigonometric expression 2sin²θ = -sinθ are θ = 0, π, 2π/3, 7π/6, and 11π/6 which are lies between 0 ≤ θ<2π.

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[tex]\huge\boxed{7\ \text{inches}}[/tex]

We're trying to find how many inches of wire can be purchased with 28 cents, so we'll start by finding how much wire can be bought with just one cent.

This amount will be represented with [tex]w[/tex].

[tex]14=56w[/tex]

Divide both sides of the equation by 56.

[tex]\dfrac{14}{56}=w\\\\\dfrac{1}{4}=w[/tex]

Now, we'll multiply this value by 28 cents to find the final answer.

[tex]\dfrac{1}{4}\cdot28=\boxed7[/tex]

midpoint of the line segment is (1/2 , -3)

A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.

Let (a1, b1) and (a2, b2) be the ending point of the line segment. The midpoint formula of a line segment joining these two points is given as:

(a , b ) = ((a₁ +a₂)/2 , (b₁ +b₂)/2)

Here ,

a₁ =-2

a₂=3

b₁=-1

b₂= -5

(a , b ) = ((-2 +3)/2 , (-1 -5)/2)

(a , b ) = (1/2 , -3)

midpoint of the line segment is (1/2 , -3)

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Step-by-step explanation:

18^4 (18 with a smaller 4 on the top right corner)

Answer:

Is there any picture to go with it perhaps?

Step-by-step explanation:

The values of positive integers n (n-11)(n-13) prime would be 6 and the solution are; 5 and 7.

Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities.

For an integer, factorization is decomposition of that integer in terms of smaller integers which when multiplied with each other give back that considered number. Those composing integers are called factors of that considered integers.

The Prime factorization is when all those factors are prime numbers.

Since prime factorization expresses an integer in terms of multiples of prime numbers.

Prime factorization is unique for each integer.

The value of n would be 6

(n-11) = 6- 11 = 5

(n-13) = 6 - 13 = 7

Therefore, the  values of positive integers n (n-11)(n-13) prime would be 6.

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