Im really confused on how do i find x?

Answer:

8/45 or 0.177...... (the seven continues forever).

Step-by-step explanation:

8/9 ÷ 5

First, turn 5 into a fraction. That will be 5/1

8/9 ÷ 5/1

When you're dividing fractions, you flip the second fraction and turn the division sign to a mutiplication sign

8/9 ÷ 1/5

8/9 * 1/5

Now you multiply. We will multiply the numerator and then the denominators through since there are no common factors.

8 * 1/9 * 5

8/45

Rewrite the equation in expanded form:

(X+2)^2 -1 = x^2 + 4x + 3

The parabola parameters are : a = 1, b = 4, c = 3

The x vertex is -b/2a = -4/2(1) = -2

Replace x with -2 in the expanded equation to solve for the y vertex:

Y = -1

The vertex is (-2,-1)

x-value of the vertex:-2

Answer:

Solution given:

we have

f(x)=(x+2)²-1

y=x²+4x+3......(I)

parameters of parabola are:

a=1

b=4

c=3

we have

vertex=-b/2a=-4/(2*1)=-2

substitute value of x in equation 1.

y=4-8+3= -1

So

vertex(-2,1)

The area of the walkway is 24π square meters.

To find the area of the walkway, we need to subtract the area of the inner circle from the area of the outer circle.

The inner circle has a radius of 5 meters, so its area can be calculated using the formula for the area of a circle: A_inner = π * \((r_inner)^{2}\).

A_inner = π * \(5^{2}\) = 25π square meters.

The outer circle has a radius equal to the sum of the inner radius and the width of the walkway. In this case, the outer radius is 5 + 2 = 7 meters.

The area of the outer circle can be calculated in the same way: A_outer = π * \((r_outer)^{2}\).

A_outer = π * \(7^{2}\) = 49π square meters.

Now, we can find the area of the walkway by subtracting the area of the inner circle from the area of the outer circle: A_walkway = A_outer - A_inner.

A_walkway = 49π - 25π = 24π square meters.

The area of the walkway is 24π square meters, where π (pi) is a mathematical constant approximately equal to 3.14159.

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Length of the diagonal of rectangular prism is equals to 13units.

" Rectangular prism is a three dimensional figure which has six faces in rectangular shape."

Formula used

Total surface area of the rectangular prism = 2(l b + b h +l h)

Sum of all the  edges of the prism = 4 (l +b + h)

length of the diagonal  of the prism = √l² + b² + h²

l = length of the prism

b = width of the prism

h = height of the prism

According to the question,

Given,

Total surface area of the rectangular prism = 56 units

⇒2(l b + b h +l h) = 56

Sum of all the edges of the prism = 60 units

⇒4(l + b + h) = 60

Divide both the side by 4 we get,

 (l + b + h) = 60 / 4

⇒(l + b + h) = 15                               ____(1)

Squaring both the side of (1)  we get,

  (l + b + h)² = (15)²

⇒l² + b² + h² + 2 (l b + b h +l h) = 225

Substitute the value of total surface area  to get length of the diagonal,

 l² + b² + h² + 56 = 225

⇒l² + b² + h²  = 225 - 56

⇒l² + b² + h²  = 169

⇒√l² + b² + h²  = √169

⇒√l² + b² + h²  =  13

Hence, length of the diagonal of rectangular prism is equals to 13units.

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Let's translate the argument into symbolic form using the following symbols:

B: Brazil has a huge foreign debt.

A: Argentina has a huge foreign debt.

The argument can be represented as follows:

B → (B ∨ A)

To determine the validity of the argument, we can construct a truth table for the expression (B → (B ∨ A)). The truth table will include all possible combinations of truth values for B and A, and we will evaluate the truth value of the entire expression for each combination.

The truth table for the argument is as follows:

B A B ∨ A B → (B ∨ A)

T T T T

T F T T

F T T T

F F F T

As we can see from the truth table, regardless of the truth values of B and A, the expression B → (B ∨ A) always evaluates to true. Therefore, the argument is valid because the conclusion is always true when the premise is true.

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Answer:

-1/9

Step-by-step explanation:

We need to solve out and find out the value of p . The given equations is.

=> 2p + 1/ 5p + 6 = 1/7

=> 7 ( 2p + 1) = 5p + 6

=> 14p + 7 = 5p + 6

=> 14p - 5p = 6-7

=> 9p = -1

=> p = -1/9

• Hence the value of p is -1/9

Answer:

y^2

Step-by-step explanation:

a^m/a^n = a^(m - n)

y^5/y^3 = y^2

The given function y= x² + c/x² is a solution of the differential equation xy′ + 2y = 4x² for all values of c.

The value of c for which the solution satisfies the initial condition y(4) = 3 is -208.

The given function y= x² + c/x² is a solution of the differential equation xy′ + 2y = 4x², when c= 1/16. The solution satisfies the initial condition y(4)=3. Find the value of c for which the solution satisfies the initial condition y(4)=3.The given differential equation is xy′ + 2y = 4x²Given function y = x² + c/x²To prove that the given function is a solution of the differential equation, we need to differentiate the given function y with respect to x.

We get y′ = 2x - 2c/x³ Put these values of y and y′ in the given differential equation xy′ + 2y = 4x²x(2x - 2c/x³) + 2(x² + c/x²) = 4x²2x² - 2c/x² + 2x² + 2c/x² = 4x²4x² = 4x² Therefore, the given function y= x² + c/x² is a solution of the differential equation xy′ + 2y = 4x² for all values of c.

To find the value of c such that the solution satisfies the initial condition y(4) = 3.We know thaty = x² + c/x²At x = 4, y = 3 Substitute the value of x and y in the above equation3 = 4² + c/4²3 = 16 + c/16c/16 = 3 - 16c = (3 - 16)×16 = -208

Thus, the value of c for which the solution satisfies the initial condition y(4) = 3 is -208.

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Given:

The function is:

\(y=2x^2+3x\)

Domain is the set {-2, -1, 0).

To find:

The range of the given relation.

Solution:

We have,

\(y=2x^2+3x\)

Substituting \(x=-2\), we get

\(y=2(-2)^2+3(-2)\)

\(y=2(4)+(-6)\)

\(y=8-6\)

\(y=2\)

Substituting \(x=-1\), we get

\(y=2(-1)^2+3(-1)\)

\(y=2(1)+(-3)\)

\(y=2-3\)

\(y=-1\)

Substituting \(x=0\), we get

\(y=2(0)^2+3(0)\)

\(y=0+0\)

\(y=0\)

The range for the given relation is {2, -1,0}. Therefore, the correct option is (c).

Answer:

\(\textsf{A)} \quad f(x) =x^3-3x^2-25x-21\)

\(\textsf{B)} \quad g(x)=\dfrac{(x-7)(x+3)}{x-2}\)

    Slant asymptote:  y = x - 2

C)  Removable discontinuity at x = -1  ⇒  (-1, ¹⁶/₃)

     Infinite discontinuity at x = 2

Step-by-step explanation:

Factor Theorem

If f(x) is a polynomial, and f(a) = 0, then (x – a)  is a factor of f(x).

Therefore, if the polynomial f(x) has the given zeros of 7, -1 and -3 then:

\(f(x) = (x - 7)(x + 1)(x + 3)\)

Expanded:

\(\implies f(x) = (x - 7)(x + 1)(x + 3)\)

\(\implies f(x) = (x - 7)(x^2+4x+3)\)

\(\implies f(x) = x(x^2+4x+3) - 7(x^2+4x+3)\)

\(\implies f(x) =x^3+4x^2+3x - 7x^2-28x-21\)

\(\implies f(x) =x^3-3x^2-25x-21\)

Factor \(x^2-x-2\) :

\(\implies x^2-2x+x-2\)

\(\implies x(x-2)+1(x-2)\)

\(\implies (x+1)(x-2)\)

Therefore:

\(\begin{aligned}\implies g(x) & = \dfrac{f(x)}{x^2-x-2}\\\\ & = \dfrac{x^3-3x^2-25x-21}{x^2-x-2}\\\\& = \dfrac{(x-7)(x+1)(x+3)}{(x+1)(x-2)}\\\\& = \dfrac{(x-7)(x+3)}{x-2}\end{aligned}\)

A slant asymptote occurs when the degree of the numerator polynomial is greater than the degree of the denominator polynomial.

To find the slant asymptote, divide the numerator by the denominator.

\(\large \begin{array}{r}x-2\phantom{)}\\x-2{\overline{\smash{\big)}\,x^2-4x-21\phantom{)}}}\\\underline{-~\phantom{(}(x^2-2x)\phantom{-b)))}}\\0-2x-21\phantom{)}\\\underline{-~\phantom{()}(-2x+4)\phantom{)}}\\-25\phantom{)}\\\end{array}\)

Therefore, the slant asymptote is y = x - 2.

Discontinuous function:  A function that is not continuous.

Removable Discontinuity (holes):  When a rational function has a factor with an x that is in both the numerator and the denominator.

Jump Discontinuity:  The function jumps from one point to another along the curve of the function, often splitting the curve into two separate sections.

Infinite Discontinuity:  When a function has a vertical asymptote (a line that the curve gets infinitely close to, but never touches).

Therefore, the discontinuities of function g(x) are:

In our original example with 10 questions and 6 different variations, there are 60 different versions of the assignment that can be created.

There are a total of 60 different versions of the 803 assignment that can be created if each of the 10 questions has 6 different variations. To illustrate this, let's consider a simple example.

Suppose you have 2 questions in the assignment, each with 2 different variations. In this case, there are 4 possible versions of the assignment: (1.1 and 2.1), (1.1 and 2.2), (1.2 and 2.1), and (1.2 and 2.2).

If you added a question with 2 variations, there would be 8 possible versions of the assignment: (1.1, 2.1 and 3.1), (1.1, 2.1 and 3.2), (1.1, 2.2 and 3.1), (1.1, 2.2 and 3.2), (1.2, 2.1 and 3.1), (1.2, 2.1 and 3.2), (1.2, 2.2 and 3.1), and (1.2, 2.2 and 3.2).

Therefore, in our original example with 10 questions and 6 different variations, there are 60 different versions of the assignment that can be created. This is because, for each additional question with 6 variations, you multiply the number of variations by 6. For example, 10 questions and 6 variations means 10 x 6 = 60 different versions of the assignment.

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Therefore, the preceding equation, which states that Brittany will be twice as old as Steve in 9 years, is proven when Brittany is 54 years old and Steve is 18 years old.

Equations are mathematical statements with the equals (=) sign on each side and two algebraic expressions in the center.

Coefficients, variables, operators, constants, terms, and the equal to sign are just a few of the components that make up an equation. The "=" symbol and terms on both sides are always needed when writing an equation.

calculation

Let s = brittany 's age now

Let t = steve's age now

s = 3t

s + 9 = 2 (t+9)

s + 9 = 2t + 27

s = 2t + 27 - 9

s = 2t + 18

Substitute 3t for s and find t

3t = 2t + 18

3t - 2t = 18

t = 18 yrs is steve's age

then

s = 3(18)

s = 54 yrs is brittany's age

Therefore, the preceding equation, which states that Brittany will be twice as old as Steve in 9 years, is proven when Brittany is 54 years old and Steve is 18 years old.

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Answer:

5x-2

Step-by-step explanation:

distribute the negative to get

7x+3-2x-1

simplify by combining like terms

5x-2

Answer:

76

Step-by-step explanation:

The caramel topping demand curve will not change:

The cost of caramel topping is falling; there will be an increase in demand for caramel topping:

Butterscotch topping costs more money;

There will be less demand for caramel topping:

Ice cream now costs more money.

The quantity of caramel topping demanded would increase if the price of the topping dropped. Consequently, the demand curve for caramel topping would go lower.

Ice cream and caramel toppings are complementary products.

Products that are consumed together are said to be complementary.

The amount of ice cream demanded would drop if the price went up. There would be a drop in the number of caramel toppings needed as a result of the fall in demand.

a decline in the popularity of caramel toppings. With less demand, the demand curve for caramel toppings would move inward.

Butterscotch and caramel ice cream toppings serve as stand-ins.

Products that can be used in place of one another are known as substitute goods.

The quantity demanded for butterscotch topping would decline if the price of butterscotch topping rose, making it more expensive overall. Customers might switch to caramel topping. As a result, demand for caramel topping would rise and the demand curve would move outward.

Demand curve: what is it?

The demand curve is a graphical representation of how the cost of an item or service relates to how much is demanded over a given period of time.

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Answer:

the answer is 22 percent which is science

Answer:

100 marks have been obtained in the hindi subject.

Step-by-step explanation:

First you have to find how many marks are obtained by one degree. So you have:

450marks/360°=1.25marks/degree

Then you have to find how many marks are obtained for each subject.

1.25marks/degree×80°= 100 marks

1.25×72= 90 marks

1.25×70= 87.5 marks

1.25×90= 112.5 marks

1.25×48= 60 marks

100+90+87.5+112.5+60=450 marks

The substitution that has been applied to B(x, y) is dt B(x, y) = √(1+t) (1+t)x+y tx-1.

The substitution that has been applied to B(x, y) is t = tan² 0

The substitution for x and y using the trigonometric identities is given by,

x = sin² 0 / cos² 0 = tan² 0   …(1)

y = sin² 0   …(2)

Differentiating both sides of equation (1) with respect to θ, we get

dx / dθ = 2tan 0 sec² 0

Putting the values of x and y in B(x, y), we get

B(x, y) = I 25 (sin 0)² (sin² 0 / cos² 0)-1 (cos 0)² (sin² 0)-1 dθ

= I 25 (sin 0)² / cos² 0 * cos² 0 / sin² 0 dθ

= I 25 tan² 0 dθ

= 25

∫ t dt √1+t

Now, we need to find the value of dt B(x, y) in terms of t.

To find dt B(x, y), we use the chain rule of differentiation and get

dt B(x, y) = ∂B/∂x dx/dt + ∂B/∂y dy/dt

= 25(2 sin 0 cos 0 sin² 0 / cos³ 0) * 2 sin 0 cos 0 sin 0 cos 0 dθ

= 100 (sin 0)³ (cos 0)³ / cos⁴ 0 dθ

= 100 (sin 0)³ / cos 0 dθ

Now, putting the values of x, y, and t, we get

dt B(x, y) = 100 sin³ 0 / cos 0 dθ

= 100 sin³ θ / cos θ dθ

Using the identity 1+t = sec² 0 or cos² 0 = 1 / (1+t), we can rewrite the above integral as

∫ 100 sin³ θ / cos θ dθ

= ∫ (1+t) (1+t)½ dt

Substituting the limits, we get

∫ 100 sin³ θ / cos θ dθ

= ∫ √(1+t) (1+t)x+y tx-1 dt

Answer: dt B(x, y) = √(1+t) (1+t)x+y tx-1.

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The equation of the line in standard form is 2x + y = -4.

The standard form equation of a line is given as ax + by = c, where a, b, and c are al integers.

Find the slope (m), using two points, (-2,0) and (-1,-2).

Slope of the line (m) = (-2 - 0) / (-1 -(-2))

m = -2 / 1

m = -2

Substitute m = -2 and (a, b) = (-1, -2) into y - b = m(x - a).

y - (-2) = -2(x - (-1))

y + 2 = -2(x + 1)

Rewrite the equation in standard form.

y + 2 = -2x - 2

y + 2 - 2 = -2x - 2 - 2

y = -2x - 4

2x + y = -4

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Answer:

B

Step-by-step explanation:

I THINK B

Answer:

The answer is (8x20)-(8x1)

(18x-44) + (8x-10) = 180

26x-54 = 180

26x = 234

x = 9

8(9)-10 + (13y-38) = 180

72-10+13y-38 = 180

13y+24 = 180

13y=156

y=12

Answer:

52 yards across

Step-by-step explanation:

Hakim drew a scale drawing of a neighborhood park. he used the scale 5 inches : 2 yards. a soccer field in the park is 130 inches wide in the drawing. how wide is the actual field?

130/5 = 26

26*2 = 52 yards across

Answer:

x = -12

Step-by-step explanation:

3/4x + 12 = 3

3/4x = -9

3x = -36

x = -12

The expression (-9+i)-(12-5i) can be represented to -21+6i.

A complex number is represented by the following form: a+bi, where a and b are real numbers.  The variables: a is the real part and bi imaginary part. See an example:

2 + 5i , then:

2 real part

5i imaginary part

About operations, the same properties used for real numbers can be applied to complex numbers. And for solving the operations math with these numbers, it is important to know that i²= -1. Thus, 9i² = 9*(-1)=-9.

When you sum or subtract complex numbers, you can only sum or subtract: the real part with the real part of each complex number and the imaginary part with the imaginary part of each complex number. See examples:

(2 + 5i) + (2 + 5i) = 4+10i

(4 + 10i) - (2 + 5i) = 2+5i

Therefore, the result for the (-9+i)-(12-5i) will be:

-9+i-12+5i= -21+6i

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We are given an economy with two goods and Leontief consumers who have utility functions that depend on the minimum of the two goods. The initial endowments of the consumers are positive, and we are assuming that the aggregate endowment of the economy has more of the first good than the second. If a price system p=(p1,p2) is an equilibrium with market clearing, we need to show that p1=0 and p2>0.

We start by considering the demand function for a Leontief consumer, which is given by xi1(p) = xi2(p) = (p1 + p2)mi/pi, where mi represents the initial endowment of consumer i and pi represents the price of good i.

Since the aggregate endowment ω=(ω1,ω2) of the economy satisfies ω1 > ω2, we know that the total supply of the first good is greater than the total supply of the second good.

Now, if p1 > 0, then for any positive value of p2, the demand for the second good xi2(p) will be positive for all consumers. This implies that the total demand for the second good will be greater than the total supply, leading to a market imbalance.

To achieve market clearing, where total demand equals total supply, we must have p1 = 0. This is because if p1 = 0, the demand for the first good xi1(p) will be zero for all consumers, and the total supply of the first good will match the total supply. Additionally, p2 must be positive to ensure positive demand for the second good.

Therefore, we have shown that in an equilibrium price system with market clearing, p1 = 0 and p2 > 0, given the initial endowment condition ω1 > ω2.

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Answer:

46

Step-by-step explanation:

15% of 40 is 6 so you add 6 to 40

Answer:46

Step-by-step explanation:

15% of 40=?

multiply 15 by 40 and divide by 100

15 * 40 / 100 = 6

add 6 to 40

40+6=46

Therefore, the number of cats that they expect is 46.

Answer:

104°

Step-by-step explanation:

The principle to apply here is that angle subtended at the center of a circle is twice the angle at circumference.

  Angle subtended at arc  = 52°

  Angle at the center  = 2 x 52°  = 104°

Answer:

104°

Step-by-step explanation:

in Algebra. If Brett wants an average score of at least 80 after his fourth test, which can be represented by the inequality (252 +x/4) ≥ 80, what is/are the possible score(s) he can make on the last test? Select all that apply.

65

68

41

67

81

The given expression is \(\frac{(n^2-1)!}{(n!)^n}\), and we need to determine the number of integers between 11 and 5050, inclusive, for which this expression is an integer.

To solve this problem, let's consider the factors involved:

1. The numerator \((n^2-1)!\) is the factorial of \(n^2-1\). This means it is the product of all positive integers from 1 to \(n^2-1\), denoted as \((n^2-1)! = 1 \cdot 2 \cdot 3 \cdot \ldots \cdot (n^2-1)\).
2. The denominator \((n!)^n\) is the factorial of \(n\) raised to the power of \(n\). So, it can be expressed as \((n!)^n = (n!) \cdot (n!) \cdot (n!) \cdot \ldots \cdot (n!)\).

To determine whether the expression \(\frac{(n^2-1)!}{(n!)^n}\) is an integer, we need to ensure that the denominator divides the numerator completely. This means that every factor in the denominator must be a factor of the numerator.
Let's consider an example to understand this better:

Suppose \(n = 3\). Then the expression becomes:
\[\frac{(3^2-1)!}{(3!)^3} = \frac{8!}{(3!)^3}\]

The numerator, \(8!\), is the product of all positive integers from 1 to 8: \(8! = 1 \cdot 2 \cdot 3 \cdot \ldots \cdot 8\).

The denominator, \((3!)^3\), is the product of \(3!\) three times: \((3!)^3 = (3!)(3!)(3!) = (1 \cdot 2 \cdot 3)(1 \cdot 2 \cdot 3)(1 \cdot 2 \cdot 3)\).

We can see that every factor in the denominator, \((1 \cdot 2 \cdot 3)\), is a factor of the numerator, \(8!\). Therefore, the expression is an integer for \(n = 3\).

To find the range of \(n\) for which the expression is an integer, we need to consider the largest power of each prime number in the denominator and ensure it does not exceed the largest power of that prime number in the numerator.

In this case, the prime numbers involved are 2, 3, 5, 7, 11, and so on. We need to analyze each prime number and determine the largest power in the numerator and denominator.

Since we are asked to find the number of integers between 11 and 5050, inclusive, for which the expression is an integer, we need to check all integers from 11 to 5050 and count the ones that satisfy the condition.

This process can be time-consuming and requires checking each integer individually.

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Taner will only need to run 3 km this week to complete his 6 km running goal.

If we require a definition, we may start by saying that fractional numbers are numbers that symbolize one or possibly more portions of a unit that has been subdivided into equal parts.

Given that, Taner's overall running goal is 6 km (including last week and this week)

So,

Taner's 2-week goal is 6 kilometres.

Now,

Taner's goal for the week is 3 kilometres = (6/2).

As the Taner completed 3 km of running last week. Taner can achieve his objective this week by running just 3 miles.

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The type of error occurs when certain sample elements are excluded is sample frame error. Then the required answer for the given question is Option B.

The type of error that takes place when a particular sample elements are eliminated or when the whole population is not accurately projected in the sampling frame is called sample frame error.

There are 4 types of sampling error

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