What is the value of x in the figure shown below?
C
5.5
D
20
80°
3.4
3.4
20°
A
B
5.5

Answer:

I think the constraint of proportionality is 25 because each dot it increases buy 25.

I also believe that at 10 the total should be at 225.

The composition id_t  f is equal to f, as it preserves the output of the function f for all elements in set s.

Given sets s and t, and a function f: s -> t, we need to prove that id_t  f = f, where id_t is the identity function on set t. The identity function id_t(x) = x for all x ∈ t.

Consider any element x ∈ s. Since f is a function from s to t, f(x) ∈ t. Now, let's apply the composition of id_t and f, denoted as (id_t  f)(x). By definition, (id_t  f)(x) = id_t(f(x)).

Since f(x) ∈ t and id_t is the identity function on t, we have

id_t(f(x)) = f(x).

Therefore, (id_t  f)(x) = f(x) for all x ∈ s.

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To prove that idt ◦f = f, we need to understand what each term means. "Function" is a mathematical concept that maps elements from one set to another. "Sets" are collections of objects. "idt" is the identity function, which maps every element of a set to itself.

To prove that idt ◦f = f, we need to show that they have the same mappings. This can be done by applying both functions to each element of set s and comparing the results. By definition of the identity function, we know that idt(x) = x for all x in set t. Therefore, idt ◦f(x) = f(x) for all x in set s. This shows that idt ◦f and f have the same mappings, and thus they are equal.Given that S and T are sets, and f is a function from S to T, denoted by f: S → T, we want to prove that id_T ◦ f = f, where id_T is the identity function on the set T.
Step 1: Define the identity function id_T: T → T. For any element x in T, id_T(x) = x.
Step 2: Recall the composition of functions. If g: T → U and f: S → T, then the composition g ◦ f: S → U is defined as (g ◦ f)(x) = g(f(x)) for all x in S.

Step 3: Prove id_T ◦ f = f. To show this, we need to verify that (id_T ◦ f)(x) = f(x) for all x in S.
For any x in S, (id_T ◦ f)(x) = id_T(f(x)) by definition of composition. Since id_T is the identity function on T and f(x) is an element of T, id_T(f(x)) = f(x). Thus, (id_T ◦ f)(x) = f(x) for all x in S, proving that id_T ◦ f = f.+

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Answer:

100 meters  20/5=100

Not sure about the second one

hope this helps

Step-by-step explanation:

The slope of the line is undefined.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (-4, 6) and (-4, 1)

Now,

Since, The equation of line passes through the points (-4, 6) and (-4, 1)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (1 - 6) / (-4 - (-3))

m = - 5 / 0

m = ∞

Thus, The slope of the line is undefined.

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a=1

Hope this helps

have a great day!

Step-by-step explanation:

Answer:

I attached a picture, just connect the dots (left side)

u₂ = (0, 2/√3, -1/√3, 2/√3) and u₃ = (2/√3, -1/√3, -1/√3, -1/√3). The set {u₁, u₂, u₃} is an orthonormal basis for W. The standard basis vectors e₂ = (0, 1, 0, 0), e₃ = (0, 0, 1, 0), and e₄ = (0, 0, 0, 1) are orthogonal to B.

To find an orthonormal basis for the subspace W spanned by v₁, v₂, and v₃ in R¹, we first normalize v₁ to obtain the vector u₁. Then we use the Gram-Schmidt process to orthogonalize and normalize v₂ and v₃ with respect to u₁, resulting in two new vectors u₂ and u₃. The set {u₁, u₂, u₃} forms an orthonormal basis for W. Next, to find an orthonormal basis for R that contains B, we extend B with additional vectors that are orthogonal to B. Finally, we normalize the extended set to obtain an orthonormal basis for R.

First, we normalize v₁ by dividing it by its Euclidean norm, ||v₁||, which gives us the vector u₁ = (1/√3, 0, 1/√3, 1/√3).

Next, we apply the Gram-Schmidt process to orthogonalize and normalize v₂ and v₃ with respect to u₁. We subtract the projection of v₂ onto u₁ from v₂ to obtain a vector orthogonal to u₁. Then we divide this orthogonal vector by its norm to obtain u₂. Similarly, we subtract the projection of v₃ onto both u₁ and u₂ from v₃ to obtain a vector orthogonal to both u₁ and u₂. Dividing this vector by its norm gives us u₃.

After performing these calculations, we find that u₂ = (0, 2/√3, -1/√3, 2/√3) and u₃ = (2/√3, -1/√3, -1/√3, -1/√3). The set {u₁, u₂, u₃} is an orthonormal basis for W.

To find an orthonormal basis for R that contains B, we extend B with additional vectors that are orthogonal to B. We can choose vectors such as the standard basis vectors that are not already in B. For example, the standard basis vectors e₂ = (0, 1, 0, 0), e₃ = (0, 0, 1, 0), and e₄ = (0, 0, 0, 1) are orthogonal to B.

Finally, we normalize the extended set {u₁, u₂, u₃, e₂, e₃, e₄} to obtain an orthonormal basis for R that contains B.

Note that the calculations and normalization process may involve rounding or approximations, but the overall method remains the same.

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The sum of the first five terms of a geometric series is 242/27

The given parameters are

a1 = 6

r = 1/3

The sum of the first five terms of a geometric series is represented as;

Sn =a * (1 - r^n)/(1 - r)

This gives

S5 = 6 * (1 - (1/3)^5)/(1 - 1/3)

Evaluate the exponent

S5 = 6 * (1 - 1/243)/(2/3)

Evaluate the difference

S5 = 6 * (242/243)/(2/3)

This gives

S5 = 2 * (242/81)/(2/3)

So, we have:

S5 = 2 * (242/81) * 3/2

Evaluate the product

S5 = 242/27

Hence. the sum of the first five terms of a geometric series is 242/27

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The domain of the Riemann zeta function, denoted by ζ(x), is the set of real numbers x for which the series ∑n=1 ∞ n^(-x) converges. The domain of the function can be expressed using interval notation as (-∞, 1).

To understand the domain of the Riemann zeta function, we need to consider the convergence of the series ∑n=1 ∞ n^(-x). The series converges when the real part of x is greater than 1. Therefore, the right half-plane Re(x) > 1 represents a region where the series converges.

On the other hand, when the real part of x is less than or equal to 1, the series diverges. This means that the left half-plane Re(x) ≤ 1 is excluded from the domain of the Riemann zeta function.

Combining these conditions, we find that the domain of the Riemann zeta function is (-∞, 1) in interval notation, indicating that the function is defined for all real numbers less than 1.

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Answer:

decimal 0.55 percentage 55%

Step-by-step explanation:

In fractions, the numerator is the number above the line and the denominator is the number below.

The line in a fraction that separates the numerator and the denominator represents division.

To convert a fraction to a decimal, divide the numerator by the denominator.

Answer:

x=37/20

Step-by-step explanation:

4(2x-7)+3(3x-1)=3(2-x)

8x-28+9x-3=6-3x

17x+3x=6+31

20x=37

Answer:

x = \(\frac{71}{3}\)

Step-by-step explanation:

1. Simplify/distribute each side.

\(4(2)(-7)+3(3)(-1)=3(2-x)\)

\(4(2)(-7)+3(3)(-1)=(3)(2)+(3)(-x)\)

\(-56+-9=6+-3x\)

2. Flip the equation around.

\(-3x+6=-65\)

3. Subtract 6 to balance the equation.

\(-3x+6-6=-65-6\)

\(-3x=-71\)

4. Divide each side by 3. We know they are in the same fact family.

\(\frac{-3x}{-3} = \frac{-71}{3}\)

This is an absolute value problem. In mathematics, absolute value is simply defined as the distance of a number from zero on the number line, irrespective of the direction on either side of zero.

In the absolute value given which is; |2x + 9| = -4, we can see that there is an absolute value when the right hand side is negative and not when it is only positive.

We are given the equation;

|2x + 9| + 7 = 3

Now when dealing with absolute values, it means that the solution is either positive or negative.

For example;

|x| = 5 means that x = +5 or -5

Thus in this question, let us first of all simplify the equation to get;

|2x + 9| = 3 - 7

|2x + 9| = -4

From |2x + 9| = -4, we can see that there is an absolute value when the right hand side is negative and not when it is only positive.

Thus, the friend is not correct.

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Answer:

Flase

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

For example, speed energy releases air to move in one direction

Answer:

\(26.666666667\)

Step-by-step explanation:

To find the volume of a pyramid, you can use the formula:

Volume = (1/3) * base area * height

If the base is a rectangle, the base area is calculated by multiplying the length by the width.

Let's call the original length "L", the original width "W", and the original height "H".

The volume of the original pyramid is:

(1/3) * L * W * H = 40 cubic inches

If the length of the base is doubled, the new length is 2L.

The width is tripled, so the new width is 3W.

The height is increased by 50%, so the new height is 1.5H.

The volume of the new pyramid is:

(1/3) * (2L) * (3W) * (1.5H) = (2/3) * L * W * H = (2/3) * 40 cubic inches = 26.666666667 cubic inches.

So the volume of the new pyramid is approximately 26.666666667 cubic inches.

(a) To eliminate the parameter and find a Cartesian equation of the curve, we can use the given parametric equations x = 5cos(θ) and y = sec^2(θ). First, we express sec^2(θ) in terms of cos(θ) using the identity sec^2(θ) = 1/cos^2(θ). Substituting this into the equation for y, we have y = 1/cos^2(θ). Rearranging, we get cos^2(θ) = 1/y.

Taking the square root of both sides gives cos(θ) = ±sqrt(1/y). Now, we can substitute this into the equation for x to obtain x = 5 * ±sqrt(1/y). Simplifying further, we have x = ±5 * sqrt(1/y). Thus, the Cartesian equation of the curve is x^2 = ±25/y.

(b) The sketch of the curve depends on whether the positive or negative square root is used in the Cartesian equation. When the positive square root is used (x = 5 * sqrt(1/y)), the curve consists of two branches, one in the first quadrant and one in the third quadrant. As the parameter increases, the curve is traced counterclockwise. When the negative square root is used (x = -5 * sqrt(1/y)), the curve consists of two branches, one in the second quadrant and one in the fourth quadrant. As the parameter increases, the curve is traced clockwise. It's important to note that the curve is symmetric with respect to the y-axis.

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Step-by-step explanation:

step 1. mPOS = 180 - 125 = 55° (supplementary angles)

step 2. mQOS = 125° (vertical angles)

step 3. mQOR = 55° (supplementary angles).

Answer:

There are three general classes of substitution reactions, depending on the following factors.

Reactant or substituent.

Intermediate – carbocation, carbanion, or free radical.

Substrate (compound) – aliphatic or aromatic.

Step-by-step explanation:

Hope it helps!

L = k/f, where k is the variational constant, is the formula for the inverse variation.

A mathematical relationship between two variables in which they vary in opposing directions is referred to as an inverse proportion, also known as an inverse relationship. When one variable increases while the other decreases, this is known as having inverse proportions.

Using the variables length of violin 'l' and frequency of vibration 'f'

If the length of violin 'l' is inversely proportional to the frequency of vibration 'f', this is expressed as:

l α 1/f

l = k/f

Hence the formula for the inverse variation is l = k/f where k is the constant of variation.

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In a proportional relationship between two quantities, the constant of proportionality, often denoted by the letter "k," represents the value that relates the two quantities. The equation y = kx is the standard form for expressing a proportional relationship, where "y" and "x" are the variables representing the two quantities.

Here's a breakdown of the components in the equation:

y: Represents the dependent variable, which is the quantity that depends on the other variable. It is usually the output or the variable being measured.

x: Represents the independent variable, which is the quantity that determines or influences the other variable. It is typically the input or the variable being controlled.

k: Represents the constant of proportionality. It indicates the ratio between the values of y and x. For any given value of x, multiplying it by k will give you the corresponding value of y.

The constant of proportionality, k, is specific to the particular proportional relationship being considered. It remains constant as long as the relationship between x and y remains proportional. If the relationship is linear, k also represents the slope of the line.

For example, if we have a proportional relationship between the distance traveled, y, and the time taken, x, with a constant of proportionality, k = 60 (representing 60 miles per hour), the equation would be y = 60x. This equation implies that for each unit increase in x (in hours), y (in miles) will increase by 60 units.

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Answer:

Tell me about it..

Step-by-step explanation:

Step-by-step

explanation:

math is hard because is hard

Answer:

sqrt(29)

Step-by-step explanation:

We can find MN using the Pythagorean theorem

The height is 2 and the length is 5

a^2 + b^2 = c^2

2^2 + 5^2 = MN ^2

4 + 25 = MN^2

29 = MN ^2

taking the square root of each side

sqrt(29) = MN

The total points scored by both teams in the 2006 super bowl was 14 less than the total points for 2005. The total points for 2005 were 36.

Let's say the total points scored by both teams in the 2005 Super Bowl be x.

Then, the total points scored by both teams in the 2006 Super Bowl would be (x - 14)

We can now write an equation based on the given information:

Total points for 2006 = Total points for 2005 - 14x - 14 = Total points for 2005

Since we need to find the total points for 2005, we can rearrange the equation as

Total points for 2005 = x - 14

Therefore, the equation to find the total points for 2005 is:

x - 14 = Total points for 2005

Let's suppose the total points scored by both teams in the 2005 Super Bowl was 50.

Total points for 2005 = 50 - 14 = 36

Therefore, the total points for 2005 were 36.

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The solution x = 2 is valid for the original equation.

To solve the rational equation (4/x) = (3x + 2)/x², we can start by multiplying both sides of the equation by x² to eliminate the denominators:

x² * (4/x) = x² * [(3x + 2)/x²]

Simplifying:

4x = 3x + 2

Next, we can isolate the x term by subtracting 3x from both sides:

4x - 3x = 3x + 2 - 3x

x = 2

So, the solution to the rational equation is x = 2.

Now, let's check for extraneous solutions by substituting x = 2 back into the original equation:

(4/2) = (3(2) + 2)/(2²)

2 = (6 + 2)/4

2 = 8/4

2 = 2

Since the equation is true when x = 2, there are no extraneous solutions.

Therefore, for the initial equation, x = 2 is a viable answer.

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∠A = ∠C for every isosceles triangle and not only for this specific isosceles triangle.

We are given that:

AB = BC

Now, draw a angle bisector from point B to the line AC in a way that it intersects AC at D.

Now, we get that:

∠ABD = ∠CBD ( BD is the angle bisector)

BD = BD ( common line)

So, ΔABD ≅ Δ CBD ( SAS property)

So,

∠A = ∠ C ( CPCT rule)

Also, it will be true for every isosceles triangle.

Therefore, we get that, ∠A = ∠C for every isosceles triangle and not only for this specific isosceles triangle.

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Your question was incomplete. Please refer the content below:

There is an isosceles triangle with AB = BC. Prove that ∠A = ∠C.

Did we prove the conclusion true for every isosceles triangle or only for this specific isosceles triangle.

Answer:

Well there is no problem there what are the problems I will answer it

Answer:

Albert needs 32 cars to wash to reach his goal.

Step-by-step explanation:

We know that the slope-intercept form of a linear function is

\(y = mx+b\)

where m is the slope or rate of change and b is the y-intercept

It is stated that Albert needs $133 to buy a new hard drive.

As earns $4.75 for each car he washes. Thus, $4.75 the rate of change or slope will be.

As he spends $19 on supplies. Since it is an expense, so -19 is basically the y-intercept 'b'.

Let 'x' be the number of cars he needs to wash to reach his goal.

Thus, substituting the value m = 4.75, y = 133, and b=-19 in the slope-intercept form of a linear function

y = mx+b

133 = 4.75x - 19

133+19 = 4.75x

152 = 4.75x

x = 152 / 4.75

x = 32

Therefore, Albert needs 32 cars to wash to reach his goal.

Answer:

no

Step-by-step explanation:

The radius of a circle in 3 centimeters the rate of change of the area is 60π square centimeters per minute.

To find the rate of change of the area of a circle when the radius is 3 centimeters and the radius is increasing at a rate of 10 centimeters per minute, the formula for the area of a circle: A = πr².

The equation that represents the relationship between the radius and the area. A = πr².

To differentiate the equation with respect to time (t) to find the rate of change of the area (dA/dt) with respect to time:

dA/dt = d/dt (πr²)

Using the chain rule of differentiation,

dA/dt = 2πr (dr/dt)

Substituting the given values: r = 3 cm and dr/dt = 10 cm/min, calculate the rate of change of the area:

dA/dt = 2π(3)(10)

dA/dt = 60π cm²/min

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