Vhich graph shows the solution of the inequality X+5 > 2?

The diagonals of a parallelogram bisect one another. This is illustrated below.

A parallelogram is a straightforward quadrilateral with two parallel sides. A parallelogram's opposite or facing sides are equal in length, and its opposite angles are equal in size.

A quadrilateral with two pairs of parallel sides is known as a parallelogram. A parallelogram's opposite sides are equal in length, and its opposite angles are equal in size. Furthermore, the interior angles on the same transversal side are supplementary. The total of all interior angles is 360 degrees.

Let's illustrate the parallelogram as ABCD.

AC and BD are diagonals  

AC and BD intersect at point E

AB is parallel to CD | opposite sides of a parallelogram are parallel

AB = CD | are congruent opposite sides of a parallelogram  

angle BAC = angle DCA |interior angles of parallel lines

angle ABD = angle CDB |interior angles of parallel lines

Triangle ABE = Triangle CDE | ASA

EA = EC | corresponding sides of congruent triangles are congruent.

E bisects AC| AE = EC

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Answer:

x + gh = -11

Step-by-step explanation:

x + gh

= -3 + 4(-2)

= -3 + (-8)

= -11

Answer:

- 11

Step-by-step explanation:

= -3+4x-2

=-3+ (-8)

= -3-8

=-11

Answer: No

Step-by-step explanation:

     If we rotate them so they are both facing the same direction, the congruency between sides and angles do not make the two triangles congruent as a whole.

    See attached for the pictures I drew of the triangles rotated. They are not to scale, but I kept the markings on.

Answer:

if this is a fraction, then negative 5 over a⁶

Answer:

2

Step-by-step explanation:

1+1=2

F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.

If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.

Explanation:

Instance 1

Inverse functions of both functions can be found using the first method.

Example.

Inverse of f (x) = x + 7 is what we're looking for.

We attempt to determine x using the equation y = x + 7.

y = x + 7

Inferring that g (x) is the inverse of f (x) from the fact that x = y 7

Finding g (x inverse )'s is now necessary.

g( x ) = x − 7

y = x − 7

x = y + 7

As a result, we discovered that f (x) is the inverse function of g (x).

f and g are equal if g is inverse of f and vice versa.

The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.

Example:

f ( g ( x ) =  [ x − 7 ] + 7

G ( x ) placed as x is the expression in brackets.

f ( g ( x ) ) = x − 7  + 7 = x

g (f ( x ) =  [ x + 7 ] − 7

f ( x ) inserted as x is the expression in brackets.

g ( f ( x ) ) = x + 7 − 7 = x

The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.

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Answer:

The measure of CD is 46

Step-by-step explanation:

From the midpoint theorem, we have,

FG = (1/2)CD

so,

\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)

Now,

\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)

Answer:

\(-\frac{8}{45}\)

Step-by-step explanation:

Multiply the numerator by the reciprocal of the denominator.

4/5( −2/9)

Answer:

Step-by-step explanation:

The distance between the points will be the difference between the points as shown;

Difference = -2.1 - (-2.6)

Difference = -2.1 + 2.6

Difference = 2.6 - 2.1

Difference = 0.5

Hence the difference between the numbers -2.6 and -2.1 on the number line is 0.5

Answer:

Areas under the curve

Step-by-step explanation:

The area under a curve on an interval [a, b] is the integral of the function computed in this interval :  \(A=\int _a^b|f\left(x\right)|dx\)

(1) For \(f\left(x\right)=3\sqrt{x}\) with \(a=1,\:b=4\)

area \(=\int _1^4\left3\sqrt{x}\;dx\) = \(3\cdot \int _1^4\sqrt{x}dx\) =

\(\int \sqrt{x}\) = \(\frac{2}{3}x^{\frac{3}{2}}\)

\(3\cdot\frac{2}{3}x^{\frac{3}{2}}\) = \(2x^{\frac{3}{2}}\)

At \(x = 4,\) we get \(2\cdot4^{\frac{3}{2}}\) = \(2\cdot8 = 16\)

At \(x = 1,\) we get \(2\cdot1^{\frac{3}{2}}\) = \(2.1 = 2\)

So area under the curve for \(f(x) = \:3\sqrt{x}\) in the interval \([1, 4] = 14\)

(2) \(f\left(x\right)=x-\frac{2}{3}\\\)

\(\int \:x-\frac{2}{3}dx\) = \(\int \:xdx-\int \frac{2}{3}dx\)  \(=\frac{x^2}{2}-\frac{2}{3}x\)

\(\left[\frac{x^2}{2}\right]^{27}_1 = \frac{27^2}{2} - \frac{1}{2} = \frac{729}{2}-\frac{1}{2} = \frac{728}{2} = 364\)

\(\left[\frac{2}{3}x\right]^{27}_1 = \frac{2}{3}\cdot \:27 - \frac{2}{3}\cdot \:1 = 18-\frac{2}{3} = \frac{52}{3}\)

\(\int _1^{27}\left|x-\frac{2}{3}\right|dx = 364-\frac{52}{3} = \frac{1040}{3}\)  (Answer)

Answer:

3

Step-by-step explanation:

subtract 4 from 1/6 of 42. In middle school my traxhers always told me that of menas multiply, and in this situation it still holds. 1/6 x 42 is 42/6 or 42 divided by 6 which is 7. So now that makes this simpler, its saying subtract 4 from 7, so 7-4 =3

Answer:

Step-by-step explanation:

y= 265

The rate of change of the equation is 25.

The rate at which one quantity changes in relation to another quantity is known as the rate of change function. Simply put, the rate of change is calculated by dividing the amount of change in one item by the corresponding amount of change in another.

Given that the linear equation is y = 25x + 115. The rate of change of the equation is represented by the slope or gradient of the equation of the line.

Here in the equation y = 25x + 115 the rate of change is 25. Which is equivalent to the slope of the line.

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Considering the discrete probability distribution, it is found that:

a) The mean is of: 6.3

b)

The mean of the distribution is given by the sum of each outcome multiplied by it's probability, hence it is obtained as follows:

E(X) = 0.1 x 2 + 0.3 x 5 + 0.4 x 7 + 0.2 x 9 = 6.3.

The variance of the distribution is given by the sum of the difference squared between each observation and the mean, multiplied by it's probability, hence it is obtained as follows:

Var(X) = 0.1 x (2 - 6.3)² + 0.3 x (5 - 6.3)² + 0.4 x (7 - 6.3)² + 0.2 x (9 - 6.3)² = 4.01.

The standard deviation is the square root of the variance of the distribution, hence it is obtained as follows:

S(X) = sqrt(4.01) = 2.

We have that:

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Step-by-step explanation:

The answer is not in the option.

The answer is 29/24.

Answer:

The length of the arc ADB is (8/3)π ft and the area of the shaded region is 4.5 ft^2 - 4π ft^2.

Step-by-step explanation:

In the given circle with center O and radius 3 ft, let's consider the angle AOB, which is given as 160°. We need to find the length of the arc ADB and the area of the shaded region.

To find the length of the arc ADB, we can use the formula for the circumference of a circle and calculate the fraction of the total circumference represented by the angle AOB.

The circumference of a circle is given by 2πr, where r is the radius. In this case, the radius is 3 ft. Therefore, the total circumference is 2π(3) = 6π ft.

To find the length of the arc ADB, we calculate the fraction of the total circumference represented by the angle AOB. Since the angle AOB is 160° out of 360°, the length of the arc ADB is (160/360) * 6π ft = (4/9) * 6π ft = (8/3)π ft.

Next, to find the area of the shaded region, we need to subtract the area of the sector AOB from the area of triangle AOB. The area of the sector AOB is (160/360) * π * (3)^2 = (4/9) * 9π = 4π ft^2. The area of triangle AOB is (1/2) * 3 * 3 = 4.5 ft^2.

Therefore, the area of the shaded region is 4.5 ft^2 - 4π ft^2 = 4.5 ft^2 - 4π ft^2.

In summary, the length of the arc ADB is (8/3)π ft and the area of the shaded region is 4.5 ft^2 - 4π ft^2.

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The linear system l has one solution. This can be determined by examining the augmented matrix to find the row echelon form. The row echelon form is a matrix with zeroes below the leading entries and all the leading entries are in different columns.

By converting the augmented matrix into the row echelon form, we can identify the number of variables and the number of equations. Since there are three equations and three variables in the row echelon form, the linear system l has one solution. The row echelon form of the given augmented matrix is

\($\begin{bmatrix}1&-3&2&3\\0&-5&-9&-10\\0&0&4&5\end{bmatrix}$\)

By counting the number of equations and variables in the row echelon form, it can be seen that there is only one solution for the linear system l. This is because the number of equations is equal to the number of variables, indicating that there is a single solution.

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the linear system l has an augmented matrix which is a row equivalent to the following. how many solutions does l have?

 \($\begin{bmatrix}1&-3&2&3\\-3&8&-11&-14\\2&-7&5&7\end{bmatrix}$\)

The value of the variable is 1. 40

we need to know that algebraic expressions are described as expressions that are made up of term, variables, constants, factors and coefficients.

these algebraic expressions are also made up of arithmetic operations.

These arithmetic operations are listed as;

From the information given, we have that;

7.5x/11=4.8/5

cross multiply the values, we get;

7.5x(5) = 4.8(11)

multiply the values

37. 5x = 52. 8

Divide both sides by the coefficient of x, we get;

x = 1. 40

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a) the initial condition as 0 kg sugar in the tank at time = 0 (pure water)

b) with the net rate of change the amount of sugar after t minutes is S(t) = 236.8 [1 - e (t/740)]

c) time goes to infinity, the amount of sugar in is 236.8 kg.

a) Let A(t) denote the amount of sugar in the tank at time. The tank starts with only pure water, so A(0) = 0 OR you can say that you give the initial condition as 0 kg sugar in the tank at time = 0 (pure water)

b) Sugar flows in at a rate of (0.07 kg/L) * (7 L/min) = 0.49 kg/min = 49/100 kg/min and flows out at a rate of (A(t)/1080 kg/L) * (7 L/min) = 7A(t)/1080 kg/min, so that the net rate of change of is governed by the ODE, multiply both sides by the integrating factor  to condense the left side into the derivative of a product, if t = time and S(t) is the amount of sugar in the tank as a function of time, then the equation that we get is S(t) = 236.8 [1 - e (t/740)]

c) As t---> ∞, the exponential term converges to 0 and we're left with the means when time goes to infinity, the amount of sugar in is 236.8 kg.

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Answer:

52

Step-by-step explanation:

4 1/2 x + 2x

Let x = 8

4 1/2 (8) + 2(8)

Change to an improper fraction

9/2(8) +2(8)

36+16

52

Answer:

1.029 is greater than 1.0275

Step-by-step explanation:

Answer:

1.029

Step-by-step explanation:

What is greater 1.0275 or 1.029

.027 < .029

So, 1.029 is greater.

Answer:

is the equation of the line:

y=-3x

The general form of the standard line is:

So, we need to change the given equation to the standard form

the given equation is;

Making x and y on the left side

So,

And can be written as:

The double integral \(\int\limits^a_b {(x+y)} \, dx dy\)over the rectangle r with vertices (0,1), (1,0), (3,4) and (4,3) is equal to 22.

Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.

There are two main types of integration: definite and indefinite integration.  The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.

To evaluate the double integral  \(\int\limits^a_b {} \, dx dy\)over the rectangle r with vertices (0,1), (1,0), (3,4) and (4,3), we first need to find the limits of integration for x and y.

The x-coordinates of the vertices of the rectangle range from 0 to 4, so the limits of integration for x are 0 to 4. The y-coordinates of the vertices of the rectangle range from 1 to 4, so the limits of integration for y are 1 to 4.

So, the double integral becomes:

\(\int\limits^a_b {(x+y)} \, dx dy\) =  (2 × 4² + 8 × 4) - (2 × 1² + 8 × 1) = 32 - 10 = 22.

Therefore, the double integral \(\int\limits^a_b {(x+y)} \, dx dy\) over the rectangle r with vertices (0,1), (1,0), (3,4) and (4,3) is equal to 22.

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Answer:

Down Here

Step-by-step explanation:

Step 2:

Statement: m∠A ≅m∠B

Reason: Base angle theorem

Step 3:

Statement: AD = BD

Reason: Def. of an isosceles triangle

Step 4:

Statement: m∠CAD ≅ m∠CBD

Reason: Parts whole Postulate

Step 5:

Statement: ΔCAD ≅ ΔCBD

Reason: SAS

Step 6:

Statement: m∠ACD ≅m∠BCD

Reason: CPCTC, angle bisector

-Chetan K

Answer:

The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580

Step-by-step explanation:

The loss percentage is 91%.Given that Venessa bought 80 apples for 4$, out of these apples, 25% were rotten and had to be thrown away. Venessa sold the remaining apples at 6 cents per apple.To calculate the profit or loss percentage, we need to determine the cost price, selling price, and the number of apples sold.

Cost price (CP) = 4 $.Selling price (SP) = 80 × 0.75 × 6 cents= 36 cents = 0.36 $.Now, let's calculate the profit.Profit = SP – CP= 0.36 $ – 4 $= – 3.64 $Loss = CP – SP= 4 $ – 0.36 $= 3.64 $.

Therefore, Venessa incurred a loss of $3.64 when she sold 80 apples at 6 cents per apple.Now let's calculate the loss percentage Loss Percentage = (Loss / CP) × 100= (3.64 / 4) × 100= 91%.

Therefore, the loss percentage is 91%.Note: If the result obtained after the subtraction of SP from CP is negative, it means there is a loss, and the percentage of loss can be calculated by (loss/CP) × 100.

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Answer:

Step-by-step explanation:

In the first part, we are given the function:

\(\int \dfrac{x^6}{\sqrt{1+x}^2} \ dx\)

Suppose we make x = tan θ

Then dx = sec² θ.dθ

\(= \int \dfrac{tan^6 (\theta)}{\sqrt{1+ tan ^2 \theta }}* dx\)

\(= \int \dfrac{tan^6 (\theta)}{\sqrt{1+ tan ^2 \theta }}* sec ^2 (\theta) * d\theta\)

Since; sec² θ - tan² θ = 1

sec² θ = 1+ tan² θ

\(sec \ \theta = \sqrt{1 + tan^2 \ \theta}\)

∴

\(= \int \dfrac{tan^6 (\theta)}{sec \ \theta}* sec ^2 (\theta) * d\theta\)

\(= \int tan^6 (\theta)* sec (\theta) * d\theta\)

Thus; In the first part, Use x = tan θ, where  \(- \dfrac{\pi}{2} < \theta <\dfrac{\pi}{2}\), since the integrand comprise the expression \(\sqrt{1+x^2}\)

From the second part by using substitution method;

\(\int \dfrac{x^6}{\sqrt{1+x^2}} \ dx = \int \mathbf{tan^6(\theta) * sec ( \theta) } \ d \theta\)