Solve 5.4p+13.1=−2.6p+3.5 . Check your solution.



p= __

If triangle ABC is congruent to triangle DEF, then all four statements must be true about the triangles: AB=EF, AB=DE, ∠A=∠E, and ∠B=∠D.

When two triangles are congruent, it means that they have the same size and shape. To show that triangle ABC is congruent to triangle DEF, we need to show that all corresponding sides and angles are equal.

The statement AB=EF means that the lengths of side AB and EF are equal. Similarly, the statement AB=DE means that the lengths of side AB and DE are equal.

The statement ∠A=∠E means that angle A in triangle ABC is equal to angle E in triangle DEF. Similarly, the statement ∠B=∠D means that angle B in triangle ABC is equal to angle D in triangle DEF.

By the Congruence of Triangles axiom (SSS), if two triangles have three sides of equal length, then they are congruent. Therefore, since AB=EF, AB=DE, and ∠A=∠E, we can conclude that triangle ABC is congruent to triangle DEF.

Furthermore, since ∠B=∠D, we can conclude that all four statements (AB=EF, AB=DE, ∠A=∠E, and ∠B=∠D) must be true in this case.

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x = 0 and Reduced cost = -4: This combination is not possible for decision variable x and its corresponding reduced cost.

Based on the complementary slackness condition in linear programming, the values of the decision variable x and its corresponding reduced cost can provide insights into the feasibility and optimality of the solution.

In the given scenarios:

x = 20 and Reduced cost = -4:

This combination is possible as a non-zero value of x with a negative reduced cost indicates that x is a non-basic variable and has a potential to increase in order to improve the objective function value.

x = 0 and Reduced cost = -4:

This combination is not possible because if x is a non-basic variable with a reduced cost of -4,

it implies that increasing x from zero would improve the objective function value, violating the complementary slackness condition.

x = 0 and Reduced cost = 0:

This combination is possible as x can be a basic variable with a reduced cost of zero,

indicating that it is at its lower bound and does not need to change.

x = 20 and Reduced cost = 0:

This combination is possible as a non-zero value of x with a reduced cost of zero implies that x is a non-basic variable and has already reached its upper bound,

so it does not need to change to improve

the objective function value.

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The equation of the line that passes through (8, -5) and is parallel to the graphed line is y = (1/4)x - 7.

To find the equation of a line that is parallel to the graphed line and passes through the point (8, -5), we need to determine the slope of the given line first.

Since the parallel line has the same slope as the given line, we can use the point-slope form of a linear equation to find the equation of the parallel line.

The point-slope form is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

In this case, we have the point (8, -5) and we need to find the slope of the given line.

Let's assume the given line passes through the point (4, -6).

Using the slope formula:

m = (y2 - y1) / (x2 - x1)

m = (-6 - (-5)) / (4 - 8)

m = (-6 + 5) / (-4)

m = -1 / -4

m = 1/4

Now that we have the slope, we can substitute the values into the point-slope form:

y - (-5) = (1/4)(x - 8)

Simplifying the equation:

y + 5 = (1/4)x - 2

Subtracting 5 from both sides:

y = (1/4)x - 7

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Answer: B. (x − 6)^2

Step-by-step explanation: The factored form of the expression x^2 − 12x + 36 is (x - 6)^2.

Therefore, the correct answer is B.

Answer:

The correct answer is B. (x - 6)^2. The factored form of the expression x^2 - 12x + 36 is (x - 6)(x - 6), which can be simplified as (x - 6)^2.

Answer:It is irrational since it will never stop going on

Step-by-step explanation:

The probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.

Let X denote the time required to process a package of five tasks. X is an exponentially distributed random variable with mean 2 minutes.

The probability of X being less than 8 minutes is given by:

P(X ≤ 8) = 1 - P(X > 8)

= \(1 - (1 - e^{(-8/2)}^{5}\)

= 0.963

Therefore, the probability that a package of 5 tasks is processed in less than 8 minutes is 0.963.

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Answer:

14

Step-by-step explanation:

-7 + 21

21 = Positive

-7 = Negative

Since, there are more positive than negative Thus, answer is positive

21 - 7 = 14

Hence, the answer is 14.

~`Lenvy`~

The gross profit is computed by adding the income and subtracting the costs. In this problem we have:

• incomes: $102,100 + $504,900,

• costs: $437,000.

Gross profit = $102,100 + $504,900 - $437,000 = $170,000

Answer: $170,000

When the temperature increased by 19.8 degrees fahrenheit , the temperature in degrees Celsius got increased by 11 degree

The equation C that gives the temperature in degree Celsius is

C = \(\frac{5}{9}(x - 32)\)

Where x denotes the degree Fahrenheit

According to the question,

Temperature has increased by 19.8 degree Fahrenheit

So, let the new temperature be " x' "

x' = x + 19.8

Therefore, For calculating temperature in degree Celsius

=> C' = 5/9 (x' - 32)

Substituting the value of x'

=> C' = 5/9 (x + 19.8 - 32)

=> C' = 5/9 ( x - 32) + 5×19.8/9

=> C' = C + 99/9

=> C' = C + 11

Hence , The temperature increased by 11 degree Celsius

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Answer:

The discount will take the total down to 71.00$

Step-by-step explanation:

i think this is the answer im not for sure but i hope this helps you :)

If the force and acceleration are in the same direction, the mass of the object would be 0.83 kg.

The mass of the object cannot be determined with the given information. Acceleration is related to force and mass through Newton's Second Law: F = ma. However, in this case, we are given the acceleration and force, but not the mass. To find the mass, we would need either the acceleration and the force, or the force and the mass.

However, if we assume that the force and acceleration are both in the same direction, we can use the formula F = ma to find the mass. Rearranging the formula, we get m = F/a.

Substituting the given values, we get:

m = 10 N / 12 m/s²

m = 0.83 kg

So, if the force and acceleration are in the same direction, the mass of the object would be 0.83 kg.

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Complete Question:

A moving train accelerates at a rate of 12 meters per second. What would your mass be if the applied force were 10N?

Answer:

Step-by-step explanation:

We need a picture of what you're talking about.

Answer:

you cant see the picture

Step-by-step explanation:

Answer:

-1.67

Step-by-step explanation:

Answer:

here are 1000 meters in a kilometer so the conversion factor is 1000. To change within the metric system it is helpful to visualize the metric system ... Going up the staircases moves the decimal point one place to the left for each step. ... to convert 65 km to metres, you choose the conversion factor

Step-by-step explanation:

The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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Answer:

0.5(5 × 10) - 1

Step-by-step explanation:

((5 × 10) × 0.5) - 1

((50) × 0.5) - 1

25 - 1

24

Therefore, the closest option to the probability that the person selected will be someone who responded "No," given that the person selected is age 55 or older, is (E) 0.818.

To find the probability that the person selected will be someone who responded "No," given that the person selected is age 55 or older, we need to calculate the conditional probability.

Let's denote the event of selecting someone who responded "No" as N and the event of selecting someone who is age 55 or older as O.

We are given the following information:

Number of people who responded "No" and are age 55 or older: 36

Total number of people who are age 55 or older: 44

The probability can be calculated as follows:

P(N | O) = P(N and O) / P(O)

P(N and O) represents the probability of selecting someone who responded "No" and is age 55 or older, which is 36.

P(O) represents the probability of selecting someone who is age 55 or older, which is 44.

P(N | O) = 36 / 44 ≈ 0.818

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The volume of right prism is equal to 464 cubic inches.

Volume of right prisms (V), in cubic inches, is equal to the product of cross area (A), in square inches, and height (h), in inches:

V = A · h

According to figure, cross area is the result of adding the areas of three rectangles. Area formula for rectangles is:

A' = w · l

Where:

First, determine the cross area of the prism:

A = 2 · (3 in) · (7 in) + (4 in)²

A = 42 in² + 16 in²

A = 58 in²

Second, calculate the volume of the right prism:

V = (58 in²) · (8 in)

V = 464 in³

The right prism has a volume of 464 cubic inches.

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Answer:

65

Step-by-step explanation:

The inequality to model the situation will be 24b ≤ 250

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Based on the information, the inequality to model the situation will be 24b ≤ 250. The number of baseball will be:

24b ≤ 250

b ≤ 250 / 24

b ≤ 10

The number of baseball will be 10 or less.

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Suppose A = 30 - 34, the value of A using 2's complement arithmetic of -4 is (1100)2. The result of A + B cannot be represented in 5-bit 2's complement representation. Therefore, the result of A + B will result in overflow.

Given, A = 30 - 34A = -4. We need to find the 2's complement representation of -4. To obtain 2's complement representation, we have to perform the following steps:

Convert the absolute value of the decimal number into binary.4 = (0100)2

Take the 1's complement of the binary number.1's complement of (0100)2 = (1011)2

Add 1 to the 1's complement to obtain the 2's complement.(1011)2 + 1 = (1100)2

Therefore, the 2's complement representation of -4 is (1100)2.

Now, let us solve the second part of the question. Assume A = 15, B = 10 in 5-bit 2's complement representation.

When A + B is performed, will this result in overflow? We need to perform 5-bit 2's complement arithmetic as follows:

A = (01111)2, B = (01010)2, and A + B = (11001)2

The MSB (Most Significant Bit) of A and B is 0, which is positive. The MSB of the result of A + B is 1, which is negative.

So, the result of A + B cannot be represented in 5-bit 2's complement representation. Therefore, the result of A + B will result in overflow.

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Answer:

470 g

Step-by-step explanation:

1 cm^3 = 1 gram

210 grams + 260 grams = 470 grams

Answer:

(f/g)(x) = 5-x

Step-by-step explanation:

f(x)=25-x², g(x)=x+5

then (f/g)(x) = f(x) / g(x)

= 25-x² / x+5

\(=\frac{\left(5+x\right)\left(5-x\right)}{x+5}\)    ................simplify here

\(=\frac{\left(x+5\right)\left(5-x\right)}{x+5}\) ................. (x+5) cancel outs

= 5-x          ..............we have (5-x) left and this is the answer.

The fraction of the tiled floor is made of darker tiles is = \(\frac{4}{9}\)

Now, According to the question:

Let's know:

What is a fraction in math?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

The given data is;

A corner of a tiled floor is shown.

If the entire floor is tiled in this way and each of the four corners looks like this one.

To find fraction of the tiled floor is made of darker tiles.

Take the total darker portion is 16

All is = 6 x 6 = 36

The fraction of the tiled floor is made of darker tiles will be:

\(\frac{16}{36}=\frac{4}{9}\)

The answer is:

= \(\frac{4}{9}\)

Hence, The fraction of the tiled floor is made of darker tiles is = \(\frac{4}{9}\)

The dimensions of the largest box that can be made are 18 inches by 18 inches by 3 inches, and its volume is 2160 cubic inches.

To find the dimensions and volume of the largest box that can be made from a square piece of cardboard by removing a square from each corner, we need to use optimization techniques. This problem can be solved by finding the maximum volume of the box, subject to the constraint that a square is removed from each corner.

Let x be the length of the side of the square that is removed from each corner. Then the length and width of the base of the box are (24-2x) and (24-2x), respectively, and the height of the box is x. The volume of the box is given by the product of the length, width, and height, i.e., V = x(24-2x)(24-2x).

To find the maximum volume of the box, we need to take the derivative of V with respect to x and set it equal to zero. Solving for x, we get x = 3, which gives a maximum volume of V = 2160 cubic inches. Therefore, the dimensions of the largest box that can be made are 18 inches by 18 inches by 3 inches, and its volume is 2160 cubic inches.



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The equation of the line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5) is y = (-5/3)x + 5.

To find the equation of a line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5), we can use the slope-intercept form of a linear equation, which is y = mx + b. Given the point (3, 0) on the x-axis, we know that when x = 3, y = 0. This gives us one point on the line, and we can use it to calculate the slope (m).

Using the slope formula: m = (y2 - y1) / (x2 - x1)

Substituting the values (0 - 5) / (3 - 0) = -5 / 3

So, the slope (m) is -5/3. Now, we can substitute the slope and one of the given points (0, 5) into the slope-intercept form (y = mx + b) to find the y-intercept (b).

Using the point (0, 5):

5 = (-5/3) * 0 + b

5 = b

The y-intercept (b) is 5. Therefore, the equation of the line that intersects the x-axis at point (3, 0) and intersects the y-axis at point (0, 5) is:

y = (-5/3)x + 5

To sketch the diagram, plot the points (3, 0) and (0, 5) on the x-y plane and draw a straight line passing through these two points. This line represents the graph of the equation y = (-5/3)x + 5.

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