PLZ HELP REALLY FAST

CPCTC is the missing reason in step six.

CPCTC states that corresponding part of the congruent triangles are congruent.

Here, Given: ABCD is a quadrilateral,

In which AD ≅ BC and AD║BC

Prove : ABCD is a parallelogram.

Statement                                                  Reason

1. AD ≅ BC; AD║BC                                      1. Given

2.∠CAD and ∠ACD are alternative angles  2. Definition of alternative angles

3. ∠CAD ≅∠ACB                                           3. alternative angles are congruent

4. AC ≅ AC                                                    4. Reflexive property

5.△CAB ≅ △ACB                                           5. SAS congruence postulate

6. .AB ≅ CD                                                   6. CPCTC

7. ABCD is a parallelogram                         7. Parallelogram side theorem

Therefore, CPCTC is six step.

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The possibility of selecting a 4 characters long password consisting of 3 letters and one number if letters cannot be repeated and the password must end with a number is 156000

An equation is an expression that shows the relationship between two or more number and variables.

The possibility of selecting the password = 26 * 25 * 24 * 10 = 156000

The possibility of selecting a 4 characters long password consisting of 3 letters and one number if letters cannot be repeated and the password must end with a number is 156000

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To solve the equation 3,532.5 = (3.14)(r^2)(x/3) for the variable r, we can follow these steps:

Multiply both sides of the equation by 3/3 to eliminate the fraction:

3,532.5 * 3/3 = (3.14)(r^2)(x/3) * 3/3

This simplifies to:

10,597.5 = (3.14)(r^2)(x)

Divide both sides of the equation by (3.14)(x) to isolate the variable r:

10,597.5 / (3.14)(x) = (r^2)

Take the square root of both sides of the equation to solve for r:

r = sqrt(10,597.5 / (3.14)(x))

Therefore, the solution to the equation 3,532.5 = (3.14)(r^2)(x/3) for the variable r is:

r = sqrt(10,597.5 / (3.14)(x))

Answer:

The area of this triangle is (1/2)(9)(8) = 36.

Answer:

1) B = 88°, a = 13.1, b = 26.9

2) C = 73°, a = 20.9, b = 12.6

Step-by-step explanation:

To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies B=180^{\circ}-A-C\)

\(\implies B=180^{\circ}-29^{\circ}-63^{\circ}\)

\(\implies B=88^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}\)

\(\implies a=13.0876493...\)

\(\implies a=13.1\)

Solve for b:

\(\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}\)

\(\implies b=26.9194211...\)

\(\implies b=26.9\)

\(\hrulefill\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies C=180^{\circ}-A-B\)

\(\implies C=180^{\circ}-72^{\circ}-35^{\circ}\)

\(\implies C=73^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}\)

\(\implies a=20.8847511...\)

\(\implies a=20.9\)

Solve for b:

\(\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}\)

\(\implies b=12.5954671...\)

\(\implies b=12.6\)

Here's the solution :

In a sphere,

\( \boxed{ \mathsf{surface \: \: area = 4\pi {r}^{2} }}\)

now, let's solve :

hence, correct answer is B. 100π unit²

The surface area of the sphere is 100 π unit².

The correct option is B.

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

We have,

Radius of Sphere= 5 unit

Now, the formula for Surface area of Sphere is

= 4πr²

= 4 (3.14) (5)(5)

= 4 x 3.14 x 25

= 314

= 10 π unit²

Thus, the Surface area is 10 π unit².

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Answer:

Step-by-step explanation:

your supposed to learn things in class pay attetion

The x-intercepts of the graph of f(x) are x = 3/2 and x = 1,the Vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point, The vertex is at (5/4, 3/8). This is the minimum point of the graph.

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x^2 - 5x + 3 = 0

To factor this quadratic equation, we look for two numbers that multiply to give 3 (the coefficient of the constant term) and add up to -5 (the coefficient of the linear term). These numbers are -3 and -1.

2x^2 - 3x - 2x + 3 = 0

x(2x - 3) - 1(2x - 3) = 0

(2x - 3)(x - 1) = 0

Setting each factor equal to zero, we get:

2x - 3 = 0   -->   x = 3/2

x - 1 = 0   -->   x = 1

Therefore, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient indicates that the parabola opens upwards, so the vertex will be a minimum.

To find the coordinates of the vertex, we can use the formula x = -b/2a. In the equation f(x) = 2x^2 - 5x + 3, the coefficient of the x term is -5, and the coefficient of the x^2 term is 2.

x = -(-5) / (2*2) = 5/4

Substituting this value of x back into the equation, we can find the y-coordinate:

f(5/4) = 2(5/4)^2 - 5(5/4) + 3 = 25/8 - 25/4 + 3 = 3/8

Therefore, the vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point.

Part C: To graph f(x), we can use the information obtained in Part A and Part B.

- The x-intercepts are x = 3/2 and x = 1. These are the points where the graph intersects the x-axis.

- The vertex is at (5/4, 3/8). This is the minimum point of the graph.

We can plot these points on a coordinate plane and draw a smooth curve passing through the x-intercepts and the vertex. Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the graph will be concave up.

Additionally, we can consider the symmetry of the graph. Since the coefficient of the linear term is -5, the line of symmetry is given by x = -(-5) / (2*2) = 5/4, which is the x-coordinate of the vertex. The graph will be symmetric with respect to this line.

By connecting the plotted points and sketching the curve smoothly, we can accurately graph the function f(x).

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Answer:

the unit cost of each lemon is $0.60

Step-by-step explanation:

divide 3.00 by 5 to get 0.6

Answer:

T⟨–9, –2⟩(ΔABC) = ΔDEF

Step-by-step explanation:

The question ask what the translation from A is to D(-6,-2). When you solve, you will get (-9,-2) as your answer.

Answer: The answer is 11x+4y+13

The two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let \($&\overline{A B} \cong \overline{D E} \\\) and \($&\overline{A C} \cong \overline{D F}\)

Angle between \($\overline{A B}$\) and \($\overline{A C}$\) exists \($\angle A$\).

Angle between \($\overline{D E}$\) and \($\overline{D F}$\) exists \($\angle D$\).

Therefore, \($\triangle A B C \cong \triangle D E F$\) by SAS, if \($\angle A \cong \angle D$$\).

Given:

\($&\overline{A B} \cong \overline{D E} \\\) and

\($&\overline{A C} \cong \overline{D F}\)

According to the SAS congruence property, two triangles exist congruent if they contain two congruent corresponding sides and their contained angles exist congruent.

Let \($&\overline{A B} \cong \overline{D E} \\\) and \($&\overline{A C} \cong \overline{D F}\)

Angle between \($\overline{A B}$\) and \($\overline{A C}$\) exists \($\angle A$\).

Angle between \($\overline{D E}$\) and \($\overline{D F}$\) exists \($\angle D$\).

Therefore, \($\triangle A B C \cong \triangle D E F$\) by SAS, if \($\angle A \cong \angle D$$\).

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Answer:

-18z3+(-15z3)

-18z3-15z3

-33z6

Answer:

0.67

Step-by-step explanation:

all you need to do is divide 10 by 15

Answer:

Step-by-step explanation:

58 x 12 = 696    696 + 129 = $825 for a year

they are 9 months in

Answer:

9 bags

Step-by-step explanation:

2 1/4 ÷ 1/4

9/4 ÷ 1/4

9/4 x 4/1 = 9

Answer:

a. 0.58

b. 0.78

Step-by-step explanation:

a. The probability of egg come from B1 or B2

P(B1) = 3000/10000 = 0.3

P(B2) = 4000/10000 = 0.4

P(P1 ∪ B2) = 0.3 + 0.4 -(0.3)(0.4)

P(P1 ∪ B2) = 0.7 - 0.12

P(P1 ∪ B2) = 0.58

b. The probability that the market received an egg that is acceptable

P(received an egg that is acceptable) = P(B1 acceptable) + P(B2 acceptable) + P(B3 acceptable)

P(received an egg that is acceptable) = 0.80*3000 + 0.90*4000 + 0.60*3000 / 10000

P(received an egg that is acceptable) = 2400 + 3600 + 1800 / 10000

P(received an egg that is acceptable) = 7800 / 10000

P(received an egg that is acceptable) = 0.78

Answer:

c. $100,000

Step-by-step explanation:

Calculation of the expected net profit of Ephemeral services corporation

Since we are been told that 9 other companies besides esco are as well bidding for the $900,000 government contract, it means we have to find the expected net profit by dividing 1 by 9×$900,000 .Thus ESCO can only expect to cover its sunk cost.

Hence ,

E(X) = (1/9) × $900,000

E(X)=0.111111111×$900,000

E(X)= $100,000

Therefore the expected net profit would be $100,000

Answer: C. Use the numbers 1-3 to represent all the outcomes.

Step-by-step explanation: I got this question correct on Edmentum.

Answer:

100

Step-by-step explanation:

Forming algebraic equations and solving:

Let the number of boys originally  at the stop = 'x'

Let the number of girls originally at the stop = 'y'

25  girls get on the first bus.

⇒ The number of girls now at the stop = y -25

Ratio of boys to girls:

        \(\sf \dfrac{x}{y -25}= \dfrac{3}{2}\\\\Cross \ multiply,\\\\2x = 3*(y- 25)\\\\2x = 3y - 3*25\\\\2x = 3y - 75 ------\)(I)

15 boys get on the second bus.

Now, the number of boys at the stop = x - 15

Number of girls at the stop = y - 25

Ratio of boys to girls,

     \(\sf \dfrac{x - 15}{y -25} = \dfrac{1}{1}\\\\Cross \ multiply, \\\\x - 15 = y -25\\\\\)

             x = y -25 + 15

             x = y - 10

Plugin x = y - 10 in equation (I)

          2*(y-10) = 3y -75

          2y - 20  = 3y -75

                -20 = 3y - 75 - 2y

                -20 = y -75

         -20 +75 = y

                 \(\sf \boxed{\bf y = 55}\)

Plugin y = 55 in equation (I)

       x = 55 -10

        \(\sf \boxed{\bf x = 45}\)

Number of students originally at the stop = x + y

                                                                     = 55 + 45

                                                                     = 100

The two items that together cost 34% of her budget have a summed cost of $170

From the question, we have the following parameters that can be used in our computation:

She has a budget of $500.

To calculate which two items together cost 34% of her budget, we use

Amount = 34% * Budget

substitute the known values in the above equation, so, we have the following representation

Amount = 34% * 500

Evaluate

Amount = 170

Hence, the two items would have a summed cost of $170

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The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

4399.98 ft per min

Step-by-step explanation:

The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).

In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:

3(2a^2 - 5a + 2)

Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.

The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:

3(2a - 1)(a - 2)

Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

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Answer: 172 ounces

Step-by-step explanation:

We are given 10 pounds and 12 ounces to convert to ounces.

There are 16 ounces in 1 pound.

We can create a proportion to find out how much ounces 10 pounds is.

10 pounds / x ounces = 1 pound / 16 ounces

We need to solve for x by isolating the variable x.

10/x = 1/16

10 = x/16

10 * 16 = x

160 ounces = x

so 10 pounds is equivalent to 160 ounces. But we are not done yet.

We were asked to convert 10 pounds and 12 ounces.

So add together the ounces to find the total ounces:

160 ounces + 12 ounces = 172 ounces.

Answer:

c

Step-by-step explanation:

Substitute the first equation into the second one

3(2x-1)=6x-5

6x-3=6x-5

0=6x-6x-5+3

0=-2

no solution as the variable was canceled out

True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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The simplified expression involving complex numbers is given as follows:

5 + 5i.

Complex numbers are number that have a real and an imaginary part, and are defined as follows:

z = a + bi.

In which:

The basic relation of complex numbers is given as follows:

i² = -1.

The fraction for this problem is given as follows:

(2 + i)(4 - 2i)/(1 + i).

The numerator is simplified as follows:

(2 + i)(4 - 2i) = 8 - 4i + 4i - 2i² = 8 + 2 = 10.

Hence the fraction is of:

10/(1 + i).

To remove the complex number from the denominator, the entire fraction is multiplied by the conjugate of the denominator, hence:

10/(1 + i) x (1 - i)/(1 - i) = 10(1 + i)/(1 - i²) = 10(i + 1)/2 = 5 + 5i.

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The value of x in the polygon will be 13.25 degrees.

The value of x is 10.

We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.

The sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.

Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees

Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:

Measure of one angle = 3960/24 = 165 degrees

165 = 12x + 6

159 = 12x

x = 13.25

Therefore, the value of x is 13.25 degrees.

Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.

Therefore, we have:

731x+86° = 7380°

Solving for x, we get:

731x = 7294°

x = 10

Therefore, the value of x is 10.

The equation that can be used to find the value of x is:

(9x+48)° + (15x-24)° = (n-2)*180°

24x + 24 = (n-2)*180°

Dividing both sides by 24, we get:

x + 1 = (n-2)*15°

Subtracting 1 from both sides, we get:

x = (n-2)*15° - 1

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