A. Use the AA Similarity Theorem in writing an if-then statement to describe the illustration
or in completing the figure based on the if-then statement.
R
Н.
If:
P
Then:
AHEY​

Answer:

9) JK = 24.5

10) LM = 24.5

11) m∡L = 51°

12) m∡M = 129°

Step-by-step explanation:

in a parallelogram, adjacent angles are supplementary (add to 180 degrees) and are also congruent

so, ∡K = ∡M and ∡J = ∡L

since ∡'s L and M are adjacent we can add them and set them equal to 180

5z - 6 + 2z - 3 = 180

7z - 9 = 180

7z = 189

z = 27

therefore, m∡M = 5(27)-6 = 129 and m∡L = 180-129, or 51

Also in a parallelogram, opposite sides are equal; so KJ = LM and KL = JM

7x = 3x + 14

subtract 3x from each side to get:

4x = 14

x = 14/4 = 3.5

to find measure of JK, substitute 3.5 for 'x' to get (3.5)(7) = 24.5

to find measure of LM, substitute 3.5 for 'x' to get (3.5)(3)+14 = 24.5

A. The solution to the congruence 3x - 107 ≡ 0 (mod 12) is x ≡ 1 (mod 12).

B. The solution to the congruence 5x + 3 - 102 ≡ 0 (mod 7) is x ≡ 6 (mod 7).

C. The solution to the congruence 66 + 9 ≡ 0 (mod 11) is x ≡ 4 (mod 11).

To solve modulo equations or congruences, we need to find values of x that satisfy the given congruence.

A. For the congruence 3x - 107 ≡ 0 (mod 12), we want to find an x such that when 107 is subtracted from 3x, the result is divisible by 12. Adding 107 to both sides of the congruence, we get 3x ≡ 107 (mod 12). By observing the remainders of 107 when divided by 12, we see that 107 ≡ 11 (mod 12). Therefore, we can rewrite the congruence as 3x ≡ 11 (mod 12). To solve for x, we need to find a number that, when multiplied by 3, gives a remainder of 11 when divided by 12. It turns out that x ≡ 1 (mod 12) satisfies this condition.

B. In the congruence 5x + 3 - 102 ≡ 0 (mod 7), we want to find an x such that when 102 is subtracted from 5x + 3, the result is divisible by 7. Subtracting 3 from both sides of the congruence, we get 5x ≡ 99 (mod 7). Simplifying further, 99 ≡ 1 (mod 7). Hence, the congruence becomes 5x ≡ 1 (mod 7). To find x, we need to find a number that, when multiplied by 5, gives a remainder of 1 when divided by 7. It can be seen that x ≡ 6 (mod 7) satisfies this condition.

C. The congruence 66 + 9 ≡ 0 (mod 11) states that we need to find a value of x for which 66 + 9 is divisible by 11. Evaluating 66 + 9, we find that 66 + 9 ≡ 3 (mod 11). Hence, x ≡ 4 (mod 11) satisfies the given congruence.

Modulo arithmetic or congruences involve working with remainders when dividing numbers. In a congruence of the form a ≡ b (mod m), it means that a and b have the same remainder when divided by m. To solve modulo equations, we manipulate the equation to isolate x and determine the values of x that satisfy the congruence. By observing the patterns in remainders and using properties of modular arithmetic, we can find solutions to these equations.

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The probability of randomly selecting a tree or an insect is 3/10

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

10 insects, 8 trees, 8 flowers, and 4 birds.

To find the probability of randomly selecting a tree or an insect,

We need to find the number of tree and insect cards and divide by the total number of cards.

There are 8 tree cards and 10 insect cards, for a total of 8 + 10 = 18 cards.

So the probability of randomly selecting a tree or an insect

P = 18/30

P = 3/5.

hence, the probability is 3/5.

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The correct answer is, P(X > 18) is the same as P(X < 18). Option b is correct. The probability P(X > 18) is related to P(X < 18) in such a way that: P(X > 18) is the same as 1 − P(X < 18).

Explanation:

The mean length of a certain product X is μ = 18 inches.

As we know that the length of a certain product X is normally distributed.

So, we can conclude that: Z = (X - μ) / σ, where Z is the standard normal random variable.

Let's find the probability of X > 18 using the standard normal distribution table:

P(X > 18) = P(Z > (18 - μ) / σ)P(Z > (18 - 18) / σ) = P(Z > 0) = 0.5

Therefore, P(X > 18) = 0.5

Using the complement rule, the probability of X < 18 can be obtained:

P(X < 18) = 1 - P(X > 18)P(X < 18) = 1 - 0.5P(X < 18) = 0.5

Therefore, the probability P(X > 18) is the same as P(X < 18).

Hence, the correct answer is, P(X > 18) is the same as P(X < 18). Option b is correct.

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1. Create a direction field by calculating slopes at various points on a grid using the differential equation y' = (11/2)y.

2. Plot three solution curves by selecting initial points and following the direction field to connect neighboring points.

3. Note that the solution curves exhibit exponential growth due to the positive coefficient in the equation.

To sketch a direction field for the differential equation y' = (11/2)y and then plot three solution curves, we will utilize the slope field method.

First, we choose a set of x and y values on a grid. For each point (x, y), we calculate the slope at that point using the given differential equation. These slopes represent the direction of the solution curves at each point.

Now, let's proceed with the direction field and solution curves:

1. Direction Field: We start by drawing short line segments with slopes determined by evaluating the expression (11/2)y at various points on the grid. Place the segments in a way that reflects the direction of the slopes at each point.

2. Solution Curves: To sketch solution curves, we select initial points on the graph, plot them, and follow the direction field to connect neighboring points. Repeat this process for multiple initial points to obtain different solution curves.

For instance, we can choose three initial points: (0, 1), (1, 2), and (-1, -2). Starting from each point, we follow the direction field and draw the curves, connecting neighboring points based on the direction indicated by the field. Repeat this process until a suitable range or pattern emerges.

Keep in mind that the solution curves will exhibit exponential growth or decay, depending on the sign of the coefficient. In this case, the coefficient is positive, indicating exponential growth.

By combining the direction field and the solution curves, we gain a visual representation of the behavior of the differential equation y' = (11/2)y and its solutions.

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Answer: -5

If f(t) = t^2 - 2t - 5, then f(0) = 0^2 - 2(0) - 5. That simplifies to be f(0) = -5

Step-by-step explanation:

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

Answer:

,a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. 

the answer is x equal to 18

Given:

The expression is 6/5 ÷6/7​.

Explanation:

Simplify the expression.

So answer is 7/5 or 1.4.

Answer:

LLOOOL

Step-by-step explanation:

Answer:

d= 90 degrees

e= 66 degrees

f= 114

Step-by-step explanation:

D is 90 because the measure of the angle on the line is 180 and it shows that the other angle is 90 and 180- 90= 90. E is 66 because opposite angles are congruent. F is 114 because they lie on a straight line which has the measure of 180 and 180- 66= 114

Answer:

d = 90°

e = 66°

f = 114°

Step-by-step explanation:

d = 90°

e = 66°

Reason : Vertically opposite angles

Angles f and 66° are in the linear pair.

f + 66° = 180°

f = ( 180 - 66 )°

f = 114°

Answer:

दवणडतडडथवणतणलतवलडथलडद

Answer:

2,601

Step-by-step explanation:

the sum of AP = 51/2 × (1+101)

= 51/2 × 101 = 2,601

Answer:

no

Step-by-step explanation:

If x = 3 is a zero, then f(3) = 0

f(3)

= 4\((3)^{4}\) - 3³ - 52(3)² - 35(3) + 12

= 324 - 27 - 468 - 105 + 12

= - 264

Since f(3) ≠ 0 then x = 3 is not a zero of f(x)

Answer: p-12 would find how many points Jason scored

Step-by-step explanation

Answer:

(50,-30)

Step-by-step explanation:

Reflecting a point across the y axis is just like flipping a page on a book. The x  coordinate is flipped and the y coordinate stays the same.

Answer: B and D

Step-by-step explanation:

Step-by-step explanation:

soye9685e06e96elhfouo9tsr0yee3079e97

Answer:

he is weird

Step-by-step explanation:????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

Answer:

container A

Step-by-step explanation:

In Container A, we can plot the points (0,60) adn (2, 35)

The slope is :

\(m_A = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{35-60}{2-0} \\\\= \frac{-25}{2}\\ \\m_A = -12.5\\\)

For container B, the slope is:

\(m_B = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{32-54}{3-1} \\\\= \frac{-22}{2}\\ \\m_B = -11\\\)

The negative sign of the slope indicates the direction of the slope

\(|m_A| = 12.5\\\\|m_B| = 11\)

12.5 > 11

The slope of container A is steeper than container B

Therefore, the water is draining out of container A at a faster rate than container B

Answer:

the answer will be 4x²...last option

Answer:

Answer is 4x² = 36

Step-by-step explanation:

Let that number be x:

\(4 \times x {}^{2} = 36 \\ {4x}^{2} = 36\)

further more:

\( {x}^{2} = \frac{36}{4} \)

take a square root:

\( \sqrt{ {x}^{2} } = \sqrt{ \frac{36}{4} } \\ \\ x = \frac{ \sqrt{36} }{ \sqrt{4} } \\ \\ x = \frac{6}{2} \\ \\ x = 3\)

The expressions that show the number of students for each activity are;

Note that this is a fraction problem.

We are given;

Total number of students in the middle school = x

A) From the given table, we can deduce that;

B: Now, the expression to show the students that like either drama or dance is;

(1/7)x + 26 + (1/7)x + 22

⇒(2/7)x + 48

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Full Question:

A middle school with x students ran a survey to determine the students' favorite activities. The table indicates the number of students who enjoy each activity. Answer parts A and B.

Table:

Activity:

Dance- 22 more than one-seventh of the students

Baseball- 24 fewer than four-sevenths of the students

Drama- 26 more than one-seventh of the students.

The length of the straw is √101 inches

The rectangular box has:

length (l) = 6 inches

breadth (b) = 4 inches

height (h) = 7 inches

The straw is said to fit into the box diagonally from the bottom.

So, the length of the straw is calculated as:

S= √(l² + b² + h²)

S = √(6² + 4² + 7²)

S = √101 inches

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Answer:

3/8 of the area is shaded

Step-by-step explanation:

this can be determined by deviding the total shape into parts and determining those parts

so we see the top right 1/4 of the shape has a square that is shaded, with the triangle only covering 1/2 of this shape becuase the hypotenuse ((diagnal edge of a right triangle)) devides the square in half

beings that 1/2 of the 1/4 square is shaded, we know that in reation to the whole shape that the small shaded area is equal to 1/8 ((1/2 ÷ 1/4 = 1/8))

same can be said for the bottum shape, with the bottum half of the whole shape half covered we can determine its total shaded area in relation to the shape ((1/2 ÷ 1/2 = 1/4))

the left top shape is completely unshaded so we wont need to calculate any shadded area into the equation

with the total shape covered by 1/4 + 1/8 we can find the least common denominator between the two fractions to get a simplifide answer for the total shaded area

1/4 = 2/8
2/8 + 1/8 = 3/8

this leaves 5/8 of the shape unshaded

3/8 fraction of the square is to be shaded.

A triangle is a three-sided polygon that consists of three edges and three vertices.

In the top right 1/4 of the shape has a square that is shaded, with the triangle only covering 1/2 of this shape because the hypotenuse divides the square in half.

1/2 of the 1/4 square is shaded, we know that in relation to the whole shape that the small shaded area is equal to 1/8.

same can be said for the bottom shape, with the bottom half of the whole shape half covered we can determine its total shaded area in relation to the shape.

1/4 = 2/8

2/8 + 1/8 = 3/8

Hence, 3/8 fraction of the square is to be shaded.

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Answer:

No , because The Pythagorean equation isn't true.

Step-by-step explanation:

a² = b² + c²

14² = 11² + 8²

196 = 121 + 64

196 ≠ 185

a) We can say that the point P(6,5) lies on the hyperbola.

b) The quantity (F1P − F2P)2 is approximately 122.5.

(a) To verify that the point P(6,5) lies on the hyperbola, we need to substitute x=6 and y=5 into the equation of the hyperbola and see if the equation holds true.

So, substituting x=6 and y=5, we get:

5(6)^2 - 4(5)^2 = 80

180 - 100 = 80

80 = 80

Since the equation holds true, we can say that the point P(6,5) lies on the hyperbola.

(b) To compute (F1P − F2P)2, we need to first find the coordinates of the foci F1 and F2.

5x^2 - 4y^2 = 80 can be rewritten as (x^2)/(16) - (y^2)/(20) = 1, where a^2=16 and b^2=20.

The distance between the center (0,0) and the foci is c=√(a^2+b^2)=√(336)/2. So, the foci lie on the x-axis and have coordinates (±c,0).

Therefore, F1 has coordinates (√(336)/2,0) and F2 has coordinates (-√(336)/2,0).

Now, we can calculate the distance between P(6,5) and each focus using the distance formula.

F1P = √((6-√(336)/2)^2 + (5-0)^2) ≈ 3.26

F2P = √((6+√(336)/2)^2 + (5-0)^2) ≈ 13.92

So, (F1P − F2P)^2 = (3.26 - 13.92)^2 ≈ 122.5.

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Answer:

126 calories per servings

Step-by-step explanation:

756/6=126

Answer:

Answer: It will take about 16.4 days. Example: The half-life of carbon-14 is 5730 years. If it is determined that an old bone contains 85% of it original carbon-14 how old is the bone? Answer: It takes about 1,343.5 years for a bone to lose 15% of its carbon-14.