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The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

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The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

Answer: 3x-1

Step-by-step explanation:

Combine like terms, 4x-x=3x, 4/3-1/3=1

3x-1

Step-by-step explanation:

It is important to know that the diagonals of a rhombus are PERPINDICUALR bisectors of each other .   Opposite angles are equal and adjacen angles sum to 180 degrees .

Then remember alternate angles are equal  and there are 180 degrees inside of a triangle .....then you should be able to solve these...here is the first one

Simplified form of the equations are

4.1)5/8

4.2) 18

4.3) -3.,6×10⁶

4.4) 23/8

Multiplication is a basic arithmetic operation that involves combining two or more numbers to obtain a product, which represents the total value of the quantities being multiplied.

The operation is represented by the multiplication sign (×) or an asterisk (*) and is read as "times" or "multiplied by". For example, 3 × 4 can be read as "3 times 4" or "3 multiplied by 4" and results in a product of 12.

Solving part 4.1

1\(\frac{2}{3}\):2\(\frac{2}{3}\)

=5/3:8/3

=5:8

=5/8

Solving part 4.2

2(∛64+√25)

=2(4+5)

=2×9

=18

Solving part  4.3

=(3.6×10⁶)-(5.2×10⁶)

=-3.6×10⁶

Solving part 4.4

=½+2 ¾-⅜

=½+11/4-⅜

=4+22-⅜

=23/8

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Answer:

  y = -5/2x +1

Step-by-step explanation:

You want the slope-intercept form equation for the line through the point (-2, 6) that is parallel to 5x +2y = -4.

The equation of a parallel line can be the same as the given equation, except for the constant. The new constant can be found by substituting the given point coordinates:

  5(-2) +2(6) = c

  -10 +12 = c

  2 = c

Now we know the equation of the parallel line can be written as ...

  5x +2y = 2

Solving for y puts this in slope-intercept form:

  2y = -5x +2 . . . . . . . . subtract 5x

  y = -5/2x +1 . . . . . . . . divide by 2

We don't know what your boxes look like, but we can separate the numbers to make it look like this:

  \(\boxed{y=\dfrac{-5}{2}x+1}\)

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Answer:

21°

Step-by-step explanation:

In an sosceles trapezoid, the lower base and upper base angles are congurent

⇒ ∠HGF = ∠EFG

⇒ 9y + 3 = 8y + 5

⇒ 9y - 8y = 5 - 3

⇒ y = 2

⇒ ∠HGF = 9(2) + 3

= 18 + 3

= 21

The measure of angle HGF in the given isosceles trapezoid EFGH is calculated to be 21 degrees.

This problem deals with the properties of an isosceles trapezoid, which is a type of quadrilateral. In an isosceles trapezoid, opposite angles are equal. In this case, angle EFG and angle HGF would be equal to each other given the shape is an isosceles trapezoid. So, their measures should be equal.

Here, the measure of angle HGF is given as (9y + 3)°, and the measure of angle EFG is (8y + 5)°. Setting these equal to each other to find the value of y, we get 9y + 3 = 8y + 5. By simplifying, we get the value of y is 2. Substituting the found value of y in angle HGF we get, 9*2+3 = 21 degrees.

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The value of h is -1/4

please see the attached picture for full solution

hope it helps

Good luck on your assignment

Answer:

\(h = - \frac{1}{4} \)

Step-by-step explanation:

\( - h = - 3(3h + 1) + 1 \\ - h = - 9h - 1 - 1 \\ -h + 9h = - 2 \\ 8h = - 2 \\ \frac{8h}{8} = \frac{ - 2}{8} \\ h = - \frac{1}{4} \\ \)

hope this helps

brainliest appreciated

good luck! have a nice day!

The statement translated to an algebra equation will give the value of the unknown number w = 11/5

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical expressions using letters to represent unknown values.

Let us represent the unknown number with the letter w so that the statement can be written as the equation:

5w - 8 = 3

add 8 to both sides

5w - 8 + 8 = 3 + 8

5w = 11

divide through by 5

5w/5 = 11/5

w = 11/5

Therefore, the statement translated to an algebra equation will give the value of the unknown number w = 11/5

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The positions will be filled in 56,280 ways

There are 11 qualified candidates applying for 7 positions. The order of the positions does not matter. after choosing a position the number of persons drop so we solve as follows

For the position of president

11 combination 1 = 11

For the position of secretary

10 combination 1 = 10

For the position of treasurer

10 combination 1 = 10

For the position of three directors

8 combination 3 = 56 ways

the total number of ways to fill these positions is

11 x 10 x 9 x 56 = 56,280.

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Answer:

1. We can't see any boat on the river at this scale.

2. 0.025 inches. We won't be able to see it

Step-by-step explanation:

the beginning of the question states that; according to this map, the driving distance is 3 miles, we're most interested in the graphics at the bottom left, which indicates that 1 inches on the map corresponds to 2,000 ft in real life.

If 1 inches = 2000 ft,

x inches = 50 ft

we cross multiply to give

2000x ft = 50 ft-inches

x = 50/2000 = 0.025 inches

Answer:

It is 198

Step-by-step explanation:

(Width)(Height)

mutliply (11) times (18)

The area of rectangle ABCD is 198 square inches

The given parameters are:

\(\mathbf{AB = 11}\)

\(\mathbf{KH = 18}\)

Because the rectangles are congruent, then:

\(\mathbf{HG = AB = 11}\)

\(\mathbf{KH = DA= 18}\)

So, the area of rectangle ABCD is the product of side lengths AB and DA

So, we have:

\(\mathbf{Area = AB \times DA}\)

Substitute values for AB and DA

\(\mathbf{Area = 11 \times 18}\)

\(\mathbf{Area = 198}\)

Hence, the area of rectangle ABCD is 198 square inches

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The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Answer:

0 or 0.62921348314 (if done by the calculator)

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 89 on the left side and the dividend 56 on the right side like this:

8 9 ⟌ 5 6

Step 2:

The divisor (89) goes into the first digit of the dividend (5), 0 time(s). Therefore, put 0 on top:

0

8 9 ⟌ 5 6

Step 3:

Multiply the divisor by the result in the previous step (89 x 0 = 0) and write that answer below the dividend.

0

8 9 ⟌ 5 6

0

Step 4:

Subtract the result in the previous step from the first digit of the dividend (5 - 0 = 5) and write the answer below.

0

8 9 ⟌ 5 6

- 0

5

Step 5:

Move down the 2nd digit of the dividend (6) like this:

0

8 9 ⟌ 5 6

- 0

5 6

Step 6:

The divisor (89) goes into the bottom number (56), 0 time(s). Therefore, put 0 on top:

0 0

8 9 ⟌ 5 6

- 0

5 6

Step 7:

Multiply the divisor by the result in the previous step (89 x 0 = 0) and write that answer at the bottom:

0 0

8 9 ⟌ 5 6

- 0

5 6

0

Step 8:

Subtract the result in the previous step from the number written above it. (56 - 0 = 56) and write the answer at the bottom.

0 0

8 9 ⟌ 5 6

- 0

5 6

- 0

5 6

The coordinates of the image of the point (2, 8) under the same translation is (1, 3)

Translation is a way of changing the position of an object in an xy plane.

If the image point of the point (6, -3)(6,−3) under a translation is (5, -8)(5,−8), then the translation rule will be;

(x, y) - > (x - 1, y -5)

Given the coordinate (2, 8), if this coordinate point is under the same translation, then the required coordinate point is expressed as;

(2, 8) -> (2-1, 8-5)

(2, 8) - > (1, 3)

Hence the coordinates of the image of the point (2, 8) under the same translation is (1, 3)

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The midpoint of segment YZ is (-a, -2b).

Given the coordinates of the rhombus WXYZ:

W(0, 4b)

X(2a, 0)

Y(0, -4b)

Z(-2a, 0)

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Substituting the coordinates of Y and Z:

Midpoint of YZ = ((0 + (-2a)) / 2, (-4b + 0) / 2)

= (-a, -2b)

Therefore, the midpoint of segment YZ is (-a, -2b).

To demonstrate that the segments joining the midpoints of the rhombus are perpendicular, we need to prove that the slopes of these segments are negative reciprocals of each other.

Let's consider the segments joining the midpoints:

Segment joining the midpoints of WX and YZ:

Midpoint of WX: ((0 + 2a) / 2, (4b + 0) / 2) = (a, 2b)

Midpoint of YZ: (-a, -2b)

Slope of WX = (2b - 4b) / (a - 0) = -2b / a

Slope of YZ = (-2b - (-4b)) / (-a - 0) = 2b / a

The slopes of WX and YZ are negative reciprocals of each other, indicating that these segments are perpendicular.

We have shown that the segments joining the midpoints of a rhombus are perpendicular to each other and have equal lengths. Therefore, these segments form a rectangle.

Additionally, the midpoint of segment YZ is (-a, -2b).

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Answer:

8x6

12x4

24x2

48x1

3x16

Step-by-step explanation:

the area is calculated by the length multiplied by the width. There are multiple possibilities in this case. anything that multiplies to 48 could be a possibility

The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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Answer:

that's the quadratic formula:)

Step-by-step explanation:

Answer:

9 points

Step-by-step explanation:

took the quiz edge2020

Answer:

B 9 Units

Step-by-step explanation:

According to the information, the perimeter of the triangle is ≈ 31.18

To find the distance between two points, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Let's label the coordinates as follows:

Point 1: (-2, 3)

Point 2: (3, -2)

Now we can substitute these values into the distance formula:

distance = sqrt((3 - (-2))^2 + (-2 - 3)^2)

distance = sqrt((5)^2 + (-5)^2)

distance = sqrt(25 + 25)

distance = sqrt(50)

distance ≈ 7.07

Therefore, the distance from (-2, 3) to (3, -2) is approximately 7.07 units.

To find the perimeter of the triangle, we need to find the length of all three sides of the triangle and then add them up.

Using the distance formula, we can find the length of the sides:

Side 1: (-2,3) to (3,-2)

d = √[(3 - (-2))^2 + (-2 - 3)^2]

= √[5^2 + (-5)^2]

= √50

= 5√2

Side 2: (3,-2) to (-7,-2)

d = √[(-7 - 3)^2 + (-2 - (-2))^2]

= √[(-10)^2 + 0^2]

= 10

Side 3: (-7,-2) to (-2,3)

d = √[(-2 - (-7))^2 + (3 - (-2))^2]

= √[5^2 + 5^2]

= 5√2

Therefore, the perimeter of the triangle is:

5√2 + 10 + 5√2 = 15√2 + 10 ≈ 31.18 (rounded to two decimal places)

An two of the three sides are equal, so it is an isosceles triangle.

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Answer:240

Step-by-step explanation:

400/5 = 80
80 x 3 = 240
240/400 people bought choc chip

The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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The value of x based on the equation illustrated as 3x - 1 + 5 < 1 is x < 1.

It should be noted that an equation is simply used to show the relationship between the expression or variables.

From the information, 3x - 1 + 5 < 1.

Collect like terms

3x - 1 + 5 < 1.

3x < 1 + 1 - 5

3x < -3

Divide

3x / 3 < -3 / 3

x < 1

Therefore, the value of x based on the equation illustrated as 3x - 1 + 5 < 1 is x < 1.

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Answer:

The construction is a parallel line to a given line  from a point not on the line.

Step-by-step explanation:

For a given figure,

To construct a parallel line

Step 1 : Draw transversal line through any point not on line which is given.

Step 2: Using construction copy an angle, construct same angle formed by transversal line and given line.

Step 3: This is the last step in which when the copy of an angle completed draw a line parallel to the line

Step-by-step explanation:

Answer:

Step-by-step explanation:

8.008.009