use logical equivalence theorem to verify the logical equivalence below
p ∨ q → r ≡ (p → r) ∧ (q → r)

Step-by-step explanation:

hope this helps!:).....

Answer:

Average speed = Total distance travelled / Total time taken

 = 170 miles / 2.34 hours

 = 72.65 miles per hour or 72.65 mph

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Answer:

6375 mcg

Step-by-step explanation:

hopes this helps :)

Answer:

-15,-14,-13

Step-by-step explanation:

Let x = the first integer

Let x + 1 = the second integer

Let x + 2 = the third integer

The addition of all three equal -42

x + x + 1 + x + 2 = -42  Combine like terms

3x + 3 = -42  subtract 3 from both sides

3x + 3 - 3 = -42 - 3

3x = -45  Divide both sides by 3

x  = -15

Check

-15 + -14 + -13 = -42

-42 = -42

Answer:

[tex] \frac{2257}{2400} [/tex]

Step-by-step explanation:

2400 - (120+23)

=2400 - 143

=2257

Therefore,

2257

2400

Belle's house is approximately 5.83 miles away from Cora's house.

What is a Pythagoras Theorem?

The Pythagorean theorem is a fundamental concept in mathematics, named after the ancient Greek mathematician Pythagoras. The theorem states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as an equation: [tex]c^2 = a^2 + b^2[/tex], where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

We can use the Pythagorean theorem to solve this problem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We can consider this problem as two right triangles with Rosa's house being the common point, and therefore the right angle.

Let x be the distance between Belle's house and Cora's house.

So, we can set up the equation as:

x^2 = 3^2 + (5)^2

x = sqrt(3^2 + (5)^2)

x = sqrt(9 + 25)

x = sqrt(34)

x = approximately 5.83 miles.

Hence, Belle's house is approximately 5.83 miles away from Cora's house.

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-1

8 is bigger than 0, so according to the function, we need to use the third one so it would be -1

Answer:

A, B and E

Step-by-step explanation:

The solution is: Correct option is 3: Equally likely and unlikely.

We have,

Equally likely indicates the likelihood that the outcomes of each experiment will occur. For instance, if you roll a fair, six-sided die, there is an equal probability of getting any of the faces (1, 2, 3, 4, 5, or 6). The likelihood of a coin landing on its head (H) or tail (T) is equal (T).

What has equal and unequal likelihood?

Equally likely suggests that the event is fair and that all possible outcomes have an equal chance of happening. If two outcomes are not equally likely to occur, then the event would be unfair and one or more of the events would be more likely to do so.

Given that, P(terriers) is 50%

i.e., P(terriers) = 1/2

So, P(not terriers) = 1 - 1/2 = 1/2

This is an equally likely and unlikely event. i.e., The likeliness and unlikeliness of the event are equal and equal to 50%.

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Answer: No, it is not possible to have a 3/8-inch pipe with an inside diameter of 21/32 inches

Step-by-step explanation:

The inside diameter of a pipe is always smaller than the outside diameter. The outside diameter of a pipe is a measurement of the pipe's exterior, while the inside diameter is a measurement of the pipe's interior. Therefore, if the pipe is 3/8 inches in outside diameter, the inside diameter will be less than 3/8 inches.

In addition, 21/32 inches is greater than 3/8 inches, so it is not possible to have a 3/8 inches pipe with an inside diameter of 21/32 inches. This is because the inside diameter is always smaller than the outside diameter.

- C

The value of expression is ,

10) 6

11) 18

12) 2

13) 4

14) [tex]\frac{1}{4}[/tex]

15) [tex]\frac{1}{3}[/tex]

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression

10) 7+x+(-3)

Put x=2 then

=> 7+2-3

=> 7-1 = 6

11) 4[tex]x^2[/tex]+2

put x=2 then

=> [tex]4*2^2+2[/tex]

=> 4*4+2

=> 16+2=18

12) Ix+10I

put x=-12 then

=> I-12+10I

=> I-2I = 2

13) |2x + 1|

put x= 3/2 then

=> I2*[tex]\frac{3}{2}[/tex]+1I

=> I3+1I

=> I4I = 4

14)(x - 3)/4

put x=4 then

=> [tex]\frac{4-3}{4}[/tex]

=> [tex]\frac{1}{4}[/tex]

15) (5 - x)/6

put x=3 then

=> [tex]\frac{5-3}{6}[/tex]

=> [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

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Answer:

A. 2¾

Step-by-step explanation:

The person needs the difference. This is a subtraction problem.

3 1/2 - 3/4 =

3/4 is just a fraction, but you can think of 3/4 as a mixed numeral by writing 3/4 as 0 3/4. The whole part is 0 and the fractional part is 3/4.

= 3 1/2 - 0 3/4

Now we are subtracting two mixed numerals. You need to subtract the whole part, 0, from the whole part, 3, and the fractional part, 3/4, from the fractional part, 1/2.

For the fractional parts, we need a common denominator of 4.

= 3 2/4 - 0 3/4

Now we have both fractions with a common denominator of 4, but since we cannot subtract 3/4 from 2/4, we borrow 1 from 3 as 4/4.

3 goes down 1 to 2, and the 1 which is borrowed as 4/4 is added to the 2/4 to give you 2 6/4. 2 6/4 has the same value as 3 2/4. Now we have:

= 2 6/4 - 0 3/4

We subtract 0 from 2, and we subtract 3/4 from 6/4.

= 2 3/4

Answer: 2 3/4

Answer:28 sq mm

Step-by-step explanation:

Triangle's area: length times the height then divided by 2.

8×7÷2

=56/2

=28

Step-by-step explanation:

fufj5655 and I hope that you will be able to help me with the following to help me with the application for the role of the temple and many other people in the forest and a small village known as change in indirect speech to be the oldest

Answer:

1the answer for this is easy it is 4.4

Answer:

y(y-5) =750 squared-feet

Step-by-step explanation:

[tex] {y}^{2} - 5y = 750 \\ 750 - y(y - 5) = 0 \\ (y + 25)(y - 30) = 0[/tex]

the solution of number line is all the options are correct.

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

Here,

Kendra and Jamal are standing in line. The number line shows their positions in meters with positive numbers representing positions to the right.

The position of Kendra is -6 and Jamal is 0.

Kendra is 6 meters left of Jamal.

Kendra and Jamal are 1-6 meters apart.

Jamal is 6 meters right of Kendra.

Hence, all the options are correct.

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The cost of a candy bar is equal to $1.61.

In order to write an equation that model this situation, we would assign variables to the cost of candy bars and the cost of soda respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that three (3) candy bars and one (1) soda costs $5.63 as follows;

3x + y = 5.63   ...equation 1.

Additionally, one candy bar and four sodas cost $4.81 at the same price;

x + 4y = 4.81 ...equation 2.

x + 4(5.63 - 3x) = 4.81

x + 22.52 - 12x = 4.81

11x = 22.52 - 4.81

x = 17.71/11

x = $1.61

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Answer: The perimeter of a rectangle is given by the formula P = 2L + 2W, where L is the length and W is the width of the rectangle.

We know that the rectangular school banner has a length of 44 inches and a perimeter of 156 inches. And we can use the formula above to find the width of the rectangular school banner:

P = 2L + 2W = 156 inches

P = 2(44) + 2W = 88 + 2W = 156 inches

So the width of the rectangular school banner is W = 156 inches - 88 inches = 68 inches

Now, we know that the cheerleaders make signs similar to the banner. the length of a sign is 11 inches, we can use the same formula to find the perimeter of the sign.

P = 2L + 2W = 2(11) + 2W

So the perimeter of the sign is P = 22 + 2W inches

Since we don't know the width of the sign (W) we can't find the perimeter of the sign.

Step-by-step explanation:

After calculating The perimeter of rectangle is 46.52 in the given rectangle.

What is area of rectangle?

area of rectangle can be defined as the product of length and breadth.

Given ,

A rectangle has a length 20 5 /6 and

breadth = 2 3/7

The perimeter of rectangle  = 2 (l+b)

length = (120 + 5 ) / 6 = 125/ 6

breadth = (14+3) / 7  = 17/7

perimeter  = 2 (125/6 + 17/7 )

= 2 ( (125*7 + 17 * 6) / 42 )

= 2 (875+102) / 42

= 2 * 23.26

= 46.52

Hence, after calculating The perimeter of rectangle is 46.52 in the given rectangle.

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Answer:

When a mixed number is written as a decimal, the whole number does not change but the fraction is changed to an equivalent decimal.

For example, if a mixed number is 2 1/4, the whole number is 2 and the fraction is 1/4. When this mixed number is written as a decimal, the whole number remains 2, but the fraction 1/4 is changed to the equivalent decimal 0.25. So the mixed number 2 1/4 is written as 2.25 in decimal form.

Answer:

Since slope of line passing through two points (x

1

​

,y

1

​

) and (x

2

​

,y

2

​

) is m=

x

2

​

−x

1

​

y

2

​

−y

1

​

​

We now find the slope of the line passing through the points (2,3) and (4,6) as shown below:

m=

4−2

6−3

​

=

2

3

​

Therefore, the slope of the line is  

2

3

​

.

Now use the slope and point (2,3) to find the y-intercept.

y=mx+b

⇒3=(

2

3

​

×2)+b

⇒3=3+b

⇒b=3−3=0

Write the equation in slope intercept form as:

y=mx+b

⇒y=

2

3

​

x+0

⇒y=

2

3

​

x

Step-by-step explanation:

Answer:  Lily babysits for less than 4 hours.

Step-by-step explanation:

We can start by multiplying 4 hours by 7/8 to find out how many hours Lily spends babysitting.

4 * (7/8) = 7/2 = 3.5 hours

Since 3.5 is less than 4, Lily babysits for less than 4 hours.

Answer: Less than 4. (3 1/2 hours)

Step-by-step explanation:

When you multiply a number by a number smaller than 1, the answer gets smaller.

Lily babysits for 3 1/2 hours because 4 x 7/8 = 3 1/2

The values of x can be that is x = 6 or x > 6 or x < -2 .

What is algebraic expression ?

Algebraic expression can be defined as the combination of variables, constants and exponents.

Given expressions,

2x-7 < -11 or 2x-7  >= 5

So, from the first expression,

2x-7 < -11

2x < -11+7

2x < -4

x < -2 or x>2

From the second expression,

2x - 7 >= 5

2x >= 5+7

2x >= 12

x >= 6

So , in this case x = 6 or x can be greater than 6.

Hence, The values of x can be that is x = 6 or x > 6 or x < -2 .

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The quadratic expression for the curves is written as

The curve opening up y = a(x + 4)² - 7

The curve opening down y = -1/8(x - 4)² + 3

The equation of the quadratic equation is written using the formula

y = a(x - h)² + k

where h and k are points of the vertex v(h, k)

The curve opening up

h = -4 and k = ?

using points C and B

-5 = a(0 + 4)² + k, -5 = 16a + k

1 = a(4 + 4)² + k, 1 = 64a + k

solving simultaneously

-5 = 16a + k

1 = 64a + k

subtraction

-6 = -48a

a = 1/8

solving for k

-5 = 16a + k

-5 = 16 * 1/8 + k

k = -7

substituting the values

y = a(x + 4)² - 7

The curve opening down

A is the vertex (4, 3)

y = a(x - 4)² + 3

using D (0, 1) to solve a

1 = a(0 - 4)² + 3

1 - 3 = 16a

a = -1/8

hence the equation is y = -1/8(x - 4)² + 3

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Answer:

25

Step-by-step explanation:

5/9 x 45  Cross cancel the 9 and 45. 9 goes into 9 once and 9 goes into 45 5 times

5/1 x 5/1 = 25/1 = 25

The division of the given polynomial would be (x^4) + 81.

What is the synthetic division?

Synthetic division is a method for dividing polynomials that allows you to divide a polynomial by a linear factor (a factor in the form of (x-c) where c is a constant) without actually performing the long division process. It is a short cut method that simplifies the process of dividing polynomials.

To divide the polynomials using polynomial division, we will use the following steps:

Write the polynomials in descending order of exponents.

(2x^3 + x^4 - 6x^2 + 11x - 10) (x^2 + 2 - x)

Create a grid with the dividend on the left and the divisor on the right.

2x^3 x^4 -6x^2 11x -10

x^2 2 -x  

Bring down the leading coefficient of the dividend, which is 2x^3 in this case. Write it in the next row of the grid.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

Multiply the divisor (x^2 + 2 - x) by the leading coefficient (2x^3) and write the result in the next row.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

2x^5 2x^4 4x^3 -2x^4  

Subtract the second row from the third row and write the result in the next row.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

2x^5 2x^4 4x^3 -2x^4  

0 -x^4 -2x^2 11x -10

Divide the new leading term by the leading term of the divisor, which is x^2, and write the result in the next row.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

2x^5 2x^4 4x^3 -2x^4  

0 -x^4 -2x^2 11x -10

-x^2

So the final answer would be (-x^2) + (x^4 + 2x^2 - 11x + 10).

Hence, the division of the given polynomial would be (x^4) + 81.

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The amount of mulch that he put on each vegetable bed will be 1/9.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

In this situation, the gardener spread 1/3 of a bag of mulch evenly over his 3 equal-sized vegetable beds.

The amount of mulch that he put on each vegetable bed will be:

= 1/3 ÷ 3

= 1/3 × 1/3

= 1/9

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