(a) Which of the following expresses the zero product property formally using quantifiers and variables? ∀ real numbers x and y, if xy = 0 then x = 0 and y = 0. ∀ real numbers x and y, if x = 0 and y = 0 then xy = 0. ∀ real numbers x and y, if x = 0 or y = 0 then xy = 0. ∀ real numbers x and y, if xy = 0 then x = 0 or y = 0. (b) Which of the following is the contrapositive of the zero product property? ∀ real numbers x and y, if x ≠ 0 or y ≠ 0 then xy ≠ 0. ∀ real numbers x and y, if xy ≠ 0 then x ≠ 0 or y ≠ 0. ∀ real numbers x and y, if x ≠ 0 and y ≠ 0 then xy ≠ 0. ∀ real numbers x and y, if xy ≠ 0 then x ≠ 0 and y ≠ 0. (c) Which of the following is an informal version (without quantifier symbols or variables) for the contrapositive of the zero product property? For any two real numbers, if at least one of them is nonzero then their product is nonzero. If the product of two real numbers is nonzero, then both numbers are nonzero. If the product of two real numbers is nonzero, then neither number is zero. If neither of two real numbers is zero, then their product is nonzero.

Answer:

Try relaxing, forget all problems at once, take deep breaths, because if you stress it could cause headaches. Listen to calming music, take a break every once in while. Try not to focus on the bad things that happened in your past! Focus on the good things in future that your smartness is allowing you to achieve! Trust me focusing on the bad things in life cause major headaches...never look back always look forward

Answer:

2

Step-by-step explanation:

If 1 = 1.5

2 = 3

That is the answer

Answer: 3 cups will make 4.5 cups of cooked rice.

Step-by-step explanation: 3 * 1.5

Answer:

1) -0.016 pounds per square inch per cubic inch.

2) [tex]\displaystyle V'(P)=-\frac{800}{P^2}[/tex]

Step-by-step explanation:

We are given the equation [tex]PV=800[/tex].

Part A)

We want to determine the average rate of change of P as V increases from 200 cubic inches to 250 cubic inches.

To find the average rate of change between two points, we find the slope between them.

Rewrite the given equation as a function of V:

[tex]\displaystyle P(V)=\frac{800}{V}[/tex]

Hence, the average rate of change for V = 200 and V = 250 is:

[tex]\displaystyle \begin{aligned} m &= \frac{P(250) - P(200)}{250 - 200} \\ \\ & = \frac{3.2 - 4}{250 - 200} \\ \\ & = -0.016\end{aligned}[/tex]

Therefore, the average rate of change is -0.016 pounds per square inch per cubic inch.

Part B)

We want to express V as a function of P. This can be done through simple division:

[tex]\displaystyle V(P)=\frac{800}{P}[/tex]

We want to show that the instantaneous change of V with respect to P is inversely proportional to the square of P. So, let's take the derivative of both sides with respect to P:  

[tex]\displaystyle \frac{d}{dP}\left[V(P)\right]=\frac{d}{dP}\left[\frac{800}{P}\right][/tex]

Differentiate. Note that 1/P is equivalent to P⁻¹. This allows for a simple Power Rule:

[tex]\displaystyle \begin{aligned} V'(P) & = 800\frac{d}{dP}\left[ P^{-1}\right] \\ \\ & = -800(P^{-2}) \\ \\ & = -\frac{800}{P^2}\end{aligned}[/tex]

Therefore, the instantaneous change of V is indeed inversely proportional to the square of P.

Answer:

0 The product will be smaller than both the factors.

0 There will be a zero in the tenths place.

0 The answer is 0.04.

Answer:

0.35x +65=1100+x

Step-by-step explanation:

Hey ya didnt get the question here

so I creat a equation that ya can use

let x be the number of the phone calls Min that is MORE THAN 1100 min

0.35x +65=1100+x

Hope this help ya

<3

Red

Answer:

Amount of cd after 3 years=2240

Step-by-step explanation:

principal==$2000

simple interest=4%

interest /year =80

for 3 years =80 x 3 = 240

Answer:

[tex]2.5\; \rm m^3[/tex].

Step-by-step explanation:

Let [tex]V_1[/tex] and [tex]P_1[/tex] denote the volume and pressure of this gas before the change. Let [tex]V_2[/tex] and [tex]P_2[/tex]denote the pressure of this gas after the change.

The ratio between the volume of this gas before and after the change would thus be [tex]\displaystyle \frac{V_1}{V_2}[/tex].

The ratio between the pressure of this gas before and after this change would be [tex]\displaystyle \frac{P_1}{P_2}[/tex].

Because the volume of a given mass of (ideal) gas varies inversely with pressure, these two ratios should be reciprocal of each other. That is:

[tex]\displaystyle \frac{V_1}{V_2} = \frac{1}{\displaystyle \displaystyle \left(\frac{P_1}{P_2}\right)}[/tex].

In other words:

[tex]\displaystyle \frac{V_1}{V_2} = \frac{P_2}{P_1}[/tex].

Rearrange and solve for [tex]V_2[/tex], the volume of this gas after the change:

[tex]\displaystyle V_1 = V_2\cdot \left(\frac{P_2}{P_1}\right)[/tex].

[tex]V_2 = \displaystyle V_1 \cdot \left(\frac{P_1}{P_2}\right)[/tex].

From the question:

Solve for [tex]V_2[/tex]:

[tex]\begin{aligned} V_2 &= V_1 \cdot \left(\frac{P_1}{P_2}\right) \\ &= 2\; \rm m^3 \times \frac{500\; \rm N \cdot m^{-2}}{400\; \rm N \cdot m^{-2}} = 2.5\; \rm m^3\end{aligned}[/tex].

Answer: 14/8 or 1 and 3/4 of a gallon

Step-by-step explanation: Since its leaking 7/8 every half hour, you would multiple 7/8 by two

Answer:  y= -2x - 500  

Step-by-step explanation:

Parallel lines have the same slopes but different y-intercepts. This means that the line parallel to y=-2x + 3 will have the same slope which is -2.

We will input the x and y coordinates for the given point into the formula and solve for the y-intercept to write the equation.

-100 = -2(-100) + b      where b is the y-intercept

-100 = 400 + b

-400  -400  

b = -500  

The y intercept is -500 and the slope is -2 therefore, the equation will be  

 y= -2x - 500

Answer:

[tex]\huge\boxed{a=\frac{bc}{d}}[/tex]

Step-by-step explanation:

In order to find the value of a when we have the equation [tex]bc=ad[/tex], our goal is to isolate a on one side.

The key question here is: what's stopping a from being alone on one side? That would be it being multiplied by [tex]d[/tex]. If we were able to remove the d, we would have a by itself.

Since we are multiplying a and d, we can get rid of the d by dividing both sides by d.

We have to divide both sides of the equation by the same value in order to keep it equal.

[tex]bc \div d = ad \div d\\\\\frac{bc}{d}=a\\\\a = \frac{bc}{d}[/tex]

Hope this helped!

Answer: no

Step-by-step explanation:

because you can do what is known as the vertical line test to determine if it is a function you do that by plotting it and if it goes in a vertical line then it is a function

40.96 mm

3.2(10) = 32; 3.2 cm → 32 mm

each side of scale drawing is 32 mm

2(10) = 20; 2 cm → 20 mm

scale is 4 mm to 20 mm

[tex]\frac{4}{20}= \frac{x}{32}[/tex]

cross-multiply:

32(4) = 128

128 / 20 = 6.4

each side of the actual drawing is 6.4 mm.

6.4 * 6.4 = 40.96

40.96 mm

40.96 mm

What is scaling ?

It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.

It is given that the scaling of drawing is 4mm to 2cm of actual drawing and the scaled drawing side of square earring is 3.2cm.

Now, corelating the scale given which means for 1mm of actual side of earring the drawing scale is 0.5 cm or 5mm. Therefore, for having 3.2 cm of side of earring in drawing let [tex]x[/tex] be the actual side this is calculated below :

                                                [tex]\begin{aligned}20 \text{mm}&\rightarrow 4\text{mm}\\32\text{mm}&\rightarrow x\text{\:mm}\\\frac{4}{20}&=\frac{x}{32}\\x&=6.4 \text{mm}\end{aligned}[/tex]

Now, the actual side of earring is 6.4 mm therefore, the area of the front of earring will be : 6.4 mm x 6.4 mm =40.96 mm  

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Answer:

The least value of perimeter is:

[tex]Perimeter = 26m[/tex]

The greatest value is:

[tex]Perimeter = 86m[/tex]

Step-by-step explanation:

Given

Shape: Rectangle

[tex]Area = 42m^2[/tex]

Required

Determine the least and greatest possible Perimeters

Area is calculated as:

[tex]Length * Width = Area[/tex]

So; first, we need to determine the factors of the given Area;

[tex]Length * Width = Area[/tex]

[tex]1 * 42 = 42[/tex]

[tex]2 * 21 = 42[/tex]

[tex]3 * 14 = 42[/tex]

[tex]6 * 7 = 42[/tex]

Perimeter is then calculated as:

[tex]Perimeter = 2 * (Length + Width)[/tex]

When Area is:

[tex]1 * 42 = 42[/tex]

[tex]Perimeter = 2 * (1 + 42)[/tex]

[tex]Perimeter = 2 * 43[/tex]

[tex]Perimeter = 86m[/tex]

When Area is:

[tex]2 * 21 = 42[/tex]

[tex]Perimeter = 2 * (2 + 21)[/tex]

[tex]Perimeter = 2 * 23[/tex]

[tex]Perimeter = 46m[/tex]

When Area is:

[tex]3 * 14 = 42[/tex]

[tex]Perimeter = 2 * (3 + 14)[/tex]

[tex]Perimeter = 2 * 17[/tex]

[tex]Perimeter = 34[/tex]

When Area is:

[tex]6 * 7 = 42[/tex]

[tex]Perimeter = 2 * (6 + 7)[/tex]

[tex]Perimeter = 2 * 13[/tex]

[tex]Perimeter = 26m[/tex]

Comparing the above.

The least value of perimeter is:

[tex]Perimeter = 26m[/tex]

The greatest value is:

[tex]Perimeter = 86m[/tex]

Answer:

360 degrees

Step-by-step explanation:

when we look at images of isosceles triangle it fits itself 1 time during a full rotation of 360 degrees

Answer:

56

Step-by-step explanation:

f (-4)=(-4^2)-8 (-4)+8

f(-4)=54

The two points on the graph of the function are (2, -4) and (6, -4).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

A quadratic function,

f(x) = x²−8x+8.

When f(x) = -4

That means,

quadratic equation,

x²−8x+8 = -4

x²−8x+12 = 0

x²−6x -2x + 12 = 0

x(x - 6) - 2(x - 6) = 0

x = 2 and x = 6

Therefore, the two points are (2, -4) and (6, -4).

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Answer:

1.92 litres

Step-by-step explanation:

1l=1000ml

1 jar=240ml=0.24l

8 jars= 240x8=1920ml=1.92l

Answer:

given

2x-1-x+3=0

x+2=0

x= -2

hope it helps you mate

please mark me as brainliast...

Answer:

2x-1-x+3=5

subtract 3 both sides

add 1 both sides

after that now its

2x-x=3

2x-x= x

x=3 thats the answer

Answer:

Step-by-step explanation:

Transformation involves changing the position of a shape in the coordinate.

See attachment for the image of the triangle

Assume the triangle is triangle ABC.

The coordinates of ABC are:

[tex]\mathbf{A = (-1,-4)}[/tex]

[tex]\mathbf{B = (-2,-7)}[/tex]

[tex]\mathbf{C = (5,-6)}[/tex]

The transformation rule is given as:

[tex]\mathbf{(x,y) \to (x -5,y+6)}[/tex]

So, we have:

[tex]\mathbf{A' = (-1 -5,-4+6)}[/tex]

[tex]\mathbf{A' = (-6,2)}[/tex]

[tex]\mathbf{B' = (-2 -5,-7+6)}[/tex]

[tex]\mathbf{B' = (-7,-1)}[/tex]

[tex]\mathbf{C' = (5 -5,-6+6)}[/tex]

[tex]\mathbf{C' = (0,0)}[/tex]

So, the coordinates of the new triangle would be:

[tex]\mathbf{A' = (-6,2)}[/tex]

[tex]\mathbf{B' = (-7,-1)}[/tex]

[tex]\mathbf{C' = (0,0)}[/tex]

See attachment for the image of ABC

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Answer:

{x,y,z}={5,−3,3}

Step-by-step explanation:

  [1]    2x + 4y + z = 1

  [2]    x - 2y - 3z = 2

  [3]    x + y - z = -1

// Solve equation [3] for the variable  y  

 [3]    y = -x + z - 1

// Plug this in for variable  y  in equation [1]

  [1]    2x + 4•(-x +z -1) + z = 1

  [1]    -2x + 5z = 5

// Plug this in for variable  y  in equation [2]

  [2]    x - 2•(-x +z -1) - 3z = 2

  [2]    3x - 5z = 0

// Solve equation [2] for the variable  x  

 [2]    3x = 5z

 [2]    x = 5z/3

// Plug this in for variable  x  in equation [1]

  [1]    -2•(5z/3) + 5z = 5

  [1]    5z/3 = 5

  [1]    5z = 15

// Solve equation [1] for the variable  z  

  [1]    5z = 15

  [1]    z = 3

// By now we know this much :

   x = 5z/3

   y = -x+z-1

   z = 3

// Use the  z  value to solve for  x  

   x = (5/3)(3) = 5

// Use the  x  and  z  values to solve for  y  

 y = -(5)+(3)-1 = -3

Solution :

{x,y,z} = {5,-3,3}

Answer:

(2,-5)

Step-by-step explanation:

The slope of the line is 3/4. You need to find 2/3 of this, which is quite easy. Since the slope is 3/4, then 2/3 of 3/4 would be 2/4, or 1/2. 2/4 slope of this line brings you to the point (2,-5) which is point B.

Answer:

-3

Step-by-step explanation:

Answer:

It's nine 9...........

Step-by-step explanation:

Its nine

Answer:

9

Step-by-step explanation:

Notice that 27 can be factored out as 3 * 3 * 3

and 12 can be factored out as: 2 * 2 * 3

then when we study the ratio 27/12, we can cancel out a factor 3, leaving us with:   (3 * 3) / (2 * 2) = 9 / 4

Then 9 is the number you need to type in the box.

Answer: (8)(-4.5)

Step-by-step explanation:

If you were to multiply-4.5 • -8 that would equal a positive number but if you were to divide (8)(-4.5) it would equal a negative number

Answer:

(8)(-4.5)

Step-by-step explanation:

please mark brainliest

Answer:

48 square feet

Step-by-step explanation:

A = length x width. (A =lw)

So, 8 x 6 = 48

Answer:

WALA NG VALUE ANG X DAHIL INIWAN KA NA NIYA

Answer:

I think the answer is B :)

Step-by-step explanation:

The solution is Option B.

The value of x is given from the inequality equation 0 < x < 27

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

From the parallelogram , AB ≈ BC

So , The ( ∠ CBD ) > ( ∠ ABD )

Substituting the values in the equation , we get

( 2x ) < 54°

Divide by 2 on both sides of the equation , we get

x < 54/2

x < 27°

And , ∠ ABD cannot be negative or zero ,

So , 2x < 0

Divide by 2 on both sides of the equation , we get

x < 0

Hence , the inequality equation is 0 < x < 27

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Answer: $41.472 or $41.50

Step by step solving: First convert 20% to a decimal which is .20 now multiply that by $51.84 which equals 10.368 now subtract that number from 51.84 which equals 41.472

If you are allowed to round to the nearest hundreth then that would be $41.50 before the tip.

Answer: 3mph/seconds

Step-by-step explanation:

Divide 30 by 10. 30mph/10seconds = 3mph/seconds