Identify the property shown by each statement
1. 4m x 0 x 3m = 0
2. 5 + (a + 17) = (5 + a) + 17

The shape of the parallelogram with vertices P(−4,0), Q(0,4), R(4,0), and S(0,−4) is a square

In order to get the shape using the vertices that we have, we would have to find the length of the diagonals

We have P(−4,0), Q(0,4), R(4,0), and S(0,−4)

The length of the diagonal PQ is given as:

PQ = [tex]\sqrt{(0-4)^2+(4-0)^2}[/tex]

= [tex]\sqrt{32}[/tex]

Next we have to solve for the length of the diagonal RS

RS = [tex]\sqrt{(4-(-4))^2+(0-(-4))^2[/tex]

RS = [tex]\sqrt{32}[/tex]

Since PQ = RS we would have to conclude that the shape is a square.

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Answer:

x = 4

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.

We can write the following equation to find the value of x based on this information:

6x + 6 + 17x + 2 = 100

23x + 8 = 100

23x = 92

x = 4

Since in the diagram, transversal t cuts parallel lines a and b, an equation which is necessarily true include the following: B. m∠3 = m∠6.

In Mathematics, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent.

Based on the diagram representing (showing) the two parallel horizontal lines a and b, we can reasonably infer and logically conclude that angle 3 (m∠3) and angle 6 (m∠6) forms a pair of alternate interior angles because line a is parallel to line b and transversal (t) cuts parallel lines a and b.

Similarly, angle 4 (m∠4) and angle 7 (m∠4) forms a pair of alternate interior angles because line a is parallel to line b.

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Approximately 20 years will it take a $1000.00 investment to double its value at an interest rate of 3.60%, compounded annually.

Approximately 20 years will it take a $1000.00 investment to double its value at an interest rate of 3.60%, compounded annually.

The complete question is,
Approximately how many years will it take a $1000.00 investment to double its value at an

interest rate of 3.60%, compounded annually?

A. 5

B. 7.2

C. 20

D. 50

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The reduced price of the item will be $44.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the price of an item has been reduced by 20%. The original price was $55.

The reduced price of the item will be calculated as,

Price  = 55 x ( 100% - 20 %)

Price = 55 x ( 1 - 0.2

Price = ( 55 x 0. 8 )

Price= $44

Hence, the price of the item will be $44.

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The equation as per the information that has been provided, the answer will be computed as:

The function's limit indicates its value as the independent variable gets closer to a certain point.

Finding the limit as the independent variable approaches both the positive and negative limits is necessary to determine whether a function's limit is present. If both limits are the same, the limit of the function is present.

L=limx→0.5(cos(x)+2sin(3x))

L=cos0.5+2sin3×0.5

L=0.87+2sin1.5

L=0.87+2(0.99)

L=0.87+1.99

L=2.86

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If 3/4 cup of chai tea latte concentrate is 60 calories, we can use proportion to find out how many calories 1/2 cup of chai tea latte concentrate is.

What does a math ratio mean?

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could athe ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

We know that:

(3/4 cup) = 60 calories

To find out the number of calories in 1/2 cup, we can set up a proportion using the information we have:

(1/2 cup) / x = (3/4 cup) / 60

we can cross-multiply to get:

x = (1/2 cup) * (60 / (3/4 cup))

then we can simplify

x= (1/2)*(4/3)*60

x= 80/3

Therefore, 1/2 cup of chai tea latte concentrate is 80/3 calories.

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It would not be unusual for a household to have three dogs, as the data you provided shows that there are households in the small town with three dogs.

The frequency of households with three dogs is 173, which is the third highest number after households with one or two dogs. Therefore, having three dogs in a household is not uncommon in this small town,

Frequency refers to the number of times an event or a value occurs within a specific data set. It can be represented as a count or a percentage. In statistics, frequency is used to describe the distribution of data, which can help to identify patterns and trends. For example, in the data you provided, the frequency of households with three dogs is 173, which means that there are 173 households in the small town that have three dogs. It's a way to understand how common or rare is something in the dataset. By counting the number of times each value appears on the dataset and organizing it, we can have a better understanding of how the variable is distributed.

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Answer: C

Step-by-step explanation:

This is simple algebra! First, try to find the slope which would be -3.

Let's say x is hours and y is degrees. We will find the slope by finding the change in x and y.

change in y    45  - 54 =  -9

change in x     5   -   2  =   3

The slope is -3. Therefore the temperature decreases by 3 degrees every hour.

Hope that helps! :-)

The values of F, G and H are given as follows:

F = 5, G = 29, H = 1.

The expression at the right side of the equality represents the entire expression after the least common factor is applied at the left side.

The least common side of the denominators is given as follows:

(x - 3)(4x + 7).

Hence the simplified numerator is given as follows:

(2x + 1)(4x + 7) + (-3x + 2)(x - 3).

Expanding the operations, and combining the like terms, we have that:

(2x + 1)(4x + 7) + (-3x + 2)(x - 3) = 8x² + 18x + 7 - 3x² + 11x - 6.

(2x + 1)(4x + 7) + (-3x + 2)(x - 3) = 5x² + 29x + 1.

Then the equality of the two numerators is given as follows:

5x² + 29x + 1 = Fx² + Gx + H.

Hence the values of the letters are given as follows:

F = 5, G = 29, H = 1.

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Answer: 8 pounds

Step-by-step explanation: Let’s first identify the main key details

Strawberry- 2 pounds

Apple- 6 more of strawberry

What is 6+2

8

The apple weighs 8 pounds.

Hope this helped

Answer: 63 bottle caps

Step-by-step explanation:

3591 caps collected

57 days

3591/57=63

Caps collected per day 63 caps

The standard form of the equation for the line which is as described is; x - 4y = 8.

It follows from the task content that the equation of the line in discuss in point-slope form as given in the question is;

( y - 1 ) = 1/4 ( x - 12 )

Therefore, the equation above can be written so that we have that;

4 ( y - 1 ) = ( x - 12 )

4y - 4 = x - 12

4y - x = -12 + 4

x - 4y = 12 - 4

x - 4y = 8

Therefore, the standard form equation of the line as required is; x - 4y = 8.

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Answer: h = 16

Step-by-step explanation:

       We will isolate the variable, h, with inverse operations and simplifying to solve for h.

   Given:

[tex]\displaystyle -\frac{5}{6}h-\frac{2}{3}h=-24[/tex]

   Multiply both sides of the equation by 6:

       ➜ Why would we do this? This allows us to work without fractions.

-5h - 4h = -144

   Combine like terms:

-9h = -144

   Divide both sides of the equation by -9:

h = 16

The equation that shows Group A's distance from the start, given their speed and the number of hours is C. y = 3 x.

When trying to find the distance that a person or object has travelled in a given time, the general formula is;

= Speed x Time

The speed is given as 3 miles per hour for Group A.

The time is given as x for either group

This means that the distance that Group A has gone since the hike up the glacier started is :

Distance from the start = Speed x Time

y = 3 miles per hour × x

y = 3x

In conclusion, given the speed that Group A is using, this means that their distance from the start can be modelled by the equation, y = 3 x.

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Answer:

Step-by-step explanation:

Answer:

Robert will spend $27 on shirts for the team.

Step-by-step explanation:

Therefore, Robert will spend $27 on shirts for the team.

Please let me know if this helped!!!

Answer:

Step-by-step explanation:

-5x-1>9

add 1 to both sides

-5x>10

divide by negative 5

x<-2

the sign flips since you divided by a negative

and your answer is x<-2

We were informed that an is a matrix with numerous elements in this query. A is an order matrix, and we also have  an order matrix.

3 by 3, resulting in a determinant of b that is -5. We were successful in locating a matrix c that is equal to minus three times of a b cube times a.

We must determine the determinant because an is equivalent to a transport and an is equal to an identity matrix. If I take into account the period of a transposition, what is the determinant of a so-called determinant of this identity, which is equal to 1 accurate and we are aware of this characteristic.

This will be the result of those who are in a situation where a transposition is crucial. This is the first result is that the cube's time has the same determinant as a matrix's time.

Because a 3 by 3 matrix and lambda are real numbers, we can leverage this property. Using this property, it will be -3 q in this case. Once more, I'll be able to obtain a transposition b times c times a determinant. Splitting it is a possibility. The times of the b cube determinant are determined by minus 3 c. We know that the determinants of a transpose and the determinant of a that is 1 are, so what we are obtaining is just minus 27.

We shall obtain the b cube's determinant from this location. This is only multiplied by 1 minus 27. There won't be an entire cube. The determinant of c is equal to 3125, which is the product of -27 and -125.

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The value of y given the inverse proportional relationship between the variables is 16.

When two variables vary inversely, as one of the variable increases, the other variable decreases.

The equation that represents inverse proportion : x = k / y

where b = constant of proportionality

k = xy

k = 12 x 4 = 48

y = k / x

48 / 3 = 16

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Answer: I can't solve all of them but I will give tips. i repeats in cycles so i^1 is sqrt-1, i^2 is -1, i^3 is -i and i^4 is 1. Look at the exponent and first divided out 4 then use the  1 2 3 answers. When you divided i and a number such as (1-i)/1+i) multiply by the conjugate of the denominator which is 1-i. To find conjugate replace the + with a -.

Step-by-step explanation:

By ASA (Angle side angle) theorem, triangle △ABD≅ triangle △CBD.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now

As BD is common for both triangles ABD and CBD.

and

∠ADB=∠CDB=90°

also as DB bisects ∠ABC

∠ABD=∠CBD

Hence,

By Angle Side Angle theorem, triangle △ABD≅ triangle △CBD

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The time that Mrs James have her eyes open than closed will be 13 19/20 hours.

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.

From the information, the average person spends about 1/10 of their walking hours with their eyes closed. If Mrs. James was awake for 15 1/2 hours today.

The more time that she have her eyes open than closed will be:

= 15 1/2 - (1/10 × 15 1/2)

= 15 1/2 - 1 11/20

= 13 19/20

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The expression denominator is 1.

What is denominator?

In mathematics, a denominator is the lowest number in a fraction that indicates how many equal parts are divided into a whole. It is a fraction's divisor. In this case, the denominator is 4, thus there are four components overall.

Here the given is x-3+5

Now simplifying them

=> x-3+5 = x+2.

We know that the whole number or Integer always has 1 as Denominator. Then,

=> [tex]\frac{x-2}{1}[/tex]

Hence the denominator of the given is 1.

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The equation 7.5s + 1.6t - 4.2s is simplified to give a result of

The given equation 7.5s + 1.6t - 4.2s is simplified by following the mathematical operator that is acting on the values after a consideration of like terms

The variables in the equation are t and s

terms in t: 1.6

terms in s: 7.5, -4.2

collecting like terms

this will lead to rearranging the equation to give

7.5s - 4.2s + 1.6t

using the mathematical operator (addition and subtraction)

= 3.3s + 1.6t

unlike terms cannot be operated on, because of this the answer is 3.3s + 1.6t

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Answer:

35⁰

Step-by-step explanation:

because the sum of the interior angle of triangle is 180⁰ so 90+55+x=180

x=35

The equation of line that has a slope of 1/2 and goes through (4,-1) is y=-3.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

y = mx + c

where m denotes the line's slope and c is the y-intercept.

In the question, we have been given the slope and the (x,y) through which it passes.

Substituting these in y = mx + c, we get

-1= 0.5(4)+c

-1= 2+c

-3=c

c=-3.

Hence, the equation of line is y=-3.

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Answer:

300 degrees.

Step-by-step explanation:

a = 180 degrees

c = 180 - 60 = 120 degrees

The equations that represent the circle are x² + (y - 3)² = 36 and x² + (y + 8)² = 36.

A circle is a two dimensional figure which consist of all the points which are at equal distance from a fixed point called center of the circle.

Standard equation of a circle is,

(x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Given that,

Diameter = 12

Radius = Half of diameter = 6

Center lies on the y axis.

So the coordinates of center (h, k) will be of the form (0, k).

So the equation will be of the form,

(x - 0)² + (y - k)² = 6² or x² + (y - k)² = 36

The equations of this form in options are,

x² + (y - 3)² = 36 and

x² + (y + 8)² = 36

Hence the equations are x² + (y - 3)² = 36 and x² + (y + 8)² = 36.

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Answer:

answer is 341

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