Determine which equation is false, based on the solution set S:{2}.

7 = 6p − 5
4t = 8
3(3c + 1) = 21
5m + 8 = 16
pls help ill give 45 points

B. Due to the fact that ABCD has at least two parallel sides in one pair.

The y-coordinates of the two points A(-3, 1) and D(5, 1) are identical.

Then

The x-axis and the line AD are parallel.

As opposed to that,

The y-coordinates of the two points B(1,5) and C(5,5) are identical.

Then

The x-axis and the line BC are perpendiculars.

We discover:

• AD lies along the x-axis.

BC is perpendicular to the x-axis.

Therefore

AD / BC

Conclusion:

Due to the fact that ABCD contains at least two parallel sides in one pair.

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If the car goes to the top of spike's peak and back, the mileage of the car is 16 miles per gallon

The mileage of car in uphill = 12 miles per gallon

The mileage of car in downhill = 24  miles per gallon

The total distance traveled in up hill = 48 miles

The number of gallon of gas used = 48/12

= 4 gallon

The total distance traveled in down hill = 48 miles

The number of gallon of gas used = 48 / 24

= 2 gallon

Total distance traveled = 48 + 48

= 96 miles

Total number of gallons of gas = 4 + 2

= 6 gallon

The mileage = Total distance / The number of gallon

= 96 / 6

= 16 miles per gallon

Therefore, the mileage of the car is 16 miles per gallon

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For example, if the given data set is {2, 3, 5, 8, 10, 3, 12, 6, 15}. Then the range will be 15 – 2 = 13.

In the given question, we have to find an example of range.

As we know that;

The group of all possible dependent values that a function or relation can produce from its domain values is known as its range. It consists of every potential output.

The difference between both the highest and lowest numbers in a collection or set is known as the range.

For example, if the given data set is {2, 3, 5, 8, 10, 3, 12, 6, 15}

The largest number of the given set is 15.

The smallest number of the given set is 2.

Then the range will be 15 – 2 = 13.

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Equation which is used to find the distance between the given points A and B for the given θ = 28° is equal to AB = x cos28°.

Diagram is attached.

As given in the question,

Diagram is attached.

Given angle θ = 28°

Hypotenuse = x

Two points A and B is on the base

Base - length = AB

In the given triangle,

Equation represents the distance between two points is:

cosθ = base / hypotenuse

⇒ cos 28° = AB / x

⇒ AB = x cos 28°

Therefore, the equation used to represent the distance between two point A and B is equal to AB = x cos28°.

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Two or more figures are said to be similar if and only if there are common properties of the sides and/or angles of the figures. The height of the tree is 8.85 meters.

Similar shapes have some common properties with respect to either their length of sides or measures of the internal angles. The relationship between similar sides can be expressed as a form of ration. But similarity of two or more shapes does not mean that the shapes are congruent.

In the given question, the construction gives similar triangles. Let the height of the tree be represented by h. Thus by similar properties of the sides of the triangles, we have;

[tex]\frac{1.65}{h}[/tex] = [tex]\frac{5.25}{28.15}[/tex]

h = [tex]\frac{1.65*28.15}{5.25}[/tex]  

= 8.8471

h = 8.85 meters

Thus, the height of the tree is 8.85 meters.

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Answer:

32, 16, 8, 4, 2, 1

Step-by-step explanation:

32, 16, 8, 4, 2, 1

Rule: Divide by 2 the previous number

The general convention is to reject a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect. This is False.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

After a performing a test, scientists can reject the null hypothesis meaning there is a definite, consequential relationship between the two phenomena

In this case, the convention is to accept a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect.

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The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.

Given

In line with the posed question.

Triangle ABC's vertices are A(-2, 3), B(0, 0), and C. (1, 2).

As we are aware,

The x-coordinates of each point must be negative while keeping the y-value constant in order to reflect a triangle over the y axis.

As a result, when triangle ABC is mirrored across the y-axis, its vertices are

A'(2,3)

B'(0, 0)

C'(-1, 2)

The vertices of the triangle will also change when it is dialated by a scale factor of 2.

A'(4, 6)

B'(0, 0)

And, C'(-2, 4)

The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.

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Answer:

48 and 15/16

Step-by-step explanation:

49+1/8(-1/2)

49+(-1/16)

48 and 15/16

The required value of the expression is 3 when substituting the value of -1/2 for y.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The expression is given in the question as:

49 + 1/8y

To evaluate the expression, we need to substitute the value of -1/2 for y. Doing this gives us:

⇒ 49 + 1/8(-1/2)

⇒ 49 + (-1/16)

Simplifying the expression further gives us:

⇒ 49 - 1/16

⇒ (16 × 3 + 1 - 1)/16

⇒ 48/16

Apply the division operation, and we get

⇒ 3

Therefore, the final value of the expression is 3.

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Answer: The original price is 200$

Step-by-step explanation:

original price = 100 percent

100-64=36

36% =72

100%= x

use cross multiply

36x=100*72

36x=7200

x=200

The original price is 200$

Answer:$200

Step-by-step explanation:

$72 is 100-64 or 36% if the original price.

First, we convert the percentage into a decimal number.

So, 0.36.
Next we divide that by $72

The answer is $200

When an adverb requires emphasis or wouldn't fit anyplace else in the sentence, an infinitive should be split. Split infinitive might occasionally help to clarify a sentence's meaning.

In the given question we have to explain, when we allow a split infinitive and why.

When an adverb requires emphasis or wouldn't fit anyplace else in the sentence, an infinitive should be split.

A split infinitive might occasionally help to clarify a sentence's meaning. It is not apparent if the requesting was done softly or whether the leaving should be done quietly in the sentences "I requested her gently to leave" or "I asked her to leave quietly."

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The system of inequalities that represents the possible dimensions of the pen is given as follows:

The graph of the system is given by the image given at the end of the answer.

The first step in building the system of inequalities is identifying the variables, which are given as follows:

The length of the fence should be at least 60 ft, hence:

x ≥ 60.

The distance around should be no more than 260 ft, hence, considering the perimeter of the fence:

2x + 2y ≤ 260

x + y ≤ 130.

The dimensions cannot be negative, hence another restriction needed is:

y > 0.

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1945 men and 2849 women register to audition for a singing competition. The number of participants who are not successful in their auditions what’s five times the number of those who are successful. There are 799  participants were successful.

The successful  participants  can be calculate by solving a linear equation as follows

First, it's crucial to understand linear equations.

Equation connects the two algebraic expressions with an equal to sign to demonstrate the equality between the two algebraic expressions.

Linear equations are those with one degree.

In this case, a linear equation must be resolved.

1945 for the men's total

Women are present in 2849.

Participants in total: 1945 + 2849 = 4794

Let x be the proportion of participants that were successful.

Men who failed were 5 times as numerous.

Participants in total: 5x + x = 6x

Due to the issue,

The linear formula is

6x = 4794

x = 4794/6

x = 799

799 of the participants had success.

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The values of x in the cyclic quadrilateral are 6.67 and 25 and the angle

m∠ ACB is 115°

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also sometimes called inscribed quadrilateral. The circle which consists of all the vertices of any polygon on its circumference is known as the circumcircle.

1)

Let's solve to find the value of x

Using proportions;

12/8 = 10 / x

x = 20 / 3

x = 6.67

2) To find x;

(4x + 15)° + (6x + 3)° + 92° = 360°

Sum of angles in a circle is 360°

4x + 15 + 6x + 3 + 92 = 360

10x + 110 = 360

10x = 250

x = 25

To find the value of m ∠ACB in the quadrilateral, we have to evaluate the value of x in the expression  = 4x + 15

m∠ ACB = 4(25) + 15

m ∠ ACB = 115°

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The effort you put in while ascending the stairs is equal to the sum of the force you exerted (your weight) and the elevation you moved.

Which is: Work (in joules) is equal to your weight in newtons divided by the stairs' height in meters.

Your Body Weight It goes without saying that moving a heavy object up a flight of stairs takes more strength than moving a light object. However, you still need to push your body weight against gravity even if you don't carry anything. Therefore, the more weight you have, the more power you need to climb the stairs.

Student 1 would have a power of 467 W, while Student 2 would have a power of 433 W. The fourth option—student 1 would have a power of 467 W, while student 2 would have a power of 433 W—is the correct one.

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The probability that Ephraim gets the same number of heads that Keiko gets is 3/8.

What is probability?

The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.

Here, we

Let K(n) be the probability that Keiko gets n heads, and let E(n) be the probability that Ephriam gets n heads.

K(0) = 1/2

K(1) =1/2

K(2) = 0 (Keiko only has one penny!)

E(0) = 1/2 ×1/2 = 1/4

E(1) =  1/2 ×1/2 +  1/2 ×1/2 = 1/2  (because Ephraim can get HT or TH)

E(2) =  1/2 ×1/2 = 1/4

The probability that Keiko gets 0 heads and Ephriam gets 0 heads is K(0)×E(0). Similarly for 1 head and 2 heads.

We get

P = K(0)× E(0) + K(1)×E(1) + K(2)× E(2)

P = 1/2 ×1/4 + 1/2 ×1/2 +0

P = 3/8

Hence, the probability that Ephraim gets the same number of heads that Keiko gets is 3/8.

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The measure of this angle is 172°.

Circumference: Any shape's circumference establishes the path or boundary that encircles it. To put it another way, the circumference and perimeter both refer to the length of a shape's outline.

When two of its rays pass through the endpoints of an arc, line segment, or other section of a curve, the angle is subtended by that arc, line segment, or other section of the curve.

From the information provided.

The circle's 1/360th circumference measures 0.5 cm in length.

Total circumference of circle now will be

360*0.5cm

= 180cm

However, if a 360° angle is equivalent to a circumference of 180 cm;

Then, an angle that subtends with 86 cm long will be:

=(86/180)*360

=172°.

Therefore, the measure of this angle is 172°

Given Question is incomplete complete question here

A circle is centered at the vertex of an angle, and the angle's rays subtend an arc that is 86 cm long. 1/360th of the circumference of the circle is 0.5 cm long. What is the measure of this angle in degrees?

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The function are Linear that would best model Monica's and Shanna's total savings.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Monica and Shanna are saving the money they earn from their after-school jobs to go on a school trip.

Here, Monica starts with $20 and then saves $14 each week. Shanna's savings are shown in the table.

Hence, The function for Monica is,

⇒ y = 20 + 14x

Where, x is number of weeks and y is total cost.

And, For Shanna's;

The equation is find as;

Two points from table are (0, 0) and (1, 18)

Hence, The equation is,

⇒ y - 0 = (18 - 0) / (1 - 0) (x - 0)

⇒ y = 18x

Thus, Both function for best model Monica's and Shanna's total savings is Linear function.

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∠1 ≅ ∠3 is congruent by AAA postulate where ∠1 and ∠2 form a linear pair and m∠2 + m∠3 = 180

If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.

Given,

∠1 and ∠2 form a linear pair

m∠2 + m∠3 = 180

Statements                     Reasons

∠1 and ∠2                            Linear pair

∠1 and ∠3                             Linear pair theorem

m∠2 and m∠3                     Given

∠3 and ∠2                           Definition of supplementary angle

∠1 ≅ ∠3                               AAA postulate

∠1 ≅ ∠3 is congruent by AAA postulate where ∠1 and ∠2 form a linear pair and m∠2 + m∠3 = 180

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Answer:

Below

Step-by-step explanation:

Due to the triangle side length rule, these two sides added together must be greater than the third side

so the third side could be     11   10   9      

         8 -7-6-5-4-3-2-1   will not work because 2 + these sidelengths do not sum to greater than  the third side 10

After dilation, the shape of the image and preimage will be same, but the size will be different

The dilation is the one form of transformation, that will change the size of the original figure, but the shape of the figure remains same

Consider a triangle and dilating the triangle by a scale factor of 3

The scale factor 3 means the size of the original image will enlarge by three times of the original size .

Still the shape of the triangle will be same, but the size of the triangle changed according to the dilation

Therefore, size of the image will change, but the shape will not change

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The shortest length possible in the given question is 4.0×[tex]10^{-10}[/tex] cm .

Distance is measured by length. The quantity of length has the dimension of distance in the International System of Quantities. Most measurement systems choose a base unit for length from which all other units are derived. The metre serves as the fundamental unit of length in the International System of Units.

Most people interpret length to mean an object's longest dimension. Nevertheless, depending on the object's position, this is not always the case.

There are several terms for the length of a fixed object, including height, which is also known as vertical length or vertical extent, and width, breadth, or depth. When a base exists from which vertical measurements can be taken, height is used.

Nanometer(nm)- In the International System of Units (SI), a nanometer (American spelling) is a unit of length that is equal to 1000 picometres and one billionth (short scale) of a meter (0.000000001 m).

now , for find the shortest length we can covert all the given units into centimeter,

1 pm = [tex](10)^{-10}[/tex] cm

1 nm = [tex](10)^{-7}[/tex] cm

1 m =  100 cm

we have , 400 pm = 4× [tex](10)^{-8}[/tex] cm

                4.0 nm  =  4 × [tex](10)^{-7}[/tex] cm

      4.0 x [tex](10)^{-4}[/tex]m = 4 × [tex](10)^{-2}[/tex] cm

and   4.0 x [tex](10)^{-10}[/tex] cm

hence , clearly it is shown that shortest length is 4.0 x [tex](10)^{-10}[/tex] cm .

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Answer:

Step-by-step explanation:

10% of $520 is $52, so that's what Oliver usually saves each week.

This week he earned 10% more, which is $52. $520 + $52 = $572

10% of $572 is $57.20

His pay minus his living expenses is $572 - 57.20

He has $514.80 to spend

Since 10% of $520 is $52 and that's what he usually saves, it looks like he just went with that instead of adding the $52 to the $520 and then deducting 10%

Answer:

90%

Step-by-step explanation:

Do 18 divided by 20 you get 0.9 which equals 90% since the 9 is in the tens place.

The size of a matrix is ​​its dimension,

AB and BA are of size 4 x 4 and 2 x 2 respectively

Matrix A has dimension 4 x 2 and matrix B has dimension 2 x 4

Matrix:

In mathematics, a matrix (multiple matrices) is a rectangular array or table of numbers, symbols, or formulas, arranged in rows and columns, used to represent mathematical objects or properties of such objects .

Product of Matrix:

Multiplication of two matrices is defined only if the number of columns in the left matrix equals the number of rows in the right matrix. If A is an m-by-n matrix and B is an n-by-p matrix, then its matrix product AB is an m-by-p matrix whose entries correspond to the corresponding rows of A in the matrices.

A column of B whenever a product of different sizes is such that it is defined.  The product AB can be defined without BA being defined. That is, if A and B are m-by-n and n-by-k matrices, respectively, and m ≠ k. In general, even if both products are defined, they need not be the same. So, AB ≠ BA,

Product AB:

The dimensions of AB are the rows of matrix A multiplied by the columns of matrix B.

Matrix A has 4 rows and Matrix B has 4 columns.

Therefore, the dimension of the matrix AB is 4 x 4.

Product BA:

The dimensions of matrix BA are the rows of matrix B multiplied by the columns of matrix A.

Matrix B has 2 rows and Matrix A has 2 columns.

Therefore the dimension of the matrix BA is 2 x 2.

Therefore, the sizes of AB and BA are 4 x 4 and 2 x 2 respectively.

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The slope-intercept form of the line is y = - 2x - 5.

What is the slope of a line?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the Δy and Δx coordinates, respectively. Consequently, it is possible to write the change in y coordinate with respect to the change in x coordinate as m = Δy/Δx.

Given that the slope of the line is -2.

The line passes through the point (2,-9).

The equation of line that passes through (x₁, y₁)  with slope m is

y - y₁ = m (x - x₁).

y - (-9) = -2(x -2)

y +9 = -2x + 4

y = -2x - 5

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the students that like music also like dance is 30%.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

40% of the students like music

12% of the students like music and dance.

p(A)=0.4

p(A∩B)=.12

p(A|B)= p(A∩B)/p(A)

=0.4/0.12= 0.3

Hence the students that like music also like dance is 30%.

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Synonym for the word split is given by many words like tear, to break apart,  bisect or divide it into parts and so.

Explanation:

Synonym of the given word split is given by:

Many words represents the synonym of the word split.

Therefore, the synonym of the given word split is given by cleave, tear, divide it into two equal parts.

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Answer:

C

Step-by-step explanation:

If they both ran a mile its the same thing I think