The perimeter of the triangle and the perimeter of the square are equal. Create and solve an equation to find the value of x.

Answer:

OptionB) \(5940\)

Step-by-step explanation:

Formula to Find the Interior Angles of Any Polygon

\((n-2)\)x\(180\)

\((35-2)X180\\5940\)

Answer:

The formula that calculates the sum of the interior angles of a regular polygon is equal to : (n-2)180° ; n represents the number of sides of the polygon.

So now, we've to replace n by 35 in the formula :

(35-2)180°

And by carrying out the calculation, we obtain: 5940°.

Therefore, the sum of all the interior angles of a regular 35-sided polygon is 5940°.

Answer:

The mode is 15

Step-by-step explanation:

The mode is the number which appears most often in a set of numbers. Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 (it occurs most often).

Answer:

The mode of this set is 15.

Step-by-step explanation:

the mode is 15 bcoz 15 is repeated two times where as other numbers aren't repeated..

Answer:

Step-by-step explanation:

It's given that a║b and m∠6 = 128°

Since, ∠1 and ∠3 are the consecutive interior angles,

m∠6 + m∠1 = 180°

128° + m∠1 = 180°

m∠1 = 180° - 128°

= 52°

Since, ∠6 and ∠3 are the corresponding angles,

Therefore, ∠6 ≅ ∠3

m∠3=52°

Answer:

33 i think

Step-by-step explanation:

The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters

What is measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.

Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.

Since we have 30 meters of fencing available, the total length of wire fencing used is:

L + 2W = 30 - W

Simplifying this equation, we get:

L = 30 - 3W

The area of the garden is:

A = LW

Substituting the expression for L from the previous equation, we get:

A = W(30 - 3W)

Expanding the expression, we get:

A = 30W - 3W²

To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:

dA/dW = 30 - 6W = 0

Solving for W, we get:

W = 5

Substituting this value back into the expression for L, we get:

L = 15

Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:

A = 5(15) = 75 square meters

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Answer: in the third draw 33.33% people eliminated.

Step-by-step explanation:

Answer:

a²/(b²ce^7)

Step-by-step explanation:

a^2b^-2c^-1 / e^7 =

= a²/(b²ce^7)

The number of strides the runner will make during 1 hour run will be =

10,800.

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

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The length of the parking lot will be 212 yards

From the question, we are to determine what the length of the parking lot needs to be

From the given information, we have that

"A rectangular-shaped parking lot is to have a perimeter of 546 yards"

and

"the width must be 61 yards"

From the formula for perimeter of a rectangle,

P = 2(l +w)

Where P is the perimeter

l is the length

and w is the width

From the given information,

P = 546 yards

w = 61 yards

Putting the parameters into the equation,

546 = 2(l + 61)

546 = 2l + 122

2l = 546 - 122

2l = 424

l = 424/2

l = 212 yards

Hence, the length of the parking lot will be 212 yards

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Answer:

21.44 All you need to do is divide the 2.68 by 2 then multiply it by 16

Step-by-step explanation:

To solve the problem, we'll use the information given to find the values of A and k in the equation T = 20 + Ae^(-kt), where T is the temperature in degrees Celsius at time t.

a. Finding the value of A:

We're given that the initial temperature of the tea was 70℃. Substituting this into the equation, we get:

70 = 20 + Ae^(0) (since e^0 = 1)

70 - 20 = A

A = 50

So the value of A is 50.

b. Finding the value of k:

We're told that it takes 4 minutes for the tea to decrease in temperature from 70℃ to 50℃. We can use this information to set up an equation and solve for k.

Substituting T = 70 and t = 4 into the equation, we have:

70 = 20 + 50e^(-4k)

Subtracting 20 from both sides:

50 = 50e^(-4k)

Dividing both sides by 50:

1 = e^(-4k)

Taking the natural logarithm (ln) of both sides:

ln(1) = ln(e^(-4k))

0 = -4k

Dividing both sides by -4:

0 = k

However, we need to check if this solution satisfies the condition for the tea to decrease in temperature from 70℃ to 50℃ in 4 minutes.

Substituting T = 50 and t = 4 into the equation, we have:

50 = 20 + 50e^(-4(0))

50 = 20 + 50e^0

50 = 20 + 50(1)

50 = 20 + 50

50 = 70

Since 50 is not equal to 70, the value of k = 0 does not satisfy the given condition.

Let's try another approach:

Substituting T = 50 and t = 4 into the equation, we have:

50 = 20 + 50e^(-4k)

Subtracting 20 from both sides:

30 = 50e^(-4k)

Dividing both sides by 50:

0.6 = e^(-4k)

Taking the natural logarithm (ln) of both sides:

ln(0.6) = ln(e^(-4k))

ln(0.6) = -4k ln(e)

ln(0.6) = -4k(1)

ln(0.6) = -4k

Simplifying further:

k = ln(0.6) / -4

Using a calculator or computer to evaluate ln(3/5) / -4, we get approximately:

k = ln(5/3) / 4

To recap:

a. The value of A is 50.

b. The value of k is approximately k = ln(5/3) / 4

.

Note: The calculations provided are based on the given information and assumptions. If there are any additional details or specific conditions provided, please let me know, and I'll be happy to assist you further.

Therefore, B's share is Rs. 30,000 and C's share is Rs. 40,000.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let the total sum of money be x.

Then, according to the given ratio, A's share is 2/9 of the total sum, so we have:

2/9 * x = 20000

Multiplying both sides by 9/2, we get:

x = 90000

Now, we can find the shares of B and C as follows:

B's share = 3/9 * 90000 = 30000

C's share = 4/9 * 90000 = 40000

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The required information, obtained by the analysis of the data in the question to create a frequency table,  are presented as follows;

2 a. Please find attached the frequency table created using MS Excel and MS Word

b. n = 20

3. a. n = 14

ΣX = 48

ΣX² = 190

A frequency table consists of two columns, including the value of a data point and the frequency of the value of a data points.

The data in the question table can be presented as follows;

2, 6, 4, 4, 3, 6, 7, 5, 4, 8, 4, 5, 8, 3, 5, 5, 7, 6, 1, 4

Sorting the numbers in an order of increasing value, we get;

1, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8

The above scores can therefore be arranged in a frequency distribution table as follows;

x   \({}\) f(x)   Proportion   Percentage

1   \({}\) 1       1/20 = 0.05     5%

2   \({}\) 1      1/20 = 0.05     5%

3   \({}\) 2     2/20 = 0.1        10%

4   \({}\) 5      5/20 = 0.25     25%

5   \({}\) 4      4/20 = 0.20     20%

6   \({}\) 3      3/20 = 0.15      15%

7   \({}\) 2      2/20 = 0.1         10%

8   \({}\) 2      2/20 = 0.1          10%

b. The variable n is the count of the set of data which can is obtained through counting the data points, therefore;

n = 20

3. a. The number of datapoints in the histogram is equivalent to the number of squares in the histogram, therefore;

n = 14

b. ∑X is the sum of the x-values in the set of data

The x-values in the dataset includes; 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6

Therefore; ∑X = 1 + 2 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 5 + 5 + 6 = 48

∑X = 48

c. The value of ∑X², can be obtained by finding the sum of the squares of the x-values as follows;

∑X² = 1² + 2² + 2² + 2² + 3² + 3² + 3² + 4² + 4² + 4² + 4² + 5² + 5² + 6² = 190

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i had to do the answer as a pic cuz my iPad is gonna die.

sorry <:)

Answer:

Step-by-step explanation:

x = - 23

y = - 5

z = - 10

(x - 12)/(y+z)=

(-23 - 12)/(-5-10)=

45/15=

7/3

Answer:

y = (-1/3)x + 2

Step-by-step explanation:

Equation of line in slope-intercept form is given by

y = mx +c

where m is the slope of line

c is y intercept

Slope of line having points (x1, y1) and (x2,y2) is given by (y2-y1)/(x2-x1)

_________________________________________________

let the equation of required line be y = mx +c

Since points given are  (3,1) and (-6,4)

Then, its slope is

m = 4-1/-6-3 = 3/-9 = -1/3

Thus, slope of line is m = -1/3

lets use m = -1/3 in place of m in equation y = mx +c

y = (-1/3)x + c

Since points   (3,1) and (-6,4) lie on y = (-1/3)x + c , it should satisfy the this equation.

hence lets plug 3 in place of x and 1 in place of y

1 =  (-1/3)3 + c

=> 1 = -1 + c

=> c = 1 +1 = 2

Thus, intercept is 2.

Thus, Equation of line in slope-intercept form is y = (-1/3)x + 2.

The required two column proof is explained below.

A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.

The two column proof for the information is given as:

M is the midpoint of CD    (Given)

CD = CM + MD   (addition property of a line segment)

CM = MD  (definition of a midpoint)

So that;

5x – 2 = 3x + 2    (Definition of midpoint)#

Then,

5x - 3x = 2 + 2 (collecting like terms)

2x = 4

x = 2

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The range of the given equation is [-1, infinity).

We are given that;

Equation  y= underroot(x+5​)

Now,

The domain of this equation is the set of x values that make the expression under the square root non-negative.

That is, x+5 >= 0, or x >= -5. So the domain is [-5, infinity).

The range of this equation is the set of y values that are obtained by plugging in the domain values into the equation. Since the square root function is always non-negative, and we are subtracting 1 from it, the smallest possible value of y is -1, when x = -5. As x increases, y also increases, and there is no upper bound for y.

Therefore, by the range the answer will be [-1, infinity).

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Answer:

Everyone likes a subject so 0 students like none.

15+10+20+5=50

Answer:

43 messages

Step-by-step explanation:

Given:

146 messages = $21.90

x messages = $6.45

Finding x by cross-multiplication:

x = 146*6.45/21.90 = 43

Hope this helps! :)

An example of a literal equation is ax - by = k. Option D

A literal equation is simply defined as any equation with two or more variables.

A literal equation, in contrast to a regular equation, allows you to solve for a single variable in terms of the others.

To determine the variable that is needed, the equation must be algebraically modified.

Literal equations are also frequently employed in a variety of scientific and mathematical disciplines.

From the information given, we have that;

ax - by = k is a literal equation

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The solution to the given expression by using distributive law is 114

The distributive property posits that an expression that is provided in the form of A (B + C) can be further expressed as A × (B + C) = AB + AC. This distributive law is also useful for subtraction and is expressed as, A (B - C) = AB - AC. This implies that operand A is distributed between the other two operands.

From the given information, we are to expand 19 × 6 using the distributive law. The first step would be to expand 19 into two integers.

Let the two integers be 10 and 9.

So, we can have can express this by using the addition distributive law: A(B+ C)

Mathematically, we have:

= 6(10 + 9)

= 6(19)

= 114

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The odds of drawing a 9 card or a black card from a standard 52- card deck is \(\frac{7}{13}\)

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

A regular deck of cards contains 4 nines, therefore P(A) = \(\frac{4}{52}\)

In a typical deck of cards, there are 26 black cards, hence P(B) = \(\frac{26}{52}\).

When a card is both a 9 and black, there is overlap between the two events. Since there are only two such cards in a typical deck of cards, P(A and B) = \(\frac{2}{52}\).

Using the P-formula (A or B),

P(A or B) = P(A) + P(B) (A and B)

P(A or B) = \(\frac{4}{52}+ \frac{26}{52} -\frac{2}{52}\)

P(A or B) = \(\frac{28}{52} =\frac{7}{13}\)

Therefore, the odds of drawing a 9 or a black card is \(\frac{7}{13}\)

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Answer:

1≠0.346485

Step-by-step explanation:

The relationship in the figure is a function because each input has only one output to which they are linked

A function is a definition or rule that maps each element in a set of input values to exactly one element in a set output values.

The data in the sets can be presented as follows;

x  \({}\)               f(x)

-1 \({}\)      →         2

0\({}\)        →        2

1\({}\)         →        -3

2\({}\)         →       -2

8\({}\)         →        3

The above table indicates that each x-value has only one f(x) value, which indicates that the relationship s a function. The relationship is still a function with the presence of an f(x) value, 2, having two x values, -1 and 0, as the condition satisfies the definition of a function.

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Answer with explanation:

A x% confidence interval interprets the percentage of certainty that a person can believe that the true population parameter.

It is also represented as Point estimate ± Margin of error

Confidence level is proportional to the Margin of error.

Answer:

m∠T = 72°

m∠U = 54°

Step-by-step explanation:

Property of an isosceles triangle,

Opposite angles of two equal sides of an isosceles triangle are equal in measure.

By this property, in the given triangle STU,

Since, ST ≅ TU,

m∠S = m∠U = 54°

Since, sum of interior angles of a triangle is 180°

m∠T + m∠S + m∠U = 180°

m∠T + 54° + 54° = 180°

m∠T = 180° - 108°

m∠T = 72°

Answer:

x=0

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

10(x−2)=−20

(10)(x)+(10)(−2)=−20(Distribute)

10x+−20=−20

10x−20=−20

Step 2: Add 20 to both sides.

10x−20+20=−20+20

10x=0

Step 3: Divide both sides by 10.

10x/10 = 0/10

Answer:

x=0

Step-by-step explanation:

0-2= -2

So

10 x -2= -20

Hope that helped.

The minimum number of aunts that Shamar must have based on the information provided is 10.

It is known that uncles will take a photograph in groups of 10, while aunts will take a photograph in groups of 5. Based on this, the possible number for each are:

Uncles: 10, 20, 30, 40, 50

Aunts: 5, 10, 15, 20, 25

In this case, the minimum number is the LCM or Least Common Multiple and based on the previous list, this number is 10.

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