What is the height of a triangle of area 67.2 cm² and the corresponding base 16cm?​

Answer:

x+6+x-y = 2x-y+6

Step-by-step explanation:

Darren's salary will be $102,724.24 in 9 years.

Annual salary can be defined as the amount of money a company pays you in exchange for the job you do during the year.

We can calculate Darren's salary in 9 years by multiplying his current salary by (1 + 5.5%) raised to the power of 9.

The formula would look like this:

Salary in 9 years = $66,648 * (1 + 0.055)^9

Plugging in the numbers and using a calculator, we get:

Salary in 9 years = $66,648 * 1.55946429

Salary in 9 years = $102,724.24

So, Darren's salary will be $102,724.24 in 9 years.

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If the stadium parking lot holds 20,000 cars and lisa prints 240,000 passes then 12 home games are scheduled next month.

Given that Lisa prints parking passes for the baseball stadium a month in advance the stadium parking lot holds 20,000 cars.
Lisa prints 240,00 passes,

We have to find the number of  home games are scheduled next month.

To find this we have to division of 240000 by 20000
240000/20000 = 12
Divide Two lakh forty thousand by twenty thousand we get twelve.

By means of division we get 12 Hence, 12 mant home games are scheduled next month

A division is a process of splitting a specific amount into equal parts.

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Answer:−2π, -6.25, 67/10, 3√5, 6 3/4

Step-by-step explanation: Search math w ay on the internet for any further math questions :)

In the expression "3(x+2)," there is only one variable, "x." There are two factors in this expression: "3" and "(x + 2)." The "3" is performing multiplication , so it is multiplying the expression "(x + 2)" by 3, the answer is product.

In mathematics, a variable is a symbol that represents a value that can change or vary. Variables are often used in mathematical equations and formulas to represent unknown or unspecified values.

A factor is an element in a mathematical expression that is being multiplied by another element In general, a mathematical expression can have multiple factors. The factors of a polynomial are the terms that are being multiplied together to form the polynomial.

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Answer:

p = 975

Step-by-step explanation:

Divide both sides by 25

 25 (p - 949)

-------------------- = 650/25

         25

Then Simplify

p - 949 = 26

Move 949 to the right side

And For your answer you will get:

p = 975 (sorry if i got it wrong)

An expression for the amount of money Dominick has received from his grandfather and mother after m months is 300 + 75m + 40(m - 3).

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given that,

Dominick’s grandfather gave him $300 to start his college savings account.

There will be 300 in the expression.

Dominick’s grandfather also gives him $75 each month to add to the account.

So after m months, total amount that grandfather gave = 75m

Dominick’s mother gives him $40 each month, but has been doing so for 3 fewer months than Dominick’s grandfather.

After m months, Dominick's mother would be giving $40 for (m - 3) months

Total amount that the mother gave after m months = 40(m - 3)

Total amount in the account after m months can be expressed as,

300 + 75m + 40(m - 3)

Hence the required expression is 300 + 75m + 40(m - 3).

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Answer:

899

Create a divison

17÷9=12

1222

7888

909

6762

177÷12×22+22

Note that the step that is not involved in graphing a logarithmic function is: "Switch the order of the x and y values in the ordered pairs." (Option A)

With regard to the graphing problem above, note that switching the order of the x and y values in an ordered pair is not a step in graphing a logarithmic function because it is not a necessary or relevant step in the process.

To graph a logarithmic function, one typically follows the steps of creating a table of values, plotting the points, and then drawing a line of best fit to show the graph. The order of the x and y values in the ordered pair remains unchanged in this process.

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The type of measurement scale is interval. A quantitative measuring scale with order, meaningful and equal differences between the two variables, and arbitrary zero presence is known as an interval scale.

In mathematics, an interval is quantified in terms of numbers. Every number between two specific integers is considered to be an interval. Between those two values, this range encompasses all real numbers. Real numbers can be of any type you can imagine. A fourth is a musical interval that spans four staff positions in Western music notation, and a perfect fourth is one that spans five semitones. The interval can be calculated by counting both the lines or spaces that the two notes are on as well as all the lines or spaces in between. A third of a second separates B from D. A sixth space separates A from F.

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Each athlete receives about 0.95 liters of sports drinks.

In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.

For example 4/2 = 2

To find out how much sports drink each player receives, we need to divide the total amount of sports drinks by the number of players.

20.9 liters ÷ 22 players

Apply the division operation, and we get

= 0.95 liters per player

So, each player receives approximately 0.95 liters of sports drinks. To the nearest hundredth, this is 0.95 liters.

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The coordinates of the other endpoint include the following: C. (32.5, 47.7).

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and then divide by two (2):

Midpoint BC = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Next, we would determine the coordinate of B with midpoint AB at (25.4, 60.1) as follows;

25.4 = (18.3 + x₂)/2

50.8 = 18.3 + x₂

x₂ = 50.8 - 18.3

x₂ = 32.5.

For the other co-ordinate of B on line segment BC, we have:

60.1 = (72.5 + y₂)/2

120.2 = 72.5 + y₂

y₂ = 120.2 - 72.5

y₂ = 47.7.

Therefore, the coordinate of B is (32.5, 47.7).

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It will cost you to have all the dirt hauled away [tex]6.43*10^{4}[/tex]

A COST Action is an interdisciplinary research network that unites scientists and entrepreneurs to study a subject of their choice for four years. SMEs, public institutions, academic researchers, and other pertinent entities or interested parties often make up COST Actions. The cost is the total amount of money spent by a company on the creation or production of goods or services. The markup for profit is excluded. The sum of money spent to create a good or product, as seen from the seller's perspective, is the cost. The expense incurred for manufacturing a good or rendering a service that is made available by a business is often referred to as the cost. The customer's willingness to pay determines the price of a good or service.

Based on the given condition,

Formulate

[tex]20*6*30*18[/tex]

Calculate the product or quotient

[tex]120*30*18=64800[/tex]

Simplify.

[tex]6.43*10^{4}[/tex]

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The solution is Option C.

The measures of the legs of the isosceles trapezoid is given by the proportion equation L₂ = 15.5 inches

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the measure of legs of PQRS trapezoid be L₂

Let the first trapezoid be represented as T₁ = ABCD

The measure of the legs of T₁ = L₁

And , Let the second trapezoid be represented as T₂ = PQRS

The measure of the legs of T₂ = L₂

The perimeter of T₁ = 72.8 inches

The perimeter of T₂ = 91 inches

The measure of L₁ = 12.4 inches

Now , the two trapezoids are similar

So , measure of L₁ / perimeter of T₁ = measure of L₂ / perimeter of T₂

Substituting the values in the equation , we get

( 12.4 / 72.8 ) = L₂ / 91

Multiply by 91 on both sides of the equation , we get

The measure of L₂ = ( 12.4 x 91 ) / 72.8

The measure of L₂ = 15.5 inches

Hence , the measure of legs of trapezoid is 15.5 inches

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Y = (1/6)*e^5t  is  differential equation .

What exactly does differential equation mean?

An equation that connects one or more unknown functions and their derivatives is known as a differential equation in mathematics.  

                                     Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to define a relationship between the two.

y′′−9y′+26y=e^(5t)

The characteristice equation of the differential equation is : r^2 -9r +26 =0

On solving we get the values of r=4.5 + 2.34i (z1) ,  4.5 - 2.4i(z2)--- (complex roots)

homogeneous solution is: yh = c1e^z1t + c2e^z2t

Plug  Y = Ae^5t in the ODE:

=   25Ae^5t -9*5Ae^5t +26Ae^5t =e^(5t)

25A -45A +26A =1 ;  6A = 1; A =1/6

Y = c1e^z1t + c2e^z2t  is a general solution but we wnata particular solution

So, simply Y = (1/6)*e^5t

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Number of bacteria that would be in a sample weighing 24 grams is,

⇒ 1.296 × 10¹⁰

Scientific notation is a way of writing a very large or very small numbers. For example; 230,000,000 can be written in scientific notation as 2.3 x 10⁸.

We have to given that;

There are 5.4 x 10⁷ bacteria are measured to be in a dirt sample that weighs 1 gram.

Hence, Number of bacteria that would be in a sample weighing 24 grams is,

⇒ 24 × 5.4 × 10⁷

⇒ 129.6 × 10⁷

⇒ 1.296 × 10¹⁰

Thus, Number of bacteria that would be in a sample weighing 24 grams is,

⇒ 1.296 × 10¹⁰

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Answer:

The Isosceles Base Angles Theorem states that if two sides of a triangle are equal, then the angles opposite to those sides are equal.

Given: GB = GD

Since GB = GD, triangle ZDGB is isosceles.

By definition of bisects, GU bisects ZDGB.

By the Angle Bisector Theorem, ZG/ZU = GD/GU.

Because GB = GD, ZG = ZU.

By substitution, ZG/ZU = ZG/ZU. Hence, ZB = ZD.

Therefore, ZB ZD, which proves the Isosceles Base Angles Theorem.

The value of x in the first figure is 10

The value of x in the second figure is 12

In the first figure the value of x is solved using the concept of angels on a straight line which  is 180 degrees

Therefore,

6x - 10 + 4x + 6 + 7x + 14 = 180

collecting like terms

6x + 4x + 7x + 6  + 14 - 10  = 180

17x + 10 = 180

17x = 180 - 10

17x = 170

x = 10

The second figure is solved using alternate interior angles

4x + 10 = 58

solving for x

4x = 58 - 10

4x = 48

x = 12

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An octagon is a two-dimensional shape with eight sides, the degree measure of the largest interior angle of the octagon.

Each pair of opposite sides of the octagon are parallel. We can use the formula to determine the degree measure of the largest interior angle of the octagon.

The formula used is: 180(n-2)/n, where n represents the number of sides in the shape. In this case, n is 8, so the equation would be: 180(8-2)/8, which would give us the result of 160.

Therefore, the degree measure of the largest interior angle of the octagon is 160 degrees. This can also be calculated by adding up the internal angles of the octagon, as each interior angle is equal to 360 divided by the number of sides, in this case 8. 360/8 = 45, so 8x45 = 360. If we add all the angles together (4x45 + 3x45 + 3x45) we get 360, which is equal to the degree measure of the largest interior angle of the octagon.

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It is important to remember that model selection and improvement is an iterative process and may require trying several different approaches before arriving at the best solution.

A high R^2 value of 1 on the training data and a low R^2 value of 0 on the validation data suggests that the model is overfitting. Overfitting occurs when a model is too complex and has learned the training data too well, but has poor generalization performance on new, unseen data (validation data in this case).

To address this issue, you can try the following:

Reduce the amount of features in the model or regularise it to restrict the size of the coefficients.

Increase the size of the training dataset: A bigger training dataset may provide the model a better grasp of the link between the features and the target variable.

Cross-validation: Use cross-validation techniques to better estimate the model's performance on fresh data.

Attempt a different model: A other model may be more appropriate for the problem and data.

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Therefore , the solution of the given problem of expression comes out to be the 8 expressions are given below.

Addition, multiplication, division, and other mathematical operations are required. When combined, they produce the following: A mathematical operator, some data, and an equation A statement of fact contains values, parameters, and operations like additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various phrases and words.

Here,

Given :

Original expression of eight terms including 3 operations are:

=> 10*2-10 =10

=> 100 * 2 -100 = 100

=> 50/2 - 10 = 15

=> 400/2 - 100 + 100 = 200

=> 500 - 100 + 200 = 600

=> 10/2 - 5=0

=> 6 * 10 - 8 = 52

=> 10*8 - 8 =72

Therefore , the solution of the given problem of expression comes out to be the 8 expressions are given below.

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The y intercept is $25000, the percentage loss is 10% and the decay factor is 0.9

An equation is a mathematical expression that contains two or more numbers and variables linked together by mathematical operations such as exponents, multiplication, division, addition, subtraction and so on.

The standard form of an exponential function is:

y = abˣ

where a is the initial value and b is the multiplication factor.

Let y represent the cost of a van after x years. It is given by:

y = 25000(0.9)ˣ

hence, comparing gives a = 25000, b = 0.9

a) The y intercept is $25000

b) Percentage loss = 1 - 0.9 = 0.1 = 10%

b) Decay factor = b = 0.9

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The total number of samples in the sample space is 15,504.

The total number of samples in the sample space can be calculated by using the formula for combinations, which is the number of ways to select r items from n distinct objects. The formula is written as nCr and is calculated as n!/(r!(n-r)!). In this case, n is equal to 60, and r is equal to 4.

To calculate the total number of samples in the sample space, we will first calculate n!, which is 60! = 60*59*58*57*...*2*1. Then, we will calculate r! which is 4!, which is 4*3*2*1. Finally, we will calculate (n-r)!, which is (60-4)!, which is [tex]56! = 56*55*54*53*...*2*1.[/tex]

Using the formula, the total number of samples in the sample space is calculated as 60!/(4!(60-4)!) = 60!/(4!*56!) = 15,504. Therefore, the total number of samples in the sample space is 15,504.

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The dimensions of the sides DH, VW, and WX are, respectively, 14, 12, and 30.

Two figures are known to be similar if the ratio of their similar sides is equal to a constant.

From the polygons given, the following expressions are true;

DH/12 = 21/18

18DH = 12 × 21

18DH = 252

DH = 14

Similarly:

VW/14 = 18/21

21VW = 14 * 18

21VW = 252

VW = 12

Also;

35/WX = 21/18

21WX = 35 * 18

21WX = 630

WX = 30

Therefore the measure of the sides DH, VW and WX are 14, 12 and 30 respectively.

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Answer:

0.238

Step-by-step explanation:

Make any multiplication or division from left to right:

[tex]\frac{2}{7} - \frac{1}{21}[/tex]

0.286 - [tex]\frac{1}{21}[/tex]

0.286 - 0.048

Calculate:

0.286 - 0.048 =

0.238

Hope it helps

Subtraction is what difference means.

Therefore, the fractional difference between 2/7 and 1/21 is 5/21

0.238 in decimal form.

21 is the least common multiple between 7 and 72. (LCM). Divide the numerator and denominator of each fraction by the number that will bring the denominator of each fraction to the LCM:

2/7-1/21 = 2*3/7*3 - 1/21

Subtract the numerators such that the fractions have like denominators now:

6/21 - 1/21 = 6 - 1/21 = 5/21

Consequently, the outcome is

2/7 - 1/21 = 5/21

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The probability of the sum of the upturned faces equal to 7 is Decimal answer is 0.1666667  and rounding to the hundredths place is 16.6%.

There are 66=36 potential pairs of die rolls because the two are independent of one another. Only the following pairs of rolls total seven out of those. (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). The probability of our two die rolls adding up to 7 would then obviously be: 6 ÷ 36 = 1 ÷ 6 = 0.1666667  rounding to the hundredths place = 16.6%. Probability is simply the possibility that something will happen. When we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several.

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Answer:

x = 0.37686455

Step-by-step explanation:

Answer: x≈0.37686455

Step-by-step explanation: