2. What is the area of a triangle whose vertices are

a. What is the formula for the area of the triangle?


b. Find the length of the base. Round to the nearest tenth if needed.




c. Find the length of the height. Round to the nearest tenth if needed.




d. Find the area of the triangle.

The result in the form of a mixed number if we multiply the numerator of the complex fraction in part D by the reciprocal that you found in part E is  8[tex]\frac{1}{4}[/tex].

A whole number and a legal fraction are both expressed together as a mixed number. A number between any two whole numbers is typically represented by it. An integer (whole number) plus a correct fraction together make up a mixed number, also known as a mixed fraction (a fraction whose numerator is less than its denominator).

Pretzels, peanuts, Cheerios, and of course rice and corn Chex are all included in this mix, which is why it is called a mix. It is possible for a number to contain both an integer and a fraction. As a result of combining these two sorts of numbers, they are known as "mixed numbers."

PART D:

(33/8)/(11/4)

Reciprocal of PART E is:

11/4

Therefore, multiplying it with PART D, we get:

=((33/8)/(11/4))×(11/4)

=(33/8)×(4/11)×(11/4)

=33/8

=8[tex]\frac{1}{4}[/tex]

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The person can buy a total of 36 distinct systems from three models of the basic unit, three models of keyboard, and four models of printer.

Given, a person buying a personal computer system is offered a choice of three models of the basic unit, three models of keyboard, and four models of printer.

we have to find the number of distinct systems that can be purchased.

Using the concept of Permutations and Combinations, we get

Choose One model of basic unit from three models, Choose one model of keyboard from three models of keyboards and also choose one model of printer from four models of printers.

C(3 , 1)×C(3 , 1)×C(4 , 1)

= 3×3×4

= 36

So, the total of 36 systems can be purchased.

Hence, the total of 36 systems can be purchased.

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The equation which shows the correct way to find the product out of the exponents is (A) (y∧a)∧b=y∧a⋅b.

The way of representing huge numbers in terms of powers is known as an exponent.

Exponent, then, is the number of times a number has been multiplied by itself.

For instance, the number 6 is multiplied by itself four times, yielding 6 * 6  * 6 * 6.

We can write this as 64. Here, 4 is the exponent, and 6 is the base.

So, multiply the exponents to find the product as follows:

(W^c)^d = W^c•d (RULE)
So, we will  have:

(y∧a)∧b=y∧a⋅b

Therefore, the equation which shows the correct way to find the product out of the exponents is (A) (y∧a)∧b=y∧a⋅b.

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Correct question:
Which equation shows that you can find the power of power by finding the product of the exponents?

clear check

a. (y∧a)∧b=y∧a⋅b

b. (ya)∧b=ya∧b

c. (y∧a)b=ya∧b

d. (y∧a)∧b=ya ⋅ b

Step-by-step explanation:

This is the answer for 1., but the steps are the same for the rest of the questions, so I am sure you will be able to get the rest!

Slope is the value in front of the X and basically tells us how far up or down the line moves in 1 square across the line. It goes up if it is positive, and down if it is negative.

Y-intercepts can be found by plugging in 0 for x.

For question 1:

y=[tex]\frac{3}{5}[/tex](0)+3=3 so the y-intercept is 3 up from 0.

Then, we can use our slope which is a fraction, the top can be thought of as rise and the bottom is run. This means each point will be 3 up and 5 to the right.

Answer:

2/ Points at (0,-5), ( 1,-4), (2,-3)

Step-by-step explanation:

The slope is rise/run

The slope is x, which mean = 1

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The component that is missing from the biologist's process is: c. The biologist did not randomly assign the each of the bats to the treatment groups.

When we carry out a research study that has  created groups that you want to study, then the differences between and within groups can be thoroughly checked to make sure that they are not systematic when subjects are randomly assigned to groups.

Therefore this random assignment of subjects, gives the researcher the confidence that groups are the same in terms of variables, and any differences can be confidently allocated to experimental treatments.

Therefore, we can conclude that the component that is missing from the biologist's process is given in option C because the biologist did not randomly assign the each of the bats to the treatment groups.

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For the given log function, the value of y is 8.

An exponent is a logarithm. In logarithmic form, any exponential expression can be rewritten.

Here given, log function :

Log 5 + Log y = Log 40

Can be also written as,

Log y = Log 40 - Log 5  => (eq1)

Based on log property we know that,

Log m - Log n = Log

That is,

Log 40 - Log 5 = Log

Also be written as,

Log 40 - Log 5 = Log 8   => (eq2)

By solving eq1 and eq2, we get,

Log y = Log 8

∴  y = 8

Therefore, The value of will be y = 8

Hence by solving  Log 5 + Log y = Log 40 , the value of y is 8.

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Value of y is 8.

What is a logarithmic equation?

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 is equal to 10³, its logarithm in base 10 is 3, or log₁₀ (1000) = 3. When there is no possibility of mistake or when the base is irrelevant, as in big O notation, the logarithm of x to base a is written as logₐ (x), logₐ x, or even without the explicit base, log x.

Given, the equation is log5 + logy = log40

log 40 can be written as log (5*8)

According to the logarithmic equation of log ab = log a + log b

Thus log 40 = log 5 + log 8

Now, the expression becomes

log5 + logy = log 5 + log 8

⇒ log y = log 8

⇒ y = 8

Thus, value of y is 8.

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The chi-square goodness-of-fit test is a statistical test that is used to determine whether a sample comes from a population with a specific distribution. There are a few conditions that must be met in order to use this test:

1. The data must be collected from a random sample. This ensures that the sample is representative of the population, which is necessary for the test to be valid.

2. The data must be categorical. This means that the observations must fall into distinct categories, rather than being continuous or ordinal.

3. The expected frequencies for each category should be at least 5. This ensures that the chi-square test statistic is approximately normally distributed, which is necessary for the test to be valid.

4. The data must be independent. This means that the outcome of one observation should not influence the outcome of another observation.

If these conditions are not met, the chi-square goodness-of-fit test may not be appropriate. In such cases, it may be necessary to use a different statistical test.

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The required straight equation will be y = -0.5x + 27.5 passes through the points  (-5, 0) and (5, 2).

What are equations in a straight line?

A straight line's equation is given by y=mx+c, where c is the height at which the line intersects the y-axis (often referred to as the y-intercept) and m is the gradient.

According to the given graph,

We can see two points are (-5, 0) and (5, 2)

The linear equation will be: y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Here

x₁ = -5, y₁ = 0

x₂ = 5, y₂ = 2

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]

Substitute values in the equation, we get

⇒ y - 0 = (2 - 0)/(8-4)(x-(-5))

⇒ y - 30 = (2)/(-4)(x + 5)

⇒ y - 30 = -1/2(x + 5)

⇒ y = (-1/2)x - 5/2 + 30

⇒ y = -0.5x + 27.5

Thus, the required equation will be y = -0.5x + 27.5 passes through the points  (-5, 0) and (5, 2).

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Write an equation for the graph shown in the form y=ax+b.

Answer:

Around 3000 BC

Answer:

It is difficult to pinpoint a specific year or time period in which math was "invented," as math is a fundamental aspect of human thought and has likely been present in some form since ancient times.

The study of mathematics has a long and rich history, dating back to ancient civilizations in Mesopotamia, Egypt, Greece, and India. These early societies developed mathematical concepts and techniques to aid in practical tasks such as measuring land, calculating the volume of objects, and tracking the movement of celestial bodies.

As human civilizations developed and advanced, so too did the study of mathematics. Over time, new mathematical concepts and techniques were developed and refined, leading to the development of more advanced branches of mathematics such as algebra, geometry, trigonometry, and calculus.

In summary, math has a long and complex history, and it is difficult to pinpoint a specific year or time period in which it was "invented." It has likely been present in some form since ancient times and has evolved and developed over the course of human history.

Step-by-step explanation:

SELF EXPLANATORY

The Probability that the sock is black or gray is

What is Probability?

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.

Total number of socks in a bag = 7+3+1 =11

so total number of outcomes possible = 11

The chance that black or gray will occur, resulting in a greater number of favorable outcomes

Number of favourable outcome will be -

Number of Black sock + Number of gray sock

=7+1

=8

Therefore probability (P) will be 8/11

=0.7272

and individual probability of coming black and gray sock will be

Probability for black socks is 7/11

Probability for gray socks is 1/11

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Answer:

147+64=c

Step-by-step explanation:

you would add the two numbers together to get the original.

The tangent theta is a Trigonometric function, the simplified value of 1 + tan²θ is sec²θ.

Trigonometric functions are also called circular functions. They are easily defined as functions of triangle angles. This means that the relationships between the angles and sides of triangles are given by these trigonometric functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant. Also read the triangle identity here.

We have given an expression, 1 + tan²θ

we know that , tanθ = sinθ /cosθ

sin²θ + cos²θ =1 and 1/cosθ = secθ

Now, 1 + tan²θ = 1 + sin²θ/cos²θ

taking LCM cos²θ

=> 1 + tan²θ = (cos²θ + sin²θ )/cos²θ

=> 1 + tan²θ = 1/cos²θ

=> 1 + tan²θ = sec²θ

Hence, the required expression is sec²θ.

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The measure of angle EBF is 40 degrees

The complete question is added at the end of this solution

From the question, we have the following parameters that can be used in our computation:

EBF = 6x + 4

CBF = 7x - 2

Also from the question, we understand that the measures of angle EBF and the measure of angle CBF are congruent

This can be represented mathematically as follows

EBF = CBF

Substitute the known values in the above equation, so, we have the following representation

6x + 4 = 7x - 2

Multiply through by 1

6x + 4 = 7x - 2

Collect the like terms

7x - 6x = 4 + 2

Evaluate the like terms

x = 6

Recall that

EBF = 6x + 4

Substitute the known values in the above equation, so, we have the following representation

EBF = 6 x 6 + 4

Evaluate

EBF = 40

Hence, the measure is 40 degrees

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Complete question

If the measures of angle EBF and the measure of angle CBF are congruent and EBF = 6x+4 and CBF = 7x-2 find EBF

A test's large p-value does not necessarily mean that the null hypothesis should be accepted.

In a test, a low P-value will favor rejecting the null hypothesis.

The P-value approach evaluates whether something is "likely" or "unlikely," assuming that the null hypothesis is correct, by calculating the probability of observing a test statistic that is more extreme in the direction of the alternative hypothesis than the one actually seen. If the P-value is low, such as less than, it is "unlikely" (or equal to) α.

The null hypothesis is disregarded in favor of the alternative hypothesis if the P-value is less than (or equal to) α. Additionally, the null hypothesis is not disproved if the P-value is higher than α.

As a result, the right response is false.

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When a store is offering a 30% discount on all jeans. If the regular price of a pair of jeans is $49.99, then the sale price of the jeans after discount will be $34.99 per pair.

The computation of the discounted price or the actual sales price of the jeans after applying the given discount can be calculated using the generalized formula, and putting the values of the provided information, as below,

Sale Price = Regular Price – Discount Rate

Sale Price = 49.99 – 30%

Sale Price = 49.99–14.97

Sale Price = $34.99

Therefore, the actual sales price of the pair of jeans will be $34.99.

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In 12 years the two trees will be at the same height of 120 inches for the given condition of the equation.

What is an equation?

A mathematical statement called an equation demonstrates the equality of two mathematical expressions.

Based on the given condition of a question,

Let X be the required time duration, and then the equation will be

or, (48+6X)=(72+4X)

or, 48+6X=72+4X

or, 6X-4X=72-48

or, 2X=24

or, X=24/2

or, X=12 year

And height = 48 + 6*12 = 48 + 72 = 120 inches

Hence, In 12 years the two trees will be at the same height of 120 inches.

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Answer:

8−72+12−8

Step-by-step explanation:

The probability that both switches are defective is 1%.

What is a probability answer?

Mathematics' branch of probability, where probability is the likelihood that any event will occur, deals with the occurrence of random events.                      

                            Probability values range from 0 to 1, with 1 being the most likely value.

Given that a shipment contains 10,000 switches, and of these, 1000 are bad, and an inspector draws 2 switches at random, one after the other, to find the probability that both switches are defective the following calculation must be performed:

1000/10000 = 1/10

1/10 x 1/10 = X

0.1 x 0.1 = X

0.01 = X

0.01 x 100 = 1

Therefore, the probability that both switches are defective is 1%.

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The complete question is -

Inspecting switches A shipment contains 10,000 switches. Of these, 1000 are bad. An inspector draws 2 switches at random, one after the other.A) Draw a tree diagram that shows the sample space of this chance process.B) Find the probability that both switches are defective.

Linear equations are equations with a leading degree of 1. This shows that there is no solution since 4 =7 is a false statement .

What are linear equations ?

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Solving linear equation

Linear equations are equations with a leading degree of 1. Given the linear equation

Given

13+4x-9=7x+7-3x

Simplify

4 + 4x = 4x + 7

Collect the like terms

4x - 4x = 7 - 4

0x = 3

This shows that there is no solution since 4 =7 is a false statement

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Answer:

you remember vertex: h,k in (x-h)²+k..

replace in that. In that graph vertex: (10, -20)

So in that Equation, a(x-10)²-20, a<0 since it is maximum graph.

I cannot find the full Equation but from what I can see you can find h,k and the fact that a<0

The equation of the circle in general form is x² + y² - 2 · x - 2 · y - 8 = 0.

In this problem we need to derive the equation of a circle that contains three points: (x₁, y₁) = (- 2, 2), (x₂, y₂) = (2, 4), (x₃, y₃) = (4, 0). The general form of the equation of the circle is a second order polynomial of the form:

x² + y² + B · x + C · y + D = 0

Where B, C, D are real coefficients.

First, use the points to generate a system of linear equations:

- 2 · B + 2 · C + D = - 8

2 · B + 4 · C + D = - 20

4 · B + D = - 16

Second, resolve the system by means of numerical methods:

(B, C, D) = (- 2, - 2, - 8)

Third, write the general form of the equation is:

x² + y² - 2 · x - 2 · y - 8 = 0

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Answer:

brawl

Step-by-step explanation:

(C) F = (2, -4) are the coordinates of the pre-image of F'.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

So, the result of reflecting Figure ABCDEF across y = -x is A'B'C'D'E'F'.

The transformational rule is:

(x, y) ⇒ (-y, -x)

Which means:

(x, y) ⇒ (-y, -x)  ⇒ (4, -2)

In contrast:

-y = 4

-x = -2

Solving for x and y as follows:

y = -4

x = 2

Therefore, (C) F = (2, -4) are the coordinates of the pre-image of F'.

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Complete question:
Figure ABCDEF was reflected across the line y = –x to create figure A'B'C'D'E'F'.

On a coordinate plane, a 6-sided figure has points A prime (negative 2, negative 2), B prime (negative 4, 2), C prime (negative 2, 6), D prime (4, 6), E prime (6, 2), and F prime (4, negative 2).

What are the coordinates of the pre-image of F'?

a. (–2, 4)

b. (4, 2)

c. (2, –4)

d. (–4, –2)

The congruency of a triangle is not determined by SSA. As a result, choice C is the right response.

What is a triangle and the response?

Triangles are a particular kind of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here.

                    Three-sided polygons include triangles. Three triangle angles added together equal 180 degrees.

The sides (S) and angles (A) of two triangles are said to be congruent if they are equal.

The triangle must meet the SAS, ASA, SSS, and RHS criteria in order to be congruent.

The congruency of a triangle is not determined by SSA. As a result, choice C is the right response.

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The value of n that makes a system of equations with a solution that has a y-value of 2 is n = 5

A system of equations is a pair of equation that contain two unknowns.

Given the system of equations

5x+6y= 32  (1)

2x + ny = 18  (2)

We desire the value of n where the value of y is 2

First, we make x subject of the formula from equation (1)

So, x = (32 - 6y)/5

Substituting x into equation (2), we have that

2x + ny = 18  (2)

2(32 - 6y)/5 + ny = 18  (2)

(64 - 12y)/5 + ny = 18

Multiplying through by 5, we have

64 - 12y + 5ny = 90

We now make n subject of the formula.

64 - 12y + 5ny = 90

- 12y + 5ny = 90 - 64

(- 12 + 5n)y = 26

-12 + 5n = 26/y

5n = 26/y + 12

n = 26/5y + 12/5

Since y = 2, substituting y into the equation, we have

n = 26/5(2) + 12/5

n = 26/10 + 12/5

n = (26 + 24)/10

n = 50/10

n = 5

So, the value of n = 5

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√100000 = 100√10 ≈ 316.227766

10 =2⋅5 has no more square factors, so √10 cannot be simplified further.

So it may be simply

√100000 = 100√10

Unless you want a decimal approximation or an expression using a continued fraction...

Irrational Number

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0.

√10 is an irrational number. It cannot be expressed as a fraction. Its decimal representation does not terminate or recur.

If  use a calculator, it will  an approximation like:

√10 ≈ 3.16227766

Then

√100000 = 100√10 ≈ 316.227766

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Answer: -4/3x—2

Step-by-step explanation:

Answer:

-15

Step-by-step explanation:

if its just asking for what number would represent a loss of 15 it would be negative 15

i dont know if there's more to the problem or not

Answer:

-15

Step-by-step explanation:

This is because whatever much water was in the tank is now decreasing by 15, therefore, you can write it as -15,

hope this helps!

y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1] is the orthogonal basis for w using Gram-Schmidt process.

Given,

The set;

x₁ = [1  -4  0  1]

x₂ = [7  -7  -6  1]

We have to produce the orthogonal basis for w using the Gram-Schmidt process;

Here,

y₁ = x₁ =  [1  -4  0  1]

Now,

Solve for y₂

y₂ = x₂ - [x₂y₁ / y₁y₁] y₁

That is,

y₂ = [7  -7  -6  1] - ( [7  -7  -6  1] [1  -4  0  1] / [1  -4  0  1] [1  -4  0  1] ) × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - (7 + 28 - 0 + 1) / (1 + 16 + 0 + 1) × [1  -4  0  1]

y₂ = [7  -7  -6  1]  - 36/18 × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - 2  × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - [2  8  0  2]

y₂ = [5  1  -6  -1]

That is,

The orthogonal basis for w using Gram-Schmidt process is,

y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1]

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