(5)^2/-10 please help

Fraction amount left 21/50

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The area of △ABC is equal to 6√6 / 2.

What is the area of triangle 3-dimensional space?

The area of a triangle in 3-dimensional space can be found using the cross product of two vectors formed by the three vertices of the triangle.

The formula for the area of a triangle with sides u and v is given by:

Area = |u × v| / 2

Where × represents the cross product of the two vectors u and v, and |•| represents the magnitude of the resulting vector.

To find the area of △ABC, we can form the vectors AB and AC and find their cross-product:

AB = B - A = (1 - 2, -3 - (-1), 2 - (-1)) = (-1, -2, 3)

AC = C - A = (2 - 2, -3 - (-1), 0 - (-1)) = (0, -2, 1)

Cross product of AB and AC: AB × AC =

| i j k |

|-1 -2 3 |

| 0 -2 1 |

= (6, 6, -6)

Area of △ABC = |AB × AC| / 2 = |(6, 6, -6)| / 2 = √(6^2 + 6^2 + (-6)^2) / 2 = 6√6 / 2

Hence, the area of △ABC is equal to 6√6 / 2.

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The value function for g(7), g(0) and g(-5) are 14, 7 and 2 respectively.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

From the graph, we have y-intercept (0, 7) and slope (m)=3/3 =1

Here, y=x+7

g(x)=x+7

g(7)=7+7

g(7)=14

g(0)=0+7

g(0)=7

g(-5)=-5+7

g(-5)=2

g(x)=3

So, x+7=3

x=-4

Therefore, the value function for g(7), g(0) and g(-5) are 14, 7 and 2 respectively.

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37.7 °Celsius = 99.8 °Fahrenheit. Your normal body temperature is approximately 37°C. A fever is usually when your body temperature is 37.8°C or higher.

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The statement that is correct on Quadrilateral EFGH is B. Quadrilateral EFGH is a rectangle.

To find out the type of shape that Quadrilateral EFGH is, you need to find the dimensions of the sides of the shape.

This can be found by the formula :

d=√(( x2 – x1 ) ² + ( y2 – y1 ) ² )

Using the formula, Side EF is 6 units

Side FG = 4 units

Side GH = 6 units

Side EH = 4 units

Two sides are therefore the same which means that this is a rectangle.

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Options for this question include:

A. Quadrilateral EFGH is a square.

B. Quadnlateral EFGH is a rectangle.

C. Quadrilateral EFGH is a rhombus

D. Quadriateral EFGH is a trapezium.

The required volume of the given figure made up of two rectangular prisms is 1728 cubic feet.

The volume of the rectangular prism is the product of the base area and the height.

The volume of the larger rectangular prism is 19 feet x 12 feet x 6 feet = 1368 cubic feet.

The volume of the smaller rectangular prism is 10 feet x 12 feet x 3 feet = 360 cubic feet.

Overall volume of rectangular prisms = 1368 cubic feet + 360 cubic feet

Overall volume of rectangular prisms = 1728 cubic feet

Therefore, the volume of the figure made up of two rectangular prisms is 1728 cubic feet.

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The graph of y = tan x is concave up on the interval (0,π/2).

The graph of y = tan x is concave up on the interval (0,π/2). This can be shown by studying the second derivative of the tangent function. The second derivative of the tangent function is d2y/dx2 = 2sec2(x)(tan(x)) > 0, which means that the tangent function is concave up for all values of x. This implies that the graph of y = tan x is concave up on the interval (0,π/2). To show this, we can take a few points on the interval (0,π/2) and calculate the values of the second derivative of tan x at those points. For example, for x = π/4, the second derivative of tan x is 2sec2(π/4)(tan(π/4)) = 2(1.1547)(1.7321) = 4.9289 which is positive. This shows that the graph of y = tan x is concave up on the interval (0,π/2).

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The 6.005 g of carbon contains 0.5000 moles of C. option  C

The mole is a unit of measurement in chemistry used to quantify the amount of a substance. One mole of a substance contains Avogadro's number of entities of that substance. Avogadro's number is defined as 6.022 x 10^23 entities per mole and is a fundamental constant in chemistry.

The mole is used to convert the amount of a substance in mass or volume to the number of entities (such as atoms, molecules, or ions) of that substance. The mole is useful in chemical reactions, where it provides a convenient way to express the amounts of reactants and products involved in a reaction.

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The triangles are not congruent. Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C.

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[1, 0, 0, 0] [1] + [0, 1, 0, 0] the span of the columns of A and the general solution of the system of equations Ax = [ 9, -3, 3, -6, 27, 78, 60].

An equation is a mathematical statement that shows the equality of two expressions. It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus. They can also involve constants, variables, functions, and symbols.

An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.

[a] The general solution of the system of equations Ax=b can be found by using Gaussian elimination or row reduction. The augmented matrix [A b] is:

[-3, 1, -1, 2, -9, -26, -20]

[15, -5, 5, -10, 45, 130, 100]

[-30, 10, -8, -62, 12, 32, -178]

[ 9, -3, 3, -6, 27, 78, 60]

[b] The first step in row reduction is to get a 1 in the first row and 0s below it in the first column. We can do this by dividing the first row by -3 and subtracting multiples of it from the other rows:

[1, -1/3, 1/3, 2/3, 3, 26/3, 20/3]

[0, 20/3, 4/3, 8/3, 12, 104/3, 140/3]

[0, -40/3, 20/3, 4, -24, 68/3, 140/3]

[0, 3, -3, 0, 9, -78/3, 180/3]

Next, we can use row operations to get 0s in the second column below the first row:

[1, -1/3, 1/3, 2/3, 3, 26/3, 20/3]

[0, 1, 2/5, 4/5, 6, 42/5, 70/5]

[0, 0, 2/5, 2, -18, 26/5, 110/5]

[0, 0, 0, 0, 3, -78/5, 180/5]

Continuing with this process, we get the reduced echelon form of the augmented matrix:

[1, 0, 0, 0, 3, -26/5, 20/5]

[0, 1, 0, 0, 6, 42/5, 70/5]

[0, 0, 1, 0, -18, 26/5, 110/5]

[0, 0, 0, 1, 3, -78/5, 180/5]

[c] The reduced echelon form of [A b] is:

[1, 0, 0, 0, 3, -26/5, 20/5]

[0, 1, 0, 0, 6, 42/5, 70/5]

[0, 0, 1, 0, -18, 26/5, 110/5]

[0, 0, 0, 1, 3, -78/5, 180/5]

[d] The homogeneous system Ax=0 has the general solution:

x1 = t

x2 = 6t

x3 = -18t

x4 = 3t

where t is an arbitrary constant. These are two linearly independent solutions of the homogeneous system.

[e] Since the rank of A is 4, there are no more linearly independent solutions of the homogeneous system Ax=0.

[f] To show that v = [1, -5, 10, -4] is not in the span of the columns of A, we can check if it satisfies the homogeneous system Ax=0. Plugging in the values, we have:

[1, 0, 0, 0] [1] + [0, 1, 0, 0]

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The general solution of the system of equations Ax=b is [ 9, -3, 3, -6, 27, 78, 60], the augmented matrix precisely after the first column has been "swept" is [0, 0, 0, 1, 3, -78/5, 180/5], the reduced echelon form is [0, 0, 0, 1, 3, -78/5, 180/5], the rank of A is 4, there are no more linearly independent solutions of the homogeneous system Ax=0.

An equation is a mathematical statement that shows the equality of two expressions. It is represented by an equal sign (=) and is used to solve for unknown values or to describe relationships between variables. Equations can be simple or complex, involving basic arithmetic operations or advanced mathematical concepts like trigonometry and calculus. They can also involve constants, variables, functions, and symbols.

An equation can be used to solve for a single unknown value, for example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving us 2x = 4 and then dividing both sides by 2, giving us x = 2. In this example, x = 2 is the solution to the equation.

[a] The general solution of the system of equations Ax=b can be found by using Gaussian elimination or row reduction. The augmented matrix [A b] is:

[-3, 1, -1, 2, -9, -26, -20]

[15, -5, 5, -10, 45, 130, 100]

[-30, 10, -8, -62, 12, 32, -178]

[ 9, -3, 3, -6, 27, 78, 60]

[b] The first step in row reduction is to get a 1 in the first row and 0s below it in the first column. We can do this by dividing the first row by -3 and subtracting multiples of it from the other rows:

[1, -1/3, 1/3, 2/3, 3, 26/3, 20/3]

[0, 20/3, 4/3, 8/3, 12, 104/3, 140/3]

[0, -40/3, 20/3, 4, -24, 68/3, 140/3]

[0, 3, -3, 0, 9, -78/3, 180/3]

Next, we can use row operations to get 0s in the second column below the first row:

[1, -1/3, 1/3, 2/3, 3, 26/3, 20/3]

[0, 1, 2/5, 4/5, 6, 42/5, 70/5]

[0, 0, 2/5, 2, -18, 26/5, 110/5]

[0, 0, 0, 0, 3, -78/5, 180/5]

Continuing with this process, we get the reduced echelon form of the augmented matrix:

[1, 0, 0, 0, 3, -26/5, 20/5]

[0, 1, 0, 0, 6, 42/5, 70/5]

[0, 0, 1, 0, -18, 26/5, 110/5]

[0, 0, 0, 1, 3, -78/5, 180/5]

[c] The reduced echelon form of [A b] is:

[1, 0, 0, 0, 3, -26/5, 20/5]

[0, 1, 0, 0, 6, 42/5, 70/5]

[0, 0, 1, 0, -18, 26/5, 110/5]

[0, 0, 0, 1, 3, -78/5, 180/5]

[d] The homogeneous system Ax=0 has the general solution:

x1 = t

x2 = 6t

x3 = -18t

x4 = 3t

where t is an arbitrary constant. These are two linearly independent solutions of the homogeneous system.

[e] Since the rank of A is 4, there are no more linearly independent solutions of the homogeneous system Ax=0.

[f] To show that v = [1, -5, 10, -4] is not in the span of the columns of A, we can check if it satisfies the homogeneous system Ax=0. Plugging in the values, we have:

[1, 0, 0, 0] [1] + [0, 1, 0, 0]

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The unit tiles that needs to be added to the equation  x²+4x+3 will be 1. The correct answer is A.

A square number, also known as a perfect square, is an integer that is the square of another integer. It results from dividing two integers by two.

When converting an expression to a perfect square trinomial

x²+4x+3

We must rearrange the statement in order to transform it into the perfect square.

x²+(2x+2x)+3

Extend the formula (x+2)²

(x+2)² = x² + 2(2x) + 2(2) (2)

(x+2)² = x² + 4 + 4x

(x+2)² = x² + 4x + 4

Add the constant terms together, then subtract them.

Difference is 4 minus 3.

Difference = 1

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The measure of the variable z is 44.

Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.

Given:

As, the Triangles are similar.

and, we know that similar triangles have their ratio of the corresponding sides equal.

Then, z/ 45 = 44/ 45

45z = 44 x 45

z = 44

Hence, the measure of z is 44.

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The slope of the line would be theta = cos⁻¹ (r/6)

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

By taking the derivative of the polar equation with respect to theta and evaluating it at the provided value of theta, one can determine the slope of the tangent line to the polar curve at the indicated position.

The rise divided by the run formula is used to calculate the percent of slope, which is calculated by multiplying the result by 100 and dividing the elevation change by the horizontal distance travelled.

d(r)/d(theta) = -6 sin(theta)

So, for theta = ????/3, the slope of the tangent line is:

-6 sin(????/3)

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The probability that a student studied for 5 hours is 0.23.

Probability refers to the likelihood or chance that an expected success is observed over many possible observations, outcomes, or events.

Probability can be expressed as a percentage, decimal, or fraction.

here, we have,

In this situation, the probability that a student studied for 5 hours is the quotient of the division of the number of students who studied for 5 hours and the total number of students who studied.

Number of hours   Total number                                                                      

                                of students

          0                         1

          1                          3

         2                          2

         3                          5

         4                          9

         5                          7

         6                         3

Total                            30

Probability a student studied 5 hours = 0.23 (7/30)

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The largest digit number that can be formed from 1720 is 7210

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

Examples of integers include -2, 567, -1000, 0, e.t.c

Numbers that can be formed from 1720 are:

1270,

1072,

1027

1207

7201

7102

7210

Among all the numbers , 7210 is the highest number that can be formed from 1720

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It suggests that the communities are unsaturated and that the size of the regional pool determines local species richness.

The correct option is (A)

Now, According to the question:

This suggests that the processes structuring the butterfly community are likely related to the presence and abundance of resources such as food plants and suitable habitat for the butterflies. As the number of individuals in the community increases, the number of different species that can be supported also increases, resulting in a linear relationship between the two. Additionally, this indicates that the butterfly community is likely experiencing a relatively stable and predictable environment, where resources are available to support a diverse population of butterflies.

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The complete question in the form is:

Now examine the lower panel (butterflies), where the curve continues to rise linearly. What does this indicate about the processes structuring the butterfly community?

(A) It suggests that the communities are unsaturated and that the size of the regional pool determines local species richness.

(B) It suggests that the communities are becoming saturated and that local processes are likely becoming increasingly important.

(C) It does not tell us anything about the relative importance of the regional species pool and local interactions.

13 less than b as an algebraic expression would be [tex]b - 13[/tex].

This is because 13 less than a number is the same as that number being subtracted by 13. Let me know if you have any questions, thanks!

If a rigid motion of the plane—that is, a combination of rotations, translations, and reflections—can turn one tile into the other while without stretching or contracting, then two tiles are said to be congruent.

What is congruent ?

Congruent refers to having a precise match in size and shape. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.

We are surrounded by tiling. Human nature makes us curious about how various small bits fit together when presented.

In the broadest sense, tiling simply refers to the process of breaking up a large area into several little parts (tiles) that seamlessly interlock one another.

Even human bodies, for instance, can be thought of as tilings with cells serving as the "tiles." The earth's surface is tiled by land ownership! There are tiles almost everywhere.

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We can simplify the expression to get:

2*(b + b²)

Here we want to simplify the following expression:

b + 3b² + b - b²

We can reorder that expression in the following way.

b + b + 3b² - b²

And now group like terms, we will get:

b + b + 3b² - b²

2b + (3 - 1)* b²

2b + 2b²

Now we can take 2 as a common factor to get:

2*(b + b²)

That is the expresion simplfied.

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The correct statement is "Each point on the​ least-squares regression line represents the predicted y-value at the corresponding value of x". Thus, Option C is correct.

A least-squares regression line is a mathematical model that is used to predict the value of a dependent variable (y) based on the value of an independent variable (x). The regression line is created by fitting a line to the data set that minimizes the differences between the actual y-values and the predicted y-values (the line).

Each point on the regression line represents the predicted y-value for a given value of x. In other words, if we know the value of x, we can use the regression line to predict the value of y that is most likely to occur based on the data set. The least-squares regression line is a useful tool for understanding the relationship between two variables and making predictions about future values.

A is incorrect because it states that each point on the least-squares regression line represents the actual y-value of the data set at that corresponding value of x, which is not necessarily the case. The regression line is a model that predicts y-values based on the relationship between x and y, but it is not necessarily equal to the actual y-values in the data set.

B is incorrect because it states that each point on the least-squares regression line represents the ideal y-values at that corresponding value of x, which is not a characteristic of a regression line. A regression line represents a predicted y-value based on the data set and the relationship between x and y, but it does not necessarily represent ideal values.

D is incorrect because it states that each point on the least-squares regression line represents one of the points in the data set, which is not necessarily the case. A regression line represents a predicted y-value based on the data set and the relationship between x and y, and it may not necessarily match the actual data points in the data set.

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Answer: T=4

Step-by-step explanation:

Good evening.

The first thing you want to do is distribute the 2.

[tex]2t+2=10[/tex]

Then, we need to subtract the 2 on both sides.

[tex]2t=8[/tex]
Then we divide both sides by 2, giving us the ultimate answer of T=4.

[tex]t=4[/tex]

Answer:

∠ C = 40° , x = y = 118

Step-by-step explanation:

10

BC is the diameter of the circle then ∠ A = 90° , angle in a semicircle.

the sum of the 3 angles in Δ ABC = 180° , then

∠ A + ∠ B + ∠ C = 180°

90° + 50° + ∠ C = 180°

140° + ∠ C = 180° ( subtract 140° from both sides )

∠ C = 40°

11

ABCD is a cyclic quadrilateral

• the opposite angles are supplementary, sum to 180°

x + 62 = 180 ( subtract 62 from both sides )

x = 118

similarly

y + 62 = 180

y = 118

thus x = y = 118

Answer:

Step-by-step explanation:

4x+5y=15

-4x. -4x

5y=-4x+15

divide by 5 on both sides

y = 4/5x+3

Two points would be : (0,3) & (7,5)

extra : 4/5 means on the graph you go up 4 spaces, and to the right 5 spaces, in reverse you would go down 4 spaces and 5 spaces to the left

hope this helped =)

-YinAhara

Answer:

Step-by-step explanation:

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Consider the initial value problem y' = 3y^2, at the value of y(0) = 1/6 will the solution have a vertical asymptote at t = 2.

The differential equation is y'=3y^2.

We can write this equation as:

dy/dt = 3y^2

dy/y^2 = 3dt

Now integrating on both side

[tex]\int \frac{dy}{y^2} = \int 3dt[/tex]

After integrating we get,

- 1/y = 3t + c

Multiply by y on both side, we get

(3t + c)y = -1

Divide by (3t + c) on both side, we get

y = -1/(3t + c).................(1)

Since there is vertical asymptote at t = 2

So 3t + c = 0 at t = 2

3(2) + c = 0

6 + c = 0

Subtract 6 on both side, we get

c = -6

Put the value of c in equation 1

y = -1/(3t - 6)

At t = 0

y(0) = -1/(3(0) - 6)

y(0) = 1/6

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the percent discount is 14% when the original price and new price are given $36 and $30.96.

Given that,

Original price of item = $36       (that is before discount and the tax)

Price after discount = $30.96

Let the percentage discount be = x

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

To get the percent discount :

x = (original cost - new price)/original price

x = (36 - 30.96)/36

x = 5.06/36

x = 0.14

Percentage discount x , in percentage = 0.14 x 100

Percentage discount = 14%

therefore, the percent discount is 14%

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The test statistic be Pearson's correlation test.

What is Null hypothesis ?

The null hypothesis assumes that any difference between the selected attributes in a set of data is attributable to chance.

The test statistic could be Pearson's correlation coefficient, which measures the linear association between two continuous variables (here, amygdala activity and memory score).

The null hypothesis would be that there is no association between amygdala activity and memory score, which can be represented as:

H0: r = 0

The type of test would be a Pearson's correlation test, which is a parametric test that assesses the strength and direction of the linear relationship between two continuous variables.

Hence, The test statistic be Pearson's correlation test.

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The provided function's definite integral from 0 to 10 is closest to 4.

The area of each zone that the function, the x-axis, and the two vertical lines at x = 0 and x = 10 bounds is added to form the definite integral of the function. The definite integral that results from adding up each of these areas is the one that is closest to 4. The area of the region above the x-axis is larger than the area of the region below the x-axis, which explains this. The area of the region above the x-axis is higher than the area below the x-axis because the function is rising across the interval. The overall area is closer to 4 since the area of the region below the x-axis is negative. As a result, 4 is the closest value for the definite integral of the 0–10 function.

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The probability of Hans winning the competition and taking no more than three shots is 0.784.

To calculate the probability that Hans wins after taking no more than 3 shots, we can use the cumulative distribution function (CDF) of the binomial distribution.

The CDF gives the probability of getting k or fewer successful shots in n trials, with a success probability of p.

In this case, n = 3, p = 0.4, and k = 2 (since Hans wins if he hits the bull's-eye with 2 shots or fewer).

Using the cumulative binomial distribution formula, the probability of Hans winning the competition and taking no more than three shots is 0.784.

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The domain of the composite function (f o g)(-5) for f(x) = 4x + 8 and g(x) = x² + x is equal to 88.

A function is composite when the co- domain of the first mapping is the domain of the second mapping

We shall evaluate the domain of the function (f o g)(-5) as follows:

(f o g) = 4(x² + x) + 8

(f o g) = 4x² + 4x + 8

(f o g)(-5) = 4(-5)² + 4(-5) + 8

(f o g)(-5) = 100 - 20 + 8

(f o g)(-5) = 88

Therefore, the domain of the composite function (f o g)(-5) for f(x) = 4x + 8 and g(x) = x² + x is equal to 88.

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