The sum of two numbers is 15
and their quotient is 2.

The homogeneous system of linear equations has a solution space with a basis of {(1, 2, -1)}. The dimension of the solution space is 1.

To find a basis for the solution space of the given homogeneous system of linear equations, we need to solve the system and express the solutions in terms of a linear combination of vectors.

The system of equations is as follows:

Equation 1: -x + y - z = 0

Equation 2: 2x - y = 0

Equation 3: 2x - 3y - 4z = 0

We can start by using the equations to eliminate variables. From Equation 2, we can express y in terms of x as y = 2x. Substituting this into Equation 1 gives us -x + 2x - z = 0, which simplifies to x - z = 0. Rearranging this equation, we have x = z.

Now, we can express the variables in terms of a single parameter. Let's choose z as the parameter. Thus, x = z and y = 2x = 2z.

Now, we can express the solutions in vector form as (x, y, z) = (z, 2z, z) = z(1, 2, 1). This means that the solution space is spanned by the vector (1, 2, 1).

To find the basis for the solution space, we need to check if the vector (1, 2, 1) is linearly independent. Since it is the only vector spanning the solution space, it is linearly independent. Therefore, the basis for the solution space is {(1, 2, 1)}.

The dimension of the solution space is equal to the number of vectors in the basis, which in this case is 1. Therefore, the dimension of the solution space is 1.

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Answer:

-3/2x + 8

Step-by-step explanation:

To find the slope of the perpendicular line, you take the negative reciprocal first.

2/3 -> -3/2

So far, we have y = -3/2 x + b. (since we use mx + b)

Since you asked for the line to go through (0, 8), we would usually sub in values like below, but since 8 is the y-intercept since x = 0 of the point, and we need the y-intercept, put 8 as the y-intercept.

y = -3/2 x + b

8 = -3/2(0) + b

8 = 0 + b

b = 8

So the equation that passes (0, 8) and is perpendicular to y = 2/3 x + 3 is

-3/2x + 8

Your welcome!

Kayden Kohl

8th Grade

Answer:

\(4ab-6a^{2}\)

Step-by-step explanation:

1) 2a×2b=4ab

2)2a×-3a=\(-6a^{2}\)

3)\(4ab-6a^{2}\)

Answer:

1.3

Friend is wrong

Step-by-step explanation:

Given:

friend's claim: height of his building is more than 1.50 times the height of yours

line of sight to the top edge of the other building makes an angle of 21° above the horizontal

line of sight to the base of the other building makes an angle of 52° below the horizontal

Solution:

Let A be the height of your building is A

Let B+A his building is B higher than yours.

Let the distance between the buildings is x.  

then

tan 52 = A/x

tan 21 = B/x  

A/B = tan 52 / tan 21

      =  1.27994 / 0.38386

A/B = 3.33

(A + B) / A = 1.5 0

A/A + B/A = 1.50

1 + B/A = 1.50

B/A is basically (B/x) / (A/x)

So

1+ 3.33 / 3.33

= 4.33/3.33

= 1.3

Since 1.3 is not equal to 1.5

Hence the friend's claim is wrong.

The height of the taller building can be given in relation to the height of

the other building using trigonometric ratios.

Correct response:

The given parameters are;

Angle of elevation to the top of the other building = 21°

Angle of depression to the base of the other building = 52°

The claim of the friend = The height of his building > 1.5 × The height of the other building

Required:

To state whether the claim is right or wrong.

Solution:

Let h represent the height of the smaller building, let l represent the

distance between the two buildings, and let d represent the height by

which one building is taller than the other, we have;

l·tan(21°) = d

l·tan(52°) = h

Height of the taller building, H = h + d = l·tan(52°) + l·tan(21°)

Height of the other building = h = l·tan(52°)

Therefore;

H ≈ 1.3·h

Which gives that the taller building, H, is approximately 1.3 times the other building.

Therefore;

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As a result of demonstrating that two pairs of corresponding sides and their included angles are congruent in both triangles

A triangle is a closed, double-symmetrical object composed of three line segments known as sides that intersect at three points known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are less than 90 degrees), okay (one angle is equal to 90 degrees), or orbicular (all angles are greater than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.

Triangle ABC with AB, BC, and AC sides.

Triangle DEF with DE, EF, and DF sides.

Angle ABC and angle DEF are vertical angles, which means they are congruent, as shown in the diagram. As a result, angle ABC = angle DEF.

We can see from the diagram that BC and EF are both vertical, so they must be congruent because they are opposite sides of a parallelogram. As a result, BC = EF.

Because they are opposite sides of a parallelogram, they must be congruent. As a result, AC = DF.

As a result of demonstrating that two pairs of corresponding sides and their included angles are congruent in both triangles, we can conclude that Triangle ABC and Triangle DEF are congruent using the Side-Angle-Side (SAS) criterion.

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The 99% confidence interval for the population standard deviation of body temperature is (0.61°F, 0.80°F). Since the entire interval is below 1.80°F, it is safe to conclude that the population standard deviation is less than 1.80°F.

To construct a confidence interval estimate of the standard deviation of body temperature, we can use the formula:

s/sqrt(n-1) * sqrt((n-1)/chi-square(alpha/2, n-1)) < σ < s/sqrt(n-1) * sqrt((n-1)/chi-square(1-alpha/2, n-1))

where s is the sample standard deviation, n is the sample size, α is the significance level (1- confidence level), and chi-square is the chi-square distribution function.

Plugging in the values given, we get:

0.69/sqrt(107-1) * sqrt((107-1)/chi-square(0.01/2, 107-1)) < σ < 0.69/sqrt(107-1) * sqrt((107-1)/chi-square(1-0.01/2, 107-1))

0.69/10.344 * sqrt(106/71.605) < σ < 0.69/10.344 * sqrt(106/146.577)

0.177 < σ < 0.233

Therefore, we can say with 99% confidence that the population standard deviation of body temperature is between 0.177 and 0.233.

As for whether it is safe to conclude that the population standard deviation is less than 1.80°F, we can see that the confidence interval we calculated does not include this value. However, we cannot definitively say that the population standard deviation is less than 1.80°F without further evidence or a wider confidence interval.

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The equation x³ - 15x + c = 0 has at most one real root in the interval (-2, 2)

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

x³ - 15x + c = 0

Let a polynomial function be represented with f(x)

If f(x) is a polynomial, then f is continuous on (a , b).

Where (a, b) = (-2, 2)

Also, its derivative, f' is a polynomial, so f'(x) is defined for all x .

Using the hypotheses of Rolle's Theorem, we have

f(x) = x³ - 15x + c

Differentiate

f'(x) = 3x² - 15

Set to 0

3x² - 15 = 0

So, we have

x² = 5

Solve for x

x = ±√5

The root x = ±√5 is outside the range (-2, 2)

This means that it has 0 or 1 root i.e. at most one real root

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The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

What is derivative?

The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).

The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.

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Answer:

41,775.34724 or 41,775 rounded

Step-by-step explanation:

So this is a growth function we are working with, the typical formula is population(1-percentage)^time

so formatting to the problem at hand would be:

79,300(1-.038)^(30-13)

79,300(.963)^17

41775.34724 or 41775 rounded

In physics lab, when you measure three quantities of x, y, and z, you can use these mathematical combinations to find meaningful relationships between these quantities:  

In this case, x=2.5 kg, y=0.8 m, and z=4.9 kg/m.

Based on the given quantities' scale, we know that x, y, and z have a relationship where:

z = x/y

Then, the mathematical combinations that might be meaningful are:

- (x/y) - z: This combination gives you the difference between the ratio of x and y, and z. This could be meaningful if you are trying to find the difference between two quantities that have different units.

- (x/z) - y: This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.

- x - (yz): This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.

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Answer:

I am not sure but

Step-by-step explanation:

try to use to website https://www.symbolab.com/solver/pre-algebra-calculator

you can chose what your learning and it gives you the right answer. make sure you put the numbers in correctly. if you don't it will mess every thing up for that problem. That one reason I have a B in math cuz i use that site for my math. and it shows you how to do it with steps

please give me a heart if the site really helps you guys :)

Answer:

Step-by-step explanation:

The probability of occurring event A is 23% or 0.23.

To find the probability of event A:

Divide the number of events in A to the total number of events.

Number of events in A = 12

Total number of events = 12+20+20

=52

P(A)=Number of events in A/Total number of events

\(=\frac{12}{52}\)

Divide both sides by 12:

\(=\frac{3}{13}\)

\(=0.23\)

\(=23\) %

Hence, the probability of occurring event A is 23% or 0.23.

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Answer:

question one:

x = 6.018150231520483

adjacent angle = 7.986355100472928

Step-by-step explanation:

i have no links, but try to search triginometry calculator and pick carbide calculator for fast trigonometry calculations

it automaticly does sin, cos, and tan for you.

Answer:

(4,0)

Step-by-step explanation:

add the 2 equations together

6x = 24

x=4

put x into the first equation

16+3y=16

y=0

The correct order of the processes of letter of credit payment is:

IV -> III -> II -> V -> I. b

Explanation:

The first step is to establish a sales contract (IV) between the importer and the exporter.

Then, the importer's bank issues a letter of credit (III) to the exporter's bank, which guarantees payment to the exporter if the terms of the sales contract are met.

The letter of credit is in place, the exporter's bank ensures the exporter that payment will be made (II).

The exporter then ships the goods (V) to the importer.

The importer receives and verifies the goods, the exporter's bank receives payment from the importer's bank and the exporter receives the payment. (I)

Establishing a sales contract (IV) between the importer and the exporter is the first stage.

Then, if the conditions of the sales contract are satisfied, the importer's bank sends a letter of credit (III) to the exporter's bank, guaranteeing payment to the exporter.

The exporter's bank guarantees that payment will be made because the letter of credit is in place (II).

The items (V) are subsequently delivered to the importer by the exporter.

The exporter's bank gets payment from the importer's bank, the exporter receives the money when the importer receives and inspects the items. (I)

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Answer:

2x + 8y = 16

Step-by-step explanation:

Subtract 2x from both sides of the equation.

8y = 16 − 2x

Divide each term by 8 and simplify.

Step-by-step explanation:

BASARILAR...

......

.

.

GOOD BYE

Answer:

\(x = -6\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

\(x - 2 = \frac{5x - 2}{4}\)

Step 2: Solve for x

\(\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right]\) is the representation of system of equation x+5y=7, 7x-2y=3

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.

The system of linear equations

-x + 5y = 7

7x - 2y = 3

can be represented in matrix form as:

\(\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right]\)

The matrix on the left represents the coefficients of the variables x and y, and the matrix on the right represents the constants on the right-hand side of each equation.

The vector on the left contains the variables x and y, and the vector on the right contains the constants.

Hence, \(\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right]\) is the representation of system of equation x+5y=7, 7x-2y=3

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Answer:

2

Step-by-step explanation:

lim x ---> 2^- f(x) = 2

lim x ---> 2^+ f(x) = 2

Answer:

The opposite of multiplication is division. The opposite of division is multiplication. The opposite of taking a square root is squaring

Step-by-step explanation:

Answer:

x = 8cm

Step-by-step explanation:

17² = 15² + x²

289 = 225 + x²

- x² = 225 - 289

x² = 64

x = √64

x = 8

\({ \boxed{ \sf \color{blue}{answer}}}\)

x = 8 cm

Step-by-step explanation:

17² = 15² + x²

289 = 225 + x²

x² = 225 - 289

x² = 64

x = √64

x = 8

Teorema pythagoras

Answer:

\(f^{8} + 7\)

Step-by-step explanation:

Betrys needs another 400 grams of diced potatoes to make her vegetable stew for 8 people.

We know that Betrys is cooking for 8 people, and we know that a recipe for 2 people needs 10 ounces.

8 people is 4 times 2 people, then for 8 people you need 4 times 10 ounces, this is 4*10 oz = 40 ounces.

Now we can apply a change of units, remember that:

1 oz = 28 grams

Then the total amount she needs is:

40 oz = 40*28 g = 1,120 g

So she needs in total 1,120 grams, and in the balance, she already has 720 grams, so the amount that she needs is given by the subtraction:

1,120 g - 720g = 400

Betrys needs another 400 grams of diced potatoes to make her vegetable stew for 8 people.

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Answer:

(3-x) is the other factor.

Step-by-step explanation:

The given function is :

\(F(x)=-x^{2}+7x-12\)

One of the factor is (x-4)

We need to find the other factor.

It can be solved as follows :

\(F(x)=-x^{2}+4x+3x-12\\\\=(-x+3)(x-4)\)

So, the other factor is (3-x).

The null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.

What is the null hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

Here,

We have to find out the slope of the line predicted by the null hypothesis if we are doing a linear regression.

We concluded that the null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope is not equal to zero.

Hence, the null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.

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Answer:

$3,379.50.

Step-by-step explanation:

7.51% = . 0751 as a decimal. (. 0751) * $45,000 = $3,379.50.

Answer:49

Step-by-step explanation:

Answer:

the third graph is correct

Step-by-step explanation:

edge

the second part is x<1

Answer:

the third graph and the send part it is x<1

Step-by-step explanation:

Answer:

5v+35 = 5(v+7)

Step-by-step explanation:

5(v+7) = 5v+35

Answer:

5

Step-by-step explanation:

Because

5(v+7)

5v+35..

hope it helps