find 2 numbers whose product is -10 and whose sum is 3

The kernel of A is {(0,0,1,0)^T} and  the basis is {(1,0,2,4)^T, (0,1,0,-3)^T}.

The kernel of a matrix A is the set of all vectors x such that Ax = 0, where 0 is the zero vector.

To find a basis for the kernel of A, we can row reduce the augmented matrix [A | 0] to reduced row echelon form using Gaussian elimination.

The row reduced echelon form of the matrix A is

1 0 2 4

0 1 0 -3

0 0 0 0

0 0 0 0

Write out the elements in the second column

0 1 0 0

Reverse the elements

0 0 1 0

So, the basis for the kernel of A is {(0,0,1,0)^T}.

The image of a matrix A is the set of all linear combinations of the columns of A.

So, the basis for the image of A is {(1,0,2,4)^T, (0,1,0,-3)^T}.

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The value of the segment BA for the similar triangles is equal to 12.6.

The triangles ABC and ADE are similar, this implies that the length EA of the smaller triangle is similar to the length CA of the larger triangle

and the length DA of the smaller triangle is similar to the length BA of the larger triangle

so;

DA/BA = EA/CA

DA/(7 + DA) = 3.2/7.2

7.2DA = 3.2(7 + DA) {cross multiplication}

7.2DA = 22.4 + 3.2DA

7.2DA - 3.2DA = 22.4

4DA = 22.4

DA = 22.4/4 {divide through by 4}

DA = 5.6

BA = 7 + DA = 12.6

Therefore, the value of the segment BA for the similar triangles is equal to 12.6.

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The value of the unknown number x is given as follows:

x = -65.

The number is unknown, hence the variable is given as follows:

x.

-1/5 of the number is given as follows:

-1/5x = -x/5.

The difference of -1/5 of a number and 1 is given as follows:

-x/5 - 1.

The difference has a result of 12, hence:

-x/5 - 1 = 12.

Then the variable x is obtained as follows:

-x/5 = 13

x = -13 x 5

x = -65.

The problem asks for the value of the unknown number.

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Answer:

each bar costs $3.

Step-by-step explanation:

The inequality that describes the problem is:

3x > 18

This inequality states that the total cost of the soap bars, represented by 3x, is greater than Colleen's budget of $18. The variable x represents the number of bars of soap Colleen bought. So, if x represents the number of bars of soap Colleen bought, 3x represents the total cost of those bars, since each bar costs $3.

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Answer:

7 + [x/(3x9)]

Step-by-step explanation:

The normal vector of the plane containing the lines is the cross product of (-12, 3, 6) and (4, -1, -2), which is (48, -66, 0).

The direction vector of a line is a vector that points in the direction of the line and the position vector of a line is a vector that represents any point on the line.

Let's start with line r1(t) = - (-12t, 3t + 1,6t + 5).

The derivative of r1(t) = - (-12t, 3t + 1,6t + 5) is (-12, 3, 6).

So, the direction vector of line r1(t) is (-12, 3, 6).

We repeat this process for line r2(t) = (4t – 4, -t + 4,5 – 2t).

The derivative of r2(t) = (4t – 4, -t + 4,5 – 2t) with respect to t is (4, -1, -2), so the direction vector of line r2(t) is (4, -1, -2).

If we plug in t = 0 into the line equation, we get the point

=> (4t – 4, -t + 4,5 – 2t) = (-4, 4, 5).

So, the position vector of line r2(t) is (-4, 4, 5).

So, we find the cross product of (-12, 3, 6) and (4, -1, -2). If the cross product is equal to the zero vector, then the lines are parallel.

If not, then the lines are not parallel.

The cross product of (-12, 3, 6) and (4, -1, -2) is (48, -66, 0).

Since the cross product is not equal to the zero vector, the lines are not parallel.

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Check the picture below.

now, doing a prime factoring on both the denominators, notice, the repeated factors get used only once in the LCD calculation, so the red "3" only goes once in the LCD and then the others, so the LCD for both of those is 3*3*2*2 = 36.

"L" in LCD stands for Least, so that's the smallest, however we can have a CD that's no small and is simply a multiple of the LCD, let's check who isn't an LCD or CD

[tex]\begin{array}{rllll} 108=3\cdot 36 & \bigotimes\\\\ 72=2\cdot 36& \bigotimes\\\\ 36=1\cdot 36&\bigotimes\\\\ 24&\textit{\LARGE \checkmark} \end{array}[/tex]

The height of the cylinder-shaped pool is approximately 0.5 feet. The equation is h = 56.52 / (3.14 × 6²)

The equation to determine the height of a cylinder-shaped pool can be found using the formula for the volume of a cylinder:

V = πr²h

Where V is the volume, π is the constant pi, r is the radius of the pool, and h is the height.

Given that the volume is 56.52 cubic feet and the radius of the pool is 6 feet, we can substitute these values into the equation:

56.52 = π * 6² * h

Dividing both sides by π * 6²:

h = 56.52 / (π * 6²)

Using the approximate value of π as 3.14:

h = 56.52 / (3.14 * 6²)

So the equation to determine the height of the cylinder-shaped pool is:

h = 56.52 / (3.14 * 6²)

And the correct answer choices would be:

h = 56.52 / (π * 6²)

π = 3.14

r = 6

The equation would look like this:

h = 56.52 / (3.14 * 6²)

The equation h = 56.52 / (3.14 * 6²) is used to determine the height of a cylinder-shaped pool.

To find the actual value of h, we need to simplify the equation by substituting the value of π as 3.14 and the radius of the pool as 6:

h = 56.52 / (3.14 * 6²)

h = 56.52 / (3.14 * 36)

h = 56.52 / 113.04

h = 0.5

So the height of the cylinder-shaped pool is approximately 0.5 feet.

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Answer:

the answer is

1/8, 3/24, 5/40

For given parallelogram which is a quadrilateral,   The coordinates of the fourth vertex of parallelogram is (0,3).

what are quadrilaterals?

A quadrilateral is a polygon with four sides, four vertices, and four angles.

It is formed by joining four non-collinear points. The sum of the interior angles of quadrilaterals is always equal to 360 degrees. The word quadrilateral is derived from the Latin words ‘Quadra’ which means four and ‘Latus’ means ‘sides’. Not all the four sides of a quadrilateral need to be equal in length. Hence, we can have different types of quadrilaterals based on sides and angles.

Five special quadrilaterals are shown below in the image, along with their definitions and pictures, and points for them to get proven.

Now,

Let A(-4,0), B(4,-3), C(-2,-6) and D(x,y)

As for parallelogram diagonals bisect each other.

The midpoint of Diagonal AC= The midpoint of BD

((-4+4)/2,(0-3)/2)=(x-2)/2,(y-6)2

x-2=0     y=-3+6

x=0        y=3

Hence,

              The coordinates of the fourth vertex of parallelogram is (0,3).

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Answer:

coordinates r the: (-2, -4.50)

Step-by-step explanation:

option b is the ans

According to the representation of the linear model, the balloon's height is zero feet after 15 seconds.

Depending on the context, the word "linear model" in statistics might signify many things.

The phrase is frequently used interchangeably with a linear regression model since it most frequently relates to regression models.

The phrase has a different connotation when applied to time series analysis.

In each instance, "linear" refers to a subclass of models for which the complexity of the underlying statistical theory can be greatly reduced.

The linear model shows that the water balloon is launched from a height of 40 feet above.

The linear model shows that the water balloon is launched from a height of 40 feet above.

Now, the balloon rises to a height of 70 feet before falling back to the ground as a result of gravity.

After about ten seconds, the balloon lands on the surface and makes a splash.

The balloon will therefore stay on the ground for a while longer.

As a result, the balloon's height at time 15 seconds is always 0 feet, according to the linear model.

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The number of years it will take the population of the city to reach 1million is 14.1 years

Exponential function, in mathematics, a relation of the form y = ax, with the independent variable x ranging over the entire real number line as the exponent of a positive number a.

1000000 = 10⁶

10⁶ = P(t)

10⁶ = 244115e0.1t

10⁶/244115 = 0.1t

e0.1t = 4.096

ln0.1t = ln 4.096

0.1t = 1.41

t = 1.41/0.1

t = 14.1 years

therefore the years it will take the city to be populated with 1million is 14.1 years

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Answer:C

Step-by-step explanation:

the filled in circle means that it is equal to as well as lesser than or greater than where as a hollow circle means it is just lesser/greater than.

Answer:

---------------------

Evaluate expressions using respective points on graphs :

The science of statistics focuses on creating and researching strategies for gathering, analysing, interpreting, and presenting empirical data.

Data is frequently presented in graphs, tables, and charts that analyse the data and aid in problem- and decision-solving. Calculating the sample size and population, determining the mean, mode, and median, as well as the standard deviation and variance, are some of the most crucial statistical calculations. Data, which can take the form of words or numbers, are the actual values of the variable.

Statistics is a technique for interpreting, analysing, and summarising data in mathematics. In light of these characteristics, the various statistical types are divided into: Statistics that are descriptive and inferential.

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Answer:

Deniz's expected winnings if she chooses rock are $30. If she chooses paper, her expected winnings are $20. If Deniz wants the best payoff in the long run, she should choose paper.

Expected winnings for rock:

Deniz wins against scissors with probability of 30%, and loses against paper with probability of 20%, so her expected winnings are (0.3100) - (0.2100) = 30

Expected winnings for paper:

Deniz wins against rock with probability of 50%, and loses against scissors with probability of 30%, so her expected winnings are (0.5100) - (0.3100) = 20

Hence the answer is

( i )  - 8/27   (ii) -4/9

Given question answer is

( i ) (-2/3)³

 = (-2/3) * (-2/3) *(-2/3)

=   (-8/27)

( ii )  (-4/3²)

      =  -4/3*3

      =  (-4/9)

You must substitute a number for each variable and conduct arithmetic operations to evaluate an algebraic statement. Because 6 + 6 = 12, the variable x in the preceding example is equal to 6. We can evaluate the expression after replacing the variables with their values if we know their values.

When x=4, calculate 2x2+3x+8. When x = 4, calculate 2 x 2 + 3 x + 8. When an expression contains a variable with an exponent, we must exercise caution. This phrase, 2x2 2 x 2, indicates 2xx 2 x x, as opposed to the expression (2x)2 (2 x) 2, which implies 2x2x 2 x 2 x.

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If sample variance were to be computed by dividing SS by n, then the average value of the sample variances from all the possible random samples would consistently underestimate the population variance.

The sample variance is an estimate of the population variance, and it is calculated by dividing the sum of squared deviations (SS) by the sample size minus one (n - 1).

The reason for dividing by n-1 instead of n is due to the fact that the sample variance is an estimate of the population variance and not the exact value. When computing the sample variance, we use the sample data to make an estimate of the population variance. By dividing by n-1 instead of n, we adjust for the fact that the sample is a subset of the population and introduce a small amount of bias into the estimate to correct for this lack of representation.

This correction is known as the Bessel's correction and it makes the sample variance a more accurate estimate of the population variance by adjusting for the variability inherent in sampling. As a result, when sample variance is computed using the Bessel's correction (dividing by n-1), the average value of the sample variances from all possible random samples will consistently underestimate the population variance.

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The equivalent ratios for the given cost to toss the ring are found as:

For the stated question:

The cost to toss 34 rings = $17.

Part a: ___ to $1.

$17 ---> 34 toss

$1 ---> 34/17 toss

$1 ---> 2 toss

Part b:

34 toss   ---> $17

20 toss ---> $17*20 / 34

20 toss ---> $10

Thus, the equivalent ratios for the given cost to toss the ring are found as:

2 toss --->  $1

20 toss ---> $10

Thus, the graph is plotted for the points on the coordinate axes.

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The complete question is attached:

Answer:

A

Step-by-step explanation:

In a systems of equations we have to set up two equations which relate to each other and in this case we're setting up two linear equations, so let's take a look at the question.

Let's first make an equation from: "A monster pizza, m, has 7 fewer slices than twice the number on a large pizza, l" That means if we subtracted  twice the large pizza from monster pizza, we would get 7 slices. [tex]2l-m=7[/tex] and if we multiply by -1 on both sides: [tex]m-2l=-7[/tex]

Now let's use the second piece of information given: "the difference between the number of slices on a monster pizza and the number of slices on a large pizza is 4 slices" this means if we take away 4 slices from the monster pizza we get the same amount of slices on a large pizza: [tex]m-4=l[/tex] and rearranging we get: [tex]m-l=4[/tex] making A the correct option

By using elimination method, the solution of the system of equations are x = - 8, y = 9.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equations are,

⇒ 5x + 4y = - 4

⇒ 4x + 4y = 4

Now, We can solve by using elimination method as;

The system of equations are,

⇒ 5x + 4y = - 4  .. (i)

⇒ 4x + 4y = 4

⇒ x + y = 1 .. (ii)

Multiply by 5 in (ii) and subtract from (i);

⇒ 5x + 4y - 5x - 5y = - 4 - 5

⇒ - y = - 9

⇒ y = 9

And, From (ii);

⇒ x + y = 1

⇒ x + 9 = 1

⇒ x = 1 - 9

⇒ x = - 8

Thus, The solution of the system of equations are x = - 8, y = 9.

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Answer:

8

Step-by-step explanation:

Let's call the first of the three consecutive even integers x.

Since the integers are consecutive and even, we know that the next integer will be x+2, and the next one will be x+4.

We can use this information to set up an equation:

x + (x+2) + (x+4) = 30

Simplifying this equation, we get:

3x + 6 = 30

Subtracting 6 from both sides:

3x = 24

Dividing by 3:

x = 8

So the first of the three consecutive even integers is 8

Answer:

k=8 is not part of the solution set

Step-by-step explanation:

5(8) < 39

40 < 39

If you plug in 8 for K it makes the inequality incorrect. 40 is not less than 39.

When revolved over the {x} axis will occupy more volume as compared to when revolved over the {y} axis.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the volume occupied between the lines -

x = 4, y = x and x - axis.

Refer to the image attached. The reflection over the {x} axis will occupy more volume as compared to the reflection over the {y} axis. The figure generated in both the cases would be a cuboidal prism structure.

Therefore, when revolved over the {x} axis will occupy more volume as compared to when revolved over the {y} axis.

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