Simplify by combining like terms: 5x + 3x + 10x

To compute a basis of the eigen space corresponding to eigen value -2, we need to find the null space of the matrix A + 2I, where A is the 3x3 matrix and I is the identity matrix.

The null space will give us the basis vectors of the eigen space

To find the eigen space corresponding to the eigen value -2, we start by constructing the matrix A + 2I, where A is the given 3x3 matrix and I is the 3x3 identity matrix. Next, we solve the homogeneous system of linear equations (A + 2I)x = 0, where x is a vector. The solutions to this system form the null space of the matrix A + 2I.

By finding a basis for this null space, we can obtain the basis vectors of the eigen space corresponding to the eigen value -2.

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Answer: I think that FG and MB are parellel, but I think the way to confirm is to measure with a ruler

Step-by-step explanation:

Answer:

that look like  complementry and supplementry angles

Step-by-step explanation:

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

<a & <h are alternate exterior angles because they're a pair of angles on the outer side of each of those two parallel lines but on opposite sides of the transversal.

Answer:

Ax+By=C

Step-by-step explanation:

The value of x is 5.

The length of ST is 16.

Collinear points are the points that lie on the same straight line or in a single line.

Given:

RS = 5x - 9 and RT = 3x + 17

As, R, S and T are collinear points.

so, we can write

RS = ST

and, RS + ST = RT

2ST = Rt

ST= RT/2

ST = (3x+ 17)/2

Now,

RS = ST

5x - 9 =  (3x+ 17)/2

10x - 18 = 3x+ 17

7x = 35

x=5

So, the value of x is 5.

Now, length of ST

= (3x+ 17)/2

=(3*5 + 17)/2

=32/2

=16

Thus, length of ST is 16 units

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Answer: Use cross product to determine if the two ratios form a proportion. Here we can see that 2/16 and 5/40 are proportions since their cross products are equal. Percent means hundredths or per hundred and is written with the symbol, %. Percent is a ratio were we compare numbers to 100 which means that 1% is 1/100.

Answer:5

Step-by-step explanation:

25 miles divided by 5 days equal the 5 miles

5 times 5 =25

The percent of students in grade 8 those who like to join dance club is equal to 25%.

Total number of students in grade 8 = 20

Total number of students of grade 8  join in dance club = 5

Percent of students of grade 8 prefer to join dance club

= ( total number of students prefer dance club ) / ( Total number of students in grade 8 ) × 100

Substitute the value in the formula we get,

⇒ Percent of students of grade 8 prefer to join dance club

= ( 5 ) / ( 20 ) × 100

⇒ Percent of students of grade 8 prefer to join dance club  = 0.25 × 100

⇒ Percent of students of grade 8 prefer to join dance club  = 25%

Therefore, percent of grade 8 students who preferred to join dance club is equal to 25%.  

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The above question is incomplete, the complete question is:

What percent of students in grade 8 prefer to join a dance club?

                      Dance club      Hiking club     Total

Grade 7               15                       15                 30

Grade 8               5                        15                  20

Total                    20                     30                    50

315 m²

area of rec + area of rec + area of rec +  area of triangle

⇒ length + width + length + width + length + width + 1/2 * base * height

⇒ 19 * 6 + 9 * 9 + 18 * 5 + 1/2 * 12 * 5

⇒ 90 + 30 + 81 + 114

⇒ 315 m²

Answer:

315 m²

Step-by-step explanation:

As this figure may seem complicated, we can split it into four separate figures.

Area

An inscribed angle is formed by two chords of a circle that intersect at a vertex located on the circle.

The angle itself is formed by the two sides of the angle, which are the line segments connecting the vertex to the endpoints of the chords. The property that makes inscribed angles interesting is that the measure of an inscribed angle is half the measure of the intercepted arc on the circle.

This relationship holds true for any inscribed angle in a circle, making it a useful concept in geometry for solving problems involving angles, arcs, and circles.

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Answer:

\(yes \\ 1 : 3 = 3 : 9\)

Step-by-step explanation:

yes.

\(1 : 3 = 3 : 9\)

Let see how is it possible,

\(3 \times 1 : 3 \times 3 = 3 :9 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3 : 9 = 3 : 9\)

Also,

\(1 : 3= 3 \div 3 : 9 \div 3 \\ 1 : 3 = 1 : 3\)

hope this helps

brainliest appreciated

good luck! have a nice day!

He will pick a sample of seniors in this instance.

Given statement,

Dr. Stuart wants to study whether there is a relationship between the number of hours a high school senior spends on social networking sites and their grade point average. he obviously cannot study every 12th grader, so instead, he will select a smaller of seniors to study.

→ In this case he will select a sample of seniors.

→ Dr. Stuart is interested in determining whether there is a correlation between a high school senior's grade point average and the number of hours spent on social networking sites. He will instead choose a smaller sample of seniors to study because he certainly cannot study every student in the 12th grade.

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Completing the square – can be used to solve any quadratic equation. It is a very important method for rewriting a quadratic function in vertex form. Quadratic formula – is the method that is used most often for solving a quadratic equation.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Any quadratic problem may be solved by completing the square. It is a critical way for expressing a quadratic function in vertex form. The quadratic formula is the most often used method for solving a quadratic problem.

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Step 1

State an expression for the probability of an event.

Number of required events = 4

Total number of events = 7

Step 2

Find the probabilities of defective batteries with replacement and without replacement

Step 3

Find the probabilities that both are defective.

Hence the probability that 2 batteries selected at random without replacement are both defective is 2/7

The given series is ∑(n=0 to infinity) ((-1)^n * 5^n * x^4n) / n!. This is the Maclaurin series expansion of the function f(x) = e^(-5x^4).

By comparing with the Maclaurin series expansion of e^x, we can see that the sum of the given series is f(1) = e^(-5).
Therefore, the sum of the series is e^(-5).
The given series is a sum of terms in the form:
Σ(−1)^n * 5n * x^(4n) * n! for n = 0 to ∞
Unfortunately, this series does not have a closed-form expression or a simple formula for finding the sum, since it involves alternating signs, factorials, and exponential terms. To find an approximate sum, you can calculate the first few terms of the series and observe the behavior or use numerical methods to estimate the sum.

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From the formula of expansion series for \(e^x\), the sum of series, \(\sum_{n = 0}^{\infty} (-1)^n \frac{5^n x^{4n}}{n!} \\ \) is equals to the \( e^{-5x⁴}\).

A series in mathematics is the sum of the serval numbers or elements of the sequence. The number or elements are called term of sequence. For example, to create a series from the sequence of the first five positive integers as 1, 2, 3, 4, 5 we will simply sum up all. Therefore, the resultant, 1 + 2 + 3 + 4 + 5, form a series. We have a series, \(\sum_{n= 0}^{\infty} (-1)^n \frac{5^n x^{4n}}{n!} \\ \).

The sum of a series means the total list of numbers or terms in the series sum up to. Using the some known formulas of series, like \(1 + x + \frac{x²}{2!} + ... + \frac{x^n}{n!}+ ... = \sum_{n = 0}^{\infty } \frac{ x^n}{n!} = e^x \\ \) Similarly, \(1 - x + \frac{x²}{2!} - ... + \frac{x^n}{n!}+ ... = \sum_{n = 0}^{\infty } (-1)^n \frac{ x^n}{n!} = e^{-x } \\ \) Rewrite the expression for provide series as \(\sum_{n = 0}^{\infty} (-1)^n \frac{(5x⁴)^n}{n!} \\ \). Now, comparing this series to the series of e^{-x}, here x = 5x⁴ so, we can write the sum of series as \(\sum_{n = 0}^{\infty} (-1)^n \frac{(5x⁴)^n}{n!} = e^{-5x⁴} \\ \). Hence, required value is \(e^{ - 5x^{4} } \).

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Complete question:

find the sum of the series

\(\sum_{n = 0}^{\infty} (-1)^n \frac{5^n x^{4n}}{n!} \\ \).

Answer:

Is should be  1 1/8. cups of flour to make one fruitcake.

Glokk8x - The Album 8x out on all platforms

25% of___ is 30

Answer: 120

Answer:

120

Step-by-step explanation:

25%=0.25

0.25x=30

x=30/0.25

x=120

Answer:

cannot be determined

Step-by-step explanation:

The sample mean used to construct the confidence interval (2.4, 9.8) cannot be determined without the confidence level. The confidence interval provides a range of possible values for the true population parameter (in this case, the population mean), based on the sample data and a chosen confidence level. The sample mean itself is not provided in the confidence interval, but rather the range within which the true population mean is likely to fall with a certain level of confidence. Therefore, without knowing the confidence level used to construct the interval, we cannot determine the sample mean.

The two possibilities for its x component is ±53.9 units, and its direction is θ=26.60°

The two possibilities for its x component which is given as :

Using an equation, we have

⇒\(z^{2} =x^{2} +y^{2}\)

\(x=\sqrt{z^{2}-y^{2} }\)

where, z = magnitude of z component = 86

y = magnitude of y component = - 67

then, we get

⇒\(x=\sqrt{86^{2}-67^{2} }\)

⇒\(x = \sqrt{2907}\)

⇒x = ±53.9 units

Assuming the x component is known to be positive, specify the magnitude of the vector which, if we add it to the original one, would give a resultant vector that is 80 units long and points entirely in the −x direction.

Resultant x-component = Sum of x-components of the 86-unit vector and that of the unknown vector.

⇒-80 = +53.9 + u

⇒-80-53.9 = u

⇒u = -133.9 units

Resultant y-component = Sum of y-components of the 86-unit vector and that of the unknown vector.

⇒0 = -67 + v

⇒0 + 67 = v

⇒v = +67 units

Magnitude of unknown vector is given by,

⇒\(Z = \sqrt{u^{2}+v^{2} }\)

⇒\(Z = \sqrt{(-133.9)^2 + (67)^{2} }\)

⇒Z = 149.7 units

And its direction is given by,

⇒ \(\theta\) = tan-1 (67 / -133.9)

⇒ \(\theta\) = tan-1 (-0.5003734)

⇒ \(\theta\) = 26.60°

Therefore, the two possibilities for its x component is ±53.9 units, and its direction is θ=26.60°

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You are given a vector in the xy plane that has a magnitude of 86.0 units and a y component of-67.0 units.

What are the two possibilities for its x component

Assuming the x component is known to be positive, specify the magnitude of the vector which, if you add it to the original one, would give a resultant vector that is 80.0 units long and points entirely in the −x direction.

Specify the direction of the vector.

Answer:

A.) combinations of the hours he can work at the two jobs and earn at least $300

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

The answers to both the subparts using probability are shown:

(A) The probability that every sign is unique is 378/845.

(B) The probability that each sign is unique and that the first number is the biggest one among the others is 189/1690.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

The probability is calculated by dividing the total number of outcomes by the total number of potential events.

Odds and probability are two different concepts.

Calculating odds involves dividing the probability of an event by the probability that it won't happen.

(A) Since there are three positions for letters and four places for numbers.

Consequently, the final result will be 10⁴×26³.

Since each letter and number should be distinct, the necessary probability is:

= 10 * 9 * 8 * 7 * 26 * 25 * 24 / 10⁴ * 26³

= 378/845

(B) In this instance, the likelihood that the first number will be the greatest among the four numbers is 1/4 because it should be.

In order to obtain the result, multiply the result in (a) by 1/4 as follows:

= 378/845 * 1/4

= 189/1690

Therefore, the answers to both the subparts using probability are shown:

(A) The probability that every sign is unique is 378/845.

(B) The probability that each sign is unique and that the first number is the biggest one among the others is 189/1690.

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The given system of equations can be represented as a matrix equation of the form AX = B, where A is the coefficient matrix, X is the column vector of variables, and B is the column vector of constants.

The given system of equations can be rewritten as:

3x - 5y - 3z = -5

2x + 4y - z = -8

-2x + 3y + 5z = 3

To represent this system as a matrix equation AX = B, we collect the coefficients of x, y, and z into the matrix A, and the constants on the right-hand side into the column vector B. The resulting matrix equation is:

[3 -5 -3] [x] [ -5]

[2 4 -1] [y] = [- 8]

[-2 3 5] [z] [ 3]

In this matrix equation, A is the coefficient matrix [3 -5 -3; 2 4 -1; -2 3 5], X is the column vector [x; y; z], and B is the column vector [-5; -8; 3]. Therefore, the given system of equations can be represented as the matrix equation AX = B.

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The required weight of a male zebra weighs 750 pounds as of the given condition.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
The diagram that models the ratio in the story is:

Male zebra : Female zebra = 5 : 4

Let's say the female zebra weighs "x" pounds. Then, according to the ratio, the male zebra weighs 5/4 times the weight of the female zebra, which is:

Male zebra = (5/4) x

We also know that the male zebra weighs 150 pounds more than the female zebra. So, we can set up an equation:

Male zebra = Female zebra + 150

Substituting the expression for male zebra from the ratio, we get:

(5/4) x = x + 150

5x = 4x + 600

x = 600

Therefore, the female zebra weighs 600 pounds, and the male zebra weighs,

Male zebra = (5/4) x 600 = 750 pounds

Therefore, the male zebra weighs 750 pounds.

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268 degrees is the equivalent measure of angke 't'

The given polygon is a heptagon and the measure of the exterior angle of a heptagon sums up to 540 degrees. Hence:

81 + t + 35 + 40 + 116 = 540

Simplify to have:
81 + t + 35 + 40 + 116 = 540

272  + t = 540

Subtract 272 from both sides

272 + t = 272 = 540 - 272

t = 540 - 272

t = 268

Hence the measure of angle t is equivalent to 268 degrees

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Answer:

y= 3/4x + 1/4

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

It does not pass the vertical line test, so the relation is not a function. This is because there are x-values that have several y-values. To be a function, a relation must have x-values that only have one y-value each.

Hope this helps!

Answer:

No

Step-by-step explanation:

Because for any given point along the x-axis it has 2 values along y-axis.

For a relation to be a function it must have only one value at y-axis along any given point along the x-axis

In the passage above, a parallel is drawn between Karen's friend, Brody, and a shining beacon of light. The Option B.

A parallel sentence occurs when words are formed in the same way or have the same structure.

In the passage, Brody is compared to a shining beacon of light. This suggests that Brody is portrayed as someone who brings brightness and positivity into Karen's life just like a beacon of light guides and illuminates the way.

So, the comparison implies that Brody has a significant and uplifting impact on Karen's experiences or emotions.

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