Solve the equation

22 = -13 + a

Answer:

the midpoint would be:(0,5)

Step-by-step explanation:

The correct option is B. The statement "The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A." is true. The statement is the definition of the algebraic multiplicity of an eigenvalue of A.

A matrix is diagonalizable if and only if each eigenvalue of the matrix has an algebraic multiplicity that is equal to its geometric multiplicity. To get the characteristic equation of a matrix, the determinant of the matrix A   I is set to zero. The characteristic equation of an nn matrix A is given by AI = 0. The characteristic equation's roots are the matrix's eigenvalues.

The algebraic multiplicity of an eigenvalue is the number of times it appears as the root of the characteristic equation. The geometric multiplicity of an eigenvalue is the number of linearly independent eigenvectors corresponding to that eigenvalue. So, the correct option is B.

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If last week Salazar played 13 more tennis games than Perry and they played a combined total of 53 games, then Salazar played a total of 33 games.

Let the total number of games played by Perry be x.

It is given that, Salazar played 13 more tennis games than Perry.

⇒ Total games played by Salazar = x + 13

Also, Salazar and Perry played a combined of 53 games.

Hence, total number of tennis games played by Salazar and Perry = 53

⇒ Games played by Salazar + Games played by Perry = 53

⇒  x + (x + 13) = 53

2x + 13 = 53

2x = 53 - 13

2x = 40

x = 40 / 2

x = 20

Therefore, total number of games played by Salazar = x+13

= 20 + 13

= 33

Thus, Salazar played total 33 games.

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The probability that a homebuilder takes 200 days or less to complete a house is approximately 0.8238, or 82.38%.

Explanation :

To answer this question, we can use the concept of the z-score. The z-score tells us how many standard deviations a data point is from the mean.

Let's calculate the z-score for a completion time of 200 days:
z = (x - μ) / σ
where x is the completion time, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get:
z = (200 - 176.7) / 24.8 = 0.93

To find the probability associated with this z-score, we can use a z-table or a calculator. In this case, the probability is 0.8238.

This means that there is an 82.38% chance that the completion time of a house will be 200 days or less, given that the completion time follows a normal distribution with a mean of 176.7 days and a standard deviation of 24.8 days.

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Answer:

Step-by-step explanation:

Answer:

Well there isn't really a question

Step-by-step explanation:

y=3x means anything on the x axis times 3 = the number on the y axis. This is an example of an proportional relation ship and will create a straight line on a graph.

Let's take the subspace (X,T) of (Y,T*), where (Y,T*) is a subspace of (Z,T**). Here, we are required to show that (X,T) is also a subspace of (Z,T**). Let's start our proof.

To show that (X,T) is a subspace of (Z,T**), we must show that (X,T) satisfies the subspace axioms. The subspace axioms that must be satisfied are:

1. The zero vector, 0, is in (X,T).

2. If u and v are in (X,T), then u + v is also in (X,T).

3. If u is in (X,T) and a is a scalar, then au is also in (X,T).

So, let's prove each axiom for (X,T) to be a subspace of (Z,T**):

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Answer:

strength, availability, preference, and cost

Step-by-step explanation:

Stability, purpose, texture, appearance, structure, and size.

Answer: a₁=31    a₁₁=-9

Step-by-step explanation:

\(\displaystyle\\\left \{ {{a_4=19} \atop {a_7=7}} \right. \\\\a_n=a_1+(n-1)d\\\\\left \{ {{a_1+(4-1)d=19} \atop {a_1+(7-1)d=7}} \right. \\\\\left \{ {{a_1+3d=19\ \ \ \ (1)} \atop {a_1+6d=7\ \ \ \ \ (2)}} \right.\)

Subtract equation (2) from equation (1):

\(3d=-12\)

Divide both parts of the equation by 3:

\(d=-4\)

Thus,

\(a_1+(3)(-4)=19\\a_1-12=19\\a_1-12+12=19+12\\a_1=31\\a_{11}=a_1+(11-1)d\\a_{11}=31+(10)(-4)\\a_{11}=31-40\\a_{11}=-9\)

Answer:

a = 43

d = -6

\(\sf a_{11} = -17\)

Step-by-step explanation:

Arithmetic sequence:

 Use the formula to find the nth term:

    \(\sf \boxed{\bf a_n= a+(n-1)d}\)

Here, a is the first term, n is the number of terms and d is the common difference.

\(\sf a_4 = 19\\\\a+(4-1)*d = 19\\\\a + 3d = 19 -------------------(i)\)

        \(\sf a_7 = 7\\\\a + 6d = 7 ------------------(ii)\\\)

Subtract equation (i) from (ii) and thus 'a' will be eliminated and we can find the value of 'd'.

     (ii)       a + 6d = 7

     (i)        a + 4d = 19

                -    -     = -    

                       2d = -12

                          d = -12/2

                          \(\sf \boxed{\bf d = -6}\)

Now, plugin d = -6 in any of the two equations. We are substituting the 'd' value in equation (i)

  a + 4*(-6) = 19

  a - 24      = 19

               a = 19 + 24

               \(\sf \boxed{\bf a = 43}\)

\(\sf a_{11} = a + 10d\)

      = 43 + 10*(-6)

      = 43 - 60

\(\sf \boxed{\bf a_{11} = -17 }\)

Domain is the set of x-values. In this case, since this is an inequality your domain in set notation is (-2,2] or -2<x<=2. Range is the set of y-values in set notation it would be (-2, 1] or -2<y<=1.

Finally, for the function find the slope of your equation (you can do this on your own)

Answer:

74°

Step-by-step explanation:

A rhombus is a quadrilateral that has its opposite sides to be parallel to be each other. This means that the two interior opposite angles are equal to each other. Since the sum of the angles of a quadrilateral is 360°.

According to the triangle, since one of the acute angle is 32°, then the acute angle opposite to this angle will also be 32°.

The remaining angle of the rhombus will be calculated as thus;

= 360° - (32°+32°)

= 360° - 64°

= 296°

This means the other two opposite angles will have a sum total of 296°. Individual obtuse angle will be 296°/2 i.e 148°

This means that each obtuse angles of the rhombus will be 148°.

To get the unknown angle m°, we can see that the diagonal cuts the two obtuse angles equally, hence one of the obtuse angles will also be divided equally to get the unknown angle m°.

m° = 148°/2

m° = 74°

Hence the angle measure if m(1) is 74°

Answer:negative 12 x cubed y squared z

Step-by-step explanation: So it would be -12^2y^2z

C. F-test statistic for testing the validity of the regression equation.

In multiple regression analysis, the ratio of MSR (Mean Square Regression) to MSE (Mean Square Error) is used to calculate the F-test statistic.

This statistic is used to test the overall validity of the regression equation, determining whether the regression model as a whole is statistically significant in explaining the variation in the dependent variable.

The F-test assesses whether the regression model as a whole provides a significant improvement over the null model (a model with no independent variables).

A large F-statistic indicates that the regression equation is statistically significant, implying that at least one of the independent variables has a significant effect on the dependent variable.

Therefore, option C, the F-test statistic for testing the validity of the regression equation, is the correct answer.

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Answer:

A, B, C, E, F

Step-by-step explanation:

In order to identify the applicable statements to the given graph, we must first determine the slope and y-intercept of the equation.

Choose two points from the graph.

Let (x₁, y₁) = (-1, 1)

     (x₂, y₂) = (3, 2)

Substitute these coordinates into the following slope formula:

m = (y₂ - y₁)/(x₂ - x₁)

\(m = \frac{2 - 1}{3 - (-1)} = \frac{1}{3 + 1} = \frac{1}{4}\)

Therefore, the slope of the line is, m = ¼.

Next, we need to determine the y-intercept of the equation. The y-intercept is the y-coordinate of the point (0, b ) where the graph crosses the y-axis. The y-intercept also provides the value of y when x = 0. There are two ways of identifying the y-intercept: by referencing the graph, or solving for the value of b algebraically.

To solve for the y-intercept algebraically, use the slope, m = ¼, and one of the points on the graph, (-1, 1). Substitute these values into the following slope-intercept form: y = mx + b.

y = mx + b

1 = ¼(-1) + b

1 = -¼ + b

Add ¼ to both sides of the equation:

1 + ¼ = -¼ + ¼ + b

5/4 = b

The y-intercept is \((0, \frac{5}{4})\) where \(b = \frac{5}{4}\).

The linear equation in slope-intercept form is \(y = \frac{1}{4}x + \frac{5}{4}\)  ⇒ Option F.

We must test whether Option C provides a true statement by substituting the value of \((1, \frac{3}{2})\) into the equation.

\(y = \frac{1}{4}x + \frac{5}{4}\)

\(\frac{3}{2} = \frac{1}{4}(1) + \frac{5}{4}\)

\(\frac{3}{2} = \frac{1}{4} + \frac{5}{4}\)

\(\frac{3}{2} = \frac{6}{4}\)

\(\frac{3}{2} = \frac{3}{2}\)  ⇒ True statement.

Therefore, Option C is a valid answer.

Option A and B are also valid answers. We used the coordinates in Options A and B to solve for the slope.

Option D is an invalid answer, as there are more than 2 solutions to the given linear equation.

Option E is also a valid answer, as the points along the graph of a linear equation are solutions.  Therefore, the given linear equation has infinitely many solutions.  

Option G is also an invalid answer, as we have already determined that the linear equation that represents the given graph is represented by Option F.

Therefore, Options A, B, C, E, and F provide true statements about the given line.

Answer:

(12,-7)

Step-by-step explanation:

The required ordered pair of the pre-image of D'(4, -3) is D(12, -7).

Given that,
To determine the preimage of the ordered pair of D'(4, -3) by the translation, (x, y)  to (x – 8, y+4).

Coordinate, is represented as the values on the x-axis and y-axis of the graph.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let the ordered pair of the preimage be (x, y)
Now,

according to the question,
x - 8 = 4
x = 12
y + 4 = -3
y = -7

Thus, the required ordered pair of the pre-image of D'(4, -3) is D(12, -7).

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Answer:

21x-22

Step-by-step explanation:

Try using m a t h w a y if you need help with any other questions

Answer:

linear monomial

Step-by-step explanation:

Answer:

The base and height of three parallelograms with the same area as the 12 square inches rectangle are

1) First parallelogram;

Base length of parallelogram = 4 units

Height of parallelogram, = 3 units

2) Second parallelogram

Base length of parallelogram = 6 units

Height of parallelogram, = 2 units

3) Third parallelogram

Base length of parallelogram = 5 units

Height of parallelogram, = 2.4 units

Step-by-step explanation:

The vertices of the rectangle are; (0, 0), (4, 0), (4, 3), and (0, 3)

Let ABCD represent the vertices of the rectangle such that we have;

A(0, 0), B(4, 0), C(4, 3), and D(0, 3)

The area of the rectangle, A = The length of AB × The length of CB

The length of AB = √((4 - 0)² + (0 - 0)²) = 4

The length of CB = √((4 - 4)² + (3 - 0)²) = 3

∴ The area of the rectangle, A = 4 × 3 = 12 square units

The area of a parallelogram = Base length × Height

The base and height of three parallelograms with the same area as the 12 square inches rectangle are;

1) Base length of parallelogram = 4 units

Height of parallelogram, = 3 units

The area of the parallelogram, A = Base × Height;

∴ A = 4 units × 3 units = 12 units²

2) Base length of parallelogram = 6 units

Height of parallelogram, = 2 units

The area of the parallelogram, A = Base × Height;

∴ A = 6 units × 2 units = 12 units²

3) Base length of parallelogram = 5 units

Height of parallelogram, = 2.4 units

The area of the parallelogram, A = Base × Height;

∴ A = 5 units × 2.5 units = 12 units².

Answer:

The measurement of the third angle would be 139 degrees.

Step-by-step explanation:

Using the triangle sum theorem, you already know that all interior angles of a triangle add up to 180 degrees. So since you already have two angle measurements, all you have to do is add them together and subtract them from 180 degrees. In this case it is 29+12, which equals 41. Now you subtract that from 180 and get 139.

I hope this helps!

Answer: 1st one : degree = 5; number of terms = 3

              2nd one:  degree = 6; number of terms = 4

              3rd one: degree = 4; number of terms = 2

Step-by-step explanation: First you have to simplify everything.

So for the first one you would get 14x^5 -30x^4 + 2x^3; After that you just say that the degree is 5, and number of terms is 3. For the second one you do the same thing; simplify and then find the degree and number of terms. If your confused on how to simplify then look at the work that I've showed below (my work) And if your confused on how to find the degree, it's just what term has the highest power, to be more clear lets say we have x^3 + x^4*y^7. We have 2 terms, and the degree of the 1st is 3, and the degree of the second term is 11. Meaning the degree of the polynomial is 11 (the larger one) If your confused on how to find the amount of terms, then it's just counting them, they're divided by subtraction and addition.

The probability that a student chosen at random dislikes at least one of them is 0.2. Probability is the likelihood of occurrence of an event.

Probability a student likes math's = 0.7

Probability a student dislikes maths = 1 - 0.7 = 0.3

Probability a student likes history = 0.2

Probability a student dislikes history = 1 - 0.2= 0.8

Probability a student likes maths and history = 0.1

Probability a student dislikes maths = 1 - 0.1= 0.9

Probability a student dislikes at least one of them = probability he dislikes math's + Probability a student dislikes history- Probability a student dislikes math's and history = 0.3+0.8-0.9 = 0.2

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How do you classify a triangle by its angle?

An acute triangle has three angles that each measure less than 90 degrees. An equilateral triangle is a triangle in which all three sides are the same length. An obtuse triangle is a triangle with one angle that is greater than 90 degrees. A right triangle is a triangle with one 90 degree angle.

Step-by-step explanation:

The area of the shaded region will be equal to the (area of the hexagon - area of pentagon) + (area of a square - area of equilateral triangle).

From the complete question, the area of the shaded region 1 will be:

= Area of regular hexagon - Area of regular pentagon

The shaded region 2 will be:

= Area of a square - Area of equilateral triangle

Therefore, the area of the shaded region will be equal to the (area of the hexagon - area of pentagon) + (area of a square - area of equilateral triangle).

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Tavon can make 1.5 gallons of lemonade (equivalent to 1.5 * 12 = 18 lemons and 1.5 * 3 = 4.5 cups of sugar) and 5.5 gallons of lemon-flavored tea (equivalent to 5.5 * 3 = 16.5 lemons and 5.5 * 1 = 5.5 cups of sugar).

To determine how much of each type of drink Tavon can make, we can set up a system of equations based on the given information. Let's use the variables L for lemons and S for cups of sugar.

From the information provided, we know that for each gallon of lemonade, Tavon needs 12 lemons and 3 cups of sugar. Similarly, for each gallon of lemon-flavored tea, he needs 3 lemons and 1 cup of sugar. Tavon has a total of 36 lemons and 10 cups of sugar.

Let's set up the equations:

12L + 3S = 36  (equation for lemons)

3L + S = 10    (equation for sugar)

To solve this system of equations, we can use substitution or elimination. Let's use the elimination method.

First, multiply the second equation by 4 to make the coefficients of L the same:

12L + 4S = 40

Now, subtract the modified second equation from the first equation:

(12L + 3S) - (12L + 4S) = 36 - 40

-L - S = -4

S = 4 + L

Now, substitute this expression for S into the second equation:

3L + (4 + L) = 10

4L + 4 = 10

4L = 6

L = 6/4

L = 1.5

Substituting the value of L into the expression for S:

S = 4 + 1.5

S = 5.5

Therefore, Tavon can make 1.5 gallons of lemonade (equivalent to 1.5 * 12 = 18 lemons and 1.5 * 3 = 4.5 cups of sugar) and 5.5 gallons of lemon-flavored tea (equivalent to 5.5 * 3 = 16.5 lemons and 5.5 * 1 = 5.5 cups of sugar).


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Discount amount = price x discount percentage as a decimal:

Discount amount = 62.00 x 0.15 = 9.30

Discount = $9.30

Answer:

$52.70

Step-by-step explanation:

The inequality shaded in the graph is given as follows:

y ≥ 5x/2 + 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:

b = 3.

When x increases by 2, y increases by 5, hence the slope m is given as follows:

m = 5/2.

Then the equation of the line is given as follows:

y = 5x/2 + 3.

The line is a solid line, and values above it are plotted, hence the inequality is given as follows:

y ≥ 5x/2 + 3.

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Answer:

the cube root of 262144 is 512

Answer:

64

Step-by-step explanation:

The cube root of 262144 is 64

Answer:

$8,000 is the correct

Step-by-step explanation:

is right

The function used to represents the time spend by Jasmine in biking for a distance of d miles is given by f(d) = d / 18.

The time Jasmine spends biking is indeed a function of the distance she bikes.

The formula to calculate the time Jasmine takes to bike a certain distance is equal to,

time = distance / speed __(1)

Here the speed is the rate at which Jasmine bikes = 18 miles per hour.

Let us consider 'd' be the distance representing the number of miles Jasmine bikes.

This implies,

The function that represents the time Jasmine spends biking in terms of the distance .

Function f(d)  representing the time Jasmine spends biking for a distance of d miles

Substitute all the values in the formula (1) we get,

⇒ f(d) = d / 18

Therefore, the function representing the time spend by Jasmine for distance d is equal to f(d) = d / 18.

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The above question is incomplete , the complete question is:

The time Jasmine spends biking is a function of the distance she bikes. Jasmine bikes 18 miles per hour. Assume she bikes at a constant rate.

Write the function representing the time Jasmine spends biking in terms of the distance?