write a poem about linear functions.

The interpretation of the given question is as follows:

Use the given inverse to solve the system of equations

\(x- y - z = -6 \\ \\ 2y + z = -6 \\ \\ 3x -8 y = - \dfrac{1}{2}\)

The inverse of  \(\left[\begin{array}{ccc}1&-1&1\\0&2&1\\3&-8&0\end{array}\right] is \left[\begin{array}{ccc}-8&8&3\\-3&3&1\\6&-5&-2\end{array}\right]\)

x =

y =

z =

Answer:

x = - 1.5

y = - 0.5

z =  - 5

Step-by-step explanation:

Using the correlation  of inverse of matrix AX = B to solve the question above;

AX = B

⇒ A⁻¹(AX)  = A⁻¹ B

X =  A⁻¹ B

So ;

X         =        A⁻¹                             B

\(\left[\begin{array}{c}x\\y\\z\end{array}\right] =\)     \(\left[\begin{array}{ccc}-8&8&3\\-3&3&1\\6&-5&-2\end{array}\right] =\)   \(\left[\begin{array}{ccc}-6\\ -6\\- \dfrac{1}{2}\end{array}\right]\)

 \(\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}(-8*-6)+(8*-6)+(3*-\dfrac{1}{2})\\(-3*-6)+(3*-6)+(1*-\dfrac{1}{2})\\(6*-6)+(5*-6)+(-2* - \dfrac{1}{2})\end{array}\right]\)

\(\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}(48)+(-48)+(\dfrac{-3}{2})\\(18)+(-18)+(\dfrac{-1}{2})\\(-36)+(30)+(1)\end{array}\right]\)

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

\(\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}-1.5\\-0.5\\ -5\end{array}\right]\)

So, only option C is a counterexample of the conditional statement "If a number is divisible by 4, then it is divisible by 8."

A counterexample of a conditional statement is a specific case or example that contradicts the statement or goes against its logical implications.

In this case, the conditional statement is "If a number is divisible by 4, then it is divisible by 8."

Option C, 36, is a counterexample of this conditional statement.

This is because 36 is divisible by 4 (9 x 4 = 36), but it is not divisible by 8 (36 / 8 = 4.5). This contradicts the statement that if a number is divisible by 4, it must also be divisible by 8.

Option A, 12, is not a counterexample of the conditional statement because 12 is divisible by 4 (12 / 4 = 3) and also divisible by 8 (12 / 8 = 1.5).

Option B, 32, is not a counterexample of the conditional statement because 32 is divisible by 4 (32 / 4 = 8) and also divisible by 8 (32 / 8 = 4).

Option D, 20, is not a counterexample of the conditional statement because 20 is not divisible by 4 (20 / 4 = 5)

So, in summary, only option C is a counterexample of the conditional statement "If a number is divisible by 4, then it is divisible by 8."

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Answer:

I dont but want to.

Hope this helps! :) ;-;

Step-by-step explanation:

Answer:

i have a fixed mindset

Step-by-step explanation:

if i want something i will work on it no matter how hard or long it will take me i will persevere and be positive

Answer:

D

Step-by-step explanation:

The actual base of the building is 1890 square feet.

A rectangle is a two-dimensional figure with length and width.

The area of a rectangle is Length x width.

We have,

1 inch = 15 feet

Rectangular base:

Length = 4.2 in

Width = 2 in

So,

4.2 in = 4.2 x 15 feet = 63 feet

2 in = 2 x 15 = 30 feet

Now,

The actual base of the building.

= 63 x 30

= 1890 square feet

Thus,

1890 square feet.

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Answer:

The length of the third side is approximately ≈ 14.79 inches

Step-by-step explanation:

A piece of wire is bent into the shape of a triangle. Two sides have lengths of 16 inches and 23 inches. The angle between these two sides is 40°. What is the length of the third side to the nearest hundredth of an inch?

Use the law of cosines to find the length of the missing side.

Let C be the third side.

A = 18

B = 23

Angle C = 40^∘

c^2  =  a^2  +  b^2 - 2ab  cos C

c =  √a^2 + b^2 - 2ab cos C

c =  √18^2 + 23 ^2 - 2 (18) (23) cos 40^∘

c = √583 - 828 cos40^∘

≈ 14.79

Thus, The length of the third side is approximately  14.79 inches.

Hope this helps!

Answer: It’s not correct, the equality is false. The reasoning behind this is the equality is the left-hand and right-hand side are different when you do the math.no

Answer:

its been awhile since I've done this bit i think its B

The the number of construction toys that must be bought so that the profit for Jacelyn's company and Richie's company is the same. is t= 204.3269230769231

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

As, per the given situation the equation can be

2125 + 49.99 t = 39.95 t

10.4 t= 2125

t= 2125 / 10.4

t= 21250/104

t= 204.3269230769231

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Answer:

O✓ (0,-5)

Step-by-step explanation:

Identify the x-value in the ordered pair and plug it into the equation. When you simplify, if the y-value you get is the same as the y-value in the ordered pair, then that ordered pair is indeed a solution to the equation.

Answer:

c. x=65

f. Alternate Exterior Angles

Step-by-step explanation:

2x+2=3x-63

2x=3x-65

-x=-65

x=65

They would be Alternate Exterior Angles because, they are 1, both on the outside of the parallel lines, and they are on different sides of the intersecting line, making them alternate. So, Alternate Exterior Angles

The range and domain of the graph shown is

domain -4 ≤ x < ∞

range ∞ ≤ x < 3

All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.

The domain of a graph is every value in the graph, from left to right.

Examining the curve the extreme left has x coordinate value of -4 and the right end have an arrow which means the value continues. this is written as

-4 ≤ x < ∞

The graph's entire range, from lower to higher numbers, in the vertical line represents the range.

Examining the curve the lowest point the curve reached in y-coordinate have an arrow which means the value continues and the top end have the value of 3. this is written as

∞ ≤ x < 3

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An odd function is a function that satisfies:

If f(x) is an odd function, we can try with to see if each of the options to see if they are odd functions:

a) In the case of the absolute function, it can not be an odd function, as it will always be positive for all x.

b) f(x-1) is a translation of f(x) to the right. If f(x) is an odd function, f(x-1) will not be neither an odd function or an even function, as it will not have symmetry respect to the origin.

c) -f(x) will change the sign of f(x), so it will have the same symmetry respect to the origin but rotated 180° from f(x). Then, it is still an odd function.

d) f(|x|) will not have the same symmetry properties of f(x) so it will not be an odd function.

Answer: - f(x) [Option C]

Answer:

Step-by-step explanation:

20

Greetings !

The function has no undefined points nor domain constraints Therefore, the domain is

\(domain \: of \: 3 {}^{x} = \\ interval \: notation \: ( - \infty ,\infty ) \\ solution \: - \infty < x < \infty \\ \\ \)

The range of an exponential function of the form

\(c.n {}^{ax + b} + k \: is \: f(x) > k \\ k = 0,f(x) > 0\)

And also the range is given as

\(range \: of \: 3 {}^{x} = \\ solution \: x > 0 \\ interval \: notation \: (0,\infty )

Hope it helps!

The probability values for the questions posed are :

A.)

Number of students Taking a public speaking class majoring in business administration.

P(PS or BA) = 55/100 = 11/20

Therefore, the probability of PS or BA is 11/20

B.)

For the survey described, P(taken a public speaking class | majoring in Business Administration) represents the probability that a selected student has taken a public speaking class given that the student is majoring in business administration.

Hence, as inferred from P(A|B) ; probability of A given B.

C.)

P(PS|BA) = n(PSnBA) / n(BA)

n(PS) = 10+20 = 30

n(PSnBA) = 10

P(PS|BA) = 10/30 = 1/3

Therefore , the probability of PS|BA is 1/3.

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A. The system of equations in standard form is: 4x + 5y = 540 and 3x + 5y = 440.

B. The y-intercept of the equation representing the prices on Saturday night is 108, and the y-intercept of the equation representing the prices at the matinee on the second day is 88.

A) Let's define the variables:

Let x represent the number of children attending.

Let y represent the number of adults attending.

On Saturday night:

The equation for the revenue generated on Saturday night is:

4x + 5y = 540 (since children's tickets cost $4 and adults' tickets cost $5, and the total revenue is $540).

Matinee on the second day:

The equation for the revenue generated at the matinee is:

3x + 5y = 440 (since children's tickets cost $3 and adults' tickets still cost $5, and the total revenue is $440).

Therefore, the system of equations in standard form is:

4x + 5y = 540

3x + 5y = 440

B) Let's rewrite the system of equations in slope-intercept form:

On Saturday night:

4x + 5y = 540

Rearranging the equation, we get:

5y = -4x + 540

Dividing both sides by 5, we get:

y = (-4/5)x + 108

The y-intercept of this equation is 108.

Matinee on the second day:

3x + 5y = 440

Rearranging the equation, we get:

5y = -3x + 440

Dividing both sides by 5, we get:

y = (-3/5)x + 88

The y-intercept of this equation is 88.

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............, .......

Answer:

{ \(\frac{3}{5}\), 3 }

Step-by-step explanation:

Given

(3x - 9)(5x - 3) = 0

Equate each factor to zero and solve for x

3x - 9 = 0 ( add 9 to both sides )

3x = 9 ( divide both sides by 3 )

x = 3

and

5x - 3 = 0 ( add 3 to both sides )

5x = 3 ( divide both sides by 5 )

x = \(\frac{3}{5}\)

Therefore, out of the 24 students that Blake interviewed, 9 of them participate in sports.

An equation is a mathematical statement that indicates that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign "=" which means that the two expressions have the same value.

Here,

According to the table, Blake interviewed a total of 24 students. To find out how many of these students participate in sports, we need to add up the number of students who collect sports cards and participate in sports, as well as the number of students who do not collect sports cards and participate in sports. So:

Total students who participate in sports = Number of students who collect sports cards and participate in sports + Number of students who do not collect sports cards and participate in sports

Total students who participate in sports = 6 + 3

Total students who participate in sports = 9

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Answer: 258 \(yard^{2}\)

Step-by-step explanation: To find the surface area you add the area of all the sides. And the unit for a surface area is unit (yards) squared.

Front: 5 • 9 = 45

Back: 5 • 9 = 45

Left: 6 • 5 = 30

Right: 6 • 5 = 30

Top: 9 • 6 = 54

Bottom: 9 • 6 = 54

45 + 45 + 30 + 30 + 54 + 54 = 258.

Answer:

is the answer A????????????

to be honest I’m only here for the answers but I also need the points

The correct option regarding whether the relation is a function is:

B. The relation is a function. Each input value is paired with one output value.

A relation represent a function if each value of the input is paired with one value of the output.

In this problem, when the input - output mappings are given by:

{(–2, 3), (–1, 3), (0, 2), (1, 4), (5, 5)}.

Which means that yes, each input value is paired with one output value, hence the relation is a function and option B is correct.

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In this case, we are to determine the probability of selecting two even numbers. This can be solved as follows:There are six even numbers: {2, 4, 6, 8, 10, 12}.We can use the concept of conditional probability since the first event affects the probability of the second event. This can be expressed as follows:

In this case, P(A) represents the probability of selecting an even number, and P(B|A) represents the probability of selecting an even number given that the first card selected was even. P(A) = 6/12 = 1/2 (there are six even numbers and twelve cards in total)P(B|A) = 5/11 (there are five even numbers left in the box after the first even number is selected, and eleven cards are left in total).

The probability of selecting two even numbers can be found by multiplying these probabilities: P(A) x P(B|A) = (1/2) x (5/11) = 5/22Therefore, the probability of selecting two even numbers is 5/22.Answer: 5/22

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Answer:

a. gh³

b. xy³

Step-by-step explanation:

a. \(g^{3-2}\)\(h^{5-2}\) = gh³

b. \(x^{3-2} y^{4-1} p^{1-1}\) = xy³

Use the negative exponent rule.

Answer:

a)b= 5

b)45

Step-by-step explanation:

a) 5 times ten is 50 . the two factors of 50 are 25 and 2. The square root of 25 is 5, so that's the answer.

b) 27 × 75 is 2025 and the base root is 45², then with the radical and exponent we reduce the index by 2 to get 45.

\(\textbf{a)}\\\\~~~\sqrt 5 \times \sqrt{10}\\\\=\sqrt{5} \times \sqrt{5 \times 2}\\\\=\sqrt{5} \times \sqrt 5 \times \sqrt 2\\\\=\left(\sqrt 5 \right)^2 \times \sqrt 2\\\\=5\sqrt 2\\\\\text{It is now in a form of} ~ b\sqrt2 ~ \text{where} ~b = 5.\\\\\\\)

\(\textbf{b)}\\\\~~~\sqrt{27} \times \sqrt{75}\\\\=\sqrt{9 \times 3} \times \sqrt{25 \times 3}\\\\=\sqrt 9 \times \sqrt 3 \times \sqrt{25} \times \sqrt 3\\\\=3\times 5 \times \left(\sqrt 3 \right)^2\\\\=15 \times 3\\\\=45\)

Answer: 9(9+2) is equivalent to 81+18 because 9 plus 2 equals 11 and 11 times 9 is 99 and 81+18 is 99.

Step-by-step explanation:

Answer:

V = 1/3 * π * r^2 * h OR V = π * r^2 * h/3

Step-by-step explanation:

hope it will help you dear

you told only formula if you need derevation then say :)