50 points!

a. Use the Point-Slope form to find the equation of the line through the points (-5, 2) and (-2, 6).

b. Write the equation from part (a) above into the General as well as the slope-intercept form showing every step.

c. Find the x and y-intercepts of the equation above.

Thus, for any vector x = (x1, x2, x3) in R3, we have: L(x) = Ax where A is the matrix given above.

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Matrices are used extensively in mathematics, science, engineering, and computer science to represent and manipulate linear equations, systems of equations, vectors, and other mathematical objects. Matrices can be added, subtracted, multiplied, inverted, and transformed in various ways to solve problems in algebra, calculus, statistics, and other fields. Matrices are also used in computer graphics, machine learning, and other areas of artificial intelligence to represent data, images, and other information. The size of a matrix is given by its number of rows and columns, and matrices can be classified as square (when they have the same number of rows and columns) or rectangular (when they have different numbers of rows and columns).

Here,

To find the matrix A that corresponds to the linear transformation L, we need to write L(e1), L(e2), and L(e3) as linear combinations of the standard basis vectors in R2.

L(e1) = (1+0, 0+0) = (1, 0)

L(e2) = (0+1, 1+0) = (1, 1)

L(e3) = (0+0, 1+0) = (0, 1)

So we can write:

L(x) = L(x1 e1 + x2 e2 + x3 e3)

= x1 L(e1) + x2 L(e2) + x3 L(e3)

Now we can assemble the coefficients of this linear combination into a matrix A:

A=  \(\left[\begin{array}{ccc}1&1&0\\0&1&1\end{array}\right]\)

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2 + 2 = 4

* * + * *

* * * *

Answer:

4

Step-by-step explanation:

2 + 2 is 4 cause if you add 2 two two’s it would be 4

Answer:

I think that it is

C

Please let me know if it is not correct!!!!

Answer:

A would most likly be the answer

Step-by-step explanation:

because in the equation sinse A =  -5 1/4 which is whe he was at the end hopefully you understand

Thomas' installment payment that he pays in one fortnight is approximately k523.08.

To calculate Thomas' installment payment, we need to consider the principal amount (k10,000) and the interest rate (36%).

First, let's calculate the total amount to be repaid at the end of the year, including the interest. The interest is calculated as a percentage of the principal amount:

Interest = Principal × Interest Rate

= k10,000 × 0.36

= k3,600

The total amount to be repaid is the sum of the principal and the interest:

Total Amount = Principal + Interest

= k10,000 + k3,600

= k13,600

Now, we need to calculate the number of fortnights in a year. There are 52 weeks in a year, and since each fortnight consists of two weeks, we have:

Number of Fortnights = 52 weeks / 2

= 26 fortnights

To find the installment payment for each fortnight, we divide the total amount by the number of fortnights:

Installment Payment = Total Amount / Number of Fortnights

= k13,600 / 26

≈ k523.08

Therefore, Thomas' installment payment that he pays in one fortnight is approximately k523.08.

It's important to note that this calculation assumes equal installment payments over the course of the year. Different repayment terms or additional fees may affect the actual installment amount. It's always advisable to consult with the bank or financial institution for accurate information regarding loan repayment.

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Answer: A. AB = BC can be proven true.

An isosceles triangle has two equal side lengths, and since the vertex angle is angle C, it means that sides AB and BC are the equal sides.

B. angle A = angle B can be proven true.

In an isosceles triangle, since the two sides are equal, the base angles are also equal.

D. segment BC = segment AC can be proven true.

In an isosceles triangle, since the two sides are equal, the base segments are also equal.

E. segment AB = segment AC can be proven true.

In an isosceles triangle, since the two sides are equal, the base segments are also equal.

C. angle B = angle C is not true.

Because the vertex angle is angle C, and it is formed by the two base segments, so it will be different than angle B and angle A.

Step-by-step explanation:

Answer:

  B, D

Step-by-step explanation:

You want to know what you can prove, given that the vertex angle of isosceles triangle ABC is angle C.

A triangle is isosceles if it has two congruent sides or two congruent angles. In either case, the angles opposite the congruent sides are congruent, and vice versa.

The vertex angle is opposite the "base" of the isosceles triangle. The sides of the vertex angle are the congruent sides, and the angles that are not the vertex angle are the congruent angles.

These sides share point B, which is not the vertex. This cannot be proven.

These are the base angles of the triangle, hence congruent. This can be proven.

These angles cannot be proven congruent using the given information. This will be true if and only if the isosceles triangle is also an equilateral triangle.

These sides share point C, which is the vertex. This can be proven.

These sides share point A, which is not the vertex. This cannot be proven.

Step-by-step explanation:

you can find the answer by vertical opposite angle

if the value of x is computed and it's equal to 78 you will find the answer

78=(12x+18)^

78=(12×5+18)

78=(60+18)

78=78 the problem is solved

may u get branliest please please

Answer:

for 2nd figure answer is 18

Step-by-step explanation:

4x+6x=180°(Being co-interior angle)

or,10x=180°

or,x=180°/10

or,x=18

Answer:

image 1 ---- x = 11

image 2 ---- x = 22.5

Step-by-step explanation:

finding the value at EFB

180 - 147  = 33 degrees

since DEBC is a "Z" angle means that the value at DEB and EBC is the same value of 4x.

therefore :

FEB = 180 - 4x

therefore to find x

NB : total value of triangle is 180 degrees

180 = 33 + (180-4x) +x

180 = 33 + 180 -4x + x

180 = 213 -3x

make x the subject of formula

180-213 = -3x

-33 = -3x

x = -33/-3

x = 11

DEA = BAE

therefore BAE = 2x

DEB = 180 - 4x

ABE = 180 - 6x

NB : total value of triangle is 180 degrees

180 = 2x + (180- 4x) + (180 - 6x)

180 = 2x + 180 - 4x +180 - 6x

180 = -8x + 360

-180 = -8x

x = 22.5

Answer:

What is the angle of rotation for this counterclockwise rotation about the origin?

answer:

270°

Step-by-step explanation:

On solving the provided question, we can say that the expression will be

an = a + (n-1)d => 20.75 = 5 + (n-1)1.75 => n = 10

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

Given that

a=5

d = 1.75

an = 20.75

the expression will be

an = a + (n-1)d

20.75 = 5 + (n-1)1.75

15.75 = (n- 1) 1.75

n-1 = 15.75/1.75

n- 1 = 9

n = 10

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The total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.

To determine the number of possible outcomes, we need to consider the number of outcomes for each event and then multiply them together.

1. Picking a marble: Let's assume there are n marbles to choose from. If there are n marbles, then the number of outcomes for this event is n.

2. Rolling a die: A standard die has 6 sides numbered 1 to 6. Therefore, the number of outcomes for this event is 6.

3. Picking a card: A standard deck of cards has 52 cards. Hence, the number of outcomes for this event is 52.

To find the total number of possible outcomes, we multiply the number of outcomes for each event together:

Total number of outcomes = (number of outcomes for picking a marble) × (number of outcomes for rolling a die) × (number of outcomes for picking a card)

Total number of outcomes = n × 6 × 52

Therefore, the total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.

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Answer:

A.

Step-by-step explanation:

400 is a flat rate. adding that to the variable. c × 15 represents the earnings per c customers. this is the right answer I promise.

Answer:

I thinks it A

Step-by-step explanation:

it seems right

Answer:

Example: π (Pi) is a famous irrational number.

We cannot write down a simple fraction that equals Pi.

Step-by-step explanation: true

Answer:

  x = 0 and x = 16

Step-by-step explanation:

You want the solution to √(2x+4) -√x = 2.

We eliminate the radicals by squaring until there aren't any. After the first squaring, we have to separate the radical term from the others.

  \(\sqrt{2x+4}-\sqrt{x}=2\\\\(2x+4)-2\sqrt{(2x+4)(x)}+(x)=4\qquad\text{square both sides}\\\\3x=2\sqrt{x(2x+4)}\qquad\text{add $\sqrt{x(2x+4)}-4$}\\\\9x^2=4(2x^2+4x)\qquad\text{square both sides}\\\\x^2-16x=0\qquad\text{subtract the right side from both sides}\\\\x(x -16) = 0\qquad\text{factor}\)

The solutions to this are the values of x that make the factors zero. Those values are x=0 and x=16. Trying these in the original equation, we have ...

  √(2·0 +4) -√0 = 2 -0 = 2 . . . . . . x=0 is a solution

  √(2·16 +4) -√16 = 6 -4 = 2 . . . . . x=16 is a solution

The two solutions to the equation are x=0 and x=16.

Answer:

x=16

Step-by-step explanation:

All sides of an equilateral triangle are congruent, so:

\(x+6=22 \implies x=16\)

Answer:

Volume=96.7

Step-by-step explanation:

V=πr^2h=

V=π·1.8^2·9.5=

96.69822

Answer:

the answer is C

the y intercept is +3

if you do rise over run, the slope will be 1/2

1) We can start with the coefficients separately, so let's find the GCF of 20,40, and 10. We'll divide all of these numbers by prime numbers. But we can only divide them if we can divide them simultaneously.

So the Greatest Common Factor of those coefficients is 10

2) Examining the variables we can see that the least x term is:

And the least y term is:

3) Therefore we can write out the GCF as:

With the GCF we can rewrite that expression as a product.

And that's the answer

Answer:

80 square units

Step-by-step explanation:

The figure given can be decomposed to have two trapezoids of equal dimensions and a rectangle.

Area of the figure = (2*area of a trapezoid) + (area of a rectangle)

Area of the 2 trapezoids:

Area of the two trapezoid = 2(½(a + b)*h)

Where,

a = 2 + 6 + 2 = 10 units

b = 6 units

h = 2 units

Plug in the values:

Area of the two trapezoid = 2(½(10 + 6)*2)

= 2(½(16)*2)

Area = 32 units²

Area of the rectangle:

Area = length × width

Length = 8 units

Width = 6 units

Area = 8 × 6 = 48 units²

✔️Area of the figure = 32 + 48 = 80 units²

Answer:

Step-by-step explanation:

Given the following logarithmic expressions \(log_ax = 3, log_ay = 7, log_az = -2\), we are to find the value of \(log_a(\frac{x^3y}{z^4} )\)

\(from\ log_ax = 3, x = a^3\\\\from\ log_ay = 7,y = a^7\\\\from\ log_az = -2, z = a^{-2}\)Substituting x = a³, y = a⁷ and z = a⁻² into the log function \(log_a(\frac{x^3y}{z^4} )\) we will have;

\(= log_a(\frac{x^3y}{z^4} )\\\\= log_a(\dfrac{(a^3)^3*a^7}{(a^{-2})^4} )\\\\= log_a(\dfrac{a^9*a^7}{a^{-8}} )\\\\= log_a\dfrac{a^{16}}{a^{-8}} \\\\= log_aa^{16+8}\\\\= log_aa^{24}\\\\= 24log_aa\\\\= 24* 1\\\\= 24\)

Hence, the value of the logarithm expression is 24

Answer:

$8,511.1147

Step-by-step explanation:

Compound interest formula is expressed as;

A = P(1+r)^n

P is the amount invested = $6000

r is the rate = 6% = 0.06

t is the time = 6yrs

A is the compound amount

A = 6000(1+0.06)^6

A = 6000(1.06)^6

A  = 6000(1.4185)

A = 8,511.1147

Hence the compound amount to 4dp is $8,511.1147

The probability of Miguel selecting a tile number less than 3 from each bag -1 is 1/5 and bag-2 is 2/5.

The given tiles in bag-1 = {2, 4, 5, 8, 9}

Total number of tiles in bag-1 = 5

The number of tiles less than number 3 in the bag - 1 = 1

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 1/3

The given tiles in bag-2 = {0, 1, 3, 6, 7}

Total number of tiles in bag-2 = 5

The number of tiles less than number 3 in the bag-2 = 2

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 2/3

From the above analysis, we solved the problem.

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The expression that represents how much more Company X​ charges, in​ cents, for n minutes is 15 + n

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. It can be used to represent a specific value or a range of values e.g. 2x+3.

For Company X:

Since it costs 30c to connect and then 4c for each minute, we can write the expression as:

30 + 4n

For Company Y:

Since it costs 15c to connect and then 3c for each minute, we can write the expression as:

15 + 3n

An expression that represents how much more Company X​ charges, in​ cents, for n minutes is:

(30 + 4n) - (15 + 3n) = 30 - 15 + 4n -3n = 15 + n

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Answer:

x>1

Step-by-step explanation:

Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and  the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.

To find the fifth power of the matrix A, we can simply multiply A by itself five times:

A^5 = A * A * A * A * A

= (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2)

= (0.22 0.12 0.14 0.14 0.34)

To find the probability that state 2 changes to state 4 after five repetitions of the experiment, we need to look at the element in the fifth power matrix A^5 that corresponds to state 2 and state 4. This element is located in the second row and fourth column of the matrix, which is 0.14.

Therefore, Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.

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A^5 = A * A * A * A * A

= (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2) * (0.2 0.1 0.2 0.1 0.4) * (0.4 0.1 0.1 0.2 0.2)

= (0.22 0.12 0.14 0.14 0.34)

Therefore, Fifth power of the given transition matrix is (0.22 0.12 0.14 0.14 0.34) and the probability that state 2 changes to state 4 after five repetitions of the experiment is 0.14.

Answer:

Your age(a) is 15 in this case.

If your brother is 1/3 of your age, that means multiply your brother's age by 3

Your sister is 9, and is 4 years older than your brother. In that case, we now know that your brother is 5

With that information, we can put this into a valid equation.

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

turn 1/3 into a flipped fraction, 3/1 which is equal to 3

your brother's age is 5, so the first value would be 5

5 times 3 is 15, so that means a is 15

\(5 * 3/1 = 15\)

Answer:

Some units are inches and some are feet. In that case, you would need to convert in order for the equation to be solved.

Step-by-step explanation:

I got 100% on edgen

Cautious of when calculating the area of geometric figures is different unit.

A measurement unit is a standard quantity used to express a physical quantity.

The main caution while calculating the geometric figures is units.

Sometimes units are inches and some are feet.

In this case, we need to convert in order to get the correct calculation because different measurements can cause error in finding the solution.

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Answer:

  2.908 s

Step-by-step explanation:

The "work" is most easily done by a graphing calculator. We only need to tell it the equation of motion.

For speeds in feet per second, the appropriate equation for vertical ballistic motion is ...

  h(t) = -16t² +v₀t +s₀

where v₀ is the initial vertical velocity in ft/s and s₀ is the initial height in feet. The vertical velocity is the vertical component of the initial velocity vector, so is (65 ft/s)(sin(44°)). We want to find t for h=0.

  0 = -16t² +65sin(44°) +4

Dividing by -16 gives ...

  0 = t^2 -2.82205t -0.2500

Using the quadratic formula, we find ...

  t ≈ (2.82205 ±√(2.82205² -4(1)(-0.25))/2 ≈ 1.41103 +√2.24099

  t ≈ 2.90802

It will take about 2.908 seconds for the discus to reach the ground.

_____

Comment on the question

You're apparently supposed to use the equation for ballistic motion even though we know a discus has a shape that allows it to "fly". It doesn't drop like a rock would.

Answer:

D) xy/2 = 28

Step-by-step explanation:

Inverse Variation:

y = k/x

Given:

k = 56

Work:

y = k/x

y = 56/x

xy = 56

xy/2 = 28

xy = 28 * 2

xy = 56

Answer:

38.0

Step-by-step explanation:

38.0 to the nearest whole number

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