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In the given exercise option a, b and c are in reduced echelon form and option d is in echelon form.

Row echelon form suggests that: Each row's leading (first) entry must be

Each following row's first entry must be on a new column to the right.

All rows with zero entries are listed below rows with non-zero items.

If the leading entry in each column is the only nonzero element in that column, reduced echelon form also results from echelon form conditions.

According to the definitions we see that, in the given exercise option a, b and c are in reduced echelon form and option d is in echelon form.

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Do u have a screen protector cuz if u do thats probably why

Step-by-step explanation:

Answer:

light diffraction and a dirty phone screen.

To find out how much Quadra spent, we can use this equation:

Fitting the numbers into the equation would look like this:

We multiply by 0.75 because it is equivalent to 3/4.

If we now know that Quadra spent £90, we can subtract that from her total amount of money to get the amount of money she saved.

Therefore, Quadra saved £30.

As stated in the preceding statement When 4 points are given in one method for calculating grade point averages (GPA), the resulting mean grade rating is 3.41.

Average While calculating the arithmetic mean, a group of integers is added, their count is divided, and the result is then taken. For instance, the average of 2, 3, 5, 7, and 10 is 5, this is the result of 30 reduced by 6.

The quality points by each grade every course must first be calculated before being added together to determine the GPA.

3 credit hours times 4 points for A equals 12 quality points.

B - ( 3 points x 2 credit hours ) x 2 (because there are 2 courses) = 18 quality points

C - 2 points x 4 credits = 8 quality points

D - 1 point x 3 credits = 3 quality points

Now add up all the quality points = 12 + 18 + 8 + 3 = 41

Add the credit hours as well = 3 + 2 + 4 + 3 = 12

Divide the total kit by total semester credit to calculate the GPA = 41/12 = 3.41

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The cost per kg of clay is $0.7 and cost per kg of wood is $ 8.

Linear Equation in two variables:

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.

Now according to the given question,

Let cost per kg of clay be x and cost per kg of wood be y.

Then according to the given information in  table, we can get two equations,

5x + 4y = 35.50                                   .....(1)

3.5x + 6y = 50.45                               .....(2)

Now multiply equation (1) by 3 and equation (2) by 2, we get,

15x + 12y = 106.50                               ......(3)

7x + 12y = 100.90                                 ......(4)

Now subtract equation (4) by equation (3), we get,

8x = 5.60

x = 0.7

Now put this value of x in (1),

we get,

5(0.7) + 4y = 35.5

3.5 + 4y = 35.5

subtracting both sides by 3.5, we get

4y = 32

by dividing both sides by 4, we have

y = 8

Therefore, cost per kg of clay is $0.7

and cost per kg of wood is $ 8.

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There are several strategies that can be used to help students understand that a whole number can be divided into parts:

Remember, it may take time for some students to fully grasp the concept of dividing a whole number into parts. Keep practicing and using different strategies until the concept clicks for them.

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La condición para convertir una fracción impropia en una fracción mixta es que el denominador sea menor que el numerador. de modo que en esta pregunta solo (4) se puede cambiar a una fracción mixta.

El número 4 se cambia a una fracción mixta se convierte en:

1 372/1000

Una Fracción Ordinaria cuyo cuantificador es menor que el denominador no se puede convertir en una Fracción Mixta.

Entonces, de los números 1-5, solo el número 4 se puede convertir en una fracción mixta.

4)

Convertido a fracciones comunes se convierte en 1371/1000

Convertido a un número mixto se convierte en 1 371/1000

léase uno - trescientos setenta y uno - por mil.

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The steps that an accountant generally follows to prepare a bank reconciliation statement will be:

A company's prepared bank reconciliation statement demonstrates that the balance of its recorded bank account matches the balance the bank lists.

This report comprises every transaction from a specific time period, including deposits and withdrawals.

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Answer:

(8,-5)

x=8

y=-5

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can use similar triangles to find the function that models the length of the woman's shadow. If the woman is standing at a distance d from the base of the lamp, the length of her shadow will be proportional to her height, so the ratio of the shadow length to the height will be equal to the ratio of the distance from the base of the lamp to the height of the lamp.

So, if h is the woman's height and L is the length of her shadow, we have:

L/h = d/13

And since h = 6 feet, we can write:

L = (d/13) * 6

So the function that models the length of the woman's shadow in terms of her distance from the base of the lamp is:

L = (d/13) * 6

Answer:

The player has an annual salary of $305,000, and they have decided to donate 1/8 of their salary to charity. To calculate this, we simply divide their salary by 8.

305,000 / 8 = $38,125

So, the player is donating $38,125 to charity every year. This is calculated by taking 1/8 of their annual salary.

The fraction 1/8 represents one out of eight equal parts of the player's salary, and when this fraction is multiplied by the player's salary, it gives the exact amount that they are donating to charity.

The speed and the direction of the resulting blob of clay is 1.4m/s and 57.46 deg below +ve x-axis respectively.

The Latin word for carrier is vector. Points A and B are transported by vectors. The magnitude of the vector is the length of the line connecting points A and B, and the vector's direction is the direction in which point A moves in relation to point B. Other names for vectors are Euclidean vectors and spatial vectors. In many different domains, including mathematics, physics, engineering, and others, vectors are used.

Since there is no external force applied, So using momentum conservation:

Pi = Pf

Since the wreckage is locked onto each other after collision, So their final velocity will be same

m1*v1 + m2*v2 + m3*v3 = (m1 + m2 + m3)*V

m1 = mass of ball1 = 60 g

m2 = mass of ball2 = 20 g

m3 = mass of ball3 = 30 g

v1 = initial velocity of m1 = 4.0 m/sec towards 45 deg South of east = (4*cos(45deg) i - 4*sin(45 deg) j) m/sec

v2 = initial velocity of m2 = 2.0 m/sec towards North = (2.0 j) m/sec

v3 = initial velocity of m3 = 2.9 m/sec towards west = (-2.9 i) m/sec

V = final velocity of blob = x i + y j

So,

60*(4*cos(45deg) i - 4*sin(45 deg) j) + 20*(2.0 j) + 30*(-2.9 i) = (60+20+30)*(x i + y j)

(60*2.83 - 30*2.9) i + (-60*2.83 + 20*2.0) j = 110x i + 110 j

82.8 i - 129.8 j = 110x i + 110y j

By comparing both sides:

x = 82.8/110 = 0.753 i

y = -129.8/110 = -1.18 j

then, final speed will be:

V = 0.753 i - 1.18 j

Part - A

Speed of resulting blob of clay,

|V| = √((0.753)² + (1.18)²)

|V| = 1.4 m/s

Part-B

Direction after collision will be:

Direction = arctan (Vy/Vx) = arctan (-1.18/0.753) = -57.46 deg

Direction = 57.46 deg below +ve x-axis

Hence, the speed and the direction of the resulting blob of clay is 1.4m/s and 57.46 deg below +ve x-axis respectively.

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The value of the x is 19.9.

A planar triangle's side's square is equal to the sum of the squares of the other sides minus the product of those sides and the cosine of the angle between them, divided by two.

Given:

The angle C is 98°.

Applying law of cosines:

c² = a² + b² -2ab cosC.

Substituting the values,

c² = (17)² + (13)² -2(17)(13) cos98°.

c² = 458 -  (-0.13917)442

c² = 396.48686

c = 19.9

Hence, x = 19.9.

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Answer:

Yes

Step-by-step explanation:

Dilations shrink or expand a figure.  If the scale factor is one, the two figures will be identical.

Answer:

Step-by-step explanation:

1. the variable 'y' is absent in the equation given in the condition. It means, the given line is vertical. Then

2. if line is vertical, it is parallel to Y-axis, then no y-interception.

3. if to re-write the given equation into x=1, then x-interception is x=1.

4. graph is in the attachment.

a. The vector equation for the given line is (x,y,z) = (1,0,7) + t(1,3,1) and the parametric equations are x = 1+t, y = 3t, z = 6+t.

b. The vector equation for the given line is

(3 + 3t)i + (2.3 + 3t)j + (3.6 - t)k and the parametric equation is

x = 3 + 3t, y = 2.3 + 3t, z = 3.6 - t.

What is a parametric equation?

A series of equations known as a parametric equation specifies a point's location in the xy plane in terms of a third variable, which is typically referred to as a parameter.

a. We are given that a line passes through the point (1,0,7) and is perpendicular to the plane x + 3y + z = 2.

Now, since the line is perpendicular to the plane, the normal vector (1,3,1) for the plane is parallel to the line.

So the vector equation for the line is

(x,y,z) = (1,0,7) + t(1,3,1)

The parametric equations for the line are

x = 1+t, y = 3t, z = 6+t

b.  We are given that a line passes through the point (3, 2.3, 3.6) and parallel to the vector 3i + 3j - k.

So the vector equation "r" for the line is

r = (3i + 2.3j + 3.6k) + t(3i + 3j - k)

r = (3 + 3t)i + (2.3 + 3t)j + (3.6 - t)k

The parametric equations for the line are

x = 3 + 3t, y = 2.3 + 3t, z = 3.6 - t

Hence, the required vector and parametric equations have been obtained.

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Answer: First, let's calculate Jason's weekly earnings:

Jason's weekly tips = $2100 * 18% = $378

Jason's total weekly earnings = $2100 + $378 = $2478

Next, let's calculate David's weekly earnings:

David's weekly commission = $3500 * 6% = $210

David's total weekly earnings = $185 + $210 = $395

To find the monthly earnings, we need to multiply their weekly earnings by 4 (since there are 4 weeks in a month):

Jason's monthly earnings = $2478 * 4 = $9912

David's monthly earnings = $395 * 4 = $1580

So, Jason makes more money in one month, earning approximately $9912, compared to David's $1580.

Step-by-step explanation:

The individual who makes more money in a month between Jason and David is David.

Jason's weekly tips = 18% of $2100

= $378

David weekly salary= $185

David's weekly tips = 6% of $3400

= $210

Total weekly salary of David = $185 + $210

= $395

Total monthly salary of Jason= $378 × 4

= $1,512

Total monthly salary of David= $395 × 4

= $1,580

Therefore, David makes more money than Jason in a week.

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The solution that works for both the equations is (-4, 5) and the two lines intersect at this point.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

The given equation are:

y = -1/2x + 3

y = 5

Substitute the value of y in first equation:

5 = -1/2x + 3

5 = -x + 6 / 2

10 = -x + 6

10 - 6 = -x

x = -4

The solution that works for both the equations is (-4, 5) and the two lines intersect at this point.

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The formula in this problem is classified as recursive.

The terms are given as follows:

The features that we are given for the formula are given as follows:

Considering that we need the previous term to obtain the nth term, this is an recursive formula.

Then the terms are given as follows:

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The value of the last one is 18.

The solution of the diagram can be modelled with an equation. Therefore, let's find the last value.

we will use variable to represent the fruit names.

Hence,

yellow fruit = x

red fruit = y

green fruit = z

Therefore,

x + y + z = 29

2y + z = 26

2z + y = 25

Using substitution,

y = 25 - 2z

2(25 - 2z) + z = 26

50 - 4z + z = 26

50 - 3z = 26

-3z = 26 - 50

-3z = -24

z = 8

y = 25 - 2(8)

y = 25 - 16

y = 9

Therefore,

x + 9 + 8 = 29

x = 29 - 17

x = 12

Finally,

x + 1 / 2x  = 12 + 1 / 2(12) = 12 + 6 = 18

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Ha:mu<10  is the appropriate alternative hypothesis that the consumer group wishes to test .

How would you define hypothesis?

An assumption or notion is called a hypothesis when it is put forth with the purpose of debating whether it might be true.

                               In the scientific process, the hypothesis is developed prior to the completion of any relevant study, other than a brief background review.

Ha:mu<10

Because A consumer group is suspicious of this claim, believing that the weight lose is, on average, much less.

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The costs of 5 oranges and 15 oranges are R15 and R45

From the question, we have the following parameters that can be used in our computation:

Six oranges cost R18,00

This means that the unit rate is

Unit rate = R18,00/6 = R3.00

For 5 oranges, we have

Cost = 5 * R3.00 = R15.00

For 15 oranges, we have

Cost = 15 * R3.00 = R45.00

So, the costs are R15.00 and R45.00

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Answer:

Step-by-step explanation:

This is just the normal parent sin graph, y = sinx

Δ BAD and Δ CAD are congruent by SAS rule.

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Given that, in a Δ BAC, AD bisects ∠ BAC, AB = AC,

We need to prove, BD = DC

         STATEMENT                                                     REASON

1) AD bisects ∠ BAC                                                      given

2) ∠ 1 = ∠ 2                                                           definition of angle bisector

3) AB = AC                                                                      given

4) AD = AD                                                             Reflexive property

5) Δ BAD ≅ Δ CAD                                                       SAS rule

Hence, Δ BAD and Δ CAD are congruent by SAS rule.

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Using the principle of alternate angles we can say that the value of x will be 120°.

The intersection of two parallel lines by a transversal produces alternate angles.

The alternate angles are equivalent when a transversal cuts two parallel lines.

The total of all the angles created on a transverse that are inside either of the two parallel lines is always 180 degrees.

Alternate interior angles for non-parallel lines don't have any special characteristics.

Angles of the same size that are found on opposing sides of the transversal line are known as alternate angles.

So, do not observe the given image:
We know that it is the pair of alternate angles that is equal.

Then, x = 120°.

Therefore, using the principle of alternate angles we can say that the value of x will be 120°.

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The solution is, the value we get 3:4.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

given that,

1/2 (x+8) -:xy +z

when x=4 y=12 and z=-40

so, we get,

1/2*12 : 48+ (-40)

=6:8

=3:4

Hence, The solution is, the value we get 3:4.

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