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Option C, If your row reduces the matrix A and obtains a row of all zeros except for a single 1 in the rightmost column, then the set {u, v, w} is linearly dependent.

This is because the row of all zeros except for a 1 in the rightmost column indicates that one of the vectors in the set can be expressed as a linear combination of the other vectors.

On the other hand, if your row reduces the matrix A and does not obtain a row of all zeros except for a single 1 in the rightmost column, then the set {u, v, w} is linearly independent. This is because the absence of such a row indicates that none of the vectors in the set can be expressed as a linear combination of the other vectors.

If you are unable to row reduce the matrix A for any reason, then it is not possible to determine if the set {u, v, w} is linearly independent or not.

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Answer:

Step-by-step explanation:

area = pi * r^2

area = pi * 2^2

area = 4pi

area = pi * 4^2

area = 16pi

"Increasing" means the y-values are increasing as x-values increase.  Or visually, if you were walking along the graph, from left-to-right, where would you be walking uphill?

The uphill portion is from (-infty, -4).  Once you get to an x-value of -4, then it levels off (so it's "constant") until you get to x = 1, when it goes downhill (the function is decreasing).  

The interval of the domain in which the function is increasing is(-∞, -4). so option C is correct.

A function that is composed of several smaller functions, each with a distinct domain, is said to be piecewise. The term "piecewise" refers to the way in which these sub-functions are defined in terms of various intervals or "pieces" of the function's overall domain.

Given that,

The piecewise function which is discontinuous  at x =1

In the interval  

(-∞, -4)  the value of the function is increasing.

[-4, 1) the value of the function is constant.

(1, ∞)  the value of the function is decreasing.

Hence, the function is increasing in the domain (-∞, -4)

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Answer:

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

Let the width be x, then the length is 4x - 11.

The perimeter of the rectangle is:

Solve it for x:

By using the concept of function, it can be calculated that-

  (h.g)(x) = 4x - 21

  (h + g)(x) = 5x - 3

  (h - g)(-1) = 6

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here,

a) The given functions are

   g(x)= x - 6

   h(x) = 4x + 3

  (h.g)(x) = h(g(x)) = 4(x - 6) + 3 = 4x - 21

   (h + g)(x) = h(x) + g(x) = 4x + 3 + x - 6 = 5x - 3

    (h - g)(x) = h(x) - g(x) = 4x + 3 - x + 6 = 3x + 9

     (h - g)(-1) =  3 [tex]\times[/tex] (-1) + 9 = 6

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This looks like a fill-in the blanks question for a two column proof :]

3. CPCTC

The reasoning for this is that because triangle ABC and EDC are congruent, their corresponding parts are also congruent, (CPCTC; Corresponding Parts of Congruent Triangle are Congruent) or AC = EC

4. ACE

Because AC = EC, triangle ACE is isosceles

5. Base Angles Theorem

The base angles of a isosceles triangle are congruent

:]

Answer:

Step-by-step explanation:

3/8(4a-5)-5/12(3a-4)=

9/24(4a-5)-10/24(3a-4)=1/6  |  x24

9*(4a-5)-10(3a-4)=4

36a-45-30a+40=4

6a=9

a=3/2

Answer: 1890

Step-by-step explanation:

a)  The constant of proportionality of the given problem is; 4

b) An equation that represents the relationship is; y = 4x

c) The graph is as attached.

d) The gallons of water that are needed for 10 scoops of drink mix is; 2.5 gallons

The general equation for the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope of line which tells us the unit rate of change of y with respect to x

c is the y - intercept

Now, it is pertinent to note that y = mx also represents direct proportionality. Making m the subject gives;

m = y/x

Thus, with proportion, we can say;

y₁/x₁ = y₂/x₂

The proportional relationship will be written as;

y = kx

where k is constant of proportionality

From the question, we can say that;

2 scoops require 0.5 gallon of water

6 scoops require 1.5 gallon of water

a) Thus;

k = 2/0.5

k = 2/(1/2)

k = 2 * 2 = 4

b) Equation that represents the relationship can be written as;

y = 4x + c

Since 2 scoops require 0.5 gallon of water, then;

2 = (4 * 1/2) + c

2 = 2 + c

c = 0

The equation will be; y = 4x.

c) Graph of y = 4x is attached at the end.

d) For 10 scoops of water;

10 = 4x

x = 2.5 gallons of water required.

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Answer:

2

Step-by-step explanation:

add 2 by 6 to get 02

A line parallel to one side of a triangle divides the other two sides proportionally.

What is triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

Let ΔADE and ΔABC are two triangles.

Given: DE∥BC

To prove:  DB/AD = EC/AE

ΔADE and ΔAC share ∠A

∠A ≅∠A  reflexive property

DE∥BC is given

∠ADE ≅ ∠B   because they are corresponding angles when transversal

            AB cuts parallel lines DE and BC  

ΔADE ∽ ΔABC  a pair of angles in each are congruent.

AB / AD = AC / AE

because corresponding sides of similar triangle's are proportional.

Now subtract 1 from each side

AB / AD - 1 = AC / AE - 1

Combining fractions,

(AB - AD) / AD = (AC - AE) / AE

⇒ DB / AD = EC / AE

Hence, a line parallel to one side of a triangle divides the other two sides proportionally.

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Geometric figure:

Answer:

The 72nd term is -708

Step-by-step explanation:

Answer:

87

Step-by-step explanation:

If Shelby and Aisha baked a total of 116 dog treats to sell, and Shelby baked 3 times as many dog treats that Aisha, then we need to figure out what 3/4 of 116 dog treats is.

116 ÷ 4 = 29

29 × 3 = 87

Shelby baked 87 dog treats.

Answer:

Yes, [tex]\triangle UXC \cong \triangle QRS[/tex]

Step-by-step explanation:

The triangles are congruent by SAS.

Answer: The jars of jam sales and the T-shirt sales have a positive correlation, but neither may cause the other.

Step-by-step explanation:

The correlation is a positive slope but selling T-Shirts and Jam shouldn't correlate to each other.

When time is also known, distance—the measurement of how far something has travelled in a straight line—can be used to determine speed.

Distance, D = 260 miles

Velocity, V = 80 miles/hour

Time taken, t = distance/velocity

= D/V

= 260/80

= 3.25 hours

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Answer:

x + 2 < y < 5x + 12

Step-by-step explanation:

given 2 sides of a triangle then the third side y is within the limits

difference of 2 sides < y < sum of 2 sides

3x + 7 - (2x + 5) < y < 3x + 7 + 2x + 5

3x + 7 - 2x - 5 < y < 5x + 12

x + 2 < y < 5x + 12

Answer:

Y+Z/Z = X/L

X= (44/14)4 = 12.57(nearest 2 decimal

Answer:

This is a function

Step-by-step explanation:

For every input there is only one output.

The linear function would be y = -4x - 7 which passes through the points (- 2 , 3 ) and ( - 3 , 5 ).

Given that linear function passes through the points (- 2 , 3 ) and ( - 3 , 5 ).

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = -2, y₁ = 3

x₂ = -3, y₂ = 5

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 3 = (5 - 1)/(-3 - (-2))[x -(-2)]

⇒ y - 3 = (4)/(-1)[x +2]

⇒ y - 1 = -4(x +2)

⇒ y = -4x - 8 + 1

⇒ y = -4x - 7

Therefore, the linear function would be y = -4x - 7 which passes through the points (- 2 , 3 ) and ( - 3 , 5 ).

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The required number of hours  does it take for the size of the sample to double is 11 hours.

Percentages are basically divisions where the denominator is 100. To show that a number is a percent, we utilize the percent image (%) close to the number. For instance, in the event that you got 75 inquiries right out of 100 on a test (75/100), you would have scored 75%.

Let initial population be x.

As question says number of bacteria increases by 9.6% per hours.

9.6% of x takes 1 hours,

So, in 11 hours size of sample become 105.6%, means almost double of initial size.

Thus, 11 hours will be taken to make size double.

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Answer:

1.7

Step-by-step explanation:

Hello,

I hope you and your family are doing well!

To find the length of each side of the triangle, we can use the formula for the perimeter of a rectangle: perimeter = 2 * (width + length). In this case, the perimeter of the rectangle is 2 * (5cm + 16cm) = 42 cm. Since each side of the triangle has the same length, and the perimeter of the triangle is equal to the perimeter of the rectangle, the length of each side of the triangle is 42cm / 3 = 14 cm.

Therefore, the length of each side of the triangle is 14 cm.

---

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Happy Holidays!

The theoretical probability of rolling a two with one standard die in three equivalent form is 1/6, 0.167 and 16.7%

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

The rolling of a standard die

In this case, we assume that the standard die is a fair die

i.e. the faces have  equal chance of appearing

This means that the sample space of the die is

Sample space = {1. 2. 3. 4. 5. 6}

In this sample space, we have

Number of occurrence of 2 = 1

Number of items in the sample space = 6

The theoretical probability of 2 is then calculated as

Probability = Number of occurrence of 2/Number of items in the sample space

Substitute the known values in the above equation, so, we have the following representation

Probability = 1/6 --- in fraction

Evaluate the quotient

Probability = 0.167 -- in decimal

Express as percentage

Probability = 16.7%

Hence, the probability is 16.7%

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The solution to the inequality (x - 4)(x - 5) < 0 is given as follows:

4 < x < 5.

The test values are given as follows:

The graph of the inequality is given by the image shown at the end of the answer.

The inequality in this problem is given as follows:

(x - 4)(x - 5) < 0

The inequality is a product, meaning that there is two cases for when it is negative, which are:

For the first case, the solution is given as follows:

x > 4 and x < 5 -> 4 < x < 5 (intersection).

For the second case, the solution is given as follows:

x < 4 and x > 5 (impossible).

Hence the compound inequality that gives the solution is of:

4 < x < 5.

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Answer:

w=12

Step-by-step explanation:

w+5-9=8

w-4=8

w=12

Answer:

w = 12

Step-by-step explanation:

Subtract the numbers.

5 + w - 9 = 8

-4 + w = 8

Rearrange terms

-4 + w = 8

w - 4 = 8

Add 4 to both sides

w - 4 = 8

w - 4 + 4 = 8 + 4

Add

w - 4 + 4 = 8 + 4

w = 8 + 4

Add

w = 8 + 4

w = 12

Answer:

the answer is: 01111001 01101111 01110101 00100000 01101000 01100001 01110110 01100101 00100000 01101000 01100001 01110110 01100101 00100000 00110011 00110000 00100101 00100000 01100011 01101000 01100001 01101110 01100011 01100101 00100000 01101111 01100110 00100000 01110111 01101001 01101110 01101110 01101001 01101110 01100111 00100000 01100001 01110011 01110011 01110101 01101101 01101001 01101110 01100111 00100000 01110100 01101000 01100101 00100000 01100100 01101001 01100011 01100101 00100000 01101000 01100001 01110011 00100000 00110110 00100000 01110011 01101001 01100100 01100101 01110011 00101110 . do a bit of work decoding it to get the right answer

Step-by-step explanation:

Jonah runs 2 (19/20) laps more than the remaining two days

The fractions that have the same denominator are like fractions, to add like fractions directly, But if the denominators are not the same then we need to change their denominators to the same then we can add the fractions.  

To make denominators as same we need to take the LCM of denominators of two fractions.  

Here we have

Jonah ran 1(3)/(4) laps on Monday

=> 1 3/4 = 7/4 laps

On Tuesday he ran 2(3)/(10) laps

=> 2 3/10 = 23/10 laps

On Wednesday he ran 6(1)/(5) laps

=> 6 1/5 = 31/5 laps

The total number of laps ran combining Monday and Tuesday

= 7/4 laps + 23/10 laps  

= (35 + 46)/20         [ take Lcm of 4, 10 i.e 20 ]  

= 81/20

From the above calculations,

Jonah ran 81/20 laps on combining Monday and Tuesdays

The difference between Wednesday's counted laps and Monday, and Tuesday's counted laps

= 31/5 - 81/20

= (140 - 81)/20             [ Take Lcm of 5, 20 i.e 20 ]    

= 59/20            

= 2 (19/20)

Therefore,

Jonah runs 2 (19/20) laps more than the remaining two days

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Complete Question:

Jonah ran 1(3)/(4) laps on Monday, 2(3)/(10) laps on Tuesday, and 6(1)/(5) laps on Wednesday. How much farther did he run on Wednesday than on the other two days combined? Show your work.    

Answer:

C, (0, 9)

Step-by-step explanation:

The y-intercept is when the x-value is 0. We pug in 0 for x, getting f(0) = 3^2=9. The x-coordinate must be 0, and the y-value is 3^2, or 9. The correct answer is (0, 9)