Tristan has $1.40 worth of nickels and dimes. He has twice as many nickels as dimes. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Tristan has. Define the variables that you use to write the system.

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 range  of this absolute value function is  -∞ < y ≤ 7

What are the domain and range of a function?

The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

Consider the vertical extent of the graph along y axis.

It starts from +7 extends till    -∞

So, the range is  -∞ < y ≤ 7

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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:

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.

A system of hardware, software, information, people, and used to further an organization's goal is known as a business information system (BIS).

Given that,

Students can prepare for a range of positions in business, industry, government, and the military with a Bachelor of Business Administration with a major in Business Information Systems (BIS). Business information systems, often utilising computer systems and technology, provide information that firms utilise to govern themselves successfully and efficiently. Hardware, software, data, procedures (design, development, and documentation), and people make up the bulk of business information systems. Students majoring in BIS will learn how to use technology and information systems to enhance corporate processes and decision-making.

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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:

Step-by-step explanation:

area = pi * r^2

area = pi * 2^2

area = 4pi

area = pi * 4^2

area = 16pi

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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Answer: 1890

Step-by-step explanation:

We can conclude that it will take Bob 10 years and 10 months to triple his investment when the compounding is happening semi-annually.

Compounding is the method through which interest is added to both the principal balance already in place and the interest that has already been paid.

Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."

So, the time that will be taken to make the investment triple is:

Amount invested: $2500

Interest rate: 3.4%

Compounding: Semiannually

Now, consider a period of 2 years:

3.4 * 6/12 = 1.7%

The interest rate that is effective will be 1.7%.

Currently, the future value of the compounded rate at 1.7% for a period of 65 factors equals 2.9913.

Consequently, the value will be $2,500 2.9913 = 7,478.25.

65 months divided by six years equals 10.833 years in total.

0.833 * 12 makes up  10 months a year.

Therefore, we can conclude that it will take Bob 10 years and 10 months to triple his investment when the compounding is happening semi-annually.

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Answer:

Y+Z/Z = X/L

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

Answer:

9-|12x-1|=9

Step-by-step explanation:

Solve for x over the real numbers:

9 - abs(12 x - 1) = 9

Subtract 9 from both sides:

-abs(12 x - 1) = 0

Multiply both sides by -1:

abs(12 x - 1) = 0

Eliminate the absolute value:

12 x - 1 = 0

Add 1 to both sides:

12 x = 1

Divide both sides by 12:

Answer: x = 1/12

Answer:

Answer is B

Step-by-step explanation:

Answer:

This is a function

Step-by-step explanation:

For every input there is only one output.

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)

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:

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.

Answer:

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

Step-by-step explanation:

The triangles are congruent by SAS.

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

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:

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

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

The perimeter of the rectangle is:

Solve it for x:

The total volume is given as 195.36 m³.

Volume can be defined as the capacity of any object. It can be calculated by multiplying the base area to the height.

The composite figure consists of three cuboids and two right circular cylinders.

The volume of a cuboid is the product of its length, breadth and height.

And, the volume of cylinder is given as πr²h

As per the figure given in the question the total volume is given as,

3(1 × 5 × 8) + 2 (π × 2² × 3)

= 40 × 3 + 12π × 2

= 120 + 24 × 3.14

= 195.36

Hence, the volume of composite figure is given as 195.36 m³.

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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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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:

2

Step-by-step explanation:

add 2 by 6 to get 02

Answer:

The 72nd term is -708

Step-by-step explanation:

The simplified expression of 2√x²y is 2x√y

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

2\sqrt[]{x^2y}

Rewrite properly

So, we have the following representation

2√x²y

Take the square root of x²

So, we have

2x√y

Hence, the solution is 2x√y

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For  102 batches of chilli, 85 number of teaspoons of seasoning needed.

What do you mean by fraction?

Fraction represents a part of a whole, or more generally, any number of equal parts. In everyday English, fractions represent how many parts of a particular size are there.

For positive common divisors, the numerator and denominator are natural numbers. The numerator represents the number of equal parts and the denominator shows the number of parts that make up the unit or whole. A zero part can never make up a whole, so the denominator is never zero.

It is given that a recipe calls for 5 teaspoons of seasoning for every 6 batches of chilli.

For  6 batches of chilli, number of teaspoons of seasoning needed = 5

For 1 batch of chilli, number of teaspoons of seasoning needed = 5/6

For  102 batches of chilli, number of teaspoons of seasoning needed = [tex]\frac{5}{6}\times 102[/tex] = 85

Therefore, For  102 batches of chilli, 85 number of teaspoons of seasoning needed.

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Answer:

the total number of random sample n 10

probability of is 0.267

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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The probability of 'It will definitely turn dark tonight' would be 1.

So option (B) is correct.

What is a probabilty?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

If by "likelihood" probability, the word definitely implies the probability would be 1, certainty.

Because definitely after daylight, the light will turn dark at the night.

So the probability would be 100% or 1.

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