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Answer:

Step-by-step explanation:

To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.

Given:

y = -3a + 3

a = -5x + 1

Substituting the value of "a" in the first equation:

y = -3(-5x + 1) + 3

Now, let's simplify this expression:

y = 15x - 3 + 3

y = 15x

Therefore, y can be expressed as a function of x as:

y = 15x

Answer:

Step-by-step explanation:

To simplify the expression 3 x (3/4) whole to a unit fraction, we can start by multiplying the whole number 3 by the denominator of the fraction, which is 4:

3 x (3/4) = (3 x 4)/4 x (3/4) = 12/4 x 3/4

We can simplify the fraction 12/4 by dividing both the numerator and denominator by 4:

12/4 = 3

Substituting this back into the expression, we have:

3 x (3/4) = 3/1 x (3/4) = 9/4

Therefore, 3 x (3/4) whole is equal to the unit fraction 9/4.

(i) Probability is a notion in Mathematics which describes the likelihood of an event or a set of events occurring. It is a measure of uncertainty when estimating the outcome of an experiment or an observation.

(ii) The axioms of probability are:

the non-negativity (that the probability of an event is greater than or equal to zero), and

the additivity (that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities).

(iii) When two fair dice are thrown the probability of getting:

a) The sum of 9 = 1/9

b) Two odd numbers = 1/4

c) two prime numbers = 1/9

d)  two factors of 12 = 1/9

(iv) Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, presentation, etc.

To find probability when two dice are thrown, we have:

(a) The sum of 9:

We will estimate the number of ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3) = 4 ways

A die has 6 possible outcomes, the total number of possible outcomes is 6x6=36 = 4/36 = 1/9.

(b) Two odd numbers:

We count the number of ways to get two odd numbers: (1,3), (1,5), (1,7), (3,1), (3,5), (3,7), (5,1), (5,3), and (5,7).

possible outcomes = 9,

So, the total possible outcomes = 6x6=36 = 9/36 = 1/4.

(c) Two prime numbers

We estimate the number of ways we can get two prime numbers: (2,3), (3,2), (5,2), and (2,5)

possible outcomes = 4,

So, the total possible outcomes = 6x6 =36 = 4/36, = 1/9.

(d) Two factors of 12:

We count the number of ways and divide by the total possible outcomes.

The factors of 12 are 1, 2, 3, 4, 6, and 12: (2,6), (3,4), and (4,3) = 3 ways

possible outcomes = 6

Therefore, the total number of possible outcomes = 6x6=36 = 3/36, = 1/12

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The lengths of the sides of the triangle are as follows;

Short leg = 12 cm.

Longer leg = 16 cm.

Hypotenuse = 20 cm.

In Euclidean geometry, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

Note: Let the variable x represent the smaller leg.

The hypotenuse is 8 cm longer than the longer leg: x + 8 = x + 8.

Substituting the given parameters into the Pythagorean's theorem formula, we have the following;

c² = a² + b²

(x + 8)² = x² + (x + 4)²

x² + 16x + 64 = x² + x² + 8x + 16

x² - 8x - 128 = 0

Adjacent leg, x = 12.

For the hypotenuse, we have:

Hypotenuse, c = x + 8

Hypotenuse, c = 12 + 8

Hypotenuse, c = 20 cm.

For opposite side, we have:

opposite side, b = 12 + 4

opposite side, b = 16 cm.

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Complete Question:

The shorter leg of a right triangle is 4 cm shorter than the longer leg. The hypotenuse is 8 cm longer than the longer leg. Find the lengths of the sides of the triangle.

A relation represented in an X-Y coordinate is the graph of a function if and only if there is no vertical line which passes through two points of the relation. In other words, each vertical line passes through at most one point in the relation.

This is the case of the given line. Therefore, it is the graph of a function.

Price = x

Quantity = 200 - 3x

The formula for revenue is Price x Quantity. To be able to get the maximum revenue, let's multiply the price of each coffee maker and the number of coffee makers sold each week.

The formula for the revenue as we can see above is R = 200x - 3x². To be able to solve for the maximum revenue, let's solve for the vertex of this quadratic equation.

The formula for the vertex is:

where b = the first degree term and a = second degree term.

On our equation, our a = -3, and b = 200. Let's plug it in to our formula above.

Therefore, the price that will yield a maximum revenue is when it is $33.33.

Since a kite is a quadrilateral, it has the value of 360 total degrees.

Answer:

y=-\(\frac{1}{4}\)x

Step-by-step explanation:

Answer:

y=-1/4x

Step-by-step explanation:

Answer:

1the answer for this is easy it is 4.4

Answer:

C. x+y = 1 and -x-y = -1

Step-by-step explanation:

Remember that if a system of equations has an infinite number of solutions, then the resulting equation from using the first step of the elimination method would have no variables and would be true.  

1) Let's try canceling out the equations in option C, x+y =-1 and -x-y =-1. Add the two equations together. (Work shown in attached picture.)

2) All of the terms cancel out with each other, leaving only a true statement of 0 = 0. Thus, option C is the answer.  

The reliability of experts who interpret lie detector tests in criminal investigations can be determined by analyzing the results of the random sample of 280 cases that were studied. It is important to look at the overall accuracy of the interpretations, as well as any potential biases or errors that may have affected the results.

To analyze the results, we can look at the number of correct and incorrect interpretations, and calculate the percentage of accurate interpretations. This will give us an overall measure of the reliability of the experts.

We can also look for any potential biases or errors that may have affected the results. For example, we may want to examine whether certain experts were more likely to make accurate interpretations than others, or whether there were any factors that may have influenced the interpretations, such as the type of crime or the suspect's behaviour.

Overall, the reliability of experts who interpret lie detector tests in criminal investigations can be determined by analyzing the results of a random sample of cases and looking for any potential biases or errors that may have affected the results. By doing this, we can gain a better understanding of the accuracy and reliability of these experts and their interpretations.

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Answer:9a-2

Step-by-step explanation: see photo

Answer:

It is the first one 15 is the y intercept slope 8/1

For the function,

F(x)  = (x² + 11x +28)/(x² + 8x + 15) limit doesn't exist at x = -5 so it is dis-continuous at that point.

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  = (x² + 11x +28)/(x² + 8x + 15)

To check whether it is continuous at x = -5

First taking LHL,

\(\lim_{h \to \ 0}\) [(-5-h)² + 11(-5 -h) +28]/[(-5 -h)² + 8(-5 -h) + 15]

It is approaching at negative infinity

Now, taking RHL

\(\lim_{h \to \ 0}\)  [(-5+h)² + 11(-5 +h) +28]/[(-5 +h)² + 8(-5+h) + 15]

Again, It is approaching at negative infinity

Hence, here limit doesn't exist so it is not continuous at x = -5

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Answer:680

Step-by-step explanation:

160x.75=120

160x1.5=240

160x2=320

The wrench having the size as 5/8inch will accommodate the largest bolt.

When the denominator of all the fractions is same , then the fraction with largest numerator is the largest .

For Example : in 2/9 and 7/9   , the largest is 7/9.

In the given question  

the different sizes of wrenches are 1/2 inch, 7/16 inch, 5/8 inch and 15/32 inch.

For comparison , first make the denominator equal

To make the denominator equal , take LCM of denominator

LCM of 2,16,8,32 is 32.

so in 1/2  multiplying the denominator and numerator by 16 we get

1/2 inches as 16/32inches    ...(i)

In 7/16  multiplying the denominator and numerator by 2 we get

7/16 inches as 14/32 inches     ...(ii)

In 5/8  multiplying the denominator and numerator by 4 we get

5/8inches as 20/32 inches    ...(iii)

Writing all sizes of wrenches with same denominator

{16/32 , 14/32 , 20/32 , 15/32 }

Rearranging in descending order we get ,

{20/32 > 16/32 > 15/32 > 14/32}  

Which means {5/8 > 1/2 > 15/32 > 7/16}    ...(from (i),(ii)&(iii)  )

Therefore , the wrench having the size as 5/8 inch will accommodate the largest bolt. the correct option is (c)5/8inch .

The given question is incomplete , the complete question is

Workers use box end wrenches in sizes such as 1/2 inch, 7/16 inch, 5/8 inch and 15/32 inch. Which size of wrench accommodates the largest bolt?

(a)1/2 inch

(b)7/16 inch

(c)5/8 inch

(d)15/32 inch

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Answer:

{-2, 3, 4, 5}

General Formulas and Concepts:

Math

Algebra I

Step-by-step explanation:

According to our graph, our y-values are 3, 4, 5 and -2. Since they are all closed dots, they are inclusive in the range:

Remember to put it in number line order.

{-2, 3, 4, 5}

Answer:

The exponential function is

\(y = {2}^{x} \)

Answer:

The correct equation that initially models the value of Rob's boat is option A, y = 40,000(0.93)*.

Since the value of the boat decreased by 7% each year, the value of the boat after three years can be represented by:

y = 40,000(0.93)^3

where y is the value of the boat after three years, and 40,000 is the initial value of the boat.

Simplifying this equation, we get:

y = 40,000(0.7951)

y = 31,804

However, we know that the actual value of the boat after three years was $32,174.28. This means that our initial assumption that the boat decreased by 7% each year is incorrect and we need to adjust the equation accordingly.

To find the correct equation, we can use the formula for exponential decay:

y = a(1 - r)^t

where y is the final value, a is the initial value, r is the rate of decay (expressed as a decimal), and t is the time in years.

In this case, we know that the final value of the boat is $32,174.28, and that the boat was owned for three years. We also know that the value of the boat decreased by 7% each year.

So we can set up an equation:

32,174.28 = 40,000(0.93)^3

Simplifying this equation, we get:

32,174.28 = 31,804.00

This equation is approximately true, which means that the initial value of the boat was $40,000 and the correct equation that initially models the value of Rob's boat is:

y = 40,000(0.93)^t

where t is the time in years.

Answer:θ ≈ 2.57 radians

θ ≈ 0.58 radians

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by factoring:

4sin^2(θ) + 7sin(θ) - 5 = 0

(4sin(θ) - 1)(sin(θ) + 5) = 0

Therefore, either:

4sin(θ) - 1 = 0

sin(θ) = 1/4

or:

sin(θ) + 5 = 0

sin(θ) = -5 (not possible, since sin(θ) is between -1 and 1)

So, we have sin(θ) = 1/4. Since 0 ≤ θ < 2π, we can find the two solutions in the interval [0, 2π) by using the inverse sine function:

θ = arcsin(1/4)

Using a calculator, we find:

θ ≈ 0.2531 or θ ≈ 2.8887

Therefore, in radians, the solutions for θ are approximately:

0.2531 (which is less than 2π)

2.8887 (which is greater than 2π)

So the only answer that satisfies 0 ≤ θ < 2π is:

answer:

6 more hundreds

step-by-step explanation:

\(Your\) \(answer\) \(would\) \(be.\)

\(g/4 = 24 // - 24\\g/4-24 = 0\\1/4*g-24 = 0 // + 24\\1/4*g = 24 // : 1/4\\\g = 24/1/4\\g = 96\\g = 96\)

\(- Yaoii\)

Answer:

g = 96

Step-by-step explanation:

Rewrite : g ÷ 4 = 24

Write the division as a fraction : 1/4g = 24

Multiply both sides : 1/4g = 24

Multiply both sides of the eqaution by 4 :

g = 96

Final answer g = 96

Answer:

It will take 2.2 hours for the trains to meet.

Step-by-step explanation:

Given,

Distance between two trains = 396 miles

Speed of one train = 95 mph

Speed of other train = 85 mph

Combined speed of trains = 95+85 = 180 mph

Distance = Speed * Time

Time =

Time =

Time = 2.2 hours

It will take 2.2 hours for the trains to meet.

Keywords: speed, distance

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Step-by-step explanation:

Answer

Measure the shape yourself and follow the explanation.

Step-by-step explanation:

Measure each side of the Triangles with your ruler. Record it.

For example,

I measured and got 3cm, 3.5cm, 3.5cm.

Multiply by scale factor r 2.

for example, 3cm × 2 = 6cm

3.5cm × 2 = 7.0cm

3.5cm × 2 = 7.0cm

Use your pencil to draw your new numbers to form the new Triangle.

As for the second shape, measure each four sides using ruler

for example, I measured and had 4cm, 6cm, 4cm, 6m.

Multiply by scale factor r 2.

for example, 4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

4cm × 1/4 = 1 cm

6cm × 1/4 = 1.5cm

Use your ruler to measure 1cm, 1.5cm, 1cm and 1.5cm, then to draw your new shape

We would expect John to weigh approximately 216.4 pounds at the end of week 8.

To answer this question, we need to fit a regression model to the data to determine the relationship between the number of calories burned and John's weight. We can use linear regression to find the line of best fit that represents this relationship.

We can see that there is a negative relationship between the number of calories burned and John's weight, which is consistent with the statement that "the more someone exercises the less they will weigh." We can use linear regression to find the line of best fit that represents this relationship.

Using a linear regression model, we get the following equation:

Weight = 219.9 - 0.0007 * Exercise

We can use this equation to predict John's weight at the end of week 8 based on the number of calories he burned. Plugging in Exercise = 5000, we get:

Weight = 219.9 - 0.0007 * 5000

Weight = 216.4

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The correct answer is A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.

To determine the amount of sauce and oregano needed to make 8 servings, we can use the ratio of sauce to oregano from the table.

According to the table, for 3 servings, 6 cups of sauce are used along with 1 & 1/2 teaspoons of oregano. We need to find the ratio of sauce to oregano to scale it up for 8 servings.

Ratio of sauce to oregano:

6 cups of sauce / 1 & 1/2 teaspoons of oregano = 6/1.5 = 4 cups of sauce per teaspoon of oregano

Now, for 8 servings, we need to multiply the ratio by the number of teaspoons of oregano required:

8 servings * 1 teaspoon of oregano = 8 teaspoons of oregano

Therefore, for 8 servings, we would need:

8 teaspoons of oregano * 4 cups of sauce per teaspoon of oregano = 32 cups of sauce

Therefore, the correct answer is A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.

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Answer:

\(\displaystyle m=-11\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (3, -10)

Point (4, -21)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

we can represent the fractions like decimal to order them

now order least to greatest

and rewrite on fraction form

and plot on number line