D) 5. Which situation can be represented by 3s = 5s– 6?

Answer:

5y3 without exponents would be 15.

the normal answer would be 15 y but they're no exponents.

Part A

The notation \(\lim_{x \to 2^{+}}f(x)\) means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

We don't actually arrive at x = 2 itself. We simply move closer and closer.

Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

f(x) = (x/2) + 1

f(2) = (2/2) + 1

f(2) = 2

This shows \(\lim_{x \to 2^{+}}f(x) = 2\)

Then for the left hand limit \(\lim_{x \to 2^{-}}f(x)\), we'll involve x < 2 and we go for the first piece. So,

f(x) = 3-x

f(2) = 3-2

f(2) = 1

Therefore, \(\lim_{x \to 2^{-}}f(x) = 1\)

===============================================================

Part B

Because \(\lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x)\) this means that the limit \(\lim_{x \to 2}f(x)\) does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

===============================================================

Part C

You'll follow the same type of steps shown in part A.

However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.

So you'd only involve the second piece f(x) = (x/2) + 1

You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.

===============================================================

Part D

As mentioned earlier, since \(\lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3\), this means the limit \(\lim_{x \to 4}f(x)\) does exist and it's equal to 3.

As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.

Answer:

y = 5

Step-by-step explanation:

Because of the perpendicular bisector, we know that WZ is congruent to WX. Therfore, we can set their equations as equal to eachother and solve for y.

Answer:

age of the Father is 46 and age of the son is 24

Step-by-step explanation:

13 years ago x was thrice y's age, or

(x - 13) = 3(y - 13); or

x - 3y = -26

2 years ago, x was twice y's age, or

(x - 2) = 2 (y - 2); or

x - 2y = -2

Subtracting equation 1 from 2:

x - 2y - (x - 3y) = -2 - (-26)

or y = 24

Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484

Answer:

x=12

y=8

Point form: (12,8)

Step-by-step explanation:

I've done this question before

Answer:

y=8 and x=12

Step-by-step explanation:

2x+y =32

multiply by 1

= 2x+y=32

x+3y=36

multiply by 2

=2x+6y=72

2x+y=32 - 2x+6y=72

=5y/5=40/5

=y=8

2x+y=32

=2x+8=32

=2x=32-8

=2x=24

=2x/2=24/2

=x=12

Answer:

I got 24.1, but you missed a equasion sign between the 0.6 and 13. If you tell me what the sign is I can help more! :)

Step-by-step explanation:

Have an amazing day! :D <3

Answer: 23.1

Step-by-step explanation:

\(\frac{x}{14}=\frac{33}{20}\\\\x=\frac{(33)(14)}{20}\\\\x=23.1\)

Answer:

x-intercept: \(\bigg(\frac{5}{2}, \:0\bigg)\)

y-intercept: \((0,\:5)\)

Step-by-step explanation:

To find the x-intercept, substitute in \(0\) for \(y\) and solve for \(x\).

\(-4x + 7 = 2y - 3\)

\(-4x+7=2\left(\bold{0}\right)-3\)

Simplify 2(0):                                          \(-4x+7=2\cdot \:0-3\)

Subtract 0 - 3 = -3:                         \(-4x+7=-3\)

Subtract 7 from both sides:          \(-4x+7-7=-3-7\)

Simplify:                                         \(-4x=-10\)

Divide both sides by -4                \(\frac{-4x}{-4}=\frac{-10}{-4}\)

\(\bold{x=\frac{5}{2}}\)

To find the y-intercept, substitute in \(0\) for \(x\) and solve for \(y\).

\(-4x + 7 = 2y - 3\)

\(-4(\bold{0})+7=2y-3\)

Switch sides:                               \(y-3=-4\left(0\right)+7\)

Simplify -4(0):                              \(2y-3=-0+7\)

Add 3 to both sides:                  \(2y-3+3=7+3\)

Simplify:                                      \(2y=10\)

Divide both sides by 2:             \(\frac{2y}{2}=\frac{10}{2}\)

\(\bold{y=5}\)

Answer:

y = 5

Step-by-step explanation:

3(3y-8)=21

expand:

9y - 24 = 21

+24 to both sides to get 9y on its own.

9y = 45

divide both sides by 9 to get y on its own.

therefore

y = 5

hope this makes sense!

Answer: Solve for

y

by simplifying both sides of the equation, then isolating the variable.    

y≈−1.21698677,2.94165923

Step-by-step explanation:

Answer:  the best answer is option A: the data is symmetric with an approximate range of 20. The lowest value of 6 might mean that most students did not participate in activities.

Step-by-step explanation: From the line plot, we can see that the data is not symmetric because the dots are not equally distributed on both sides of the plot. Therefore, we can eliminate options A and C.

Option D suggests that the data is bimodal, meaning that there are two peaks in the distribution. However, there is no clear indication of two peaks in the plot. Therefore, we can eliminate option D.

Option B suggests that the data is skewed, and the most frequent number of activities is 16 or more. However, this is not the case as the highest number of dots is above 14 and 16. Therefore, we can eliminate option B.

Answer:

66 not parallel or transversal I believe its supplementary

Step-by-step explanation:

The length of the second trial will be equal to 2(⁵/₈) miles.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that two bicycle trails were developed in a new housing development. One trail is 3¹/₂ miles long. The other trail is 3/4 as long.

The length of the second trial will be calculated as,

Length =  3/4 x ( 3¹/₂ )

Length = 2(⁵/₈)

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Answer:

I can't see anything to read

Answer:

um

Step-by-step explanation:

explaino moreo

Answer/Step-by-step explanation:

6. To know who cycled faster between Sam and Bobby, find the constant of proportionality of both of them. The person with the least value of constant of proportionality is the fastest.

Constant of proportionality for Sam = \( \frac{distance (y)}{time (x)} = \frac{20}{2} = 10 mph \)

Constant of proportionality for Bobby:

Use (0, 0) and (2, 18) to find the constant of proportionality, which is:

\( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{18 - 0}{2 - 0} = \frac{18}{2} = 9 mph \).

Bobby's unit rate/constant of proportionality is smaller than Sam's.

So, Bobby cycled faster.

7. y = 15x is given as representing the amount of Pauli's Pizzeria Pizza.

15 in the equation is the slope/constant of proportionality, which represents the cost of a unit of pizza.

From the graph, the unit rate/constant of proportionality of Leo's Pizzeria Pizza can be calculated as, y/x.

Using (2, 24), we have 24/2 = 12

This means Leo's Pizzeria cost $12 per pizza.

Therefore:

Pauli's Pizzeria takes in $15 per pizza

Leo's Pizzeria takes in $12 per pizza

Pauli's Pizzeria takes in more money per pizza.

Answer:

Step-by-step explanation:

x + 5 = 20

x = 15

Answer:

x=15

Step-by-step explanation:

We are given the equation:

\(\frac{1}{4} = \frac{5}{x+5}\)

We want to solve for x. Therefore, we must isolate x on one side of the equation.

Let's begin by cross multiplying. Multiply the numerator of the first fraction by the denominator of the second. Then, multiply the denominator of the first by the numerator of the second.

\(1(x+5)=(4*5)\)

\(x+5=(4*5)\)

\(x+5=20\)

5 is being added to x. The inverse of addition is subtraction, so subtract 5 from both sides of the equation.

\(x+5-5=20-5\)

\(x=20-5\)

\(x=15\)

Let's check our solution. Plug 15 in for x.

\(\frac{1}{4} = \frac{5}{x+5}\)

\(\frac{1}{4} = \frac{5}{15+5}\)

\(\frac{1}{4} = \frac{5}{20}\)

\(\frac{1}{4} = \frac{5/5}{20/5}\)

\(\frac{1}{4} = \frac{1}{4}\)

Our solution checks out, so we know it is correct.

The solution to this equation is x=15

The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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The  volume of rectangular prism is 90 unit³.

We can consider the 1 block = 1 unit.

Length of prism = 5 unit

width of prism = 6 unit

Height of prism = 3 unit

So, Volume of rectangular prism

= l w h

= 5 x 6 x 3

= 90 unit³

Thus, the volume of rectangular prism is 90 unit³.

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Answer:5/6

Step-by-step explanation:

Domain of the function represented by the graph of a quadratic function y = \(x^2\) – 4 with a minimum value at the point (0,-4) is all real numbers.

The correct answer is option D.

To determine the domain of the quadratic function y = \(x^2\) - 4, we need to consider the x-values for which the function is defined. Since a quadratic function is defined for all real numbers, the domain of this function is "all real numbers."

Let's analyze the given function and its graph to understand why the domain is "all real numbers."

The function y =  \(x^2\) - 4 represents a parabola that opens upward, which means it extends infinitely in both positive and negative x-directions. The vertex of the parabola is at the point (0, -4), indicating that the minimum value of the function occurs at x = 0.

Since there are no restrictions or limitations on the x-values for which the function is defined, the domain is unrestricted and encompasses all real numbers. In other words, the function can be evaluated and calculated for any real value of x, whether it is a negative number, zero, or a positive number.

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The statement that the one with a higher coefficient of variation exhibits higher variability is true.

The coefficient of variation expresses the proportionate level of variability present in a random variable and can be determined by dividing the mean by the standard deviation.

If the coefficient of variation is higher, it means that the random variable shows more variation in relation to its mean.

To illustrate, suppose that the average height of a set of males is 6 feet with a standard deviation of 2 inches.

The variance ratio would result in a coefficient of variation of 0. 033 Suppose that a group of females has an average height of 5 feet with a standard deviation of 1 inch.

The women's coefficient of variation is calculated to be 0. 02 The variance of men's height in relation to their average height is indicated by their higher coefficient of variation.

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Answer:

\(1 \frac{1}{2}\)

The essays that she can review in 1 hour would be; 2 2/3.

A fraction represents a part of a number or any number of equal parts.

We are given that English teacher reviewed 2 /3 of an essay in 1/ 4 of an hour.

Thus, Fraction of the essay reviewed = 2/3

Amount of time used = 1/4

Therefore, the fraction of essay for an hour can be calculated as;

= Fraction of the essay reviewed / Amount of time used

= 2/3 ÷ 1/4

= 2/3 × 4

= 8/3

= 2 2/3

Hence, She will review 2 2/3 essay.

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There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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Your analysis is correct. Here's a summary:

If it is sunny, then it is 80° Fahrenheit. (Original statement)

Converse: If it is 80° Fahrenheit, then it is sunny. (Valid)

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Valid)

If it is not sunny, then it is not 80° Fahrenheit. (Original statement)

Converse: If it is not 80° Fahrenheit, then it is not sunny. (Invalid)

Counterexample: A day that is not 80° Fahrenheit and not sunny (e.g., 70° and cloudy).

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Invalid)

Counterexample: A day that is 80° Fahrenheit and cloudy.

In cases 1 and 2, the original statements and their converses are valid because the relationship between "sunny" and "80° Fahrenheit" holds in both directions. However, in cases 3 and 4, the converses are invalid because there are counterexamples where the second part of the statement (either "not 80° Fahrenheit" or "cloudy") does not necessarily imply the first part ("not sunny" or "80° Fahrenheit").

Answer:

1. a7

2.b4

Step-by-step explanation:

Answer:

Answer: See image

Step-by-step explanation:

The bases are 5cm times 3cm, meaning that 2 parallel sides have to be 5cm by 3cm, 2 other parallel sides have to 2cm by 3cm, and the 2 other parallel sides have to be 5cm by 2cm.

Answer:

refer to workings

Step-by-step explanation:

Perimeter=15+15+8+8=46cm

Area=15×8=120cm²

Step-by-step explanation:

-2a4 - 3a2 + 7a + 6 - 6a3 + a4 + 7a2 - 6

Solving like terms

-a4 - 6a3 + 4a2 + 7a

Option A is the correct answer

Answer:

Step-by-step explanation:

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