4c) Solve each equation.

Answer:

7

Explanation:

Use the distance formula to find the answer

Answer:

7 units

Step-by-step explanation:

since the x- coordinates of L and M are equal , both - 1 then the length of LM is the absolute value of the difference of the y- coordinates.

LM = | 4 - (- 3) | = | 4 + 3 | = | 7 | = 7

or

LM = | - 3 - 4 | = | - 7 | = 7

In this scenario, where the bank only recognizes and deals with whole numbers, the extra 50 cents cannot be directly represented. The bank only considers the integer portion of the amount and ignores the fractional part.

When Mary puts all her money, $6.50, into a bank, but the bank only understands numbers as integers, the extra 50 cents are lost or forfeited as they cannot be converted to integers. Therefore, Mary will only be credited with 6 dollars in the bank.

However, there are a couple of ways Mary could prevent losing the extra 50 cents. She could either round up to the nearest dollar and deposit $7, or she could exchange the coins for bills at a currency exchange, bank or other establishment.

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The slope intercept form of a line which passes through the points (-2, 5) and (6, -4)  is  y = (-9/8)x + 11/4.

According to the question.

A line passes through the two points (-2, 5) and (6, -4).

As we know that, the slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.

So, the slope of the line = -4 -5/(6 + 2) = -9/8

And, the slope intercept form of a line which passes through the points (-2, 5) and (6, -4) is given by

y = (-9/8)x + b

Since, the line passes through (-2, 5) and (6, -4). So, both the points must statisfy the above equation.

⇒ 5 = (-9/8)(-2) + b

⇒ 5 = 9/4 + b

⇒ b = 5 - 9/4

⇒ b = (20 - 9)/4

⇒ b = 11/4

Therefore, the slope intercept form of a line which passes through the points (-2, 5) and (6, -4)  is  y = (-9/8)x + 11/4.

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Answer:

\((2x - 1)(x + 3) = \)

\(2 {x}^{2} + 5x - 3\)

A = 2, B = 5, C = -3

Answer:    The elimination method is a technique for solving systems of linear equations. Let's walk through a couple of examples.

Example 1

We're asked to solve this system of equations:

\begin{aligned} 2y+7x &= -5\\\\ 5y-7x &= 12 \end{aligned}

2y+7x

5y−7x

​

=−5

=12

​

We notice that the first equation has a 7x7x7, x term and the second equation has a -7x−7xminus, 7, x term. These terms will cancel if we add the equations together—that is, we'll eliminate the xxx terms:

\begin{aligned} 2y+\redD{7x} &= -5 \\ +~5y\redD{-7x}&=12\\ \hline\\ 7y+0 &=7 \end{aligned}

2y+7x

+ 5y−7x

7y+0

​

=−5

=12

=7

​

​

Solving for yyy, we get:

\begin{aligned} 7y+0 &=7\\\\ 7y &=7\\\\ y &=\goldD{1} \end{aligned}

7y+0

7y

y

​

=7

=7

=1

​

Plugging this value back into our first equation, we solve for the other variable:

\begin{aligned} 2y+7x &= -5\\\\ 2\cdot \goldD{1}+7x &= -5\\\\ 2+7x&=-5\\\\ 7x&=-7\\\\ x&=\blueD{-1} \end{aligned}

2y+7x

2⋅1+7x

2+7x

7x

x

​

=−5

=−5

=−5

=−7

=−1

​

The solution to the system is x=\blueD{-1}x=−1x, equals, start color #11accd, minus, 1, end color #11accd, y=\goldD{1}y=1y, equals, start color #e07d10, 1, end color #e07d10.

We can check our solution by plugging these values back into the original equations. Let's try the second equation:

\begin{aligned} 5y-7x &= 12\\\\ 5\cdot\goldD{1}-7(\blueD{-1}) &\stackrel ?= 12\\\\ 5+7 &= 12 \end{aligned}

5y−7x

5⋅1−7(−1)

5+7

​

=12

=

?

12

=12

​

Yes, the solution checks out.

If you feel uncertain why this process works, check out this intro video for an in-depth walkthrough.

Example 2

We're asked to solve this system of equations:

\begin{aligned} -9y+4x - 20&=0\\\\ -7y+16x-80&=0 \end{aligned}

−9y+4x−20

−7y+16x−80

​

=0

=0

​

We can multiply the first equation by -4−4minus, 4 to get an equivalent equation that has a \purpleD{-16x}−16xstart color #7854ab, minus, 16, x, end color #7854ab term. Our new (but equivalent!) system of equations looks like this:

\begin{aligned} 36y\purpleD{-16x}+80&=0\\\\ -7y+16x-80&=0 \end{aligned}

36y−16x+80

−7y+16x−80

​

=0

=0

​

Adding the equations to eliminate the xxx terms, we get:

\begin{aligned} 36y-\redD{16x} +80&=0 \\ {+}~-7y+\redD{16x}-80&=0\\ \hline\\ 29y+0 -0&=0 \end{aligned}

36y−16x+80

+ −7y+16x−80

29y+0−0

​

=0

=0

=0

​

​

Solving for yyy, we get:

\begin{aligned} 29y+0 -0&=0 \\\\ 29y&=0 \\\\ y&=\goldD 0 \end{aligned}

29y+0−0

29y

y

​

=0

=0

=0

​

Plugging this value back into our first equation, we solve for the other variable:

\begin{aligned} 36y-16x+80&=0\\\\ 36\cdot 0-16x+80&=0\\\\ -16x+80&=0\\\\ -16x&=-80\\\\ x&=\blueD{5} \end{aligned}

36y−16x+80

36⋅0−16x+80

−16x+80

−16x

x

​

=0

=0

=0

=−80

=5

​

The solution to the system is x=\blueD{5}x=5x, equals, start color #11accd, 5, end color #11accd, y=\goldD{0}y=0y, equals, start color #e07d10, 0, end color #e07d10.

Want to see another example of solving a complicated problem with the elimination method? Check out this video.

Practice

PROBLEM 1

Solve the following system of equations.

\begin{aligned} 3x+8y &= 15\\\\ 2x-8y &= 10 \end{aligned}

3x+8y

2x−8y

​

​

Step-by-step explanation:

Answer: Option B

Step-by-step explanation:

Answer:

Function A: f(x) = -8^x

Function B: f(x) = 2^x

Function A has a greater horizontal asymptote. As x approaches negative infinity, Function A approaches y = 0 faster than Function B.

The stock side of Brenda’s investment has gained a greater percent return.

Here, we have

Given:

Brenda invested her money in Esti Transport in the form of two par value $1,000 bonds and 116 shares of stock.

When Brenda initially invested her money, the market rate for Esti Transport bonds was 96.562, and the stock had a share price of $13.40. Currently, the market rate for Esti Transport bonds is 101.345, and the stock has a share price of $15.22.

Brenda needs to calculate which side of her investment has gained a higher percentage of return, and the difference between the returns.

To find out which side of her investment gained a higher percentage of return, Brenda needs to calculate the percentage of change for each side.

The percentage of change is calculated using the formula:

Percentage of change = (New Value - Old Value) / Old Value * 100

The percentage of change for Brenda’s two bonds can be calculated as follows:

Market value of one bond = $1,000 * 101.345 / 100 = $1,013.45

Value of two bonds = $1,013.45 * 2 = $2,026.90

The percentage of change for the two bonds = (2,026.90 - 1,931.24) / 1,931.24 * 100 = 4.96%

The percentage of change for Brenda’s 116 shares of stock can be calculated as follows:

The market value of one share of stock = $15.22

Value of 116 shares = $15.22 * 116 = $1,764.52

The percentage of change for the stock = (1,764.52 - 1,548.40) / 1,548.40 * 100 = 13.95%

Therefore, the stock side of Brenda’s investment has gained a greater percent return.

The percentage of return for Brenda’s stock side is 13.95%, and the percentage of return for her bond side is 4.96%.

The difference between the percentage of return for the stock and bond sides is:

13.95% - 4.96% = 8.99%

Hence, the percentage of return for the stock side is 8.99% greater than the percentage of return for the bond side.

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Answer:999

Step-by-step explanation:

Step-by-step explanation:

discretion data is something that will never change

continous data is data that will continue to become either larger or smaller

discret = ticket sales, number of employees

continuous = age,height

The data can be tallied into a frequency distribution using a class interval of 100 and a starting point of 0.

To create a frequency distribution, we group the data into intervals or classes and count the number of data points falling within each interval. The class interval represents the range of values covered by each class, and the starting point determines the first interval.

Here is an example of how the data can be tallied into a frequency distribution using a class interval of 100 and a starting point of 0:

```

Class Interval    Frequency

0 - 99            12

100 - 199         18

200 - 299         24

300 - 399         15

400 - 499         10

500 - 599         8

600 - 699         5

700 - 799         3

800 - 899         2

900 - 999         1

```

In this frequency distribution, the data is divided into classes based on the class interval of 100. The first class, from 0 to 99, has a frequency of 12, indicating that there are 12 data points falling within that range. The process is repeated for each subsequent class interval, resulting in a frequency distribution table.

By organizing the data into a frequency distribution, we gain insights into the distribution and patterns within the dataset. It provides a summarized view of the data, allowing us to identify the most common or frequent values and analyze the overall distribution.

In summary, the data has been tallied into a frequency distribution using a class interval of 100 and a starting point of 0. The frequency distribution table presents the number of data points falling within each class interval, enabling a better understanding of the distribution of the data.

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Answer:

90

Step-by-step explanation:

So, you need to calculate both of the areas of the shapes and then subtract them.

so, 9×12=108

and

3×6=18

108-18=90

Answer:

90

Step-by-step explanation:

area of the big rectangle

minus

the area of the small rectangle

108 - 18 = 90

The mass of the decoration and of each passenger car are 200 kg and 550 kg, respectively

The given parameters in the question are

These can be represented as

(6, 3500) and (4, 2400)

The slope of the above points represent the mass of each passenger car

This is calculated as

Slope = Difference in mass/Difference in number of cars

So, we have

Slope = (3500 - 2400)/(6 - 4)

Evaluate

Slope = 550

When there are no passenger cars in the train, we have

(0, Mass of decoration)

Using the slope formula, we have

Slope = (Mass of decoration - 3500)/(0 - 6)

So, we have

Slope = (Mass of decoration - 3500)/(-6)

This gives

(Mass of decoration - 3500)/(-6) = 550

Cross multiply

Mass of decoration - 3500 = -3300

Add 3500 to both sides

Mass of decoration = 200

Hence, the mass of each car is 550 kg

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Let's break down the expression for Tony's combined total earnings step by step.

First, we consider Tony's earnings as a tutor. He earns $11 per hour as a tutor, so the amount he earns from tutoring is given by the product of his hourly rate ($11) and the number of hours he worked as a tutor (t). This can be represented as $11t.

Next, we consider Tony's earnings as a waiter. He earns $13 per hour as a waiter, so the amount he earns from waiting tables is given by the product of his hourly rate ($13) and the number of hours he worked as a waiter. Since Tony worked a total of 106 hours this month and spent t hours as a tutor, he must have worked (106 - t) hours as a waiter. This can be represented as $13(106 - t).

To calculate Tony's combined total earnings for the month, we add the amount he earned as a tutor ($11t) to the amount he earned as a waiter ($13(106 - t)). This yields the expression:

Earnings = $11t + $13(106 - t)

This expression represents the total dollar amount Tony earned this month, considering the number of hours he worked as a tutor (t) and waiter (106 - t).

the criteria used when deciding upon the inclusion of a variable are A - Theory, B - t-statistic, C - Bias, and D - Adjusted R^2.

When deciding upon the inclusion of a variable, the following criteria are commonly used:

A - Theory: Theoretical justification is often considered to include a variable in a model. It involves assessing whether the variable is relevant and aligns with the underlying theory or conceptual framework.

B - t-statistic: The t-statistic is used to determine the statistical significance of a variable. A variable with a significant t-statistic suggests that it has a meaningful relationship with the dependent variable and may be included in the model.

C - Bias: Bias refers to the presence of systematic errors in the estimation of model parameters. It is important to consider the potential bias introduced by including or excluding a variable and assess whether it aligns with the research objectives.

D - Adjusted R^2: Adjusted R^2 is a measure of the goodness of fit of a regression model. It considers the trade-off between the number of variables included and the overall fit of the model. Adjusted R^2 helps in assessing whether the inclusion of a variable improves the model's explanatory power.

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If a mill worker measures the width of a plank and the width of the plank is 15.8 dm, then the width of the plank in meters is 1.58

The width of the plank in decimeter = 15.8 dm

Conversion is the process of the converting the given measurement like length, mass etc, from one unit to another unit

We have to find the width of the plank in meter

We know that,

1 decimeter = 0.1 meter

Convert the given decimeter to meter  

15.8 decimeter = 15.8 × 0.1

Multiply the numbers

= 1.58 meters

Therefore, the width of the plank in meter is 1.58

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The given question in incomplete, the complete question is :

A millworker measures the width of a plank. The width is 15.8 dm . what is the width in meters?

Answer:

c. 15

Step-by-step explanation: 15 is divisible by 3

Boys are taller than girls on average, with a larger center of data and larger range in height;

the dot plots are not shown.

To find the reference angle of a negative angle, follow these steps:

Determine the positive equivalent: Add 360 degrees (or 2π radians) to the negative angle to find its positive equivalent. This step is necessary because reference angles are always positive.

Subtract from 180 degrees (or π radians): Once you have the positive equivalent, subtract it from 180 degrees (or π radians). This step helps us find the angle that is closest to the x-axis (or the positive x-axis) while still maintaining the same trigonometric ratios.

For example, let's say we have a negative angle of -120 degrees. To find its reference angle:

Positive equivalent: -120 + 360 = 240 degrees

Subtract from 180: 180 - 240 = -60 degrees

Therefore, the reference angle of -120 degrees is 60 degrees.

In summary, to find the reference angle of a negative angle, first, determine the positive equivalent by adding 360 degrees (or 2π radians). Then, subtract the positive equivalent from 180 degrees (or π radians) to obtain the reference angle.

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The function f(x) = x^2 - 4 defined for all x ∈ ℝ does not have an inverse function because it fails the horizontal line test, meaning that multiple x-values map to the same y-value.

To determine if a function has an inverse, we need to check if it is a one-to-one correspondence, meaning that each input x corresponds to a unique output y and vice versa. In other words, no two distinct x-values can have the same y-value.

For the function f(x) = x^2 - 4, we can observe that different x-values can produce the same y-value. For example, f(2) = f(-2) = 0. This violates the one-to-one correspondence requirement, as two distinct inputs (2 and -2) map to the same output (0).

Because the function fails to satisfy the one-to-one correspondence, it does not have an inverse function. In order for a function to have an inverse, it must pass the horizontal line test, meaning that no horizontal line intersects the graph of the function more than once. In the case of f(x) = x^2 - 4, horizontal lines can intersect the graph at multiple points, indicating a lack of invertibility.

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Answer:

m1 = 122°

m2= 58°

Step-by-step explanation:

M1 is an alternate interior angle, of 122°, which means that that angle is also 122°.

The line with m1 and m2 added together equal 180°, so we can subtract 122 from 180 to find m2.

180-122= 58

The probability that all 7 graduates selected at random received a starting salary of $60,000 or more is , 0.0065

This is a binomial probability problem where we have a sample of size 7 and want to find the probability that all 7 graduates received a starting salary of $60,000 or more.

We know that 40% of mathematics graduates received a starting salary of $60,000 or more,

So, the probability of any one graduate receiving a salary of $60,000 or more is 0.4.

Using the binomial probability formula, we can calculate the probability as follows:

P(X = 7) = (n choose X) pˣ (1-p)ⁿ⁻ˣ

where n is the sample size, x is the number of graduates who received a starting salary of $60,000 or more, p is the probability of success (i.e., receiving a salary of $60,000 or more), and (n choose X) is the number of ways to select X graduates out of n.

So in this case, we have:

n = 7, X = 7 and p = 0.4

Plugging into the formula, we get:

P(X = 7) = (7 choose 7) 0.4⁷ (1-0.4)⁷⁻⁷

P(X = 7) = (1) 0.4⁷ (0.6)⁰

P(X = 7) = 0.0065

Therefore, the probability that all 7 graduates selected at random received a starting salary of $60,000 or more is , 0.0065

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Answer:

I'm sorry this is hard, what grade is this?

Step-by-step explanation:

Answer:

G) AC = 12

Step-by-step explanation:

5/10 = (x + 5)/(3x + 3)

15x + 15 = 10x + 50

5x = 35

x = 7

AC = 7 + 5 = 12