The equation 5x-10y=30is written in standard form. What is the first step when solving for x? Add 5x to both sides of the equation. Subtract 5x from both sides of the equation. Add 10y to both sides of the equation. Subtract 10y from both sides of the equation.

Answer:

the answer is 154 cm, area = 1,452 cm2 I took the test

Step-by-step explanation:

Answer:

the answer is 26 units

Step-by-step explanation:

The slope of the line in the given graph with the coordinates  (x₁ , y₁ ) = (4, 5) and (x₂ , y₂) = (2, 3) is equal to 1.

The slope of a line is calculated by rise over run.

Here is the formula for calculating the slope of a line:

Slope = (y₂ - y₁) / (x₂ - x₁)

Here, the points (x₁ , y₁ ) = (4, 5) and (x₂ , y₂) = (2, 3) are on the line. Plugging these points into the formula, we get:

Slope

= (3 - 5) / (2 - 4)

= (-2) / (-2)

= 1

Therefore, the slope of the line is 1.

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Answer: The inequality that represents the temperature t in degrees Fahrenheit at any time on this day is [tex]t\leq 9[/tex] degree Fahrenheit.

Explanation:

It is given that on a winter’s day, 9 degrees Fahrenheit is the highest temperature recorded. It means the temperature on this day must be less than or equal to 9 degree Fahrenheit.

Let t represents the temperature in degrees Fahrenheit at any time on this day. Then,

[tex]t\leq 9[/tex]

Therefore, the inequality that represents the temperature t in degrees Fahrenheit at any time on this day is [tex]t\leq 9[/tex] degree Fahrenheit.

Answer:

[tex]t\leq 9^{0}F[/tex]

Step-by-step explanation:

We have been given that highest temperature recorded on a winter’s day is 9 degrees Fahrenheit and we are asked to write an inequality that represents the temperature t in degrees Fahrenheit at any time on this day.

Since we know that highest temperature can't exceed 9 degrees Fahrenheit on the given day and it will be less than or equal to 9.

Therefore, our inequality will be,[tex]t\leq 9^{0}F[/tex]

The smallest number of new spools that Ted will need for this job is 8 spools of cable.

Given that, Ted is installing lighting in a new block of 12 apartments. He will need 60 metres of cable for each apartment. Each new spool holds 100 metres of cable.

We need to find the smallest number of new spools that Ted will need for this job.

A cylindrical device on which film, magnetic tape, thread, or other flexible materials can be wound; a reel.

Now, 60 meters per apartment x 12 apartments =720 total meters for all 12 apartments.

720 meters / 100 meters per spool =7.2 spools

so, Ted will need at least 8 spools of cable.

Therefore, the smallest number of new spools that Ted will need for this job is 8 spools of cable.

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The recurrence relation is given by bn = 8bn-1 - 15bn-2 with b1 = 2 and b2 = 16.

Since it is linear homogeneous recurrence relation ,so first find its characteristic equation.

r² - 8r + 15 = 0

( r - 3 )( r - 5 ) = 0

r = 3 , 5

So, the general solution of the given recurrence relation is

bn = u(3)n + v(5)n ------------ ( 1 )

Now use the initial conditions b1 = 2 and b2 = 16.

From ( 1 ) , b1 = u(3)1 + v(5)1

2 = 3u + 5v ---------- ( 2 )

and b2 = u(3)2 + v(5)2

16 = 9u+ 25v------- ( 3 )

Solving ( 2 ) and ( 3 ) , we get u= - 1 and v = 1

Therefore, the required solution is bn = - (3)n + (5)n

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Answer:

A- The final price of the shirt was $27.36.

B- If it were reduced by 30% from the original price, the price of the shirt would be $26.6.

C- There is a difference between both prices because in the first case, the discount is split, making a first discount on a larger basis, and the second on a smaller basis, already made the first discount.

In contrast, at the second price, the entire percentage is made on the major basis. Therefore, the discount is larger.

Step-by-step explanation:

A- The final price of the shirt is determined by the following calculation:

(38 x 0.8) x 0.9 = FINAL PRICE

38 is multiplied by 0.8 because the price was reduced by 20% (0.2 is the 20% of 1, that is, of a unit. Therefore, the remaining price would be that 0.8 or 80%)

Then, using the same logic, we have to multiply that result by 0.9 in order to get the final price.

Therefore:

(38 x 0.8) x 0.9 = 30.4 x 0.9 = 27.36

B- Here, we would have to multiply 38 x 0.7, which gives a result of 26.6

Answer: Hence, There is vertical distance of 19 inches the pipe must drop between its ends.

Step-by-step explanation:

Since we have given that

Rainwater outflow pipe must drop exactly 1 inch for every 25 inches of horizontal distance.

For 1 inch = 25 inches of vertical distance the pipe must drop.

If there is a 40 foot long rain water pipe runs under the edge of a roof.

Then, we need to find the vertical distance in inches the pope must drop.

First, we change 40 feet into inches.

Since 1 foot = 12 inches

40 feet = 40×12 inches = 480 inches

So, Vertical distance the pipe must drop is given by

[tex]\dfrac{480}{25}\\\\=19.2\ inches[/tex]

Hence, There is vertical distance of 19.2 inches ≈ 19 inches the pipe must drop between its ends.

The volumes of the rectangular prism 'X' (126 cu.cm.) is greater than the volumes of the rectangular prism 'Y' (110 cu.cm.).

[tex]V=l\times w\times h[/tex]

where, 'l' be the length of the rectangular prism,

'w' is the width  of the rectangular prism,

'h' is the height of the rectangular prism

For given question,

We have been given two rectangular prisms 'X' and 'Y'.

The dimensions of the rectangular prism 'X',

[tex]l=7~cm,w=3~cm,h=6~cm[/tex]

Using the formula for the volume of the rectangular prism,

[tex]\Rightarrow V=l\times w\times h\\\\\Rightarrow V=7\times 3\times 6\\\\\Rightarrow V=126~cu.cm.[/tex]                      ...................(i)

The dimensions of the rectangular prism 'Y',

[tex]l=5~cm,w=2~cm,h=11~cm[/tex]

Using the formula for the volume of the rectangular prism,

[tex]\Rightarrow V=l\times w\times h\\\\\Rightarrow V=5\times 2\times 11\\\\\Rightarrow V=110~cu.cm.[/tex]                        ...............(ii)

From (i) and (ii),

the volume of the rectangular prism 'X' is greater than the volume of the rectangular prism 'Y'.

Therefore, the volume of the rectangular prism 'X' (126 cu.cm.) is greater than the volume of the rectangular prism 'Y' (110 cu.cm.)

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Final answer:

Thomas spelled 18 out of 20 words correctly, which, when divided, gives us 0.9. This decimal represents the portion of the words he spelled correctly on his quiz.

Explanation:

To find the decimal that represents the portion of words Thomas spelled correctly on his quiz, we follow a simple process of division and conversion to a decimal.

Thomas spelled 18 out of 20 words correctly. So, we divide 18 by 20 which equals 0.9. This is the decimal that represents the portion of words Thomas spelled correctly.

Statistics is a branch of mathematics dealing with data collection, analysis, interpretation, and presentation, consisting of two main types: descriptive and inferential. Statistical models use probability distributions to describe expected behaviors and variability within observations.

About Statistics

The field of statistics is an essential discipline within mathematics that entails the collection, analysis, interpretation, and presentation of data. In our daily lives, we encounter data in various forms, which can be meticulously examined and understood through statistical methods. Two main types of statistics exist: descriptive statistics and inferential statistics. Descriptive statistics summarize and describe the features of a specific data set, providing a way to visualize data through graphs, charts, and summary measures like the mean and standard deviation. On the other hand, inferential statistics allow us to make predictions or inferences about a population based on a sample of data.

Statistical models are used to describe phenomena, utilizing probability distributions to account for the expected behavior and variability of observations. When researchers collect data, they often use a random sample to represent the larger population. A statistic is a numerical characteristic derived from the sample that helps estimate the corresponding population parameter, which is a characteristic of the entire population.

Statistics and probability are intertwined; as we gather and inspect data, we use statistical tools to distinguish good data from bad and create accurate predictions. Properly understanding and applying statistics can lead to more informed decisions in science, business, policy-making, and virtually every other field where data is essential.