Are the terms 2x and -5x like or unlike terms?

Answer:

Step-by-step explanation:

To find sin(alpha-beta), we can use the trigonometric identity:

sin(alpha - beta) = sin(alpha)cos(beta) - cos(alpha)sin(beta)

We are given that sin(alpha) = 11/12 in the second quadrant and cos(beta) = 15/17 in the fourth quadrant. We can use the Pythagorean theorem to find sin(beta):

sin^2(beta) + cos^2(beta) = 1

sin(beta) = sqrt(1 - cos^2(beta))

sin(beta) = sqrt(1 - (15/17)^2)

sin(beta) = sqrt(1 - 225/289)

sin(beta) = sqrt(64/289)

sin(beta) = 8/17 (since sin(beta) is positive in the fourth quadrant)

Now we can plug in the values we know into the identity:

sin(alpha - beta) = sin(alpha)cos(beta) - cos(alpha)sin(beta)

sin(alpha - beta) = (11/12)(15/17) - cos(alpha)(8/17)

We still need to find cos(alpha), which we can do using the Pythagorean identity:

sin^2(alpha) + cos^2(alpha) = 1

cos(alpha) = sqrt(1 - sin^2(alpha))

cos(alpha) = sqrt(1 - (11/12)^2)

cos(alpha) = sqrt(23/144)

Now we can substitute this value into the expression for sin(alpha - beta):

sin(alpha - beta) = (11/12)(15/17) - cos(alpha)(8/17)

sin(alpha - beta) = (11/12)(15/17) - sqrt(23/144)(8/17)

sin(alpha - beta) ≈ 0.210

Therefore, sin(alpha - beta) is approximately equal to 0.210.

Therefore , the solution of the given problem of equation comes out to be slope of 1 and a y-intercept of -1, passing through the points (-3, -4) and (1, 0).

Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this case, leveling generates b + 7 rather than another algorithm that could analyze data provided by y + 7, split 12 into two parts, and create y + 7.

Here,

This linear relationship's expression can be found by first determining the slope using the following formula:

=> slope = (y-change) / (change in x)

=> slope = (2 - (-2)) / (4 - 0) = 4/4 = 1

Consequently, the line's inclination is 1. We can now determine the equation using the point-slope form of a line's equation:

=> y - y1 = m(x - x1)

where (x1, y1) is a location on the line and m denotes the slope. We have a choice between the two points provided, so let's use (0, -2):

=> y - (-2) = 1(x - 0)

=> y + 2 = x

By taking 2 away from both edges, we arrive at:

=> y = x - 2

slope = (0 - (-4)) / (1 - (-3)) = 4/4 = 1

=> y - y1 = m(x - x1)

=> y - (-4) = 1(x - (-3))

=> y + 4 = x + 3

=> y = x - 1

A line with a slope of 1 and a y-intercept of -1, passing through the points (-3, -4) and (1, 0), represents the graph of this linear connection.

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Answer:

The height of a rectangular prism is 26 inches and its base is a rectangle with an area of 6 cubic inches. What is the volume of the prism in cubic inches?

Step-by-step explanation:

The height of a rectangular prism is 26 inches and its base is a rectangle with an area of 6 cubic inches. What is the volume of the prism in cubic inches?

According to the information, the volume of the three-dimensional rhombus is 61.92 cm³.

The three-dimensional rhombus is a geometric solid in the shape of a prism whose lateral faces are rhombuses and the bases are parallelograms. To calculate its volume, the area of the base must be multiplied by the height of the prism.

In this case, the height of the prism is 3 cm and the dimensions of the base rhombus are 5.2 cm wide and 8 cm long. Since the rhombus has two diagonals of equal length, its area can be calculated using the formula (major diagonal x minor diagonal) / 2.

First, the length of the diagonals of the base rhombus must be calculated using the Pythagorean theorem, since its width and length are known:

Then, the area of the base rhombus can be calculated:

Finally, the volume of the prism can be calculated:

Therefore, the volume of the three-dimensional rhombus is 61.92 cm³.

Note: This question is incomplete. Here is the complete information:

Find the volume of the prism

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An approximate of 68% of American women have shoe sizes that are between 6.54 and 9.58.

To use the empirical rule, we need to assume that the distribution of women's shoe sizes is approximately normal. Given a mean of 8.06 and a standard deviation of 1.52, we can standardize the values of 6.54 and 9.58 by subtracting the mean and dividing by the standard deviation:

Ζ1 = (6.54 - 8.06) / 1.52

Ζ1 = -1.00

Ζ2 = (9.58 - 8.06) / 1.52

Ζ2 = 1.00

The standardized values tell us that the value of 6.54 is 1 standard deviation below the mean, while the value of 9.58 is 1 standard deviation above the mean. According to the empirical rule, about 68% of the data falls within one standard deviation of the mean. Therefore, we can say that: [tex]P(6.54 < x < 9.58) = P(-1.00 < z < 1.00) = 68%[/tex]

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All eligible voters voted for Shelley= 3/20 ,

All eligible voters voted for Morgan= 31/100,  Morgan received most votes.

Multiplication is a mathematical operation that embodies the basic idea of numerous additions of the same number. The outcomes of multiplying two or more numbers are referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplication facilitates the process of adding the same number again.

Let's suppose Precinct 5 has 100 registered voters. There were 50 voters who participated in the election because only 50% of those who were eligible to vote actually did so.

3/10 of the votes were cast for Shelley, which translated as 3/10 x 50 or 15 votes.

With 5/8 of the vote, Morgan received 5/8 x 50 votes, or 31.25 votes. Therefore, we must round this figure down to 31 votes as we are dealing with whole voters.

We must divide the number of votes received by the total number of eligible voters in order to determine the percentage of all eligible voters who cast a ballot for Shelley: 100 eligible voters x 15 votes = 3/20.

Morgan won the most votes since she received more than Shelley.

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Solving a system of equations we can see that they have 4 lizards and 5 spiders.

We know that each spider has 8 legs, and each lizard has 4 legs.

Now we can define the variables:

x = number of lizards.

y = number of spiders.

We know that the total number of animals is 9, so:

x + y = 9

And the total number of legs is 56, then we can write:

4x + 8y = 56

Then we have a little system of equations:

x + y = 9

4x + 8y = 56

We can isolate x in the first equation to get:

x = 9 - y

Replacing that in the other one, we wll get:

4*(9 - y) + 8y = 56

36 - 4y + 8y = 56

4y = 56 - 36

4y = 20

y = 20/4 = 5

They have 5 spiders, and the other 4 animals must be lizards.

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The answer of the given question based on the hypothesis the answer is the calculated t-value of -2.58 is less than the critical t-value of -2.009, we cannot reject the null hypothesis.

A hypothesis is an educated guess or prediction that is used to explain an observation or set of observations. It is a proposed explanation or possible answer to a research question or problem that is based on prior knowledge, experience, and research. In science, a hypothesis is often tested through experiments or observations to determine if it can be supported or rejected by the evidence.

Hypothesis:

The city of Goose Pimple, Vermont, hypothesizes that contracting with Grimms Health Maintenance Organization will result in a significant reduction in health care costs per employee.

Null Hypothesis:

The null hypothesis is that there is no significant difference in health care costs per employee between last year and this year with the contract with Grimms Health Maintenance Organization having no impact.

Evaluation:

To evaluate the hypothesis, we will perform a one-sample t-test. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Assuming a significance level of 0.05, we will reject the null hypothesis if the calculated t-value is greater than the critical t-value.

Population mean = $3,261 (given)

Sample mean = $3,015

Sample standard deviation = $1,745

Sample size = 50

t = (3015 - 3261) / (1745 / sqrt(50)) = -2.58

Using a t-table with 49 degrees of freedom (sample size - 1) and a significance level of 0.05, the critical t-value is ±2.009.

Since the calculated t-value of -2.58 is less than the critical t-value of -2.009, we cannot reject the null hypothesis. This means that there is not enough evidence to suggest that there is a significant difference in health care costs per employee between last year and this year with the contract with Grimms Health Maintenance Organization having no impact.

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Answer:

This is a guess but I think it's 5 min per table.

Step-by-step explanation:

The reason being:

if we know that she has 9 tables to get to and each table can seat 4 people, we would have to multiply both numbers to find how many TOTAL people are in the restaurant during the first few hours.

9x4 = 36 people in total

then, we need to convert 3hrs into minutes to get a more accurate rep as to how much time she would spend at each table (she isn't going to spend the entire 3 hrs with only one table now, is she?)

so for this, we convert 3hrs into minutes

1 min = 60 secs

1 hr = 60 minutes

3hrs -> 60 x 3 = 180 minutes

now, to understand how many time she spends at each table, we need to figure out by dividing the # of people by the amount of minutes.

180 minutes/36 people = 5 mins per table.

The linear equation that models the number of days it will take Sheila's team to edit x pages, y = (1/85)·x indicates that the correct statement is option C.

C. Her team can edit 85 pages in one day

The slope-intercept form of linear equations is; y = m·x + c, where the coefficient m is the slope and c is the y-intercept.

The parameters of the model, y = (1/85)·x are;

x = The number of pages that require editing

y = The number of days required to complete the editing

Therefore, the model is in the slope and intercept form of a linear equation, where;

1/85 =  The slope

The y-intercept is zero

The slope indicates that 85 pages can be edited in one day, therefore the number of days to edit 170 (2 × 85) pages is 2 days

Similarly, when the number of days, y = 1, and the number of pages to be edited, x = 1, we get;

y = (1/85)·x

1 = (1/85)·x

x = 1/(1/85) = 85

The number of pages that can be edited in one day is 85 pages

The correct statement is therefore;

C. Her team can edit 85 pages in one day

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Answer:

30

Step-by-step explanation:

41.25-10=31.25

31.25/1.25=25

25+5=30

Hope this helps!

The measure of angle mLQ is 125°. we got the answer with the concept of  inscribed angle in the figure .

what is inscribed angle?

An inscribed angle is an angle formed by two chords in a circle that have a common endpoint on the circle. In other words, the endpoints of the angle are on the circle, and the angle "opens up" inside the circle. The measure of an inscribed angle is equal to half the measure of the arc that it intercepts.

In the given question,

We know that the measure of angle mWC is 108° and the measure of angle m/U is 37°. Since angle QCU is an inscribed angle that intercepts arc CQ, its measure is equal to half the measure of arc CQ. Similarly, angle LUW is an inscribed angle that intercepts arc WL, so its measure is equal to half the measure of arc WL.

We can use these facts to set up the following equation:

mLQ = (mCQ / 2) + (mWL / 2)

We can find the measures of arcs CQ and WL by subtracting the measures of angles QCU and LUW from 360°, respectively. Therefore:

mCQ = 360° - 2mQCU

= 360° - 2(mWC - m/U)

= 360° - 2(108° - 37°)

= 182°

mWL = 360° - 2mULW

= 360° - 2(m/U + mWC)

= 360° - 2(37° + 108°)

= 68°

Substituting these values into the equation for mLQ, we get:

mLQ = (mCQ / 2) + (mWL / 2)

= (182° / 2) + (68° / 2)

= 125°

Therefore, the measure of angle mLQ is 125°.

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For the given statements f(-x) = -4|x| - 5x^3 = -f(x), we can conclude that f(x) is an even function.

A function that fulfils f(-x) = f(x) for any x inside the function's domain is said to be even. The graph of an even function displays reflected y-axis symmetry geometrically. The even functions [tex]f(x) = x^2 and f(x)[/tex] = cos are two examples (x).

A function is considered odd if it meets the condition f(-x) = -f(x) for all x inside its domain. An odd function's graph displays origin rotational symmetry geometrically. Odd functions include such like [tex]f(x) = x^3 and f(x) = sin (x).[/tex]

The given function is [tex]f(x) = -4|x| + 5x^3.[/tex]

An even function is a function that satisfies f(-x) = f(x).

For the function:

[tex]f(-x) = -4|-x| + 5(-x)^3[/tex]

[tex]f(-x) = -4|x| - 5x^3[/tex]

[tex]f(x) = -4|x| + 5x^3[/tex]

Since[tex]f(-x) = -4|x| - 5x^3 = -f(x)[/tex], we can conclude that f(x) is an even function.

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Step-by-step explanation:

23-x >19

make x the coefficient by subtracting 23 from both sides

23-23 - x > 19 - 23

-x > -4

Divide both sides by -1, thus making the sign to change

-x / -1 > -4/-1

x < 4

Answer:

(6,-5)

Step-by-step explanation:

Parallel lines have the same slope.

After answering the provided question, we can conclude that Mean = (13 + 13 + 11 + 10 + 8) / 5 = 11 for Condition 3 (Loud Noise). 2.28 is the standard expression deviation.

An expression in mathematics is a collection of representations, digits, and transnational corporations that imitate a statistical correlation or regimen. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, growing influence, division, but instead exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

To compute the experiment summaries, we must first compute the mean and standard deviation for each condition:

Mean = (15 + 13 + 14 + 12) / 4 = 13.5 in Condition 1 (Low Noise).

1.5 is the standard deviation.

Mean = 19 in Condition 2 (Medium Noise).

3 is the standard deviation.

Mean = (13 + 13 + 11 + 10 + 8) / 5 = 11 for Condition 3 (Loud Noise).

2.28 is the standard deviation.

 Condition 1 (Low Noise)    Condition 2 (Medium Noise)    Condition 3 (Loud Noise)

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

|          |         |     |          |         |        |  |          |          |        |

|          |         |     |          |         |        |  |          |          |        |

|          |         |     |          |         |        |  |          |          |        |

|          |         |     |          |         |        |  |          |          |        |

|          |         |     |          |         |        |  |          |          |        |

|          |         |     |          |         |        |  |          |          |        |

|          |         |     |          |         |        |  |          |          |        |

|          |         |     |          |         |        |  |          |          |        |

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

        Median = 13.5             Median = 19                Median = 11

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we can conclude that there is no strong evidence of a statistically significant difference between the means of the two groups.

What is the t-statistic?

A t-statistic is a test statistic that is used to determine if there is a significant difference between two groups based on their means.

A t-statistic with an absolute value greater than 1.96 indicates statistical significance at the 0.05 level of significance.

In this case, the t-statistic is -0.38, which is less than the absolute value of 1.96.

This means that the difference between the means of the two groups is not statistically significant at the 0.05 level of significance.

Without information on the specific groups being compared, it is not possible to make definitive conclusions about the differences between them based solely on the t-statistic.

Hence, we can conclude that there is no strong evidence of a statistically significant difference between the means of the two groups.

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5) The total surface area of the pentagonal prims is 500 cm².

6) The total surface area of the pentagonal prims is 243 mi².

The formula for determining the surface area of the prism is expressed as:

Total Surface Area of Pentagonal Prism,

T = 5ab + 5bh sq. units.

where is altitude, b is base and h is height

5) here, a = 5.5 cm

b = 8 cm

h = 7 cm

Total Surface Area = 5ab + 5bh

T = 5(5.5)(8) + 5(7)(8)

T = 220 + 280

T = 500 cm²

The total surface area of the pentagonal prims is 500 cm².

6) here, a = 4.1 mi

b = 6 mi

h = 4 mi

Total Surface Area = 5ab + 5bh

T = 5(4.1)(6) + 5(4)(6)

T = 123 + 120

T = 243 mi²

The total surface area of the pentagonal prims is 243 mi².

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The complete question is in the attached figure:

Find the surface area of each figure. Round your answers to the nearest hundredth if necessary

Answer:

There are 1760 yards in one mile and the rink is 250 yard in perimeter.

This means 3 miles is 5280 yards.

If Sam has already gone around the whole rink 6 times, that means he was traveled a total of 1500 yards.  

Sam has 3780 more yards to travel 3 miles.

This means he needs to do 15.12 more laps around the rink.  Or 16 if you are rounding.

A sketch of the algebra-tile shape is shown in the image attached below.

An expression for the perimeter of the shape is 4x + 4.

The perimeter for each of the given values of x are 32 units, 26 units, and 13.33 units respectively.

In Mathematics and Geometry, the perimeter of a rectangular shape can be calculated by using this mathematical expression;

P = 2(L + B)

Where:

Based on the sketch of the algebra-tile shape, an expression for its perimeter is given by:

Perimeter of the shape = 4x + 4

When x = 7 units, the perimeter of the shape can be calculated as follows;

Perimeter of the shape = 4(7) + 4

Perimeter of the shape = 32 units.

When x = 7 units, the perimeter of the shape can be calculated as follows;

Perimeter of the shape = 4(5.5) + 4

Perimeter of the shape = 26 units.

When x = 7 units, the perimeter of the shape can be calculated as follows;

Perimeter of the shape = 4(7/3) + 4

Perimeter of the shape = 13.33 units.

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Hannah made an error in her calculations by using simple interest instead of compound interest. To find the balance of a savings account with compound interest, you need to take into account the effect of compounding, where the interest earned is added to the principal and then earns interest as well.

To calculate the actual balance of the account after 3 years, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the ending balance of the account

P = the principal amount (the initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years the money is invested

In this case, we have:

P = $4,000

r = 2% = 0.02

n = 4 (since interest is compounded quarterly)

t = 3

Plugging in these values, we get:

A = $4,000(1 + 0.02/4)^(4*3) = $4,493.72

Therefore, the actual balance of the account after 3 years with compound interest is $4,493.72.

Hannah's calculation of $4,244.83 was based on using the formula for simple interest, which only takes into account the initial investment and the annual interest rate, but not the effect of compounding.

Answer:

Her account balance after 3 years is $4,246.71

Step-by-step explanation:

In this question, we are tasked with calculating what Hannah's account balance will be after 3 years and the error she made in her calculations

Mathematically, to calculate the account balance after 3 years, we use the formula for the compound interest as follows.

Mathematically, the amount A earned on a compound interest is calculated as

A = P

where A is the account balance after the number of years which is what we want to know

P is the initial amount invested which is $4000

r is the interest rate which is 2%(2/100 = 0.02) according to the question

n is the number of times interest is compounded per year which is 4(quarterly means every 3 months)

t is the number of years which is 3

We plug the values into the question;

A = 4000(1 + 0.02/4)^(3)(4)

A = 4000(1+0.005)^12

A = 4000(1.005)^12

A = $4,246.71

P.S ; I do not see Hannah's calculation and as such I cannot spot where she made the error in her calculations

1617.0 , is her annual premium.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

A = p(r)t,

where t = years that have passed,

A = amount of money after t years,

p = principal amount of money, and

r = rate of growth (interest plus 1)

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Answer: 1/3

Step-by-step explanation:

Quotient is another word for the solution to a division problem.

So in this case the quotient is the answer to -5/-15.

When you divide a negative by another negative, you get a positive answer. The same can be said about dividing a positive number by another positive number.

So, in this case, we can change -5/-15 to 5/15.

Now we just need to simplify by finding a GCF (greatest common factor)

Both 5 and 15 shares 5 as a factor, so divide them both by 5.

Then you would get 1/3 or .33333333333333333...

Step-by-step explanation:

Find the 360° circumference of the circle ( pi * d)   then you want                   90 / 360ths of that

Radius  = 10 mi       then  d = 20 miles

Circumference = pi * 20  = 20 pi miles

    90 / 360   * 20 pi =  15.7 mi

The incorrect statement is Only 3 people did not watch TV each week.

What is the frequency?

The frequency of a repeated event is its number of instances per unit of time. It differs from angular frequency and is sometimes referred to as temporal frequency for clarification. One event occurs per second when measuring frequency in hertz.

Here, we have

Given: Jason conducted a survey among his friends to determine the number of hours they watch TV each week.

We have to determine which statement is NOT true about the frequency chart.

We concluded that the incorrect statement is Only 3 people did not watch TV each week.

Hence, the incorrect statement is Only 3 people did not watch TV each week.

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The factory has 172 litres of dye available.

Liters (also spelled litres) is a unit of volume in the International System of Units (SI). It is commonly used to measure the volume of liquids, gases, and solids that can be poured or contained in a container. One liter is equivalent to 1000 cubic centimeters (cc) or milliliters (ml), and it is roughly equal to 1.057 quarts or 0.264 gallons.

In the given question,

First, we need to find out how much dye is needed for one roll of fabric. We know that 43 liters of dye are needed for 1 roll of fabric that is 1,067 feet long. Therefore, we can say that:

1 roll of fabric = 43 liters

1,067 feet

To find out how much dye is needed for 5 rolls of fabric, we can multiply both sides of this equation by 5:

5 rolls of fabric = 5 × 43 liters

1,067 feet = 215 liters

1,067 feet

So, 5 rolls of fabric would require 215 liters of dye.

Next, we need to check if the 4 buckets of dye are enough to dye 5 rolls of fabric. Each bucket contains 43 liters of dye, so 4 buckets would contain:

4 buckets of dye = 4 × 43 liters

= 172 liters

Therefore, the factory has 172 liters of dye available.

Since 215 liters of dye are required for 5 rolls of fabric, and the factory has only 172 liters of dye available, it cannot dye 5 rolls of fabric with the given amount of dye.

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After answering the provided question, we can conclude that As a result, function Joel cannot satisfy the constraints by purchasing two games and six puzzles.

A function appears to be a hyperlink between two sets of numbers in mathematics, where each member of the first set (referred as the domain) corresponds to a certain representative of the second set (called the range). In other utterance, a function takes input from a set and produces output by another. Inputs are frequently represented by the variable x, and outputs are represented by the variable y. A function can be represented by a formula or a graph. The method y = 2x + 1 is an example of a conceptual model in which each value assigned to x yields a value of y.

Part A:

8x + 12y 96

x + y ≥ 9

x ≥ 0

Part B

If Joel purchases two games and six puzzles, he will spend:

[tex]2 * $12 + 6 * $8 = $48 + $48 = 96\\8x + 12y \leq 96\\8(6) + 12(2) = 48 + 24 = 72 < 96\\x + y \geq 9\s6 + 2 = 8 < 9[/tex]

As a result, Joel cannot satisfy the constraints by purchasing two games and six puzzles.

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Answer:

Step-by-step explanation:

[tex]24\div 6+2\times 9 =4+18=22[/tex]

÷  and × first followed by + and -.  But otherwise work left to right.

Answer:  22

Step-by-step explanation:

1.)  Solve using PEMDAS.

Therefore, the quantity of heat absorbed by 70 g of water that warms from 30∘C to 90∘C is 17,645.6 J (joules).

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), separated by an equals sign (=). The expressions on either side of the equals sign can contain numbers, variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.

Here,

The amount of heat absorbed by a substance can be calculated using the formula:

Q = mcΔT

where Q is the amount of heat absorbed, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature. For water, the specific heat capacity is 4.184 J/g⋅K.

Using the given values, we can calculate the amount of heat absorbed as follows:

m = 70 g

c = 4.184 J/g⋅K

ΔT = (90 - 30)∘C = 60∘C

Q = mcΔT

Q = (70 g) x (4.184 J/g⋅K) x (60∘C)

Q = 17645.6 J

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