In QRS, the measure of angle S=90°, the measure of angle Q=6°, and RS = 20 feet. Find the


length of SQ to the nearest tenth of a foot.


R


20


6°


s


Q


X

Answer:

1. A. 12a^2 + 8a + 4

2. C. 4xy+16x-4y^2-16y

3. C. 64q^6r^8s^4

4. A. -4x^4y^6

Step-by-step explanation:

48a^3 + 32a^2 + 16a / 4a = (48a^3) / 4a + (32a^2) / 4a + (16a) / 4a = 12a^2 + 8a + 4.

So, the answer is A. 12a^2 + 8a + 4.

(2x-2y)(2y+8) = 4xy - 4y^2 + 16x -  16y.

So, the answer is C. 4xy+16x-4y^2-16y.

(-8q^3 * r^4 * s^2)^2 = (-8)^2 * q^6 * r^8 * s^4 = 64q^6r^8s^4.

So, the answer is C. 64q^6r^8s^4.

-12x^8y^8 / 3x^4y^2 = (-12 / 3) * (x^(8 - 4)) * (y^(8 - 2)) = -4x^4y^6.

So, the answer is A. -4x^4y^6.

Hope this helps!

If the magnitude of vector w is 48 and the direction is 235 degrees, we can find the vector w in component form by using trigonometry.

Let's denote the horizontal component as wx and the vertical component as wy.

The horizontal component, wx, can be found using the cosine of the angle:

wx = Magnitude × cos(Direction)

Substituting the given values:

wx = 48 × cos(235 degrees)

The vertical component, wy, can be found using the sine of the angle:

wy = Magnitude × sin(Direction)

Substituting the given values:

wy = 48 × sin(235 degrees)

Now we can calculate the values using a calculator or software. Rounding to two decimal places, we have:

wx ≈ 48 × cos(235 degrees) ≈ -32.73

wy ≈ 48 × sin(235 degrees) ≈ -32.00

Therefore, the vector w in component form is approximately (wx, wy) ≈ (-32.73, -32.00).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

The answer is B.

Step-by-step explanation:

f(6) = 146 & g(6) = 731 /// The difference of the two is 585.

In the analyze stage of the data life cycle, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

The data life cycle is defined as the time period that that data exist in you system. Usually the data management experts finds the six or more stages in the data life cycle

The data analyst is the person who use the interpreted data and analyze the data in order to solve the problems

The analyze stage is the one of the main stages of the data life cycle. In the stage data analyst will use the spreadsheet to aggregate the data in the system and use the formulas to perform the calculations in the system

Therefore, the data analyst will use the spreadsheet to aggregate the data and use the formulas to perform the calculations

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Answer:

Step-by-step explanation:

y=2x-7

y=-1/2x+6

-1/2x+6 = 2x-7

x= 4

y= 2(4)-7

 = 1

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The given expression:

The expression can be written as :

Take 9 common :

Since 3 x 3 = 9

Apply the property of factorization:

So, the expression can be written as :

So, the factorization is : 9(x + 3) (x - 3)

Answer :

Answer:

1) 5.9

2) 8.1

3) 54

Step-by-step explanation:

A is opposite, so we have sine 36=a/10

sine 36(10)=a

a=5.9

B is adjacent, so we have cosine 36=b/10

cosine 36(20)=b

b=8.1

Angles of a triangle add to 180

we have a angle of 36 and a right angle which is 90

36+90=126

180-126=54

Answer:

D. ("24.")

Step-by-step explanation:

it is D

Answer:

0.23

Step-by-step explanation:

Using either long division or a calculator, divide 23 by 100; you will get the result 0.23.

Answer:

0.23 hope tbis helps :)

Step-by-step explanation:

The number of cavities each person has had is an example of a survey involving quantitative data.

Quantitative data is any data that can be expressed in numerical terms and can be measured or counted. It includes variables such as counts, amounts, measurements, or ratings. In the given options, the number of cavities each person has had is a numerical variable that can be counted and analyzed statistically, making it an example of quantitative data. Other options, such as favorite food or color of the walls, are qualitative data, which is non-numerical and cannot be measured in numerical terms.

Quantitative data is commonly used in surveys, experiments, and statistical analyses to study patterns and relationships between variables. It allows for precise measurements, comparisons, and statistical modeling. Examples of quantitative data include age, height, weight, temperature, test scores, sales figures, and population counts. By contrast, qualitative data is often used to explore attitudes, beliefs, perceptions, or opinions, and is typically recorded as text or verbal data. Examples of qualitative data include interviews, open-ended survey questions, observations, and focus group discussions.

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The complete question is:

Which survey uses quantitative data, as an example?

each person individual's preferred food.

how many cavities each individual has had.

the color of each person's bedroom's walls.

the type of car each individual person owns.

A NORMAL distribution is a symmetrical probability distribution with a bell-shaped curve. It is also called a Gaussian distribution or a normal curve. This distribution is often used in statistics to represent a large number of natural phenomena, such as the distribution of height, weight, or IQ scores in a population.

The first deviation of a NORMAL distribution includes 68.2% of the data. This means that if we were to take a random sample of data from a normally distributed population, about 68.2% of the data would be within one standard deviation of the mean.

The second deviation includes 95.4% of the data. This means that about 95.4% of the data would be within two standard deviations of the mean.

The third deviation includes 99.7% of the data. This means that about 99.7% of the data would be within three standard deviations of the mean.

It is important to note that while these percentages hold true for a NORMAL distribution, they may not apply to other types of distributions.

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Answer:

4x + 17

Step-by-step explanation:

10x+5-2(3x-6)

10x + 5-6x+12

The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.

A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.

B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.

\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.

That leaves \(27-14=13\) matches. These represent the matches team lost.

Finally, the answers are below.

\(A)29\)
\(B)13\)

Answer:

  a) 29 points

  b) 13 losses

Step-by-step explanation:

You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.

The number of points the team has is ...

  P = 3W +D

  P = 3(8) +(5) = 29

The team has 29 points.

You want the number of losses the team has if it has 54 points and 12 draws after 39 games.

The number of wins is given by ...

  P = 3W +D

  54 = 3W +12

  42 = 3W

  14 = W

Then the number of losses is ...

  W +D +L = 39

  14 +12 +L = 39 . . . substitute the known values

  L = 13 . . . . . . . . . . subtract 26 from both sides

The team lost 13 games.

__

Additional comment

In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)

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Answer:

5x+56

Step-by-step explanation:

5x+8(5+2)

5x+8(7)

Total number of selecting three partners randomly in which at least one junior partner must be there out of 23 senior and 24 junior partners is 14,444

Combination:

                       Combination is the number of possible ways, where order is irrelevant and replacements are not permitted, to select a sample of r elements from a set of n different objects.

                             \(C(n,r)=nCr = \frac{n!}{(n-r)! r!}\)

  C(n, r) means, Selection of r things out of n different things

           According to question,

        Given,

                    A firm has 23 senior and 24 junior partners.

      We have to select three partners randomly in which at least one junior partner must be there.

Case I : 2 senior and 1 junior partners

            2 senior partners can be selected out of 23 in C(23,2) ways

            1 junior partner can be selected out of 24 in C(24,1) ways

      hence number of ways of selecting 2 senior and 1 junior partners is equal to

                      C(23,2) x C(24,1)

Case II :  2 senior and 1 junior partners

               1 senior partners can be selected out of 23 in C(23,1) ways

               2 junior partner can be selected out of 24 in C(24,2) ways

      hence number of ways of selecting 1 senior and 2 junior partners is equal to

                          C(23,1) x  C(24,2)    

Case III :  0 senior and 3 junior partners

               0 senior partners can be selected out of 23 in C(23,0) ways

               3 junior partner can be selected out of 24 in C(24,3) ways

      hence number of ways of selecting no senior and 3 junior partners is equal to

                          C(23,0) x  C(24,3)    

Thus,

        Total number of selecting three partners randomly in which at least one junior partner must be there is

           C(23,2) x C(24,1) +  C(23,1) x  C(24,2)   + C(23,0) x  C(24,3)  

Using formula,

                           \(C(n,r)=nCr = \frac{n!}{(n-r)! r!}\)

       C(23,2) x C(24,1) +  C(23,1) x  C(24,2)   + C(23,0) x  C(24,3)  

    =    253    x 24        +  23        x  276        + 1           x 2024

    =    6072   +  6348 + 2024

    =    14,444

Total number of selecting three partners randomly in which at least one junior partner must be there is 14,444

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The sets A = {biology, computer science, trigonometry} B = {computer science, calculus, trigonometry, biology) are equivalent.

This is because they have the same number of elements, but the elements are not in the same order. Two sets are equal if they have the same elements in the same order, and two sets are equivalent if they have the same number of elements, but the elements are not in the same order. Therefore, the correct answer is "Equivalent."

Here is the answer in HTML format:

<p>The sets A and B are <strong>equivalent</strong>. This is because they have the same number of elements, but the elements are not in the same order. Two sets are equal if they have the same elements in the same order, and two sets are equivalent if they have the same number of elements, but the elements are not in the same order. Therefore, the correct answer is "<strong>Equivalent</strong>."</p>

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The 95% confidence interval is larger because it provides a higher level of confidence and captures a wider range of values.

The best point estimate of the mean is indeed 28 pounds, as provided in the information.

To find the 90% confidence interval of the mean, we can use the formula:

Confidence interval = sample mean ± (critical value) * (standard deviation / √sample size)

Using a confidence level of 90%, we find the critical value associated with a two-tailed test to be approximately 1.645 (from a standard normal distribution table).

Calculating the confidence interval:

Lower bound = 28 - (1.645 * (44 / √60)) ≈ 27.1

Upper bound = 28 + (1.645 * (44 / √60)) ≈ 28.9

Therefore, the 90% confidence interval of the mean weight for the overweight men is approximately 27.1 pounds to 28.9 pounds.

To find the 95% confidence interval of the mean, we follow the same process as in part (b) but with a different critical value. For a 95% confidence level, the critical value is approximately 1.96 (from a standard normal distribution table).

Calculating the confidence interval:

Lower bound = 28 - (1.96 * (44 / √60)) ≈ 26.9

Upper bound = 28 + (1.96 * (44 / √60)) ≈ 29.1

Therefore, the 95% confidence interval of the mean weight for the overweight men is approximately 26.9 pounds to 29.1 pounds.

The 95% confidence interval is larger than the 90% confidence interval. This is because a higher confidence level requires a wider interval to capture a larger range of possible values and provide a higher level of certainty. The 95% confidence interval is associated with a greater range of values and is more likely to contain the true population mean.

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The mixture would contain approximately 0.849 cups of caramel popcorn and 1.698 cups of cheese popcorn.

Let's define the variables:

Let x be the number of cups of caramel popcorn in the mixture

Let y be the number of cups of cheese popcorn in the mixture

We are given that the mixture has two times as much cheese popcorn as caramel popcorn, so y = 2x.

We are also given that the total number of calories in the mixture is 254. To find an equation that relates x and y, we can use the calorie information for each type of popcorn:

Calories from caramel popcorn = 183x

Calories from cheese popcorn = 58y = 58(2x) = 116x

Total calories in the mixture = 183x + 116x = 299x

Setting the total calories equal to 254 and solving for x:

299x = 254

x = 0.849

So we would need 0.849 cups of caramel popcorn in the mixture.

To find the number of cups of cheese popcorn, we can use the equation y = 2x:

y = 2(0.849) = 1.698

So we would need 1.698 cups of cheese popcorn in the mixture.

Therefore, the mixture would contain approximately 0.849 cups of caramel popcorn and 1.698 cups of cheese popcorn.

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The required answer of single logarithm and simplify,\(\log(e^x) + log(cy^2) - \log(e^{x^4}) + \log(x^2)\)  is the expression of logarithm can be simplified as \(\log[(c * x^2 * y^2) / (e^{3x})].\)

To express the given expression as a single logarithm, we can apply the properties of logarithms.

Using the product rule of logarithms, we can combine the terms involving the same base:

\(\log(e^x) + log(cy^2) - \log(e^{x^4}) + \log(x^2)\)

Now, using the quotient rule of logarithms, we can simplify further:

\(\log[(e^x * cy^2 * x^2) / (e^{x^4})]\)

Applying the power rule of logarithms, we can simplify the expression inside the logarithm:

\(\log[(c * x^2 * y^2) / (e^{3x})].\)

Therefore, the expression of logarithm can be simplified as \(\log[(c * x^2 * y^2) / (e^{3x})].\)

Note: If there are any additional restrictions or given values for the variables, the expression may be simplified further.

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A two–way table that shows data from Leslie's survey is presented as follows;

Dog. No dog Total

Cat. 17. 24. 41

No cat. 30. 9. 39

Total 47. 33. 80

The given parameters are;

Solution;

The number that have dogs and no cat = 47 - 17 = 30

Therefore, we have;

Dog and cat = 17

No dog and cat = 24

No dog no cat = 9

Total number that have cats = 17 + 24 = 41

Number that have no cats = 30 + 9 = 39

Sum total of students that have no dogs = 24 + 9 = 33

A two way table is presented as follows;

Dog. No dog Total

Cat. 17. 24. 41

No cat. 30. 9. 39

Total 47. 33. 80

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Hence the formula of \(a ^2 + b^ 2 + c^ 2\) is \(( a + b + c )^ 2 - 2 ( ab + bc + ca ) .\)

Formulas are equations that compute values from your spreadsheet. A formula always starts with the equal sign (=).

Using a calculating operator and a constant, you can make a straightforward formula.

For instance, the equation =5+2*3 multiplies two numbers before adding one more to the outcome.

A formula is a rule or relationship in mathematics that utilizes letters to indicate amounts that might change; these amounts are known as variables. For instance, the triangular area calculation formula.

The word "formula" is pluralized to "formulas." A list of elements that are employed in various concoctions and potions is referred to as a formula, which can also refer to a specific mathematical calculation.

Because English might be erratic at times, newborns can also be fed formula.

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The solution to the equation -18 = -x using the multiplication principle is x = 18. To check the solution, substitute x = 18 back into the original equation: -18 = -(18). This simplifies to -18 = -18, which is true. Therefore, the solution x = 18 satisfies the equation.

The multiplication principle states that if two quantities are equal, then multiplying both sides of the equation by the same non-zero number will yield an equivalent equation. In this case, we have -18 = -x. To solve for x, we can apply the multiplication principle by multiplying both sides of the equation by -1.

(-1)(-18) = (-1)(-x)

This simplifies to 18 = x, or x = 18. Therefore, the solution to the equation is x = 18.

To check the solution, we substitute x = 18 back into the original equation:

-18 = -(18)

This simplifies to -18 = -18, which is a true statement. Since the equation holds true when x = 18, we can conclude that the solution is correct.

By using the multiplication principle, we were able to solve the equation and verify the solution by substituting it back into the original equation.

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It is given that the friend agrees to pay half of the total cost of gas for the trip.

It is required to find the amount of money the friend is owing.

To do this, calculate the total cost of gas and evaluate half of it.

The total cost of gas is the sum of the gas charges given:

Calculate half of the total cost:

It follows that the friend is owing $44.

The answer is $44.

Answer:

2/1 or 2 per hour

Step-by-step explanation:

divide 4 by 2 and make it a fraction like thing

Answer:

\((Number\ of\ Hours) / (Total\ Pottery\ Pieces)\)

\((2\ hours) / (4\ pieces)\)

\(0.5\ hours\ per\ piece\)

The artist makes a potter piece in 30 minutes or 0.5 hours

Paco was able to sell a total of 1,582 gallons more in March than he was able to in February.

Paco was able to sell 4,510 gallons of gas in February and then a further 6,092 gallons in March.

The amount that he sold in March that was more than what he sold in February was:

= Amount sold in March - Amount sold in January

= 6,092 - 4,510

= 1,582 more gallons

In conclusion, Parco sold 1,582 gallons more in March than in February.

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The quadratic equation are equations that have an axis of symmetry

passing through the vertex.

Reasons:

2. The x-intercepts are given by the point at which the y-value of the equation are zero.

Therefore;

The quadratic equation are;

(x + 3)·(x - 1) = 0

x² + 2·x - 3 = 0

The equation can also be written in the form;

(-x - 3)·(x - 1) = 0

-x² - 2·x + 3 = 0

The quadratic equations are;

3. The points through which the quadratic equation passes are;

(-4, 2) and (1, 2)

The value at the vertex = Maximum value

Taking the vertex as the point midway between the two given points, we have;

\(\displaystyle Coordinates \ of \ the \ vertex = \left( \frac{-4 + 2}{2} , \, k \right) = \left(-1, \, k)\)

The coordinates of the vertex, (h, k) = (-1, y)

The vertex form of a quadratic equation is presented as follows;

(y - k) = a·(x - h)²

y = a·(x - h)² + k

Which gives;

y = a·(x - (-1))² + k = a·(x + 1)² + k

y = a·(x + 1)² + k

At the point (-4, 2), we have;

2 = a·((-4) + 1)² + k = 9·a + k

2 = 9·a + k

Taking the value of k as 11, we have;

(h, k) = (-1, 11)

2 = 9·a + 11

\(\displaystyle a = \frac{2 - 11}{9} = -1\)

Which gives;

y = -1·(x + 1)² + 11 = -x² - 2·x + 10

y = -x² - 2·x + 10

When x = -4, we have;

y = -(-4)² - 2·(-4) + 10 = 2

When x = 2, we have;

y = -(2)² - 2·(2) + 10 = 2

4. The points through which the graph passes are; (-4, 2) and (1, 2)

The x-coordinate of the minimum vertex is given by the equation;

\(\displaystyle Coordinates \ of \ the \ vertex, \ (h, \, k) = \left( \frac{-4 + 1}{2} , \, k\right) = \left(-1.5, \, k)\)

(h, k) = (-1.5, y)

The vertex form of the equation of a quadratic equation is presented as follows;

y = a·(x - h)² + k

Which gives;

y = a·(x - (-1.5))² + k

y = a·(x + 1.5)² + k

\(\displaystyle a = \mathbf{\frac{y - k}{\left(x + 1.5\right)^2}}\)

At the point (1, 2), we have;

\(\displaystyle a = \frac{2 - k}{\left(1 + 1.5\right)^2} = \frac{2 - k}{6.25}\)

When k = -4.25, we have;

\(\displaystyle a = \frac{2 - k}{\left(1 + 1.5\right)^2} = \frac{2 - \left(-4.25 \right)}{6.25} = 1\)

The equation is therefore;

y = 1·(x + 1.5)² - 4.25 = x² + 3·x - 2

y = x² + 3·x - 2

At the point where x = -4, we have;

y = (-4)² + 3·(-4) - 2 = 2

At the point where x = 1, we have;

y = (1)² + 3·(1) - 2 = 2

Therefore;

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The answer is 60%

According to the original information given, the estimated average number of shoppers in the original store at any time(x) is 45.

In the question, it states that, in the new store, the manager estimates that an average of 90 shoppers per hour(60 minutes) enter the store, which is equivalent to 1.5 shoppers per minute(s).

The manager also estimates that each shoppers stays in the store for an average of 12 minute (t). Thus, by Little's law there are, on average,

x = s x t

=> x = 1.5 x 12

=> x = 18

Hence, there are 18 shoppers at any time in the new store.

Now, Percentage of shoppers

\(\frac{45-18}{45}\) x 100 = 27/45 x 100 = 2700/45 = 60%

Therefore, the answer is 60%

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The probability of rolling a winning combination will be 7/12 as the winning combination is 21 and Total combination will be 36.

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't. By dividing the number of positive outcomes by the entire number of potential outcomes, probability—the likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are only two outcomes when you flip a coin: either it comes up heads or tails.

Here,

If the first die is red and the second one is green, then the sample space S is the following:

S=

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2, 1), (2,2), (2,3), (2,4), (2,5), (2,6), (3, 1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5, 1), (5,2), (5,3), (5,4), (5,5), (5,6), (6, 1), (6, 2), (6,3), (6,4), (6,5), (6,6)

Hence n(S)=36.

Let's list the losing combinations:

E={(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (2, 1),

(2, 3), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), (6,5)}

n(E)=15

There are 36 total possiblities.

Out of which, winning probability is 21.

=21/36

=7/12

Given that the winning combination is 21 and the total combination is 36, the chance of rolling a winning combination is 7/12.

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Answer:

(2⁵/x²)⁴

(32/X²)

32⁴+x⁶

1,048,576 + X⁶

Step-by-step explanation:

i don't know if this is right. this is all I know

In geometry, projection is the mapping of a 2D or 3D figure onto a flat or 3D surface. For our purposes, we think of a projection as an association between a point on an object and a point on a plane .

Projection:

In geometry, projection is the mapping of a 2D or 3D figure onto a flat or 3D surface. For our purposes, we think of a projection as an association between a point on an object and a point on a plane (called the image plane). This association - between a geometrical figure and its image - is the branch of geometry which studies projection, including the study of the properties conserved under the projection, from the name of projective geometry, which is abolished by dotted lines on the figures à The corresponding points are on the image in the image plane. These lines are called projection lines.

Descriptive Geometry:

Descriptive geometry is the branch of geometry that allows the representation of three-dimensional objects in two dimensions using a specific set of procedures. The resulting technology is important for engineering, architecture, design and the arts. Planar geometric projections provide a theoretical basis for describing geometry. The first known publication on this technique is "Underweysung der Messung mit dem Zincked und Richtscheyt", published by Albrecht Dürer in Linien in Nuremberg in 1525. The Italian architect Guarino Guarini was also a pioneer of projective and descriptive geometry, as in witness his Placita Philosophica (1665), Euclides Adauctus (1671) and Architettura Civile (1686 - not published before 1737). He anticipated the work of Gaspard Monge (1746)-1818), who is generally considered the inventor of descriptive geometry. Gaspard Monge is often considered the "father of descriptive geometry" due to his developments in solving geometric problems. His first discoveries were made in 1765 while working as a draftsman for military fortifications, although his findings were published later.

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Answer:

B

Step-by-step explanation:

Trisha has $100. So she has to spend less than $100 or exactly 100 on her friends. The sign to represent this is ≤ ( the less than or equal to sign )

so if she has 4 friends and wants to spend x on each friend, she would spend a total of 4x on her 4 friends.

Remember that she has to spend less than or equal to $100. The equation to represent this is 4x ≤ 100