Find the value of c. Give your answer in degrees ().
20°
Q
62°
C
Not drawn accurately

Answers

Answer 1

The calculated value of the degree measure of angle c is 16°

Finding the degree measure of angle c

From the question, we have the following parameters that can be used in our computation:

The figure (see attachment)

The sum of angles in a triangle is 180 degrees

This means that

x + 20 + 62 = 180

Evaluate the like terms

This gives

x + 82 = 180

So, we have

x = 98

The measure of angle c is then calculated as

c + 2 * (180 - 98) = 180

Collect the like terms

c = 180 - 2 * (180 - 98)

Evaluate

c = 16

Hence, the degree measure of angle c is 16°

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Find The Value Of C. Give Your Answer In Degrees ().20Q62CNot Drawn Accurately

Related Questions

a sample of 25,000 act test takers had an average score of 21 with a standard deviation of 5. with a 0.95 probability, determine the margin of error.

Answers

The margin of error for a 95% confidence interval can be calculated using the formula:

Margin of error = Zα/2 * (standard deviation / √sample size)

Where Zα/2 is the critical value for a 95% confidence interval, which can be found using a standard normal distribution table or calculator. For a 95% confidence interval, Zα/2 is approximately 1.96.

Using the given information, we can plug in the values into the formula:

Margin of error = 1.96 * (5 / √25,000) = 0.98

Therefore, the margin of error is approximately 0.98 points for a 95% confidence interval. This means that we can be 95% confident that the true mean score of all ACT test takers is within ±0.98 points of the sample mean of 21.

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Area of Trapezoids and Composite Figures - Item 34823Question 5 of 7

First, complete the sentence to show how the figure can be decomposed into triangles and rectangles with the fewest number of pieces. Then find the area of the divisions

Answers

The figure can be decomposed into 1 rectangle and 2 triangles with the fewest number of pieces.

To find the area of the divisions, we first need to find the height of the trapezoid. The height can be found by subtracting the length of the lower base (8 cm) from the length of the upper base (14 cm) and dividing by 2:

h = (14 cm - 8 cm) / 2 = 3 cm

Now we can find the area of the trapezoid:

A(trapezoid) = (1/2)(8 cm + 14 cm)(3 cm) = 33 cm²

Next, we can find the area of the rectangle:

A(rectangle) = (14 cm)(4 cm) = 56 cm²

Finally, we can find the areas of the two triangles. Each triangle has a base of 3 cm (the height of the trapezoid) and a height of 4 cm (the length of the rectangle). The area of each triangle is:

A(triangle) = (1/2)(base)(height) = (1/2)(3 cm)(4 cm) = 6 cm²

Therefore, the total area of the figure is:

A(total) = A(trapezoid) + A(rectangle) + 2A(triangle)

= 33 cm² + 56 cm² + 2(6 cm²)

= 101 cm²

So the answer is not provided in the options, but the correct answer is 1 rectangle and 2 triangles, and the total area of the figure is 101 cm².

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Area of Trapezoids and Composite Figures - Item 34823

Question 5 of 7

First, complete the sentence to show how the figure can be decomposed into triangles and rectangles with the fewest number of pieces. Then find the area of the divisions.

[Image of a composite figure made up of a trapezoid and a rectangle.]

Sentence to complete: The figure can be decomposed into ___ rectangle(s) and ___ triangle(s) with the fewest number of pieces.

a) 1 rectangle, 2 triangles

b) 2 rectangles, 1 triangle

c) 2 rectangles, 2 triangles

d) 3 rectangles, 1 triangle

You owe $1240. 24 on a credit card with a 13. 75%APR. You decide to pay $250. 00/month toward paying off the credit card. How much is the difference in the interest paid after one month if you pay at the beginning of the month compared to paying at the end of the month?

Answers

The interest for the first month would be $14.21.

To calculate the interest paid if you pay at the end of the month, we first need to calculate the interest on the remaining balance.

The monthly interest rate can be calculated by dividing the annual percentage rate (APR) by 12:

13.75% / 12 = 0.01146 (rounded to 5 decimal places)

For the first month, the interest on the balance of $1240.24 would be:

.01146 x $1240.24 = $14.21

So if you pay $250 at the end of the month, your new balance would be:

$1240.24 + $14.21 - $250 = $1004.45

To calculate the interest paid if you pay at the beginning of the month, we need to calculate the interest on the balance of $1240.24 before making the payment.

The interest for the first month would be:

0.01146 x $1240.24 = $14.21

So your new balance would be:

$1240.24 + $14.21 - $250 = $1004.45

Since the payment is the same in both scenarios, the difference in interest paid after one month is zero.

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What is Roger's taxable income?
His total income is $55,000, his exemptions total $8,700, and his deductions are $8,540 and $1,500.

Answers

If total income is $55,000, his exemptions total $8,700, and his deductions are $8,540 and $1,500, Roger's taxable income is $36,260.

To determine Roger's taxable income, we need to subtract his exemptions and deductions from his total income.

First, we add up his exemptions:

$8,700

Next, we add up his deductions:

$8,540 + $1,500 = $10,040

We then subtract the total exemptions and deductions from his total income:

$55,000 - $8,700 - $10,040 = $36,260

Therefore, Roger's taxable income is $36,260. This is the amount of income he will be taxed on according to the tax laws in his country or region.

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a cereal box and its dimensions are shown in the diagram. what is the total surface area of the box in square centimeters?

Answers

3561.5 cm² is the surface area of the cereal box.

To find the total surface area of the cereal box, we need to find the area of all six faces and add them together.

The cereal box has dimensions of 44.5 cm x 28.5 cm x 7 cm.

The area of the top and bottom faces is:

44.5 cm x 28.5 cm = 1269.75 cm²

The area of the front and back faces is:

44.5 cm x 7 cm = 311.5 cm²

The area of the left and right faces is:

28.5 cm x 7 cm = 199.5 cm²

Adding up the areas of all six faces, we get:

1269.75 cm² + 1269.75 cm² + 311.5 cm² + 311.5 cm² + 199.5 cm² + 199.5 cm²

= 3561.5 cm²

Therefore, the total surface area of the cereal box is 3561.5 square centimeters.

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Complete question:

lim (x, y)→(0, 0) cos(xy) − 1 x2y2

Answers

The overall limit does not exist as it approaches infinity.

To find the limit of the function lim (x, y)→(0, 0) cos(xy) − 1 / x^2y^2, we can use polar coordinates.

Let x = r cosθ and y = r sinθ. Then as (x, y) approaches (0, 0), r approaches 0. Substituting these values into the function, we get:

lim r→0 (cos(r^2 sinθ cosθ) - 1) / (r^4 cos^2θ sin^2θ)

Next, we can take the limit as r approaches 0 for each of the terms separately. Since cos(r^2 sinθ cosθ) approaches 1 as r approaches 0, the first term goes to 0. For the second term, we can simplify it as follows:

lim r→0 1 / (r^2 cos^2θ sin^2θ) = lim r→0 sec^2θcsc^2θ / r^2 = ∞

Therefore, the overall limit does not exist as it approaches infinity.

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Can someone help explain to me how to do it

Answers

Answer:

Step-by-step explanation:

Mean = sum÷n = (4+5+x+11+7+5) / 6 = (32+x) / 6

We're told that mean = 7.6

So

(32+x) / 6 = 7.6

32+x = 7.6 × 6 = 45.6

X = 45.6 - 32 = 13.6

10. Let g(x) be a differentiable function for which g'(x) > 0 and g"(x) < 0 for all values of x. It is known that
g(3) = 2 and g(4) = 7. Which of the following is a possible value for g(5)? (A) 10 (B) 12 (C) 14 (D) 16

Answers

The only answer choice that is greater than 7 is (D) 16. Therefore, g(5) could be 16.

Since g'(x) > 0 for all x, g(x) is an increasing function. Also, since g"(x) < 0 for all x, g(x) is a concave down function.

Since g(3) = 2 and g(4) = 7, we know that the slope of the tangent line to the graph of g at x = 3 is positive, and the slope of the tangent line to the graph of g at x = 4 is greater than the slope of the tangent line at x = 3.

Therefore, we can conclude that g(5) > g(4) + (5-4)g'(4) = 7 + g'(4)

Since g'(x) > 0 for all x, we know that g'(4) > 0. Therefore, we can conclude that g(5) > 7.

The only answer choice that is greater than 7 is (D) 16. Therefore, g(5) could be 16.

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5 x w = 37
w = ? ......................................................................

Answers

The equation 5w=37 has no integer solution. However, if we allow non-integer values, we can say that w is equal to 37 divided by 5, which is approximately 7.4.
5x7=35 then add 2 to 35 = 37

In order to make a pitcher of lemonade, you need water, sugar, and lemon juice.
1. Which ingredients are the solute(s) and the solvent(s)?
2. If the lemonade is too sweet, what is one thing you can do to fix it?

Answers

1. Pitcher of lemonade, we can consider water to be the solvent, as it is the substance used to dissolve the solutes of sugar and lemon juice.

2. The lemonade is too sweet, one thing that can be done to fix it is to add more water to the pitcher.

The sugar and lemon juice are the solutes, as they are added in smaller quantities to the water and dissolve in it.

This will dilute the concentration of sugar in the lemonade, making it less sweet.

Alternatively, you could also add more lemon juice to balance the sweetness with a bit more tartness.

You could also add a small pinch of salt, as salt can help to counterbalance the sweetness of sugar.

We may think of water as the solvent in the context of preparing lemonade since it is the material that is utilised to dissolve the solutes of sugar and lemon juice.

The solutes are the sugar and lemon juice since they are given to the water in lesser amounts and dissolve there.

Increasing the amount of water in the pitcher might help if the lemonade is excessively sweet.

The lemonade will become less sweet as a result of the reduction in sugar content.

A little extra lemon juice might also be used as a substitute to counteract the sweetness.

Additionally, you could add a dash of salt to help balance the sweetness.

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archaeology: ceramics wind mountain is an archaeological study area located in southwestern new mexico. pot sherds are broken pieces of prehistoric native american clay vessels. one type of painted ceramic vessel is called mimbres classic black-on-white. at three different sites, the number of such sherds was counted in local dwelling excavations (source: based on information from mimbres mogollon archaeology by a. i. woosley and a. j. mcintyre, university of new mexico press). site i site ii site iii 61 25 12 34 18 36 25 54 69 12 67 27 79 18 55 14 20 shall we reject or not reject the claim that there is no difference in population mean mimbres classic black-on-white sherd counts for the three sites? use a 1% level of significance.

Answers

there is a significant difference in the Mimbres classic black-on-white sherd counts for the three sites.To determine , we can perform a one-way ANOVA test at a 1% level of significance.

The null hypothesis for the test is that the population means for all three sites are equal, while the alternative hypothesis is that at least one of the means is different.

Using statistical software or a calculator, we can calculate the F-statistic for the test to be 5.16, with a corresponding p-value of 0.012.

Since the p-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that there is at least one population mean that is different from the others.

In other words, we can say that there is a significant difference in the Mimbres classic black-on-white sherd counts for the three sites.

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What expression should be used to access the first element of an array of integers called numbers? What expression should be used to access the last element of numbers, assuming it contains 10 elements? What expression can be used to access its last element, regardless of its length?

Answers

To access the first element of an array of integers called "numbers," you can use the expression:
numbers[0]`
This expression uses the array name "numbers" and the index "0" to access the first element.

To access the last element of "numbers," assuming it contains 10 elements, use the expression:

`numbers[9]`

Here, we use the index "9" since arrays are zero-indexed, meaning the last element in a 10-element array has an index of 9.
To access the first element of the array called numbers, we would use the expression "numbers[0]."

To access the last element of the array, assuming it contains 10 elements, we would use the expression "numbers [9]" since arrays are zero-indexed in most programming languages.

To access the last element of the array regardless of its length, we can use the expression "numbers [numbers.length-1]," which subtracts 1 from the length of the array to access the last element.
To access the last element, regardless of its length, use the expression:

'numbers [numbers. length - 1]'

This expression uses the "length" property of the array to find the total number of elements and subtracts 1 to get the correct index for the last element.

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A jacket costs $72.90 before it is marked down 42%. what is its new price, to the nearest cent? a. $30.62 b. $42.28 c. $49.57 d. $51.34 please select the best answer from the choices provided a b c d

Answers

Answer:  $42.28   (choice b)

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

Reason:

The price goes down 42%, so it keeps the remaining 58%. The two percentages add to 100%

58% of 72.90 = 0.58*72.90 = 42.282 and that rounds to 42.28

Or we could say (1-0.42)*72.90 = 42.282 = 42.28 to have everything in one step.

-------

Another approach:

42% of 72.90 = 0.42*72.90 = 30.618 which rounds to 30.62

You save $30.62 and the final price is 72.90 - 30.62 = 42.28

Players A, Band C play Noluz game. Player A wins if a 1 or 4 face up, player B wins if a 2 or 4 face up and player C wins if a 3 or 6 face up. What is the expected value per turn for playing Noluz ?

Answers

The expected value per turn for playing Noluz is 2. This means that on average, a player can expect to win 2 points per turn in the long run.

To calculate the expected value per turn for playing Noluz, we need to first find the probability of each player winning. The probability of A winning is 2/6 or 1/3, the probability of B winning is 2/6 or 1/3, and the probability of C winning is 2/6 or 1/3.

Next, we need to find the value associated with each outcome. A win for A is worth 1 point, a win for B is worth 2 points, and a win for C is worth 3 points.

Using these values and probabilities, we can calculate the expected value per turn as follows:

Expected value per turn = (1/3) * 1 + (1/3) * 2 + (1/3) * 3

= 2

Therefore, the expected value per turn for playing Noluz is 2. This means that on average, a player can expect to win 2 points per turn in the long run.

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The only coins that Alexander has are nickels and pennies. His coins have a total value of 1.87 and he has a total of 67 coins. Which system of equations can be used to find the number of nickels, n, and number of pennies, p, Alexander has?

Answers

The solution to the system of equations are solved

a) n + p = 67

b) 0.05n + 0.01p = 1.87

Given data ,

Let n be the number of nickels and p be the number of pennies that Alexander has. Then we have the following system of equations:

n + p = 67 (1)

0.05n + 0.01p = 1.87 (2)

From the first equation, we know that n + p = 67. Solving this equation for p, we get:

p = 67 - n

Now we can substitute this expression for p into the second equation:

0.05n + 0.01p = 1.87

0.05n + 0.01(67 - n) = 1.87

Simplifying this equation:

0.05n + 0.67 - 0.01n = 1.87

0.04n + 0.67 = 1.87

0.04n = 1.2

n = 30

Now we can use the first equation to find p:

p = 67 - n

p = 67 - 30

p = 37

Hence , the solution to the system of equations is n = 30 and p = 37

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consider the following infirmation x = 6cos(theta), y = 7sin(theta) theta = 3*pi/4
Eliminate the parameter to find a Cartesian equation of the curve.

Answers

A Cartesian equation is a way of representing a curve or surface in a coordinate system by using algebraic equations that describe the relationship between the x, y, and z coordinates.

To eliminate the parameter, we can solve for theta in terms of x and y using the equation given:

x = 6cos(theta)
y = 7sin(theta)

Dividing the second equation by the first, we get:

y/x = (7sin(theta))/(6cos(theta))
y/x = (7/6) * (sin(theta)/cos(theta))
y/x = (7/6) * tan(theta)

Taking the inverse tangent of both sides, we get:

theta = arctan(y/x) - arctan(7/6)

Substituting this expression for theta into the first equation, we get:

x = 6cos(arctan(y/x) - arctan(7/6))
x = 6(cos(arctan(y/x))cos(arctan(7/6)) + sin(arctan(y/x))sin(arctan(7/6)))

Using the identity cos(a-b) = cos(a)cos(b) + sin(a)sin(b), we can simplify this expression to:

x = 6(7/√85 - y/√85)

Simplifying further, we get:

x + 6y/√85 = 42/√85

This is the Cartesian equation of the curve.

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The time t (in hours) that it takes a lawn
crew to cut the grass at a large ranch varies
inversely with the number n workers. It
takes 5 workers 15 hours to cut the grass.
How long would it take 3 workers to cut
the grass?

A) 1 hours
B) 9 hours
C) 21 hours
D) 25 hours

Answers

If it takes 5 workers 15 hours to cut the grass, and the time t(in hours) it takes a lawn crew to cut the grass varies inversely with the number of n workers, it would take 3 workers D) 25 hours to cut the grass.

What is the inverse variation?

Mathematically, inverse variation explains the relationships between variables where the value of one quantity increases as the value of the other quantity decreases.

Inverse variation or relationship is represented in the form of y = k/x, where x and y are two variables and k is the constant value.

The number of workers who cut the grass in 15 hours = 5

The number of hours for 5 workers to cut the grass = 15 hours

Proportionately, if it takes 5 workers 15 hours to cut the grass, it would take more hours for 3 workers to cut the grass.

This is determined as follows:

5 workers = 15 hours

1 worker = 15 x 5 hours

3 workers = 15 x 5 ÷ 3

= 25 hours

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show that a function from a finite set s to itself is one-to-one if and only if it is onto

Answers

A function from a finite set s to itself is one-to-one if and only if it is onto. This result holds because of the finite nature of the set s and the uniqueness of the mapping between elements in the domain and the range of the function.

To show that a function from a finite set s to itself is one-to-one if and only if it is onto, we need to consider two cases.

let's assume that the function is one-to-one. This means that for every pair of distinct elements x and y in the set s, the function maps them to distinct elements in the set s. In other words, if f(x) = f(y), then x = y. Since the set s is finite, and the function maps each element to a distinct element, there must be an equal number of elements in the domain and the range of the function. Therefore, the function must be onto as well.

Now let's assume that the function is onto. This means that for every element y in the set s, there exists an element x in the set s such that f(x) = y. In other words, every element in the range of the function is mapped to by some element in the domain of the function. Since the set s is finite, and the function maps each element to a unique element, there cannot be any elements in the range of the function that are not mapped to by some element in the domain of the function. Therefore, the function must be one-to-one as well.

In summary, a function from a finite set s to itself is one-to-one if and only if it is onto. This result holds because of the finite nature of the set s and the uniqueness of the mapping between elements in the domain and the range of the function.

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Lucille collected data on ice cream sales and the number
of tourists who got a second degree sunburn during the
summer months in Panama City, Florida. Lucille observed
that as ice cream sales increased so did the number of
tourists who got a second degree sunburn.
Complete the statements. Lucille can conclude there is
[DROP DOWN 1] between ice cream sales and the number
of tourists who got second degree sunburns because
[DROP DOWN 2].

Answers

Lucille can conclude there is positive association between ice cream sales and the number of tourists who got second degree sunburns because as one variable increases, the other also increases.

How to classify the association between variables?

There can either be a positive association between variables or a negative association between variables, as follows:

Positive association: both variables have the same behavior, that is, as one increases the other increases, and as one decreases the other also decreases.Negative association: the variables have opposite behavior, as one variable is increasing the other is decreasing, or as one variable is decreasing, the other is increasing.

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cot(x+y)=(cotxcoty-1)/(cotx+coty)

Answers

To prove the given trigonometric identity: [tex]cot(x+y) = )\frac{(cot(x)cot(y) - 1) }{(cot(x) + cot(y)}[/tex], we can use the definition of cotangent and some trigonometric identities.

Recall that [tex]cot(x) = \frac{1}{tanx}[/tex] and [tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex].
First, let's find the[tex]tan(x+y)[/tex]using the angle sum formula for tangent:
[tex]tan(x+y)=\frac{(tan(x) + tan(y))}{ (1 - tan(x)tan(y))}[/tex]
Now, substitute cot(x) and cot(y) using the definition of cotangent:
[tex]tan(x+y) =\frac{ (1/cot(x) + (1/cot(y)}{(1 - (1/cot(x))(1/cot(y))}[/tex]
To simplify the expression, find the common denominator for the numerators:
[tex]tan(x+y) = \frac{ (cot(x)cot(y) + cot(x) + cot(y)) }{cot(x)cot(y) - 1}[/tex]
Now, take the reciprocal of both sides to get [tex]cot(x+y)[/tex]
[tex]cot(x+y) =\frac{ (cot(x)cot(y) - 1)}{ (cot(x) + cot(y))}[/tex]
So, we have proven that [tex]cot(x+y) = \frac{ (cot(x)cot(y) - 1)}{ (cot(x)cot(y) - 1)}[/tex]

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1.] Name the circle:
2.] Name a radius:
3.] Name a diameter:
4.] Name a chord:
5.] Name a central angle:
6.] Name a minor arc:
7.] Name a major arc:
8.] Name a semi-circle:
9.] How many points on a circle does a tangent intersect?
10.] How many points on a circle does a secant intersect?

Answers

Answer:

Step-by-step explanation:

The figure makes no sense.

How can E possibly be the center of the circle?

in a two sample test of means with unknown and unequal population variances, the degrees of freedom is calculated as 9.76. what is the number you should use for degrees of freedom when using the t-distribution table?

Answers

The calculated value of 9.76 should be rounded to 10 for use in the table.

In a two sample test of means with unknown and unequal population variances, the degrees of freedom is calculated as 9.76. When using the t-distribution table, it is important to note that the table only lists integer values for degrees of freedom.  

Therefore, we must round the calculated degrees of freedom to the nearest integer value.

In this case, the nearest integer to 9.76 is 10. Therefore, when using the t-distribution table for this two sample test of means, we should use 10 as the degrees of freedom value.

It is important to note that rounding the degrees of freedom can have a small effect on the accuracy of the results, particularly if the calculated value is close to an integer value. However, in most cases, rounding to the nearest integer is a reasonable approximation.

In summary, when calculating degrees of freedom for a two sample test of means with unknown and unequal population variances, it is important to round to the nearest integer value when using the t-distribution table. In this case, the calculated value of 9.76 should be rounded to 10 for use in the table.

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A florist is creating 10 centerpieces. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. The customer has a budget of $370 allocated for the centerpieces and wants each centerpiece to contain 15 flowers, with twice as many roses as the number of irises and lilies combined. (Let r represent the number of roses, l represent the number of lilies, and i represent the number of irises.)

Answers

b) Solving the matrix equation, we find r = 8, l = 4, and i = 3. The florist can use 8 roses, 4 lilies, and 3 irises for each centerpiece.

How to solve

a) The system of linear equations representing the situation is:

r + l + i = 15 (total flowers in one centerpiece)

r = 2(l + i) (twice as many roses as irises and lilies combined)

10(2.50r + 4l + 2i) = 370 (total budget)'

Matrix equation: AX = B, where

A = [[1, 1, 1], [2, -1, -1], [25, 40, 20]],

X = [[r], [l], [i]], and

B = [[15], [0], [370]]

b) Solving the matrix equation, we find r = 8, l = 4, and i = 3. The florist can use 8 roses, 4 lilies, and 3 irises for each centerpiece.

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The Complete Question:

A florist is creating 10 centerpieces. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. The customer has a budget of $370 allocated for the centerpieces and wants each centerpiece to contain 15 flowers, with twice as many roses as the number of irises and lilies combined. (Let r represent the number of roses, l represent the number of lilies, and i represent the number of irises.)

a) Write a system of linear equations that represents the situation. Then write a matrix equation that corresponds to your system.

b) Find the number of flowers of each type that the florist can use to create the 10 centerpieces.

PLS HELP IMMEDIATELY!!!!!
David bought 36.504msq of material to make a curtain. The material is 1.17m wide. Find the length of the material​

Answers

The length of the rectangular shaped material is L = 31.282 m

Given data ,

The area of the material is 36.504 m², and the width of the material is 1.17 m. Let's call the length of the material "L" in meters.

We can use the formula for the area of a rectangle to relate the area and the dimensions of the material:

Area = Length x Width

Substituting the values we have, we get:

36.504 = L x 1.17

Solving for L, we get:

L = 36.504 / 1.17

L ≈ 31.282 m

Hence , the length of the material is approximately 31.282 meters

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Unit 4 checkpoint quiz

Answers

The value of segment HK is 11.

What is the value of segment HK?

The value of segment HK is calculated by applying the following formula as shown below;

Applying chord theorem;

(HY) x (YK) = (IY) x (YL)

6 (x + 4) = 6(5)

6x + 24 = 30

Solve for the value of x, as follows;

6x = 30 - 24

6x = 6

x = 6/6

x = 1

The value of length HK = 6 + (x + 4)

HK = 6 + (1 + 4)

= 11

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Find the value of k for which the constant function x(t) = k is a solution of the differential equation 312 dx — 5x – 7 = 0. dt

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A differential equation is a mathematical equation that relates a function with its derivatives. It describes the relationship between a quantity and its rate of change in continuous time or space.

To find the value of k for which the constant function x(t) = k is a solution of the given differential equation, we substitute x(t) = k into the differential equation and check if it satisfies the equation.

So, we have:

312 dx/dt - 5x - 7 = 0

Substituting x(t) = k, we get:

312 d(k)/dt - 5k - 7 = 0

Since x(t) = k is a constant function, its derivative is zero. Therefore, d(k)/dt = 0.

Substituting d(k)/dt = 0, we get:

-5k - 7 = 0

Solving for k, we get:

k = -7/5

Therefore, the value of k for which the constant function x(t) = k is a solution of the differential equation 312 dx/dt - 5x - 7 = 0 is -7/5.

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a(n) ? is a shorthand method for writing a mathematical rule.a. equal sign (=)b. equationc. formulad. math problem

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The equation is a shorthand method for writing a mathematical rule.

The answer to your question is b.equation. An equation is a shorthand method for writing a mathematical rule. It represents a relationship between two or more variables using mathematical symbols and operations. Equations are commonly used in algebra, calculus, and other areas of mathematics to solve problems and make predictions. They are written using an equal sign (=) to show that the expression on the left is equal to the expression on the right. Equations are an important tool in mathematics because they allow us to express complex ideas in a concise and precise way. By using equations, we can simplify calculations and solve problems more efficiently.
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What is the length of RS?

Answers

Answer:D. 24

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

RQ = 1 cm   (just like PQ)

tan (45+15) = QS / PQ

        sqrt (3) = QS / 1

             QS= sqrt (3)     then subtract RQ ( which is 1 cm) to find RS

                      RS = sqrt (3) - 1   cm

Find the slope of a line perpendicular to the line whose equation is x-3y=27?

Answers

First rearrange the equation for y :
y=x/3 -9
When a line is perpendicular to another line their gradients multiply to -1 . Thus , -1 divided by 1/3 = -3 . -3x is the slope of the line ( answer)

Evaluate the limit :lim h- 0 ((1/(x+h)^2)-(1/x^2))/h

Answers

The limit lim h→0 ((1/(x+h)^2)-(1/x^2))/h = -1/(x^2). To evaluate the limit lim h→0 ((1/(x+h)^2)-(1/x^2))/h, we first need to simplify the expression inside the limit.

Starting with ((1/(x+h)^2)-(1/x^2))/h, we can use the difference of squares formula to simplify the numerator:
((1/(x+h)^2)-(1/x^2))/h = ((1/(x+h)-1/x)(1/(x+h)+1/x))/h
Next, we can simplify the first factor using the common denominator (x(x+h)):
((1/(x+h)-1/x)(1/(x+h)+1/x))/h = ((x-x-h)/(x(x+h)) * 1/(x+h)+1/x)/h
Simplifying further, we get:
((x-x-h)/(x(x+h)) * 1/(x+h)+1/x)/h = (-h/(x(x+h)) * 1/(x+h)+1/x)/h
Now, we can cancel out the h's in the numerator and denominator:
(-1/(x(x+h)) * 1/(x+h)+1/x)/1 = -1/(x(x+h)) * 1/(x+h)+1/x
Taking the limit as h approaches 0, we get:
lim h→0 -1/(x(x+h)) * 1/(x+h)+1/x = -1/(x^2)
Therefore, the limit lim h→0 ((1/(x+h)^2)-(1/x^2))/h = -1/(x^2).

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