Mathematics College

The area of a trapezoid is 243 cm² the height is 18 cm and the length of one of the parallel sides is 10 cm find the length of the second parallel side

Answers

Answer 1

Given:

Area of trapezoid is, A = 243 cm².

The height of the trapezoid is, h = 18 cm.

One parallel side of the trapezoid is, a = 10 cm.

The objective is to find the second parallel side is, b.

The formula to find the area of the trapezoid is,

$A=\frac{1}{2}\times h\times(a+b)$

Now substitute the given values in the above formula to find the second parallel side b.

$\begin{gathered} 243=\frac{1}{2}\times18\times(10+b) \\ 10+b=\frac{243\times2}{18} \\ 10+b=27 \\ b=27-10 \\ b=17\text{ cm} \end{gathered}$

Hence, the length of the second parallel side is, b is 17 cm.

Related Questions

(09.01 LC)
What is the relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc
length s of the arc?

A)C=360°(s)(A)
B)C=360 degrees s over A
C)C=360 degrees(s+A)
D)C = 360°A over s

Answers

The relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc is

B) C=360 degrees s over A

How to find the relationship

The relationship between the circumference C of a circle and the degree measure A of a central angle that intercepts an arc length s of the arc can be described by the formula:

s = A / 360 * C

Make C the subject of the formula

s = AC / 360

360s = AC

rearranging

AC = 360s

C = 360 degrees s / A

C = (s / A) * 360°

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Answer:

$\textsf{B)} \quad C=\dfrac{360^{\circ}\:s}{A}$

Step-by-step explanation:

In a circle, the ratio of an arc length (s) to the circumference (C) is equal to the ratio of the measure of the arc's central angle (A) to 360°.

This is because:

The circumference (C) represents the distance around the entire circle, and so an arc (s) is a fraction of the whole circumference. In a circle, there are 360° in total, and so a central angle (A) is a fraction of 360°.

Therefore, this can be expressed as:

$\dfrac{s}{C}=\dfrac{A}{360^{\circ}}$

Cross multiply:

$360^{\circ} \cdot s=C \cdot A$

Now, divide both sides by A to isolate C:

$\dfrac{360^{\circ} \cdot s}{A}=C$

Therefore, the relationship between the circumference (C) of the circle in which the degree measure (A) of a central angle of a circle intercepts an arc length (s) of the arc is:

$\large\boxed{\boxed{C=\dfrac{360^{\circ}\:s}{A}}}$

salesperson earns $345 for selling $2300 in merchendice find the commison rate

Answers

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

solve 4n-6(n+1)>12 (first blank is the inequality sign, second blank is the value) n

Answers

The solution to the inequality expression is n < -9

How to solve the inequality expression?

The inequality expression is given as

4n - 6(n + 1) > 12

Open the bracket in the above inequality expression

4n - 6n - 6 > 12

Evaluate the like terms

-2n > 18

Divide both sides by -2

n < -9

Hence, the solution to the inequality expression is n < -9

Answers

The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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Given that, for all values of x,
2x^2 – 3x + 21 = a(x - b)^2 + c
find the value of a, the value of b and the value of c.

Answers

Step-by-step explanation:

To find a, the leading coeffiecent of the quadratic is a.

So a is 2.

To find b, we must use the formula

$ - \frac{b}{2a} $

$ \frac{ - ( - 3)}{2(2)} = \frac{3}{4} $

So b=3/4.

To find c, plug in 3/4 into the function,

which we get

$2( \frac{9}{16} ) - 3( \frac{3}{4} ) + 21$

$ \frac{9}{8} - \frac{9}{4} + 21 = \frac{9}{8} - \frac{18}{8} + 21 = - \frac{9}{8} + 21 = 19.875$

So c=19.875

Use a calculator to evaluate the expression.
log 94.4

Answers

Answer:

1.97497

Step-by-step explanation:

Using my calculator, I just put in log(94.4).

HELP ASAP! I NEED HELP RN AND I PROMISE TO GIVE YOU BRAINELIST IF YOU ANSWER THIS

Answers

Answer:

B. (-4, 4)

Step-by-step explanation:

The triangle is being translated 2 units left and 3 units up. This means that you subtract 2 from the x-coordinate of every point on the triangle, and add 3 to every y-coordinate. If you were translating it right, you’d add to the x-coordinate, and down would be subtracting from the y-coordinate. Basically, you’re moving the triangle, meaning every point goes along with it.

On the graph, point A has the coordinates (-2, 1). If you subtract 2 from -2, you get -4. Then, if you add 3 to 1, you get 4. Therefore, the answer is (-4, 4), or B.

Hope this helps! Sorry, I don’t know what Brainlist is, so don’t worry about giving me anything :D

Allen was making trail mix, but he only wanted to make of the recipe. If the whole recipe called for of a cup of peanuts, how many cups will he need to make of the recipe? Choose the model that matches the situation.

Answers

It can be inferred that the amount of nuts that Allen requires depends on the amount of the recipe that he wants to make.

How many cups of nuts does Allen require to make the recipe?

According to the information provided, one serving of the recipe calls for one cup of nuts. According to this, it can be inferred that to make a smaller or larger portion of the recipe, this amount must be divided or multiplied.

For example, if Allen calls for making two servings of the recipe, he would use two cups of nuts, while if he calls for making a half serving, he would use half a cup of nuts.

Note: The question is missing because there is some missing information. However I can answer it based on my general prior knowledge.

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Answer:

1/6

Step-by-step explanation:

Find and prove an inequality relating 100n and n^{3} .

Answers

An inequality relating 100n and n³ is 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.

What is inequality?

An inequality is comparison of two values, showing if one is less than, greater than, or simply not equal to another value.

Since 100n and n³ for n = 1, 2, 3, . . . 9, 10, 11 are 100, 200, 300, . . . 900, 1000, 1100 and 1, 8, 27, . . . 729, 1000, 1331 respectively.

Therefore, an inequality relating 100n and n³ will be 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.

Induction hypothesis:

Suppose 100n ≤ k³ for some positive integer k ≥ 10.

We need to show that 100( k + 1 ) ≤ ( k + 1 )³ = k³ + 3k² +3k + 1.

Note 100( k + 1 ) = 100k + 100 ≤ k³ + 100

≤ k³ + 3k² (∵ k ≥ 10 )

≤ k³ + 3k² + 3k

≤ k³ + 3k²+3k + 1

So 100( k + 1 ) ≤ ( k + 1 )³, which is true.

Hence by the principle of mathematical induction, 100n ≤ k³ for every integer k ≥ 10.

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A fair 6-sided die is rolled 480 times. What is a reasonable prediction for the number of times the event of landing on an odd number will occur?

160
240
320
500

Answers

The probable number of odd outcomes possible in 480 rolls is 240

The number of odd values on a six-sided die :

Odd values = (1, 3, 5) = 3

The probability of obtaining an odd outcome on a single roll :

favorable outcome/total possible outcomes

P(odd) = 3/6 = 1/2.

Expected value :

Number of rolls * probability per roll

Expected value = 480 * 1/2 = 240

Therefore, the probable number of odd outcomes would be 240

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For which intervals the graphs of the functions f(x) = x^3 + x^2 - 4x - 4 is positive

Answers

Step-by-step explanation:

Consider a function

(

)

which is twice differentiable. The graph of such a function will be concave upwards in the intervals where the second derivative is positive and the graph will be concave downwards in the intervals where the second derivative is negative. To find these intervals we need to find the inflection points i.e. the x-values where the second derivative is 0.

Noah is going to see a movie and is taking his 2 kids. Each movie ticket costs $14 and there are an assortment of snacks available to purchase for $3 each. How much total money would Noah have to pay for his family if he were to buy 4 snacks for everybody to share? How much would Noah have to pay if he bought x snacks for everybody to share?

Cost for 4 snacks:
Cost for x snacks:

TwT

Answers

Answer: Cost for 4 snacks : 42 + 3(4) = 54

Cost for X snacks : 42 + 3x

f (x) = (2x −10)³
What is f (8)?

Answers

Answer:

f(8) = 216

Step-by-step explanation:

f(x) = (2x −10)³

f(8) = (2(8) −10)³

= (16 - 10) ^3

= 6^3

= 216

f(8) = 216

The value of the equation f ( 8 ) when f ( x ) = ( 2x - 10 )³ is f ( 8 ) = 216

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

f ( x ) = ( 2x - 10 )³

To calculate the value of f ( 8 ) , substitute the value of x as x = 8 in the equation , we get

f ( x ) = ( 2x - 10 )³

On simplifying the equation , we get

f ( x ) = ( 2x )³ - ( 10 )³ - 3 ( 2x )²( 10 ) + 3 ( 2x ) ( 10 )²

So , the equation is

f ( x ) = 8x³ - 1000 - 120x² + 600x

So , the equation is

f ( x ) = 8x³ - 120x² + 600x - 1000

Now , substituting x = 8 ,

f ( 8 ) = 8 ( 8 )³ - 120 ( 8 )² + 600 ( 8 ) - 1000

f ( 8 ) = 4096 - 7680 + 4800 - 1000

On simplifying the equation , we get

f ( 8 ) = 216

Therefore , the value of f ( 8 ) = 216

Hence ,

The value of the equation f ( 8 ) when f ( x ) = ( 2x - 10 )³ is f ( 8 ) = 216

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plz help.............

Answers

Answer: triangles are similar.

Step-by-step explanation:

Givn : OK = 3, OJ = 30, KN = 1, JM = 3#

Angle O is common in both the triangles.

Two sides are in same proportion and the included angle is common (SAS) . Hence both the triangles are similar.

That means

That means the three angles of triangle OKJ are equal to the corresponding three angles of triangle ONM.

Hence the to triangles are similar.

PLEASE HELP I’M IN MIDDLE SCHOOL AND I CANT FIND THE ANSWERS. ITS ALSO DUE IN A FEW HOURS.

Answers

To form a triangle the three angles must follow the inequality principle that says: The sum of any two sides must always be greater than the length of the third side. With this in mind let's check the angles.

For the first item we have:

$\begin{gathered} 70+90>20\rightarrow160>20 \\ 70+20>90\rightarrow90>90 \\ 20+90>70\rightarrow110>90 \end{gathered}$

Since the second inequality is invalid the angles don't form a triangle.

For the second item we have:

$\begin{gathered} 55+45>75\rightarrow100>75 \\ 55+75>45\rightarrow130>45 \\ 45+75>55\rightarrow120>55 \end{gathered}$

Since all the inequations are valid then the angles form a triangle. Since all the angles are smaller than 90 degrees, then this is an acute triangle.

For the third item we have:

$\begin{gathered} 27+27>126\rightarrow54>126 \\ 27+126>27\rightarrow153>27 \end{gathered}$

Since the second inequation is invalid, then the angles don't form a triangle.

For the fourth item we have:

$\begin{gathered} 38+87>55\rightarrow125>55 \\ 38+55>87\rightarrow93>87 \\ 55+87>38\rightarrow142>38 \end{gathered}$

Since all the inequalities are valid, then the angles form a triangle. All of its angles are smaller than 90 degrees, therefore this triangle is an acute triangle.

convert 1200 second to hours (with calculation)

Answers

1200 seconds divided by 3600=

0.33333333 of an hour or a third of an hour.

Or just 20 minutes lol

Determine if the product CA is defined. If the product is defined, state its dimensions. Do not calculate the product.

Answers

Answer:

The product can be calculated.

The resulting matrix will have 3 rows and 3 columns.

Step-by-step explanation:

Matrix multiplication

To find the product of two matrices is only possible when the number of columns of the first matrix is equal to the number of rows of the second matrix.

If X is the first matrix with dimensions (n x m) and Y is the second matrix with dimensions (m x p), the product XY is possible and the dimensions of the resulting matrix are (n x p).

Matrix A has two rows and three columns (2x3)

Matric C has three rows and two columns (3x2)

If we wanted to calculate the product CA, the number of columns of C must be equal to the number of rows of A.

Since both numbers are 2, the product can be calculated.

The resulting matrix will have 3 rows and 3 columns.

find the value of x in this parellogram

Answers

Answer:

Step-by-step explanation:

4x-15=x-3 subtract x from both sides

3x-15=-3 add 15 to both sides

3x=12 divide both sides by 3

x=4

Create a scale drawing of the Colombian flag with a scale of 2 cm to 1 ft

Answers

Step 1: Draw a square with sides of 8 cm.

Draw a diagonal line across the square and then two 45° lines from each corner to the opposite corner. Connect these four points with a line.

There are many correct ways to draw this flag - you can use any method you like, as long as it gets all the elements in the right place.

75 % of the students are boys . There are 24 boys . What is the total number of Students
PLEASE HELLPPPPPO

Answers

Answer:

32 students

Step-by-step explanation:

24 divided by .75 is 32

Based on the information given, there'll be 32 students.

Let the total number of students be represented by x.

From the information, it was stated that 75% of the students are boys and that there are 24 boys. Therefore, the total number of students will be:

75% × x = 24

0.75x = 24

x = 24/0.75

x = 32

There are 32 students.

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Factor.
8xy - 54x^2 how to solve this

Answers

Factor 8xy is 128392

PLEASE HELP! For a concert 5,000 tickets were sold, and the proceeds were $72,000. Tickets for children 16 and younger were $10, adults were $20, and seniors 60 and older were $15. There were 3 times more children than seniors at the concert. What system of equations represents the number of children, c, adults, a, and seniors, s, that attended the concert?

Answers

A: the first answer is the best option

if there is a total of 5000 tickets, and we know there were adults, children, and seniors, then the equation:
c + a + s = 5000 is correct

if we are using c, a, and s as variables for how many children, adults, and seniors were in attendance, then by matching the corresponding price, we should have the equation:
$72000= 10c + 20a + 15s

lastly, if we know the amnt of children in attendance was 3x more than the amnt of seniors, the equation:
3s = c is best because by multiplying the number of seniors in attendance by 3, you will get 3x more children than seniors

hope this helps, and is correct :)!

simplify each algrebraic expression. drag tiles to correct boxes to complete the pairs.
-5x-2 5x+2 5x-2 -5x+2

Answers

(a) The algebraic expression, -5x - 2 + 5x + 2 is simplified as 0.

(b) The algebraic expression, 5x -2 - (5x + 2) is simplified as -4.

What is the simplification of the algebraic expression?

The given algebraic expression is simplified by adding similar terms together, as it will make the expression to be in simplest form.

The given algebraic expressions are;

-5x - 2 + 5x + 2

5x -2 - (5x + 2)

The first algebraic expression is simplified as follows;

-5x - 2 + 5x + 2

collect similar terms;

(-5x + 5x) + (-2 + 2)

= 0 + 0

= 0

The second algebraic expression is simplified as follows;

5x - 2 - (5x + 2)

= 5x - 2 - 5x - 2

collect similar terms;

= (5x - 5x) + (-2 - 2)

= 0 - 4

= - 4

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PLEASE HELPP!!!!!
If the sample follows a normal distribution, does this make sense? Why?

Answers

It is possible for a sample to follow a normal distribution, depending on the nature of the data being accumulated.

The regular distribution is a bell-shaped curve that is symmetric across the mean, and it's far typically used to model various natural phenomena and measurements in fields such as information, engineering, and social sciences.

If the data being gathered is continuous and the sample length is large sufficient, it is regularly assumed that the pattern follows a normal distribution.

This assumption is based at the critical limit Theorem, which states that the sampling distribution of the suggest of any independent, random variable will tend toward a ordinary distribution because the sample size increases.

But, it's far critical to notice that not all samples will observe a ordinary distribution, and in a few cases, different distributions may be greater suitable for the records being amassed.

It's far consequently essential to analyze the information and evaluate the assumptions being made before using the regular distribution as a model.

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What is the quotient of 7,966 divided by 569? Please tell me bc im in school and idk the answer :(

Answers

Answer:

Step-by-step explanation:

divide them by 7966 and 569

is 7 a solution to 21-w<14?
(please answer asap!)

Answers

Answer:

Step-by-step explanation:

well, is 21-7 < 14?

PLEASE HELP WITH GEOMETRY

Answers

Step-by-step explanation:

If 76° gives 7.5 meters, we must find out how many meters it is for 360°.

Find how much for 1°: $\frac{7.5}{76}$

For 360°: $\frac{7.5}{76} \times 360$ = 35.53 meters

Jillian is thinking of the smallest
number that is a multiple of 12 and
has 9 and 8 as factors. What
number is she thinking of?

Answers

Answer:

$72$

Step-by-step explanation:

$lcm[12, 9, 8] = 72$

For more information, research LCM (Least Common Multiple). PLZ Mark as Brainliest! :)

The smallest number that is a multiple of 12 and has 9 and 8 as factors is 72.

Explanation: 12x6=72 and 9x8=72

which equation represents a linear function?

Answers

Answer:

Equation 3

Step-by-step explanation:

Answer:Equation 3

linear functions dont have exponents

Step-by-step explanation:

During the 2008 - 2009 financial crisis, the GDP of the USA reduced from $14.72 trillion in 2008 to $14.42 trillion in 2009. What is the percentage change between these two years? around your answer to the nearest hundredth of a percent.

Answers

The percentage change in GDP is 2.04%

Percentage Change

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

The formula of percentage change is given as

Percentage change =[ (New increase - old value) / old value] * 100

Percentage change = [(14.72 - 14.42) / 14.72] * 100

Percentage change = 2.04%

In this case, there is a percentage decrease of 2.04%

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Other Questions

Explain the difference between a CNA, an RN, and an LPN. Which was a positive consequence from WWI?A. The 19th AmendmentB. The Espionage & Sedition ActsC. German Americans' experiencesD. Trench warfare 3) There are 24 applicants for three jobs: computer programmer, software tester, and manager. How many ways can this be done? How long will it take if you travel at 4 m/s for 100m?10 s20 sO04s25 s In what ways does the Dawes Act seem to remedy the problems? 10. Which of the following statements is (are) correct? (x) An orderly marketing agreement is a market-sharing pact negotiated by trading partners to moderate the intensity of international competitio Trata de identificar la idea principal de los siguientes prrafos. Subryala usando un lpiz de color. Ayer a las nueve de la noche se realiz un robo en el principal banco de la ciudad. Al parecer, los ladrones entraron abriendo un hueco por una de las ventanas del edificio mientras el vigilante descansaba. Algunos vecinos aseguran haber escuchado ruidos extraos y visto luces dentro del banco, sin embargo, ninguno alert a la polica. An no se sabe con exactitud cunto dinero fue robado del banco. will the product of 6 x 4/7 be greater than, equal to,or less than 6 what is the sequence of objects in a solar eclipse What are the pure substances that make up all kinds of matter and are made up of atoms. since 1980 the difference between the earnings of college graduates and high school graduates has: What else would need to be congruent to show that ABC=DEF by AAS? The diameter of a circle is 8 m.find the circumference to the nearest tenth Why might several authors have used "Shakespeare" as a pseudonym? A)(to protect their identity) A hot air balloon company charges for evening sunset flights are based on the function y=25x +100, where x is the number of people traveling in the basket (note the baskey capacity limit is 8) and y is the cost of the trip in dollar. What is the base fee for the balloon ride before passengers are figured in? What does the 25 represent? What is the cost for 5 people to fly? 11 of 14A train leaves at 14.54 and arrives at its destination at 15.47.If the train travelled 66 km, what was it's average speed in km/h?Give your answer rounded to 1 dp.km/h A piano teacher charges students $20. 25 each month, plus $5. 25 per hour for lessons. Which expression and value represent the total the instructor will charge a student for x hours of lessons in a month and the amount the instructor would charge a student for 15 hours of lessons in a month? $20. 25 x; $15 $20. 25 x; $25. 50 $20. 25 $5. 25x; $58. 50 $20. 25 $5. 25x; $99. By studying the suffix, the reader can determine that impetuous most likely means having the quality of acting impulsive or with emotion. someone who is filled with impulsiveness and emotion. someone who acts without impulsiveness or emotion. having a state or condition that is impulsive or emotional. What does a novel often have more of than a short story? (5 points) A. 3(x + 2) = 18B. X + 2 = 18

The area of a trapezoid is 243 cm² the height is 18 cm and the length of one of the parallel sides is 10 cm find the length of the second parallel side￼

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The area of a trapezoid is 243 cm² the height is 18 cm and the length of one of the parallel sides is 10 cm find the length of the second parallel side