Before proving that a shape is a rectangle or a rhombus, you must first prove that it is a parallelogram by showing that its opposite sides are parallel and then use specific properties to prove its rectangle or rhombus nature.
Before proving that a given shape is a rectangle or a rhombus, you must first prove that it is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel to each other. To prove that a shape is a parallelogram, you can show that its opposite sides are parallel by using the slope formula or by showing that the opposite sides have the same length and are parallel to each other.
Once you have established that a shape is a parallelogram, you can then proceed to prove whether it is also a rectangle or a rhombus. To prove that a shape is a rectangle, you must show that it is a parallelogram with four right angles. To prove that a shape is a rhombus, you must show that it is a parallelogram with four sides of equal length.
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To prove that a quadrilateral is a rectangle or a rhombus, you must first establish some key properties. For a rectangle, you need to prove that it has four right angles and opposite sides are parallel. For a rhombus, you must demonstrate that all four sides are of equal length and opposite sides are parallel.
Before proving that something is a rectangle or a rhombus, you must first prove that it is a parallelogram. This means showing that opposite sides are parallel and congruent in length. Once this is established, you can then prove additional properties to determine whether the shape is a rectangle (where all angles are 90 degrees) or a rhombus (where all sides are congruent).
To prove that a quadrilateral is a rectangle or a rhombus, you must first establish some key properties. For a rectangle, you need to prove that it has four right angles and opposite sides are parallel. For a rhombus, you must demonstrate that all four sides are of equal length and that opposite sides are parallel. Once these properties are verified, you can confidently classify the shape as a rectangle or a rhombus.
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what do parallel and perpendicular cross sections of a sphere look like?
Parallel cross sections of a sphere look like circles with the same radius as the sphere, while perpendicular cross sections look like points. Cross sections taken at other angles will be ellipses.
What you understand by sphere?A sphere is a three-dimensional geometric shape that is perfectly round in shape, like a ball. It is defined as the set of all points in three-dimensional space that are at a constant distance (the radius) from a given point called the center.
If we take a cross section of a sphere, the resulting shape will depend on the angle at which the section is taken relative to the center of the sphere.
If we take a plane that is parallel to the base of the sphere, the cross section will be a circle with the same radius as the sphere. This is because the intersection of the plane with the sphere will be a circle, and since the plane is parallel to the base of the sphere, the circle will have the same radius as the sphere.
On the other hand, if we take a plane that is perpendicular to the base of the sphere, the cross section will be a point. This is because the plane will intersect the sphere at only one point, which is the point at which the plane is perpendicular to the sphere.
If we take a plane that is neither parallel nor perpendicular to the base of the sphere, the resulting cross section will be an ellipse. The size and shape of the ellipse will depend on the angle at which the plane intersects the sphere.
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What is 10/9 minus negative 1 1/3 equal?
hi
10/9 - 11/3 = 10/9 - 33/9 = -23/9
Answer:
-23/9
Step-by-step explanation:
You would need to find a common denominator which would be 9.
The next step would be to combine the top 10-11 (times)3 over 9
Then you multiply -11 by 3 tp get 10 -33 /9
The last and final step would be tp subract 33 from 10 to get 33 -10
Which will led you to your final awnser which is -23/9
In Apextown there are 320,000 29-year-olds. Based on the table below, how many are not expected to be alive in a year? • A. 422 • B. 419 • C. 315 • D. 485
The number of 29 year olds who are not expected to be alive in a year would be A. 422 people.
What does the table show about Apextown ?We see that in Apextown, the percentage of people who are expected to be alive in a year, based on their ages, is given.
For those who are 29 years of age, we see that the percentage of people who are expected to be alive in a year would be 99. 868 %. This means that the number of 29 year olds who would not be alive would be:
= Number of 29 years x ( 1 - percentage to be alive)
= 320, 000 x ( 1 - 99. 868 % )
= 320, 000 x 0. 00132
= 422. 4
= 422 people
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Please help me I cannot do this (BUT it might be easy for u if ur an expert) B]
Answer:
a
Step-by-step explanation:
Answer:
The answer is B) -35.16 grams per half-life cycle
Jazmin and Justine went shopping for back to chool clothes. Jazmin purchasrd three shirts and one pair of shorts ans spent $38. 0. Justine bought four shirts and three pairs of shorts and spent $71. 50.
Part A: Assumibg all the shirts cost the same amount and all the shorts cost the same amount, write a system os equations to represent each girl's shoppins spree
Part B: Use the elimination method to solve for the price of one pair of shorts
The equations to represent each girl's shoppins spree is 3x + y = 38.0 and 4x + 3y = 71.50. Price of one shirt costs $8.50 and price of one pair of shorts costs $12.50.
Let x be the price of one shirt, and y be the price of one pair of shorts. Then, we can write the following system of equations
For Jazmin
3x + y = 38.0
For Justine
4x + 3y = 71.50
To solve for the price of one pair of shorts using elimination method, we need to eliminate one of the variables. We can do this by multiplying the first equation by 3 and the second equation by -1, and then adding them together
9x + 3y = 114.0
-4x - 3y = -71.50
5x = 42.50
x = 8.50
So, one shirt costs $8.50.
To find the price of one pair of shorts, we can substitute the value of x into either of the original equations and solve for y. Using the first equation
3(8.50) + y = 38.0
25.50 + y = 38.0
y = 12.50
Therefore, one pair of shorts costs $12.50.
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what is 493 square rooted
Read the screenshot please answer this ASAP!!!!!!!! PLEASEEEEE
According to the information, the surface area of the prism is approximately 777.868 square inches, and its volume is approximately 3156.846 cubic inches.
How to calculate the surface area and volume of this prism?Since the hexagonal bases are regular, we know that all the six triangles are congruent to each other.
Let's call the side length of the hexagon s. Then, the apothem of each triangular face is given as 9 inches, and the base of each triangular face is given as 10 inches. Using the Pythagorean theorem, we can calculate the side length of the hexagon as follows:
s^2 = (10/2)^2 + 9^2
s^2 = 25 + 81
s^2 = 106
s ≈ 10.2956 inches
The surface area of the prism can be calculated by adding up the areas of its faces. The hexagonal base has an area of:
A_base = (3√3/2) * s^2 ≈ 450.978 square inches
The area of each triangular face is:
A_tri = (1/2) * base * height = (1/2) * 10 * 9 = 45 square inches
So the total surface area of the prism is:
A_total = 2A_base + 6A_tri
A_total = 2(450.978) + 6(45)
A_total ≈ 777.868 square inches
The volume of the prism can be calculated by multiplying the area of the base by the height of the prism:
V = A_base * height
V = 450.978 * 7
V ≈ 3156.846 cubic inches
Therefore, the surface area of the prism is approximately 777.868 square inches, and its volume is approximately 3156.846 cubic inches.
Note: This question is incomplete. Here is the complete information:
Calculate the surface area and volume of this prism.
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see the scatter plot of Wins compared to Free Throw Attempts per Game.
Then use the scatterplot to write your line of best fit and determine the correlation.
I'm confused what's being asked here...but if you're looking for someone to check it then:
The line of best fit is drawn correctly; there are about the same amount of dots on the top and bottom of the line.
And the correlation is positive
USE A MODEL In a mathematics exam with a maximum score of 100, Machelle loses less than 27 points. The table shows the grade that matches the exam score. Compare points to grades and identify which grade Machelle can get.
Machelle can get a grade of D or higher on her exam.
Describe Inequality?In mathematics, an inequality is a mathematical statement that describes a relationship between two quantities that are not necessarily equal. An inequality can express that one quantity is less than, less than or equal to, greater than, greater than or equal to, or not equal to another quantity.
Inequalities can be represented using various symbols. For example, the symbol < represents "less than," the symbol > represents "greater than," the symbol ≤ represents "less than or equal to," and the symbol ≥ represents "greater than or equal to." The symbol ≠ represents "not equal to."
Inequalities are also used in algebra to solve equations and to represent the solution set of an equation. In this context, an inequality can represent all the possible values of a variable that satisfy the equation. For example, the inequality x > 5 represents all the values of x that make the expression x - 5 positive.
We can write an inequality to represent the number of points, m, obtained by Machelle on her exam:
m > 100 - 27
Simplifying this expression, we get:
m > 73
This means that Machelle must have scored more than 73 points on her exam. Based on the table, we can see that a score of more than 73 points corresponds to a grade of at least a D. Therefore, Machelle can get a grade of D or higher on her exam.
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The complete question is:
Area use a 7. 2 pans of blue pink and white paint to paint her bedroom walls 1/4 of this month is blue pants and the rest is wipe it how many pensive white paint did you use to paint her bedroom walls
If 1/4 of this amount is blue paint, and the rest is white paint, Area used 5.4 pints of white paint to paint her bedroom walls.
Given that Area used a total of 7.2 pints of blue and white paint to paint her bedroom walls. And 1/4 of the amount is blue paint, then the remaining 3/4 of the amount must be white paint.
To find the amount of white paint used, we can use the following formula:
Amount of white paint = Total amount of paint - Amount of blue paint
Since we know that the total amount of paint used is 7.2 pints and 1/4 of that amount is blue paint, we can calculate the amount of blue paint as:
Amount of blue paint = (1/4) x 7.2 = 1.8 pints
Now we can substitute these values in the formula to find the amount of white paint used:
Amount of white paint = 7.2 - 1.8 = 5.4 pints
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What is the area of the shaded region in the figure below? (7.G.6)
Answer:
The area of the shaded region is 21 square units.
7 × 3 = 21 square units
a bridge crosses a river that is 1,400 feet wide. one bank of the river holds of the bridge while the other holds of the bridge. how long is the bridge?
The length of the bridge is 980 feet.
What is the length of a bridge crossing a 1,400 feet wide river if one bank holds 3/7 of the bridge and the other bank holds 4/7 of the bridge?Let's denote the length of the bridge as x. According to the problem, one bank of the river holds 3/7 of the bridge, which means that the other bank holds 4/7 of the bridge.
Therefore, we can write the following equation:
3/7 x + 1400 + 4/7 x = x
Simplifying this equation, we get:
6/7 x + 1400 = x
Subtracting 6/7 x from both sides, we get:
1/7 x + 1400 = 0
Subtracting 1400 from both sides, we get:
1/7 x = -1400
Multiplying both sides by 7, we get:
x = -9800
Since the length of the bridge cannot be negative, we need to discard this solution. Therefore, the only valid solution is:
x = 980
So the length of the bridge is 980 feet.
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what value of c is such that 99% of all parcels are at least 1 lb under the surcharge weight? (round your answer to four decimal places.)
the value of c is 11.165 lbs. This was calculated using the z-score formula, assuming a normal distribution with a mean weight of 10 lbs and a standard deviation of 0.5 lbs. This ensures that 99% of all parcels are at least 1 lb under the surcharge weight.
To find the value of c, we need to use the standard normal distribution and the z-score formula. Since we know that 99% of all parcels are at least 1 lb under the surcharge weight, we can use the z-score associated with the 99th percentile, which is 2.33 (from a z-score table).
The formula for the z-score is:
z = (x - μ) / σ
where x is the weight of the parcel, μ is the mean weight, and σ is the standard deviation.
In this case, we want to find the weight of the parcel that is at the 99th percentile, which is 1 lb under the surcharge weight. Let's call this weight x. We know that the surcharge weight is c, so the weight of the parcel that is 1 lb under the surcharge weight is (c - 1).
Using the z-score formula and substituting the values we know, we get:
2.33 = ((c - 1) - μ) / σ
We want to solve for c, so we need to rearrange the equation:
c - 1 = 2.33σ + μ
c = 2.33σ + μ + 1
We don't know the values of μ and σ, but we can use the fact that the distribution is normal to estimate them. We can assume that the distribution is centered at the mean weight of all parcels, and that the standard deviation is equal to the average difference between the weight of each parcel and the mean weight.
Let's say that the mean weight is 10 lbs, and the standard deviation is 0.5 lbs. Then, we can plug these values into the equation for c:
c = 2.33(0.5) + 10 + 1
c = 11.165
So, the value of c that ensures that 99% of all parcels are at least 1 lb under the surcharge weight is approximately 11.165 lbs.
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The interior angles formed by the sides of a regular octagon have measures that total 1080. What is the measure of each angel
Step-by-step explanation:
Welll.... there are EIGHT of them that total 1080
1080 / 8 = 135 degrees each
if we know that t.05= 1.812 when df = 10, then it is correct to say
Knowing that t.05 = 1.812 when df = 10 helps us to determine the critical value of t for hypothesis testing in this scenario.
If we know that t.05 = 1.812 when df = 10, then it is correct to say that the critical value of t at the 5% significance level for a two-tailed test with 10 degrees of freedom is 1.812.
The t-distribution is a family of probability distributions that depend on the sample size and the degrees of freedom (df). The degrees of freedom represent the number of independent observations available to estimate the population parameters. In this case, when df = 10, the t-distribution has thicker tails compared to the standard normal distribution.
The value t.05 represents the critical value of t at the 5% significance level (or alpha level) in a two-tailed test. This means that if the calculated t-value falls outside the range of -t.05 to +t.05, then the null hypothesis can be rejected.
Therefore, knowing that t.05 = 1.812 when df = 10 helps us to determine the critical value of t for hypothesis testing in this scenario.
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This means that for a t-distribution with 10 df, 95% of the data lies within ±1.812 standard deviations from the mean.
If we know that t.05= 1.812 when df = 10,
then it is correct to say that the probability of obtaining a t-value greater than
1.812 or less than -1.812 is 0.05,
assuming a two-tailed test and a significance level of 0.05.
This means that if we calculate the t-value for a sample with 10 degrees of freedom and the calculated t-value falls
outside the range of -1.812 to 1.812,
we can reject the null hypothesis at the 0.05 significance level.
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Solve the inequality for the variable: 2(3c + 15) + 4c > 100
Answer:
c > 7
Step-by-step explanation:
Now we have to,
→ Find the required value of c.
The equation is,
→ 2(3c + 15) + 4c > 100
Then the value of c will be,
→ 2(3c + 15) + 4c > 100
Applying Distributive property:
→ 2(3c) + 2(15) + 4c > 100
→ 6c + 30 + 4c > 100
Combining the like terms:
→ 10c + 30 > 100
→ 10c > 100 - 30
→ 10c > 70
Dividing the value 70 with 10:
→ c > 70 ÷ 10
→ [ c > 7 ]
Hence, the answer is c > 7.
Hello !
Answer:
[tex]\boxed{\sf c > 7 \ \ \ ||\ \ \ \sf (7,+\infty)}[/tex]
Step-by-step explanation:
We are looking for the values of c that satisfy the following inequality :
[tex]\sf 2(3c + 15) + 4c > 100[/tex]
Let's expand the left side of the inequality.
[tex]\sf 2\times 3c +2\times 15+4c > 100\\6c+30+4c > 100[/tex]
Now we will combine like terms :
[tex]\sf 10c+30 > 100[/tex]
Let's substract 30 from both sides of the inequality.
[tex]\sf 10c+30-30 > 100-30\\10c > 70[/tex]
Finally, let's divide both sides by 10.
10>0 so the inequality remains the same.
[tex]\sf\frac{10c}{10} > \frac{70}{10} \\\boxed{\sf c > 7}[/tex]
Have a nice day ;)
if a cube numbered 1 to 6 is tossed 300 times, about how many times would you predict the cube to land on a number greater than 4?
Answer: 100 times
Step-by-step explanation:
The cube is numbered 1 to 6. That is, 1, 2, 3, 4, 5, 6. That means there are 6 possible outcomes for each toss. But there are 2 outcomes we want, 5 and 6 (greater than 4).
So, for each toss, there is a probability of 2/6 = 1/3 that this will occur.
With 300 tosses, we can say that this will probably happen 300 times. This means that it will happen
1/3 * 300 times = 100 times.
Therefore, we can predict we will get a 5 or 6 about 100 times.
Use #18 to then find how much it costs to paint the room if the paint costs 8$ a gallon and each gallon covers 300 ft of wall
The cost to paint the room with two coats of paint is $48, using paint that costs $8 per gallon and covers 300 square feet per gallon.
To determine how much it costs to paint the room if the paint costs $8 a gallon and each gallon covers 300 square feet of wall, we first need to determine how many gallons of paint we need. From problem #18, we know that the room has a total wall area of 800 square feet, and we need to apply two coats of paint.
The total wall area that needs to be covered by paint is:
800 square feet x 2 coats = 1600 square feet
To determine how many gallons of paint we need, we divide the total square footage by the coverage of one gallon of paint:
1600 square feet ÷ 300 square feet/gallon = 5.33 gallons (rounded up to the nearest gallon)
Therefore, we need 6 gallons of paint to complete the job (since we can't purchase a fractional amount of a gallon).
The cost of the paint can now be calculated by multiplying the number of gallons of paint by the cost per gallon
6 gallons x $8/gallon = $48
So it would cost $48 to paint the room.
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Creating an Exponential Model
In this activity, you will formulate and solve an exponential equation that models a real-world situation.
Emma doesn't have experience using credit cards. In fact, she just got her first one. She is also about to start her first year
of college. She uses her new credit card to purchase textbooks for her classes. The total comes to $300. These are the
terms of her credit card:
• It has a 15% annual interest rate.
• The interest is compounded monthly
• The card has $0 minimum payments for the first four years it is active.
The expression that models this situation is P(1 + r/n)^nt, where (1 + r/n) represents the growth factor of the interest rate. Emma also wonders how long it will take her balance of $300 to reach $450
It will take Emma about 4.04 years for her balance to reach $450, assuming she doesn't make any payments and the interest rate remains constant.
The formula that models this situation is P(1 + r/n)ⁿˣ, where P is the principal (the initial amount borrowed or invested), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time (in years) that the money is invested or borrowed.
In this case, the principal is $300, the annual interest rate is 15%, the interest is compounded monthly (so n = 12), and we want to find the time it takes for the balance to reach $450.
P = 300(1 + 0.15/12)¹²ˣ
To find out how long it will take for Emma's balance to reach $450, we need to solve for t in the equation above. We can do this by using logarithms to isolate the variable t:
=> log(1.5) = 12t x log(1 + 0.15/12),
we can use the properties of logarithms. Specifically, we can use the property that log(a x b) = log(a) + log(b) to separate the logarithm on the right side of the equation:
log(1.5) = 12t x log(1 + 0.15/12)
log(1.5) = log[(1 + 0.15/12)¹²ˣ] (using log(a x b) = log(a) + log(b))
Now we have two logarithms that are equal to each other. Therefore, we can take the exponential of both sides to eliminate the logarithms:
1.5 = (1 + 0.15/12)¹²ˣ
Simplifying this expression further, we get:
1.5 = (1.0125)¹²ˣ]
log(1.5) = log[(1.0125)¹²ˣ]]
log(1.5) = 12t x log(1.0125)
Finally, we can solve for t by dividing both sides by 12 x log(1.0125):
log(1.5) / [12 x log(1.0125)] = t
t ≈ 4.04
Therefore, the simplified expression is t ≈ 4.04.
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19PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST ALL FAKE ANSWERS WILL BE REPORTED AND PLS PLS PLS EXPLAIN THE ANSWER OR HOW U GOT IT PLEASE AND TY
Using trigonometric functions, we can find the value of the missing sides as follows:
AC = 15.48units.
AB = 9units.
Define trigonometric functions?The right triangle's angle serves as the domain input value for the six fundamental trigonometric operations, which return a range of numbers as their output. The angle, expressed in degrees or radians, is the domain of the trigonometric function of f(x) = sin, also referred to as the "trig function," and its range is [-1, 1]. In terms of their domain and scope, the other functions are comparable. Algebra, geometry, and calculus all make extensive use of trigonometric functions.
Here in the question,
As per the trigonometric function:
Sin30° = opposite side/hypotenuse
⇒ 1/2 = AB/18
Cross multiplying:
⇒ AB = 18/2
⇒ AB = 9units.
Now,
Cos30° = adjacent side/hypotenuse
⇒ 0.86 = AC/18
Cross multiplying:
⇒ AC = 15.48units.
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9 divided 7/3
sdfghjkl;lkjhgfdsaedrtyujiuhgfd
The result of 9 divided by 7/3 is 12 3/7.
What is the result of 9 divided by 7/3?When dividing by a fraction, it's the same as multiplying by its reciprocal. Therefore, to divide 9 by 7/3, we can multiply 9 by 3/7. This gives us (9 x 3) / 7 = 27/7.
However, this fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 3.
Thus, 27/7 can be simplified to 9 and 6/7, or 12 and 3/7 when expressed as a mixed number. Therefore, the answer to 9 divided by 7/3 is 12 and 3/7.
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A cone has a radius of 6 m and a height of 24 m. What is the volume of the cone in terms of π? 864π m3 432π m3 288π m3 144π m3
The volume of the cone in terms of π is 288π cubic meters, which corresponds to option (c) in the given answer choices.
The formula for the volume of a cone is:
V = (1/3)πr^2h
where V is the volume, r is the radius, and h is the height of the cone.
Plugging in the given values, we get:
V = (1/3)π(6 m)^2(24 m)
V = 288π m^3
Therefore, correct option is C.
This is because π is an irrational number that cannot be expressed as a finite decimal or fraction, so any approximation would be less precise than the exact value in terms of π.
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please give a step by step ASAP
The correct option is the fourth one, the slope and y-intercept are different.
Which statement is correct?Here we have the linear equation:
3x - 5y = 4
We know that it is dilated by a scale factor of 5/3, so let's find the dilation.
We can rewrite the linear equation as:
-5y = 4 - 3x
y = (3/5)x - 4/5
Now let's apply the dilation:
y = (5/3)*[ (3/5)x - 4/5]
y = x - 4/3
Then we can see that the slope and the y-intercept are different, the correct option is 4.
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The diameter of a circle is 18 inches. What is the area of a sector bounded by a 30° arc?
Answer: [tex]6.75\pi[/tex] inches^2
Step-by-step explanation:
If the diameter is 18 inches, the radius must be 18/2 = 9 inches.
Thus, we can calculate the area using the area of a circle = [tex]\pi r^{2}[/tex].
Plugging in the values, we get the area = [tex]81\pi[/tex] inches^2.
Since 30 degrees is 1/12 of 360 degrees, a 30-degree sector would be equal to 1/12 the area of the circle.
Therefore, we divide [tex]81\pi[/tex]/12 to get the area of the sector = [tex]6.75\pi[/tex] inches^2.
The question is: Emily sold 56 of the 145 bracelets. What percent of the bracelets did she sell? Show your strategy.
Answer:
[tex]percentage = \frac{56}{145} \times 100[/tex]
56/145×100
0.386...×100
38.6%
What are the coordinates of F' and G' for D(6.(2,5)) [F (3,11), G (2,8)]?
Answer: To find the coordinates of F' and G', we need to reflect points F and G across the line y = 5, since point D is located on this line.
For point F, the y-coordinate changes from 11 to -1, since the distance between the line y = 5 and point F is 6 units (2 times the distance between D and the line). Therefore, the coordinates of F' are (3,-1).
For point G, the y-coordinate changes from 8 to 2, since the distance between the line y = 5 and point G is 3 units (1.5 times the distance between D and the line). Therefore, the coordinates of G' are (2,2).
Thus, the coordinates of F' are (3,-1) and the coordinates of G' are (2,2).
You work in a pharmacy that mixes different concentrations of saline solutions for its customers. The pharmacy has a supply of two concentrations, 0.50% and 2%. The function
100(0.02) + x(0.005)
y=
100 +x
gives the amount x in milliliters of the 0.5% solution you must add to 100 milliliters of the 2% solution to form a new concentration y of saline solution. How
many milliliters of the 0.5% solution must you add for the combined solution to have a concentration of 0.88%?
You must add approximately mL.
(Round to one decimal place as needed)
Answer:
294.7 mL
Step-by-step explanation:
You want to know the volume (x) in mL of 0.5% solution to be added to 100 mL of 2% solution to make a mix that has a concentration of 0.88%.
SetupThe given equations seem to be missing something. We want ...
100(0.02) +x(0.005) = (100 +x)(0.0088)
SolutionWe like to play with larger numbers, so we'll multiply this equation by 100 as we simplify it.
200 +0.5x = 88 +0.88x
112 = 0.38x . . . . . . . . . . . . . subtract 88+0.5x
294.7 = x . . . . . . . . . . . . divide by 0.38
You must add approximately 294.7 mL of 2% solution.
Solve for length of segment c.
3 cm
12 cm
18 cm
C = [?] cm
If two segments intersect inside
or outside a circle: ab = cd
The value of c for the intersecting secants is derived to be equal to 2 cm
What is the intersecting secant theoremThe intersecting secant theorem, also known as the secant-secant theorem, states that when two secant lines intersect outside a circle, the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.
c × 18 cm = 3 cm × 12 cm
c18 cm = 36 cm²
c = 36 cm²/18 cm
c = 2 cm
Therefore, the value of c for the intersecting secants is derived to be equal to 2 cm.
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Answer:
c=2cm
Step-by-step explanation:
ab=cd
3•12=18•c
36=18(c)
36/18=2
18(c)=c
c=2
Almed Company reported the following information for 2013 and 2014.Prepaid insurance, December 31, 2013 $ 2,400Prepaid insurance, December 31, 2014 1,500Insurance expense--2014 14,200How much cash was paid for insurance during 2014?A. $13,300B. $14,200C. $15,100D. $15,700
Cash paid for insurance during 2014 was $15,100.The following formula can be used to determine the cash spent on insurance in 2014:
Insurance expense in 2014 minus an increase in prepaid insurance = Cash paid for insurance.
The difference between the prepaid insurance balance at December 31, 2014, and December 31, 2013, can be used to compute the rise in prepaid insurance:
Prepaid insurance at December 31, 2014 minus Prepaid insurance at December 31, 2013 equals $1,500 minus $2,400, or -$900.
The fact that the prepaid insurance balance fell between 2013 and 2014 indicates that the business used more insurance coverage than it had purchased for the year. As a result, the 2014 insurance premiums paid in cash are:
Insurance expense for 2014 minus the increase in prepaid insurance is $14,200 - (-$900) = $15,100 in cash paid for insurance.
The correct response is (C) $15,100.
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5. A cylinder has radius 3 inches and height 5 inches. A cone has the same radius and height. (Lesson 5-13)
b. Find the volume of the cone.
c. What fraction of the cylinder's volume is the cone's volume?