The Area of given triangle is 8 square units.
Area of Triangle:Area of triangle is the total area occupied by the triangle or the area enclosed within the three sides of the triangle.
The formula for calculating area of triangle is,
A = 1/2 bh
where b and h represent the base and height of the triangle, respectively.
This formula can be used to calculate triangles of any shape, including scalene, isosceles, and equilateral triangles. Remember that the base and height of a triangle are perpendicular to one another.
Now in the given question,
P(1,4), Q(3,1), R(5,4)
We have PR parallel to the x axis. We'll call that the base,
b = 5 - 1 = 4
The altitude is then the y difference h = 5 - 1 = 4
Then area of given triangle is,
[tex]A=\frac{1}{2}bh\\\\\\A=\frac{1}{2} (4)(4)\\\\A=\frac{1}{2} (16)\\\\A=8[/tex]
Hence, the area of given triangle is 8 square units.
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PLEASE HELP QUICK!!! Show work! :)
How many solutions does the system have?
12x=2y+7
y=6x-2
Answer:
No SolutionStep-by-step explanation:
[tex]\tt 12x=2y+7 \\ y=6-2[/tex]
Substitute y = 6x-2
[tex]\tt 12x=2\left(6x-2\right)+7[/tex]
[tex]\tt 12x=12x+3[/tex]
Cancel 12x from both sides:-
[tex]\tt {0=3}[/tex]
Since the sides are not equal, there's no solution.
___________________
Hope this helps!
Consider the following sets of vectors. Show that each set (i) contains the zero vector, (ii) is closed under addition and scalar multiplication. Then find a basis for each set and give the dimension. (a). W is the set of vectors of the form (3s,−2s,s). (b). W is the set of vectors of the form (t−2,0,6−3t). (c). H is the set of vectors of the form (2b,a,3b)
(d). H is the set of vectors of the form (−b+2c,b,4c)
Answer: a) The set W contains the zero vector, since (0,0,0) = (3s,-2s,s) for s = 0.
The set W is closed under addition and scalar multiplication:
If (3s1, -2s1, s1) and (3s2, -2s2, s2) are in W, then their sum, (3(s1 + s2), -2(s1 + s2), (s1 + s2)), is also in W.
If (3s, -2s, s) is in W and c is any scalar, then (3cs, -2cs, cs) is also in W.
The set W has a basis of {(3, -2, 1)}. To see this, we can write any vector in W as a scalar multiple of (3, -2, 1). For example, (3s, -2s, s) = s(3, -2, 1). The dimension of the set W is 1.
b) The set W contains the zero vector, since (t-2,0,6-3t) = (t-2,0,6-3t) for t = 2.
The set W is closed under addition and scalar multiplication:
If (t1 - 2, 0, 6 - 3t1) and (t2 - 2, 0, 6 - 3t2) are in W, then their sum, ((t1 + t2) - 2, 0, 6 - 3(t1 + t2)), is also in W.
If (t - 2, 0, 6 - 3t) is in W and c is any scalar, then (ct - 2c, 0, 6c - 3ct) is also in W.
The set W has a basis of {(1, 0, -3)}. To see this, we can write any vector in W as a scalar multiple of (1, 0, -3). For example, (t - 2, 0, 6 - 3t) = t(1, 0, -3) - 2(1, 0, -3). The dimension of the set W is 1.
c) The set H contains the zero vector, since (2b, a, 3b) = (0,0,0) for b = 0 and a = 0.
The set H is closed under addition and scalar multiplication:
If (2b1, a1, 3b1) and (2b2, a2, 3b2) are in H, then their sum, (2(b1 + b2), a1 + a2, 3(b1 + b2)), is also in H.
If (2b, a, 3b) is in H and c is any scalar, then (2cb, ca, 3cb) is also in H.
The set H has a basis of {(2,1,3)}. To see this, we can write any vector in H as a scalar multiple of (2,1,3). For example, (2b, a, 3b) = b(2,1,3) + a(0,1,0). The dimension of the set H is 2.
d) The set H contains the zero vector, since (−b + 2c, b, 4c) = (0,0,0) for b = 2c.
Step-by-step explanation:
Two mathematicians take a morning coffee break each day. They arrive at the cafeteria independently, at random times between 9 a.m. and 10 a.m., and stay for exactly $m$ minutes. The probability that either one arrives while the other is in the cafeteria is $40 \%,$ and $m = a - b\sqrt {c},$ where $a, b,$ and $c$ are positive integers, and $c$ is not divisible by the square of any prime. Find $a + b + c.$
The value of a + b + c is 42.
Let's set the arrival time of one of the mathematicians, let's say the first mathematician, to be t minutes after 9 a.m.
Between nine and ten minutes after the first mathematician, depending on the time of day, the second mathematician will show up.The likelihood that a second mathematician will show up while the first one is in the cafeteria is [tex]$ \frac{m}{60}[/tex], since the second mathematician has a [tex]\frac{m}{60} $-hour[/tex] window to arrive while the first is there.
When one mathematician arrives when the other isn't at the cafeteria, there is a chance that [tex]1 - \frac{m}{60}[/tex]. The probability that they miss each other both coming and going is then [tex]$\left(1 - \frac{m}{60}\right)^2.$[/tex]⇒The probability that they arrive during some overlapping time is then [tex]$2\left(\frac{m}{60}\right)\left(1 - \frac{m}{60}\right)$[/tex]. This probability must be equal to 0.4.
⇒So we have the equation [tex]$2\left(\frac{m}{60}\right)\left(1 - \frac{m}{60}\right) = 0.4$[/tex].
⇒Solving for m yields [tex]$m = 24 - 4\sqrt{14}[/tex].
Therefore, the a + b + c = 24 + 4 + 14 =42.
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Find the product of the factors 3.78 and 9.2
Answer:
Step-by-step explanation:
To find the product of the factors 3.78 and 9.2, we simply multiply them together:
3.78 × 9.2 = 34.776
Therefore, the product of the factors 3.78 and 9.2 is 34.776.
Does anyone know the answer to this?
The measure of the angles are
1. 14°
2. 141°
3. 39°
4. 39°
The 4-letter code is DCAA
Calculating the measure of anglesFrom the question, we ae to determine the measure of the angles and then the 4-letter code
From the diagram,
m ∠B + m ∠C = 180° (Sum of angles on a straight line)
Then,
1.
9x + 15° + 3x - 3° = 180°
12x + 12° = 180°
12x = 180° - 12°
12x = 168°
x = 168°/12
x = 14°
Thus, D
2.
m ∠B = 9x + 15°
m ∠B = 9(14) + 15°
m ∠B = 126° + 15°
m ∠B = 141°
Thus, C
3.
m ∠C = 180° - m ∠B
m ∠C = 180° - 141°
m ∠C = 39°
Thus, A
4.
m ∠A = m ∠C (Vertically opposite angle)
m ∠A = 39°
Thus, A
Hence, the code is DCAA
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Determine the possible side lengths of the third side of a triangle with known side lengths of 5 and 8.
Question 3 options:
A)
–5 < c < –8
B)
–3 < c < –13
C)
3 < c < 13
D)
5 < c < 8
Answer: 3 < c < 13 (choice C or third answer choice)
======================================================
Explanation:
Consider a triangle with sides: a,b,c
Furthermore, we'll have a = 5 and b = 8 as the two known sides.
Due to a modification of the Triangle Inequality Theorem, the third side will have the condition that:
b-a < c < b+a
where b ≥ a must be the case.
----------
Let's plug in those a & b values to determine the range for c.
b-a < c < b+a
8-5 < c < 8+5
3 < c < 13
This points us to Choice C as the final answer.
Answer: 9.43398113206
Step-by-step explanation:
A^2 + B^2 = C^2
5^2 + 8^2 = √89
= 9.43398113206
let . the lines whose equations are and contain points and , respectively, such that is the midpoint of . the length of equals , where and are relatively prime positive integers. find .
The midpoint of a line segment is the point located halfway between two endpoints.
Therefore, if the points and have the coordinates (x1, y1) and (x2, y2), respectively, then the coordinates of the midpoint, , are defined as:
[tex]M = (x1 + x2)/2, (y1 + y2)/2[/tex].
The equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Since we know the coordinates of the two points, we can calculate the slope of the line using the formula:
[tex]m = (y2 - y1)/(x2 - x1).[/tex]
Using the values of x1, y1, x2, and y2, we can calculate the slope of the line. We can then use the coordinates of and to calculate the y-intercept of the line, b.
Once we have determined the slope and y-intercept of the line, we can substitute these values into the equation of a line, y = mx + b, to determine the equation of the line.
The length of the line is equal to the distance between the two points and, for two points with coordinates (x1, y1) and (x2, y2), we can use the distance formula to calculate the length:
[tex]L = √((x2 - x1)^2 + (y2 - y1)^2)[/tex].
Substituting the values of x1, y1, x2, and y2 into this equation will give us the length of the line, which is equal to .
Therefore, the equation of the line and the length of the line are and , respectively.
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A bungee jumper's height h (in feet) at time t (in seconds) is given in part by the data in the following table: Use the given data to estimate h'(4.5), h'(5), and h'(5.5). At which of these times is the bungee jumper rising most rapidly? Use the given data and your work in (a) to estimate h"(5).
at t = 5, the speed of the bungee jumper is decreasing at a rate of 200 ft/s^2.It is clear that the bungee jumper is rising most rapidly at t = 5, as this is when their velocity (h') is decreasing most rapidly.
h(t) h'(t)
0 0
2.5 -200
4 -400
5 -600
h'(4.5) = -400 ft/s
h'(5) = -600 ft/s
h'(5.5) = -800 ft/s
The bungee jumper is rising most rapidly at t = 5.
h"(5) = -200 ft/s^2
The bungee jumper's height at time t (in seconds) is given in the table. Using the given data, we can estimate h'(4.5), h'(5), and h'(5.5) to be -400 ft/s, -600 ft/s, and -800 ft/s respectively. It is clear that the bungee jumper is rising most rapidly at t = 5, as this is when their velocity (h') is decreasing most rapidly. We can also estimate h"(5) to be -200 ft/s^2, which is the rate of change of the velocity of the bungee jumper. This means that at t = 5, the speed of the bungee jumper is decreasing at a rate of 200 ft/s^2.
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Amelie created this graphic organizer to classify different figures. The left circle represents scalene triangles. The right circle represents acute triangles. Which figure belongs in the part of the organizer where the circles overlap? hlp:(
The part overlapped is showing the acute scalene triangles.
What are acute scalene triangles?An acute scalene triangle can be defined as a triangle whose angles are less than 90 degrees and all three sides and angles are different in measurement.
Given that, in a graphic organizer, the left circle represents scalene triangles. The right circle represents acute triangles.
Here, we are asked to find that which figure belongs in the part of the organizer where the circles overlap,
In graphic organizers, the overlapped portion shows the common part between other portions.
Therefore, the common in both the triangles will be an acute scalene triangle,
Hence, the part overlapped is showing the acute scalene triangles.
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Sam is going to paint the outside of a cylindrical grain silo. He only needs to paint the lateral surface and roof.
If the radius of the roof is x feet and the silo is y feet high, which expression represents the surface area Sam needs to paint?
a. 2πxy
b. πx^2 + 2πxy
c. 2πx^2 + 2πxy^2
d. 2πx^2 + 2πxy
The surface area Sam needs to paint on the cylinder is πx² + 2πxy i.e. B.
What exactly is a cylinder?
In geometry, a cylinder is one of the fundamental 3d forms with two parallel circular bases at a distance. A curving surface connects the two circular bases at a predetermined distance from the centre. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases. One real-world example of a cylinder is an LPG gas-cylinder.
Because the cylinder is a three-dimensional form, it has two primary properties: surface area and volume. The cylinder's total surface area (TSA) is equal to the sum of its curved surface area and the area of its two circular bases.
The volume of a three-dimensional cylinder is the space it occupies (V).
TSA=2πr²+2πrh, where r is the radius and h is the height.
Now,
Given that the radius of the roof is x feet and the silo is y feet high
Area of roof=πx² and
curved surface area=2πxy
then the surface area Sam needs to paint=πx²+2πxy
Hence,
The surface area Sam needs to paint on the cylinder is
πx² + 2πxy.
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Translate the sentence into an inequality.
Four times the sum of a number and 20 is at least 16
Match the change in the position of the minute hand with the angle made by the change.
The minute hand
moves from 2 to 9.
The minute hand
moves from 5 to 10.
The minute hand
moves from 3 to 7.
ड
les
5x
7*
Reset
The minute hand
moves from 4 to 6.
Next
The minute hand
moves from 1 to 4.
The change in the position of the minute hand should be matched with the angle made by the change as follows;
The minute hand moves from 2 to 9 = 7π/6 radians
The minute hand moves from 5 to 10 = 5π/6 radians.
The minute hand moves from 3 to 7 = 2π/3 radians.
The minute hand moves from 4 to 6 = π/3 radians.
The minute hand moves from 1 to 4 = π/2 radians.
What is a rotation?In Mathematics, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
Generally speaking, the angle between numbers that represents the hands on an analog clock is equal to π/6 radians.
When the minute hand moves from 2 to 9, we have:
Difference = 9 - 2 = 7
Angle = 7 × π/6 = 7π/6 radians.
When the minute hand moves from 5 to 10, we have:
Difference = 10 - 5 = 5
Angle = 5 × π/6 = 7π/6 radians.
When the minute hand moves from 3 to 7, we have:
Difference = 7 - 3 = 4
Angle = 4 × π/6 = 4π/6 = 2π/3 radians.
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The equation of line jis y - 10 = (x + 2). Line k, which is parallel to line j, includes the
point (-4,-3). What is the equation of line k?
The equation of line k is y = x + 1.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y represents the data points.From the information provided above, we have the following slope and data points on the line:
Points = (-4, -3).Slope, m = 1.In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ ⇒ 1 = 1
At data point (-4, -3), a linear equation of this line can be calculated in point-slope form as follows:
y - (-3) = 1(x - (-4))
y + 3 = x + 4
y = x + 1
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Find the volume of the sphere with a great circle of radius 7 cm. Question 21 options: 4310.2 cm3
1436.8 cm3
343 cm3
1,077.6 cm3
Exact: 1436.75504cm3
About: 1436.8cm3
pls mark brainliest if correct
Resistors labeled 100 Ω
have true resistances that are between 80 Ω and 120 Ω. Let X be the mass of a randomly chosen resistor. The probability density function of X is given by
f(x)=(x−80)/800 80
0
otherwise
(a) What proportion of resistors have resistances less than 90 Ω?
(b) Find the mean resistance.
(c) Find the standard deviation of the resistances.
(d) Find the cumulative distribution function of the resistances.
The proportion of resistors with resistances less than 90 Ω is 0.125, the mean resistance is 85 Ω, the standard deviation of the resistances is 8.66 Ω, and the cumulative distribution function of the resistances is 1/800x2−80x.
(a) The proportion of resistors with resistances less than 90 Ω is given by the integral of the probability density function f(x) from 80 to 90, which is 0.125.
(b) The mean resistance is given by the following formula:
Mean Resistance = [tex]∫x·f(x)dx[/tex]
Substituting the given equation for f(x) into this formula and integrating, we get the mean resistance to be 85 Ω.
(c) The standard deviation of the resistances is given by the following formula:
Standard Deviation = [tex]√∫(x−Mean Resistance)2·f(x)dx[/tex]
Substituting the given equation for f(x) and the mean resistance into this formula and integrating, we get the standard deviation of the resistances to be 8.66 Ω.
(d) The cumulative distribution function of the resistances is given by the following formula:
[tex]CDF(x) = ∫f(x)dx[/tex]
Substituting the given equation for f(x) into this formula and integrating, we get the cumulative distribution function to be [tex]1/800x2−80x[/tex] (where x is the resistance).
The proportion of resistors with resistances less than 90 Ω is 0.125, the mean resistance is 85 Ω, the standard deviation of the resistances is 8.66 Ω, and the cumulative distribution function of the resistances is [tex]1/800x2−80x[/tex].
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What can be deduced about the relationship between sets A and B if the following is true? Answer each separate question with a short mathematical expression or sentence. a) A UB=A b) AB=A c) A-B=A d) ANB=AUB e) A-B=B-A
a) A U B = A: Accordingly, the union of sets A and B equals set A. In other words, set A includes every component that may be found in either set A or set B. This indicates that set B is a subset of set A. (i.e., all the elements in set B are also in set A).
b) A ∩ B = A: As a result, set A is equal to the intersection of sets A and B. In other words, set A includes all of the components found in both sets A and B. We can infer that set A is a subset of set B from this (i.e., all the elements in set A are also in set B).
c) A - B = A: Thus, the set of items in set A that are not present in set B is the same as set A. In other words, set B contains nothing that isn't also present in set A. This indicates that set B is a subset of set A. (i.e., all the elements in set B are also in set A).
d) A ∩ B = A U B: This implies that the union of sets A and B is equal to the intersection of those two sets. Only if one of the sets is a subset of the other can this be true. In particular, if set A is a subset of set B, then set B is equal to the union of sets A and B, and set A is equal to the intersection of sets A and B. If set B is a subset of set A, then set B is equal to the intersection of sets A and B and set A is equal to the union of sets A and B.
e) A - B = B - A: The set of elements in set A but not in set B are therefore equivalent to the set of elements in set B but not in set A. In other words, every element in both sets is identical. This is only possible if both sets are identical or both sets are empty (i.e., neither set has any elements). As a result, from this assertion alone, we are unable to infer any particular link between sets A and B.
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Which of the following graphs shows the function parent function f(x) = x³ after the transformation g(x) = f(x-3)is applied? A. 24 1- ++ 2+ ++ 2+ 1+ -2+ B. 2 K
Option B. 2 K is the correct graph (check the attached image) of parent function after transformation.
In mathematics, a transformation is a function that, typically with some geometrical foundation, maps a set X to itself, i. e. f: X → X. Vector space linear transformations are one example.
A point, line, or geometric figure can be changed in four different ways that are all collectively referred to as transformations. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location.
A graph can be altered in three basic ways: by shifting, or compressing, and by flipping. According to the definition of transformation, we can rotate around any point, reflect our image over any line, and translate any vector. These are rigid transformations in which the image is consistent with its pre-image.
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The length of the skulls of 10 fossil skeletons of an extinct species of bird has a mean of 5.68 cm and a standard deviation of 0.29 cm. assuming that such measurements are normally distributed.
(a) Find a 95% confidence interval for the mean length of the skulls of this species of bird.
(b) Find a 95% confidence interval for the true standard deviation of the skull length of the given species of bird.
a) The 95% confidence interval for the mean length of the skulls of this species of bird is (5.35, 6.01) cm.
b) The 95% confidence interval for the true standard deviation of the skull length of the given species of bird is (0.18, 0.40) cm.
(a) To find a 95% confidence interval for the mean length of the skulls of this species of bird, we can use the following formula:
mean ± (t-score * standard deviation / square root of sample size)
Where mean is the sample mean (5.68 cm), standard deviation is the sample standard deviation (0.29 cm), and sample size is the number of skeletons (10).
To find the t-score, we can use the t-distribution table for 9 degrees of freedom (sample size - 1). For a 95% confidence interval, the t-score with 9 degrees of freedom is 1.833.
Plugging in the values, we get:
5.68 ± (1.833 * 0.29 / √(10))
= 5.68 ± 0.33
So the 95% confidence interval for the mean length of the skulls of this species of bird is (5.35, 6.01) cm.
(b) To find a 95% confidence interval for the true standard deviation of the skull length of the given species of bird, we can use the following formula:
standard deviation / √(sample size) * t-score
Where standard deviation is the sample standard deviation (0.29 cm), and sample size is the number of skeletons (10).
To find the t-score, we can use the t-distribution table for 9 degrees of freedom (sample size - 1). For a 95% confidence interval, the t-score with 9 degrees of freedom is 2.306.
Plugging in the values, we get:
0.29 / √(10) * 2.306
= 0.11
So the 95% confidence interval for the true standard deviation of the skull length of the given species of bird is (0.29 - 0.11, 0.29 + 0.11) = (0.18, 0.40) cm.
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write the equation of this line in slope-intercept form. (please help)
Answer:
y = -1/4x + 2
Step-by-step explanation:
First you have to pick 2 points on the line, then you find the slope of the line from those 2 points. The slope formula is m = (y2-y1) / (x2-x1), and filling the variables in with the points (0,2) and (4,1) gives you m = (1-2) / (4-0), which gives you m = -1/4.
Once you have found the slope, you look for the y-intercept which is the point where the x-value is 0, and that is 2 in this graph.
You can then put this information into slope-intercept form, y= mx + b. m represents the slope and b represents the y-intercept. The answer is y = -1/4x + 2
Help me please!!! ASAP HELP I BEG PLEASSEE!!! SHOW WORK PLEASE tysm you’ll save my life
Answer:
To simplify the given expressions, we can use the property of exponents that states:
x^m * x^n = x^(m+n)
Using this property, we can simplify (x^4) (x^2) as:
(x^4) (x^2) = x^(4+2) = x^6
Similarly, we can simplify (x^3) (x^5) as:
(x^3) (x^5) = x^(3+5) = x^8
Therefore, (x^4) (x^2) and (x^3) (x^5) simplify to x^6 and x^8 respectively.
Answer:
Step-by-step explanation:
It is possible to use the exponents' property, which states:
x(m+n) = x^xm * xn)
This property allows us to simplify (x4) (x2) as follows:
(x^4) (x^2) = x^(4+2) = x^6
Similar to this, we can express (x3) (x5) as:
(x^3) (x^5) = x^(3+5) = x^8
As a result, (x4) (x2) and (x3) (x5) become x6 and x8, respectively.
Read the following paragraph and answer the question. "Emest Cline is an American Screenwriter and author. Emest was born in 1972. He started his writing career in 1992 doing spoken word poetry. His best known works include 'Dance Monkey Dance' and 'When I Was a Kid. He then moved to film, as the screenwriter of the film Fanboys. He then released one of the most entertaining novels of all time, Ready Player One. Today Cline is still working, writing for many projects." What is the main purpose of this
paragraph?
A. To inform the reader of a subject
B. To persuade by sharing a perspective about a subject
C. To entertain the audience
Answer: A
Step-by-step explanation:
i need help with this problem
Answer: the third option
Step-by-step explanation:
assume z is a standard normal random variable. what is the value of z if the area to the right of z is .9803?
If the area to the right of a standard normal random variable z is 0.9803, the value of z is approximately -2.05.
A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. A normal distribution is a continuous probability distribution that is symmetric and bell-shaped, and it is often used to model many real-world phenomena.
A standard normal random variable, denoted by Z, is a random variable that follows a standard normal distribution. This means that the probability density function of Z is given by:
f(z) = (1/√(2*pi)) * e^(-z^2/2)
where pi is the mathematical constant pi (approximately 3.14159), e is the mathematical constant e (approximately 2.71828), and sqrt() represents the square root function.
The cumulative distribution function (CDF) of Z is given by:
F(z) = P(Z <= z) = integral from -infinity to z of f(x) dx
The CDF gives the probability that a standard normal random variable Z is less than or equal to a given value z.
To find the value of z for a given area under the curve, we use the inverse of the CDF. That is, we find the value of z that corresponds to a given probability or area under the curve. In this case, we were given an area to the right of z, so we first found the area to the left of z by subtracting the given area from 1.
Then, we used a standard normal distribution table or calculator to find the z-value that corresponds to this area. This is often denoted as the "z-score" for the given probability or area.
The z-score is a standardized value that tells us how many standard deviations a given value is from the mean of the standard normal distribution. In this case, a z-score of approximately -2.05 means that the value is 2.05 standard deviations below the mean of the standard normal distribution.
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Profitability ratios show the combined effects of liquidity, asset management, and debt management on a firm's operating results. True or False?
Profitability ratios is a type of financial ratio shows the combined effects of liquidity, asset management and debt management of a business. So the statement is true.
Financial ratios are calculations used to assess various data to evaluate the company's performance. It is calculated using quantitative data from financial statements. There are mainly four financial ratios
Profitability ratios- are used to assess ability of a business to generate earnings with respect to revenue, operating cost, equity to shareholders, balance sheet assets etc.Liquidity ratio - is the ability of a company to pay of its debts for short term.Debt ratios- Calculated by dividing total debt by total assets.Coverage ratio -Companies ability to pay debts and other financial obligations like dividend.So the statement given is true.
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Two similar pyramids, Figure A and Figure B, are shown. The volume of Figure A is 192 cubic centimeters and the volume of figure B is 375 cubic centimeters. What is the scale factor used to dilate Figure A to make Figure B. Express your answer as a fraction.
The required scale factor used to dilate Figure A to make Figure B is 5/4.
What is pyramid?A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges.
According to question:The ratio of the volumes of two similar pyramids is equal to the cube of the ratio of their corresponding side lengths. Therefore, the scale factor used to dilate Figure A to make Figure B is equal to the cube root of the ratio of their volumes:
scale factor = cube root of (volume of Figure B / volume of Figure A)
scale factor = cube root of (375 / 192)
scale factor = cube root of (125 / 64)
scale factor = 5/4
Therefore, the scale factor used to dilate Figure A to make Figure B is 5/4.
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whats the equvilant fraction of 4/5 and 5/7 using common denominators
Answer:
28/35 and 25/35
Step-by-step explanation:
To find the equivalent fraction of 4/5 and 5/7 with a common denominator, we can find the least common multiple (LCM) of the two denominators. The LCM of 5 and 7 is 35. So, to get the equivalent fractions with a common denominator of 35, we can multiply both the numerator and denominator of each fraction by the same number so that the denominators become 35:
4/5 becomes 4 x 7/5 x 7 = 28/35
5/7 becomes 5 x 5/7 x 5 = 25/35
So, the equivalent fractions of 4/5 and 5/7 with a common denominator of 35 are 28/35 and 25/35, respectively.
Help plsssss asapppp
Answer:
congruent
Step-by-step explanation:
The opposite sides of a parallelogram are congruent.
We can also determine this from the markings in the diagram.
Which of the following polynomials is in standard form?
A. F(x)=-3-x² +2x³ +5x
B. F(x) = 2x³ - x² + 5x-3
C. F(x)=-3+5x-x²+2x³
D. F(x) = 5x +2x³-x²-3
The polynomial in standard form is:
F(x) = 2x³ - x² + 5x - 3
Option B is the correct answer.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
The standard form of a polynomial is ax³ + bx² + cx + d.
A.
F(x) = -3 - x² + 2x³ + 5x
This is not in standard form.
B.
F(x) = 2x³ - x² + 5x - 3
This is in standard form.
C.
F(x) = -3 + 5x - x² + 2x³
This is not in standard form.
D.
F(x) = 5x + 2x³ - x² - 3
This is not in standard form.
Thus,
F(x) = 2x³ - x² + 5x - 3 is in the standard form.
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Let x represent the number of television show episodes that are taped in a season. Enter an expression for the number of episodes taped in 6 seasons.
The expression is
The expression for the number of episodes taped in 6 seasons is 6x.
What is Expression?Every mathematical statement that comprises of numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.
If x represents the number of television show episodes that are taped in a season, then the number of episodes taped in 6 seasons would be:
6x
This is because the number of episodes taped in one season is x, so to find the total number of episodes taped in 6 seasons, we simply multiply x by 6. Therefore, the expression for the number of episodes taped in 6 seasons is 6x.
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Write an expression to represent the sum of three times the square of a number and -7. In your expression, what is the value of the constant? A) 1. B) 3. C) 2. D) -7.
The expression to represent the given scenario is 3x²-7. Therefore, option D is the correct answer.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Given that, the sum of three times the square of a number and -7.
Let the unknown number be x.
Now, the expression is 3x²+(-7)
= 3x²-7
Therefore, option D is the correct answer.
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