0 |-1| , 1.3 , 2, |2.7|
Step-by-step explanation:
it's right because |-1| is an absolute value and the absolute value is 1
Answer:
0, |- 1| , 1.3, 2, |2.7|
Step-by-step explanation:
The absolute value of any number, x, denoted by |x| is the positive of that number
So | 2.7 | = 2.7
| - 1 | = 1
Therefore the order of the absolute values is
0, 1, 1.3, 2, 2.7 which is the same as 0, |- 1| , 1.3, 2, |2.7|
the perimeter of a ractangle is 280cm the ratio of the width to the length is 3:4. what is the length of the rectangle?
For the given width length ratio and perimeter of rectangle, the length of rectangle is 80 cm.
The perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.
Let the width of the rectangle be 3x, and the length be 4x (since the ratio of the width to the length is 3:4).
The perimeter of a rectangle is the sum of the lengths of all four sides, so we have:
Perimeter = 2(length + width)
Substituting the expressions for the length and width, we get:
280cm = 2(4x + 3x)
Simplifying the right-hand side, we get:
280cm = 14x
Dividing both sides by 14, we get:
x = 20
Therefore, the length of the rectangle is 4x = 4(20) = 80 cm
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the 2 agnles and the included side of one triangle are congruent to 2 angles and the included side of another triangle
If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent by the ASA congruence condition. Hence, option a. is the right answer.
According to the definition, we know that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent by the ASA congruence condition.
Let us consider two triangles △ABC and △QRP as shown below -
So, in △ABC and △QRP, we have,
∠B=∠R
∠C=∠P
BC=RP
∴ By ASA congruence test for triangles, we get △ABC ≅ △QRP
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The complete question is -
If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, the two triangles are congruent by _____ congruence condition.
a. ASA
b. AAA
c. SAS
d. RHS
the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring.T/F
The probability of the intersection of two events occurring can never be more than the probability of the union of two events occurring.
False.
It should be stated that the likelihood of the intersection of two events occurring is always less than the likelihood of the events occurring together.
It is always less likely than or equal to the likelihood of either event occurring alone for an intersection of two events, which is the chance that both occurrences take place.
In other words, the probability of the intersection and the probability of the union are subsets of one another.
The chance of the intersection of two events occurring can never be greater than the likelihood of the union of two events occurring, hence that is the right statement.
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mr hall is doggie-paddling in the school pool at a speed of 1 m/sec when he spots his favorite rubber ducky. He increases his speed to 3m/sec over a period of 3 seconds. What is Mr. Halls acceleration?
Answer:
1m/sec
Step-by-step explanation:
Mr. Hall spent 3 seconds to increase his speed to 3m/sec increasing 1m/sec, don't over think it.
You receive 23 out of 25 points on an exam. What is your score as a percent?
Answer:
Your score as a percent is **92%**. Here is how I calculated it:
To convert a fraction to a percent, you need to divide the numerator by the denominator, multiply the result by 100, and add a "%" sign
In your case, the fraction is 23/25, so you need to divide 23 by 25, multiply by 100, and add a "%".
23 ÷ 25 = 0.92
0.92 × 100 = 92
92 + "%" = 92%
Therefore, your score as a percent is 92%.
Step-by-step explanation:
After polling a group of 48 students, you find that 36 students play the
piano and 20 students play the guitar. Given that information, what is
the number of students in the group who must play both the piano and
guitar?
Answer:
6 students must play both piano and guitar
What quantity must be added to 3-7x+4 to obtain - +4x-2?
A-4x2+3x+2
B.-412 + 11x + 2
C.-4x² + 11x-6
D. 2x²-3x+2
E. 2x²-3x+6
Answer:
Step-by-step explanation: (10)(A) Add and subtract polynomials of degree one and degree two. (10)(B) Multiply polynomials of degree one and degree two. (10)(C) Determine the quotient
Hope it helps =}
Answer:
b
Step-by-step explanation:
an equation for the line with a slope of 3 and passing through the point (5, 7).
Answer:
y – 7 = 3(x – 5)
Step-by-step explanation:
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 3}(x-\stackrel{x_1}{5}) \\\\\\ y-7=3x-15\implies {\Large \begin{array}{llll} y=3x-8 \end{array}}[/tex]
both are measured in people per hour and the time t is measured in hours after midnight. these functions are valid for , the hours during which the park is open. at time , there are no people in the park. (1) how fast are people entering the amusement park at 9:00 a.m.?
At 9:00 a.m., the rate of people entering the amusement park is 533 people per hour, while the rate of people leaving the amusement park is 67 people per hour.
(1) At 9:00 a.m., the rate of people entering the amusement park is given by the derivative of the entering function, which is:
f'(t) = 400 + 200cos(πt/12).
At t = 9, this rate is 400 + 200cos(π*9/12) = 400 + 200cos(3π/4) ≈ 533 people per hour.
(2) At 9:00 a.m., the rate of people leaving the amusement park is given by the derivative of the leaving function, which is:
g'(t) = 200 - 200cos(πt/12).
At t = 9, this rate is 200 - 200cos(π*9/12) = 200 - 200cos(3π/4) ≈ 67 people per hour.
the complete question is :
both are measured in people per hour and the time t is measured in hours after midnight. these functions are valid for , the hours during which the park is open. at time , there are no people in the park. (1) how fast are people entering the amusement park at 9:00 a.m.? (2) how fast are people leaving the amusement park at 9:00 a.m.?
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how many pattern block trapezoids would create 3 hexagons
Answer:
Step-by-step explanation:
How many pattern block trapezoids would create for hexagons?
2 trapezoids compose a hexagon using equal-size shapes: 2 trapezoids, 6 triangles, or 3 blue rhombuses. compose hexagons using different shapes. So 2 trapezoids create 1 hexagon. This means 6 trapezoids make 3 hexagons.
The exact number of trapezoids needed to create three hexagons depends on the size and shape of the hexagons.
However, in general, you would need at least 18 trapezoids.
What is Hexagon?An hexagon is a six-sided polygon. It is made up of six equilateral triangles and six trapezoids.
If you are looking to create larger hexagons you will need more trapezoids.
Depending on the size and shape, you could need as many as 24 or more trapezoids.
An hexagon is a six-sided polygon. It is made up of six equilateral triangles and six trapezoids.
Hence, To create an hexagon using pattern blocks, you need 10 equilateral triangles and 20 trapezoids.
Therefore, to create 5 hexagons.
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For your birthday, you received a $15 gift card to your favorite arcade. All of the games at the arcade cost $0. 75. Complete the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games. For your birthday, you received a $15 gift card to your favorite arcade. All of the games at the arcade cost $0. 75. Complete the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games. For your birthday, you received a $15 gift card to your favorite arcade. All of the games at the arcade cost $0. 75. Complete the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games
[tex]m=15-0.75g[/tex] is the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games.
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. While the definition of an equation in English is any well-formed formula consisting of two expressions related by an equals sign, the definition of an equation and its cognates in other languages may have subtly different meanings. For instance, an équation is defined as having one or more variables in French.
According to the question,
Total money = $15
The games at the arcade cost $0. 75.
Let total amount of money be 'm' and arcade games played by him be 'g'.
Now,
Equation to represent the remaining money,
[tex]m=15-0.75g[/tex]
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Please answer and work out for all:
Find the vertical difference in height between:
i.A and B
ii.B and C
iii.A and C.
b.Find the angle of elevation from A to C
The vertical difference in height between
i. A and B = 1.55
ii. B and C = 1.27
iii. A and C. = 2.82
the angle of elevation from A to C
34.33 degreesHow to find vertical difference in heightThe vertical difference in height is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The directions describes a right angle triangle o
A and B
sin 15 = vertical difference / 6
vertical difference = 6 sin 15
vertical difference = 1.55
B and C
sin 25 = vertical difference / 3
vertical difference = 3 sin 25
vertical difference = 1.27
A and C
A to B + B to C
= 1.55 + 1.27
= 2.82
angle of elevation from A to C
sin x = 2.82 / 5
x = arc sin (2.82/5)
x = 34.33 degrees
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Cayley says that the equation p=1. 5 and 2/3p =q both represent the same proportional relationship moriah says that cannot be true because the constant of proportionality are different with wich student do you agree with
Answer: I agree with Moriah. If two equations represent the same proportional relationship, then they should have the same constant of proportionality. In this case, the constant of proportionality in p = 1.5 and 2/3p = q is different, so the two equations cannot represent the same proportional relationship.
It's possible that the two equations represent two different proportional relationships, but without more information it's impossible to determine if that is the case.
Step-by-step explanation:
60. MODELING REAL LIFE You are designing an
obstacle course along a straight path. The distance
between obstacle three and obstacle seven is the
same as the distance between obstacle four and
obstacle nine. Show that the distance between
obstacle three and obstacle four is the same as the
distance between obstacle seven and obstacle nine.
By expression, x - y = x' - y' , Distance of 3rd and 4th obstacle is equal to distance of 7th and 9th obstacle.
What is distance?Distance is a numerical measurement of how far apart objects or points are, it is the length along a line or line segment between two points on the line or line segment.
Given,
The distance between obstacle three and obstacle seven is the same as the distance between obstacle four and obstacle nine.
Distance of 7th obstacle = x
Let,
Distance of 9th obstacle = y
Distance of 3rd obstacle = x'
Distance of 4th obstacle = y'
Distance between obstacle 3 and 7 = x - x'
Distance between obstacle 4 and 9 = y - y'
Distance between obstacle three and obstacle four = x' - y'
Distance between obstacle seven and obstacle nine.= x - y
According to the question
x-x' = y-y'
⇒ x - y = x' - y'
Hence, Distance between third and fourth obstacle is same as distance between 7th and 9th obstacle.
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on a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. what was the number of men on the sight-seeing tour?
As per the ratio, the number of men on the sight-seeing tour is 4.
In the given sight-seeing tour, we are told that there were 14 people in total. We are also given the ratio of women to children, which is 5 to 2. This means that for every 5 women on the tour, there were 2 children.
To find the number of men on the tour, we need to first find the number of women and children. We can do this by dividing the total number of people by the ratio of women to children.
Let's use a variable to represent the number of sets of 5 women and 2 children. We'll call this variable "x".
So, the number of women on the tour is 5x and the number of children is 2x.
Now, we can set up an equation to find the value of x:
5x + 2x = 14
This equation represents the total number of women and children on the tour, which is equal to 14.
Simplifying the equation, we get:
7x = 14
Dividing both sides by 7, we get:
x = 2
This means that there were 2 sets of 5 women and 2 children on the tour. So, the number of women is:
5x = 5(2) = 10
The number of children is:
2x = 2(2) = 4
Now, we can find the number of men by subtracting the number of women and children from the total number of people:
14 - 10 = 4
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Give an example of a matrix A and a vector b such that the solution set of Ax = b is a line in R^3 that does not contain the origin.
x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary, if k = 1
x = -1, y = 6, z = 1 is the solution.
Ax = [tex]\left[\begin{array}{ccc}1&1&1\\1&2&3\\1&4&7\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex]
and b = [tex]\left[\begin{array}{ccc}6\\14\\30\end{array}\right][/tex]
the augmented matrix is [A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\1&2&3:14\\1&4&7:30\end{array}\right][/tex]
we need to reduce the augmented matrix [A:B] to row echelon form by applying elementary row transformations only.
operating R₂→R₂-R₁ , R₃→R₃-R₁
[A:B] = [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&3&6:24\end{array}\right][/tex]
operating, R₃→R₃-3R₃
~ [tex]\left[\begin{array}{ccc}1&1&1:6\\0&1&2:8\\0&0&0:0\end{array}\right][/tex]
which is the row echelon, form of the matrix [A:B]
we have rank of [A:B] = the number of the non zero rows in echelon form = 2
also by the same elementary transformation we get,
A ~ [tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex]
∴ rank of A = 2
since rank A = rank [A:B] = 2 < number of unknowns
therefore, the given equation are consistent and will have an infinite number of solutions.
We see that the given system of equations is equivalent to the matrix equation
[tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\y\\z\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}6\\8\\0\end{array}\right][/tex]
which gives the equations x + y + z = 6 ........(1)
and y + 2z = 8 .......(2)
from (2), y = 8 - 2z, putting the value of y in (1) we get,
x = 6 - y - z = 6 (8 - 2z) z = z - 2
taking z = k, we get x = k - 2, y = 8 - 2k, z = k is the general solution of the given system, where k is an arbitrary,
if k = 1
x = -1, y = 6, z = 1 is the solution.
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Virat has 200 metres of wire, correct to the nearest metre.
he cuts the wire into n peices of length 3 metres, correct to the nearest 20 centimetres
The number of wires that cut from of 200 meters is 66 meters 66 centimeters.
What are the nearest two places?
The second place to the right of the decimal point, or the hundredth place, is used to round a decimal number to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70.
Given the length of the wire is 200 meters.
Assume that he cuts n pieces of length 3 meters.
The length of n pieces is 3n.
Therefore the equation is
3n = 200
n = 200/3
n= 66.66
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A geolo
gistis going to ship two granite specimen weighs 22 pounds and the crate weighs 20pounds the shipping crate weighs 8pounds the shipping crate is what percentage of the total weight of the shipment
The percentage of the shipping crate when compared to the total weight of the shipment would be = 16%
How to calculate the percentage of shipping crate?The weight of two granite specimen = 22 pounds
The weight of the crate = 20 pounds
The weight of shipping crate = 8 pounds
The total weight of the whole shipment = 22+20+8 = 50 pounds.
Therefore the percentage of shipping crate as compared to the total weight;
= 8/50 × 100/1
= 800/50
= 16%
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domain and range please help
Answer:
Domain is x-value and range is y-values
Step-by-step explanation:
Which best describes the graph of y≥-x² +8x-2?
The vertex is at (4, -14) The parabola is a solid line that opens down. Shading is above the line.
The vertex is at (4, 14). The parabola is a solid line that opens down. Shading is above the parabola.
The vertex is at (-4,-14). The parabola is a dotted line that opens down. Shading is below the parabola.
O The vertex is at (-4, 14). The parabola is a solid line that opens down. Shading is below the parabola.
A statement which best describes the graph of y ≥ -x² + 8x - 2 include the following: B. The vertex is at (4, 14). The parabola is a solid line that opens down. Shading is above the parabola.
How to determine the true statements about this quadratic function?Generally speaking, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. For this quadratic function, we can logically deduce that the graph is a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).
By critically observing the graph of the given quadratic function, we can logically deduce that the solutions (roots) and vertex are as follows;
x = 0.258, y = 0.
x = 7.742, y = 0.
Vertex = (4, 14).
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Find the image of (2,3) under a dilation with center at the origin and a scale factor of −3.
The image of (2, 3) under a dilation with center at the origin and a scale factor of −3 will be (-6, -9).
What is Image of a point ?
Dilation is the process of resizing or altering an object. With the aid of the specified scale factor, it is a transformation that reduces or enlarges the objects. The initial figure is referred to as the pre-image, while the new figure acquired after dilatation is known as the image.
Given point : (2,3)
the scale factor is -3 which means the point should be enlarged by -3 times to get the desired image.
So, we can write as : (a, b) where,
a = 2 × -3 = -6
and, b = 3 × -3 = -9
Hence, the coordinates of the image will be (-6, -9).
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in the better business bureau settled of complaints they received in the united states. suppose you have been hired by the better business bureau to investigate the complaints they received this year involving new car dealers. you plan to select a sample of new car dealer complaints to estimate the proportion of complaints the better business bureau is able to settle. assume the population proportion of complaints settled for new car dealers is , the same as the overall proportion of complaints settled in . use the z-table.
The answers are a) standard deviation ≈ 0.02 b) probability ≈ 0.95 c) standard deviation ≈ 0.031 d) probability ≈ 0.8098 e) decrease in P = 0.1402
Given: p = 75% or 0.75
n = 450
a) The sampling distribution of the sample proportion is approximately normal with mean = 0.75 and standard deviation is [tex]\sqrt \frac{p(1-p)}{n}[/tex]
= [tex]\sqrt{\frac{0.75(1-0.75)}{450} }[/tex] = 0.02
b) [tex]\^{p} - p[/tex] = 0.04
[tex]z = \frac{\^{p} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
z = ±1.96(approx.)
p(-0.04 < [tex]\^{p} - p[/tex] < 0.04)
=P(-1.96 < z < 1.96) = 1 - 2P(z < -1.96)
= 1 - 2(0.0250) = 0.95
c) The sampling distribution of the sample proportion is approximately normal with mean = 0.75 and standard deviation [tex]\sqrt \frac{p(1-p)}{n}[/tex]
= [tex]\sqrt{\frac{0.75(1-0.75)}{200} }[/tex] = 0.031
d) [tex]\^{p} - p[/tex] = 0.04
[tex]z = \frac{\^{p} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
z = ±1.31(approx.)
p(-0.04 < [tex]\^{p} - p[/tex] < 0.04)
=P(-1.31 < z < 1.31) = 1 - 2P(z < -1.31)
= 1 - 2(0.0951) = 0.8098
e) Determine the difference in probabilities (of part b) and part d))
The loss in precision by decreasing the sample size 0.9500 - 0.8098 = 0.1402
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Complete question is:
In 2008 the Better Business Bureau settled 75% of complaints they received. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.75, the same as the overall proportion of complaints settled in 2008. a) Suppose you select a sample of 450 complaints involving new car dealers. Show the sampling distribution of [tex]\overline{p}[/tex].b) Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion? c) Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of [tex]\overline{p}[/tex] . d) Based upon the smaller sample of only 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion? e) As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part (b)?
�
=
5
9
(
�
−
32
)
The equation above shows how temperature
�
, measured in degrees Fahrenheit, relates to a temperature
�
, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5
9
degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
For the given equation which shows the relation of temperature in Celsius and Fahrenheit, the correct option is Option D.
What is meant by temperature?
Indicating the direction in which heat energy will naturally flow from a hotter body (one with a higher temperature) to a colder body(one at a lower temperature), the temperature is a measure of hotness or coldness defined in terms of any of several arbitrary scales.
The given equation is:
[tex]C = \frac{5}{9} (F- 32)[/tex]
where C = temperature in Celsius
F = temperature in Fahrenheit
The above equation can be rewritten as:
C = 5/9F - 160/9
Now, this is an equation of a straight line with a formula,
y = mx + c
Comparing,
m = 5/9 which is the slope of the equation.
This means that for a temperature increase of 1 degree Fahrenheit, the equivalent increase in temperature in Celsius is 5/9.
So the option I is true.
Similarly, an increase in 1 degree Celsius of temperature is equivalent to 9/5 = 1.8 degree increase in Fahrenheit.
So option II is true.
Option III is not true as is discussed above.
Therefore for the given equation of temperature, the correct option is Option D.
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Answer:
D
Step-by-step explanation:
I have nothing else to say- lol
Calculate the amount of US dollars you can buy for R12 500 at an exchange
rate of 1 US$ R8,76.
Answer: To calculate the amount of US dollars you can buy for R12,500 at an exchange rate of 1 US$ = R8.76, you can use the following formula:
US$ = R12,500 / R8.76
Plugging in the values, we get:
US$ = R12,500 / R8.76 = 1,421.51
So, with R12,500, you can buy 1,421.51 US dollars at an exchange rate of 1 US$ = R8.76.
Step-by-step explanation:
The red triangle is a dilation of the blue triangle, with scale factor, k =
1.5.
Use the hotspots to fill in the missing measurements and similarity
statement.
R
20 cm
44°
S
Vide
26 cm
scale factor, k =
15
N
ARSTA
ange
1.5
57 cm
side
44°
121°
L
M
1. 121 degree. 2. 15 degree. The side of the dilated triangle increases by scale factor. Here, 1.5, thus: 3. LM = (20)(1.5) = 30 4. MN = 26(1.5) = 39 5. RT = 57/1.5 = 38. 6. Triangle RST is congruent to triangle LMN.
What is transformation?Transformations involve the reflection, refraction, or translation of forms on a coordinate plane. Felix Klein put forth a novel perspective on geometry in the 19th century called transfinite geometry. The majority of geometric principles depend on the transmissions of objects.
Transfrmatiions enable the modification of any image in a coordinate plane. You can better understand the graphics in video games by using the mathematical laws of transmission.
As a result, the red triangle is a dilation of the blue triangle.
When triangle is dilated the angles remain the same. Thus,
1. 121 degree.
2. 15 degree.
The side of the dilated triangle increases by scale factor. Here, 1.5, thus:
3. LM = (20)(1.5) = 30
4. MN = 26(1.5) = 39
5. RT = 57/1.5 = 38
6. Triangle RST is congruent to triangle LMN.
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I really need help! Can you help??
Answer:
To convert 6 feet into meters, first create a conversion factor to convert from feet to meters. Make sure the original unit is in the denominator, then cancel feet. Next, multiply the original measure by the conversion factor to get 1.8288 meters, or 1.83 meters if you simplified it.
Step-by-step explanation:
Find the length of the unknown side of the triangle.
10 ft
5 ft
The length of the unknown side of the triangle is?
Answer:
The length of the unknown side of the triangle is
[tex]5 \sqrt{5} [/tex]
Classify each ordered pair as a solution or not a solution of the inequality y
a inequality y <2/7 x − 5.
The ordered pairs (21, 0) and (6, -4) are the solutions to the given inequality.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is y<2/7x-5.
Here,
Put (x, y)=(21, 0) in the given inequality, we get
0<2/7(21)-5
0<1
So, it is solution
Put (x, y)=(6, -4) in the given inequality, we get
-4<2/7(6)-5
-4<12/7-5
-4<1.7-5
-4<-3.3
So, it is solution
Put (x, y)=(0, -5) in the given inequality, we get
-5<2/7(0)-5
-5<-5
Which is not true, it is not a solution
Put (x, y)=(7, -3) in the given inequality, we get
-3<2/7(7)-5
-3<-3
Which is not true, it is not a solution
Therefore, the ordered pairs (21, 0) and (6, -4) are the solutions to the given inequality.
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How to Solve this question ??
The coordinates of the fourth vertex of the parallelogram are (1, -3).
What is Parallelogram?A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
Three vertices are located at these coordinates: (-1, 2), (1, 2), and (-1,-3).
we have three points in the coordinate plane, we can use the concept of vector addition to find the fourth point.
The vectors connecting the first and second points, and the first and third points can be determined as follows:
v₁ = (1,2) - (-1,2) = (2,0)
v₂ = (-1,-3) - (-1,2) = (0,-5)
The fourth point will be located at the vector sum of the first point and the vector formed by adding v₁ and v₂.
v₃ = v₁ + v₂ = (2,0) + (0,-5) = (2,-5)
So, the fourth point will be located at:
(-1,2) + (2,-5) = (1,-3)
Thus, the coordinates are (1, -3).
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Find the circumference of each of the circle with the following radius. A. 10 cm
B. 2. 7 cm
C. 1. 2 mm
D. 9. 01 cm
A. 10 cm radius: 2 * pi * 10 cm = 62.83 cm
B. 2.7 cm radius: 2 * pi * 2.7 cm = 16.94 cm
C. 1.2 mm radius: 2 * pi * 1.2 mm = 7.54 mm
D. 9.01 cm radius: 2 * pi * 9.01 cm = 56.76 cm
A. The circumference of a circle with a radius of 10 cm is 62.83 cm.
B. The circumference of a circle with a radius of 2.7 cm is 16.94 cm.
C. The circumference of a circle with a radius of 1.2 mm is 7.54 mm.
D. The circumference of a circle with a radius of 9.01 cm is 56.76 cm.
The circumference of a circle is the distance around its edge. It can be calculated using the formula 2πr, where r is the radius of the circle. The radius is the distance from the center of the circle to any point on its edge. To find the circumference of a circle, we need to multiply the radius by 2 and then by pi (π), which is roughly 3.14.
For example, if the radius of the circle is 10 cm, then the circumference of the circle is 2πr = 2π x 10 cm = 62.83 cm. Similarly, if the radius of the circle is 2.7 cm, then the circumference of the circle is 2π x 2.7 cm = 16.94 cm. If the radius of the circle is 1.2 mm, then the circumference of the circle is 2π x 1.2 mm = 7.54 mm. Finally, if the radius of the circle is 9.01 cm, then the circumference of the circle is 2π x 9.01 cm = 56.76 cm.
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