Answer: The transformation matrix R for a rotation of 120° about an axis from the origin through the point (1,1,1) can be calculated using the formula:
R = I + (sin(θ))U + (1-cos(θ))UU'
where θ is the angle of rotation (120° in this case), I is the identity matrix, U is a skew-symmetric matrix, and U' is its transpose. The skew-symmetric matrix can be calculated as follows:
U = [0, -z, y; z, 0, -x; -y, x, 0]
where x, y, and z are the components of the vector (1,1,1) that defines the axis of rotation.
Plugging in the values and simplifying, the transformation matrix R is:
R = [ cos(120°), -sin(120°), 0; sin(120°), cos(120°), 0; 0, 0, 1 ]
Note: cos(120°) = -1/2 and sin(120°) = √(3)/2.
Step-by-step explanation:
1. Yes-AA
2. Yes- SAS
3. Yes- SSS
4. No- Not Similar
The triangles are similar to the AA property.
What are similar triangles?If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.
Similar figures are items that feature more than two figures that are the same shape but different sizes.
Given triangles ANF and HES
for ΔANF,
∠A = 29°, ∠N = 106°, and ∠F = 45°(from angle sum property)
for ΔHES
∠H = 45°, ∠S = 29° and ∠E = 106°(from angle sum property)
so ∠A = ∠S
∠N = ∠E
and ∠F = ∠H
so ΔANF ≈ ΔHES
by AA similarity.
Hence option A is correct.
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I need help please!
What did Nixon's visit to China prove to the US?
A. If you can deal with one communist nation, others will likely join in
B. The Soviet Union was close to falling apart and communism would leave Eastern Europe
C. Most communist nations actually practice capitalism and have free elections
D. The communist world was not a single entity, and had many different positions
Nixon's visit to China was intended to advance their relationship and create new trade opportunities.
Why was Nixon's visit to China?The President stated on live television that he would visit the PRC in 1972 on July 15, 1971. The American public was able to see photos of mainland China for the first time in more than 20 years during the week-long tour, which took place from February 21 to 28, 1972.
Nixon intended to protect the global populace, which meant he wanted to improve relations amongst the world's superpowers. Nixon's visit to China was intended to advance their relationship and create new trade opportunities.
A significant step in normalizing diplomatic ties with China, Nixon's visit was a big success. The following year, American tourists began to travel there, and American business organizations established a booming trade with China. The United States and China achieved complete diplomatic ties by the year 1979.
Therefore, the correct answer is option B. The Soviet Union was close to falling apart and communism would leave Eastern Europe.
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A particle that moves along a straight line has velocity
v(t)=t^2e^(-5t)
meters per second after t seconds. How many meters will it travel during the first t seconds (from time=0 to time=t)?
The dot plot shows the ages of the 20 people currently in Ms. Jens classroom.
Which MEASURE OF VARIATION would be best to describe this distribution
A. median
B. interquartile range
C. range
D. mean
The correct measure of variation for best to describe this distribution is,
⇒ interquartile range
Option B is true.
What is interquartile range?For a data set has outliers and variability is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles.
Given that;
The dot plot shows the ages of the 20 people currently in Ms. Jens classroom.
Hence, To describe this distribution we can use the interquartile range.
Thus, The correct measure of variation for best to describe this distribution is,
⇒ interquartile range
Option B is true.
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The perimeter of a square must be greater than 138
inches but less than 186
inches. Find the range of possible side lengths that satisfy these conditions. (Hint: The perimeter of a square is given by P=4s
, where s represents the length of a side).
Express your answer in interval notation. Use decimal form for numerical values.
The range of possible side lengths that satisfy the these conditions is given as follows:
34.5 < s < 46.5.
How to obtain the perimeter of a square?The perimeter of a square of side length s is given by the multiplication of 4 by s, as follows:
P = 4s.
Hence, for a square with perimeter of 138 inches, the side length is given as follows:
4s = 138
s = 138/4
s = 34.5 inches.
For a square with perimeter of 186 inches, the side length is given as follows:
4s = 186
s = 186/4
s = 46.5.
Hence the interval is given as follows:
34.5 < s < 46.5.
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Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst states we can therefore assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.
A sample of 76 stocks traded on the NYSE that day showed that 36 went up.
You are conducting a study to see if the proportion of stocks that went up is is significantly more than 0.3. You use a significance level of .
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
The test static value for the stocks is obtained as 3.482.
What is proportion?
In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.
It is given that -
The number of stocks n = 76
X = Number of stocks that got increased in price = 36
p = Proportion of stocks that got increased in price.
The formula for p is p = X/n.
Substitute the values in the equation -
p = 76/36 = 2.11111
Now find the value for q -
q = 1 - p
= 1 - 2.11111
= -1.11111
P=0.3
Q = 1 - P
= 1 - 0.3
= 0.7
Now, the values for H0 and H1 are -
H0 : P = 0.3
H1 : P > 0.3
Under H0, the test statistic is given by -
Z = (p - P)/√(PQ/n)
Substitute the values in the equation -
Z = (2.11111 - 0.3)/√(0.3 × 0.7/76)
Z = 1.81111 /√0.002763
Z = 1.81111 /0.052
Z = 3.482
Therefore, test statistic is 3.482.
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NO LINKS!! URGENT HELP PLEASE!!!
1. Make a table showing the length, width, and area for every rectangle with a perimeter of 20 meters and whole-number side lengths. Describe some patterns that you observe in the table.
2. Make a graph of the data(length, area). Describe the shape of the graph.
3. How does the pattern in the table appear in the graph?
Answer:
1. See below.
2. See attachment.
3. See below.
Step-by-step explanation:
Question 1Definition of variables:
Let w be the width of the rectangle.Let l be the length of the rectangle.A rectangle has two pairs of parallel sides of equal length.
Therefore, the equation for the perimeter of a rectangle is:
[tex]P=2(w+l)[/tex]
If the perimeter is 20 meters then:
[tex]\implies 2(w+l)=20[/tex]
[tex]\implies w+l=10[/tex]
If the side lengths are whole numbers, then the length and width are restricted to whole numbers from 1 to 9 (inclusive).
The equation for the area of a rectangle is:
[tex]A =w\cdot l[/tex]
Table
[tex]\begin{array}{|c|c|c|}\cline{1-3}\vphantom{\dfrac12}\textsf{width, m}&\textsf{length, m}&\textsf{Area, m$^2$}\\\cline{1-3}\vphantom{\dfrac12}1&9&9\\\cline{1-3}\vphantom{\dfrac12}2&8&16\\\cline{1-3}\vphantom{\dfrac12}3&7&21\\\cline{1-3}\vphantom{\dfrac12}4&6&24\\\cline{1-3}\vphantom{\dfrac12}5&5&25\\\cline{1-3}\vphantom{\dfrac12}6&4&24\\\cline{1-3}\vphantom{\dfrac12}7&3&21\\\cline{1-3}\vphantom{\dfrac12}8&2&16\\\cline{1-3}\vphantom{\dfrac12}9&1&9\\\cline{1-3}\end{array}[/tex]
As the width increases by 1 m, the length decreases by 1 m.The values for area are symmetric about the point when width and length are the same.The step pattern of the values of area in the table are 7, 5, 3, 1, ...To create a graph of the data, plot the length along the x-axis and the area along the y-axis. Plot the following points:
(9, 9), (8, 16), (7, 21), (6, 24), (5, 25), (4, 24), (3, 21), (2, 16) and (1, 9).The shape of the graph is a parabola that opens downwards.
Its vertex is (5, 25) and its axis of symmetry is x = 5.
Question 3This step pattern of 7, 5, 3, 1, ... is apparent in the graph; as you move away from the vertex in the x-direction, the graph goes down by 7, then 5, then 3, etc. This is the step pattern of a parabola that opens downwards.
There is an axis of symmetry on the graph at the side length value when the width and length are the same (x = 5).
In a trial examination session a candidate at a school has to take of these In the chemistry paper and the biology paper. No two including the physics paper, three papers may be taken consecutively. There is no restriction other examination papers may be taken.
Find the number of different orders in which these 18 examination papers may be taken.
Answer:
What I did was:
Number of possible outcomes when three science papers are together: 3!×16!
Number of possible outcomes when two science papers are together: 2!×17!
Therefore, the answer is 18!−3!×16!−2×17!
I feel like there's some faulty logic in the second line. Correct answer is 4.39×10 15th
.
The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm.
Round the probabilities to four decimal places.
It is possible with rounding for a probability to be 0.0000..
c) Find the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less.
this my homework problem
The probability that a randomly selected Atlantic cod has a length of 53.68 cm or less is given by the equation P ( x < 53.68 ) = 0.8439
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less be represented as P
Now , the equation will be
The observed value of x = 53.68 cm
The mean of the sample μ = 49.9 cm
The standard deviation of the sample σ = 3.74 cm
Now , z-score is calculated using the formula:
z = (x - μ)/σ
Substituting the values in the equation , we get
z = ( 53.68 - 49.9 ) / 3.74
z = 1.0107
Now ,the p value from the z table is
P ( x < 53.68 ) = 0.84392
And , the probability is P ( x < 53.68 ) = 84.392 %
Hence , the probability is 84.392 %
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EXTRACURRICULARS The table shows the results of a survey about what students plan to do after school. How can you determine the probability that a student selected at random will be doing homework or participating in a sport after school? Justify your reasoning.
As a result, there is a 52% chance that a pupil chosen at random will be doing homework or playing an activity after school.
What is a Probability example?By reducing the number of positive outcomes by the overall number of potential outcomes, probability—the chance that a will occur—is determined. The most basic illustration is a coin toss. There are just two results when users flip a coin: either it shows up heads or tails.
We need to discover the sum of the percentage of students who plan to do homework and the percentage of students who plan to engage in a sport in order to calculate the likelihood that a student chosen at random will be doing homework or playing a sport after school.
Therefore, the likelihood that a pupil chosen at random will be working on homework or playing an activity after school is:
24% + 28% = 52%
This is because the two events are not mutually exclusive, and a student may plan to do both activities after school.
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The deck of a bridge is suspended 205 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by y = 205 − 16t2.
(a)
Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 2 and lasting the following amount of time.
(i)
0.1 seconds
ft/s
(ii)
0.05 seconds
ft/s
(iii)
0.01 seconds
ft/s
(b)
Estimate the instantaneous velocity (in ft/s) of the pebble after 2 seconds.
ft/s
The required answers are
i) -65.6
ii) -64.8
iii) -64
iv) -64
VelocityThe pace at which an object's position changes in relation to a frame of reference and time is known as its velocity.
Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.
Its SI equivalent is the metre per second (ms-1). A body is considered to be accelerating if its velocity changes, either in magnitude or direction.
Now in the given question,
1. Average velocity
When t=2
i. [2, 2.1]
= y(2.1) - y(2) / 2.1 - 2
= 205 - 16(2.1)^2 - 205 + 16(2)^2 / 0.1
= 205 - 16*4.41 - 205 +16(4) / 0.1
= -70.56 +64 / 0.1
= -6.56 /0.1
= -65.6
ii. [2, 2.05]
= y(2.05) - y(4) / 4.05 - 4
= 205 - 16(2.05)^2 - 205 +16(2)^2 / 0.05
= 205 - 16*4.2025 - 205 + 16(4) / 0.05
= -3.24 / 0.05
= -64.8
iii. [2, 2.01]
= y(2.01) - y(2) / 2.01 - 2
= 205 - 16(2.01)^2 - 205 + 16(2)^2 / 0.01
= 205 - 16*4.0401 - 205 + 16(4) / 0.01
= -64.64 + 64 / 0.01
= -0.64 / 0.01
= -64
iv. Instantaneous velocity
y = 205 - 16t^2
dy/dx = -32t
Considering t = 2
Instantaneous velocity after 2 seconds = -32(2)
Instantaneous velocity after 2 seconds = -64
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Packages move along a conveyor belt and are dumped into an ever growing pile. After t minutes, the pile grows at a rate of 2 + 8 t packages per hour. Define p(t) to equal the approximate number of packages in the pile after t minutes. If there are 13 packages in the pile when t = 0 minutes, how approximately how many packages are there in the pile after 30 minutes?
There are 15 packages in the pile after 30 minutes.
How to determine the number of packagesFrom the question, we have the following parameters that can be used in our computation:
Rate = 2 + 8t packages per hour
To find the number of packages after t minutes, we need to integrate the rate of growth of the pile over time.
We can use the formula:
p(t) = p(0) + ∫_0^t (2 + 8t) dt
where p(0) = 13 is the number of packages in the pile at t = 0.
Evaluate
P(t) = 13 + 2t + 4t^2
For t = 30 minutes, which is equal to 0.5 hours, we have:
P(30) = 13 + 2 * 0.5 + 4 * 0.5^2
P(30) = 15
So, approximately there are 15 packages in the pile after 30 minutes.
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algebra please help evaluate the function
The required individual functions are given as g(x) = x⁴- 6 and f(x) = [tex]\sqrt[7]{x}[/tex].
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given funciton
h(x) = (f o g) (x)
Where g(x) = x⁴- 6 and h(x) = [tex]\sqrt[7]{x^4-6}[/tex]
Since, put h(x) ⇒ f(x) and g(x) = x⁴- 6
f(x) = [tex]\sqrt[7]{g(x)}[/tex]
Again put g(x) ⇒ x
f(x) = [tex]\sqrt[7]{x}[/tex]
Thus, the required individual functions are given as f(x) = x⁴- 6 and g(x) = [tex]\sqrt[7]{x}[/tex].
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2 Two points located on JK are J(-1,-9) and K(5,3). What is the slope of JK
A. -2
B. -1/2
c. 1/2
D. 2
Answer:
2
Step-by-step explanation:
To find the slope when given two points, we can use the formula
m = ( y2-y1)/ (x2-x1)
= ( 3- -9)/( 5 - -1)
= ( 3+9) / ( 5+1)
= 12/6
= 2
The slope is 2.
How many fifths are there in 6 and 4/5?
Answer:
Step-by-step explanation:
0
Solve for x
4|3x+5|-4=64
Answer:
x=4
Step-by-step explanation:
12x+20-4=64
12x+16=64
12x=64-64
12x=48
x=4
Hi HELLPPPPPPPP PLEASE HELP I WILL MARK BRAINLEST IF YOU HELP ME!!! Find the volume of each solid and round to the nearest tenth if necessary..
ANSWER BOTH!!!!!
The volume of a sphere of radius 5 yd is 523.33 yd³.
What is the volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
We have given,
the radius of a sphere is 5 yd,
To Find: the volume of the sphere solid
So,
Sphere volume = 4/3 πr³
= 4/3 * 3.14 * (5)³
= 4/3 * 3.14 * 125
= 523.33 yd³
Hence, the volume of a sphere of radius 5 yd is 523.33 yd³.
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Find a unit vector with positive first component that is orthogonal to the plane passing through the pointsP=(4,5,−7),Q=(13,14,2), andR=(13,14,8)
The unit vector with positive first component that is orthogonal to the plane passing through the points is 63i - 63j + 0k.
What is a unit vector?
A measurement that combines magnitude and direction is called a vector. A vector having magnitude 1 is referred to as a unit vector.
We are given three points P, Q and R.
The two vectors PQ and PR will lie on the plane through the three given points P(3, 0, 1), Q(4, -2, 1) & R(5, 3,-1).
The vector PQ = (9, 9, 9) and PR = (9, 9, 16) .
Therefore, the required vector is
N = PQ × PR
N = 63i - 63j + 0k
Hence, the unit vector with positive first component that is orthogonal to the plane passing through the points is 63i - 63j + 0k.
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Evaluate the definite integral of: ∫_0^π (sin(x))^3 dx
Step-by-step explanation:
The definite integral of (sin(x))^3 from 0 to π can be evaluated using a trigonometric identity.
∫_0^π (sin(x))^3 dx = -cos(x)(sin(x))^2 |_0^π
Using the fact that sin(0) = 0 and sin(π) = 0, we have:
-cos(x)(sin(x))^2 |_0^π = -cos(π)(sin(π))^2 + cos(0)(sin(0))^2
= 0 - (-1)(0)^2 = 0
Therefore, the definite integral of (sin(x))^3 from 0 to π is equal to 0.
Find the volume of a sphere with radius 13. Use 3.14 for pi, round your answer to the nearest hundredth if necessary, and do not include units.
the volume of a sphere:
V=[tex]\frac{4\pi r^3}{3} =\frac{4*3.14*13^3}{3}[/tex]≈9198.106
HOME LIFE In a survey, 837 people were asked about their living arrangements. Of the people surveyed, 329 of them lived in apartments. Of the 629 people who live with at least one other person, 218 live in an apartment.
Using this data, if a person is chosen at random, what is the probability that he or she is living with another person, given that they live in an apartment?
The probability that a person lives with another person, given that they live in an apartment, is approximately 0.664.
We need to utilise conditional probability to determine the likelihood that a person lives with another person given that they reside in an apartment.
Let's define the subsequent occasions:
A: at least one other person lives with the individual.
B: The resident is an apartment dweller.
The probability that a person shares a home with at most one other person, assuming that they reside in an apartment, is P(A|B).
We are aware of:
The probability that someone resides in an apartment is P(B) = 329/837.
The probability that a person shares a home with at most one other person, given that they reside in an apartment, is given by P(A|B) = 218/329.
P(A|B) can be calculated using Bayes' theorem as follows:
P(A|B) equals P(B|A)*P(A)/P (B)
We may calculate P(B|A), the probability that an individual resides in an apartments given that they share a residence with at most one other person, using the following formula:
P(A and B) = P(B|A) (A)
We are aware of:
The probability that someone lives in an apartment with at most one other person is P(A and B) = 218/837.
The probability that someone lives with at most one other person is P(A) = 629/837.
By entering these values, we obtain:
P(B|A) = (218/837) / (629/837) = 218/629
Now that all the numbers have been entered, we can calculate P(A|B):
P(A|B) = (218/629) * (629/837) / (329/837) = 0.664
Given that they reside in an apartment, the probability that a person lives with another individual is roughly 0.664.
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The expression of f(x)=10,000(1.15)^x represents the population of Nashville each year. If x% represents the growth rate for each year, what is the value of x?
So, the growth rate for each year, x%, can be calculated using the above formula if the population of Nashville for a specific year, f(x)= (ln(f(x) / 10,000) / ln(1.15)) * 100, is known.
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.
Here,
The expression f(x)=10,000(1.15)^x represents the population of Nashville each year, where x is the number of years after a certain reference point. The growth rate for each year can be found by taking the natural logarithm of the factor (1.15) in the expression:
ln(1.15^x) = ln(f(x) / 10,000)
x ln(1.15) = ln(f(x) / 10,000)
x = ln(f(x) / 10,000) / ln(1.15)
The value of x represents the growth rate as a percentage, so we need to multiply it by 100 to get the percentage:
x = (ln(f(x) / 10,000) / ln(1.15)) * 100
So, the growth rate for each year, x%, can be calculated using the above formula if the population of Nashville for a specific year, f(x)= (ln(f(x) / 10,000) / ln(1.15)) * 100, is known.
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Midwives Researchers Sally Tracy and associates undertook a cross-sectional study looking at the method of delivery and cost of delivery for first-time “low risk” mothers under three delivery scenarios: (1) Caseload midwifery (2) Standard hospital care (3) Private obstetric care The results of the study revealed that 58.5% of all births with midwifery were vaginal deliveries compared with 48.2% of standard hospital births and 30.8% of private obstetric care. In addition, the costs of delivery from midwifery was $3903.78 compared with $5279.23 for standard hospital care and $5413.69 for private obstetric care. (a) Why is this a cross-sectional observational study? (b) Name the explanatory variable in the study. (c) Name the two response variables in the study and determine whether each is qualitative or quantitative.
Note that:
a) This is a cross-sectional observational study because the data was collected from a single point in time and the observations were made without any manipulation of the variables by the researchers.
b) The explanatory variable in the study is the method of delivery (Caseload midwifery, Standard hospital care, Private obstetric care).
c) The two response variables in the study are the rate of vaginal deliveries (58.5%, 48.2%, 30.8%) and the cost of delivery ($3903.78, $5279.23, $5413.69). The rate of vaginal deliveries is a qualitative variable as it is a categorization of the type of delivery, while the cost of delivery is a quantitative variable as it is a measure of the amount of money spent on delivery.
What is a cross-sectional observational study?It is to be noted that a cross-sectional observational study is a type of study in which data is collected from a single point in time without any manipulation of variables by the researchers.
The data collected provides a snapshot of the variables at that point in time.
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CAN SOMEONE HELP WITH THIS?✨
In the polynomial f(x) = 3x² - 2x + 5, f(0) is solved to get -2
From the equation of the tangent line
m= -2
b = 5
How to find the derivativeThe derivative of the polynomial f(x) = 3x² - 2x + 5 is solved to be
f'(x) = 2(3)x - 1(2)
f'(x) = 6x - 2
f(0) = -2
Equation of the tangent to the parabola f(x) = 3x² - 2x + 5
f'(x) = 6x - 2 at x = 0, f'(x) = -2 hence the slope, m is -2
Using the point slope formula for (0, 5)
(y - 5) = m (x - 0)
y - 5 = -2x - 0
y = -2x + 5
comparing with y = mx + b
m = -2 and b = 5
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Express f squared - 6f + 7 in completed square form.
Find the exact lengths of the sides of quadrilateral ABCD with vertices A(4, 5), B(-3, 3), C(-6,-13) and D(6,-2).
As a result, the answers to the above quadrilateral issue are A.5, B.2, 3, C.-1/5, and D.2/3.
what is quadrilateral ?In terms of the geometry, a quadrilateral is really a four-sided polygon with four corners and four corners. Its origins originate from the Latin terms tetra and latus (meaning "side"). A rectangle is a this double form with four sides, 4 vertices, with four corners. Two main types of convex and convex exist. Convex bedbugs or bed bug also have a number of subclasses, such as trapezoids, parallelograms, quarters, rhombuses, and squares. Corresponding points come in many irregular configurations, such as quadrilaterals, trapezoids, rectangles, kites, square, and rhombuses.
given
The vertices of the quadrilateral ABCD are A(-4, -5), B(-3, 0), C(0, 2), and D. (5, 1).
We need to determine whether ABCD is a trapezoidal shape or not.
We are known that a trapezoid has one set of parallel opposed sides, making it a quadrilateral. Moreover, the slopes of two parallel lines are equal.
To start, the slopes of sides AB, BC, CD, and DA will be calculated.
It has
The incline for
AB =0+5/ -3+4
5. In the first step.
Step 2: The slope in BC is
=> 2-0 / 0+3
=> 2/3.
Step 3: The CD's gradient is
1-2/5-0 is equivalent to -1/5.
The gradient of DA is equal to in step four.
=>-5.1/-4.4/2.3
=>2/3.
As a result, the answers to the above quadrilateral issue are A.5, B.2, 3, C.-1/5, and D.2/3.
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A plumber had two pipes. The ratio of the legth of the longer pipe to the shorter pipe was 9:2. When he cut 1.65m from the longer pipe, the remaining length was 3 times that of the shorter pipe. Find the length of the shorter pipe in meters
The length of the shorter pipe will be 1.065 meters.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a plumber had two pipes. The ratio of the length of the longer pipe to the shorter pipe was 9:2.
When he cut 1.65m from the longer pipe, the remaining length was 3 times that of the shorter pipe.
L / S = 9 / 2
L - 1.65 = 3S
4.5S - 1.65 = 3S
1.5S = 1.65
S = 1.065 meters
Hence, the measure of the short pipe will be 1.065 meters.
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A light bulb consumes 1800 watt-hours per day. How long does it take to consume 5850 watt-hours?
days hours
X
S
Answer:
it takes 0.30769 days or 7.3846 hours for the light bulb to consume 5850 watt-hours.
Step-by-step explanation:
To solve for the time, we can set up a proportion:
1800 watt-hours / day = X / 5850 watt-hours
Cross-multiplying, we get:
1800 watt-hours * 1 day = X * 5850 watt-hours
Simplifying, we get:
X = (1800 watt-hours * 1 day) / 5850 watt-hours
X = 0.30769 days
To convert to hours, we can multiply by 24:
X = 0.30769 days * 24 hours/day
X = 7.3846 hours
Therefore, it takes 0.30769 days or 7.3846 hours for the light bulb to consume 5850 watt-hours.
Use synthetic division to find the result when 4x³ + 7x² - 4x - 4 is divided by
x + 1. If there is a remainder, express the result in the form q(x) + r(x)
b(x)
Solving the following expression (4x4-7x3+7x2-12x+15)/(x-1) yields the result -7x2 + 4 + 19/ in the form q(x)+r(x)/b(x) (x-1).
what is expression ?It is permissible to multiply, divide, add, or subtract in mathematics. The following is how an expression is put together: Number, term, and mathematical operator Three components of a numerical method include numbers, variable, and processes (such as addition, subtraction, multiplication or division etc.) It is possible to oppose expressions and words. An expression, often known as an analytical form, is any mathematics statement that contains variables, values, and an arithmetic procedure between them. For instance, the word m in the balanced formula is separated from the terms 4m and 5 by that of the arithmetic symbol +, as is the term m in the expression 4m + 5.
given
Given expression is (4x⁴-7x³+7x²-12x+15)/(x-1)
then dividing this
=4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1
=4x³-3x²+4x-8+7/x-1 in form of q(x)+r(x)/b(x)
= 4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1
= -7x² + 4 + 19/(x-1)
Solving the following expression (4x4-7x3+7x2-12x+15)/(x-1) yields the result -7x2 + 4 + 19/ in the form q(x)+r(x)/b(x) (x-1).
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A 30-foot ladder reaches the wall at 20 feet above the ground. Find the measure of the angle that ladder makes with the ground and round to the nearest tenth of a degree
The measure of the angle that ladder makes with the ground 41.8°.
What is the measure of the angle that the ladder makes with the ground?Given the data in the question;
This forms a right triangle.
Angle that ladder makes with the ground θ = ?Opposite of angle θ = 20ftHypotenuse = 30ftTo find the angle, we use trigonometric ratio.
Sine = Opposite / Hypotenuse
sinθ = 20ft / 30ft
sinθ = 2/3
θ = sin⁻¹( 2/3 )
θ = 41.8°
Therefore, the measure of the angle is 41.8°.
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