Answers
The trigonometric ratios of sine and cosines indicates that we get;
θ = 35 degreesθ = 62 degreesθ = 90 - yWhat are trigonometric ratios?Trigonometric ratios specify the relationship between two sides of a right triangle and the acute angle in the right triangle.
The specified equations are presented as follows;
1. sin(55) = cos(θ)
The sine of an angle is the ratio of the opposite side to the angle in a right to the hypotenuse side of the right triangle
The trigonometric ratio of the cosine of an angle is the ratio of the adjacent side to the angle to the hypotenuse side in a right triangle
The acute angles in a right triangle are complementary
Let A and B represent the acute angles of a right triangle, we get;
The adjacent side to the angle A is the opposite side to the angle B
The hypotenuse side remains the same, therefore;
cos(A) = sin(B), and sin(A) = cos(A)
Which indicates; sin(55) = cos(90 - 55) = cos(35)
sin(55) = cos(θ) = cos(35)
θ = 352. cos (28) = sin(90 - 28) = sin(62)
cos(28) = sin(62)
sin(θ) = sin(62) = cos(28)
θ = 623. cos(y) = sin(θ)
cos(y) = sin(90 - y)
cos(y) = sin(90 - y) = sin(θ)
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Related Questions
Find the
1. End behavior
2. X-intercepts
3. Positive/negative
4. Multiplicity
Answers
The end behavior is as x approaches negative infinity, f(x) approaches negative infinity as x approaches positive infinity, f(x) approaches negative infinity The only x-intercept of f(x) is x = 3.
What is the end behavior and x - intercepts of the functionThe given function is f(x) = -x³ + 2x² + 3
1. End behavior:
As the leading coefficient of f(x) is negative, -x^3 dominates the behavior of the function as x approaches negative or positive infinity. Therefore, the end behavior of the function is:
As x approaches negative infinity, f(x) approaches negative infinity.As x approaches positive infinity, f(x) approaches negative infinity.2. X-intercepts:
To find the x-intercepts of f(x), we need to solve the equation f(x) = -x^3 + 2x^2 + 3 = 0. We can factor out a common factor of -1 to simplify the equation:
-x^3 + 2x^2 + 3 = 0
x^3 - 2x^2 - 3 = 0
Using synthetic division or long division, we can find that one of the roots of this equation is x = 3. We can then factor out (x - 3) using polynomial division to find the other two roots:
x^3 - 2x^2 - 3 = (x - 3)(x^2 + x + 1)
The quadratic factor x^2 + x + 1 has no real roots, so the only x-intercept of f(x) is x = 3.
3. Positive/negative:
To determine the sign of f(x) for different values of x, we can look at the sign of each factor in the polynomial:
The leading coefficient of f(x) is negative, so for very large negative or positive values of x, f(x) is negative.The factor -x^3 is negative for negative values of x and positive for positive values of x.The factor 2x^2 is positive for all values of x.The constant term 3 is positive.Putting these together, we can make the following sign chart for f(x):
x f(x)
x < 0 -
0 < x < 3 +
x > 3 -
4. Multiplicity:
The only root of f(x) is x = 3, which has multiplicity 1. This means that the graph of f(x) crosses the x-axis at x = 3 and changes sign at that point.
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How is the series 3+5+7+...+51 represented in sigma notation?
Answers
Answer:
The third one
Step-by-step explanation:
The only one which gives the last number of the sequence is the third one as subbing in 16 you get 3×16 + 3 = 48 + 3 = 51
Share £400 between Alice and Brian in the ratio 1:4
Answers
Alice will receive £80 and Brian will receive £320
When dividing an amount of money in a given ratio, we need to first determine the total number of parts that the ratio is divided into.
In this case, the ratio between Alice and Brian is 1:4. This means that for every 1 unit of money that Alice receives, Brian receives 4 units of money. Therefore, the total number of parts in this ratio is 1 + 4 = 5.
To divide £400 in the ratio of 1:4, we need to find out how much of the total amount each part represents. To do this, we divide the total amount by the total number of parts:
£400 ÷ 5 = £80
So each part in this ratio represents £80.
Now that we know the value of each part, we can calculate how much Alice and Brian will receive.
Alice's share is one part, which represents £80. Therefore, Alice will receive
1 part x £80 = £80
Brian's share is four parts, which represents 4 x £80 = £320. Therefore, Brian will receive:
4 parts x £80 = £320
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Can someone please tell me what x+
Answers
When BD is perpendicular tο AC, the value οf x is fοund tο be 19°.
What is meant by perpendicular lines?
When twο lines crοss at a straight angle οr 90 degrees, perpendicular lines are created. Perpendicularity is the name given tο this characteristic οf lines. A straight line that fοrms a right angle (90 degrees) with anοther line is referred tο as being perpendicular.
In οther wοrds, twο lines are perpendicular tο οne anοther if they cοnnect at a right angle. The term "perpendicular tο all pοints in the plane" οr "perpendicular tο each line it intersects" is used tο describe a line that is perpendicular tο the plane. Perpendicular lines always intersect at 90 degrees but nοt all intersecting lines are perpendicular.
Given a vectοr diagram.
It is given that BD is perpendicular tο AC.
m∠CBE = (5x - 42)°
m∠CBE = (2x - 1)°
Since BD is perpendicular tο AC,
m∠DBC = m∠DBA = 90°
Nοw,
m∠DBC = 90°
m∠CBE + m∠CBE = m∠DBC
Then we can write,
m∠CBE + m∠CBE = 90°
(5x - 42)° + (2x - 1)° = 90°
7x - 43 = 90
7x = 133
x = 133 / 7 = 19°
Therefοre when BD is perpendicular tο AC, the value οf x is fοund tο be 19°.
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six factorial plus five factorial minus four factorial all divided by four factorial
Answers
= 34
Step by step solved:
We can simplify the expression using the factorial notation:
6! + 5! - 4! / 4!
= (720) + (120) - (24) / (24)
= 816 / 24
= 34
Therefore, the value of the expression is 34.
Write an equation of the line passing through the point (8,3) that is parallel to the line y=-3/4+4
Answers
The equation of the line passing through the point (8,3) that is parallel to the line y=-3/4+4 is y = (-3/4)x + 9.
The slope of the given line is -3/4. The desired line will likewise have a slope of -3/4 because it is parallel to this line.
The equation of the line travelling through the point (8,3) with a slope of -3/4 may be found using the point-slope form of a line's equation:
y - y1 = m(x - x1)
where the provided point is (x1, y1), and m is the slope.
When we change the values, we obtain:
y - 3 = (-3/4)(x - 8)
Making the right side simpler:
y - 3 = (-3/4)x + 6
To each sides, add 3:
y = (-3/4)x + 9
Hence, y = (-3/4)x + 9 is the equation of the line going through the point (8,3) that is parallel to the line y=-3/4+4.
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At a Bloomburg City Council meeting, a plan to fund more swim safety programs was presented. The reasoning behind the request was that less than 40% of children under the age of 5 could pass a swim test. If this is true, the council will agree to fund more programs for these kids. The council decides to take a 200-person volunteer sample of children under 5 years in Bloomburg City and conduct a significance test for H0: p = 0. 40 and Ha: p < 0. 40, where p is the proportion of these children that can pass a swim test. They will perform a significance test at a significance level of α = 0. 05 for the hypotheses.
Part A: Describe a Type II error that could occur. What impact could this error have on the situation? (3 points)
Part B: Out of the 200 children under 5 that volunteered to take a swimming test, 87 passed, resulting in a p-value of 0. 8438. What can you conclude from this p-value given the data of the 200 children is sufficient to perform a significance test for the hypotheses? (4 points)
Part C: What possible defect in the study can you find in Part B? Explain. (3 points)
Answers
Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test).
what is a Type II error?If the researcher does not reject a null hypothesis that is actually wrong in the population, this is known as a type II error (false-negative). Notwithstanding the fact that type I and type II mistakes cannot be completely prevented, the researcher can lessen their risk by increasing the sample size.
from the question:
Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test). This would result in a lost chance to provide these kids with more swim safety training, perhaps placing them in danger of drowning or other swimming-related mishaps.
Part B: We are unable to reject the null hypothesis since the p-value (0.8438) exceeds the significance level (0.05). This indicates that there is insufficient information to draw the conclusion that less than 40% of children under the age of five can pass a swim test. But, since the test only looked at the alternative hypothesis that the fraction is less than 40%, we cannot draw the conclusion that it is exactly 40%.
Part C: One possible defect in the study is the use of a volunteer sample. The children who volunteered to take the swimming test may not be representative of the entire population of children under 5 in Bloomburg City. For example, parents who are more concerned about their children's swimming abilities may be more likely to volunteer their children for the test, leading to a biased sample. To obtain a more representative sample, a random sample of children under 5 could be selected from the population and asked to take the swimming test.
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Suppose you are playing with someone new in soccer and you do not know how is strong, but you suspect you are. Let e be the probability that you win a single game. For now, we will treat o as discrete, with possible values 0, 0.1, ..., 1.0, and suppose you guess that the corresponding probabilities are ө teta Prior: P (0)
0 0
0.1 0.01
0.2 0.02
0.3 0.04
0.4 0.1
0.5 0.15
0.6 0.2
0.7 0.25
0.8 0.16
0.9 0.04
1 0
total Suppose you win the first time (), but then you lose twice () How does this information change your belief about the probability e. In another word, calculate the overall chances (expected values) of winning the games before/ and after you played? Note -Before you play, you believe that there is a 1% chance that your probability of winning any given game is 10%. - 2% chance that your winning probability is 20%, and so on.
Answers
The overall chances of winning the games before playing were 52%, and after playing and winning once but losing twice, the overall chances of winning are 17.33%. This shows that the new information has changed your belief about the probability of winning, and you now suspect that your chances of winning are lower than before.
Before playing the games, the expected value of winning is calculated by multiplying the probability of winning with the corresponding probabilities and adding them together. This is shown below:
E(win) = (0)(0) + (0.1)(0.01) + (0.2)(0.02) + (0.3)(0.04) + (0.4)(0.1) + (0.5)(0.15) + (0.6)(0.2) + (0.7)(0.25) + (0.8)(0.16) + (0.9)(0.04) + (1)(0) = 0.52
After playing the games and winning once but losing twice, the expected value of winning is calculated by multiplying the probability of winning with the corresponding probabilities, and adding them together. However, the probabilities are adjusted based on the new information. The new probabilities are shown below:
P(win) = (0)(0) + (0.1)(0.01)(1/3) + (0.2)(0.02)(1/3) + (0.3)(0.04)(1/3) + (0.4)(0.1)(1/3) + (0.5)(0.15)(1/3) + (0.6)(0.2)(1/3) + (0.7)(0.25)(1/3) + (0.8)(0.16)(1/3) + (0.9)(0.04)(1/3) + (1)(0)(1/3) = 0.17333
Therefore, the overall chances of winning the games before playing were 52%, and after playing and winning once but losing twice, the overall chances of winning are 17.33%. This shows that the new information has changed your belief about the probability of winning, and you now suspect that your chances of winning are lower than before.
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"Given that ( f(x)=x^{2}-5x) and ( g(x)=x+8 ), find (a) ( f+g= ) (b) ( f-g= ) (c) ( f g= ) (d).( {f}/{g}=)
Use the following functions to: find, simplify, and identify the domain of"
Answers
The following functions can be simplify as follows:
(a) f+g=x²+3x+8
(b) f-g=x²-13x-8
(c) fg=x³+3x²-40x-40
(d) f/g= (x-5)/(x+8) domain is x≠-8.
(a) To find f+g, we simply add the two functions together:
f+g=x^{2}-5x+x+8= x^{2}+3x+8
(b) To find f-g, we subtract g from f:
f-g=x^{2}-5x-(x+8)= x^{2}-6x-8= x^{2}-13x-8
(c) To find fg, we multiply the two functions together
:fg=(x^{2}-5x)(x+8)= x^{3}+3x^{2}-40x-40
(d) To find f/g, we divide f by g:
f/g= (x^{2}-5x)/(x+8)= (x-5)/(x+8)
The domain of this function is all real numbers except for -8, since dividing by zero is undefined. So the domain is x≠-8.
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Determine algebraically whether the function is even, odd or neither: g(x) = x/x^2+3
Answers
The function [tex]g(x) = \frac{x}{x^2+3}[/tex] is neither even nor odd.
To determine if a function is even, we can use the following test:
f(x) = f(-x)
If this is true, then the function is even.
For the given function, [tex]g(x) = \frac{x}{x^2+3}[/tex], let's plug in -x for x and see if the function is equal to itself:
[tex]g(-x) = \frac{-x}{(-x)^2+3} = \frac{-x}{x^2+3}[/tex]
As we can see, g(x) does not equal g(-x), so the function is not even.
To determine if a function is odd, we can use the following test:
f(x) = -f(-x)
If this is true, then the function is odd.
For the given function, let's plug in -x for x and see if the function is equal to the negative of itself:
[tex]g(x) = \frac{-x}{(-x)^2+3} = \frac{-x}{x^2+3}\\\\ -g(-x) = \frac{x}{-x^2+3}[/tex]
As we can see, g(x) does not equal -g(-x), so the function is not odd.
After the algebraic analysis, we can conclude that the function g(x) is neither, i.e., it is neither even nor odd.
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If the nth term of a number sequence is n2-3 find the first 3 terms and the 10th term
Answers
[tex]\huge\begin{array}{ccc}a_1=-2\\a_2=1\\a_3=6\\a_{10}=97\end{array}[/tex]
Numerical sequence.
[tex]a_n=n^2-3[/tex]
Find the first 3 terms and the 10th term.
Substitute
n = 1, n = 2, n = 3 and n = 10:
[tex]a_1=1^2-3=1-2=-2\\\\a_2=2^2-3=4-3=1\\\\a_3=3^2-3=9-3=6\\\\a_{10}=10^2-3=100-3=97[/tex]
3. Match each feature of the situation with
a corresponding statement in function
notation.
A maximum height
B. minimum height
C. height staying the same
D. starting height
height (feet)
26200
16
12
8
4
1
2
3 4
5
time (seconds)
1. h(0) = 7
2. h(1.5)
3. h(4)
4. h(t) = 6 for 7 ≤ 1 ≤8
6-7
Answers
Answer: A maximum height corresponds to:
B. h(t) = 26,200 - 16t^2
A minimum height corresponds to:
C. h(t) = 6 for 7 ≤ t ≤ 8
Height staying the same corresponds to:
D. h(t) = 12 for 2 ≤ t ≤ 3
Starting height corresponds to:
A. h(0) = 7
Using the provided data, we can find the function values that correspond to the given times:
h(1.5) = 26,200 - 16(1.5)^2 = 26,157
h(4) = 16
Therefore, the statement that corresponds to "6-7" is missing from the given options.
Step-by-step explanation:
6 time the quantity of a number minuse 5 is 90
Answers
Answer:
6(x)-5=90
Step-by-step explanation:
Move all terms that don't contain x to the right side and solve.
Exact Form:
x=95/6
Decimal Form:
x=15.83
Mixed Number Form:
x= 15 5/6
tbh i don't know if this is right
can some body help me
Answers
Answer: 9
Step-by-step explanation:
Working: Calculate how many boxes the line covers. This includes the negative area of the graph.
Find the output, b, when the input, a, is 6
b= -1 - 7a
Answers
When a=6, the value of b is equals to -43.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, which can be simplified and evaluated.
In other words, an algebraic expression is a collection of terms and coefficients that are connected by mathematical operators.
Substitute the value of a=6 into the expression for b:
b = -1 - 7a
b = -1 - 7(6)
b = -1 - 42
b = -43
Therefore, when a=6, the value of b is -43.
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9+what=58 im confused i used calculator the awnser is 49
Answers
A E G 2. BC AC What is the reason that we can make the statement = 11 AC CD D с a. SAS Similarity Postulate b. Corresponding sides of congruent triangles are congruent C. Corresponding sides of similar triangles are congruent d. Corresponding sides of similar triangles are proportional 3. Complete the following proof of the Pythagorean Theorem, a² + b2 = c2 A -= = As similar triangles have proportional we can write the proportions - = -and - = By the cross- property, = cf and = ce. By the a2 + b2 = cf +ce. allows the equivalent expression, a2 + b2 = By the therefore we can substitute and arrive at the statement a? + b2 = c. Word Bank fue sides á C= B b g b с addition property of equality segment addition postulate cf +e) b2 a2 product angles factoring
Answers
The Pythagorean Theorem is proven.
The reason that we can make the statement BC/AC = CD/AC is because corresponding sides of similar triangles are proportional. This is represented by option D. Corresponding sides of similar triangles are proportional.
To complete the proof of the Pythagorean Theorem, a² + b² = c², we can use the following steps:
As similar triangles have proportional sides, we can write the proportions AB/AC = AC/BC and AB/BC = BC/AC.
By the cross-product property, AB * BC = AC * AC and AB * AC = BC * BC.
By the addition property of equality, AB² + BC² = AC² + BC².
By the segment addition postulate, AC + BC = c.
By factoring, (AC + BC)² = c².
By the distributive property, AC² + 2*AC*BC + BC² = c².
By rearranging the terms, AC² + BC² = c² - 2*AC*BC.
By substituting the values of AC and BC from the proportions in step 1, we get a² + b² = c² - 2*a*b.
By simplifying, we get a² + b² = c².
Therefore, the Pythagorean Theorem is proven.
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what number is close to 48/100 is it 0 or 1 or 1/2?
Answers
Answer:
1/2
Step-by-step explanation:
Our answer options are: 0, 1, 1/2
0 = 0/100
1 = 100/100
1/2 = 50/100
Comparing the 3 options, we see that 1/2 is the closest to 48/100!
So, the answer is 1/2
Which graph represents the function f(x)=✔️x-2-2
Answers
Answer:
The given function is f(x) = √(x-2) - 2.
The graph that represents this function will have the following characteristics:
The domain of the function is x ≥ 2, since the expression inside the square root must be non-negative.
The function approaches the x-axis but never touches it as x approaches positive infinity, since the square root will always be positive.
The function has a vertical asymptote at x = 2, since the expression inside the square root becomes zero at x = 2.
The function has a horizontal asymptote at y = -2, since the square root term dominates the function as x gets large, and the -2 term remains constant.
Based on these characteristics, you can compare the given graphs to see which one matches the given function.
NEED HELP DUE TODAY!!!!!!!!!!1
Circle B is a dilation of circle A. How does the ratio of arc length compare to the scale factor?
Answers
We can conclude that the Ratio of arc = scale factor of dilation.
What is an Arc of a circle?An arc in mathematics is a section of a circle's or curve's perimeter. An open curve is another name for it.
The circumference of a circle, sometimes referred to as its perimeter, serves as its boundary. The distance between any two locations traced along the circle of an arc is hence its length.
Given : Radius of original circle A = 3
Radius of Dilation circle B = 9
We know that, Scale factor of dilation =
Dimension of Dilation shape / Dimension of original shape
So, Scale factor of given dilation = Radius of Circle B / Radius of Circle A
= 9/3
= 3.
Now, we know that arc of a circle can be found by using formula:
= Ф × π/180° × r
Arc of Circle A= 90 × π/180 × 3
= 3π/2
Arc of Circle B = 90 × π/180 × 9
= 9π/2
So, Ratio of arc = Arc of Circle B/Arc of Circle A
= 9π/2 ÷ 3π/2 = 3.
Hence, we can see that Ratio of arc = scale factor of dilation.
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Lesson 11-4 Three-dimensional Geometry Name "CHTC Lock hart 1. Identify each of the following polyhedra. Aloblique square pyramid
Answers
ABCD is the square base and A is the apex. As you can see, the apex is not directly above the center of the base, which makes this an oblique square pyramid.
An oblique square pyramid is a type of three-dimensional geometry that has a square base and four triangular faces that meet at a point, called the apex, but the apex is not directly above the center of the base. In other words, the pyramid is "tilted" or "leaning" to one side.
The key difference between an oblique square pyramid and a regular square pyramid is the location of the apex. In a regular square pyramid, the apex is directly above the center of the base, while in an oblique square pyramid, the apex is off-center.
Here is a diagram of an oblique square pyramid:
A/|\
/ | \
/ | \
/___|___\
B C D
In this diagram, ABCD is the square base and A is the apex. As you can see, the apex is not directly above the center of the base, which makes this an oblique square pyramid.
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24; can vary by 3.5%
Answers
The range of allowable values 24; can vary by 3.5% is 0.9.
What is range?
The difference between the highest and lowest values for a given data set is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.
As a result, the range can also be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.
In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. That indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations.
24 × 3.5% =0.84
so round to nearest tenth is 0.9.
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Complete question:
Find the range of allowable values based on the given information. Round to the nearest tenth.
24; can vary by 3.5%
Express the difference in median as a multiple of the IRQ for each data set.
Answers
IQR difference = 5
What is interquartile range (IQR)?The interquartile range (IQR) is a measure of variability that describes the spread of a set of data. It is calculated by finding the difference between the third quartile (Q3) and the first quartile (Q1) of the data.
The formula for calculating the IQR is:
IQR = Q3 - Q1
The Upper Quartile - Lower Quartile is the definition of the interquartile range.
The answer to the query is
Mount Vernon data set: 55, 60, 65, 70, 75, 80, 85 and 90
Lakewood data set = 65, 70, 75, 80 and 85
Mount Vernon median = 70+75/2 = 77.5
55+60+65+70/4 = 62.5 is the median for the lower half of the collection.
Upper half of set median: 82.5 (75, 80, 85, 90 divided by 4).
Mount Vernon's IQR is 82.5 minus 62.5, or 20.
Likewise, in the instance of Lakewood,
Average: 75
Lower half of the set median equals 65+70/2 = 67.5
Upper half of set median equals 80+85/2 = 82.5
IQR = 82.5 - 67.5 = 15
Hence, IQR difference = 20-15 = 5
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What is the area of the shaded area of the composite figure below? Round your answer to the nearest tenth. I NEED THE ANSWER PLEASEEE
Answers
When the smaller circle has a radius οf 6 cm, the area οf the shaded regiοn is 339.3 cm², rοunded tο the nearest tenth.
what is circle?The cοllectiοn οf all pοints in a plane that are equally spaced frοm a specific pοint knοwn as the centre is referred tο as a circle in geοmetry. It is usually represented by a clοsed, rοunded curve in twο dimensiοns. The radius is the distance acrοss the centre οf the circle, and the diameter is the distance frοm the centre οf the circle tο any spοt οn the curve. The area encircled by a circle is determined by the fοrmula A = r2, where r is the radius. The circumference οf a circle is alsο referred tο as its edge. Circles are a key idea in geοmetry and have many uses in bοth mathematics and daily living.
given:
We must deduct the area οf the smaller circle frοm the area οf the bigger circle in οrder tο determine the area οf the shaded area.
The bigger circle has a 12 cm radius, sο the fοllοwing is its area:
A = πr² = π(12 cm) (12 cm)
A ≈ 452.39 cm²
The smaller circle has a radius οf 6 centimetres, sο the fοllοwing is its area:
A = πr² = π(6 cm) (6 cm)
A ≈ 113.1 cm²
As a result, the shaded regiοn's size is:
113.1 cm² - 339.3 cm² = 452.39 cm²
When the smaller circle has a radius οf 6 cm, the area οf the shaded regiοn is 339.3 cm², rοunded tο the nearest tenth.
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i choose 10 consecutive numbers. if i exclude one of the numbers the remaining 9 sum to 2023 which number did i exclude?
Answers
The number that was excluded from the 10 consecutive numbers would be = 228.
How to calculate the number that was excluded?Let's take the smallest number of the 10 consecutive number to be = X
Then, the 10 consecutive numbers are x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, and x+9.
If we exclude one of these numbers, then the sum of the remaining 9 numbers would be:
(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8)
Collect the like terms and add up.
= 9x + 36
Recall that the sum of the remaining 9 numbers = 2023.
That is:
= 9X + 36 = 2023
=9x = 1987
x = 221
Therefore, the smallest number in the consecutive sequence is 221, and the 10 numbers are 221, 222, 223, 224, 225, 226, 227, 228, 229, and 230.
If we exclude the number 228, then the sum of the remaining 9 numbers is 2023.
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14. Find mMK
16. Find mJPK.
Answers
The measures of arcs and segments are
NK = 12, MLK = 41.5 degrees, JK = 24 and JPK = 277 degrees
How to determine the measures of arcs and segmentsLength NK
Given the triangle as the parameter.
Using the Pythagoras theorem, we have
NK = √(KL² - LN²)
So, we have
NK = √(15² - 9²)
Evaluate
NK = 12
The arc measure MK
Here, we start by calculating the central angle MLK
This is done using the following cosine ratio
cos(MLK) = NK/KL
cos(MLK) = 9/12
cos(MLK) = 0.75
Evaluate
MLK = 41.5 degrees
This means that
Arc MK = 41.5 degrees
Length JK
This is calculated as
JK = NK * 2
So, we have
JK = 12 * 2
JK = 24
The arc measure JPK
This is calculated as
JPK = 360 - 2 * MK
So, we have
JPK = 360 - 2 * 41.5 degrees
Evaluate
JPK = 277 degrees
Hence, the arc measure is 277 degrees
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600 g of 3 kg as a percentage
show method
Answers
Answer:
20%
Step-by-step explanation:
600÷3 of 100 = 20%
600/3 of 100 = 20%
Pls give simple working
Answers
Answer:
Step-by-step explanation:
sum of all angles in quadrilateral = 360
So, x+48+48+132 =360
x =132
(a) Factor f(x)=x^(3)-2x^(2)+49x-98 into factors of the form (x-c), given that 2 is a zero x^(3)-2x^(2)+49x-98
Answers
The factors of the form (x - c) are (x - 2) and (x² + 49).
To factor the polynomial f(x) = x³ - 2x² + 49x - 98 into factors of the form (x - c), we can use synthetic division with the given zero of 2.
2 | 1 -2 49 -98
| 2 0 98
1 0 49 0
The result of the synthetic division gives us the quotient (x² + 49) and a remainder of 0, confirming that 2 is indeed a zero of the polynomial.
Now we can write the polynomial as the product of (x - 2) and the quotient (x² + 49):
f(x) = (x - 2)(x² + 49)
Since the quadratic factor (x² + 49) cannot be factored further using real numbers, the final factorization of the polynomial is:
f(x) = (x - 2)(x² + 49)
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Knowledge Check Subtract. (x+8)/(x+7)-(x-2)/(x) Simplify your answer as much as possible.
Answers
The simplified form is 3/(x+7) + 14/(x)(x+7).
What is simplified form of fraction?Simplified form of a fraction is the form of a fraction in which the numerator and denominator are in their lowest form, or the greatest common factor has been taken out of both the numerator and denominator. For example, the fraction 24/36 can be simplified to 2/3.
To subtract the two fractions, we need to find a common denominator. The common denominator of (x+7) and (x) is (x)(x+7). We can then rewrite the two fractions with this common denominator and subtract the numerators:
(x+8)/(x+7) - (x-2)/(x) = (x+8)(x)/(x)(x+7) - (x-2)(x+7)/(x)(x+7)
= (x^2+8x)/(x^2+7x) - (x^2-2x+7x-14)/(x^2+7x)
= (x^2+8x - x^2+2x-7x+14)/(x^2+7x)
= (3x+14)/(x^2+7x)
= 3x/(x^2+7x) + 14/(x^2+7x)
= 3/(x+7) + 14/(x)(x+7)
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