Step-by-step explanation:
To prove that 3 + 2√5 is an irrational number, we will use the contradiction method.
Let us assume that 3 + 2√5 is a rational number with p and q as co-prime integers and q ≠ 0
⇒ 3 + 2√5 = p/ q
⇒ 2√5 = p/ q - 3
⇒ √5 = (p - 3q ) / 2q
⇒ (p - 3q ) / 2 q is a rational number.
However, √5 is an irrational number
This leads to a contradiction that 3 + 2√5 is a rational number.
Can someone help me with this problem and show work please !
Answer: Length - 20, Width - 10
Step-by-step explanation:
First we will use the formula to find area:
Area = Length * Width --- However, since it's double the length we will do 2Length.
Area = 2x*x
Given Area = 200
Next we will solve to find Width:
[tex]2x^{2} =200[/tex]
Divide by 2:
[tex]x^{2} =100[/tex]
Take square root:
[tex]x=10[/tex]
Width = 10
Now we multiply 10 by 2, as length is twice it's width:
[tex]2*10=20[/tex]
Length = 20
Final answer: Width = 10, Length = 20
I hope this helps!
Find AC please help trig is so hard
Which of the following is equal to the fraction below ?
(answers are in the picture)
Consider the two triangles. Triangles W U V and X Z Y are shown. Angles V U W and Y X Z are congruent. Angles U W V and X Z Y are congruent. Angles U V W and Z Y X are congruent. The length of side V W is 60 and the length of side Z Y is 48. The length of side Y X is 40 and the length of V U is 50. The length of side U W is 40 and the length of X Z is 32.
Two triangles are similar but not congruent if they have three congruent angles but the side lengths are not equal.
What is the congruency of triangles?
Congruent triangles are those of the same size and shape. This signifies that the respective sides are equal, as are the corresponding angles. We can determine whether two triangles are congruent without evaluating all of their sides and angles.To show how can the triangles be proven similar by the SSS similarity theorem:
The two triangles can be shown to be similar given that the ratios of the corresponding sides ΔWUV and ΔYXZ are constant
Reason:
Known parameters are:
ΔWUV and ΔXZY are shown:
∠VUW ≅ ∠YXZ
∠UWV ≅ ∠XZY
∠UVW ≅ ∠ZYX
Length of side VW = 60
Length of side VU = 50
Length of side UW = 40
Length of side ZY = 48
Length of side YX = 40
Length of side XZ = 32
The ratio of the sides are:
[tex]\frac{VW}{ZY} =\frac{60}{48} =\frac{5}{4} \\\frac{VU}{YX} =\frac{50}{40} =\frac{5}{4} \\\frac{UW}{XZ} =\frac{40}{32} =\frac{5}{4}[/tex]
Therefore, given that the angles of ΔWUV and ΔXZY are all congruent, and the sides of triangle ΔWUV and ΔXZY have a constant proportion, we have that the two triangles are congruent by the Side-Side-Side SSS congruency theorem, and we have:
ΔWUV ~ ΔYXZ given that ΔYXZ is a scaled drawing of ΔWUV.
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The complete question is given here:
Triangles W U V and X Z Y are shown. Angles V U W and Y X Z are congruent. Angles U W V and X Z Y are congruent. Angles U V W and Z Y X are congruent. The length of side V W is 60 and the length of side Z Y is 48. The length of side Y X is 40 and the length of V U is 50. The length of side U W is 40 and the length of X Z is 32.
How can the triangles be proven similar by the SSS similarity theorem?
The vectors are linearly independent if and only if?
The vectors are linearly independent if and only if k ≠ -11
How to solve the vectorIn mathematics, the definition of a vector is a quantity that is made up of both magnitude and also have direction. This type of quantity is not one that is considered based on its position. A very good example of such a quantity with magnitude and direction is acceleration.
Vectors are used to represent items such as position, velocity, physical quantities and others in mathematics and in physics.
In this question,
We have 2v - 3w
We have to multiply 2 by the values of v and multiply 3 with the values of w
this would produce
[2,6,8]-[6,6,12]
subtract w from v
= [-4, 0, -4]
We u as -1, 0 and 10+k
It is not possible to -1 = 10 + k
-11 = k
Hence we have to conclude that they are linearly independent if and only if k ≠ -11
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A bag contains different colored candies. There are 50
candies in the bag, 28 are red, 10 are blue, 8 are green and
4 are yellow.
What is the probability of choosing one candy and getting a
blue or red?
Fractions should always be in lowest terms.
о
19
25
38
4
38
50
25
19
Answer: 19/25
Step-by-step explanation: 50 candies total. 28 are red, 10 are blue 8 are green, and 4 are yellow. We want to calculate the probability of choosing a candy and either getting blue or red. The total candies that are blue or red are 28+10 = 38. So, 38/50. We can simplify by dividing by 2 to get 19/25. 19 is a prime number so that is as simple as we can get,
LOOK AT PIC!!! PLS HELP
Answer:
C. 21°C
Step-by-step explanation:
Substitute 69.8 for F in the equation, [tex]69.8=\frac{9}{5}C+32[/tex]. This becomes [tex]37.8=\frac{9}{5} C[/tex]. Divide both sides by [tex]\frac{9}{5}[/tex] to get [tex]21=C[/tex].
Answer:
21
Step-by-step explanation:
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2. (4)1 point possible (graded, results hidden)Recall for Define the kernel function Write as a function of the dot product . To answer, let , and enter in terms of . z^2 submitted
The Kernel Function K (x,x') written as a function of the dot product x *x' is K (x, x') = Z². See the working below.
What is a Kernel Function?A kernel function is a way for taking input data and transforming it into the needed form of processing data.
The term "kernel" refers to a collection of mathematical functions used in Support Vector Machine to provide a window to alter data.
What is the solution deriving the expression given above?Given x = [x₁, x₂][tex]^{T}[/tex]
β(x) = [x²₁, √2 x₁ x₂, x²₂]
K (x₁, x') = β(x)[tex]^{T}[/tex] β(x')[tex]^{T}[/tex]
Hence, X' = [x₁, x₂][tex]^{T}[/tex]
→ β(x') = [x'²₁, √2 x'₁ x'₂, x'²₂]
K (x, x') = [x²₁, √2 x₁ x₂, x²₂][tex]^{T}[/tex] [x'²₁, √2 x'₁ x'₂, x'²₂]
K (x, x') = [x²₁, [x'²₁ + 2x₁ x₂ x'₁ x'₂ + x²₂ x'²₂
Because Z = x · x' (dot product of x·x')
= x₁ x'₁ + x₂x₂'
Expressing K (x,x') as a function of Z, we have
K (x₁, x') = x²₁ x'²₁ + 2x₁x₂ x'₁ x'² + x²₂ x'²₂
Simplified, we have
(x₁ x₁¹ + x₂x¹₂)² = Z²; and
[(a+b)² = a²+2ab+b₂] = z x₁x₁¹ + x₂x₁²
Therefore,
K (x, x¹) = Z²
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percentage of 67 of 98
The percentages of 67 of 98 is 68.36%
Percentages and fractionsFractions are written as a ratio of two integers. According to the question we are to determine the percentage of 67 that is 98.
Fraction of 67 of 98 = 67/98
Percentage = 67/98 * 100
Percentages = 6700/98
Percentages = 68.37%
Hence the percentages of 67 of 98 is 68.36%
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The sampling distribution used when making inferences about a single population variance is?
We use the chi-square distribution when making inferences about a single population variance.
Short Description of Chi-Square Distribution
The continuous probability distribution known as the chi-square distribution. The number of degrees of freedom (k) a chi-square distribution has determines its shape. This type of sampling distribution has a variance of 2k and a mean equal to its number of degrees of freedom (k). The range is of a chi-square distribution is from 0 to ∞.
Variance plays a key role in the analysis of risk and uncertainty. The sample variance, an unbiased estimator of population variance, is expressed by the following formula of core statistic for a sample size 'n' and Y' as the sample mean:
S² = ∑(Yₓ - Y') / (n-1)
The formula, (n-1)S² / σ² has the central chi-square distribution as χ²ₙ₋₁. Here (n-1) represents the degrees of freedom.
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If f(x) = –x2 + 3x + 5 and g(x) = x2 + 2x, which graph shows the graph of (f + g)(x)? On a coordinate plane, a straight line with a negative slope crosses the y-axis at (0, 5) and crosses the x-axis at (1, 0). On a coordinate plane, a parabola opens down. It goes through (negative 2, negative 4), has a vertex at (0, 5), and goes through (2, negative 2) On a coordinate plane, a parabola opens up. It goes through (negative 3, 7), has a vertex at (negative 1, 2), and goes through (0, 5). On a coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5) - edge21
Answer:
Can i have the graph? THis doesn't make sense
Step-by-step explanation:
The graph of (f+g)(x) is on the coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5).
What is the graph of a parabolic equation?The graph of a parabolic equation is a curved U-shape graph from where the domain, the range, x-intercept(s), and the y-intercept(s) can be determined.
Given that:
f(x) = -x² + 3x + 5
g(x) = x² + 2x
To find (f + g)(x), we have:
(f + g)(x) = (-x² + 3x + 5)+(x² + 2x)
(f + g)(x) = -x² + 3x + 5 +x² + 2x
(f + g)(x) = 3x + 2x + 5
(f + g)(x) = 5x + 5
Use the Slope-intercept form: We are to find the graph of y = 5x + 5
y = 5x + 5
Here:
Slope = 5 x-intercept = (-1, 0)y-intercept = (0,5)Therefore, we can conclude that on the coordinate plane, a straight line with a positive slope crosses the x-axis at (negative 1, 0) and crosses the y-axis at (0, 5)
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The volume of a sphere is 500/3π cm3.
Work out the surface area of the sphere.
Give your answer in terms of π.
The answer is 100π cm².
Since we are given the volume, equate it to the formula of a sphere to find the radius.
500/3π = 4/3πr³r³ = 500/4r³ = 125r = 5 cmNow, substitute this in the formula to find surface area.
A = 4πr²A = 4π × (5)²A = 100π cm²Joanna has six beads that she wants to assemble into a bracelet. Two of the beads have the same color, and the other four all have different colors. How many different ways can Joanna assemble her bracelet
Joanna can assemble her bracelet in 30 ways.
How to find the number of ways in which the bracelet can be assembled?It is given that Joanna has 6 beads and of those 6 beads, 2 are of the same color.
The rest 4 are of different colors.
Six beads can be arranged in a circle in 6!/6 ways.
This means that the six beads can be arranged in 5! ways.
Since this is a bracelet, it can be flipped around. Therefore, it can be arranged in 5!/2 ways.
5!/2 = 5*4*3*2*1/2
= 60
Now, we know that two beads are of the same color. Therefore, we must divide this by two again.
Therefore, we get:
60/2 = 30
The six beads can be arranged in 30 ways to make the bracelet.
Therefore, we have found that Joanna can assemble her bracelet in 30 ways.
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what is trigonometric ratios
Answer:
Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle
Answer:
In mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.
Hi
How are you?
Kya kar rahi hoo?
Which points lie on the graph of f(x) = -√-x?
□(-9,3)
□(-4,-2)
□ (-1, 1)
□(0,0)
□ (1,1)
□(2,-4)
□(9,3)
Answer:
(-4, -2).
(0, 0).
Step-by-step explanation:
Both coordinates will be negative or (0.0).
It's these followings:
□(-4,-2)
□(0,0)
Hope this helps!
You are driving from your house to your office. Currently, it is 7:10 a.m., and you are 12 miles from your office. If you travel at an average speed of 30 miles per hour, at what time should you arrive at your office
We would reach our office by 7:34 a.m.
How to find the time that we would take to travel from our house to the office?The average speed is given as 30 miles per hour.
Let us convert this into miles per minute.
30 miles/1 hour = 30 miles/60 minutes
= 0.5 miles per minute
The distance between the house and the office is 12 miles.
Therefore, we can find what it would take to reach the office by dividing the distance by the average speed:
Time taken = distance/average speed
= 12 miles/0.5 miles per minute
= 24 minutes
The time is given to be 7:10 a.m. Therefore we would reach our office by 7:34 a.m.
Therefore, we would reach our office by 7:34 a.m.
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Find unknown angle
kº
68°
kº
Answer:
k = 56
Step-by-step explanation:
2k + 68 = 180
2k = 112
112 ÷ 2 = 56
k = 56
A new Concept XI bicycle cost a bike shop $800. The shop set the original list price of the bicycle at a price greater than $800. During the shop’s 30th anniversary sale, every list price in the store was marked down 30%. The shop sold this bicycle during its anniversary sale. Given that the shop made a 40% profit on the sale of this bicycle, what was the bicycle’s original list price?
Based on the fact that the shop still made a 40% profit on the concept xi bicycle, the original listing price must have been $1,600.
what price was the bicycle originally listed at?assuming the list price is x, the formula would be:
800 x 1.40 = (x × 0.7)
solving gives:
1,120 = 0.7x
x = 1,120 / 0.7
= $1,600
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What is the solution of…
Answer:
x/2>5
x>5*2
x>10.....equation 1
3x≥9
x≥9/3
x≥3.....equation 2
so by combining of the two equation we get
x>10 because it is the intersection of the. . two equations.
The answer will the Third
1. A committee of 3 men and 4 women is to be formed from 5 men and 6 women. If a particular woman is not to be included, how many different committees are possible
Step-by-step explanation:
Taking the men first: there are 5 ways to form a 4-man committee out of 5 men.
Taking the women now: There are 20 ways to form a 3-woman committee out of 6 women.
Each of the 5 possible male groups can be combined with any of the 20 possible female groups.
So: 100.
Find the diameter that represents the 49th percentile
Using the normal distribution, the diameter that represents the 49th percentile is of 1.52 units.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Using a calculator, the mean and the standard deviation for the diameters are given as follows:
[tex]\mu = 1.524, \sigma = 0.1226[/tex]
The 49th percentile is X when Z = -0.025, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.025 = \frac{X - 1.524}{0.1226}[/tex]
X - 1.524 = -0.025 x 0.1226
X = 1.52.
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Anabelle collected data on the favorite superhero of the students in her class. The table shows the relative frequencies of rows for the data collected: Favorite Superhero Superman Spiderman Batman Wonder Woman Row totals Boys 0.21 0.25 0.06 0.11 0.63 Girls 0.25 0.02 0.03 0.07 0.37 Column totals 0.46 0.27 0.09 0.18 1 Based on the data, which superhero is most likely to be the favorite
Considering the proportions given in the table, the superhero is most likely to be the favorite is Superman.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
Looking at the table, the proportions associated with each superhero is given as follows:
Superman: 0.46.Spiderman: 0.27.Batman: 0.09.Wonder woman: 0.18.As it has the highest proportion, the superhero is most likely to be the favorite is Superman.
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Answer this one please!
If the sum of the interior angle of a polygon is 1800 how many sides does it have
Answer: 12 sides
Step-by-step explanation:
The sum of the interior angles of a polygon is 180(n-2), where n is the number of sides
[tex]180(n-2)=1800\\\\n-2=10\\\\n=12[/tex]
WILL GIVE BRAINLEST!!!
Find the length of the base.
Answer:
32
Step-by-step explanation:
The length of segment AB is the average of XY and WZ.
(22 + x)/2 = 27
22 + x = 54
x = 32
Is 1/11 a irrational number?
Answer:
No
Step-by-step explanation:
Am irrational number is a number that can't be expressed by a ratio (fraction). 1/11 is a fraction so it is rational, not irrational.
After being filled, a basketball loses 3.2% of its air every day. Considering that the initial volume of the ball was 840 cubic centimetres when it was inflated, what will be the volume in cubic centimetres after 4 days? (Round your answer to one decimal place).
Answer:
volume = 840 cubic cm
(3.2/100)×840= 26.88 per day
after 4 days = 26.88×4=107.5
answer is 107.5
The volume (in cubic centimeters) after 4 days, given that the initial volume of the ball was 840 cubic centimeters, is 732.5 cubic centimeters
How to determine the volume after 4 days?First, we shall determine the volume lost per day. Details below:
Initial volume = 840 cubic centimeters Percentage loss = 3.2%Volume lost per day = ?Volume lost per day = 3.2% × Initial volume
= 3.2% × 840
= (3.2 / 100) × 840
= 26.88 cubic centimeters
Now, we shall obtain the volume after 4 days. Details below:
Initial volume = 840 cubic centimeters Volume lost per day = 26.88 cubic centimeters Volume lost in 4 days = 4 × 26.88 = 107.52 cubic centimeters Volume after 4 days =?Volume after 4 days = Initial volume - Volume lost in 4 days
= 840 - 107.52
= 732.5 cubic centimeters
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Drag an answer to each box to complete this paragraph proof. Given: Triangle ABC Prove: m/A= 66 A B (5x) By the C (x + 10) m/A+m/B +m/C= 180°. Using the the sum of the angles in a triangle is equal to 180°. Therefore, solve for x, first combine like terms to get 6x + 100 = 180. Using the (5x) +90° + (x + 10) = 180°. To 6x = 80. Then, using the division property of equality, x = 13. To find the measure of angle A, use the substitution property to get m/A = 5(13). Finally, simplifying the expression gets mA = 663"
The value of A has been illustrated, computed and proven based in the triangle given.
How to calculate the triangle?It should be noted that that a triangle is a shape that has three sides and the value of the addition of all the angles are equal to 180°.
Based on the information that's given, it should be noted that the value of angle A, angle B, and angle C will be equal to 180°.
In this case, the following can be deduced:
A = 5x
B = 90°
C = x + 10°
Therefore, A + B + C = 180° (sum of angles in a triangle)
5x + 90 + x + 10 = 180°
6x = 180° - 90° - 10°
6x = 80°
x = 80/6
x = 13 1/3
Therefore, the value of A will be:
= 5x
= 5 × 13 1/3
= 66 2/3
Therefore, A is 66 2/3.
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When rolling a single number cube, what are the odds, in simplest form, in favor of rolling a 4 or a 5?
A. 1:1
B. 1:2
C. 1:3
D. 1:5
Answer:
C
Step-by-step explanation:
You have a total of 6 outcomes (1,2,3,4,5,6). That is your numerator. Out of those numbers, you only want 2 of them (4 or 5), so the fractions would be 2/6 or 1/3 which can also be written 1:3
Is x^25+1 polynomial function
Answer:
Step-by-step explanation:
yes I believe it is an quartic binomial
Answer:
yes
Step-by-step explanation:
If because it has two terms, it is a binomial, therefore it also qualifies as a polynomial.
Hope this helps