The graph of the equation x = -4 is shown in the image attached below.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).
By critically observing the graph (see attachment), we can reasonably infer and logically deduce that the x-intercept is equal to -4.
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find the general value of theta which satisfies the equation cos theta sin theta into cos 2 theta sin 2 theta
The general value of theta which satisfies the equation (cosФ+isinФ)(cos2Ф+isin2Ф)..............(cosnФ+isinnФ) is one is 4π/(n+1)
Real and imaginary numbers:
A real number can be a natural number, a whole number, an integer, a rational number, or an irrational number. But an imaginary number is the product of a real number and "i" where i = √(-1). For example, √(-9) = √(-1) . √9 = i (3) = 3i
cosФ+isinФ = [tex]e^{i0}[/tex]
cos2Ф+isin2Ф = [tex]e^{2i0}[/tex]
............................
cosnФ+isinnФ= [tex]e^{in0}[/tex]
Now,
[tex]e^{i0}[/tex]×[tex]e^{2i0}[/tex]×.......[tex]e^{in0}[/tex] =1
[tex]e^{i0(1+2+....n)}[/tex] = 1
[tex]e^{i0(n*(n+1)/2)}[/tex] =1
So
cos(n*(n+1)/2)Ф+isin(n*(n+1)/2)Ф =1
Now comparing the real and the imaginary part we get that
cos(n*(n+1)/2)Ф = 1
n*(n+1)/2Ф = 2nπ
Ф = 4π/(n+1)
Therefore, the general value of theta which satisfies the equation (cosФ+isinФ)(cos2Ф+isin2Ф)..............(cosnФ+isinnФ) is one is 4π/(n+1).
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The correct question should be:
find the general value of theta which satisfies the equation (cosФ+isinФ)(cos2Ф+isin2Ф)..............(cosnФ+isinnФ) equals to one.
Two students were asked to graph increasing exponential functions with the same y-intercept. Would the graphs always have to be identical given the stated key features? Explain.
Answer:
No
Step-by-step explanation:
Consider the graphs of [tex]y=2^x[/tex] and [tex]y=3^x[/tex].
A bakery offers a sale price of 2.55 for 4 muffins.what is the price per dozen?
I hope someone answers fast
And explain what you did
Answer: $7.65 for a dozen/12
Step-by-step explanation: 2.55 x 3
3-(-7)
3- (-17)
3-(-27)
3-(-127)
13-(-6)
24 - (-8)
5- (-23)
How do you find the HCF using the long division method of 3 numbers?
We divide the smaller number in HCF by the remaining after dividing the smaller number by the smaller number. Until there is no more remaining, we repeat the process.
what is a HCF ?For two or more numbers, HCF can be assessed. It is the most powerful factor for dividing any pair of numbers by either half or all of them. To illustrate: 15 is the biggest number that can divide both 60 and 75 perfectly, making it the highest common factor between those two numbers.
here
Step 1 is to divide the largest integer by the smallest number.
Step 2: Divide the first divisor by the first remainder, taking the divisor as the new dividend and the remainder as the new divisor.
Step 3: Continue until the remainder is 0 and the HCF of the given numbers is the last divisor.
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Suppose f(x) = 3x + 5. Describe how the graph of g(x) = (3x+5) +8
Answer:
The graph of g(x) = (3x+5) + 8 will be shifted 8 units up from the graph of f(x). Specifically, the graph of g(x) will be 8 units higher than the graph of f(x) for all x.
Step-by-step explanation:
please give a step by step explanation
I've been doing this ixl for 2 hours, please help
Answer:
x+40= x+x-44
40+44=2x-x
x=84
How do I regroup a number?
What is the value of 1 i by 1 i?
The value of "i" squared or 1 i by 1 i results in:
(-1)
Complex NumbersAmong the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.
What are numeric sets?Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.
In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:
√(-1) = i√(-1) x √(-1) = i²
[√(-1)]² = i²
(-1) = i²
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A set of data is represented in the stem plot below.
Stem plot with stems of 3, 4, 5, 6, 7, 8, 9, 10. Leaf for stem of 3 is 5. Leaves for stem of 4 are 2 and 3. Leaves for stem of 5 are 1, 5, and 7. Leaves for stem of 6 are 2, 6, 8, and 9. Leaves for stem of 7 are 4, 5, 6, 7, 8, and 9. Leaves for stem of 8 are 2, 4, 6, and 8. Leaves for stem of 9 are 3 and 4. Leaf for stem of 10 is 1.
Key: 3 | 5 = 35
Part A: Find the mean of the data. Show each step of work. Round answer to the nearest whole number. (2 points)
Part B: Find the median of the data. Show each step of work. (2 point)
Part C: Find the mode of the data. Show each step of work. (2 point)
Part D: Compare your values for mean, median, and mode from parts A, B, and C. Explain which value would best represent the data, and why? (4 points)
A. The mean of the data set is 71.09.
B. The median of the data set is the 12th term which is 74.
C. There is no mode value in the given data set.
D. Median value best represents the data.
What is a stem leaf method?A stem leaf method is used to represent discrete data.
The first column are the stem values and the second are the leaf values.
To find the mean of the data set we'll use the weightage average method
which is sum of all the values divided by the number of values.
∴ Mean = 71.09.
Total no. of data is 23 so the median is the 12th term which is 74.
There is no particular frequently occurring data hence no mode.
Median value best represents this data set as in the stem and leaf the most no. of data are in this row.
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what is the height of the tower?
Answer:
| AD | ≈ 48 m
Step-by-step explanation:
The table represents a quadratic function C(t).
t C(t)
2 4
3 1
4 0
5 1
6 4
What is the equation of C(t)?
C(t) = −(x − 4)2
C(t) = (x − 4)2
C(t) = −x2 + 4
C(t) = x2 + 4
The equation of the quadratic function is (b) C(t) = (t - 4)²
How to determine the equation of the quadratic function?From the question, we have the table of values that can be used in our computation:
A quadratic equation is represented as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
From the graph, we have the vertex to be
(h, k) = (4, 0)
Substitute (h, k) = (4, 0) in f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 4)²
Also, from the graph, we have the point (2, 4)
This means that
a(2 - 4)² = 4
So, we have
4a = 4
Divide both sides by 4
a = 1
Substitute a = 1 in f(x) = a(x - 4)²
f(x) = (x - 4)²
Rewrite as C(t)
C(t) = (t - 4)²
Hence, the equation is C(t) = (t - 4)²
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its C(t) = (x − 4)2
use desmos graphing its very helpful
Why do we use the range () function?
The range() function outputs a list of numbers that starts at 0 by default, increases by 1 (by default), and ends before a given value .
what is range ?The statistical range for a given data collection is the range of values between the highest and lowest values. Another way to show the range is to compare the top and lowest observation differences. The sample interval can be calculated by subtracting the highest number from the lowest. For continuous variables, the sample range is an essential measure of variability.
here ,
Python has a built-in method called range() that can be used to create a series of numbers.
The range() function accepts starting and ending values as inputs, which can be supplied by the user to construct a sequence .
The range() function outputs a list of numbers that starts at 0 by default, increases by 1 (by default), and ends before a given value .
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pls answer... 2 column proof
A line bisector divides a given line into two equal sections or parts. Thus the required proof to show that BC ≅ DF is stated below:
A given line is said to have been bisected if and only if it is divided into two equal parts by a constructed line. The line that divides a given line into two equal parts is termed a line bisector.
The appropriate proof is as stated below:
STATEMENT REASON
1. AB ≅ FG Given
2. BF bisects AC and DG Given
3. AB ≅ BC Definition of a bisector
4. DF ≅ FG Definition of a bisector
5. AC ≅ DG Property of two congruent lines
6. BC ≅ DF Property of two congruent lines
Therefore it can be deduced that BC ≅ DF (property of two congruent lines)
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What is the y-intercept of the line 5x 3y =- 15?
The y-intercept is (0, 5). Hence, the intercepts of the equation 5x + 3y = 15 are (3,0) and (0,5).
To find the x-intercept we have to substitute y = 0 into the equation, as follows:
9x - 7*0 = -63
9x = -63
Dividing by 9 at both sides of the equation:
9x/9 = -63/9
x = -7
To find the y-intercept we have to substitute x = 0 into the equation, as follows:
9*0 - 7y = -63
-7y = -63
Dividing by -7 at both sides of the equation:
-7y/(-7) = -63/(-7)
y = 9
x-intercept: −7; y-intercept: 9
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What is the median of 2/3 and 4?
The median of 2/3 and 4 is 2.33.
The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.
A data set's median value is the point where 50% of the data points have values that are lower or equal to it, and 50% of the data points have values that are higher or equal to it.
To arrange the data points in ascending order for a small data set, count the number of data points (n).
To get the rank of the data point whose value is the median when the number of data points is unequal, multiply the total by 1 and divide the results by 2.
Median = (2/3+4)/2 = 4.66/2 = 2.33
Thus, the median of 2/3 and 4 is 2.33.
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To get the rank of the data point whose value is the median when the number of data points is unequal, multiply the total by 1 and divide the results by 2.
Median = (2/3+4)/2 = 4.66/2 = 2.33
Thus, the median of 2/3 and 4 is 2.33.
A lizard is climbing up a 30 metre building. Each day it climbs five metres and slides back one metre. How many days will it take to reach the top?.
The number of days the lizard that will be taken to reach the top will be 8 days .
Since we're given the information that the spider each day climbs five meters and slides back one meter, that means that it climbs for 4 meters daily .
Number of meters for each day = 5 - 1
= 4 meters
Therefore, since the spider is climbing up a 30 meter building, the number of days required will be :
= 30 / 4
= 15 / 2
= 7.5
= 8 days approximately.
Hence The number of days will be needed to reach the top is 8 days.
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What is a multiplicity of 3?
Multiplicity of 3 is the number of times that the value 3 appears as a root of an equation is the multiplicity of 3 is 3
Multiplicity of 3 (also known as a 3-fold root) is a mathematical concept used to describe the number of times a certain value appears as a root (or solution) of an equation. Specifically, it refers to the number of times a certain value appears as a root of a given equation when the equation is solved.
For example, the equation x2 = 9 has three solutions: x = 3, -3, and 0. This means that the multiplicity of 3 is 3, because 3 appears three times as a root of the equation. The general formula used to calculate the multiplicity of a given root is:
Multiplicity of x = Number of times x appears as a root of the equation
In this case, the multiplicity of 3 is 3, because 3 appears as a root of the equation three times. Similarly, if there are two solutions, x = -2 and x = 0, the multiplicity of -2 is 2, because -2 appears as a root of the equation twice.
In summary, multiplicity of 3 is the number of times that the value 3 appears as a root of an equation when the equation is solved. In the example above, the multiplicity of 3 is 3.
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Evaluate the expressions. A) 10 [12^2 + (4 x 2)] ÷ 8^2
Answer: 297492
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{10 [12^2 + (4 \times 2)] \div 8^2}[/tex]
[tex]\mathsf{= 10[12^2 + (8)] \div 8^2}[/tex]
[tex]\mathsf{= 10[12^2 + 8)] \div 8^2}[/tex]
[tex]\mathsf{= 10[12 \times 12 + 8] \div 8 \times 8}[/tex]
[tex]\mathsf{= 10[144 + 8] \div 64}[/tex]
[tex]\mathsf{= 10[152] \div 64}[/tex]
[tex]\mathsf{= 10(152) \div 64}[/tex]
[tex]\mathsf{= 1,520 \div 64}[/tex]
[tex]\mathsf{= \dfrac{1,520}{64}}[/tex]
[tex]\mathsf{= \dfrac{1,520 \div 16}{64 \div 16}}[/tex]
[tex]\mathsf{= \dfrac{95}{4}}[/tex]
[tex]\mathsf{= 23 \dfrac{3}{4}}[/tex]
[tex]\huge\text{Therefore, your answer is:}[/tex]
[tex]\huge\boxed{\mathsf{= \dfrac{95}{4}\ or \ 23 \dfrac{3}{4}\ or \ even\ 23.75}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Alvin is 11 years younger than Elga. The sum of their ages is 33. What is Elga's age?
Answer:
Elga is 22 years old
Step-by-step explanation:
Let A = Alvin's age
Let E = Elga's age
We have the equations:
A = E - 11
A + E = 33
Substitute A = E - 11 from the first equation into the second equation and solve for E
So, we have
A + E = 33
(E - 11) + E = 33
2E - 11 = 33
2E = 44
E = 22 years old
So, Alvin is 11 years old and Elga is 22 years old
What is the HCF of the polynomials x6 3x4 3x² 1 and x³ 3x² 3x 1?
The HCF of the polynomials x^6 - 3x^4+ 3x² - 1 and x³+ 3x^2+ 3x+ 1 is (x+1)^3.
Let us suppose the Polynomials to be f(x) = x^6 - 3x^4 + 3x^2 - 1 And polynomial g(x) = x^3 + 3x^2 + 3x + 1
Now, According to the question,
we have f(x) = x^6 - 3x^4 + 3x^2 - 1
Adding and subtracting 2^x2,
⇒ x^6 - x^4 - 2x^4 + 2^x2 + x^2 - 1
⇒ x^4(x^2 - 1) - 2x^2(x^2 - 1) +1(x^2 + 1)
⇒ (x^2 - 1)(x^4 - 2x^2 + 1)
⇒ (x + 1)(x - 1)(x^4 - 2x^2 + 1)
⇒ (x + 1)(x - 1)(x2 - 1)^2
⇒ (x + 1) (x - 1) (x + 1)^2 (x - 1)2
⇒ (x + 1)^3(x - 1)^3 ----(1)
And, g(x) = x^3 + 3x^2 + 3x + 1
⇒ x^3 + x^2 + 2x^2 + 2x + x + 1
⇒ x^2(x + 1) + 2x(x + 1) + 1(x + 1) ⇒ (x + 1)(x^2 + 2x + 1)
⇒ (x + 1) (x + 1)2 ⇒ (x + 1)3 ----(2)
Now, The HCF of f(x) and g(x) is the common factor of equations (1) and (2)
⇒ (x + 1)^3 .
∴ The HCF of the polynomials (x^6 - 3x^4 + 3x^2 - 1) and (x^3 + 3x^2 + 3x + 1) is (x + 1)^3.
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The proof that HG ≅ EG is shown.
Given: G is the midpoint of KF
KH ∥ EF
Two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle. Which congruence theorem can be used to prove that the triangles are congruent?
SSS
AAS
SAS
HL
Answer: B )" AAS congruence theorem" an be used to prove that the triangles are congruent .
AAS congruence theorem tells that if two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle then the triangles are congruent.
Therefore option B is the correct answer. "AAS congruence" theorem an be used to prove that the triangles are congruent
What is the standard deviation of 225?
15 is the standard deviation of 225 .
What is explained by the standard deviation?
You can tell how skewed the data is by looking at the standard deviation. It gauges how far away from the mean each observed value is.
Any distribution will have roughly 95% of its values within two standard deviations of the mean. Think about the following data: 2, 1, 3, 2, 4. The average and the sum of squares representing the observations' variances from the mean will be 2.4 and 5.2, respectively.
Variance is simply the square of the standard deviation (v=σ2) .
So if the variance is 225,
σ=√225 or 15.
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What do all equilateral triangles have in common?
How many feet do you travel going 40 mph?
Answer: 211200
Step-by-step explanation: Ok so assuming you are asking how many feet you travel per hour going 40 mph. You would travel 211200. There are 5280 ft in a mile. If you multiply that by 40 you get 211200. So you travel 211200ft per hour
find x
the area of the end surface
the volume
the total surface
Answer:
(i) x = 17 cm
(ii) one end: 360 cm²; both ends: 720 cm²
(iii) 14,400 cm³
(iv) 4000 cm²
Step-by-step explanation:
You want the slant height, base area, volume, and total surface area of a trapezoidal prism with the base isosceles trapezoid having parallel base lengths of 32 and 16, and a height of 15. The distance between bases is 40. All units are cm.
(i) Slant heightIf a center rectangle 16 cm wide and 15 cm high is cut from the base trapezoid, the remaining two triangles have a base of 8 cm and a height of 15 cm. The Pythagorean theorem can be used to find the slant height:
x² = a² +b²
x² = 8² +15² = 64 +225 = 289
x = √289 = 17
The slant height, x, is 17 cm.
(ii) Base areaThe area of the base trapezoid is given by the formula ...
A = 1/2(b1 +b2)h
A = 1/2(32 +16)(15) = 360 . . . . square cm
The area of one end surface is 360 cm²; the total area of both end surfaces is 720 cm².
(iii) VolumeThe volume of the prism is the product of the base area and the length of the prism.
V = Bh
V = (360 cm²)(40 cm) = 14,400 cm³
The volume of the trapezoidal prism is 14,400 cm³.
(iv) Total surface areaThe lateral surface area of the prism is the product of the perimeter of the base and the distance between bases.
LA = Ph
LA = (32 +16 +2·17 cm)(40 cm) = 3280 cm²
The total surface area is the sum of the lateral area and the area of the two bases:
SA = LA +2B = (3280 cm²) + 2(360 cm²) = 4000 cm²
The total surface area of the prism is 4000 square centimeters.
__
Additional comment
It appears that the top dashed line in the figure is drawn that way in error. It appears to identify a visible edge, so we expect it to be a solid line.
find the general solution of the given differential equation. dr dθ + r sec(θ) = cos(θ)
The solution of the differential equation would be [tex]r = \dfrac{(\theta - cos\theta) + C}{(sec\theta + tan\theta)}[/tex].
Using the concept of integration that states,
Integration in mathematics is a technique for integrating or adding up the parts to get the total. It involves a differentiation process in reverse.
Given that,
The differential equation is,
[tex]\dfrac{dr}{d\theta } + r sec(\theta ) = cos (\theta )[/tex]
Hence the auxiliary solution,
[tex]\mu (\theta ) = e^{\int\limits {sec\theta} \, d\theta}[/tex]
[tex]\mu (\theta ) = e^{ln |\limits {sec\theta + tan\theta|[/tex]
[tex]\mu (\theta ) = |sec\theta + tan\theta|[/tex]
Hence multiply both sides by [tex]\mu(\theta)[/tex],
[tex]({sec\theta + tan\theta)\dfrac{dr}{d\theta } + ({sec\theta + tan\theta) r sec(\theta ) = cos (\theta ) ({sec\theta + tan\theta)[/tex]
[tex]\dfrac{d}{d\theta} (r \times (sec\theta + tan\theta) = (1 + sin\theta)[/tex]
Integration on both sides,
[tex]r \times (sec\theta + tan\theta) = (\theta - cos\theta) + C[/tex]
Therefore, the solution is,
[tex]r = \dfrac{(\theta - cos\theta) + C}{(sec\theta + tan\theta)}[/tex]
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How many combinations of 3 variables are possible where each variable can take only two values?
The total number of combinations is given by the product between the numbers of options, so there are 8 combinations.
How many combinations are possible?Here we have 3 variables and each can take two values:
x = {x₁, x₂}
y = {y₁, y₂}
z = {z₁, z₂}
The total number of combinations is equal to the product between the number of options that we have for each variable, then the number of combinations is:
C = 2*2*2 = 4*2 = 8
C = 8
There are 8 combinations.
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What is the equation of the line with slope 5 and y-intercept 10?
Answer:
y = 5x + 10
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
We know slope 5 and y-intercept 10
So, our equation is
y = 5x + 10