Answer:
31.8
Step-by-step explanation:
3x − 2y = 8
slope
y -intercept
x -intercept
How did you determine each characteristic?
Answer:
Slope: 3/2
Y-intercept: (0,-4)
X-intercept: (8/3 , 0)
Step-by-step explanation:
To find the y-intercept, I just put in 0 for x.
3(0) - 2y = 8
-2y = 8
y = -4
So, the y-intercept is at (0,-4)
To find the x-intercept, I just put in 0 for y.
3x - 2(0) = 8
3x = 8
x = 8/3
So, the x-intercept is at (8/3, 0)
The slope is 3/2
What makes a set of numbers closed?
The natural numbers are “closed” under addition and multiplication.
A set is closed (under an operation) if and only if the operation on any two elements of the set produces another element of the same set. The set of whole numbers is “closed” under addition and multiplication.
A set of number with a defined operation (e.g. addition, multiplication etc.), such that the outcome of the operation between any two numbers is also a member ot the set.
A Closed Set Math has a way of explaining a lot of things, and one of those explanations is called a closed set.This closed set includes the limit or boundary of 3.
When a set has closure, it means that when you perform an operation on the set, then you'll always get an answer from within the set. This doesn't mean that the set is closed though. Open sets can have closure. Mathematical examples of closed sets include closed intervals, closed paths, and closed balls.
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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 height of the tower?
Answer:
| AD | ≈ 48 m
Step-by-step explanation:
If you get four sticks of butter to a pound, and each stick of butter is 1/2 a cup, how many cups of butter is a pound of butter? Explain your answer.
Answer: 2
Step-by-step explanation:
If you have four sticks of butter that equal a pound, and each stick is 1/2 a cup, then a pound of butter is equal to 2 cups. This is because 1/2 x 4 = 2. Each stick of butter is 1/2 a cup, and since there are four sticks in a pound, the total amount of butter in cups is 2 cups.
What are the 4 steps to copy and paste?
The four steps to copy and paste involve selecting the text, copying the text, selecting the cursor at destination and pasting the text.
What is a clipboard?When you copy or cut data from its original place, the computer temporarily stores it in a memory region called the clipboard. Data that has been copied or cut is retrieved from the clipboard and pasted to the new spot when you paste it.
What is the difference between copying and cutting text?When you copy text, a copy of the original text is made and stored in the clipboard; the original text stays in its original place. The original text is taken out of its original spot and placed in the clipboard when you cut text. The original text is retained when you copy it, but it is removed from its original spot when you cut it. The copied or cut text can be pasted into another area in both situations.
You can follow the following 4 steps to copy and paste text or other items in a computer application:
1. By highlighting it with your pointer, you may choose the text or object that you wish to copy.
2. Right-click the text or object you want to copy, then choose "Copy" from the context menu. As an alternative, you may copy by pressing "Ctrl+C" on your keyboard.
3. Place the cursor where you wish to paste the text or object that was copied.
4. "Paste" may be found in the context menu when you right-click the destination. As an alternative, you may paste by using "Ctrl+V" on your keyboard.
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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
1- An unbounded problem is one for which ________. remains feasibleA. the objective is maximized or minimized by more than one combination of decision variablesB. there is no solution that simultaneously satisfies all the constraintsC. the objective can be increased or decreased to infinity or negative infinity while the solutionD. there is exactly one solution that will result in the maximum or minimum objective2- If a model has alternative optimal solutions, ________.A. the objective is maximized or minimized by more than one combination of decision variablesB. there is no solution that simultaneously satisfies all the constraintsC. the objective can be increased or decreased to infinity or negative infinityD. there is exactly one solution that will result in the maximum or minimum objective3- The ________ indicates how much the value of the objective function will change as the right-hand side of a constraint is increased by 1.A. objective coefficientB. shadow priceC. binding constraintD. reduced cost
A) An unbounded problem is one for which the objective can be increased or decreased to infinity or negative infinity while the solution remains feasible.
B) If a model has alternative optimal solutions the objective is maximized (or minimized) by more than one combination of decision variables, all of which have the same objective function value.
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
C) The shadow price indicates how much the value of the objective function will change as the right-hand side of a constraint is increased by 1.
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What is the gradient of y =- 4x 9?
The gradient of y=-4x+9 is -4. The gradient of a line is the measure of its steepness.
It is calculated by taking the derivative of the line. When taking the derivative of a linear equation, the derivative is the coefficient of the variable (x). In this case, the coefficient of x is -4. Therefore, the gradient of y=-4x+9 is -4.
To calculate this gradient, we need to use the power rule of derivatives. This rule states that if y = ax^n, then the derivative of y is nax^(n-1). In this case, a=-4 and n=1. Therefore, the derivative of y=-4x+9 is -4*1^(1-1), which simplifies to -4.
To calculate the gradient of y=-4x+9, we applied the power rule of derivatives. The coefficient of x in this equation was -4, so the derivative of y was -4. Therefore, the gradient of y=-4x+9 is -4.
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How do I regroup a number?
the least common multiple of two whole numbers is 40. the ratio of the greater number to the lesser number is 5:4. what are the two numbers?
In a case whereby least common multiple of two whole numbers is 40. the ratio of the greater number to the lesser number is 5:4. the two numbers are 10 and 8.
How can this be calculated?Given as :
The least common multiple of two numbers = LCM = 40
The ratio of the greater number to lesser number = 5 : 4
let the greater number = 5 x
And The smaller number = 4x
∵ The LCM of numbers = 40
So, 5 × 4 × x = 40
Or, 20 × x = 60
x= 3
Then greater number = 5 x = 5 × 2 = 10
And The smaller number = 4 x = 4 × 2 = 8
Hence The two numbers are 10 and 8
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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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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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Questions are on picture
I don't see the picture. Can you send it in the message.
What is the difference between ASA and AAS congruence rule?
The difference between ASA and AAS congruence rule is While AAS refers to the two corresponding angles and the non-included side, ASA refers to any two angles and the included side.
Two postulates that assist us in determining whether two triangles are congruent are ASA and AAS. ASA means "Angle, Side, Point", while AAS signifies "Angle, Angle, Side". If two figures are the same size and shape, they are congruent. To put it another way, the same person appears in two distinct locations in two congruent figures. According to the ASA congruence rule, two triangles are congruent when the angles and included sides of one side are equal to those of another side. However, if two angles and one side of one triangle are equal to two angles and one side of another triangle, then they are congruent, as stated by AAS. Both ASA and AAS are the same as though two points of one triangle are equivalent to two points of another triangle then clearly the third points will likewise be the same.
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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.
4(2x + 3) = 3 + 8x - 11
Answer:
There is no answer.
Step-by-step explanation:
4(2x+3) = 3+8x-11
Group together common terms on the right & use the distributive property on the left.
4(2x) + 4(3) = (3-11) +8x
8x + 12 = 8x -8
Combine like terms. Subtract 8x from both sides.
12 = -8
3. The graph of a linear function is shown.
The following points lie on the line: (0,50) and (11, 90).
What is the equation of the function?
Answer:
preem
100
80
60
40
20
0 2 4 6
Answer:
y = [tex]\frac{40}{11}[/tex] x + 50
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 50 ) and (x₂, y₂ ) = (11, 90 )
m = [tex]\frac{90-50}{11-0}[/tex] = [tex]\frac{40}{11}[/tex]
the line crosses the y- axis at (0, 50 ) ⇒ c = 50
y = [tex]\frac{40}{11}[/tex] x + 50 ← equation of line
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 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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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
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
What are the types of linear inequality?
Slack and strict are the two types of linear inequalities we deal with our daily examples in mathematics.
What are the operators for linear inequalities?Addition, subtraction, multiplication, and division are the four types of operations that can be performed on linear inequalities. Equivalent inequality refers to linear inequalities with the same solution. Both equality and inequality are subject to laws.
What are the operations that can be used on linear inequality?An inequality is comparable if both sides are multiplied by a positive value. An inequality's direction can be changed by multiplying both sides by a negative amount.
There are two types of linear inequalities
Slack: inequalities containing sign ≤ or ≥ between LHS and RHS.
Strict: inequalities containing < or > between LHS and RHS.
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Use graphing to find the x-coordinate of the solution to each system.
y = 2/9 x +3
y =- 10/9 x -9
A) -9
B) 9
C) 3
D) -4
Answer:
A) -9
Step-by-step explanation:
You want a graphical solution to the system of equations ...
y = 2/9x +3y = -10/9x -9GraphThe graph is attached. It shows the solution is (-9, 1).
The x-coordinate of the solution is -9.
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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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.
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]
Consider the degree of each polynomial in the problem. The first factor has a degree of . The second factor has a degree of . The third factor has a degree of . The product has a degree of
The first factor of the expression has a degree of 2.
The second factor has a degree of 3.
The third factor has a degree of 2.
The product has a degree of 7.
[tex](a^{2} ) (2a^{3} )(a^{2}-8a+9)[/tex]
The given expression of this problem is:
The degree of an expression is deduct by the exponent of each power.
So, the first factor of the expression has a degree of 2, because that's the exponent.
The second factor has a degree of 3.
The third factor has a degree of 2.
Now, to know the degree of the product, we have to solve the expression, and see what is the degree of the resulting polynomial expression:
[tex](a^{2})(2a^{3})(a^{2} -8a+9)[/tex]
[tex]2a^{5} (a^{2} -8a+9)[/tex][tex]\\2a^{7} -16a^{6}+18a^{5}[/tex]
so, as you can see, the product has a degree of 7.
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a relative frequency distribution shows: multiple choice question. the number of observations in each class interval the number of observations of a particular value in a set of data the fraction or percentage of observations in each class interval
A relative frequency distribution shows C. the fraction or percentage of observations in each class interval.
What is a relative frequency?A relative frequency is a proportional value that indicates the relative number of a specific event in a total number of observations.
A relative frequency uses percentages, proportions, and fractions to show the value of the chosen or expected outcome.
With a relative frequency distribution, it does not merely show the number of observations in each class interval or set of data.
Thus, a relative frequency distribution indicates Option C because it compares one value against other observations in relative terms.
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