Answer:
210xyz
Step-by-step explanation:
Given
5x × 6y × 7z
= 5 × x × 6 × y × 7 × z
= 5 × 6 × 7 × x × y × z
= 210xyz
Solve the system
(4x + 7y= 41
(x-7y=-16
Answer:
{ X = 5} {Y = 3} pls mark brainliest
Step-by-step explanation:
Add the two equations: 4x + 7y + (x-7y) = 41 + (-16)
Remove parentheses: 4x + 7y + x-7y = 41 + -16
Cancel one variable:4x + x + = 41 + -16
Combine like terms: 5x = 41 - 16
Calculate the sum or difference: 5x = 25
Divide both sides of the equation by the coefficient of variable: x = 25/5
Cross out the common factor: X = 5
Substitute into one of the equations: 5 - 7y = -16
Rearrange unknown terms to the left side of the equation: 5 - 7y = -16 - 5
Calculate the sum or difference: -7y = -21
Divide both sides of the equation by the coefficient of variable: -21/-7
Determine the sign for multiplication or division: y = 21/7
Cross out the common factor: y = 3
The solution of the system is: { X = 5} {Y = 3}
How do you prove triangles are congruent using ASA?
What is the link between the transformation and congruence and similarity?
If we can move one thing without affecting its size or shape such that it perfectly overlays the other picture, then two objects are congruent. These motions are what are known as congruence transformations.
What are the characteristics of a rigid motion transformations?While the image's size and shape are unaffected by rigid body motion, its location and orientation are. The three fundamental movements of a rigid body are translation, reflection, and rotation. Prior to movement, archetypes depict points or forms.
In order for two items to be congruent, one of them must be able to be moved over the other without affecting its size or form. Congruence changes are what we refer to as these motions. The transformation of an object into a congruent object is known as a congruence transformation.
∠A = ∠B
And, also
AB = BC
AD = BD
Therefore,
ΔABC ≅ ΔDEF
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FIND THE FIRST DERIVATIVE OF g(x)=√x² + 2x
We are asked to find the first derivative of,
[tex]\longrightarrow g(x) = \sqrt{x^2+2x}[/tex]
Here we can write the term [tex]x^2+2x[/tex] by adding and subtracting 1 as,
[tex]x^2+2x = x^2+2x+1-1[/tex]
[tex]x^2+2x = (x+1)^2-1\quad[\because\, x^2+2x+1=(x+1)^2][/tex]
Thus,
[tex]\longrightarrow g(x) = \sqrt{(x+1)^2-1}\quad\dots(1)[/tex]
Now take,
[tex]x+1=\sec\theta\quad\dots(2)[/tex]
[tex]x=\sec\theta-1[/tex]
[tex]dx=\sec\theta\tan\theta\, d\theta[/tex]
[tex]\dfrac{d\theta}{dx}=\dfrac{1}{\sec\theta\tan\theta}\quad\dots(3)[/tex]
Then (1) becomes,
[tex]\longrightarrow g(x) = \sqrt{sec^2\theta-1}[/tex]
We have,
[tex]\sec^2\theta-1=\tan^2\theta[/tex]
So we get,
[tex]\longrightarrow g(x) = \tan\theta[/tex]
Now,
[tex]\longrightarrow g'(x) = \dfrac{d}{dx}\,[\tan\theta][/tex]
By chain rule,
[tex]\longrightarrow g'(x) = \dfrac{d}{d\theta}\,[\tan\theta]\cdot\dfrac{d\theta}{dx}[/tex]
[tex]\longrightarrow g'(x) = \sec^2\theta\cdot\dfrac{1}{\sec\theta\tan\theta}\quad\quad\textrm{[From (3)]}[/tex]
[tex]\longrightarrow g'(x) = \sec\theta\cdot\dfrac{1}{\tan\theta}[/tex]
[tex]\longrightarrow g'(x)=\dfrac{1}{\cos\theta}\cdot\dfrac{\cos\theta}{\sin\theta}[/tex]
[tex]\longrightarrow g'(x)=\dfrac{1}{\sin\theta}\quad\dots(4)[/tex]
But we have,
[tex]\sin^2\theta+\cos^2\theta=1[/tex]
[tex]\sin\theta=\sqrt{1-\cos^2\theta}[/tex]
[tex]\sin\theta=\sqrt{1-\dfrac{1}{\sec^2\theta}}[/tex]
[tex]\sin\theta=\dfrac{\sqrt{\sec^2\theta-1}}{\sec\theta}[/tex]
[tex]\sin\theta=\dfrac{\sqrt{(x+1)^2-1}}{x+1}\quad\quad\textrm{[From (2)]}[/tex]
[tex]\sin\theta=\dfrac{\sqrt{x^2+2x}}{x+1}[/tex]
Hence (4) becomes,
[tex]\longrightarrow\underline{\underline{g'(x)=\dfrac{x+1}{\sqrt{x^2+2x}}}}[/tex]
This is the first derivative of the given function.
How do you check continuity of a function?
Continuity of a function can be checked by examining the limits of the function as x approaches a certain value and ensuring the function's output is equal to the value of the function at that point.
Continuity of a function is an important concept in calculus and other branches of mathematics. In order to check the continuity of a function, the limits of the function must be examined as x approaches a certain value. This means that the left-hand limit and the right-hand limit must be equal. If the limits are equal, then the function is continuous at that point. If the limits are not equal, then the function is not continuous at that point. Additionally, the value of the function at that point must also be equal to the limits in order for the function to be continuous. If the function is discontinuous at any point, then it is not considered continuous. Continuity is necessary for certain properties of functions, such as derivatives and integrals, to be defined.
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A cubic polynomial with rational coefficients has the roots 7+√5 and 1/4. Find on additional root.
A. 7-√5
B. 7+√5
C. 5+√7
D. 5-√7
Answer:
Additional root of 7+√5 and 1/4 is:
D.5-√7
What is the factor of 3x² 6x?
The factors form of the given equation 3x²−6x is 3x(x−2)
Given that:
3x²−6x
To find : The factor form of 3x²−6x
The splitting or decomposition of an entity (such as a number, a matrix, or a polynomial) into the product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics. You will mostly learn this idea in your lower secondary studies, which run from grades 6 to 8.
=3×x×x−2×3×x, factor each monomial
=3x(x−2), factor out common factor 3x
The factors form of 3x²−6x is 3x(x−2)
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name the image point when the object point (4,4) is mapped by the following translations. (x,y)-->(x+1,y-1)
The image of the point after the translation is (5,3)
How to determine the image of the point?From the question, we have the following parameters that can be used in our computation:
Point =(4, 4)
This point can be represented as
(x, y) = (4, 4)
The translation equation is given as
(x,y)-->(x+1,y-1)
Substitute the known values in the above equation, so, we have the following representation
(x,y)-->(4+1,4-1)
Evaluate
(x,y)--> (5,3)
Hence, the image is (5,3)
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suppose the correlation between height and weight for adults is 0.40. what proportion (or percent) of the variability in weight can be explained by the relationship with height? group of answer choices 84% 16% 60% 40%
The 16% variability in weight can be explained by the relationship with height.
What is correlation?
In statistics, there are three different forms of correlation: positive, negative, and no correlation.
The link between two variables is said to be positive correlated when both variables move in the same direction. When one variable decline (or grows) while the other variable lowers (or increases), there is a positive perfect correlation, denoted by the number +1.
When two variables are correlated negatively, both of the variables are moving in the opposing direction. When one variable rises (or falls) while the other rises (or falls), there is a negative perfect correlation, which is symbolised by the number -1.
No correlation, which is represented by 0, means that there is no connection or reliance between the two variables.
On the basis of provided information, the correlation between the height and weight for adults is,
r = +0.4
So, the coefficient of determination is calculated as,
[tex]r^{2} = (0.40)^{2}[/tex] = 0.16 = 16%
Based on the provided information, the required answer is 16%.
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Thanks for all of the helpers
here is another slope question
Answer:
m = 5
Step-by-step explanation:
The equation is y = mx + b
The m here is the slope; in this case, the slope is 5
In the 1970s, due to world events, there was a gasoline shortage in the united states. There were often long lines of cars waiting at gas stations. 1 if there were a million cars in line, bumper to bumper, with average length of 9. 65 feet, how long would that line be in miles? round your answer to the nearest mile.
The length of the line is 1712.12 miles if there were often long lines of cars waiting at gas stations. If there were a million cars in line, bumper to bumper.
Given :
What is average?
It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
There were often long lines of cars waiting at gas stations. If there were a million cars in line, bumper to bumper.
The average length = 9.04 feet
The length of the line can be found as follows:
= 9.04 * 1,000,000
The length of the line = 9,040,000 feet/5280 feet (1 mile)
= 1712.12 miles
Thus, the length of the line is 1712.12 miles if there were often long lines of cars waiting at gas stations. If there were a million cars in line, bumper to bumper.
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At which root does the graph of f x x 5 3 x 2 2 touch the x axis?
The root of the graph of function f(x) = (x-5)³(x+2)² touch the x-axis at -2 and 5.
Given that,
The function is f(x)= (x-5)³(x+2)²
We have to find at which root does the graph function touch the x-axis.
We know that,
What is a function?Mathematical calculus' core component is functions. The unique forms of relationships are the functions. When it comes to arithmetic, a function is represented as a rule that produces a different result for each input x.
Take the function
f(x) = (x-5)³(x+2)²
f(x) = 0 if a curve touches the x-axis.
⇒ (x - 5)³(x + 2)² = 0.
But if ab = 0
So, a=0 and b=0
⇒ (x - 5)³ = 0 and (x + 2)² = 0
⇒ (x - 5) = 0 and x + 2 = 0
⇒ x=5 and x=-2.
Therefore, The root of the graph of function f(x) = (x-5)³(x+2)² touch the x-axis at -2 and 5.
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i am a number less than 3,000.when you divide me by 32, my remainder is 30. when you divide me by 58, my remainder is 44. what number am i?
The number less than 3,000.when you divide me by 32, my remainder is 30. when you divide me by 58, my remainder is 44 is one of this {798, 1726, 2654}.
There exists a, b∈N such as
N= 30+32a=44+58b
Therefore,
16a-29b= 22-15=7
Let us notice that 5×29-9×16=1
Therefore, 35×29-63×16=7
Hence, a= -63 is a non-fundamental solution to our equation.
We can show that the other solution are of the form a=-63+29k, with k∈Z
Therefore, the first positive solutions are
a= -63+3×29= 24
N= 798
a= -63+4×29= 53
N= 1726
a= -63+5×29=82
N= -63+6×29= 111
N= 3582
Therefore, the number is one of {798, 1726, 2654}.
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What is value of x if4x 64?
As per the unitary method, the value of x for the expression 4x = 64 is written as, 16.
The term unitary method in math is defined as a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here we have to find the value of x if the given expression 4x = 64.
According to the unitary method, here we have given the expression,
=> 4x = 64
Here we need to find the value of x, so we have to move the other values instead of x to the other side, then we get the expression,
=> x = 64/4
Now, we have to divide the number 64 by 4, then we get the value,
=> x = 16
Therefore, the value of x is 16.
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15. If l//m, find the measure of each angle.
If q ║ r, value of x is 17.
Define alternate exterior angle.When a transversal connects two or more parallel lines at different locations, alternate exterior angles are created. The word exterior refers to something that is located outside. Whenever the transversal intersects two lines, alternate external angles are always outside of those two lines and are situated on the opposing sides of the transversal. As a result, the pair of alternate external angles—two outside angles—that arise at the opposing ends of transversals in the exterior section are always equal. When a transversal splits two parallel lines, we obtain two of these pairs of alternate exterior angles.
Given
q ║ r
Alternate exterior angle,
7x - 10 = 9x - 44
9x - 7x = 44 - 10
2x = 34
x = 17
If q ║ r, value of x is 17.
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What is the leading coefficient example?
For a polynomial, Leading coefficient is the coefficient of the term with the degree of polynomial. For [tex]a^{2}+bx+c[/tex] , The leading coefficient is 'a'.
What do you mean by a polynomial?Sums of terms with the form kxⁿ, where K is any number and N is a positive integer, are known as polynomials.
What do you mean by leading coefficient?The term with the greatest x power is the leading term in a polynomial function. The leading coefficient is the coefficient of the leading phrase.
Example of leading coefficient are:
[tex]2x^{2}+x+1[/tex], leading coefficient=2
[tex]8x^{3}+5x^{2}+3x+1[/tex], leading coefficient =8
[tex]3x^{5}+8x^{3}+7x+6[/tex], leading coefficient = 3
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A corporate bond has a face value of p dollars. The interest each year is 6% of the face value. After received each year. The payout is the sum of the face value and the total interest. years the total interest is the product of the number of years, 1, and the interest (a) Express the total interest /, in dollars, as a function of the age f, in years, of the bond. Note that "I is already provided. Do not include this in your submitted response to this question. I .06t+p Edit (b) Express the payout P, in dollars, as a function of f. Note that "P is already provided. Do not include this in your submitted response to this question. P= Edit
A corporate bond has a face value of p dollars. The interest each year is 6% of the face value. the total interest /, in dollars, as a function of the age f, in years, of the bond is
a)I(f) = 0.06 * f * p
b) P(f) = I(f) + p
What is the function?Generally, (a) The total interest, in dollars, as a function of the age f, in years, of the bond can be expressed as:
I(f) = 0.06 * f * p
This represents the total interest paid over f years, which is calculated by multiplying the annual interest rate (0.06), the number of years (f), and the face value of the bond (p).
(b) The payout P, in dollars, as a function of f can be expressed as:
P(f) = I(f) + p
This represents the total payout over f years, which is calculated by adding the total interest paid (I(f)) and the face value of the bond (p).
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please help me with this question its urgent
Answer:
316 milliliters of compound A
Step-by-step explanation:
We know for every 7milliliters, we have 4 milliliters of compound A and 3 milliliters of compound B
So, take 553 divided by 7 = 79
So, take 4 times 79 = 316 milliliters of Compound A
So, 316 milliliters of Compound A are needed!
find the weight ? needed to hold the wall shown in fig. p2.76 upright. the wall is 10 m wide.
As per the given height of the wall, the approximate weight is 149kN
The term Hydrostatic refers to the force exerted by static water on the plate or object and its magnitude depends upon the positioning of the object inside the water.
Here we have given the following values,
Height = 2.76 upright
Width = 10 m
Here we have to consider the hydrostatic force acting on the wall about the pinned point say P then the expression is looks like,
=> F = ωAx
=> F = 9810(10 × 4) × 2
=> F = 784800 N = 785KN
Now, the weight is calculated as per the Hydrostatic method as,
=> W = (1.33/7) x 785
=> W = 149 kN
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What is the mean of 20 and 10?
15 is the mean of 20 and 10 .
What are the mean, median, and example?
A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently. The most frequent number, or the one that happens the most frequently, is known as the mode.
Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
x = 20 + 10/2
x = 30/2
x = 15
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What kind of polynomial is 3x²?
The polynomial 3xA² is a linear monomial having one term and a degree one.
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
There are many types of polynomials according to the number of terms they have.
If a polynomial has one term it is called a monomial, Has two terms called a binomial, and having three makes it a trinomial.
Given, A polynomial 3xA².
Now, The variable is 'x' and raised to the power of 1 so it is linear and consists of only one term so it is a monomial as 3 and A are constants.
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Use the summation notation to rewrite the following expression. 1 2 3 n + + + + 2! 3! 4! (n + 1)! Σ k = 1
The rewritten expression using the summation notation is ∑ k = 1 1! + 2! + 3! + ... + (n+1)!
The summation notation is a way to represent the sum of a series of terms. In the summation notation, the series of terms is represented by an expression that is followed by a summation symbol (∑). The summation symbol is usually followed by an index of the summation (k in this case), an equal sign (=), the starting value of the index, and a colon (:). The series of terms is then written below the summation symbol, with the index replacing the variable in each term.
To rewrite the given expression using the summation notation, we can use the following steps:
Identify the series of terms: 1 + 2 + 3 + ... + n.
Write the series of terms below the summation symbol: ∑ k = 1
Replace the variable in each term with the index: 1! + 2! + 3! + ... + (n+1)!
The rewritten expression using the summation notation is ∑ k = 1 1! + 2! + 3! + ... + (n+1)!
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A woman on a billboard is 8 3/8 feet tall. If the scale of the billboard is 1 foot = 8 inches, what is her actual height?
plssss answer thiss!!!!
Answer:
A = 3
B = 6
C = 4
D = 5
left rectangle = 4 x 6 = 24
mid = 5 x 6 = 30
right = 6 x 3 = 18
both triangles = 4 x 3 = 12
24 + 30 + 18 + 12
= 84 cm²
Answer: 84
Step-by-step explanation:
I need help i will choose you as the brainlyest answer is you get it right.
Answer:
6/4
1 2/4
1 1/2
Step-by-step explanation:
3 x 2/4 = 3/2 or 1 1/2
6/4 reduces to 3/2 as factors of 2
1 2/4 simplifies to 1 1/2
1 1/2 is equal to 3/2
How to find the possibility?
Answer:
Step-by-step explanation:
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes. Probability of event to happen P (E) = Number of favourable outcomes/Total Number of outcomes
10. To find the height of a tower, a surveyor positions a transit that is 2 m tall at a spot
35 m from the base of the tower. She measures the angle of elevation to the top of the tower to be 51°. What is the height of the tower, to the nearest meter? (show work pls)
The height of the tower where surveyor positions a transit that is 2 m tall = 45.19 m
What is trigonometric functions?Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent are the six trigonometric functions. The trigonometric functions in mathematics are real functions that link the angle of a right-angled triangle to the ratios of the lengths of the two sides.
given:
transit height = 2 m
distance from the base of the tower = 35 m
angle of elevation = 51°
Utilize trigonometric functions to solve this problem. The tangent trigonometric function connects the opposite side and the neighboring side.
Opposite side / Adjacent side = tan Ф
solving opposite side = Opposite side = Adjacent side x tan Ф
Opposite side = 35 x tan 51°
Opposite side = 35 x 1.234
Opposite side = 43.19 m
calculating the tower height = 43.19 + 2 m
= 45.19 m
therefore the height of the tower = 45.19 m
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What does it mean more than 2?
More than 2 in mathematical expression is written as >2.
The relationship between two quantities can be described using comparison terms. There are primarily three comparison terms: more than (>), less than (<), and equal to (=).
More than (>): When one quantity is greater than the other quantity, we use “more than”. For example, 5 > 3.
Less than (<): When one quantity is less than the other quantity, we use “less than”. For example, 8 < 10.
Equal to (=): When two quantities are the same, we use “equal to”. For example, 15 = 15.
More than 2 means, greater than but not including 2, which is written as >2
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just give me the straight answers for 1-6
Answer:
1. y=x 2. x=4 3. y=3x-10 4. y=-2/5x-1/5 5. y=-8x-13 6. y=-x+3
Step-by-step explanation:
What will be the nature of roots of quadratic equation 2x² 4x?
The roots of the given equation 2x2 + 4x = 0 are -1 and 0. It can be seen from the roots that the nature of the roots is real and equal.
The nature of the roots of a quadratic equation ax2 + bx + c = 0 with real coefficients a, b, and c can be determined by using the quadratic formula. The quadratic formula states that the two roots of the equation are given by:
x = (-b ± √(b2 - 4ac)) / 2a
For the equation 2x2 + 4x = 0, a = 2, b = 4, and c = 0. Substituting these values into the quadratic formula, we get the two roots of the equation as:
x = (-4 ± √(42 - 4(2)(0))) / 2(2)
x = (-4 ± 0) / 4
x = -1, 0
Therefore, the roots of the given equation 2x2 + 4x = 0 are -1 and 0. It can be seen from the roots that the nature of the roots is real and equal.
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