[tex]\textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\\\\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\log_2(x-3)+\log_4(x) \\\\[-0.35em] ~\dotfill\\\\ \log_4(x)\implies \stackrel{\textit{change of base rule}}{\cfrac{\log_2(x)}{\log_2(4)}}\implies \cfrac{\log_2(x)}{\log_2(2^2)}\implies \cfrac{\log_2(x)}{2}\implies \cfrac{1}{2}\log_2(x) \\\\[-0.35em] ~\dotfill\\\\ \log_2(x-3)+\log_4(x)\implies \log_2(x-3)+\cfrac{1}{2}\log_2(x)\implies \log_2(x-3)+\log_2(x^{\frac{1}{2}}) \\\\\\ \log_2(x-3)+\log(\sqrt{x})\implies {\Large \begin{array}{llll} \log_2( ~~ \sqrt{x}(x-3) ~~ ) \end{array}}[/tex]
what is a number that goes into a greater number with no remainders called?
A number that goes into a greater number with no remainders is called a factor.
A factor is an integer that divides into a greater number without any remainders.
For example, the number 6 is a factor of 18 because when 18 is divided by 6, the answer is 3 with no remainders. Similarly, the number 3 is a factor of 12 because when 12 is divided by 3, the answer is 4 with no remainders.
Factors are important in mathematics because they can be used to solve equations and determine the greatest common divisor (GCD) of two or more numbers. Factors can also be used to determine prime numbers and their multiples.
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Quadrilateral CDEF is inscribed in Circle T F Engle DEF is 3X +7 and angle DCF is 2X +8 what is the value of X?
Since Quadrilateral CDEF is inscribed in Circle A, the value of x is equal to: B. 33.
How to calculate the value of x?Since Quadrilateral CDEF is inscribed in Circle A, we can reasonably infer and logically deduce that line segment DF is the chord of Circle A. Mathematically, an equation which can be used to solve for the value of x in this circle is given by:
m∠DEF + m∠DCF = 180°
Substituting the given parameters into the formula above, we have the following;
(3x + 7)° + (2x + 8)° = 180°
3x + 2x + 8 + 7 = 180°
5x + 15 = 180°
5x = 180° - 15
5x = 165
x = 165/5
x = 33.
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Help the perimeter is about _ units_
The perimeter of the given polygon is about 16.4 units.
How to find the perimeter of the polygon?We want to find the perimeter of the polygon whose vertices are (-3, 2), (2, 2) and (-1, -3).
The perimeter will be equal to the sum of the distances between the vertices, and remember that the distance between two points (x₁, y₁) and (x₂, y₂) is:
d = √( (x₂ - x₁)² + (y₂ - y₁)²)
The distances are:
between (-3, 2) and (2, 2)
d = √( (-3 - 2)² + (2 - 2)²) = 5
between (-1, -3) and (2, 2)
d = √( (-1 - 2)² + (-3 - 2)²)
d = √( 9 + 25) = 6
between (-1, -3) and (-3, 2)
d = √( (-1 + 3)² + (-3 - 2)²)
d = √29 = 5.4
Then the perimeter is:
5.4 + 6 + 5 = 16.4
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Without using a calculator, determine between which two integers the following surds lie (b) √29 (C)-√54
(b) √29 is between 5 and 6. You can approximate it by finding the perfect squares that are closest to 29: 25 (5^2) and 36 (6^2). √29 is between 5 and 6 since 5^2 < 29 < 6^2
(c) √54 is between 7 and 8. You can approximate it by finding the perfect squares that are closest to 54: 49 (7^2) and 64 (8^2). √54 is between 7 and 8 since 7^2 < 54 < 8^2.
a+v=b-(v+5)
how would I make this solution true
To make a true equation, check your math to make sure that the values on each side of the equals sign are the same.
How would make this solution true?step1
(a) a +v = b-(v+5)
1+5=6 not equal a+ v=5
To check if a given value is a solution to an equation:
Evaluate the left-hand side expression at the given value to get a number
Evaluate the right-hand side expression at the given value to get a number.
See if the numbers match.
If you add the same number to both sides of an inequality, the inequality remains true.
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Correct question:
What criteria must meet to say that a+v=b-(v+5) is true?
if someone could show me how to do this that would be great, i appreciate it!
Discovering an antiderivative of a function is the process of integration.
What is integration?Adding or adding up the components to get the whole is a process known as integration. Reducing the functions into their component elements is a reverse differentiation procedure. Utilizing a broad scale, this method is utilised to find the sum.
A function's antiderivative is discovered by integration. It is the definite integration if a function can be integrated and if the integral of that function across the domain is finite with the given bounds. When d/dx(F(x) = f(x), dx = F(x) + C. Indefinite integrals are what these are.
As opposed to differentiation, integration is the opposite. In other words, the integral of 2 can be 2x + 3, 2x + 5, 2x, etc. Because of this, we must include a constant when integrating. The integral of 2 is therefore 2x + c, where c is a constant.
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Table 1.3 shows the hypothetical trade-off between different combinations of brushes and combs that might be produced in a year with the limited capacity for country X, ceteris paribus.
In the production range of 2 to 3 combs opportunity cost producing one more comb is
a)0.67
b)3.33
c)7.0
d)0.14
In the production range of 2 to 3 combs, the opportunity cost of producing one more comb is d) 0.14 brushes.
Explain about production range refer to:Opportunity cost is the cost of one choice in terms of the best alternative foregone. In this case, the opportunity cost of producing one more comb is the number of brushes that have to be given up in order to produce that additional comb.For example, if the country X is currently producing 2 combs, in order to produce one more comb, 0.14 brushes would have to be given up. This means that for every additional comb produced, 0.14 brushes would have to be sacrificed. This trade-off is reflected in Table 1.3 and is the opportunity cost of producing one more comb in the production range of 2 to 3 combs.In other words, the opportunity cost of producing one more comb is the number of brushes that would have to be sacrificed in order to produce that comb. The opportunity cost is 0.14 brushes per comb, which means that for every additional comb produced, 0.14 brushes would have to be given up.To learn more about production range refer to:
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If y₁=2x-1 construct for x = -5 to 7- a table
Thanks for all the help Brainlys!!!
I'll give yall some points for all the helpppp!!!!!!!!
Answer:
I am so glad you were able to do it! Congrats on 100%
Step-by-step explanation:
That's great you got 100%!!!
What is the value of x in the equation 3x+9/6=x-3
[tex] \frac{3x + 9}{6} = x - 3 \\ [/tex]
[tex]3x + 9 = 6(x - 3)[/tex]
[tex]3x + 9 = 6x - 18[/tex]
[tex]6x - 3x = 9 + 18[/tex]
[tex]3x = 27[/tex]
[tex]x = \frac{27}{3} \\ [/tex]
answer: [tex]x = 9[/tex]
determine the closest correlation coefficient (R-value) for this data
The closest correlation coefficient of the scatterplot is 0.8
How to determine the closest correlation coefficient of the scatterplotFrom the question, we have the following parameters that can be used in our computation:
The image of the scatter plot
On the scatter plot, we can see that
The points appear to be on a straight line
Also, we can see that
As the x values increases the y values increases
This represents a positive linear association.
Because the points appear to be on a straight line, but they are not on a straight line, the r value will most likely be between 0.7 and 0.9
The closest value to this is 0.8
Hence, the r value is 0.8
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How do you change Vertex to factored?.
Standard form is ax^2 + bx + c. Vertex form is a(x-h)^2 + k, which reveals the vertex and axis of symmetry. Factored form is a(x-r)(x-s), which reveals the roots.
What is quadratic equation?
Factoring, using square roots, completing the square, and the quadratic formula are the four ways to solve a quadratic problem.
Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.
x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Therefore, Standard form is ax^2 + bx + c. Vertex form is a(x-h)^2 + k, which reveals the vertex and axis of symmetry. Factored form is a(x-r)(x-s), which reveals the roots.
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Find sine, where is the angle shown.
Give an exact value, not a decimal approximation.
8
17
8
The value of sinθ is 15/17.
What are the trigonometric functions?
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Here, we have
Given:
Cosθ = 8/17
We apply here trignometric functions.
Sinθ = √1 - cos²θ
Sinθ = √1 - (8/17)²
Sinθ = √(289 - 64)289
Sinθ = √225/289
Sinθ = 15/17
Hence, the value of Sinθ is 15/17.
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what are the next five terms and conjuncture of 1, 8, 27, 64
Answer:
125, 216, 343, 512
Step-by-step explanation:
The next number in the sequence 1, 8, 27, 64 is 125.
This sequence follows the pattern of starting with the number 1, then finding the cube of each subsequent integer (the cube of a number is found by multiplying the number by itself twice, so the cube of 2 is 222=8). Therefore, the next number in the sequence would be 555=125.
The equation for line p can be written as y= 9 7 x–9. Line q is perpendicular to line p and passes through (9, – 6). What is the equation of line q?
final answer:y= - 1/97 - 6
to find slope, just do the opposite reciprocal of the given slope
to find y-intercept just substitute the given point in y=mx+b
hope this helps!
Three brothers spent different amounts of money on their recent vacation. Matt spent $25 less than Todd. Jeff spent 3 times as much as Matt. How much did each brother spend if they spent a total of $275?
Please help me!
Answer:
Todd spent 75, Matt spent 50 and Jeff spent 150
Step-by-step explanation:
Matt = y - 25
Jeff = 3(y - 25)
Todd = y
y - 25 + 3y - 75 + y = 275
5y - 100 = 275
5y = 275 + 100
5y = 375
y = 375/5
y = 75.......Todd therefore spent 75 dollars!!
I think it gets easy from here
How do you write the square root of a negative number?.
Negative numbers doesn't have real square roots since a square is either positive or 0.
Negative Square Roots Simplifying an expression involving the square root of a negative quantity is done by simplifying the quantity as if it was positive, and placing an i in front as a coefficient.
for example:-
The square root of -9 is 3i. But if you are talking about real numbers, then there would be no solution.
Square root
The square root of a number is defined as the value, which gives the number when it is multiplied by itself.
The √ symbol that is used to denote square root or nth roots.
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the velocity time graph for a cycle is shown. work out the total distance travelled on the cycle. work out the acceleration in the last 8 seconds. Need the answer before 6th of Feb 2023.
Part A - The cycle has a total distance travelled of 130 meters.
Part B - The cycle has an acceleration of 0 meters per square second at t = 8 seconds.
How to apply kinematics from a graph
In this question we find the case of a graph between time (t), in seconds, and velocity (v), in meters per second, from which we need to determine the total distance travelled (s), in meters, on the cycle and the acceleration (a), in meters per square second, at a given time.
Part A - The total distance travelled is the area below the curve, defined as the sum of the areas of two triangles and rectangle, thus:
s = 0.5 · (6 s) · (10 m / s) + (6 s) · (10 m / s) + 0.5 · (8 s) · (10 m / s)
s = 30 m + 60 m + 40 m
s = 130 m
The total distance traveled by the cycle is 130 meters.
Part B - The acceleration at a given time t is the slope of the curve at point (t, v). In this case, we find that slope can be found by secant line formula:
a = [v(12) - v(6)] / (12 - 6)
a = (0 - 0) / (12 - 6)
a = 0 m / s²
The acceleration of the cycle at t = 8 seconds is equal to 0 meters per square second.
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Graph the following functions:
1. y=2x²
2. y=x²-2x-3
One graph will pass through the origin and the second graph will meet the x-axis at 3, -1.
What is Function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given two function
y=2x² y=x²-2x-3For y=2x²:
Since the value of x = 0, the value of y is 0.
thus this graph will pass through the origin and will only have 1 solution.
For y = x²-2x-3:
At y = 0
x²-2x-3 = 0
x = 3, -1
Therefore, This graph will pass through the x-axis at 3, -1.
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Which set of points represents a function? { ( 5 , 0 ) , ( 9 , 8 ) , ( 2 , 5 ) , ( 1 , 4 ) , ( 1 , 1 ) } {(5,0),(9,8),(2,5),(1,4),(1,1)} { ( 9 , 9 ) , ( 9 , 7 ) , ( 8 , 1 ) , ( 5 , 8 ) , ( 1 , 4 ) } {(9,9),(9,7),(8,1),(5,8),(1,4)} { ( 2 , 5 ) , ( 4 , 5 ) , ( 7 , 1 ) , ( 0 , 8 ) , ( 6 , 4 ) } {(2,5),(4,5),(7,1),(0,8),(6,4)} { ( 9 , 3 ) , ( 9 , 2 ) , ( 1 , 1 ) , ( 3 , 6 ) , ( 6 , 7 ) } {(9,3),(9,2),(1,1),(3,6),(6,7)}
The set of ordered pairs that is a function is (b) (-9, 9), (-8, 1), (2, -4), (-2, 1)
How to determine the ordered pair that is a function?The list of options represents the given parameter
All ordered pairs are relations but not all ordered pair are functions
For an ordered pair to be a function, the following must be true:
The y values on the ordered pair must have different x values
Using the above as a guide,
In (a) the y values -2 and -4 have the same x value of 5In (b), all the y values have different x valuesThis means that the ordered pair in option (b) represents a function
Hence, the ordered pair that is a function is (b)
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5. Angle F and angle G are
complementary. Angle F
measures (2x+10)° and angle
G measures 30°. Find the
value of x.
Answer: 25 degrees
Step-by-step explanation:
2x + 10 + 30 = 90
2x = 50
x = 25 degrees
a 12-foot ladder is leaned against the side of a building such that the angle of depression to the far side of the sidewalk is 45 degrees, but 65 degrees to the near side of the sidewalk. how wide is the sidewalk?
Answer:
From the top of a 12 foot ladder, the angle of depression to the far side of a sidewalk is , while the angle of depression to the near side of the sidewalk
Step-by-step explanation:
Please help !!
Write equations for the vertical and horizontal lines passing through the point (-3, -9).
vertical line:
horizontal line:
Answer:
vertical line x = -3
horizontal line y = -9
Step-by-step explanation:
Write a ytem of three linear equation in two variable o that any two of the equation have exactly one olution, but the entire ytem of equation ha no olution. PLEASE HELP FAST!!!!
A system of three linear equations in two variables that satisfies the given situation can be x + y = 5, 2x + y = 5, and x + 2y = 5
To satisfy the given situation for a system of three linear equations, write any linear equation as the first equation. Let's say
x + y = 5
For the second equation, multiply the x term of the first equation by any factor, keeping the y term and the constant unchanged.
2x + y = 5
The last equation could be written using the second equation wherein the constant of the variable x and y are interchanged.
x + 2y = 5
Any two of the equations in this system have exactly one solution, because they have a unique solution when we solve them individually. However, when we try to solve the entire system by using all three equations, we find that the system has no solution.
This can be easily seen by solving the system by substitution, elimination, or graphical method.
It is also possible to use different equations but with the same criteria, the key is that at least one of the equations should be the negation or a multiple of another equation.
The problem seems incomplete/unreadable, it must have been...
"Write a system of three linear equations in two variables so that any two of the equations have exactly one solution, but the entire system of equations has no solution."
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Ratnam hired a car from a car renting agency which charges a flat amount of Rs. x for travelling up to 40 kilometers and Rs. y per km for every kilometer travelled thereafter. How much should Ratnam pay the agency for a journey of 50 kilometers?
A. x + 10 y B. 50( x + y ) C. 40 x + y D. 50 x y
The total fee that Ratnam should pay the agency for a journey of 50 kilometers, using a linear equation, is A. x + 10y.
How is the total car hire fee determined?The total fee is a function of summing the fixed charge for the first 40 kilometers and the variable charge for additional kilometers traveled.
In this situation, the variable charge per km represents the slope or the unit rate while the fixed charge for 40 kilometers represents the constant in a linear equation.
Flat charge up to 40 kilometers = Rs. x
Variable charge per kilometer after 40 km = Rs. y
Total distance traveled = 50 kilometers
Total fee paid = Rs. x + (50 - 40)y
= x + 10y
Thus, the correct fee that Ratnam should pay is represented by Option A.
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Which two equations relate the measure of ∠4, to the measures of ∠1, ∠2, and/or ∠3.
Answer:
A and C
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle so first option,
A. m∠4 = m∠1 + m∠2
is correct.
m∠3 and m∠4 are supplementary angles because they make a straight line and their sum is equal 180°, so third option,
C. m∠4 = 180 - m∠3
is also correct.
What is value of sin?.
Let's first review the Sin function before talking about Sin 0. Therefore Sin 0 value is 0.
The Sine, Cosine, and Tangent functions in trigonometry are used to determine the angles and length of a right-angled triangle, respectively.
The relationship between the angle, perpendicular side, and hypotenuse side is defined by the sine function.
Alternatively, you can use sin theta, which is equal to the right-angled triangle's perpendicular to hypotenuse ratio. Sin theta is the angle produced between the hypotenuse and adjacent side.
Definition Of Sin In Relation To Sin 0.
Sin 0 denotes that (x,y) is where the value of the x coordinate is 1, and the value of the y coordinate is 0. (1,0). In this case, the hypotenuse has a value of 1, and the opposing side or perpendicular has a value of 0.
As a result, if we set the numbers in the sin ratio for = 0, the perpendicular side to be 1, and the hypotenuse to be 0, we obtain,
Sin 0 = 0/1
Sin 0 = 0
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Ricardo has an equally likely chance of spinning an odd number as spinning a number less than 4
The given statement that " Ricardo has an equally likely chance of spinning an odd number as spinning a number less than 4" is True.
How to find the probability?When rolling a fair dice, the probability of getting an odd number is:
= Number of odd numbers / Number of sides on die
Number of odd numbers = 1, 3, 5
Probability of odd number:
= 3 / 6
= 1 / 2
Probability of number less than 4 :
= 3 / 6
= 1 / 2
Ricardo therefore has an equally likely chance.
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Options for this question are:
True FalseHow many lb is 1.4 pounds
Answer:1.4
Step-by-step explanation: Because lbs are the same thing as pounds
7. Find the value of x. (AB = 8) (show work pls)
Answer:
Step-by-step explanation:
when GDK goes up GD goes down
