[tex]6^{2x} = 10[/tex] => x = 0.642, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: [tex]6^{2x} = 10[/tex]
Taking logarithm on both sides:
=> log ([tex]6^{2x}[/tex]) = log 10
=> 2x (log 6) = log 10 ( as [tex]log_b(a)^m = m (log_b(a))[/tex])
=> 2x = [tex]\frac{log10}{log6}[/tex]
=> 2x = [tex]\frac{1}{0.778}[/tex]
=> 2x = 1.285
=> x = 0.642
Hence, [tex]6^{2x} = 10[/tex] => x = 0.642, by properties of logarithm.
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What is the approximate value of √8
Answer:
Close to 3 since 8 is close to 9.
The actual value was 2.8, so I approximated what was closest to it using rounding and the most logical explanation.
Complete the identities.
csc θ =1/?
Answer:
? = sin θ
Step-by-step explanation:
csc θ =1/?
csc θ =1/sin θ
solve 4- | 2x -1 | = -3 i need it pls help
The value of x is 3
What are algebraic expressions?Algebraic expressions are expressions made up of variables, terms, factors, constants and coefficients.
They are also made up of mathematical operations like addition, subtraction, multiplication, division, etc
It is important to note that the absolute value of a number takes a positive sign.
It is denoted with the sign ' | | '
Given the expression:
4- | 2x -1 | = -3
First, take the absolute value
4 - 2x + 1 = - 3
collect like terms
2x = -3 - 4 + 1
2x = - 7 + 1
2x = -6
Make 'x' the subject of formula
x = 6/2
x = 3
Thus, the value of x is 3
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Hilda has $210 worth of $10 and $12 stock shares. the numbers of $10 shares is 5 more than twice the number of $12 shares. how many of each does she have?
If Hilda has $210 worth of $10 and $12 stock shares and the number of $10 shares is 5 more than twice the number of $12 shares, then the number of $10 shares and $12 shares she has is equal to 15 and 5 respectively.
The number of $10 shares and $12 shares can be calculated by forming linear equations.
Consider the number of $10 shares to be x and the number of $12 shares to be y.
x = 2y + 5
10x + 12y = 210
Putting the value x = 2y + 5 in the second equation,
10x + 12y = 210
10 (2y + 5) + 12y = 210
20y + 50 + 12y = 210
32y + 50 = 210
32y = 210 - 50
32y = 160
y = 160 ÷ 32
y = 5
Putting y = 5 in the first equation,
x = 2y + 5
x = 2(5) + 5
x = 10 + 5
x = 15
Hence the number of $10 and $12 shares she has is calculated to be 15 and 5 respectively.
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Work out
(3 × 10^−3)−(6 × 10^−5)
Give your answer in standard form.
Answer:
answer is
[tex] {2.94 \times 10}^{ - 3} [/tex]
Step-by-step explanation:
3*1/1000-6*1/100000=0.003-0.00006
=
[tex] {2.94 \times 10}^{ - 3} [/tex]
need help with inequality equations
Answer:
I and III
Step-by-step explanation:
I.
-6 - x ≤ 7
-6 - (-13) ≤ 7
-6 + 13 ≤ 7
7 ≤ 7
True
II.
-6 - x ≤ 7
-6 - (-14) ≤ 7
-6 + 14 ≤ 7
8 ≤ 7
False
III.
-6 - x ≤ 7
-6 - (-6) ≤ 7
-6 + 6 ≤ 7
0 ≤ 7
True
I hope this helps!
Solve the following system of equations. What is the x -coordinate of the solution?
y-3=x
y/x²-9}=1
The x-coordinate of the given equation is x=4.
What essentially is an equation?An equation is a mathematical statement composed of two representations joined by an equal sign.An example of an equation is 3x - 5 = 16.After solving this equation, we obtain the value for the variable x as x = 7.
So,
Given:
y-3 = x ...(1)y/x²-9 = 1 ...(2)Then,
y = x+3Substitute y=x+3 in equation (2):
y/x²-9 = 1 x+3/x²-9 = 1 x+3/x²-3² = 1 1/x-3=1(Cross multiply)
x-3=1x=1+3x=4Therefore, the x-coordinate of the given equation is x=4.
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Write each equation in logarithmic form. 64=4³
The equation in logarithmic form is log₄(64) = 3
Given the equation is:
64 = 4³
The fundamental logarithmic function has the notation f(x) = log(r) y = log(x), where a > 0. The exponential function a y = x's inverse is represented by this. The common logarithm (log) or natural logarithm (ln) are examples of log functions (log).
Convert the exponential equation to a logarithmic equation using the logarithm base (10)of the right side (0.01) equals the exponent (−2).
A popular method for changing a mathematical equation from one form to another is to transform it from exponential to log form. The exponential form an x = N is translated into the logarithmic form
Log aⁿ= x.The exponent of x, which is equal to N, has the exponential form a to it is converted to the logarithm of a number N to the base of a, which is equal to x.
log₄(64) = 3
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ײ + 5× - 11 + 3ײ - 11 × + 2
hello guys please solve and give a solution tthankyou
Step-by-step explanation:
start by collecting like terms
4x² - 6x -9
use quadratic equation, a=4, b= 6 and 9 = c.
x = 5,78 or x = -4,28
One number is 19 greater than the other, the sum of these numbers is 97. What is the greater number?
Answer:
Greater number = 58
Step-by-step explanation:
The equation is,
→ (x + 19) + x = 97
Now the value of x will be,
→ (x + 19) + x = 97
→ 2x = 97 - 19
→ x = 78/2
→ [ x = 39 ]
Then the greater number is,
→ x + 19
→ 39 + 19 = 58
Hence, the answer is 58.
Answer:
58
Step-by-step explanation:
first number=x
second number= x+19
x+x+19= 97
thus, the two numbers are 39 and
a to the power of 5 divided by a to the power of 3
Answer:
Step-by-step explanation: i thank the answer is 100 .
Find the domain, points of discontinuity, and x - and y - intercepts of each rational function. Determine whether the discontinuities are removable or non-removable. y=3x-3 / x²-1
The domain of given points are :
IR x ≠ ±1
Points of discontinuity - x = -1 ( non removable / asymptote )
x = 1 ( removable / hole)
x - intercept = 1 , y - intercept = 3
What is rational functions ?Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere. First example: f(x) = x/ (x - 3).
CALCULATIONy=3x-3 / x²-1
= 3(x-1)/(x+1)(x-1)
The domain of given points are :
IR x ≠ ±1
Points of discontinuity - x = -1 ( non removable / asymptote)
x = 1( removable / hole)
x-intercept :
3(x-1)=0
3x-3=0
x=1
y - intercept :
3(0-1)/(0+1)(0-1)=3
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Tonya is paid a salary of $650 a month at her sales job. She also earns a commission on her sales in this way: 3% on all sales up to $32,000 in a month
and 8% on all higher sales. What were Tonya's total earnings for a month where her total sales were $80,000?
Tonya's total earnings for a month where her total sales were $80,000 is $5450.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
Tonya is paid a salary of $650 a month at her sales job.
She also earns a commission on her sales in this way: 3% on all sales up to $32,000 in a month and 8% on all higher sales.
= 650 + 32000(3%) + (80000 - 32000)(8%)
= 650 + 960 + 3840
= $5450
Thus, Tonya's total earnings for a month where her total sales were $80,000 is $5450.
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The grid above shows the graph of the parent function f(x) = | x | and a translated functions graph.
Write the equation for the translated graph.
Please Hurry, I will give brainliest!
By using the principles of translation, the following equation can be derived for the graph of the translated text:
g(x) = |x + 2| + 1.
What is a translation?According to operations like multiplication or sum/subtraction either in its range (including values of y) or in its domain, a translation is represented by a change in the function graph (involving values of x).
Examples include shifts to the left, right, or bottom; compression or stretching along the vertical or horizontal axis; reflections across the x or y axes; and rotations of a degree measured around the origin.
From the graph, we have that the parent function was:
Shifted left 2 units, hence x -> x + 2.
Shifted up 1 unit, hence y -> y + 1.
Hence, considering the parent function f(x) = |x|, the equation for the translated graph is given by:
g(x) = |x + 2| + 1.
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I need help figuring out what 7x + 5 divided by x is
Answer:
The way you described this question was a bit confusing- but here is what I can provide based off of what you said.
Step-by-step explanation:
7x+5/x
Please provide a picture next time
Solve for x to the nearest tenth.
Applying the Pythagorean Theorem, the value of x to the nearest tenth is: 4.5 units.
What is the Pythagorean Theorem?If c represents the length of the longest side (hypotenuse) of a right triangle, and a and b are the lengths of the other smaller legs of the right triangle, the Pythagorean Theorem states that:
c = √(a² + b²).
In the diagram given, we have a right triangle that is a part of the given shape. Where:
Hypotenuse = c = x
a = 4 units
b = 5 - 3 = 2 units
Plug in the values
x = √(4² + 2²)
x = √(16 + 4)
x = √20
x ≈ 4.5 units (nearest tenth)
Thus, applying the Pythagorean Theorem, the value of x to the nearest tenth is: 4.5 units.
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What is the difference between 10 and 5 in variable and verbal expression
As a verbal expression, the difference between 10 and 5 is 5
What is the difference between 10 and 5 in variable and verbal expression?The numbers are given as
10 and 5
The difference between the numbers is calculated as
Difference = 10 - 5
Evaluate the difference
Difference = 5
The above represents the difference in variable
As a verbal expression, the difference between 10 and 5 is 5
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10)110
help me please
Answer:
If it is a division problem, then it is 11.
If it is a multiplication problem then it is 1100.
But it looks like division, so probably 11.
Answer:
011
Step-by-step explanation:
0 1 1
--------------------------------
1 /
0 1 1 0
− 0
1 1
− 1 0
1 0
− 1 0
0
Micah is 7 years older than treasure. in 6 years the sum of their ages will be 51. how old is micah now?
The age of Micah is 23 years.
Let the age of treasure be x years. So, the present age of Micah will be (x + 7) years.
Now, age of treasure after 6 years = (x + 6) years
Age of Micah after 6 years = (x + 7 + 6) years
Age of Micah = (x + 13) years
As the question mentions, the sum of their ages is 51. So, relating the given information -
(x + 6) + (x + 13) = 51
Performing addition on Left Hand Side of the equation
2x + 19 = 51
Shifting 19 to Right Hand Side of the equation
2x = 51 - 19
Performing subtraction on Right Hand Side of the equation
2x = 32
Shifting 2 to Right Hand Side of the equation and performing division
x = 32 ÷ 2
x = 16 years
So, the present age of Micah = x + 7
Present age of Micah = 16 + 7
Present age of Micah = 23 years
Hence, the present age of Micah is 23 years.
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A women bought some large frames for $19 each and some small frames for $7 each at a closeout sale. If she brought 19 frames for $205, find how many of each type she bought
Answer:
the one I have found that would is
13 small frames
6 big ones
Step-by-step explanation:
not gonna lie I used trial and error
so I went for example 19 x 10 = 190
205 - 190 = 15 and then 15 / 7
I did this until I got an whole number on the divide by seven bit
Triangle ABC with vertices A(–4, –4), B(–1, –2), C(3, –1) is rotated 180° about the origin. What are the coordinates of triangle A′B′C′?
Answer:
A(4, 4), B(1, 2), C(-3, 1)
Step-by-step explanation:
Because the triangle is rotated 180° about the origin you are just rotating it 2 quadrants, the size stays the same.
The rule for rotating 180° is if (x, y) is rotating 180° then the new position is (-x, -y).
So:
A(-4, -4), which then becomes B(-(-4), -(-4) ) = B(4, 4)
B(–1, –2) which becomes B(-(–1), –(-2) ) = B(1, 2)
C(3, –1) which becomes C(-3, –(-1) ) = C(-3, 1)
Write each expression in radical form. y⁻⁴/₃
The radical expression of the term y-⁴/³ is ∛y-⁴ or ∛(1/y⁴).
What is a radical?A radical is a number that is denoted by a root and can be easily identified because before the number is the symbol √, which lets us know that it is a root.
In this case we have an exponential number since it is raised to a number, radicals can be expressed as powers raised to fractions as follows:
√a = a¹/²
If our term is raised to -4/3, it can be expressed as:
y-⁴/³ = y-¹/³ y-¹ = 1/y⁴/³ now we apply.
y⁴/³ = ∛y⁴ and apply to the numerator since it is not altered and we have
y-⁴/³ = ∛(1/y⁴)
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What is the value of the expression 8 + (9 -1) \div÷ 4?
Answer:10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
8 + (9- 1) ÷ 4
Use PEMDAS to determine order of operations in a mathematical expression
The order of operations is
P = parentheses
E = exponent
M = multiplication
D == division
A = addition
S = subtraction
Note that multiplication and division have the same priority and we go from left to right that case. Because it does not affect the answer.
So 12 ÷ 4 x 6 = 12 x 6 ÷ 4
Same for addition and subtraction - same priority
Using PEMDAS
(9 - 1) is executed first giving 8
The expression becomes 8 + 8 ÷ 4
Next division is performed so 8 ÷ 4 is executed giving 2 as the answer
Finally 8 + 2 is executed giving 10
How much greater is 40,000 than 4,000
Answer:
40,000 is 10x greater than 4,000
Step-by-step explanation:
Times 4,000 by 10 and you get 40,000
Manuel gave the cashier $20 to pay for 3 bottles of hand sanitizer. The cashier gave him $8.03 in change. Each bottle cost the same amount.
Answer:
Each bottle cost $3.99.
Step-by-step explanation:
$20-$8.03=11.97
Each bottle = $11.97÷3
=$3.99
So now each bottle cost$3.99
28:49 ratio in simplest form
Answer:
4:7
Step-by-step explanation:
thats the answer mate
Answer:
4 : 7
Step-by-step explanation:
28 : 49 ← divide both parts by 7
= 4 : 7 ← in simplest form
the ratio is in simplest form when no other value but 1 divides into the 2 parts of the ratio.
Carl works at a bicycle shop he earns eight dollars for each bicycle tire he repairs and $45 Dollars each week for cleaning the shop which expression shows how much Carl’s earn each week if he repaired X bicycle tires
Identify each of the following anglemeasures as acute, right, obtuse, straight, or reflex 35° 91° 65° 28°
The angles 35° 65° and 28° are acute angles and the angle 91° is an obtuse angle
How to identify each of the angle measures?The angle measures are given as:
35° 91° 65° 28°
As a general rule:
Angles that are less than 90 degrees are acute angles
This means that
The angles 35° 65° and 28° are acute angles
Also, we have
Angles that are between 90 degrees and 180 degrees are obtuse angles
This means that
The angle 91° is an obtuse angle
Hence, the angles 35° 65° and 28° are acute angles and the angle 91° is an obtuse angle
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Abby stacked two cube-shaped blocks, as shown below, and plans to paint the figure for an art project.
What is the surface area of the figure if s = 5 inches?
When Abby stacked two cube-shaped blocks, the surface area of the figure if s = 5 inches is 250 inches²
What is surface area?It should be noted that the surface area of a solid object is a measure of the total area that the surface of the object occupies.
Length (l) = 5 in
Width (w) = 5 in
Height (h) = 10 in
Surface area of figure
= 2 (lw+wh+hl)
= 2 (25 + 50 + 50)
= 2(125)
= 250
Therefore, when Abby stacked two cube-shaped blocks, the surface area of the figure if s = 5 inches is 250 inches²
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2x(4+1)+(3x+5)+(2x+1)