Use the properties of logarithms to write the expression as a single logarithm, if possible.
Answers
By logarithm properties, the logarithmic equation 2 · ㏒ₐ (5 · x³) - (1 / 2) · ㏒ₐ (2 · x + 3) is equivalent to ㏒ₐ [(25 · x⁶) / √(2 · x + 3)]. (Correct choice: A)
How to simplify a logarithmic function by propertiesIn this problems we have a logarithmic equation that must be simplified by means of logarithm properties, all of them described below:
Logarithm of a product of two numbers
㏒ₙ (a · b) = ㏒ₙ a + ㏒ₙ b
Logarithm of a division of two numbers
㏒ₙ (a / b) = ㏒ₙ a - ㏒ₙ b
Logarithm of a power of a number
㏒ₙ aˣ = x · ㏒ₙ a
Now we proceed to reduce the logarithmic equation into a single expression:
2 · ㏒ₐ (5 · x³) - (1 / 2) · ㏒ₐ (2 · x + 3)
㏒ₐ (5 · x³)² - ㏒ₐ √(2 · x + 3)
㏒ₐ (25 · x⁶) - ㏒ₐ √(2 · x + 3)
㏒ₐ [(25 · x⁶) / √(2 · x + 3)]
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Related Questions
Find the following parts of the given numbers. 3/4 of 56
Answers
The value of the fraction 3/4 of 56 is 42.
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.
The value of the fraction will be:
= 3/4 × 56
= 3 × 14
= 42
The value is 42.
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-1,8,11,-9,5,11 have a mode or is it unimodal bimodal or multimodal
Answers
Answer:
It has a mode of 11
Step-by-step explanation:
A mode is a # in a data set that occurs more then any other one
the linear function y=15.95 represents the cost y (in dollars) of x tickets for a museum. Each customer can buy a maximum of four tickets. find the domain of the function. is the domain discrete or continuous? explain
Answers
Domain of the function is (1,4) and the domain is discrete.
What is linear function?
A linear function may be a operate that forms a line during a graph. it's usually a polynomial operate whose degree is utmost one or zero. though the linear functions also are delineate in terms of calculus also as algebra.
Main body:
According to the question :
y=15.95 x
where y = cost ,
x = number of tickets
Each customer can buy a maximum of four tickets.
Plot the ordered pairs. Because you cannot buy part of a ticket,
the graph consists of individual points.
domain of the function is (1,4).
Hence , the domain is discrete.
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Find the equation of the tangent line to the graph of f(x) = e^2x-5 at the point (2, 1/e).
Answers
The tangent line to the graph of f(x) = 2e²ˣ-5 at the point (2, 1/e) is given by y=2e⁴+1-2e⁵/e
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The equation of the tangent line to the graph of f(x) = e²ˣ-5
To find the Equation of a tangent to any curve you must first find the derivative of the function.
y = e²ˣ-5
y'=2e²ˣ
sub x=2 into derivative function
y'(2)=2e⁴
so we have found that the tangent line is y=2e⁴+c
now we have to sub in the point and solve for c:
1/e=2e⁴+c
c=1/e-2e⁴
c=1-2e⁵/e
c=0 when x is 2.
The equation of tangent to the line is y=2e⁴+(1-2e⁵)/e
Hence, the equation of the tangent line to the graph of f(x) = 2e²ˣ-5 at the point (2, 1/e) is given by y=2e⁴+1-2e⁵/e
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Expression equivalent to 4(x-2)+4
Answers
Answer:4x-12
Step-by-step explanation:
Answer:
= 4x - 4
Step-by-step explanation:
4(x-2) + 4
= (4*x + 4*-2) + 4
= (4x - 8) +4
= 4x + 4 - 8
= 4x - 4
50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!! 50 POINTSSSSSS ASAP!!!! PLEASE HELP
A.
36°
B.
55°
C.
89°
D.
91°
Answers
Answer: I believe it would be 55 but It would help if it says what kind of triangle it is.
Step-by-step explanation:
Answer:
The answer is 91°
Step-by-step explanation:
In any triangle, the sum of all angles is equal to 180°
So,
35° + 54° + x = 180°
x = 180 - 89
x = 91°
Thus, The third angle is 91°
One angle measures 24°, and another angle measures (7d-4)°. If the angles are complementary what is the value of d?
d=80
d=17
d = 10
d=3
Answers
Based on the definition of complementary angles, the value of d is: 10.
What are Complementary Angles?Complementary angles can be described as two angles that have a sum of 90 degrees when added together.
Given that the two angles, 24° and (7d - 4)°, are complementary angles, it implies that their sum will give a measure of 90°. Therefore, to find the value of d, the following equation would be created based on the definition of complementary angles:
24 + (7d - 4) = 90
Open the parentheses:
24 + 7d - 4 = 90
Combine like terms:
7d + 20 = 90
Subtract 20 from both sides
7d + 20 - 20 = 90 - 20
7d = 70
Divide both sides by 7
7d/7 = 70/7
d = 10
The value of d is: 10.
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I rlly need help on this badly
Answers
3.
The value of x is 20.
The value of y is 30.
4.
The value of x is 30.
The value of y is 4.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
3,
The triangle is an equilateral triangle.
Value of all the angles = 60°
All sides are equal.
Now,
46 = 16 + y
y = 46 - 16
y = 30
Now,
The sum of the three angles of the triangle is 180 degrees.
80 + 60 + (60 - x) = 180
140 + 60 - x = 180
200 - 180 = x
x = 20
4.
There is an equilateral triangle.
5y = 20
y = 4
There is an isosceles triangle.
Where two sides are equal and the angle opposite to the equal sides are also equal.
This means,
(180 - 60) + x + x = 180
120 + 2x = 180
2x = 180 - 120
x = 60/2
x = 30
Thus,
3.
The value of x and y is 20 and 30.
4.
The value of x and y is 30 and 4.
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What’s
: 2 1/7 + 3/7 (3x - 5) = -4
Please explain step by step to get picked brainliest!
Answers
The solution to the equation is x = -28/9.To solve the equation 2 1/7 + 3/7(3x - 5) = -4, let's break it down step by step.
Step 1: Convert the mixed number 2 1/7 to an improper fraction. Multiply the whole number (2) by the denominator (7), then add the numerator (1). This gives us (2 * 7 + 1) / 7 = 15/7.
Step 2: Distribute the 3/7 to the terms inside the parentheses. Multiply 3/7 by each term, which gives us (3/7) * 3x = 9x/7 and (3/7) * (-5) = -15/7.
Step 3: Substitute the converted mixed number and the distributed terms back into the equation. The equation becomes 15/7 + 9x/7 - 15/7 = -4.
Step 4: Combine like terms. Add the fractions with the same denominator: (15/7 - 15/7) + 9x/7 = -4. The fractions cancel each other out, leaving us with 9x/7 = -4.
Step 5: Isolate the variable. Multiply both sides of the equation by the reciprocal of 9/7, which is 7/9. This gives us (7/9)(9x/7) = (7/9)(-4). The 7/9 on the left side cancels out, leaving x = (-28/9).
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write the quadratic function in standard form (show steps)
Intercept form: y=(x+2) (x-2)
Answers
FOIL means First Outer Inner Last, which means when we are given two binomials multiplying each other, we first distribute the outer term first, then the inner term last. Here’s how we do it:
Given y=(x+2)(x-2)
Using FOIL:
y=(x•x-2•x)+(2•x-2•2)
So, we took x from (x+2) and multiplied every term in (x-2) by it, then did the same for 2 in (x+2).
Let’s simplify:
y=x^2-2x+2x-4
We can combine like terms:
y=x^2-4
*Notice that -2x+2x canceled out; this is because they contain inverse operations. For example, -2+2=0 or -2(4)+2(4)=-8+8=0.
Your final equation is y=x^2-4
*Note that ^ symbol represents an exponent, so x^2 means x squared or to the second power.
What symmetries does the graph of f(x)=√2 x−1 have?
Answers
Answer:
Step-by-step explanation:
Find the asymptotes.
Vertical Asymptotes:
x
=
0
Horizontal Asymptotes:
y
=
0
No Oblique Asymptotes
A lot of points. PLEASE HELP! I will mark brainliest. Whoever gets it right first.
Answers
- the last one is your answer, you can use the small lines on the side of triangle to help you know which ones match with each other
HELP PLEASE INSTANT
Answers
Answer: number 3
Step-by-step explanation:
43. Find the length of the midsegment.
45
45
74
126
74
Answers
Answer: hi
Step-by-step explanation:
There are a adults at the fair. There are 20 more kids than adults. Write an expression
that shows how many kids there are.
a+
Submit
olo
Answers
The Number of kids in the fair is x + 12
What are Variables ?A variable is a symbol and a stand-in for any mathematical object in mathematics. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.
According to the given information
Let x be the variable
Let the number of adults in the fair = x
Number of kids in the fair is 12 more than the adults
So
Number of kids in the fair = 12 + Number of adults in the fair
= 12+x
Hence
The Number of kids in the fair is x + 12
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Sally has 2 cats and each cat eats 1/4 of a tin of cat food each day.
Sally buys 7 tins of cat food.
For how many days will the cat food feed her 2 cats?
You must show your working.
days=?
Answers
Answer:
33
Step-by-step explanation:
Find the zeros of the function.
State the multiplicity of multiple zeros.
y = 7x³ - 7x
Answers
Answer:
The zeros of the function are x = -3, x = 1, x = 3. The multiplicity of the zero x = 3 is 3.
Step-by-step explanation:
Answer:
0, 1, -1
Step-by-step explanation:
7x³ - 7x = 0
=> x(7x² - 7) = 0
=> 7x(x² - 1) = 0
=> x(x² - 1) = 0
=> x(x+1)(x-1) =0
=> x = 0 or x = -1 or x = 1
A garden table and a bench coat $788 combined. The garden table cost $62 less than the bench. What is the cost of the bench?
Answers
Answer:
Step-by-step explanation:
Let T represent table and B represent bench. The garden table costs $62 less than the bench. T = B - 62. plug T = B - 62 into T + B = 788. B - 61 + B = 788. This gives us 425. B = 425.
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A store sells a shirt that is discounted by 10%. A coupon is used for an additional 10% off the
discounted price.
What is the total percentage discount on the shirt?
Answers
Answer: B
Step-by-step explanation:
Find the equation of the tangent line that crosses the function, f(x) = x^2-5, at x=-2
Answers
Answer:
We can use the point-slope formula to find the equation of the tangent line. The point-slope formula is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line. To find the equation of the tangent line, we need to find the slope of the line and a point on the line.
To find the slope of the line, we can use the definition of derivative. The derivative of a function f(x) at a point x0 is defined as:
f'(x0) = lim(h->0) (f(x0 + h) - f(x0))/h
In our case, the function f(x) is given by f(x) = x^2 - 5, and the point x0 is -2, so we have:
f'(-2) = lim(h->0) (f(-2 + h) - f(-2))/h
Substituting the value of the function f(x) = x^2 - 5, we get:
f'(-2) = lim(h->0) (((-2 + h)^2 - 5) - ((-2)^2 - 5))/h
Simplifying the expression, we get:
f'(-2) = lim(h->0) (h^2 - 4h)/h
Since the limit is defined as h approaches 0, we can drop the h from the denominator since it will become insignificant in the limit:
f'(-2) = lim(h->0) (h^2 - 4h)
Now we can evaluate the limit as h approaches 0:
f'(-2) = lim(h->0) h^2 - 4h
In the limit, h^2 becomes 0, so we are left with:
f'(-2) = lim(h->0) - 4h
Since the limit is defined as h approaches 0, the value of the limit is simply -4 times 0, which is 0. Therefore, the slope of the tangent line is 0.
Now that we know the slope of the tangent line, we need to find a point on the line. We are told that the line passes through the point (-2, f(-2)) on the function f(x) = x^2 - 5. Substituting the value of the function, we get:
(-2, f(-2)) = (-2, (-2)^2 - 5) = (-2, -9)
So the point on the line is (-2, -9).
We now have the slope and a point on the line, so we can use the point-slope formula to find the equation of the line. Substituting the values into the point-slope formula, we get:
y - (-9) = 0(x - (-2))
Simplifying, we get:
y = -9
Therefore, the equation of the tangent line that passes through the point (-2, -9) with a slope of 0 is given by y = -9.
Hi, need fast answers and an explanation on how you got your answer please.
Answers
Answer:
x = 56
y = 124
z = 56
Step-by-step explanation:
The 124° angle and y° are vertical angles. vertical angles are congruent. they have equal measures.
y = 124
Angles 124° and x° form a linear pair. Angles in a linear pair are supplementary. Their measures add to 180°.
124 + x = 180
x = 180 - 24
x = 56
Angles x° and z° are vertical angles.
z = x = 56
Answer:
x = 56
y = 124
z = 56
a pineapple which was bought for $1.00 was sold at $1.30. calculate the profit percent
Answers
Answer: 30%
Step-by-step explanation:
You buy a watch that is $60. There is a 6% sales tax and a 15% discount. How much is the watch now?
Answers
Answer:
$54.06
Step-by-step explanation:
$60x0.85=51
51x1.06=$54.06
On a team, 3 girls and 2 boys scored a total of 43 points. The difference between the number of points scored by the 3 girls and the number of points scored by the 2 boys is 11 . Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each boy.
Answers
Answer:
each girl scored 1 point and each boy scored 20 points.
Step-by-step explanation:
Let $g$ be the number of points scored by each girl and $b$ be the number of points scored by each boy. We can set up the following system of equations:
$$3g + 2b = 43$$
$$3g - 2b = 11$$
We can solve this system of equations using substitution. From the first equation, we have that $3g = 43 - 2b$. Substituting this expression for $3g$ into the second equation gives:
$$3(43 - 2b) - 2b = 11$$
Solving for $b$, we get:
$$129 - 6b = 11$$
$$6b = 118$$
$$b = 19.5$$
Since $b$ must be a positive integer, the only possible value for $b$ is $20$. Substituting this value into the first equation, we get:
$$3g + 2(20) = 43$$
Solving for $g$, we get:
$$3g = 3$$
$$g = 1$$
Therefore, each girl scored $1$ point and each boy scored $20$ points.
Wile Coyote is chasing after the famous Road Runner one afternoon. The roadrunner sets off at a
speed of 72mph, while the coyote has issues with his rocket bike. It takes him 15 minutes to
repair it, then he shoots after him. The coyote is not worried at all because his ACME rocket bike
has a speed of 220mph. How long (in minutes) has the Road Runner been running once the
coyote catches up to him?
Answers
The time the Road Runner been running is 7.3 minutes
How to determine the time the Road Runner been running?From the question, we have the following parameters that can be used in our computation:
Roadrunner speed = 72mph
Time for repair = 15 minutes
Speed = 220mph
Represent the time the Road Runner been running with x
The speed is calculated using
Speed = Distance/Time
So, we have the following representations
Roadrunner speed = Distance/Time
Wile Coyote speed = Distance/Time
This gives
72 = Distance/(15 + x) -- for the roadrunner
220 = Distance/x for the Wile Coyote
So, we have
Distance = 72(15 + x)
Distance = 220x
Substitute the known values in the above equation, so, we have the following representation
220x = 72(15 + x)
Open the brackets
220x = 1080 + 72x
Evaluate the like terms
148x = 1080
So, we have
x = 7.3
Hence, the minutes is 7.3 minutes
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Solve for the other leg and for the hypotenuse of the 45-45-90 triangle
Answers
Answer:
4th answer option
Step-by-step explanation:
both side angles are 45°, that makes the triangle an isoceles triangle (both legs are equally long).
therefore, v = 7.
Pythagoras gives us
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), a and b being the legs.
in our case
u² = 7² + 7² = 49 × 2
u = sqrt(49 × 2) = 7 × sqrt(2)
if g(x) is the image of y=-3x[tex]y=3x^{2}-24x+2[/tex] after a translation left 5 units and up 5 units write in starnded form
Answers
The image of y which is g(x) is 3x² + 60x + 82.
What are some transformation of functions?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over y axis, (-x, y).
-f(x) = Reflection over x-axis, (x, -y).
Given, y = 3x² - 24x + 2.
Now, g(x) is an image of y after a translation left 5 units and up 5 units.
∴ g(x) = 3(x + 5)² + 2 + 5.
g(x) = 3(x² + 20x + 25) + 7.
g(x) = 3x² + 60x + 75 + 7.
g(x) = 3x² + 60x + 82.
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Amy had 30 minutes to do a three-problem quiz. She spent 10
7/10 minutes on question A and 4 2/5 minutes on question B. How much time did she have left for question C?
Answers
The time Amy has left for the question C is 13.9 minutes.
How to write a mixed fraction into a fraction?The mixed fraction can be converted into a fraction by interchanging the numerator with the sum of the product of denominator and the whole number and the numerator of the mixed fraction. It can be shown as 2(¹/₂) = (2 × 2 + 1)/2 = 5/2.
Given that,
The total time for quiz is 30 minutes.
The time taken to do problem A is 10(⁷/₁₀) and for B is 4(²/₅).
Thus, the remaining time left can be calculated by the as follows,
30 - (10(⁷/₁₀) + 4(²/₅))
Change the mixed fraction into the fraction to obtain,
30 - (107/10 + 22/5) = 13.9
Hence, the time left for question C is given as 13.9 minutes.
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Please look at the picture and answer the question, Thank you!
Answers
Inequality: x>12
Interval Notation: ( 12, ∞ )
What is the slope? also make sure to show how you got that
Answers
Answer:
The slope is a value that describes the steepness and direction of a line
Step-by-step explanation:
I think ts either 2 or nagtive 2
Answer:
gradient (slope) = 2
Step-by-step explanation:
gradient (slope) = difference of y-coordinates / difference of x-coordinates = (y₂-y₁)/(x₂-x₁)
Pick two points, ex: (0,1) and (-2,0)
= (0-1)/((-2)-0)
= -1/-2
= 1/2