use properties of logarithms to expand the logarithmic expression as much as possible.
help please!
Answers
Step-by-step explanation:
Begin by separating the division. Division in the argument of a logarithm function is equivalent to subtracting the log of the numerator and denominator:
[tex]ln( \frac{ {x}^{9} \sqrt{ {x}^{2} + 7} }{ {(x + 7)}^{7} } ) = ln( {x}^{9} \sqrt{ {x}^{2} + 7 } ) - ln(( {x + 7})^{7} )[/tex]
Multiplication under a logarithm means addition:
[tex] ln( {x}^{9}) + ln( \sqrt{ {x}^{2} + 7 }) - ln(( {x + 7})^{7} )[/tex]
Log rules say that exponents can be dragged to the front as coefficients:
[tex]9ln(x) + \frac{1}{2} ln( {x}^{2} + 7) - 7ln(x + 7)[/tex]
Related Questions
Haha please help i don't know what I'm doing
Answers
Answer:
(5x+1)(x+7)
Step-by-step explanation:
4x^2+26x+6+x^2+10x
5x^2+36x+7
(5x+1)(x+7)
Prove
5x*x + 5x*7 + 1*x + 1*7
= 5x^2 + 35x + x + 7
= 5x^2 + 36x + 7
explain how to do this please!
Answers
Answer:
The area of figure = 600 cm ²
Step-by-step explanation:
Area of this figure = area of triangle + area of rectangle
Area of triangle = 1/2 × base × height
Area of rectangle = length× breadth
=> (1/2 × 20 × 20 ) + ( 20×20 )
=> 200 + 400
=> 600 cm²
if a clock shows it is 3 o'clock, how could you describe the smaller angle made by the two hands of the clock? Solve this problem any way you choose.
Answers
Answer: 5 1/4
Step-by-step explanation:
Answer:
90°
Step-by-step explanation:
The minutes hand is vertical pointing straight up.
The hours hand is horizontal pointing right.
The smaller angle between the hands is 90°.
Please help!! Due in 15 minutes!!
Q.1. Which point is a solution to the system below?
y ≤ -2/3x - 4
y ≥ 1/5x - 3
A. (0, 3)
B. (-4, -2.5)
C. (-5, 0)
D. (-2, -4)
Q.2. Which point is a solution to the system of inequalities below?
A. (4, -9)
B. (2, -10)
C. all real numbers on y < -4x - 2
D. There is no solution to this system of inequalities
Q.3. Which statement is true about the system of inequalities below?
y ≤ 3x + 6
y > - x
I. The intersection point (-1.5, 1.5) is a solution to the system
II. The point (0, 0) is a solution to the system
III. The point (5, 5) is a solution to the system
IV. The point (-1, 6) is a solution to the system
A. I only
B. I and II only
C. III and IV only
D. III only
Answers
Answer:
aaaaaaaaaaaaaaaaa
Step-by-step explanation:
The history museum is hosting a special exhibition on history of flight. The admission ticket for each adult costs $7 and the admission
ticket for each child costs $2. On the opening day of the exhibition, 40 tickets were sold for a total of $180. How many adults visited the
special exhibition?
Answers
Answer:
Use simultaneous equation for this problem
y= number of adults
x = number of children
3y + 2x = 160
y + x = 60
then we double the second equation
3y + 2x = 160
2y + 2x = 120
we cancel x by elimination
3y - 2y = 160 - 120
y = 40
Step-by-step explanation:
hope this helps
What is the simplified expression for
44.4°?
49
40
41
42
43
Answers
Answer:
[tex]4^2[/tex]
Step-by-step explanation:
[tex]\dfrac{4^4 \cdot 4^3}{4^5}\\\\\\=\dfrac{4^{4+3}}{4^5}\\\\\\=\dfrac{4^{7}}{4^5}\\\\\\=4^{7-5}\\\\\\=4^2[/tex]
Answer:
4^2
Step-by-step explanation:
4^4*4^3=4^7
4^7/4^5=4^2
Does anyone know this correctly?
Answers
Where is the blue dot on the number line?
Answers
the blue dot on the number of line is -11.3
Answer:
-11.3
Step-by-step explanation:
Each jump/line is 0.1
As we can see the blue dot is 3 lines from -11 and 2 lines from -11.5 so our answer will be -11 + -0.3 and -11.5 - (-0.2)
-11 + -0.3 = -11.3
-11.5 - (-0.2) = -11.5 + 0.2 = -11.3
Hope this helps and brainliest please
A cone is stacked on top of a cylinder. they both share a circular base. the total height of the composite figure is 20. the height of the cylinder is 11 and the diameter is 12. what is the volume of the composite figure? use 3.14 for π and round the answer to the nearest tenth of a cubic unit. 753.6 in.3 904.3 in.3 1,582.6 in.3 1,997.0 in.3
Answers
Answer:
it is C
Step-by-step explanation:
got it right on edge
Answer:
1,582.6 in.3
Step-by-step explanation:
PLEASE HELP NEED NOW!!
Jayden has a bag that contains pineapple chews, strawberry chews, and lime chews.
He performs an experiment. Jayden randomly removes a chew from the bag, records
the result, and returns the chew to the bag. Jayden performs the experiment 41 times.
The results are shown below:
A pineapple chew was selected 31 times.
A strawberry chew was selected 4 times.
A lime chew was selected 6 times.
Based on these results, express the probability that the next chew Jayden removes
from the bag will be strawberry chew as a fraction in simplest form.
Answer:
Submit Answer
attempt 2 out of 2
Answers
Answer:
4/41
Step-by-step explanation:
Please let me know the answer to this 5^2+10^2=
Answers
Answer:
5^2+10^2=25+100=125
Step-by-step explanation:
Answer: 125
Step-by-step explanation: 5² + 10² = 25 + 100
Which three-dimensional figure has exactly three rectangular faces?
O rectangular prism
O rectangular pyramid
O triangular prism
• triangular pyramid
Answers
Answer:
Triangular prism
Step-by-step explanation:
Got it right on edge 2022 :)
The three-dimensional figure that has exactly three rectangular faces is a rectangular pyramid
What is the volume of a pyramid?The volume of a pyramid, is the product of the area of its base with the height of the pyramid, and divide by 3. We express this product with the formula V = ( 1/3) ×B×h, where B is the area of the base of the pyramid, and h is its height.
Volume of Pyramid = ( 1/3 )a²H
Given data ,
Let the pyramid be represented as A
Now , A rectangular prism has 6 faces, where each face is a rectangle.
A rectangular pyramid has 5 faces, where 4 faces are triangles and 1 face is a rectangle.
A triangular prism has 5 faces, where 2 faces are triangles and 3 faces are rectangles.
A triangular pyramid has 4 faces, where 3 faces are triangles and 1 face is a rectangle.
Hence , the only figure that has exactly three rectangular faces is a rectangular pyramid
To learn more about pyramid click :
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ed galaxy perimeter
Answers
Answer:
53 mm
Step-by-step explanation:
Perimeter is the sum of the lengths of all its sides.
Let the length of the unknown side be x mm.
123= 25 +45 +x
x= 123 -25 -45
x= 53
Thus, the unknown side is 53 mm.
PLEASE HELP!!!
If f(x) = -2x^2 + x - 5, what is f(3)?
Answers
Answer:
f(3) = -10Step-by-step explanation:
Given
f(x) = -2x² + x - 5Solving
To find f(3), substitute x = 3 in the function⇒ f(3) = -2(3)² + (3) + 5⇒ f(3) = -2(9) + 8⇒ f(3) = -18 + 8⇒ f(3) = -10Answer:
f(3) = 6
Step-by-step explanation:
f(x)=2x^2 + x -5
f(3) = 2 (3)^2 + (3) - 5
f(3) = 8 + 3 - 5
f(3) = 11-5
f(3) = 6
Two angles are complementary. The larger angle is 46∘46∘ larger than the smaller angle. Find the measure of both angles, and separate your answers with a comma
Answers
Answer:
22, 68
Step-by-step explanation:
(Complementary means that the angles together equal 90 degrees)
x + x + 46 = 90
2x + 46 = 90
2x = 44
x = 22
22 + 46 = 68
The garden in the scale drawing is 0.75 inch long.
What is the actual length of the garden?
Garden
Lawn
Scale: 1 in. = 10ft
1. Write the scale as a ratio:
Answers
Answer:
7.5 feet
Step-by-step explanation:
Hello there.
1. We know that the scale drawing is 0.75 inches long.
2. If 1 whole inch on the map is equivalent to 10 feet in real life, then how much feet in real life would be 0.75 inches on the map?
0.75 is equivalent or equals to 3/4 as a fraction.
Multiply 3/4 with 10 feet to get 7.5 feet.
Hope this helped!
- Angelo
Debbie's Cupcakes recently sold 3 vanilla cupcakes and 3 other cupcakes. What is the experimental probability that the next cupcake sold will be a vanilla cupcake?
Write your answer as a fraction or whole number.
P(vanilla cupcake)=
Answers
Answer:
P(vanilla cupcake)= 1/2
Step-by-step explanation:
Knowing that:
3 vanilla cupcakes
3 other cupcakes
Total = 6
To Find:
What is the experimental probability that the next cupcake sold will be a vanilla cupcake?
Write your answer as a fraction or whole number.
P(vanilla cupcake)=
Solve:
Experimental probability is expressed as:
(Favorable outcomes) / (Total outcomes)
The favorable outcome in this situation is vanilla cupcakes. There were 3 vanilla cupcake sold, so this is the numerator of our fraction.
To find the total outcomes we add 3 + 3, which equals 6. This will be the denominator of our fraction.
The fraction used to express experimental probability will be: 3/6
We can further simplify this to 1/2.
Thus:
P(vanilla cupcake)= 1/2 or 3/6
Kavinsky
In a ________, the researcher combines the actual results of a number of studies; the analysis consists of a set of statistical procedures that employ effect sizes to compare a given finding across many different studies.
Answers
In a meta analysis, the researcher combines the actual results of a number of studies.
What is the type of statistical study?Statistical study is used to obtain the data and examine this data in the way, that its effectiveness can be measured.
There are three main types of statistical study-
A. Experiment-In this type of statistical study, the observer or the researcher see the change in the variable of a study with change in other variable experimentally by providing the necessary conditions.B. Observational study-In the observational study of statistics, the value of the variables are recorded for different associates of the set.C. Survey-In the survey type of study, the data is gathered by directly asking the queries to the people regarding the study.When the researcher combines the actual results of a number of studies, then this study is called the meta analysis.
Here, in this analysis, he consists of a set of statistical procedures that employ effect sizes to compare a given finding across many different studies.
Thus, In a meta analysis, the researcher combines the actual results of a number of studies.
Learn more about the type of statistical study here;
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how do geometric functions differ from algebraic functions?
Answers
Answer:
happy to explain
Step-by-step explanation:
Algebra is an area in mathematics that uses variables, in the forms of letters and symbols, to act as numbers or quantities in equations and formulas. Geometry is an area in mathematics that studies points, lines, varied-dimensional objects and shapes, surfaces, and solids
Your medical research team is investigating the standard deviation of the cost of a 30-day-supply of a certain heart medication. A pharmaceutical company thinks that the standard deviation of the cost is less than $23. You want to support this claim. How would you write the null and alternative hypothesis?
Answers
Considering the situation described, the hypothesis tested are given as follows:
The null hypothesis is [tex]H_0: \sigma \geq 23[/tex]The alternative hypothesis is [tex]H_1: \sigma < 23[/tex]What are the hypothesis tested?At the null hypothesis, it is tested if the standard deviation is not less than $23, that is:
[tex]H_0: \sigma \geq 23[/tex]
At the alternative hypothesis, it is tested if there is significant evidence t conclude that the standard deviation is less than $23, that is:
[tex]H_1: \sigma < 23[/tex]
More can be learned about an hypothesis test at https://brainly.com/question/26454209
A force of 61 N is applied to an area of 750 cm2. Calculate the pressure in N/m2. Give your answer to the nearest integer
Answers
Answer:
813 N/m²
Step-by-step explanation:
The units of pressure tell you it is found by dividing force by area. Here, we need to convert the units of the given area so we can express the pressure appropriately.
__
pressure = force / area
pressure = (61 N)/(750 cm² × ((1 m)/(100 cm))²) = (61 N)/(0.0750 m²)
pressure ≈ 813 N/m²
If y varies directly with x and y is 12 when x is 9, what is x when y is 4?
Answers
Answer:
3
Step-by-step explanation:
y/x=12/9=4/3
when y is 4 x is 3
The number of calories C varies directly as the number of ounces N of avocado that is consumed by the body and C is 380 calories N is 20 ounces. Find C when N is 36 ounces.
Answers
Given that C varies directly as N, the value of Calories C when the number of ounces N is increased to the given value is 684 calories.
What is Proportional relationships?
Proportional relationships are relationships between two variables where their ratios are equivalent.
Direct variation equation is a linear equation in two variables.
It is expressed as;
a ∝ b then a = kb
Where k is the proportionality constant.
Given the data in the question;
Calories C = 380 caloriesNumber of ounces N = 20 ouncesSince Calories C and Number of ounces N varies directly, we find their proportionality constant.
a ∝ b then a = kb
C = kN
380 calories = k × 20 ounces
k = 380 calories / 20 ounces
k = 19 calories/ounces
Now,we find C when N is 36 ounces.
C = kN
C = 19 calories/ounces × 36 ounces
C = 684 calories
Given that C varies directly as N, the value of Calories C when the number of ounces N is increased to the given value is 684 calories.
Learn more about proportionality here: https://brainly.com/question/11202658
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solve work by using square root method
Answers
[tex]~~~~(x-2)^2 = 16\\\\\implies x-2 = \pm\sqrt{16}\\\\\implies x-2 = \pm4\\\\\implies x= \pm4 +2\\\\\implies x=-4+2~~ \text{or}~~ 4+2\\\\\implies x = -2~~ \text{or}~~ 6[/tex]
Answer:
[tex]x = - 2[/tex]
[tex]x = 6[/tex]
Step-by-step explanation:
[tex](x - 2)^{2} = 16[/tex]
[tex]x - 2 = ± \: 4[/tex]
[tex]x - 2 = - 4[/tex]
[tex]x - 2 = 4[/tex]
[tex]x = - 2[/tex]
[tex]x = 6[/tex]
Find the image of the given point
under the given translation.
P(3, -4)
T(x, y) = (x-6, y + 5)
P' = ([?], [])
27
Answers
Answer:
P' (- 3, 1 )
Step-by-step explanation:
the translation
(x, y ) → (x - 6, y + 5 )
means subtract 6 from the x- coordinate and add 5 to the y- coordinate, so
P (3, - 4 ) → P' (3 - 6, - 4 + 5 ) → P' (- 3, 1 )
How can you find the maximum or minimum value of the quadratic function?
A. Evaluate the function for x = 0. The resulting value is the maximum or the minimum value.
B. Find the vertex. The y-coordinate of the vertex is the minimum or the maximum value of the parabola.
C. Find the y-intercept. The y-intercept is the maximum or the minimum value of the parabola.
D. Find the vertex. The x-coordinate of the vertex is the minimum or the maximum value of the parabola
Answers
Answer:
B
Step-by-step explanation:
the y-coordinate of the vertex will be the max or min value of the quadratic function
hope this helps!
Find the missing side to the nearest tenth.
***Numerical answer only!
А
с
5
с
4
B
Answers
Answer:
6.4
Step-by-step explanation:
The hypotenuse of a right triangle can be found from the other two sides by making use of the Pythagorean theorem. It tells you the square of the hypotenuse is the sum of the squares of the other two sides:
c² = 4² +5²
c² = 16 +25 = 41
c = √41 ≈ 6.4
The missing side length is about 6.4 units.
Which will have a negative number?
A)
(-3)(-9)
B)
(-6)(4)
C
-4 --5
D)
-7+9
Answers
Answer:
B
Step-by-step explanation:
A: 27
C: 1
D: 2
B: -24
anytime you multiply two negative numbers it makes the product positive
i need help please good people
Answers
Answer:
x/x+3
Step-by-step explanation:
first off, we start by factorizing.
we start with the numerator taking x out making it x (x-3) / x^2 - 9
then we factorize the denominator a bit more...making it x (x-3) / (x-3) (x+3)
as you can tell there is a (x-3) on both sides. so we can cross them out.
x/x+3 is left. try it yourself again so you can understand other questions like this! I hope I could help!
EASY 9th GRADE MATH PLEASE HELP
Two thirds of a number is twice the number decreased by twenty-four. Write an equation and solve for the number.
Answers
Step-by-step explanation:
2/3 X = 2x -24
now just solve for X.
2X = 8X - 72
-6x = -72
X = 12