Answers
Answer: option d.
Step-by-step explanation:
To solve this problem you must keep on mind the properties of logarithms:
[tex]log(b)-log(a)=log(\frac{b}{a})\\\\log(b)+log(a)=log(ba)\\\\a*log(b)=log(b)^a[/tex]
Therefore, knowing the properties, you can write the expression gven in the problem as shown below:
[tex]5logx+6log(x+7)=logx^5+log(x+7)^6=logx^5(x+7)^6[/tex]
Then, the answer is the option d.
Answer:
D
Step-by-step explanation:
We can use 2 properties of logs to write this as single logarithm:
1. [tex]Log(A^B)=BLog A[/tex]
2. Log x + Log y = Log (x*y)
We can use property #1 to write this as:
[tex]5Logx+6Log(x+7)\\=Logx^{5}+Log(x+7)^{6}[/tex]
Now we can use property #2 to write this as:
[tex]Logx^{5}+Log(x+7)^{6}\\=Log((x^5)((x+7)^6)\\=Logx^{5}(x+7)^{6}[/tex]
We see that answer choice D is right.
Related Questions
Find sec x if tan^2 x= 1/2
(picture provided)
Answers
Answer: option d.
Step-by-step explanation:
Based on the information given in the problem, you know that:
[tex]tan^2x=\frac{1}{2}[/tex]
You also know that:
[tex]sec^2(x)=tan^2(x)+1[/tex]
Substitute values. Then, you obtain:
[tex]sec^2(x)=\frac{1}{2}+1\\\\sec^2(x)=\frac{3}{2}[/tex]
Apply square root to both sides. Therefore, you obtain:
[tex]\sqrt{sec^2(x)}=\±\sqrt{\frac{3}{2}}\\\\sec(x)=\±\frac{\sqrt{3}}{\sqrt{2}}\\\\sec(x)=\±\frac{\sqrt{3}}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}}\\\\sec(x)=\±\frac{\sqrt{3(2)}}{2}\\\\sec(x)=\±\frac{\sqrt{6}}{2}[/tex]
Answer:
D
Step-by-step explanation:
Can you help me with this question?
Answers
Sure. To make an equilateral triangle we make any segment AB, which is already done, then we draw one circle (or an arc from the circle) with center A and radius AB, and one circle with center B and radius AB. The two circles intersect at two points; we call either one of them C and ABC is equilateral.
Answer: C
Type the correct answer in each box. The length of a rectangle is 3 inches more than its width. The perimeter of the rectangle is 34 inches. The length of the rectangle is inches ?, and its width is ? Inches.
Answers
Answer:
The length is 10 inches and the width is 7 inches.
Step-by-step explanation:
A rectangle is shape with 4 sides where 2 pairs of sides are equal and form 4 perpendicular angles. 1 pair of sides is the width and is distance w. 1 pair of sides id the length and is 3 inches more than the width or 3 + w. The total distance around the shape is the perimeter. We know the perimeter is 34 inches. Add each side together and set it equal to 34. Then solve for w.
P = l + l + w + w
34 = 3 + w + 3 + w + w + w
34 = 6 + 4w
28 = 4w
7 = w
This means its length which is 3 inches longer is 7 + 3 = 10.
If 2/3x + 4 less than or equal to 14 what is the largest possible value of 7x - 2
Answers
⅔x+4≤14
⅔x≤10
2x≤30
x≤15
Max value of x is 15
7x-2≤?
7(15)-2=105-2=103
7x-2≤103
Greatest value for 7x-2 is 103
What is the recursive rule for this geometric sequence?
-64,-16,-4,-1, ...
Enter your answers in the boxes
An= __ •an-1
A1= __
Answers
A1(nilai sebutan pertama)=-64
Answer:
1/4
-64
Step-by-step explanation:
The United States of House of Representatives has 35 members more than four times the number of members in the United States Senate Define a variable and write an expression to represent the number of members in the House of Representatives then find the number of members in the House of Representatives if there are 100 members in the Senate
Answers
Answer:
House of representatives=h
United states senate= u
h=4u+35
If u=100:
h=4(100)+35
h=400+35
h=435
Hope this helps :}
Write an expression to represent: Four less than the quotient of a number x and 5
Answers
The mathematical representation of the expression 'Four less than the quotient of a number x and 5' is 'x/5 - 4'. This involves division and subtraction of the number x.
Explanation:The subject of this question is Mathematics, particularly algebraic expressions. In this case, you are being asked to express the phrase 'Four less than the quotient of a number x and 5' as an algebraic expression. The 'quotient of a number x and 5' implies division of the number x by 5, which is represented as 'x/5'. 'Four less than' signifies a subtraction of four from the preceding expression. Therefore, the whole expression can be written as 'x/5 - 4'.
Learn more about Algebraic Expressions here:https://brainly.com/question/34192827
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Colby is making a home video consisting of a 5-minute introduction followed by several short skits. Each skit is 6 minutes long. If Colby's video is 101 minutes long, how many skits are in his video?
Answers
The answer is: There are a total of 16 skits in the video.
Why?From the statement, we know that the total length of the video is 101 minutes and it contains a 5-minute introduction, the rest of the minutes are short skits (which are 6 minutes long each one).
So, we need to write the following equations:
First equation:
[tex]TotalDuration=Introduction+n*Skit[/tex]
Second equation:
[tex]Skit=6Minutes[/tex]
Where,
[tex]TotalDuration=101Minutes\\Introduction=5Minutes\\n=NumberOfSkits\\Skit=6Minutes[/tex]
So, replacing and substituting the second equation into the first equation we have:
[tex]101Minutes=5Minutes+n*6Minutes\\n*6Minutes=101Minutes-5Minutes\\n*6Minutes=96Minutes\\n=\frac{96Minutes}{6Minutes}=16[/tex]
So, there are a total of 16 skits in the video.
Let's prove it substituting "n" into the first equation:
[tex]101Minutes=5Minutes+16*6minutes\\101Minutes=5Minutes+96Minutes\\101Minutes=101Minutes[/tex]
Have a nice day!
34
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Circle O has a circumference of 88 cm. What is the length of the radius of the circle?
Answers
Answer is 44cm
Step-by-step explanation:
Evaluate each log without a calculator
[tex]log_{4} \frac{1}{16}[/tex]
[tex]log_{2}\sqrt[5]{32}[/tex]
Answers
QUESTION 1
The given logarithmic expression is
[tex]\log_4(\frac{1}{16})[/tex]
We rewrite [tex]\frac{1}{16}[/tex] in the index form to base 4.
This implies that;
[tex]\log_4(\frac{1}{16})=\log_4(4^{-2})[/tex]
We now apply the power rule: [tex]\log_a(m^n)=n\log_a(m^n)[/tex].
[tex]\log_4(\frac{1}{16})=-2\log_4(4)[/tex]
Recall that logarithm of the base is 1.
[tex]\log_4(\frac{1}{16})=-2(1)[/tex]
[tex]\log_4(\frac{1}{16})=-2[/tex]
QUESTION 2
The given logarithm is;
[tex]\log_2(\sqrt[5]{32})[/tex]
[tex]\log_2(\sqrt[5]{2^5})[/tex]
This is the same as;
[tex]\log_2(2^{5\times \frac{1}{5}})[/tex]
[tex]\log_2(2^{1})[/tex]
[tex]\log_2(2)=1[/tex]
If they are going 12 miles per 1/3 hour . What is the average speed per hour in miles
Answers
Answer:
12 miles per (1/3) hour equals
36 miles per hour
Step-by-step explanation:
Which graph represents the solution set of the system of inequalities?
Answers
Answer:
your first Graph :D Hope this helps
The first equation is greater than or equal to, so the line would be solid.
The second equation is less than so the line would be dotted.
Greater than or equal to would be above the solid line, less than would be to the left of the dotted line.
The top left graph is correct.
If f( x ) = x - 5, then match each of the following.
1 .
-6
2 .
-4
3 .
-5
4 .
3
5 .
0
6 .
-3
f(-1)
f(0)
f(1)
f(2)
f(5)
f(8)
Answers
Answer:
1. f(-1)
2.f(1)
3.f(0)
4.f(8)
5.f(5)
6.f(2)
Step-by-step explanation:
[tex]f(-1)-------------\ \ \ \ -6\\\\f(0)-------------\ \ \ \ \ \ \ -5\\\\f(1)-------------\ \ \ \ \ \ \ -4\\\\f(2)-------------\ \ \ \ \ \ \ -3\\\\f(5)-------------\ \ \ \ \ \ \ \ \ 0\\\\f(8)-------------\ \ \ \ \ \ \ \ \ 3[/tex]
Step-by-step explanation:We are given a function f(x) by:
[tex]f(x)=x-5[/tex]
It is a linear function with positive slope i.e. 1.
Also, now we will calculate the value of the function at different values of x and match the function to it's corresponding value.
a)
[tex]f(-1)[/tex]
[tex]f(-1)=-1-5\\\\i.e.\\\\f(-1)=-6[/tex]
b)
[tex]f(0)[/tex]
Now when x=0 we have:
[tex]f(0)=0-5\\\\i.e.\\\\f(0)=-5[/tex]
c)
[tex]f(1)[/tex]
when x=1
[tex]f(1)=1-5\\\\i.e.\\\\f(1)=-4[/tex]
d)
[tex]f(2)\\\\f(2)=2-5\\\\i.e.\\\\f(2)=-3[/tex]
e)
[tex]f(5)[/tex]
when x=5 we have:
[tex]f(5)=5-5\\\\i.e.\\\\f(5)=0[/tex]
f)
[tex]f(8)[/tex]
Put x=8
[tex]f(8)=8-5\\\\i.e.\\\\f(8)=3[/tex]
A division problem can be written out using repeated subtraction. Which division problem is solved below? 40 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4
Answers
Answer:
The problem that is getting solved is 40 divided by zero
Answer:
Step-by-step explanation:
This is a faulty way of showing it. What you are solving here is
40 - 10*4 which is 0. What is transcribed is not equivalent to any division that I can see.
Perhaps 0/40
If you have answers, please list them.
Write and equation of the translated or rotated graph in general form (picture below)
Answers
Answer:
The answer is ellipse; 3x² + y² + 6x - 6y + 3 = 0
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
* 3x² + y² = 9
∵ A = 3 , B = 0 , C = 1
∴ B² - 4 AC = (0)² - 4(3)(1) = -12
∴ B² - 4AC < 0
∴ The graph is ellipse or circle
* If A and C are nonzero, have the same sign, and are not
equal to each other, then the graph is an ellipse.
* If A and C are equal and nonzero and have the same
sign, then the graph is a circle.
∵ A and C have same signs with different values
∴ It is an ellipse
* Now lets study T(-1 , 3), that means the graph will translate
1 unit to the left and 3 units up
∴ x will be (x - -1) = (x + 1) and y will be (y - 3)
* Lets substitute the x by ( x + 1) and y by (y - 3) in the equation
∴ 3(x + 1)² + (y - 3)² = 9
* Use the foil method
∴ 3(x² + 2x + 1) + (y² - 6y + 9) = 9
* Open the brackets
∴ 3x² + 6x + 3 + y² - 6y + 9 = 9
* Collect the like terms
∴ 3x² + y² + 6x - 6y + 12 = 9
∴ 3x² + y² + 6x - 6y + 12 - 9 = 0
∴ 3x² + y² + 6x - 6y + 3 = 0
* The answer is ellipse of equation 3x² + y² + 6x - 6y + 3 = 0
Ben drove 350 miles in 6 1/2 hours Marcie drove 520 miles on 12 1/4 hours who drove faster
Answers
Answer:
Ben drove faster
Step-by-step explanation:
BEN:350 miles / 6.5 hours = 53.84 miles per hour
MARCIE:520 miles / 12.25 hours = 42.44 miles per hour
53.84 is faster than 42.44 therefore Ben is faster.
Write an inequality to represent "7 less than the product of a number, n, and 16 is at most 45."
Answers
Let's illustrate the idea of a sampling distribution in the case of a very small sample from a very small population. The given population is the scores of ten female students in a class. Student 0 1 2 3 4 5 6 7 8 9 Weight 136 99 118 129 125 170 130 128 120 147 The parameter of interest is the mean weight in pounds ???? in this population. The sample is an SRS of size ????=4 drawn from the population. Because the students are labeled zero to nine, a single random digit from Table A chooses one student for the sample. (a) Find the mean of the ten weights in the population. This is the population mean ???? . (Enter your answer rounded to one decimal place.)
Answers
Answer:
a: sample mean: 130.2 pounds
This is not the population mean
Step-by-step explanation:
To find the mean weight of the sample, add up all the values and divide by the total number of values entered. In this case, 10, so we have...
mean: (136 + 99 + 118 + 129 + 125 + 170 + 130 + 128 + 120 + 147)/10 =
1302/10 = 130.2
This is not the population mean. It is the mean of the sample. We would have to know more information to make a conjecture about the population mean.
Final answer:
The population mean of the students' weights is determined by summing all the weights and dividing by the number of students, resulting in 130.2 pounds.
Explanation:
To find the population mean (denoted as μ), we add up all the weights of the ten students in the population and divide it by the total number of students. Let's do the calculation:
The weights of the students are 136, 99, 118, 129, 125, 170, 130, 128, 120, and 147 pounds.
The sum of these weights is 136 + 99 + 118 + 129 + 125 + 170 + 130 + 128 + 120 + 147 = 1302 pounds.
Since there are 10 students in the population, we divide the total weight by 10 to find the mean:
μ = ΣX / N = 1302 / 10 = 130.2 pounds
Therefore, the population mean (μ) is 130.2 pounds.
Kylie and her two sisters each have 1/4 cup of chopped pineapple . How much do they have in all
Answers
you want to take 3×1/4 which would equal 0.75. but if you want to change it into a fraction it would be 3/4
True or false (Picture provided)
Answers
Answer:
The correct answer is F (false)
Step-by-step explanation:
Points to remember
Sin θ = Opposite side/Hypotenuse
Tan θ = Opposite side/Adjacent side
Sec θ = Hypotenuse/Adjacent side
To find Sin 45, Sec 45 and Tan 45
We have Sin 45 = 1/√2
Sec 45 = 1/Cos 45 = 1/(1/√2) = √2
Tan 45 = 1
To find Sec θ/Tan θ
Here θ = 45
Sec (45)/Tan (45) = √2/1 = √2 ≠ Sinθ
Therefore the correct answer is False(F)
Im on a time limit! could someone help me with this?
Answers
Answer:
B is the answer because the other equations have real numbers
Step-by-step explanation:
Answer:
B is the correct answer
Step-by-step explanation:
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 0.3x − 0.4y = 0.2 −0.2x + 0.5y = 0.1 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =
Answers
Answer:
One solution. It is (2, 1)
Step-by-step explanation:
Clear out all fractions right away by multiplying all terms by 10. Then:
0.3x − 0.4y = 0.2
−0.2x + 0.5y = 0.1
becomes
3x - 4y = 2
-(2x + 5y = 1)
Multiply the first row by 2 and the second row by 3, which produces:
6x - 8y = 4
-6x +15y = 3
Combining like terms results in: 7y = 7. Then y = 1.
Now subst. 1 for y in the first equation, to calculate x:
3x - 4(1) = 2
3x = 2 + 4 = 6. Then x = 2.
The solution is (2, 1). There is ONLY ONE SOLUTION.
(13 points) HELP PLEASEEE!
Subtract the equations
3x + 4y = 17
- (3x + 2y = 3)
Answers
Answer:
y = 7 x = -11/3
Step-by-step explanation:
3x + 4y = 17
- (3x + 2y = 3)
Distribute the minus sign and add together
3x + 4y = 17
- 3x - 2y = -3
------------------------
2y = 14
Divide by 2
2y/2 = 14/2
y = 7
Now find x
3x + 4y = 17
3x +4(7) = 17
3x +28 = 17
Subtract 28 from each side
3x+28 -28 = 17 -28
3x = -11
Divide each side by 3
3x/3 = -11/3
x = -11/3
Answer:
A.2y=14
Step-by-step explanation:
Apex
Hope this helps Have a nice day
A rectangular piece of stained glass has the dimensions shown in the diagram. What is the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid?
Answers
Answer:
The correct option is D) [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Consider the provided figure.
We need to find the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid.
For this first find the total area as shown:
The given figure is a rectangle.
The area of rectangle is [tex]l\times b[/tex]
Where, l = 6 cm + 3 cm = 9 cm and b = 5cm
Therefore the area of the rectangle is;
Area of rectangle = [tex]9cm\times 5cm=45cm[/tex]
Now find the area of trapezoid.
The area of trapezoid is: [tex]\frac{a+b}{2}h[/tex]
Where h is the height and a and b are the parallel sides.
Area of trapezoid = [tex]\frac{9+3}{2}\times 5=30[/tex]
Thus, the area of trapezoid is 30 cm.
Therefore, the probability that a random leaf that lands on the rectangle lands within the section shaped like a trapezoid is:
[tex]Probability=\frac{\text{Area of trapezoid}}{\text{Area of rectangle}}[/tex]
[tex]Probability=\frac{30}{45}=\frac{2}{3}[/tex]
Hence, the correct option is D) [tex]\frac{2}{3}[/tex]
Answer:
2/3
Step-by-step explanation:
I got it right
I f(x)= square root x-3 which inequality can be used to find the domain of f(x)
Answers
Answer:
[tex]x\ge3[/tex]
Step-by-step explanation:
The given function is [tex]f(x)=\sqrt{x-3}[/tex].
The domain of this function refers to all values of x, for which the function is defined.
This square root function is defined when the expression under the radical sign is greater or equal to zero.
That is; the domain of the function is [tex]x-3\ge0[/tex]
This implies that [tex]x\ge3[/tex]
If you roll a number cube 22 times about how many times do you expect to roll a numeber Less than 4?
Answers
Answer:
About 7 times
Step-by-step explanation:
Jimmy is selling used books at a yard sale. A customer buys 9 books at a cost of $0.75 each and pays with a $20.00 bill. Jimmy must determine c, the amount of change in dollars he should give the customer. Which equation represents c? 20-0.75c=9 20-0.75=9c 0.75(9)+c=20 0.75c+9=20
Answers
Answer:
Step-by-step explanation:
You need to multiply .75 and 9 you'll get 6.75 .. then you need to take 20 and subtract 6.75 and you'll get 13.25
Answer:
C is the correct choice.
Given csc x/cot x =square root 2, find a numerical value of on trigonometric function of x
Answers
Answer:
a. sec(x) = √2
Step-by-step explanation:
csc(x)/cot(x) = (1/sin(x))/(cos(x)/sin(x)) = 1/cos(x) = sec(x) = √2
Answer:
The correct answer is a) [tex] \sec(x) = \sqrt{2}[/tex].
Step-by-step explanation:
Here we need to use some trigonometric identities:
[tex] \csc(x) = \frac{1}{\sin(x)}[/tex],[tex] \cot(x) = \frac{\cos(x)}{\sin(x)} [/tex].Then, substituting the above identities in the given formula we have:
[tex] \frac{\csc(x)}{\cot(x)} = \frac{\frac{1}{\sin(x)}}{\frac{\cos(x)}{\sin(x)}} = \frac{1}{\sin(x)}\frac{\sin(x)}{\cos(x)} [/tex]
Notice that we can simplify the sinus in both fractions. Thus,
[tex]\frac{\csc(x)}{\cot(x)} = \frac{1}{\cos(x)} = \sec{x}[/tex].
From here, the solutions is pretty straightforward.
Write an equation that represents a linear function that has a slope of 4/5 and a y intercept of -6
Answers
The equation is y =(4/5)x -6
Answer:
[tex]\large\boxed{y=\dfrac{4}{5}x-6}[/tex]
Step-by-step explanation:
The slope-intercept form of the equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the slope [tex]m=\dfrac{4}{5}[/tex] and the y-intercept [tex]b=-6[/tex].
Substitute:
[tex]y=\dfrac{4}{5}x-6[/tex]
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 5x − 6y = 3 10x − 12y = 6 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =
Answers
Final answer:
The system of equations has infinitely many solutions because they represent the same line. The solution can be written in terms of the parameter t as (x, y) = ((3 + 6t)/5, t).
Explanation:
The student's question involves determining the type of solution a system of two linear equations has and finding the solution if it exists. The given system of equations is:
5x - 6y = 3
10x - 12y = 6
Notice that the second equation is just the first equation multiplied by 2. This means the system has infinitely many solutions because the two equations are actually the same line. To find these solutions in terms of a parameter t, we can solve the first equation for x as follows:
Choose t to represent y (i.e., let y = t).
Substitute y = t into the first equation to get 5x - 6t = 3.
Solve for x to find x = (3 + 6t)/5.
Therefore, the solutions to the system can be expressed as (x, y) = ((3 + 6t)/5, t), where t is any real number.