Final answer:
To combine the expression 4 log x - 6 log (x+2) into a single logarithm, we use the exponentiation and division rules for logarithms to obtain log((x^4)/(x+2)^6).
Explanation:
To write the expression 4 log x - 6 log (x+2) as a single logarithm, we can apply log rules.
The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number: log(x^n) = n log x.
The logarithm of a product of two numbers is the sum of the logarithms of the two numbers: log xy = log x + log y.
The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers: log(x/y) = log x - log y.
Using these rules, we can
rewrite the given expression:
4 log x - 6 log (x+2) can be rewritten as log(x^4) - log((x+2)^6), which simplifies to log((x^4)/(x+2)^6) according to the division rule for logarithms.
The expression [tex]4 log x - 6 log (x+2)[/tex] can be simplified as a single logarithm by using the logarithm properties of exponents and division, resulting in [tex]log(x^4 / (x+2)^6).[/tex]
Explanation:The student is asking to write the expression [tex]4 log x - 6 log (x+2)[/tex] as a single logarithm. To do this, we recall two important properties of logarithms:
The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number: [tex]log(a^n) = n log a.[/tex]The logarithm of the division of two numbers is the difference between the logarithms of the two numbers: [tex]log(a/b) = log a - log b.[/tex]Using these properties, we can rewrite the expression:
First, apply the exponent property: 4 log x becomes log(x^4), and 6 log (x+2) becomes log((x+2)^6).Next, apply the division property:Therefore, the expression [tex]4 log x - 6 log (x+2)[/tex] written as a single logarithm is[tex]log(x^4 / (x+2)^6).[/tex]
Which points are coplanar and non-collinear.Will mark Brainiest
Answer:
I believe A, C, and D are Coplanar and i think B. is non-collinear.
Step-by-step explanation:
A, C and D are coplanar because they lie on the same line.
B is non-collinear, because it don't lie on the same line as A, C, and D.
Hope my answer has helped you!
Use the remainder theorem to divide 5x^2+9x-2 by x+3. What is the remainder
Answer:
16
Step-by-step explanation:
Given
f(x)=5x^2+9x-2
Remainder theorem states that when f(x) is divided by x-a then the remainder can be calculated by calculating f(a).
Now Using the remainder theorem to divide 5x^2+9x-2 by x+3 to find the remainder:
f(x)=5x^2+9x-2
f(-3) = 5(-3)^2 +9(-3) -2
=5(9) - 27 -2
= 45-29
= 16 !
Answer:
16
Step-by-step explanation:
apexs
THIS IS 61 POINTS. Find the first three terms of the sequence described by the following recursive formula: an = 3an – 1 + 2 where a4 = 20
a1=
a2=
a3=
Answer:
see explanation
Step-by-step explanation:
Given the recursive formula
[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] + 2 and a₄ = 20
Then working in reverse
3a₃ + 2 = 20 ( subtract 2 from both sides )
3a₃ = 18 ( divide both sides by 3 )
a₃ = 6
3a₂ + 2 = 6 ( subtract 2 from both sides )
3a₂ = 4 ( divide both sides by 3 )
a₂ = [tex]\frac{4}{3}[/tex]
3a₁ + 2 = [tex]\frac{4}{3}[/tex] ( subtract 2 from both sides )
3a₁ = - [tex]\frac{2}{3}[/tex] ( divide both sides by 3 )
a₁ = - [tex]\frac{2}{9}[/tex]
Hence
a₁ = - [tex]\frac{2}{9}[/tex]
a₂ = [tex]\frac{4}{3}[/tex]
a₃ = 6
a1 = (-2/9)
a2 = 4/3
a3 = 6
Hope this helps!
Q4 please help thanks
Answer:
[tex]\large\boxed{A==\dfrac{3-\sqrt6}{12}\ cm^2}[/tex]
Step-by-step explanation:
The shaded region is the triangle with base b and height h.
[tex]b=BD-CD\to b=\dfrac{\sqrt2}{2}-\dfrac{\sqrt3}{3}=\dfrac{3\sqrt2}{(2)(3)}-\dfrac{2\sqrt3}{(2)(3)}=\dfrac{3\sqrt2-2\sqrt3}{6}\\\\h=AD\to h=\dfrac{\sqrt2}{2}[/tex]
The formula of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
Substitute:
[tex]A=\dfrac{\frac{3\sqrt2-2\sqrt3}{6}\cdot\frac{\sqrt2}{2}}{2}=\left(\dfrac{3\sqrt2-2\sqrt3}{6}\right)\left(\dfrac{\sqrt2}{2}\right)\left(\dfrac{1}{2}\right)\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\=\dfrac{(3\sqrt2-2\sqrt3)(\sqrt2)}{(6)(2)(2)}=\dfrac{(3\sqrt2)(\sqrt2)-(2\sqrt3)(\sqrt2)}{24}\\\\\text{use}\ \sqrt{a}\cdot\sqrt{a}=a\ \text{and}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\dfrac{(3)(2)-2\sqrt6}{24}=\dfrac{2(3-\sqrt6)}{24}=\dfrac{3-\sqrt6}{12}[/tex]
Answer:
see explanation
Step-by-step explanation:
The area of the shaded triangle = area of ΔABD - area of ΔADC
A of ΔABD = [tex]\frac{1}{2}[/tex] × AD × BD
A = [tex]\frac{1}{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex]
= [tex]\frac{2}{8}[/tex] = [tex]\frac{1}{4}[/tex]
--------------------------------------------------------------------------
A of ΔACD = [tex]\frac{1}{2}[/tex] × AD × DC
A = [tex]\frac{1}{2}[/tex] × [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{3}[/tex]
A = [tex]\frac{\sqrt{6} }{12}[/tex]
-------------------------------------------------------------------------
shaded area = [tex]\frac{1}{4}[/tex] - [tex]\frac{\sqrt{6} }{12}[/tex]
= [tex]\frac{3}{12}[/tex] - [tex]\frac{\sqrt{6} }{12}[/tex] = [tex]\frac{3-\sqrt{6} }{12}[/tex]
How many gallons of 20% salt solution must be mixed with 4 gallons of 40% salt solution to make 25% salt solution?
If [tex]x[/tex] is the amount (gal) of the 20% solution to be used, then the mixture would have a total volume of [tex]x+4[/tex] gal. We want to end up with a 25% salt solution, so that
[tex]0.2x+0.4\cdot4=0.25(x+4)[/tex]
[tex]\implies0.2x+1.6=0.25x+1[/tex]
[tex]\implies0.6=0.05x[/tex]
[tex]\implies x=12[/tex]
Nicole has $250 in ten-dollar bills. How many ten-dollar bills does Nicole have?#10
Nicole has 25 ten-dollar bills.
To find out how many ten-dollar bills Nicole has, we can divide the total amount of money she has by the value of each bill.
$250 / $10 = 25
Therefore, Nicole has 25 ten-dollar bills.
Answer in detail:
Nicole has $250 in ten-dollar bills. This means that she has 25 groups of $10.
We can divide $250 by $10 to find out how many groups of $10 she has.
$250 / $10 = 25
Therefore, Nicole has 25 ten-dollar bills.
Another way to look at it is this way:
If Nicole has 1 ten-dollar bill, then she has $10.
If Nicole has 2 ten-dollar bills, then she has $20.
If Nicole has 3 ten-dollar bills, then she has $30.
And so on.
So, to find out how many ten-dollar bills Nicole has, we can simply divide the total amount of money she has by the value of each bill.
What is the simplest form of the expression 6x(x - 4) – 16x2 - (9x - 1)?
A. -10x2 – 33x + 1
B. 10x2 – 33x + 1
C. -10x – 33x + 1
D. -10x2 + 33x + 1
Answer
b
Step-by-step explanation:
Answer:
− -10x^2-33x+1
Step-by-step explanation:
given the table of values below, which of the following ordered pairs are found on the graph of the inverse function?
Answer:
Option A. is the correct option.
Step-by-step explanation:
As per table given in this question values of the function has been given as
f(x) = -3 for x = -2
We can rewrite the function as f(-2) = -3
As we know inverse of the function means [tex]-2 = f^{-1}(-3)[/tex]
or inverse function g(-3) = -2
and the ordered pair for the inverse function will be (-3, -2)
Similarly other ordered pairs for the inverse function given will be
(3, -1), (9, 0), (15, 1), (21, 2)
Therefore, the ordered pairs will be (-3, -2), (3, -1), (9, 0), (15, 1), (21, 2)
Option A is the right option.
Write an addition equation or a subtraction equation your choice to describe the dias
CAN SEBODY HELP PLEASE ?!
Answer:
Step-by-step explanation:
Unsure of what you're asking here. What's "dias?"
I do see that the longer arrow has length 5 (there are 5 squares along this arrow from bottom to top) and that the shorter one has length 2.
If we add these two vectors together, we get a vector of length 5 + 2, or 7, that points upward just as these two original vectors do.
yes that would work but just keep that in mind that 1+1=2
Which statements are true about box plots? Check all that apply. They help describe sets of data. They include the mean. They show the data split into four parts. They show outliers through really short “whiskers.” Each section of a box plot represents 25% of the data.
Answer:
Step-by-step explanation:
a c e
is the answer
Answer:
a c e the one above me is ri
Step-by-step explanation:
The number 15. 24 is an example of a repeating decimal.
true. false.
No, the number 15.24 is not a repeating decimal.
Explanation:No, the number 15.24 is not an example of a repeating decimal.
A repeating decimal is a number whose decimal representation goes on forever and repeats a block of one or more digits. For example, the number 0.3333... is a repeating decimal because the digit 3 repeats infinitely.
In the case of 15.24, the decimal representation terminates after two decimal places.
This is because it has a fixed and finite decimal representation. The digits "15" represent the whole number part, and the "24" represents the fractional part. Since there is no repeating pattern of digits after the decimal point, 15.24 is classified as a terminating decimal, not a repeating one.
Therefore, it is not a repeating decimal.
Write the integers -7, 4, -2 and 5 in order from least to greatest. Explain how you decided.
Answer:
-7, -2, 4, 5
Step-by-step explanation:
Integers with a dash in the front of them signify a negative. With negative numbers, the higher the value of the accompanying number, the lower value it has as a negative number, so, of course the negative integers would go from the "least" end of the spectrum. Because 7 has a higher positive value than 2, it has a lower negative value, putting -7 on the lower end, following it with the -2. As 5 has a higher positive value than 4, 5 is put on the highest end on the spectrum, with 4 right behind it. With all of these integers settled, we can organize the numbers in the order of -7, then -2, then 4, then 5.
Step-by-step explanation: To write these integers from least to greatest, first draw a number line and graph each of the integers
In the image provided, notice that I've only labeled every other unit on the number line. This is a labeling technique that we can use to keep things from getting too crowded on the number line.
Now, let's graph our integers.
Integers to the left are always less than integers to to the right. So in this problem, we can see that -7 < -2 < 4 < 5.
Ari’s teacher says he may have his report grade based on either the mean or the median of his last six test scores.
88%, 73%, 97%, 76%, 90%, 80%
Which measure of center would best represent Ari’s grade?
The mean would be the best! The mean is when you add up all of those grades and divide by the amount of exams.
If you're solving it,
504 is the total divided by 6 tests would be 84.
The answer is 84 I’m glad i could help you
what is angle F to the nearest degree?
Answer:
So we already knew all three sides, there are more than one way to do it, for example:
sin∠F = HG/HF = 12/13
cos∠F = GF/HF = 5/13
tan∠F = HG/GF = 12/5
ctg∠F = GF/HG = 5/12
All of them will give you the result which is approximately 67°.
Which expression shows six less than the product 12 and 8?
Answer: (12)(8)-6
Step-by-step explanation: Product indicates you are going to multiply the numbers. When you see the phrase "less than" you want to flip the numbers.
The distance from around the Earth along a given latitude can be found using the formula C=2∏r cos L , where r is the radius of the Earth and L is the latitude. The radius of Earth is approximately 3960 miles. Describe the distances along the latitudes as you go from 0° at the equator to 90° at the poles.
Answer:
The distance reduces to 0 as you go from 0° to 90°
Step-by-step explanation:
The question requires you to find the distance using different values of L and check the trend of the values.
Given C=2×pi×r×cos L where L is the latitude in ° and r is the radius in miles then;
Taking r=3960 and L=0° ,
C=2×[tex]\pi[/tex]×3960×cos 0°
C=2×[tex]\pi[/tex]×3960×1
C=7380[tex]\pi[/tex]
Taking L=45° and r=3960 then;
C= 2×[tex]\pi[/tex]×3960×cos 45°
C=5600.28[tex]\pi[/tex]
Taking L=60° and r=3960 then;
C=2×[tex]\pi[/tex]×3960×cos 60°
C=3960[tex]\pi[/tex]
Taking L=90° and r=3960 then;
C=2×[tex]\pi[/tex]×3960×cos 90°
C=2×[tex]\pi[/tex]×3960×0
C=0
Conclusion
The values of the distance from around the Earth along a given latitude decreases with increase in the value of L when r is constant
Help on number 7 please?
Answer:
The average rate of change is 3
Step-by-step explanation:
0 to 5 is 5 in difference then the change on the next one: 1 to 9 the difference is 8 so the change is 3 and it increases by three on the rest of them.
(\) QueTooOfficial (/)officially out of brainly retirementI'm pretty sure the average rate of change would be 3
At A Sale, Sarah Bought 4 T-shirts And 3 Pairs Of Jeans For $181. Jenna Bought 1 T-shirt and 2 Pairs Of Jeans For $94. The T-shirts Were All The Same Price And The Jeans Were All The Same Price, So The Following system of Equations Represents This Situation. Determine The Best Method To Solve The System of Equations of Equations. Then Solve The System.
The T-shirts are $16 each while the jeans are $39 each Hope it helps
given that the ratio of boys to girls in a choir group is 17:23, what is the relative frequency of the number of boys?
Answer:
50 Students
You can find the number of boys and girls by dividing the total, so there are a total of 20 boys and 30 girls in the choir of 50. The ratio 2 boys : 3 girls means we can divide the chorus into groups.
What is the solution to the system of equations?
y=-3x + 6
y= 9
(-21,9) (9, -21)
(-1,9)
(9,-1)
Answer:
y=9
Step-by-step explanation:
(9,-1) is the answer.
Find the percent change from 84 to 63.
Answer:
-25%
20 characters
so the difference is 84 - 63 = 21.
if we take 84 to be the 100%, what is 21 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 84&100\\ 21&x \end{array}\implies \cfrac{84}{21}=\cfrac{100}{x}\implies 4=\cfrac{100}{x}\implies 4x=100 \\\\\\ x=\cfrac{100}{4}\implies x=25[/tex]
ANSWER CORRECTLY ILL GIVE BRAINLIST IF RIGHT :D
Use the Pythagorean theorem:
30^2 + 40^2 = X^2
900+ 1600 = x^2
X^2 = 2500
x = √2500
x = 50
The answer is 50 feet.
The length of a rectangle is 4 times its width and the perimeter is 150
feet.
What is the width of the rectangle?
A. 15 feet
B. 75 feet
C. 30 feet
D. 60 feet
Answer:
Y = W = 15 ft.
X= L = 60 ft.
So width is 15 and the length is 60.
Answer: A. 15 feet
Step-by-step explanation:
The formula used to calculate the perimeter of a rectangle is:
[tex]P=2l+2w[/tex]
Where "l" is the lenght of the rectangle and "w" is the width.
You know that the length of this rectangle is 4 times its width. This means that:
[tex]l=4w[/tex]
And you know that the perimeter is 150 feet.
Then, you need to substitute [tex]l=4w[/tex] and the value of the perimeter into the formula and solve for "w":
[tex]150=2(4w)+2w\\\\150=10w\\\\w=\frac{150}{10}\\\\w=15feet[/tex]
Equal measure? Need help with the questions? Question are at the top in the pic ?
Answer:
1. 4; 2. 32; 3. 9; 4. 8; 5. 12; 6. 16; 7. 6; 8. 8; 9. 8; 10. 8
Can anyone help me with this.
Answer:
a) third; from left most graph
b) fourth; right most graph
Step-by-step explanation:
Part a)
The graph is between the speed and time.
Nicole begin jogging faster and faster i.e. speed is increasing w.r.t time thus we have linear line in beginning.
Then she hits a comfortable speed and stayed at it i.e. speed remained constant for that time. Thus we have a straight line.
After that she gradually slows down,i.e speed is decreasing w.r.t time. Thus we have decreasing linear line.
So the graph shape is linear line with increasing slope-a constant straight line-linear line with decreasing slope
which is the third; from left most graph in option
Part b)
The graph is between Distance to campus and time.
As Dale is hiking towards campus, distance should decrease w.r.t time.
In beginning, he is hiking at constant speed towards campus thus the distance towards the campus is decreasing w.r.t time. We get a decreasing linear line.
*Note: here constant speed is not important, instead hiking towards i.e. the direction is important because of the campus distance covered
Then he sees a snake and turn and runs the other way. Thus now the distance towards the campus is increasing. And we get increasing linear line.
*Note running other way is important because of the campus distance covered
After that, he sits for a while i.e he stops and so the distance towards campus also become constant w.r.t time. we get a straight line on the graph.
So the graph shape is linear line with decreasing slope-linear line with increasing slope-a constant straight line
which is the right-most graph in option !
Which of the following statements is equivalent to P(Z21.7)?
O P(Z2-1.7)
O 1 - P(z2-1.7)
O P(Z51.7)
O 1-P(z21.7)
The equivalent expression of the expression P (z ≥ 1.7) is,
⇒ 1 - P (z ≥ - 1.7)
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
We have to given that;
The expression is,
⇒ P (z ≥ 1.7)
Now, By definition of Probability of z - score we get;
⇒ P (z ≥ 1.7) = 1 - P (z ≥ - 1.7)
Thus, The equivalent expression of the expression P (z ≥ 1.7) is,
⇒ 1 - P (z ≥ - 1.7)
Learn more about the probability visit:
https://brainly.com/question/13604758
#SPJ7
Which of the following correctly names one of the vertices of the triangle
below?
i think it is m because it simply the vertex
joke timemy boss told me to have a good day..........so I went homeMy friend says to me "What rhymes with orange" I said no it doesn'ttongue TwistersPeter Piper picked a peck of pickled peppers. How many pickled peppers did Peter Piper pick?How many cookies could a good cook cook If a good cook could cook cookies? A good cook could cook as much cookies as a good cook who could cook cookies.“Send toast to ten tense stout saints’ ten tall tents.”55:49
The height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function
h(t) = 300 - 167. Which expression could be used to determine the average rate at which the object falls during the first 3
seconds of its fall?
h(3) – h(0)
h(3)
h(3) - (0)
I believe the correct answer from the choices listed above is option D. The expression that could be used to determine the average rate at which the object falls during the first 3 seconds of its fall would be (h(3)-h(0))/3. Average rate can be calculated by the general formula:
Average rate = (change in y-axis) / (change in x-axis)
In this case,
Average rate = (change in height) / (change in time)
The average rate at which the object falls during the first 3 seconds can be calculated using the equation for average rate of change (h(3) - h(0))/3. Using the given function h(t) = 300 - 16t, this comes out to be -16 feet per second.
Explanation:In this problem, we are given a mathematical model of a falling object, as follows: h(t) = 300 - 16t. Here, the function h(t) represents the height of the object t seconds after it is dropped from a platform 300 feet above the ground.
To determine the average rate at which the object falls during the first 3 seconds, we should use the equation for average rate of change in functions. That is, the change in height divided by the change in time, or (h(3) - h(0))/3.
Let's calculate: h(3) = 300 - 16*3 = 252, and h(0) = 300. Then, the average rate = (252 - 300) / 3 = -48/3 = -16 ft/sec. This indicates that the object falls at an average rate of 16 feet per second during the first three seconds.
Learn more about Average Rate of Change here:https://brainly.com/question/34745120
#SPJ2
help me with this one
Answer: IM pretty sure its A
Step-by-step explanation: Thanks for being Brain member help.
Identify the method that will be used to solve for x for each equation.
4x = 20
x – 11 = 9
5x + 6x = 22
5(x – 2) = 30
Answer:
for 4x = 20 you have to use the division property of equality divide 20 by 4
for x - 11 = 9 you have to use the addition property of equality add 9 to 11
for 5x + 6x = 22 you have to combine like terms add 5x and 6x to make 11x
for 5(x – 2) = 30 you have to use the distributive property multiply 5 and x; 5 and -2
4x = 20; x = 5
x - 11 = 9; x = 20
5x + 6x = 22; 11x = 22; x = 2
5(x – 2) = 30; 5x - 10 = 30; x = 8
Answer:
1. B
2. A
3. A
4. B
Step-by-step explanation: