Choose the best answer that represents the property used to rewrite the expression.
log6 20 - log6 x = log6 20/x
Answer:
㏒₆ (18) - ㏒₆ (6) = ㏒₆ (3)Here subtraction of logarithm given. So we have to use the property of logarithm of quotient.The property says that㏒ₐ (M) - ㏒ₐ (N) = ㏒ₐ (M/N)So for subtraction we have to divide them. That is logarithm of difference becomes the quotient.So we can write,㏒₆ (18) - ㏒₆ (6) = ㏒₆ (18/6) If we divide 18 by 6 we will get 3.So, ㏒₆ (18) - ㏒₆ (6) = ㏒₆ (3)
Step-by-step explanation:
Answer:Quotient Property
Step-by-step explanation:The property used to rewrite the expression is the quotient rule of logarithms, which states that log_b(x/y) = log_b(x) - log_b(y).
for each of the figures, write an absolute value equation that has the following solution set 3 and 7
The solution set 3 and 7 are the true values of the absolute value equation
The absolute value equation that has a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]
How to determine the absolute value equation?The solution sets of the absolute value equation are given as:
x = {3, 7}
Calculate the mean of the solutions
[tex]x_1 = \frac{7 +3}{2}[/tex]
[tex]x_1 = 5[/tex]
Calculate the difference of the solutions divided by 2
[tex]x_2 = \frac{7 - 3}{2}[/tex]
[tex]x_2 = 2[/tex]
The absolute value equation is the represented as:
[tex]|x - x_1| - x_2 = 0[/tex]
Substitute known values
[tex]|x - 5| - 2 = 0[/tex]
Add 2 to both sides
[tex]|x - 5| = 2[/tex]
Hence, the absolute value equation that has the a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]
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Help help help help math math
Answer:
No Solution
Step-by-step explanation:
-y = -2x + 8
y = 2x - 8
2x + 8 = 2x - 8
2x - 2x = -8 - 8
0 = -16
No Solution
You can also graph y = 2x + 8 and y = 2x - 8. The slope are the same and so they are parallel
Working alone, Mr. Tough can grade the final exams in 12 hours. His assistant, Mrs. Nice, cam grade the same exams in 15 hours. What fraction of the exams can Mr.Tough and Mrs.Nice grade in 1 hour if they work together?
Answer:
9n/60
Step-by-step explanation:
add 1/12 + 1/15 which = 5/60 + 4/60.
= 9/60
YAY!!!!!!!
The fraction of the exams that Mr Tough and Mrs Nice grade in 1 hour if they work together is 3/20
What are fractions?In Maths, a fraction is used to represent the portion/part of the whole thing. A fraction has two parts, namely numerator and denominator. There are proper fractions, improper fractions and mixed fractions.
Example: 2/5, 1/4 etc.
How to solve Work and Time problems:We will this equation,
rate × time = work done
For this problem:
Mr Tough's rate:
Mr Tough's rate × 12 hours = final exam
Mr Tough's rate = 1/12
Mrs.Nice's' rate:
Mrs .Nice's' rate × 15 hours = final exam
Mrs .Nice's' rate = 1/15
To make this into a solvable equation, find the total time (T) needed for Mr Tough and Mrs.Nice to grade the final exam. This time is the sum of the rates of Mr Tough and Mrs.Nicea, or:
Total time:
T(1/12 hours + 1/15 hours) = final exam
T = final exam / (1/12 + 1/15)
Simplifying we get,
T = final exam / (0.15)
Now, to finish in 1 hour we will find what fraction of the final exam they can grade, so taking T = 1 hour,
1 hour = final exam / (0.15)
By further simplifying,
final exam = 1 × 0.15
= 0.15
= 15/ 100
= 3/20
Therefore, 3/20 fraction of the final exam they can grade if they work together for 1 hour.
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x^3-125=0
what’s the nth root
Sancho paints the new sign for his bike shop. One quart of paint covers 200 square feet, and Sancho plans on applying three coats of paint. One quart of paint cost $8.97. What is the square footage of his sign and ow much must Sancho spend to paint the sign?
I will give crown thingy
A rectangle has a perimeter of 20 cm. What will the perimeter be if the rectangle tripled in size?
ITS A VOLUME QUESTION
Answer:
Step-by-step explanation:
Holding the perimeter fixed, the shape with greatest area is square ( all sides of the same) length) For your name example a square with a perimeter of 20 cm has sides of 5 cm and area of 5 times 4=20 cm) ^3 hope this helps
what is the area of a 45 degree sector of a circle with a radius of 12 in.
given ,
a circle of radius 12 inches
and [tex]\theta[/tex] = 45°
now we know that ,
[tex]\\{Area \: of \: sector = \frac{\theta}{360\degree} \times \pi \: r {}^{2} } \\ \\ [/tex]
let's now plug in the values of radius and theta as 12 inches and 45° respectively ,
[tex]\\\dashrightarrow \: \frac{45}{360} \times \frac{22}{7} \times 12 \times 12 \\ \\ \dashrightarrow \: \frac{1}{8} \times \frac{22 \times 12 \times 12}{7} \\ \\ \dashrightarrow \: \frac{22 \times 12 \times 12}{56} \\ \\ \dashrightarrow \: \frac{3168}{56} \\ \\ \dashrightarrow \: 56.57 \: inches {}^{2} (approx.)[/tex]
hope helpful :D
Smmy pays $2 73 for each gallon of gas, which table best represents the relationship between the number of gallons
purchased, and the amount he pays for gas?
Answer:
Label ELabel E
Step-by-step explanation:
Label ELabel ELabel k
The average number of potholes per 10 miles of paved U.S. roads is 130. Assume this variable is approximately normally distributed and has a standard deviation of 5. Find the probability that a randomly selected road has more than 142 potholes per 10 miles
Answer:
54.03% probability that a randomly selected road has between 128 and 136 potholes per 10 miles.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Find the probability that a randomly selected road has between 128 and 136 potholes per 10 miles.
This probability is the pvalue of Z when X = 136 subtracted by the pvalue of Z when X = 128. So
X = 136
has a pvalue of 0.8849.
X = 128
has a pvalue of 0.3446.
0.8849 - 0.3446 = 0.5403
54.03% probability that a randomly selected road has between 128 and 136 potholes per 10 miles.
Evaluate the following limit, if it exists : limx→0 (12xe^x−12x) / (cos(5x)−1)
Answer:
[tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=-\frac{24}{25}[/tex]
Step-by-step explanation:
Notice that [tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=\frac{12(0)e^{0}-12(0)}{cos(5(0))-1}=\frac{0}{0}[/tex], which is in indeterminate form, so we must use L'Hôpital's rule which states that [tex]\lim_{x \to c} \frac{f(x)}{g(x)}=\lim_{x \to c} \frac{f'(x)}{g'(x)}[/tex]. Basically, we keep differentiating the numerator and denominator until we can plug the limit in without having any discontinuities:
[tex]\frac{12xe^x-12x}{cos(5x)-1}\\\\\frac{12xe^x+12e^x-12}{-5sin(5x)}\\ \\\frac{12xe^x+12e^x+12e^x}{-25cos(5x)}[/tex]
Now, plug in the limit and evaluate:
[tex]\frac{12(0)e^{0}+12e^{0}+12e^{0}}{-25cos(5(0))}\\ \\\frac{12+12}{-25cos(0)}\\ \\\frac{24}{-25}\\ \\-\frac{24}{25}[/tex]
Thus, [tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=-\frac{24}{25}[/tex]
what is the awnser to 5+(5x20)x 30
Answer: 3005
Step-by-step explanation: multiply 5 by 20 and it will give 100 then times 30 Equals 3000 and plus gives 3005 . Please mark brainliest
Answer:3005
Step-by-step explanation :multiply 5 by 20 and it will give 100 then multiply by 30 that Equals 3000 and plus 5 that gives you 3005
The number 3 is a common factor of _________.
A) 9 and 15
B) 6 and 10
C) 8 and 12
Answer:
A) 9 and 15.
Step-by-step explanation:
First, let's see what each number's factor is:
A)
9 : 1, 3 & 9
15 : 1, 3, 5 & 15
B)
6 : 1, 2, 3 & 6
10 : 1, 2, 5 & 10
C)
8 : 1, 2, 4 & 8
12 : 1, 2, 3, 4, 6 & 12
Therefore, The number 3 is a common factor of A) 9 and 15.
___
PLS HELP ME !! I REALLT NEED HELP
Step-by-step explanation:
it clearly says (and also shows it by specifying 4cm × 4cm side lengths) : a square base.
so, all net diagrams not having a square in the middle (but a rectangle or a triangle) are out.
and in fact, all 3 that have a square in the middle, are valid nets that would fold up to the pyramid : the 2nd, 4th and 6th.
The difference between the number of items on two grocery lists is 7. The combined total number of items on the lists is 33.
Answer:
20 and 13
Step-by-step explanation:
If one list is 'a' and the other one is 'b' then
a-b = 7 and a+b = 33
a-b+a+b = 7+33
2a = 40
a = 20
Now, 20 - b = 7
-b = -13
b = 13
11 18 The diagram shows an equilateral triangle. All measurements are in cm. NOT TO SCALE 2x+2 3x+4 3 OLTY а The perimeter of the triangle is 57 cm. Find the length of a.
Answer:
a = 7
Step-by-step explanation:
3x + 4 = 57 ÷ 3
3x + 4 = 19
3x = 15
x = 5
2x + 2 = 2(5) + 2 = 10 + 2 = 12
19 - 12 = 7
a = 7
hope this helps!! p.s. i really need brainliest :)
A chocolatier makes chocolate covered cherries in the form of spheres. Amelia
measures the outer diameter of these chocolates to be 2.8 cm. If she measures the
thickness of the chocolate to be 0.5 cm, how much chocolate is used in one of the
chocolate covered cherries? Round your answer to the nearest hundredth if
necessary. (Note: diagram is not drawn to scale.)
The volume of the chocolate is the amount of choclate used in the cherries
The amount of chocolate used is 17.24 cubic centimeters
How to determine the amoumt of chocolate?Start by calculating the volume of the cherries using:
V = 4/3 π(D/2)^3
The diameter of the cherry is 2.8 cm.
So, we have:
V = 4/3π(2.8/2)^3
Evaluate
V = 11.49
Next, calculate the volume of the cherry and the chocolate.
V = 4/3π(0.5+2.8/2)^3
V = 28.73
Calculate the difference (d) between both volumes
d = 28.73 - 11.49
d = 17.24
Hence, the amount of chocolate used is 17.24 cubic centimeters
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Please help me with this question I am having difficulty with it
Answer:
The first x=4 y=8
Step-by-step explanation:
2x-5 = y-5
x+1 = y-3
Multiply the second by -2(to eliminate x)
2x-5 =y-5
-2x-2= -2y+6
ADD BOTH
-7 = -y+1
y=8
PLUG y
x+1 =y-3
x+1 =8-3
x+1=5
x=4
Multiply 2+√10 by its conjugate and simplify.
[tex]\left(2+\sqrt{10} \right)\left(2-\sqrt{10} \right)\\\\=2^2-\left(\sqrt{10} \right)^2\\\\=4-10\\\\=-6[/tex]
What is the answer for this 4² × 4²
Answer:
4squared is 16 so 16×16=256
hope it help
Answer:
4^2=16 multiplyin 16 by 16 gets you 256
Step-by-step explanation:
PLEASE HELP I WILL GIVE BRIANLIEST
Answer:
T. Perimeter
Step-by-step explanation:
I have attached the questions below please help me
Answer:
point A is the answers for the question
Step-by-step explanation:
please mark me as brainlest
Peyton's family took a road trip to the Grand Canyon. Peyton fell asleep 77% of the way through the trip. If the total length of the trip was 1000 miles, how many miles had they travelled when Peyton fell asleep?
The miles Peyton's family had travelled when he fell asleep is 770 miles
How many miles had they travelled when Peyton fell asleep?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. The sign used to represent percentages is %.
Miles when Peyton fell asleep = 77% x 1000 = 770 miles
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The quotient of a number and three is six
What is the number?
Answer:
the quotient of 18 and 3 is 6
Step-by-step explanation:
do the inverse and get 6x3=18
please help answer by putting
"question ___ is option ___"
Answer:
B A C A B
Step-by-step explanation:
i took this test before
what is 2(9p-1/2) equil to?
Answer:
Step-by-step explanation:
Use distributive property: a*(b - c) = (a*b) -(a*c).
Here, a = 2 ; b = 9p & c = 1/2
[tex]2*(9p - \dfrac{1}{2})=2*9p-2*\dfrac{1}{2}\\\\\\ = 18p - 1[/tex]
3. Avery records her rock-climbing progress and finds that her altitude, in kilometers above sea
level, can be represented by a linear model, A = 7+ 1.3t, where t is the number of hours since
Avery started climbing.
Based on this model, how many kilometers above sea level was Avery's altitude before she started
climbing?
km
Using the given linear function, it is found that Avery was 7 kilometers above sea level before she started climbing.
What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can be interpreted as the initial value.In this problem, her altitude in kilometers after t hours is modeled by:
A(t) = 7 + 1.3t.
The y-intercept is of b = 7, which means that Avery was 7 kilometers above sea level before she started climbing.
More can be learned about linear functions at https://brainly.com/question/24808124
Help picture below problem 13
The Pythagorean theorem is the idea that the sum of the two legs which are both squared is equal to the hypotenuse's length squared.
*look at the image I attached for a better explanation
By looking at the picture, we are missing the leg's length, and by using the Pythagorean theorem, we get the equation
[tex]?^2+5^2 = 13^2\\?^2 + 25 = 169\\?^2 = 144\\? = 12[/tex]
Thus the missing side length is 12 cm
Hope that helps!
A piece of wire 20 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.
The length of the wire is the perimeter of the wire
The radius of the circle is 1.59 meters
How to determine the radius of the circle?The length of the wire is given as:
L = 20m
When cut into two pieces, we have:
Perimeter of square = 10 mCircumference of circle = 10mThe circumference of the circle is calculated using:
C = 2πr
So, we have:
2πr = 10
Make r the subject
r = 10/2π
Evaluate the quotient
r = 1.59
Hence, the radius of the circle is 1.59 meters
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Solve by completing the square
Answer:
The answer is (-6 + √41), (-6 – √41)
Step-by-step explanation:
We are given an equation
x² + 12x = 5Subtract 5 from both side we get,
x² + 12x – 5 = 5 – 5
x² + 12x – 5 = 0
we get the equation in the form of
ax² + bx + c = 0Here, a = 1, b = 12, c = (-5)
Now, Add and subtract (b/2a)² we get,
x² + 12x + (12/2)² – (12/2)² – 5 = 0
x² + 12x + (6)² – (6)² – 5 = 0
(x + 6)² – 36 – 5 = 0
(x + 6)² – 41 = 0
Now, add 41 both side we get,
(x + 6)² – 41 + 41 = 0 + 41
(x + 6)² = 41
√(x + 6)² = √41
x + 6 = ±√41
x = -6 + √41, -6 – √41
Thus, The roots of the equation is
(-6 + √41) and (-6 – √41).
-TheUnknownScientist 72