Answer: [tex]\frac{1}{3}[/tex]
Explanation:
let y = [tex]log_{8} (2)[/tex]
whenever we transfer base from log from one side to other it will remain be base after shifting to the other side.
Change log to exponent form [tex]\log_xm=n\\m =x^{n}[/tex]
here we have n = y, m=2, x=8 by substituting the values
we will get
[tex]8^{y} = 2[/tex] (1)
we can write 8 in power of 2 that is [tex]2^{3}[/tex]
we will rewrite the above equation (1) as
[tex]2^{3y} = 2[/tex]
we can equate the power when base is same then we will get
3y = 1
then
[tex]y=\frac{1}{3}[/tex]
The result of the logarithmic expression [tex]log _82=x[/tex] is 1/3
Let the given logarithmic function be x to have:
[tex]log _82=x[/tex]
This can be transformed into indices to have:
[tex]8^x = 2[/tex]
Solve the resulting indices for "x" a shown:
[tex](2^3)^x = 2^1\\2^{3x}=2^1[/tex]
Cancel the base and equate the power to have:
[tex]3x = 1\\x = \frac{1}{3}[/tex]
Hence the result of the logarithmic expression [tex]log _82=x[/tex] is 1/3
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What is the product in simplest form?
−8/9 ⋅ 5/6
You flip a coin 5 times. in how many ways could u obtain at least one tail
the senior classes at high school A and high school B planned separate trips to the indoor climbing gym. the senior class at high school A rented and filled 13 vans and 5 buses with 353 students. high school b rented and filled 9 vans and 5 buses with 309 students. each van and bus carried the same number of students. find the number of students in each van and in each bus.
1) Divide using synthetic division, and write a summary statement in fraction form.
two x to the fifth minus x to the fourth plus three x squared minus x plus five divided by quantity x minus one
a. 2x4 + x3 + 4x2 + 3x + eight divided by quantity x minus one
b. 2x4 + x3 - x2 + 2x + 1 + six divided by quantity x minus one
c. 2x4 + x3 + x2 + 4x + 3 + eight divided by quantity x minus one
d. 2x4 - 3x3 + x + six divided by quantity x minus one
2) Divide f(x) by d(x), and write a summary statement in the form indicated.
f(x) = x4 - 4x3 + 2x2 - 4x + 1; d(x) = x2 + 1
a. f(x) = (x2 + 1)( x2 + 4x + 1)
b. f(x) = (x2 + 1)( x2 - 4x + 1) + 12x + 3
c. f(x) = (x2 + 1)( x2 + 4x + 1) + 12x + 3
d. f(x) = (x2 + 1)( x2 - 4x + 1)
3) Find the remainder when f(x) is divided by (x - k).
f(x) = 3x3 - 4x2 - 3x + 14; k= 3
a. 50
b. 68
c. -12
d. 112
4) Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f.
k = -1; f(x) = 4x3 - 2x2 + 2x + 4; Lower bound?
a. yes
b. no
5) Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.
f(x) = -2x4 + 4x3 + 3x2 + 18
A veterinary office takes out a loan to purchase a new set of digital animal scales that costs $12,250. The interest rate is 6.5%, and the total interest paid is $2,388.75. How many years is the loan for?
The loan is for approximately 3 years.
Explanation:To find the number of years for the loan, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Given that the principal is $12,250, the rate is 6.5%, and the total interest paid is $2,388.75, we can rearrange the formula to solve for time:
Time = Interest / (Principal * Rate)
Plugging in the values, we get:
Time = 2,388.75 / (12,250 * 0.065)
Simplifying the expression, we have:
Time ≈ 3 years
Help me!!!!!!!!!!!!!
ASAP HELP FOR NUMBER 13!!
13a, b, c, and d!!
CORRECT ANSWERS PLS
THANK U GUYS SO MUCH!!!
1. ABCD is a trapezoid with midsegment EF. If AB = 12 and CD = 24, what is the length of EF?
2. ABCD is a trapezoid with midsegment EF. If AB = 21 and CD = 35, what is the length of EF?
3. ABCD is a trapezoid with midsegment EF. If AB = 7 and EF = 9, what is the length of CD?
4. ABCD is a trapezoid with midsegment EF. If CD = 32 and EF = 22, what is the length of AB?
5. The length of the midsegment of a trapezoid is the _____ of the length of the two bases.
PLEASE HELP ME, SERIOUS ANSWERS ONLY PLEASE
Answer:
5
Step-by-step explanation:
What is the total amount of interest with 12,560 dollar stocks borrowed 2% simple interest for 4 years?
Javier bought a microwave for $150. The cost was 30% off the original price, what was the original price
An interior decorator bought 12 1/2 yards of material to make drapes. He used 8 2/3 yards on one pair of drapes. How much material does he have left?
Tracy deposited $59 into a bank account that earned 3.5% simple interest each year. If no money was deposited into or withdrawn from the account, how much money was in the account after 112 years?
PLZ HELP
Lakita has 65 water bottles for the 5K race participants. In addition, she is considering buying boxes of water bottles that have 16 water bottles each. All of the boxes cost the same. Lakita can buy up to 5 boxes of water bottles given the amount of money she has. Let x represents the number of boxes of water bottles Lakita buys. Write a function rule to describe how many water bottles Lakita will have based on the number of boxes she buys. Find a reasonable range for the function.
A - f(x) = 65x + 16
{145}
B - f(x) = 16x + 65
{65, 81, 97, 113, 129, 145}
C - f(x) = 65x + 16
{81, 97, 113, 129, 145}
D - f(x) = 16x + 65
{65, 81, 97, 113, 129}
The function rule representing the total number of bottles Lakita will have based on the number of boxes she buys would be f(x) = 16x + 65. The reasonable range for this function, considering she can buy up to 5 boxes, is {65, 81, 97, 113, 129, 145}.
Explanation:In this problem, we want to find out the total number of water bottles Lakita will have based on the number of boxes she buys. We know that Lakita already has 65 water bottles and each box she buys contains 16 water bottles. The function rule to represent this would be: f(x) = 16x + 65. Here, x is the number of boxes she buys.
The range of the function is the possible values that f(x) can have based on the scenario. Since Lakita can buy up to 5 boxes, the range would be the number of bottles she will have if she buys 0 through 5 boxes, which is: {65, 81, 97, 113, 129, 145}.
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The function rule to describe the number of water bottles is f(x) = 16x + 65. The range for the function is {65, 81, 97, 113, 129, 145}, which represents the total water bottles counts depending on the number of boxes Lakita buys.
Explanation:The function that will describe how many water bottles Lakita will have based on the number of boxes she buys is f(x) = 16x + 65. To explain, x represents the number of boxes, each with 16 water bottles (16x), and the 65 represents the water bottles she initially has. The total number of water bottles is the sum of these two amounts.
A reasonable range for the function is the set of all possible total water bottles counts, depending on the number of boxes bought. As she can buy up to 5 boxes, we substitute values from 0 to 5 into the function to find the range. So the range will be {65, 81, 97, 113, 129, 145}, corresponding to Lakita buying 0, 1, 2, 3, 4, or 5 boxes (respectively).
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Juan's income y consists of at least $37,500 salary plus 5% commission on all of his sales x. which inequality represents juan's income in one year? answer
Answer:
y < 37,500 + 5x I believe.
PLEASE HELP
What is the equation of the line in slope-intercept form?
Which shows the best path to find the number of centimeters in 1 yard?
To find the number of centimeters in 1 yard, convert yards to feet, then feet to inches, and finally, inches to centimeters. 1 yard is equal to 91.44 centimeters after applying the conversion factors 1 yard = 3 feet, 1 foot = 12 inches, and 1 inch = 2.54 centimeters.
To find the number of centimeters in 1 yard, we need to follow a two-step conversion process. First, we convert yards to feet, knowing that 1 yard equals 3 feet. Then, we convert feet to inches, since we know that 1 foot equals 12 inches. Finally, we convert inches to centimeters, using the conversion factor that 1 inch is equivalent to 2.54 centimeters.
So the path would look like this:
Convert yards to feet: 1 yard = 3 feet.
Convert feet to inches: 1 foot = 12 inches.
Convert inches to centimeters: 1 inch = 2.54 centimeters.
Applying these conversions to 1 yard:
1 yard * 3 feet/yard = 3 feet
3 feet * 12 inches/foot = 36 inches
36 inches * 2.54 centimeters/inch = 91.44 centimeters
Therefore, 1 yard is equivalent to 91.44 centimeters.
What is the inverse to this statement? Statement : If you feel hungry then you eat.
A. if you don't eat, then you don't feel good
B. if you feel hungry,then you don't eat.
C. If you eat, then you feel hungry
D. If you don't feel hungry, then you don't eat.
Answer:
D.Because if you feel hungry then you'll eat, but if your not hungry then you won't want to eat. Hope I helped!
Step-by-step explanation:
What surprised or impressed Xuanzang on his visit to India? What features of Indian life might seem most strange to a Chines visitor?
Actually what surprised Xuanzang the most was the way how Indians ran things and their way of life because this is completely unlike to Chinese cultures. The strangest thing he found was that how everyone in India practiced Buddhism and how structured it was. Because back in China at that time, Buddhism was still much unorganized and not very popular.
List the following numbers from least to greatest -5/3, 7/3, -3/4, 7/5.
A storage tank for propane gas is to be constructed in the shape of a right circular cylinder of altitude 20 feet with a hemisphere attached to each end. determine the radius x so that the resulting volume is 216π ft3.
To determine the radius x of the storage tank, we need to break down the shape into smaller parts. We can set up a cubic equation to find the value of r, and then calculate the radius x.
To determine the radius x of the storage tank, we need to break down the shape into smaller parts. First, let's consider the cylinder. The volume of a cylinder is given by V = πr^2h, where r is the radius and h is the altitude. In this case, the altitude is 20 feet. So, the volume of the cylinder is Vcylinder = πr^2(20).
Next, let's consider the hemispheres attached to each end. The volume of a hemisphere is given by V = (2/3)πr^3. Since there are two hemispheres, the total volume of the hemispheres is Vhemispheres = (2/3)(2)(πr^3) = (4/3)πr^3.
Given that the resulting volume is 216π ft3, we can set up the equation:
216π = Vcylinder + Vhemispheres = πr^2(20) + (4/3)πr^3
Simplifying and rearranging the equation, we get:
3r^3 + 60r^2 - 216 = 0
By solving this cubic equation, we can find the value of r. Once we have the value of r, we can determine the radius x by subtracting the radius of the hemispheres (r) from the total radius of the tank (x+r).
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PLESSE HELP!! this question is super hard. it’s due tomorrow and i’m not understanding.
V(t)=t2−3t what is the meaning of the quantity v(4) ?
Solve the following for y: 9x − 3y = 18
y = −3x − 6
y = 3x − 6
y = −3x + 6
y = 3x + 6
30 points to who answers this first and will get brainliest answer
In which quadrant of the coordinate graph does point J lie?
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
If a rider stops 15 mile to take a break and Another stops at 25 miles at what distance will they stop at the same time
multiples of 15: 15,30,45,60,75
multiples of 25: 25, 50, 75
they will stop together at 75 miles
HELP ASAP 30 POINTS GIVEN
The coordinates of the vertices of quadrilateral JKLM are J(−3, 2), K(4, −1), L(2, −5), and(−5, −2). Drag and drop the choices into each box to correctly complete the sentences.
Answer:
[tex]-\frac{3}{7}[/tex],[tex]2[/tex],[tex]-\frac{3}{7}[/tex],[tex]2[/tex],is,both pairs of opposite sides are parallel
Step-by-step explanation:
Given two points
[tex]A=(a1,a2)[/tex] and
[tex]B=(b1,b2)[/tex]
We define the slope ''m'' between this points as :
[tex]m=\frac{b2-a2}{b1-a1}[/tex] or either
[tex]m=\frac{a2-b2}{a1-b1}[/tex]
The slope between the points J and K is
[tex]m=\frac{-1-2}{4-(-3)}=-\frac{3}{7}[/tex]
The slope between the points L and K is
[tex]m=\frac{-1-(-5)}{4-2}=2[/tex]
The slope between the points M and L is
[tex]m=\frac{-2-(-5)}{-5-2}=-\frac{3}{7}[/tex]
The slope between the points M and J is
[tex]m=\frac{-2-2}{-5-(-3)}=2[/tex]
We find all the slopes between the points.
For the quadrilateral JKLM the side JK is opposite to the side ML and the side KL is opposite to the side JM
The definition of parallelogram is :
A figure with 4 sides in which their opposite sides are parallel.
The side JK is parallel to the side ML because they have the same slope.
The side JM is parallel to the side KL because they have the same slope.
We answer that JKLM is a parallelogram because both pairs of opposite sides are parallel.
Solve the inequality 0>-3×-2×.
A car travels 90 miles in 1.5 hours. How many miles will it travel in 5 hours if its speed remains the same? A) 60 miles B) 180 miles Eliminate C) 222 miles D) 300 miles
HURRY I NEED THE ANSWER.
What is the product of the roots of the equation x^3-4x^2+x+6=0?
The product of the roots of the equation x³ - 4x² + x + 6 = 0 will be - 6.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ x³ - 4x² + x + 6 = 0
Now,
We know that;
If u, v, w are the roots of the equation ax³ + bx² + cx + d = 0
Then, The product of roots (uvw) = - d / a
Here, The equation is,
⇒ x³ - 4x² + x + 6 = 0
Let the three roots of the equation = a, b, c
Then, We get;
⇒ a × b × c = (-6) / 1
⇒ abc = - 6
Thus, The product of the roots of the equation x³ - 4x² + x + 6 = 0
will be - 6.
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Which equation represents a line that passes through two points in the table
Answer: C
Step-by-step explanation: A P E X