Answer:
[tex]log_{b} b^{n}[/tex] = n.
Step-by-step explanation:
Given : [tex]log_{b} b^{n}[/tex] , b is any positive number not equal to 1 and n is any number.
To find : Evaluate the expression [tex]log_{b} b^{n}[/tex].
Formula used : [tex]log_{b} x^{y}[/tex]. = y ∙ [tex]log_{b}[/tex](x) and
[tex]log_{b}(b) = 1.
Solution : We have [tex]log_{b} b^{n}[/tex].
By logarithm rule : [tex]log_{b} x^{y}[/tex]. = y ∙ [tex]log_{b}[/tex](x).
Then [tex]log_{b} b^{n}[/tex] = n∙ [tex]log_{b}[/tex](b).
By logarithm rule : [tex]log_{b}(b) = 1.
Now, n∙ [tex]log_{b}[/tex](b) = n.
Therefore, [tex]log_{b} b^{n}[/tex] = n.
Write 9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7
9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7 are 8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.
What is the rounding off numbers?Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.
We need to write 9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7
8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.
Therefore, 9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7 are 8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.
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A player moves a knight from location (3, 2) to (5, 1) on a chessboard. If the bottom-left square is labeled (1, 1), which description matches the translation?
2 squares up, 1 square right
1 square down, 2 squares left
1 square down, 2 squares right
2 squares down, 1 square right
Answer:
1 square down, 2 squares right
Step-by-step explanation:
a number of apples divided into 12 baskets
1. Which set of ordered pairs in the form of (x,y) does not represent a function of x? (1 Point)
A. (1, 1.5), (2, -1.5), (3, 1.5), (4, 1.5)
B. (0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5)
C. (1, 1.5), (-1, 1.5), (2, 2.5), (-2, 2.5)
D. (1, 1.5), (-1, -1.5), (2, 2.5), (-2, 2.5)
Which of the following expressions describes the solution set m ≥ -3?
All real numbers that are negative three or greater.
All real numbers that are greater than negative three.
All real numbers that are negative three or less.
All real numbers that are less than negative three.
The correct expression of the solution set will be;
''All real numbers that are greater than negative three.''
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The solution set is,
m ≥ - 3
Now,
Here, The solution set is,
m ≥ - 3
Clearly, a number 'm' is greater than or equal to - 3.
Thus, We can formulate;
The correct expression of the solution will be;
''All real numbers that are greater than negative three.''
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what is the answer to n/5- 9= 1/5
add any three numbers of the following and answer should be 60
2 , 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58
Mandy told Bill that she has read 16 books this year and reads 2 books each month. Bill wants to catch up to Mandy. He tracks his book reading with a table on his door. Using his table below, what month will Bill have read the same amount of books as Mandy?
Month Books
May 4
June 8
July 12
What is the simplified form of x + 6/3 - x + 2/3
The simplified form of the given expression x + 6/3 - x + 2/3 is 8/3 after combining like terms and simplifying the constants.
The question involves simplifying a mathematical expression.
The expression given is:
x + 6/3 - x + 2/3.
To simplify this expression, combine like terms.
Since x is present in both the first and third terms, they cancel each other out.
Next, combine the constant terms 6/3 and 2/3. This results in:
6/3 + 2/3 = (6 + 2) / 3 = 8/3
The simplified form of the expression is therefore 8/3.
Lisa's age is 4 years older than three times Sammy's age. Lisa is 28 years old. Let s represent Sammy's age.
Which equation can be used to solve for Sammy's age?
s + 4 = 28
3s + 4 = 28
4s + 3 = 28
3s = 28
Sammy's age can be found by using the formula 3s + 4 = 28.
Lisa's age is 4 years more than Sammy's age multiplied by 3.
Assuming Sammy's age is s, Sammy's age multiplied by 3 is:
= 3s
Lisa's age is 4 more than Sammy's age multiplied by 3 which is:
= 4 + 3s
We know that Lisa is 28 years old and Lisa's age is "4 + 3s." Equating those together will give the expression:
4 + 3x = 28
In conclusion, Sammy's age can be found by the formula 4 + 3x = 28.
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2x-3y=13 y=1/2x-7/2 as a substitution problem
-7 over -10 simplified
The length of a rectangular jewelry box is 3 inches more than twice the width. the perimeter is 18 inches
Final answer:
The width of the rectangular jewelry box is 2 inches and the length is 7 inches. These dimensions satisfy the given relationship between the length and width and the specified perimeter of 18 inches.
Explanation:
To solve the problem of finding the dimensions of a rectangular jewelry box where the length is 3 inches more than twice the width, and the perimeter is 18 inches, let's define the width of the box as w inches. Subsequently, the length will be 2w + 3 inches, as stated by the relation given in the problem. The perimeter of a rectangle is calculated by the formula P = 2l + 2w, where l is the length and w is the width of the rectangle. We can set up the equation:
18 = 2(2w + 3) + 2w
Solving the equation for w gives us:
18 = 4w + 6 + 2w
18 = 6w + 6
12 = 6w
w = 2
Now that we have the width, we can find the length:
Length = 2w + 3 = 2(2) + 3 = 7 inches
So, the width of the jewelry box is 2 inches and the length is 7 inches.
olivia has $180 to buy presents for her 3 sisters and 2 nephews. she wants to spend $20 more on each sister then she spends on each nephew.
Answer:
she spends 44 dollars per sister, 24 dollars per nephew
Step-by-step explanation:
180=3(20+x)+2x
180=60+3x+2x
120=5x
x=24
x+20=44
Classify the number 0. Check all that apply.
Real
Irrational
Rational
Integer
Whole
Natural
Identify each pair of angles as corresponding, alternate interior, alternate exterior, or consecutive interior.
1.Corresponding,2.alternate exterior, 3.corresponding, 4.consecutive interior, 5.alternate interior, 6.alternate exterior,7.alternate interior,8.alternate exterior
When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles .When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles .When two lines are cut by a transversal, the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles .When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles .So, by the definitions the angles formed are:
Correspondingalternate exteriorcorrespondingconsecutive interior. alternate interioralternate exterioralternate interioralternate exteriorLearn more:https://brainly.com/question/11342335
Corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles are different types of angle pairs formed when a transversal intersects two parallel lines.
Explanation:Corresponding angles:
Corresponding angles are formed when a transversal intersects two parallel lines.They lie on the same side of the transversal but on different lines.They have equal measures.Alternate interior angles:
Alternate interior angles are formed when a transversal intersects two parallel lines.They lie on opposite sides of the transversal and on different lines.They have equal measures.Alternate exterior angles:
Alternate exterior angles are formed when a transversal intersects two parallel lines.They lie on opposite sides of the transversal and on different lines.They have equal measures.Consecutive interior angles:
Consecutive interior angles are formed when a transversal intersects two parallel lines.They lie on the same side of the transversal and on different lines.They have a sum of 180°.Learn more about Angles here:https://brainly.com/question/13954458
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Describe a real world situation that would show a strong negative correlation explain your reasoning
Nam has a beginning balance of $815 in her checking account. She writes a check for $210 and has a debit transaction of $525. What is her new balance?
$125
$80
$1550
$120
how many times does 28 go into 126????????
Use the Distributive Property to complete the following statement:
4(x−1)=4x−
1.
–4.
4.
–1.
If 20% of all manually filed returns contain errors, and 0.05% of all electronically filed returns contain errors, how much more likely is a manual filer to make an error than an electronic filer?
a.
40,000 times more likely
b.
4,000 times more likely
c.
400 times more likely
d.
40 times more likely
Answer:
c. 400 times more likely
Step-by-step explanation:
Given f(x)=17-x^2, what is the average rate of change in f(x) over the interval [1, 5]?
Answer:A
Step-by-step explanation:
(f(5) - f(1))/(5 - 1) =
(17 - 5^2 - (17 - 1^2))/4 =
(17 - 25 - 17 + 1)/4 = 6
find the nonpermissible replacement for the variable x in this expression (x^2)/(2x-4) ? find the nonpermissible replacement for the variable x in this expression (x^2)/(2x-4) ?
The non-permissible replacements for the variable x in the expression (x^2)/(2x-4) are x = 0 and x = 2.
Explanation:An expression is undefined when its denominator is equal to zero. Therefore, we need to find the values of x that make the denominator, 2x-4, equal to zero.
Solve the equation for x: 2x - 4 = 0 2x = 4 x = 2
Therefore, x = 2 is a non-permissible replacement because it makes the denominator zero.
Additionally, the expression also includes x^2 in the numerator. Since any number multiplied by zero is still zero, dividing any non-zero number by zero results in undefined. Therefore, x = 0 is also a non-permissible replacement.
In conclusion, the non-permissible replacements for the variable x in the expression (x^2)/(2x-4) are x = 0 and x = 2.
An employee receives a weekly salary of $340 and a 6% commission on all sales.
Find the employee's earnings for a week with $660 total sales.
The employee earns a fixed salary of $340 plus a 6% commission on sales. In a week with $660 in sales, his total earnings would be $379.60.
Explanation:The employee's weekly income is a combination of a fixed salary and a percentage of sales. His fixed salary is $340. From his sales, he earns a 6% commission. So for a week with $660 in sales, the commission would be 6/100 * 660, which equals $39.60. Adding this commission to the fixed salary: $340 + $39.6 = $379.60. So, the employee's overall earnings for the week would be $379.60.
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This coordinate plane shows the shape of a hang glider. The perimeter of the glider is to be trimmed with a special material. What is the minimum length of material needed?
X = 24 ft Of Materials
Y = 2 ft Of Distance
X = (12,7)
Y = (0,2)
Using The Pythagoras Theorem
[tex]D=\sqrt{12^{2}+5^{2}}=13[/tex]
Total lenght is:
[tex]\left[\begin{array}{ccc}3*13+24+4=26\\26+28=54\end{array}\right][/tex]
What is the equation of a line that passes through point R(−4, −3) and has a slope of 7?
A: y = 7x + 25
B: y = 7x − 25
C: y = 7x + 3
D: y = −7x − 3
Write the rule for the nth term of an arithmetic sequence in which a10=46 and d=3
Final answer:
The rule for the nth term of the arithmetic sequence is given by the formula a_n = 19 + (n - 1)×3, where a1 is the first term of the sequence and d is the common difference.
Explanation:
To write the rule for the nth term of an arithmetic sequence where the 10th term a10 is 46 and the common difference d is 3, we use the formula:
an = a1 + (n - 1)d
We have that:
a10 is the 10th term of the sequence which is 46.
The common difference d is 3.
Firstly, we need to find a1, the first term of the sequence. We can use the given a10 to find a1.
a10 = a1 + (10 - 1)×3
46 = a1 + 9×3
46 = a1 + 27
a1 = 46 - 27
a1 = 19
Now we can write the rule for the nth term:
an = 19 + (n - 1)×3
This formula allows us to calculate any term in the sequence by substituting the desired term number for n.
1.) Mrs. Computer is 3 times older than her daughter, Mousy. The sum of their ages is 52> How old is Mousy?
2.)Mike is 5 years more than twice as old as Tom. The sum of their ages is 65. How old is Mike?
At time t equals or > 0, the acceleration of a particle moving on the x axis is a(t)=t+sint.? ...?
Write the equation 16x 11y = −88 in slope-intercept form.
The equation 16x + 11y = -88 when rearranged in slope-intercept form is y = (-16/11)x - 8, with a slope of -16/11 and a y-intercept of -8.
Explanation:To write the equation 16x + 11y = -88 in slope-intercept form, we need to solve for y in terms of x. The slope-intercept form of a straight line is y = mx + b, where m is the slope and b is the y-intercept. Following the algebra of straight lines, we rearrange the equation as follows:
Subtract 16x from both sides: 11y = -16x - 88.Divide each term by 11 to solve for y: y = (-16/11)x - 8.This gives us the slope-intercept form, where the slope (m) is -16/11 and the y-intercept (b) is -8. The slope means that for every increase of 11 units in the x-direction, y decreases by 16 units. The y-intercept is the point where the line crosses the y-axis, which is at y = -8 when x = 0.
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