The solution to the equation log₇343 = 3 is 7³ = 343
What is an equation?An equation is used to show the relationship between numbers and variables.
The logarithm can be defined as the exponent that raises a base to get a particular number. The law of logarithm states:
logₓm = n is the same as xⁿ = m
Given the equation:
log₇343 = 3
Applying the law of logarithm gives:
7³ = 343
The solution to the equation is 7³ = 343
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Write a piecewise-defined function for this graph please!
The piecewise-defined function for this graph will be y = -(3/5)x - 4/5 for x < 2 and y = (5/2)x - 7 for x ≥ 2.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The equation of the line that passes through (-3, 1) and (2, -2) is given as,
(y + 2) = [(- 2 - 1) / (2 + 3)](x - 2)
y + 2 = - (3/5)x + 6/5
y = -(3/5)x - 4/5
The equation of the line that passes through (2, -2) and (4, 3) is given as,
(y + 2) = [(3 + 2) / (4 - 2)](x - 2)
y + 2 = (5/2)x - 5
y = (5/2)x - 7
The piecewise-defined function for this graph will be y = -(3/5)x - 4/5 for x < 2 and y = (5/2)x - 7 for x ≥ 2.
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Draw a number line and put the following numbers in the correct location
2.5, -6, -3, 4, -2.2, 1/4, -1/2, 2 1/3
Therefore , the solution to the given problem of order comes out to be
-6< -3< -2.2 < -1/2 < 1/4 < 2[tex]\frac{1}{3}[/tex] < 2.5 < 4.
What is order?Numerical order can be used to organise a set of numbers. It is possible to use both increasing and decreasing ordering. Consider how a set of numbers would seem if they were organized in ascending order like 2, 55, 103, 256, and 802, for example. This can make sorting through a huge collection of numbers much easier.
Here,
Given : 2.5, -6, -3, 4, -2.2, 1/4, -1/2, 2 1/3
To put them according to ascending order :
So ,
negative terms are the smallest compare to positive terms as their values are lower than 0.
thus,
-6< -3< -2.2 < -1/2 < 1/4 < 2[tex]\frac{1}{3}[/tex] < 2.5 < 4
Therefore , the solution to the given problem of order comes out to be
-6< -3< -2.2 < -1/2 < 1/4 < 2[tex]\frac{1}{3}[/tex] < 2.5 < 4.
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Solve 0.5(-2+ 4d) - 2d=-13 for d.
O Infinite solutions
O No solution
O d=-11
O d = 1.375
Answer:
(b) No solution
Step-by-step explanation:
You want the solution to 0.5(-2+ 4d) - 2d = -13.
SimplifiedEliminating the parentheses using the distributive property, we have ...
-1 +2d -2d = -13
Collecting terms gives ...
-1 = -13 . . . . . false
No value of d will make this true. There is No Solution.
the ratio of students to adults at the open house is 9:7 suppose there are 832 students and adults at the open house. how many students are there
Answer:
To determine the number of students at the open house, you can use the fact that the ratio of students to adults is 9:7 and set up the following proportion:
students/adults = 9/7
You can then cross-multiply to find the value of "students":
7 * students = 9 * adults
7 * students = 9 * (832/(9+7))
7 * students = 832
students = 832 / 7
students = approximately 118.85714285714 students
To determine the number of students at the open house, you can use the fact that the ratio of students to adults is 9:7 and set up the following proportion:
Copy code
students/adults = 9/7
You can then cross-multiply to find the value of "students":
Copy code
7 * students = 9 * adults
7 * students = 9 * (832/(9+7))
7 * students = 832
students = 832 / 7
students = approximately 118.85714285714 students
Since the number of students must be an integer, the number of students at the open house is approximately 118 students.
Step-by-step explanation:
If a pair of shoes was discounted from an original price of P5000 to P2800 what is the percent decrease or discount
Work Shown:
a = old price = 5000
b = new price = 2800
c = change in price
c = b-a
c = 2800-5000
c = -2200
The value of c is negative to indicate a price decrease.
d = percent change
d = (c/a)*100%
d = (-2200/5000)*100%
d = -44%
There is a 44% decrease or discount.
A line passes through the point (-10,1) and has a slope of 3/2. Write an equation in point-slope form for this line. Please Help Best helped will get brainiest Promise PLS HELP !!!!!!!!!!!!!!!!!!!
Answer:
y - 1 = 3/2 (x + 10)
Step-by-step explanation:
Point-slope form of the equation of a line is a fill-in-the-blank shortcut to write an equation. If you know a point and the slope of a line you can fill in that info and voila! you have the equation.
Here is Point-slope equation:
y - Y = m(x - X)
Because the point given (-10,1) is in the form (X,Y), fill in -10 for X and 1 for Y.
The slope given is 3/2, fill that in for m.
y - Y = m(x - X)
y - 1 = 3/2 (x - -10)
y - 1 = 3/2 (x + 10)
The equation is
y - 1 = 3/2 (x + 10)
Solve the exponential equation. 1/16 = 64^4 x − 3
Answer:
x=7/12Step-by-step explanation:
1/16=64^4x-3
1/4^2=(4^3)^4x-3
4^-2=(4^3)^4x-3
4^-2=4^3*(4x-3)
Since the bases are equal (to 4), the exponents must be equal to each other.
-2=3*(4x-3)
-2=12x-9
-2+9=12x
7=12x
7/12=x
x=7/12
So the answer is x=7/12
Please mark me brainliest if this helped!In this case, how would it be resolved if it does not indicate any base, only brand X
The coordinates of the vertices of the square with height x is given as follows:
H(-x,x).I(0,x).J(0,0).K(-x,0).What is a square?A square is a figure for which all the four side lengths are congruent, that is, they have the same measure.
The side length of the square in this problem is given as follows:
x.
As the height is equals to the base.
The vertex J represents the origin, hence it has coordinates given as follows:
J(0,0).
Then the remaining coordinates of the square are given as follows:
H(-x,x). -> x units left and x units up from the origin.I(0,x). -> x units up from the origin.K(-x,0). -> x units left from the origin.More can be learned about squares at https://brainly.com/question/30179630
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ABC~A'B'C'. Their scale factor is 7:9. If the perimeter of smaller ABC is 42, then the
perimeter of A'B'C' is.
Pls hurry!!
Answer:
54
Step-by-step explanation:
ratio is 7:9
7=42
9=?
9×42÷7
There is a safety fence around a circular pool with a gate. The gate is 150 cm wide.
an image
What is the length of the fence not including the gate?
m
Use π
= 3.14
Length of fence = Circumference of the pool – width of the gate. Length of fence = 6.28x – 150 cm.
What is the length of the fence?Let the circular pool has the radius (r ) = x cm.Since the pool is in a circular shape so the circumference will be the length of the fence. Moreover, there is a 150cm wide so we have to subtract the 150 cm from the value of circumference in order to get the actual length of the fence.Length of fence = Circumference of the pool – width of the gate.Length of fence = 2 π r – 150Length of fence = 2 × 3.14 × x – 150Length of fence = 6.28x – 150 cm.a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin radius.To learn more about length of the fence refers to:
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Target buys a pair of shoes for 20, but they sell it to the public for 35. what is the percent of change that target marks the shoes up for
Answer:
75%
Step-by-step explanation:
To find the percent of change that Target marks the shoes up for, you need to calculate the difference between the cost of the shoes to Target and the price at which they sell it to the public, and then divide that difference by the cost of the shoes to Target. Finally, you need to multiply the result by 100 to express the answer as a percentage.
Using this formula, the percent of change that Target marks the shoes up for is:
(35 - 20) / 20 * 100 = 15 / 20 * 100 = 0.75 * 100 = 75%
This means that Target marks the shoes up by 75% of their cost.
a) Find the total mass in kilograms of 3500 books, each with mass 800.
b) If the total mass of 8000 apples is 1.04 tonnes, what is the average mass of one apple?
A) Total mass of 3500 books is 2,800 kilograms.
B) The average mass of one apple is 130 grams.
A) To find the total mass of 3500 books, each with a mass of 800 grams, we can multiply the number of books by the mass of each book:
Total mass = (3500 books) * (800 grams/book)
= 2,800,000 grams
= 2,800 kilograms
Therefore, the Total mass of 3500 books is 2,800 kilograms.
B) To find the average mass of one apple, we can divide the total mass of the apples by the number of apples:
Average mass = (1.04 tonnes) / (8000 apples)
= 130 grams/apple
Therefore, the average mass of one apple is 130 grams.
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If there are estimated to be 10 ^ 11 galaxies in the known universe and 10 ^ 11 stars in each galaxy, how many stars are estimated to be in the universe?
Answer: We can use the information given to find the number of stars in the universe by multiplying the number of galaxies by the number of stars per galaxy:
number of stars = (10 ^ 11 galaxies) x (10 ^ 11 stars per galaxy)
This is a simple arithmetic problem and we can find the solution by multiplying the numbers 10^11 and 10^11
10^11 * 10^11 = (10101010101010101010)(101010101010101010*10) = 10^(11+11) = 10^22
So, there are estimated to be 10 ^ 22 stars in the known universe.
Step-by-step explanation:
Nevaeh has $0.80 worth of nickels and dimes. She has a total of 11 nickels and dimes altogether. Graphically solve a system of equations in order to determine the number of nickels, x,x, and the number of dimes, y,y, that Nevaeh has.
Answer: We can set up a system of equations to represent this problem. The first equation represents the total value of the nickels and dimes in terms of the number of nickels and dimes that Nevaeh has:
0.05x + 0.1y = 0.80
The second equation represents the total number of nickels and dimes that Nevaeh has in terms of the number of nickels and dimes that she has:
x + y = 11
To graphically solve this system of equations, we can use the slope-intercept form of the linear equations.
y = -2x + 22
y = -1/2 x + 8
The solution would be the point where the lines intersect , which x = 4, and y = 7 .
So she has 4 nickels, and 7 dimes.
Step-by-step explanation:
is 50 tens x 4 hundreds =40 tens x 5 hundreds true or false
Answer:
True, 50 tens times hundreds equal 40 tens times 5 hundreds
Step-by-step explanation:
50 tens times 4 hundreds equals to 40 ten times 5
hundreds because if you multiply 50 by 4 hundreds
you'll get 20,000 and if you multiply 40 tens by
hundred it will still give you 20,000
Therefore:
50 × 400 = 40 × 500
20,000 = 20,000
Can someone help me with this? It's urgent.
The table is filled as described , shown below.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Here, we have,
Rate per hour is $11.25
Number of regular hours is 40
Payment for regular hours:
time multiply with payment=
40*$11.25 = $450
Again, we have,
Rate per overtime hour:
$11.25*1.5 = $16.875 ≈ $16.88 (rounded up)
Number of overtime hours:
48.5 - 40 = 8.5
Payment for overtime hours:
$16.88*8.5 = $143.48
Now, we get ,
Gross payment is the sum of regular and overtime payments:
$450 + $143.48 = $593.48
Hence, he would get $593.48
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Find the midpoint and distance between (-3,10) and (15,-2)
Find the mean, median, and mode for 0, 4, 6, 11, 9, 8, 9, 1, 5, 9, 7. Round to the nearest tenth if needed.
Answer:
Mean - 6.2 Median - 7 Mode - 9
Step-by-step explanation:
You can find the mean by adding all the given numbers and dividing them by how many numbers you added.
The median is the middle value of the set of numbers, order them from least to greatest and find the middle value.
Mode is the number that occurs the most.
Any help would be appreciated
I think the answer is 5.
Sorry if it's wrong.
Answer:
5
Step-by-step explanation:
This question is based on vector
By applying its formula
AC = AB + BC
we were given AC as 14 and BC as 9 so let find AB
AC = AB + BC
14 = AB + 9
AB = 14 – 9
AB = 5
i hope this helped
Y=(x-3)^2+3
vertex form to standard form
Answer:
y = x² -6x +12
Step-by-step explanation:
You want the quadratic equation Y=(x-3)^2+3 written in standard form.
Standard formDepending on where you go to school, the given equation may already be in standard form.
Other places, standard form means the equation is simplified and terms are written in order of decreasing degree.
y = (x -3)² +3 = (x² -6x +9) +3
y = x² -6x +12
Should stockholder wealth maximization be thought of as a long-term or a short-term goal? For example, if one action increases a firm’s stock price from a current level of Rs. 1600 to Rs. 2000 in 6 months and then to Rs. 2400 in 5 years, but another action keeps the stock at Rs. 1600 for several years but then increases it to Rs. 3000 in 5 years, which action would be better? Think of some specific corporate actions that have these general tendencies
The action which would be better is the latter since it provides a higher average return in the span of 5 years.
What is Wealth maximization?This is referred to as the concept of increasing a firm's worth to increase the value of stockholders' shares and it is usually considered a long-term goal.
In this scenario, the action which involves the stock price rising from Rs. 1600 to Rs. 3000 provides a higher average return in the span of 5 years which is a long-term goal since it is assumed that shareholders invest in a company to meet their long-term financial goal and the corporate actions which have these general tendencies is lending to people and organizations at a proposed interest rate.
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Which graph represents the solutions to this equation?
X²+8x=-20
Answer:
The one with the vertex of (-4,4)
Step-by-step explanation:
Logic, Reasoning and Puzzles Assignment
Solving a Payment Puzzle
A wealthy and generous owner of an Internet company offers two
options of payment to her new vice president.
Option 1: a monthly salary
of $50000 per month paid
at the beginning of each
month
Name: Yaseen
Option 2: a monthly salary
based on 1¢ the first day,
2¢ the second day, 4c the
third day, 8¢ the fourth day,
and so on. The monthly salary
will be the amount calculated
for the last day of the month.
Assume there are 30 days in the month.
A. How can you calculate the vice president's earnings under
Option 2?
B. Compare the monthly earnings for the two options.
1.9
C. Which payment option would you take if you were the vice
president? Why?
Answer:
very long question
Step-by-step explanation:
The daily recommended allowance of calcium for a sixth grader is 1,200 mg. One cup of
milk has 25% of the recommended daily allowance of calcium. How many milligrams of
calcium are in a cup of milk? If you get stuck, consider using the double number line.
what's the answer pls tell me
Answer:
300 milligrams are in aa cup of milk.
Step-by-step explanation:
.25 x 1200 = 300
What are four consecutive even integers if the first integer is −4? Responses
A) -4,-3,-2,-1
b) -4,-2,0,2
c) -4,-6,-8,-10
D)-4,-5,-6,-7
The asked consecutive even integers are -4,-2,0,2
What are consecutive integers?Consecutive integers are whole numbers that follow each other without gaps. For example, 15, 16, 17 are consecutive integers.
Given that, what are four consecutive even integers if the first integer is −4
We know that, Consecutive even integers are even integers that follow each other, and they differ by 2. If x is an even integer, then x + 2, x + 4 and x + 6 are consecutive even integers.
Therefore, here x = -4,
-4+2 = -2
-4+4 = 0
-4+6 = 2
Hence, the asked consecutive even integers are -4,-2,0,2
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What information will be useful to know to answer the main question? How can you get it? How will you use that information
Answer:
Step-by-step explanation:
Can u give more detail as to what the question is asking pease
Simplify the difference. (2w2 – 8w – 8) – (5w2 + 3w – 5)
Answer:
-3w2-11w-3
Step-by-step explanation:
take w2 and w as variables. you can substitute it as w2=y and w=X then expand brackets
2y-8x-8-5y-3x+5
note that the signed changed at the second part because it was expanded with the minus sign which is basically like -1, so it changes the signs
then you collect like terms:
2y-5y-8x-3x-8+5= -3y-11x-3
now put substitute back w2=y and w=X
-3w2-11w-3
if it won't be a problem solving with w2 and w, then you skip the substitution part and solve the same
hat is the following sum?
0 7(10√/x²y)
O
O
0 7(²√x²¹x²)
The sum of the given equation is 7[tex]\sqrt[5]{x^{2} y}[/tex].
What is fractional equation?A fractional equation is one in which one or more of its terms have the unknown as their denominator. Equations involving fractions can be resolved using the Cross-Product property.Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. In order to do this, we divide both the numerator and the denominator by the biggest integer that can be divided precisely into both numbers. In other words, we choose the greatest number that the top and bottom have in common and divide them by that.Equations using fractions require the solution of equations in which the unknown variable is a component of the fraction's numerator or denominator. To solve fractional equations, we must determine the value of the undetermined variable.Given data :
4 ([tex]\sqrt[5]{x^{2} y}[/tex].) + 3 ([tex]\sqrt[5]{x^{2} y}[/tex].)
Add similar elements
= 7[tex]\sqrt[5]{x^{2} y}[/tex].
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A music store sells about 50 of a new model of drum per month at a price of $120 each. For each $5 decrease in price, about 4 more drums per month are sold. What prices of the drum will reach over $6500? And write the equation to this inequality?
The prices of the drum that will reach over $6500 are between $3 and $8
And the inequality expression is (50 + 4x) (120 - 5x) > 6500
What prices of the drum will reach over $6500?From the question, we have the following parameters that can be used in our computation:
Number of models = 50
Initial price = $120
Also from the question, we have:
Decrease in price by $5Increase in the number of drums by 4So, we have
Models = 50 + 4x
Price = 120 - 5x
This means that the revenue function is
R(x) = (50 + 4x) * (120 - 5x)
When the price reaches over $6500, we have
(50 + 4x) * (120 - 5x) > 6500
Using a graphing calculator, we have
2.911 <x < 8.5
Approximate
3 ≤ x ≤ 8
Hence, the model reaches $6500 between 3 and 8
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6 divided 109 can you help?
Answer: 18.1666666667
Step-by-step explanation: