Answer:
[tex]\huge\boxed{n=\log_35}[/tex]
Step-by-step explanation:
[tex]3^n=5\Rightarrow\log_33^n=\log_35\qquad\text{use}\ \log_ab^n=n\log_ab\\\\n\log_33=\log_35\qquad\text{use}\ \log_aa=1\\\\\boxed{n=\log_35}[/tex]
Describe and correct the error(s) made in each of the problems below.
1−x / (5−x)(−x)=x−1 / x(x−5)
5/s+2/5=2/s
Answer:
[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}[/tex]
[tex]\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}[/tex]
Step-by-step explanation:
Errors in Algebraic Operations
It's usual that students make mistakes when misunderstanding the application of algebra's basic rules. Here we have two of them
When we change the signs of all the terms of a polynomial, the expression must be preceded by a negative sign When multiplying negative and positive quantities, if the number of negatives is odd, the result is negative. If the number of negatives is even, the result is positive. Not to confuse product of fractions with the sum of fractions. Rules are quite different
The first expression is
[tex]1-x / (5-x)(-x)=x-1 / x(x-5)[/tex]
Let's arrange into format:
[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =\frac{x-1 }{ x(x-5)}[/tex]
We can clearly see in all of the factors in the expression the signs were changed correctly, but the result should have been preceeded with a negative sign, because it makes 3 (odd number) negatives, resulting in a negative expression. The correct form is
[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}[/tex]
Now for the second expression
[tex]5/s+2/5=2/s[/tex]
Let's arrange into format
[tex]\displaystyle \frac{5}{s}+\frac{2}{5} =\frac{2}{s}[/tex]
It's a clear mistake because it was asssumed a product of fractions instead of a SUM of fractions. If the result was correct, then the expression should have been
[tex]\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}[/tex]
George bought a house for $210,000 and now it has increased in value by 8% how much more is the house worth?
Answer:
I think its 226800.
Step-by-step explanation:
8% of 210,000 is 16800. I added that to 210,000 and got my answer.
Perform the following multiplication. 4.7314 × 10 = 47.314 0.47314 473.14 4,731.4
Answer:
47.314
Step-by-step explanation:
We want find the results of the multiplication,
[tex]4.7314 \times 10[/tex]
When we multiply by 10, we move the decimal point forward once.
When we divide by 10, we move the decimal point backwards once.
In this case, we are multiplying, so
[tex]4.7314 \times 10 = 47.314[/tex]
Explain why parallelograms are always
quadrilaterals, but quadrilaterals are sometimes
parallelograms.
Answer:
In order to be a quadrilateral, a polygon must have 4 sides, and parallelograms always have 4 sides. In order to be a parallelogram, a polygon must have 4 sides with opposite sides parallel. Quadrilaterals always have 4 sides, but do not always have opposite sides parallel.
Step-by-step explanation:
In order to be a quadrilateral, a polygon must have 4 sides, and parallelograms always have 4 sides. In order to be a parallelogram, a polygon must have 4 sides with opposite sides parallel. Quadrilaterals always have 4 sides, but do not always have opposite sides parallel.
What is the constant of proportionality for the ratios; (2,3), (4,6), (6,9) and (8,12)
The constant of proportionality for the given ratios is 1.5.
The constant of proportionality for the given ratios can be found by dividing the second value of each ratio by the first value. Let's take the first ratio (2,3) as an example:
Constant of proportionality = 3 / 2 = 1.5
Following the same steps for the other ratios, we can find the constant of proportionality for each of them. For the second ratio (4,6), the constant of proportionality is 6 / 4 = 1.5. For the third ratio (6,9), the constant of proportionality is 9 / 6 = 1.5. And for the fourth ratio (8,12), the constant of proportionality is 12 / 8 = 1.5.
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Final answer:
The constant of proportionality for the given ratios is 1.5, as each second number in the ratio is 1.5 times the corresponding first number.
Explanation:
To find the constant of proportionality for the given set of ratios, we first look at each pair to determine if there is a common constant that each first number is multiplied by to result in the second number. Inspecting the given ratios (2, 3), (4, 6), (6, 9), and (8, 12), we can see that in each case, the second number is 1.5 times the first number.
For example, for the ratio (2, 3), if you multiply 2 by 1.5, you get 3. Similarly, for the ratio (4, 6), multiplying 4 by 1.5 gives you 6, and so on. This consistency across the ratios confirms that the constant of proportionality is 1.5.
Translate the sentence into an inequality.
The product of b and 6 is less than - 16.
The sentence 'The product of b and 6 is less than -16' translates to the inequality '6b < -16' in Mathematics.
Explanation:In mathematics, translating a sentence into an inequality involves identifying the mathematical symbols and operations represented by the words in the sentence. In this case, 'the product of b and 6' translates to '6 * b' and 'is less than' translates to '<'. So, the sentence 'The product of b and 6 is less than -16' translates to the inequality '6 * b < -16' or '6b < -16' in simplified form.
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Write the expression: the quotient of the quantity k minus 12 and m. A) 12 − m k B) m − 12 k C) 12 − k m D) k − 12 m
Answer:
Option D) (k − 12)/m
Step-by-step explanation:
We have to write an expression:
the quotient of the quantity k minus 12 and m.
k minus 12 can be written as:
[tex]k - 12[/tex]
The quotient of (k-12) and m means (k-12) is divided by m.
This can be written as:
[tex]\dfrac{k-12}{m}[/tex]
Thus, the correct answer is
Option D) (k − 12)/m
Final answer:
The expression for the quotient of 'k minus 12' and 'm' is correctly written as (k - 12) ÷ m, making option D the accurate choice.
Explanation:
The expression for the quotient of the quantity k minus 12 and m should be written as a fraction where the numerator is k minus 12 and the denominator is m. This is mathematically represented by the fraction (k - 12) ÷ m, which indicates the division of the expression k minus 12 by m. Therefore, the correct expression from the given options is D) k - 12 ÷ m.
Patricia serves the volleyball to Amy with an upward velocity of 17.5ft/s. The ball is 5 feet above the ground when she strikes it. How long does Amy have to react, before the volleyball hits the ground? Round your answer to two decimal places.
t = 1.33 sec
Solution:
Given data:
Velocity [tex](v_0)[/tex] = 17.5 ft/s
Height [tex](h_0)[/tex] = 5 ft
The height can be modeled by a quadratic equation
[tex]h(t)=-16t^2+v_0t+h_0[/tex]
where h is the height and t is the time
[tex]h(t)=-16t^2+17.5t+5[/tex]
[tex]-16t^2+17.5t+5=0[/tex]
a = –16, b = 17.5, c = 5
It looks like a quadratic equation. we can solve it by quadratic formula,
[tex]$\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
[tex]$\Rightarrow t=\frac{-17.5 \pm \sqrt{(-17.5)^{2}-4\times (-16)(5)}}{2 (-16)}[/tex]
[tex]$\Rightarrow t= \frac{-17.5 \pm \sqrt{306.25+ 320}}{-32}[/tex]
[tex]$\Rightarrow t= \frac{-17.5 \pm 25.025}{-32}[/tex]
[tex]$\Rightarrow t= \frac{-17.5 - 25.025}{-32}, \ t= \frac{-17.5 + 25.025}{-32}[/tex]
[tex]$\Rightarrow t= 1.33, \ t= -0.24[/tex]
Time cannot be in negative. So neglect t = –0.235.
t = 1.33 sec
Hence Amy have to react 1.33 sec before the volleyball hits the ground.
ANSWER ASAP, WILL NAME BRAINLIEST
What is the value of x in the equation Negative 6 x = 5 x + 22? –22 –2 2 22
First off, rename your equation as -6x=5x+22
You solve the equation by subtracting 5x on both sides to get:
-11x=22
Now divide both sides by -11 to get x=-2
So the answer is C: -2
Hope this helped! This is my first time answering!
Answer:
It is -2 (B)
Because you add -5x to both sides and you get -11x=22 and 22 divided by -11 is -2
A triangle has side lengths of 3 feet and 9 feet.which is the greatest possible perimeter of the triangle
what does x equal in the function: f(-11)=5x+1
Final answer:
In the equation f(-11)=5x+1, solving for x yields x = -2.4.
Explanation:
To find what x equals in the function f(-11)=5x+1, we start by understanding that the function f(x) identifies the relation between x and f(x). In this case, f(-11) has been given the value of 5x+1. Therefore, we solve for x by setting the expression equal to f(-11).
We have the equation 5x + 1 = f(-11). Since f(-11) is given as a constant, we substitute and solve for x:
5x = -12
x = -2.4
Hence, x equals -2.4 in the function f(-11)=5x+1.
What is the area? Plz help fast I will mark brainliest ASAP
Probably too late, but still need to know how to do this.
Formula for the area of a circle: A = πr² [pi times radius(r) squared]
The radius is half of the diameter. [diameter would be a line that would go through the whole circle, the radius would be a line that would stop/end halfway through the circle - see attached image]
They gave you the diameter, which is 3, so divide it by 2 or multiply by 1/2 to get the radius, which will be 1.5.
A = πr² Plug in 1.5 for r
A = π(1.5)² Find 1.5² [or 1.5 x 1.5 = 2.25]
A = 2.25π meters²
use the net to compute the surface area of three dimensional figure.
Option C:
Surface area of the three dimensional figure is 166 unit².
Solution:
Let us find the area of the net of the figure.
Length = 7, Width = 5, Height = 4
Area of the bottom = length × width
= 7 × 5
= 35 unit²
Area of the Top = length × width
= 7 × 5
= 35 unit²
Area of the left = width × height
= 5 × 4
= 20 unit²
Area of the right = width × height
= 5 × 4
= 20 unit²
Area of the front = length × height
= 7 × 4
= 28 unit²
Area of the back = length × height
= 7 × 4
= 28 unit²
Surface area = 35 + 35 + 20 + 20 + 28 + 28
= 166 unit²
Surface area of the three dimensional figure is 166 unit².
The factored form of 4a3b5 − 16a5b2 + 12a2b3 is
First off, use carats so its more clear that there's exponents (I'm using parentheses for simplicity):
(4*a^3*b^5)-(16*a^5*b^2)+(12*a^2*b^3)
It's best to divide the whole expression by 4a^2b^2 because it's the least common factor.
So we get (a*b^3)-(4*a^3)+(3b)
I hope this helped. It's been a while since I've done problems like these!
f(x) = 4x+8
g(x) = x+3,
Find f(x) * g(x)
f(x) * g(x) = 4 (x² + 5x + 6)
Step-by-step explanation:
Step 1: Given details f(x) = 4x + 8 and g(x) = x + 3Step 2: Substitute values and multiplyf(x) * g(x) = (4x + 8) (x + 3)
= 4x² + 12x + 8x + 24
= 4x² + 20x + 24
= 4 (x² + 5x + 6)
Carlos and Michael are collecting baseball cards. Carlos has 85 and buys 10 more each week. Michael has 120 and receives 5 more from his uncle every week.
When will Carlos and Michael have the same amount?
A
in 2 weeks
B
in 7 weeks
C
They will never have the same amount since Michael had more to begin with.
D
in 10 weeks
Make two equations:
Carlos: y=10x+85
Michael: y=5x+120
Set them equal to each other and solve:
10x+85=5x+120
5x+85=120
5x=35
x=7
So therefore, B is the correct answer
Hope this helped!
Final answer:
To determine when Carlos and Michael will have the same number of baseball cards, set up an equation based on their weekly acquisitions. After solving the equation, it is revealed that they will have the same amount in 7 weeks.
Explanation:
The subjects of interest are Carlos and Michael's baseball card collections.
Carlos starts with 85 cards and adds 10 each week, while Michael starts with 120 and receives 5 more weekly.
To find when they will have the same amount, set up an equation:
Carlos's cards: 85 + 10x (x representing the number of weeks)Michael's cards: 120 + 5xSolve the equation: 85 + 10x = 120 + 5xTherefore, x = 7 weeks, so the answer is B: in 7 weeks.
what is 1/10 of 0.04?
Answer:
0.004 or 1/250
Step-by-step explanation:
the word "of" means multiply. so just multiply 1/0 by 0.04. :)
Answer:
0.004
Step-by-step explanation:
you move the decimal a place to the left
What is the least common denominator of 1/7,2/5 and 2/3?
Answer:
105 is the least common denominator
Step-by-step explanation:
Since 7, 5 and 3 are all prime.
LCM would be 7×3×5 = 105
Collin has $500 in his bank account. He starts saving $30.00 per week. Kamryn
has $750 in her bank account, and she is saving $20.00 per week. Assume
neither Collin nor Kamryn make any withdrawals.
After how many weeks will. Collin and Kamryn have the same amount of
money in their accounts?
Answer:
x = 25
Step-by-step explanation:
You would need to start by creating an equation. X would represent the numbers of weeks.
500 + 30x = 750 + 20x
Now get the numbers on one side. To do this subtract 500 form each side.
30x = 250 + 20x
Next, get the variables to one side. This can be done by subtracting 20x from each side.
10x = 250
Finally divide by 10 to get the variable by its self.
x = 25
Hope this helps.
After 25 weeks, Collin and Kamryn have the same amount of
money in their accounts.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let's suppose the after x weeks, Collin and Kamryn have the same amount of money in their accounts:
Then we can frame a linear equation as per the problem:
Collin's amount of money = 500 + 30x
Kamryn amount of money = 750 + 20x
500 + 30x = 750 + 20x
10x = 250
x = 25
Thus, after 25 weeks Collin and Kamryn have the same amount of
money in their accounts.
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HELP ASAP PLEASE HELP ME
Answer:
She is not correct
x = -9
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180° therefore if you add all three angles in this triangle it must add up to 180°
50 - 5x + 5 - 4x + 17 - 3x = 180 add/subtract the like terms
72 - 12x = 180
- 12x = 108 divide both sides by 12
-x = 9
x = -9
Simplify simplify -2(x-2)
Answer:
-2x + 4
Step-by-step explanation:
help me plz!!!!!!!!!!!!!!!
Answer: for the third one you use x= 55
so angle = 110
for the fourth one x= 102
angle = 100
Step-by-step explanation:
Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a system of equations to represent this situation, letting x represent the number of nickels and y represent the number of quarters. What is the solution?
Answer:
Marcos had 6 nickel coins and 9 quarter coins.
Step-by-step explanation:
We are given the following in the question:
Let x be the number of nickel coins and y be the number of quarter coins.
Marcos had 15 coins in nickels and quarters.
Thus, we can write the equation:
[tex]x + y =15[/tex]
He had 3 more quarters than nickels. We can write he equation,
[tex]y = x + 3[/tex]
Solving the two equations, we get,
[tex]2y = 18\\y = 9\\x + 9 = 15\\x = 6[/tex]
Thus, Marcos had 6 nickel coins and 9 quarter coins.
The solution to the system of equations representing Marcos's coins is x = 6 and y = 9. Hence, Marcos had 6 nickels and 9 quarters.
Explanation:This question pertains to creating and solving a system of equations in mathematics. Given Marcos had 15 coins in nickels and quarters and considering the information that he had 3 more quarters than nickels, two equations can be formed from this. The first equation sets up the total number of coins: x + y = 15. The second equation sets ups the difference in quantity of each coin: y = x + 3.
To find the solution, substitute the second equation in for y in the first equation. This gives: x + (x + 3) = 15. Solve the equation and find x = 6. Furthermore, using x in our second equation, we get y = 6 + 3 = 9. Therefore, Marcos had 6 nickels and 9 quarters.
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2y−y+7−1+3+7x 2 −4y combine like terms
To combine like terms, group terms with the same variable and combine their coefficients. The simplified expression is -3y + 7x^2 + 9.
Explanation:To combine like terms, we group terms with the same variable and combine their coefficients. In this case, we have:
2y - y + 7 - 1 + 3 + 7x2 - 4y
Combining the like terms:
2y - 4y - y + 7 - 1 + 3 + 7x2
Combining the coefficients:
(2 - 4 - 1)y + (7 - 1 + 3) + 7x2
-3y + 9 + 7x2
So, the simplified expression is -3y + 7x2 + 9.
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A company provides bus trips to various events for a adults and c children. The company charges $18 for each adult and $8 for each child for a trip to an upcoming play. The bus has a maximum capacity of 40 people and the school can only spend $400 dollars on the trip. Write and solve a system of equations to determine the maximum number of adults and children that can attend the play that will satisfy these constraints.
Final answer:
To determine the maximum number of adults and children that can attend the play without exceeding the bus capacity of 40 people and the $400 budget, set up and solve a system of equations representing the capacity and budget constraints. The solution is 8 adults and 32 children.
Explanation:
We are given a situation where a company charges $18 for each adult (a) and $8 for each child (c) for a bus trip to an upcoming play, with the constraints that the bus holds a maximum of 40 people and the available budget is $400. To find the maximum number of adults and children that can attend under these constraints, we need to set up a system of equations:
For the capacity constraint: a + c = 40
For the budget constraint: 18a + 8c = 400
We can solve this system using substitution or elimination. Let's use elimination. Multiply the first equation by -8 and add it to the second equation to eliminate c:
-8a - 8c = -320
18a + 8c = 400
Adding these two equations together gives us:
10a = 80
Thus, a = 8. Plugging a = 8 back into the first equation, we get c = 32.
The maximum number of adults and children that can attend the play is 8 adults and 32 children.
Help solve and explain every step please: 4x-2=0
Answer:
Therefore,
[tex]x=\dfrac{1}{2}[/tex]
Step-by-step explanation:
Given:
[tex]4x-2=0[/tex]
To Find:
x = ?
Solution:
[tex]4x-2=0[/tex]
Step 1 : Add 2 on both the side we get
[tex]4x-2+2=0+2\\4x=2[/tex]
Step 2 : Dividing by 4 on both the side we get
[tex]\dfrac{4x}{4}=\dfrac{2}{4}\\\\x=\dfrac{1}{2}[/tex]
Step 3 :The final solution is
[tex]x=\dfrac{1}{2}[/tex]
Therefore,
[tex]x=\dfrac{1}{2}[/tex]
Need to divide 837÷9 with step by step directions
Answer:
93
Step-by-step explanation:
9 8 3 7
− 0
8 3
− 8 1
2 7
− 2 7
0
Ben’s living room is a rectangle measuring 10 yards x 168” by how many feet does the legs of the room exceed the width
Answer:
16 feet.
Step-by-step explanation:
Given:
Ben’s living room is a rectangle measuring 10 yards x 168.
Question asked:
How many feet does the legs of the room exceed the width ?
Solution:
By applying unitary method:
Length of rectangle = 10 yards = 30 feet (1 yard = 3 feet)
(10 yard = [tex]3\times10 = 30)[/tex]
Breadth of rectangle = 168 inch = 14 feet (12 inch = 1 feet)
(1 inch = [tex]\frac{1}{12}[/tex])
( 168 inch = [tex]\frac{1}{12}[/tex][tex]\times168 = 14 feet)[/tex]
By subtracting the breadth from the length of rectangle,
30 feet - 14 feet = 16 feet
Therefore, by 16 feet, length of the room exceed the width.
The measure of angle 1 is 30 degrees less than twice the measure of angle 2. What is the measure of angle 1. What is the measure of angle 2
Answer:
110°
Step-by-step explanation:
the supplement of an angle is 30 degrees less than twice the measure of the angle itself. find the angle and its supplement.
Let the angle be A, then its supplement = (180 - A)
Now, since the supplement is 30 degrees less than twice the measure of the angle itself, then we'll have:
180 - A = 2A - 30
-3A = - 210
A, or the angle = [tex]\frac{-210}{-3}[/tex]= 70 °
Its supplement, (180 - A) = 180 - 70 = 110°
Make a math problem for the problem 4 divided by 1/2= 8
Answer:
if Jara has [tex]\$4[/tex] and she wants to buy pen the Prince of each pen is [tex]\$\frac{1}{2}[/tex].
How many pens she can buy.
Step-by-step explanation:
If Jara has [tex]\$4[/tex] and she wants to buy pen the wants to buy pen the Prince of each pen is [tex]\$\frac{1}{2}[/tex] .
How many pen she can buy.
[tex]Let\ Jara\ can\ buy=x\ pens\\\\each\ pen\ cost=\$\frac{1}{2}\\\\Then\ Jara\ can\ buy\ pens=\$\frac{1}{2}x\\\\\frac{1}{2}x=4\\x=8\\Jara\ can\ buy\ =8\ pens[/tex]