Answer: log81 = 1/4
Step-by-step explanation:
Log81^3
81^x = 3
The common base is 3, so
(3^4)^x=3
3^4x = 3^1
4x = 1
x= 1/4
The ratio of two numbers is 5:6. The product of these numbers is 120. What is the smaller of these two numbers?
The smaller of the two number is 10.
What are Ratios?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
In simple words, the ratio is the number that can be used to express one quantity as a fraction of the other ones. The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things.
Given:
Ratio of two Positive number = 5:6
Let , the smaller number be 5x
then , the bigger number = 6x
According to the question,
product of these numbers = 120
Therefore,
[tex]5x * 6x = 120\\30x^{2} = 120\\x^{2} =4\\x = 2[/tex]
Smaller number = 5x = 5*2 = 10.
Hence, the smaller of the two number is 10.
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help pls
P = mgh for m
Answer:
p/gh=m
Step-by-step explanation:
divide both sides by gh to isolate m
PLEASE HELP ME ASAP!!!
Answer:
$54,742.76
Step-by-step explanation:
The equation for an exponential function is [tex]f(x)=ab^x\\[/tex], where [tex]a[/tex] is the starting value, which is 40,000. This value increases by 4%, so [tex]b[/tex] is 1.04. Finally, [tex]x[/tex] is the term that the value is increasing for, which in this case is 8.
So, the equation is [tex]f(x)=40000*1.04^8[/tex]
** [tex]f(x)[/tex] can be replaced with [tex]y[/tex]
What is the distance from the origin to pint A graphed on the complex plane below
Answer: it's [tex]\sqrt{5}[/tex]
Step-by-step explanation:
Daryl walks 10.5 miles in 3.5 hours. How many miles does he walk per hour?
Answer: 3
Step-by-step explanation: Daryl is walking 3 miles in 1 hour. When you divide 10.5 by 3.5 you get. So 3 miles in one hour. For example if you walk 12 miles in 4 hours, you divide and get 3. That three becomes the miles in one hour.
Given vector u = ⟨−3,−2⟩ and v = ⟨1,−5⟩,determine the value of u - 2v in component form.
The component form of the linear combination of the two vectors is u - 2v = < -5, 20>
How to find the vector u - 2v?Here we have the two vectors: u = <-3, -2> and v = <1, -5> We want to determine the value of the linear combination:
u - 2v
To do that we just add the correspondent components, then we get:
u - 2v = <-3, -2> - 2*<1, -5>
= <-3, -2> - <2*1, 2*-5>
= <-3, -2> - <2, -10>
= < -3 - 2, -2 -(-10)>
= < -5, 20>
That is the component form of the linear combination.
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Evaluate f(x)=2x+5 when x=0, x=1, x=5
Answer:
f(0)=5
f(1)=7
f(5)=15
Step-by-step explanation:
f(0)=2x+5
=2(0)+5
=5
f(1)=2x+5
=2(1)+5
=2+5
=7
f(5)=2x+5
=2(5)+5
=10+5
=15
Lester bought 8 t-shirts. The shirts came in p packages. Write an expression that shows how many t-shirts were in each package.
Expression for Number of t shirts in each package = [tex]\frac{8}{p}[/tex]
What is Unitary Method ?The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
Total number of shirts bought = 8 T- shirts
Total number of packages = p
So,
According to unitary method
In p packages we have t shirts = 8
In one package number of t shirts we will have = [tex]\frac{8}{p}[/tex]
Expression for Number of t shirts in each package = [tex]\frac{8}{p}[/tex]
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given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line. State True or False your answer:
a. True
b. False
It is true that given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.
A parabola is a quadratic function graph .A parabola is a curve equation in which a point on the curve is equidistant from a fixed point and a fixed line.
The fixed point is known as the parabola's focus, and the fixed line is known as the parabola's directrix. It is also worth noting that the fixed point does not lie on the fixed line.
A parabola is a locus of any point that is equidistant from a given point (focus) and a given line (directrix). The parabola is a significant curve of the coordinate geometry's conic sections.
The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h,k) denotes the vertex.
The standard equation of a regular parabola is y² = 4ax.
It's true that given a fixed point and a fixed line, a parabola consists of all points that are equidistant to the fixed point and the fixed line.
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let lines x and y be parallel, and let lines z and w be parallel. if angle a is the angle formed by lines y and z, and angle b is the angle formed by lines w and x, if the measure of angle a is 25 degrees, what is the measure of angle b?
155° is the measure of angle b .
What is an example of parallel lines?
Two lines that are equally spaced apart from one another and never cross each other are said to be parallel lines.
Both horizontal and vertical shapes are possible. In our daily lives, parallel lines can be seen in the form of zebra crossings, rows of notebooks, and the nearby railroad tracks.
from the figure , we understand that ∠1 and ∠3 together from a straight line.
thus, ∠1 + ∠3 = 180°
25° + ∠3 = 180°
∠3 = 155°
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help due tomm!!! suppppper easyy!!
Answer: b/-3<a/-3
Step-by-step explanation:
a/-3<b/-3
b/-3<a/-3
Perpendicular lines form angles that are how many degrees at their intersection?
O a. 45 dregrees
O b. 90 degrees
O c. 135 degrees
O d. 225 degrees
Answer:
Step-by-step explanation:135 degrees
please help on all PLEASE IM BEGGING YOU I CANT FAIL PLEASE
61=7-6x
3/2a -26=-5
4=n-10/-3
system of equations: n=2/3 ,a=14,x=−9
for each thing: x= −9 | a= 14 | n= 2/3
1. x = -9
2. a = 14
3. n = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:Here are the steps to the first question:1. Rearrange Terms
61 = 7 - 6x
61 = -6x + 7
2. Subtract 7 from both sides
61 = -6x + 7
61 - 7 = -6x + 7 - 7
3. Simplify
Subtract the numbers:
61 - 7 = -6x + 7 - 7
54 = -6x + 7 - 7
Subtract the numbers:
54 = -6x + 7 - 7
54 = -6x
4. Divide both sides by the same factor
54 = -6x
[tex]\frac{54}{6}[/tex] = [tex]\frac{-6x}{-6}[/tex]
5. Simplify
Divide the numbers:
[tex]\frac{54}{6}[/tex] = [tex]\frac{-6x}{-6}[/tex]
-9 = [tex]\frac{-6x}{-6}[/tex]
Cancel terms that are in both the numerator and denominator:
-9 = [tex]\frac{-6x}{-6}[/tex]
-9 = x
Move the variable to the left:
-9 = x
x = -9
Solution to Question 1:x = -9
Here are the steps to the second question:
1. Combine multiplied terms into a single fraction
[tex]\frac{3}{2}[/tex]a - 26 = -5
[tex]\frac{3a}{2}[/tex] - 26 = -5
2. Find common denominator
[tex]\frac{3a}{2}[/tex] - 26 = -5
[tex]\frac{3a}{2}[/tex] + [tex]\frac{2(-26)}{2}[/tex] = -5
3. Combine fractions with common denominator
[tex]\frac{3a}{2}[/tex] + [tex]\frac{2(-26)}{2}[/tex] = -5
[tex]\frac{3a+2(-26)}{2}[/tex] = -5
4. Multiply the numbers
[tex]\frac{3a+2(-26)}{2}[/tex] = -5
[tex]\frac{3a - 52}{2}[/tex] = -5
5. Multiply all terms by the same value to eliminate fraction denominators
[tex]\frac{3a - 52}{2}[/tex] = -5
2 · [tex]\frac{3a - 52}{2}[/tex] = 2(-5)
6. Cancel multiplied terms that are in the denominator
2 · [tex]\frac{3a - 52}{2}[/tex] = 2(-5)
3a - 52 = 2(-5)
7. Multiply the numbers
3a - 52 = 2(-5)
3a - 52 = -10
8. Add 52 to both sides
3a - 52 = -10
3a - 52 + 52 = -10 + 52
9. Simplify
Add the numbers:
3a - 52 + 52 = -10 + 52
3a = -10 + 52
Add the numbers:
3a = -10 + 52
3a = 42
10. Divide both sides by the same factor
3a = 42
[tex]\frac{3a}{3}[/tex] = [tex]\frac{42}{3}[/tex]
11. Simplify
Cancel terms that are in both the numerator and denominator:
[tex]\frac{3a}{3}[/tex] = [tex]\frac{42}{3}[/tex]
a = [tex]\frac{42}{3}[/tex]
Divide the numbers:
a = [tex]\frac{42}{3}[/tex]
a = 14
Solution to Question 2:
a = 14
Here are the steps to the third question:
1. Divide the numbers
4 = n + [tex]\frac{-10}{-3}[/tex]
4 = n + [tex]\frac{10}{3}[/tex]
2. Subtract [tex]\frac{10}{3}[/tex] from both sides
4 = n + [tex]\frac{10}{3}[/tex]
4 - [tex]\frac{10}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]
3. Simplify
Subtract the numbers:
4 - [tex]\frac{10}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]
[tex]\frac{2}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]
Subtract the numbers:
[tex]\frac{2}{3}[/tex] = n
Move the variable to the left:
[tex]\frac{2}{3}[/tex] = n
n = [tex]\frac{2}{3}[/tex]
Solution to Question 3:n = [tex]\frac{2}{3}[/tex]
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Two piece of metal meaure one and one fifth yard and three tenth yard each. Three time the amount of metal i needed for a project. How many total yard of metal i needed? one and one half yard one and nine fifteenth yard four and one half yard four and one fifth yard
As per the area of the rectangle, the amount of metal need for the total yard is 4.68
Area of rectangle
In geometry, the area of rectangle is written as,
A = l x b
where l refers the length and b refers the breadth of the rectangle.
Given,
Here we have given that the 1 1/5 and 3 1/10 is the measure of yard.
While we looking into the given question, we have identified that,
3 time of metal is need for the project,
So, as per the area of the rectangle formula, it can be written as,
=> 3 x 1 1/5 x 3 1/10
=> 3 x 6/5 x 13/10
=> 234/50
=> 4.86
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Answer:
4 1/2
Step-by-step explanation:
add 1 1/5 and 3/10 and then multiply your answr by 3
How much compound interest will $50,000 have earned in 10 years at
6.4% annual interest compounded quarterly?
The compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly would be $28,167.50.
What is Compound interest?Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
Compound Interest =P(1+r/n)^rt
We are given that
Principal amount = $50,000
Time = 10 year
Rate = 6.4%
Determine the compound interest earned on $50,000 in 10 years at 6.4% annual interest compounded quarterly, we can use the formula:
Plugging in the given values, we get:
compound interest = $50,000 (1 + 0.064/4)^(4 x 10) - $50,000
= $50,000 (1.016)^40 - $50,000
= $50,000 x 2.6335 - $50,000
= $78,167.50 - $50,000
= $28,167.50
Therefore, the compound interest is $28,167.50.
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A pet store sells a large dog kennel 98.50 the wholesale cost o the kennel is 63.55 what is the percent of markup round to the nearest percent.
Rounded to the nearest percent, the markup is approximately 55%.
What is the percent markup?
Markup percentage is calculated by dividing the gross profit of a unit (its sales price minus its cost to make or purchase for resale) by the cost of that unit.
To find the percent markup, you can use the following formula:
percent markup = (retail price - wholesale price) / wholesale price * 100
Plugging in the values given, we have:
percent markup = (98.50 - 63.55) / 63.55 * 100 = 34.95 / 63.55 * 100 = approximately 55%
Hence, rounded to the nearest percent, the markup is approximately 55%.
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a computer costs £2500 when new. Its value depreciates 12% compounded each year. How much does it cost after 3 years?
The computer will cost £ 33512.32
Given,
the cost of the computer = 2500
Depreciation = 12%
Cost after 3 years =?
compound interest is calculated as,
A = P(1 + r/n)nt
r = 12/100 = 0.12
So, A= P(1 + r/n)nt
A = 2500 (1+.12/1)1*3
A= 2500 (1.12)³
A= 2500 * 1.404928
A = 3512.32
So, The computer will cost £ 33512.32
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In the diagram below, OQ = 25, PM = 9, and QN = 15. Find the length of OP.
Round your answer to the nearest tenth if necessary.
0
Answer: OP |
P
M
Q
N
Submit Answer how do I come up with the number
In the diagram, the length of OP to the nearest tenth is 5.4
How to determine the length?We are to determine the ratio of the sides of the diagram.
The ratio of the sides using the given sides is
Let the unknown side be x
The ratio of the sides is given as follows
25:34 = 15:x+15
Put into fraction we have
25/(25+9)= 15/(x+15)
Cross multiplying we have
25x+375 = 375+135
Collecting like terms
25x=510-375
Simplify further to have
25x=135
Making x the subject
x=5.4
Therefore the length OP is 5.4 units
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Average employee salary?
Answer:
$67,680
Step-by-step explanation:
average is calculated as
average = [tex]\frac{sum}{count}[/tex]
Denver
[tex]\frac{sum}{137}[/tex] = 67,013 ( multiply both sides by 137 )
sum = 9,180,781
Anchorage
[tex]\frac{sum}{25}[/tex] = 71,332 ( multiply both sides by 25 )
sum = 1,783,300
total sum for both = $9,180,781 + $1,783,300 = $10,964,081
then average salary across both companies is
average = [tex]\frac{10,964,081}{162}[/tex] = $67,680 ( to the nearest dollar )
There are 4 chocolate chip cookies and 3 oatmeal cookies in a cookie jar. If a child randomly takes 2 cookies, what is the probability that both are chocolate chip?
If i clap my hands 20 times in 12 seconds. How many times will i do it in 2minutes. Then 3 minutes.
If i clap my hands 20 times in 12 seconds. 200 times will i do it in 2 minutes.
The friend can clap his hands 28 times in 12 seconds, according to our knowledge. The first thing we need to know is how many times he can clap in a second:
What is clap ?
Gonorrhea is known by the slang term "the clap." Gonorrhea is also referred to as "the drip." Someone who has an may feel stigmatized and shamed by these words.
To do it, we must divide the number of seconds by the number of times he can clap his hands:
20/12 =1.6667
He can clap his hands 1.6667 times in 1 second:
Now we want to know how many times will he clap his hands in 2 minutes
We have to change 2 minutes into seconds:
1 (minute) = 60 (seconds in 1 minute)
2 (minutes) * 60 (seconds in 1 minute) = 120seconds
After we get the seconds he is going to clap his hands, we have to multiply the times he claps times the seconds:
1.6667 times * 120 seconds = 200
200 times in 2.25 minutes
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How many liters of a 10% salt solution must be mixed with 5 liters of a 40% salt solution
to give a 15% solution?
Emma had to finish her 366-page novel by Friday. She had already read 244 pages. Write and solve an equation to show how many pages Emma had left to read by Friday.
p − 244 = 366; p = 610 pages
p + 244 = 366; p = 122 pages
122p = 244; p = 2 pages
p over 244 equals 2; p = 488 pages
Answer: Its b my guy :)
Step-by-step explanation: 244 + 122 = 366
and the only answer with 366 is b! hope this helps!
50 POINTS IF ANSWERED PLS!!!!
Which angle is the biggest based on the sides of the triangles below? Explain your reasoning.
Answer:
angle c
Step-by-step explanation:
since the largest angle will be across from the longest side, angle c is the right answer because it is across from the longest side which measures 35 cm.
hope this helps
Cindy had $660 in a savings account when Erika opened a savings account with zero dollars.
Cindy deposited $60 into her account each month for x months.
Erika deposited $100 into her account each month for x months.
• The accounts did not earn interest.
Which inequality represents this situation when the amount of money in Cindy's account was greater than the amount of money in Erika's accour
Answer: To represent the situation where the amount of money in Cindy's account is greater than the amount of money in Erika's account, you can set up the inequality as follows:
Cindy's account balance + (Cindy's monthly deposit * number of months) > Erika's account balance + (Erika's monthly deposit * number of months)
Substituting the known values, we get:
660 + (60 * x) > 0 + (100 * x)
Combining like terms, we get:
660 + 60x > 100x
Subtracting 60x from both sides, we get:
660 > 40x
Dividing both sides by 40, we get:
16.5 > x
Therefore, the inequality that represents the situation when the amount of money in Cindy's account is greater than the amount of money in Erika's account is 16.5 > x. This means that for the number of months (x) to be greater than 16.5, the amount of money in Cindy's account must be greater than the amount of money in Erika's account.
Rewrite 15x^4y^3 − 45x^3y^4 using a common factor
15x^4y^3 − 45x^3y^4 Can be rewritten using a common factor as 15x^3y^3(x - 3y)
What is a common factor?common factors are defined as factors that are common to two or more numbers. In other words, a common factor is a number with which a set of two or more numbers will be divided exactly.
In the algebraic expression 15x^4y^3 − 45x^3y^4,
15x^4y^3 is a term and 45x^3y^4, is another term.
if we take each variable and constant and compare
15 is common factor between 15 and 45
x^3 is a common factor between x^4 and x^3
y^3 is a common factor between y^3 and y^4
so multiplying the common factors together we have 15x^3y^3
what is left in the first term is x and second term is 3y
so that the rewritten form becomes 15x^3y^3(x - 3y)
In conclusion the other form of 15x^4y^3 − 45x^3y^4 is 15x^3y^3(x - 3y)
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Find the measure of angle f given the information below. please help !!
The measure of Angle f from the the figure is [tex]53^{o}[/tex].
What is the relation between Angles and Parallel lines ?On a shared plane, parallel lines do not cross one another. Now, if a transversal crosses two parallel lines at two separate sites, four angles are created at each location. The characteristics of parallel lines with respect to transversals are therefore listed below.
Angles that coincide are equal.Angles that are vertically opposite or vertically angled are equal.Interior angles that alternate are equal.Exterior angles that alternate are equal.On the same side of the transversal, a pair of internal angles are additional.The pair of alternative internal angles are equal when two parallel lines are crossed by a transversal.
When a transversal cuts between two parallel lines, the interior angles on the same side of the transversal are additional.
In the problem angle
a = [tex]119^{o}[/tex]
e = [tex]66^{o}[/tex]
Now , c = e ( alternate angles, interior)
⇒ c = [tex]66^{o}[/tex]
a + b = [tex]180^{o}[/tex] ( as sum of angles on a straight line is [tex]180^{o}[/tex] )
b = [tex]180^{o}[/tex] - [tex]119^{o}[/tex] = [tex]61^{o}[/tex]
f + b+ c = [tex]180^{o}[/tex] [sum of angles of a Triangle is [tex]180^{o}[/tex] ]
f = [tex]180^{o}[/tex] - [tex]61^{o}[/tex] - [tex]66^{o}[/tex] = [tex]53^{o}[/tex].
The measure of Angle f from the the figure is [tex]53^{o}[/tex].
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1. A painting crew bought 55 gallons of paint for a job, The crew members used 5 gallons of paint per hour until
they used all the paint. Sketch a graph to represent the start to the end of the job, assuming all paint was
used Be sure to title your graph, label your axes, and label your intercepts. This must be graphed by hand
or by using the tools in Word. a You may not use a web-based graphing program.
The equation is 55 = 5t and the graph is attached with the answer.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a painting crew bought 55 gallons of paint for a job, The crew members used 5 gallons of paint per hour until they used all the paint.
The equation can be written as,
55 = 5t
Here, t is the number of hours.
The graph is attached with the answer below.
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Ru buy three cake for £1. 60 each. He pay with a £20 note. How much change doe he get
We know that Ru will get back £15.2 when she buys 3 cakes for £1.60 each using simple mathematical operations.
What are mathematical operations?The process of calculating a value using operands and a math operator is known as a mathematical "operation."
The provided operands or integers must follow certain established rules that are associated with the math operator's symbol.
The rules that determine how to solve an expression with several operations are referred to as the order of operations.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).
So, we know that:
Ru buys 3 cakes for £1.60 each.
She was given £20 not.
The money she will get back is:
20 - (1.60*3)
20 - 4.8
£15.2
Therefore, we know that Ru will get back £15.2 when she buys 3 cakes for £1.60 each using simple mathematical operations.
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Your grocery bill before taxe wa $265. 24. You have to pay 7. 3 ale tax. How much i your grocery bill?
If the grocery bill before tax is $265.24 and you have to pay 7.3% tax, then he has to pay $284.6 for the grocery bill
The amount of the grocery bill before tax = $265.24
The percentage of tax = 7.3%
The amount of tax = The price of the grocery bill before tax × (7.3/100)
Substitute the values in the equation
= 265.24 × (7.3/100)
= 265.24 × 0.073
= $19.36
The final bill including tax = The price of the grocery bill before tax + The amount of tax
Substitute the values in the equation
= 265.24 + 19.36
= $284.6
Therefore, the grocery bill including tax = $284.6
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