[tex]25^{2x+1}=144[/tex] => x = 0.272, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given: [tex]25^{2x+1}=144[/tex]
Taking logarithm on both sides:
log ([tex]25^{2x+1}[/tex]) = log (144)
=> (2x + 1) log (25) = log (144) (As [tex]log_b(a)^m = m (log_b(a))[/tex])
=> 2x + 1 = [tex]\frac{log144}{log25}[/tex]
=> 2x + 1 = [tex]\frac{2.158}{1.397}[/tex]
=> 2x + 1 = 1.544
=> 2x = 0.544
=> x = 0.272
Hence, [tex]25^{2x+1}=144[/tex] => x = 0.272, by properties of logarithm.
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PLS HELP
Look at the picture I attached, please help!
The expression which models the maximum number of days in which she can rent the car is 20x + 10 ≤ 80
How to illustrate the information?The maximum amount to spend = 80
Fixed charge per day $20
Charge per mile = $0.10
The inequality which represents the number of days Can be expressed thus :
(Charge per day × number of days) + (charge per mile × number of miles) ≤ 80
20x + 0.10 × 100 ≤ 300
20x + 10 ≤ 300
Hence, the required inequality expression is 20x + 10 ≤ 80.
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Sam will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $65 and costs an additional $0.30 per mile driven. The
second plan has no initial fee but costs $0.80 per mile driven. How many miles would Sam need to drive for the two plans to cost the same?
Sam would need to drive for the two plans to cost the same is 130 miles.
Let, x = Number of miles driven
y = Total cost
The first plan:
Initial fee = $65
Cost of 1 mile = $0.3
Cost of drive x mile = $0.3x
In total, you will pay
y = 0.3x + 65 for the first plan.
The second plan:
There are no initial costs, but
Cost of 1 mile = $0.80
y = 0.80x
Now we have two equations
y = 0.3x + 65
y = 0.80x
As we know that y is equal to both 0.3x + 65 and 0.80x, this means we can equate the right hand sides and solve for x.
0.3x + 65 = 0.80x
0.80x - 0.3x = 65
0.5x = 65
x = 65÷0.5
x = 130
The cost of two plans will be same when Sam drive 130 miles.
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Can I please have answers to this question
Answer:
6. Slope = 2
7. y-intercept = 5
8. Equation: y = 2x + 5
Step-by-step explanation:
Question 6To find the slope of a line, define two points on the line:
(x₁, y₁) = (0, 5)(x₂, y₂) = (1, 7)Substitute these values into the slope formula and solve for m:
[tex]\implies \textsf{slope}\:(m)=\dfrac{7-5}{1-0}= \dfrac{2}{1}=2[/tex]
Therefore, the slope of the graph is [tex]\boxed{2}[/tex].
Question 7The y-intercept is the y-value of the point at which the line crosses the y-axis.
From inspection of the given graph, the y-intercept is [tex]\boxed{5}[/tex].
Question 8Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
Where:
m = slopeb = y-interceptSubstitute the found slope and found y-intercept into the formula to create an equation for the line:
[tex]\boxed{y=2x+5}[/tex]
Find each composition of functions. Simplify your answer.
Let f(x)=2 x-3 . Find f(1+h)-f(1) / h, h≠0
A composite function exists as a function that depends on another function. The value for (f(1+h)-f(1)) / h = 2
What is meant by composition function?In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.
Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.
Let the function be f(x) = 2x - 3
f(1+h) = 2 (1+h) -3 = 2h - 1
f(1) = 2(1) - 3 = -1
(f(1+h)-f(1)) = (2h - 1 ) + ( -1) = 2h
simplifying the equation, we get
(f(1+h)-f(1)) / h = 2h/ h
(f(1+h)-f(1))/h = 2
Therefore, the value of (f(1+h)-f(1))/h = 2.
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1-(r+2)=9 (pls help, I'm not the smartest person)
Answer:
r = -10
Step-by-step explanation:
1. Distribute
1-(r+2)=9
1-r-2=9
2. Subtract the numbers
1-r-2=9
-1-r=9
3. Rearrange the terms
-1-r=9
-r-1=9
Solution: r = -10
help please 3 2/5 ⋅ 2 1/3
Answer:
7 14/15
Step-by-step explanation:
Ranger wants to verify that the expression
8x - 20 is the correct simplified expression for 4(2x - 5) Explain how to verify the simplified expression.
Answer: It is correct.
The first step here is to distribute the numbers
4 times 2x is 8x
4 times -5 is -20
Therefore, you're left with 8x-20
I hope this helps!
how many quarts of soil are used to fill 2 flower pots
Answer: 20 quarts for two "standard" sized pots.
Step-by-step explanation:
Simplify each expression.
ln 1
ln (1) = 0, by properties of logarithms.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
ln (1) = [tex]log_e(1)[/tex]
By properties of logarithms, we get that: [tex]log_b(1) = 0[/tex], for any value of b.
Hence, ln (1) = 0, by properties of logarithms.
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2+2 (free easy answer)
Answer:
5-1, known colloquially as four, 4, or 1+3.
Step-by-step explanation:
Complete the following angle identities. tan (A+B)=
Answer:
tan A +tanb
Step-by-step explanation:
1-tan a tan b
i think so
A laptop has a listed price of $887.99 before tax. If the sales tax rate is 9.75%, find the total cost of the laptop with sales tax included.
The total cost of the laptop, including the sales tax, is $974.57.
How is the total cost determined?The total cost of the laptop is the addition of the listed price and the sales tax (dollars).
The listed price refers to the retailer's (seller's) price before the addition of the sales tax.
After adding the sales tax to the listed price, the total cost is obtained.
Therefore, sales tax, which is a proportional tax, increases the cost of goods and services to consumers.
Data and Calculations:Listed price before tax = $887.99
Sales tax rate = 9.75%
Total cost after tax = $974.57 ($887.99 x 1.0975)
Thus, the total cost of the laptop after factoring in the sales tax is $974.57.
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Multiply. (3+√2)(4+√2)
The multiplication of the expression ( 3 + √2)( 4 +√2 ) is 14 + 7√2.
Multiplication in elementary algebra is the process of figuring out the outcome of multiplying a number by a number b. The product of a and b is the outcome of multiplication, and each of the integers a and b is referred to as a factor of the product ab.
Consider the expression,
y = ( 3 + √2)( 4 +√2 )
Using the distributive property,
a( b + c ) = ab + ac
y = ( 3 + √2)( 4 +√2 )
y = 3( 4 + √2 ) + √2( 4 + √2 )
y = 3 × 4 + 3 × √2 + √2 × 4 + ( √2 )²
y = 12 + 3√2 + 4√2 + 2
y = 14 + √2( 3 + 4 )
y = 14 + 7√2
The value of the expression ( 3 + √2)( 4 +√2 ) when simplified is 14 + 7√2.
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40PTS. When you are getting dressed, you put your socks on first and then your shoes on second. But to undo this, you take your shoes off first and your socks off second. Why do you have to reverse the order? Use this scenario to help you explain why it is helpful to work backward when solving equations.
Please answer!!!!!!!!
Rectangle EFGH has vertices E(−3, 4), F(−2, 4), G(−2, −2), and H(−3, −2).
A dilation with a scale factor of 3 and centered at the origin is applied to the rectangle.
Which vertex in the dilated image has coordinates of (−6, 12)?
E′
F′
G′
H′
The vertex F(−2, 4) in the dilated image has coordinates of (−6, 12) option (B) F' is correct.
What is dilation?The transformation dilation is used to resize an item. Dilation is a technique for making items appear larger or smaller. The image created by this transformation is identical to the original shape.
It is given that:
The coordinates are:
Rectangle EFGH has vertices E(−3, 4), F(−2, 4), G(−2, −2), and H(−3, −2).
After applying dilation with a scale factor of 3:
E(−3, 4) → E'(-3x3, 4x3) = E'(-9, 12)
Similarly,
F(−2, 4) → F'(-6, 12)
G(−2, −2) → G'(-6, -6)
H(−3, −2) → H'(-9, -6)
Thus, the vertex F(−2, 4) in the dilated image has coordinates of (−6, 12) option (B) F' is correct.
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Amari and ethan planned an end-of-season soccer party. they purchased 45 hot dogs and 30 individual bags of chips.
15 is the greatest number of people they can be without having any leftovers
Given data
45 hotdogs in 30 individual bags of chips
How to solve for the greatest number of people they can be without having any leftoversGiven data
45 hotdogs in 30 individual bags of chips
The greatest common factor of 45 and 30 is 15
using ratio
45 : 30
3 : 2
This means that one person will receive 3 hotdogs in 2 bags. Also 15 people will get the equal amount without left overs
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complete question
Amari and Ethan planned an end of season soccer party to purchase 45 hotdogs in 30 individual bags of chips which person will receive the same amount of food what is the greatest number of people they can be without having any leftovers
The results of a survey of customers at a pet supply store showed that 33 owned dogs, 42 owned parrots, and 20 owned both dogs and parrots. How many owned either a dog or a parrot?
of the customers surveyed, owned either a dog or a parrot
(Type an integer or a decimal.)
Based on the number of customers who owned parrots, dogs and parrots, and dogs, the number who owned either a dog or a parrot were 55 customers
How to find the number who owned either a dog or parrot?The number of people who owned a parrot was 42. 33 people also owned a dog. Some of these people owned both a dog and a parrot and they numbered 20.
To find the number of customers who owned either a dog or a parrot, the formula is:
= Number of customers who owned a dog + Number of customers who owned a parrot - Number of customers who owned both a dog and parrot
= 33 + 42 - 20
= 75 - 20
= 55 customers
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describe fully the single transformation that takes shape a to shape b
The single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees
What is transformation?Transformation involves changing the position and size of a shape.
How to determine the transformation of the shapes?The single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees
From the figure, we have:
The side lengths of shape A are twice as large as the side lengths of shape BShape A can be rotated 180 degrees to map onto shape B, after dilation.So, the scale of dilation from shape A to B is:
Scale = 1/2
Hence, the single transformation from shape A to B is: dilate A by 1/2, then rotate by 180 degrees
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Banana Boat sunscreen sells for $12 for a 20 fluid ounce bottle. What is the cost per ounce for the sunscreen?
Answer: 20/12
Step-by-step explanation:
A bee flies at 20 feet per second directly to a flowerbed from its hive. The bee stays at the flowerbed for 19 minutes, and then flies directly back to the hive at 16 feet per second. It is away from the hive for a total of 21 minutes?
The distance is mathematically given as
D=1066.66667
What is the time function?The TIME function is included as part of Excel's Date and Time features. With the assistance of TIME, we are able to create a time by employing various components for the hours, minutes, and seconds.
While conducting financial analysis, it's possible that we'll need to date a report. Under these conditions, the TIME function may be used to convert a text string into a format that presents the time as a decimal representation of the seconds, minutes, and hours. Additionally, the function's capabilities include the ability to merge several values into a single time value.
formula= TIME (hour, minute, second)
distance = rate X time
D = RT
T = D/R
20 feet per second = 1200 feet per minute
16 feet per second = 960 feet per minute
(D/R) + 19 + (D/R) = 21
(D/R) + 19 + (D/R) = 21
(D/1200) + 19 + (D/960) = 21,
This is the equation we can use to find the distance from the flowerbed to the hive.
(D/1200) + (D/960) = 2
(D(1200)(960))/1200 + (D(1200)(960))/960 = 2(1200)960
960D + 1200D = 5(1200)960
2,160D = 2304000
D=1066.66667
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A water tank holds 18,000. How long will it take for the water level to reach 6000 gallons if the water used at an average rate of 450 gallons per day?
Answer:
You start with 18.000 gallons and want to know when you reach 6.000 gallons, with a daily use of 450 gallons. This means you need to know how many days it take to use 18.000 - 6.000 = 12.000 gallons. This can simply be calculated with 12.000/450, which gives 26 2/3 day
Step-by-step explanation:
35° 91° 65° 28 What anglemeasures is this?
The angles 35° 65° and 28° are acute angles and the angle 91° is an obtuse angle
How to identify each of the angle measures?The angle measures are given as:
35° 91° 65° 28°
As a general rule:
Angles that are less than 90 degrees are acute angles
This means that
The angles 35° 65° and 28° are acute angles
Also, we have
Angles that are between 90 degrees and 180 degrees are obtuse angles
This means that
The angle 91° is an obtuse angle
Hence, the angles 35° 65° and 28° are acute angles and the angle 91° is an obtuse angle
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Complete question
What angle measure is this? 35° 91° 65° 28°
acute, right, obtuse, straight, or reflex
The formula for the area A of a trapezoid
A = 1/2 (b + b,)h. Solve for b
[Mathematical Situation]
Solve for [tex]b_1[/tex]; [tex]A=\frac{1}{2} (b_{1} + b_2)h[/tex]
Solution:
[tex]b_1=\frac{2a}{h}-b_2[/tex]
Hope this helps!
Round your answer to the nearest hundredth B C 7 A 65°
The value of BC the nearest hundredth is 15.01 .
Trigonometric Ratios area unit outlined because the values of all the pure mathematics functions supported the worth of the quantitative relation of sides in an exceedingly trilateral. The ratios of sides of a trilateral with relation to any of its acute angles area unit referred to as the pure mathematics ratios of that exact angle.The 3 sides of the correct triangle are:Hypotenuse (the longest side)Perpendicular (opposite aspect to the angle)Base (Adjacent aspect to the angle)From the image , we are able to see that CA = seven and angle A = 65°
Using ,Trigonometric Ratios , we get
Tan A = Perpendicular / Base
Tan 65° = BC / CA
2.144 =BC / 7
2.144 ×7 = BC
15.011 = BC
On rounding off to the closest hundredth , we have a tendency to get BC = 15.01
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Find the distance between each pair of points.
Simplify each expression. x³/₅ / x³/₁₀
The result of simplifying the expression x³/₅ / x³/₁₀ using the exponent rules is [tex]\sqrt[10]{}[/tex](x³)
To solve this exercise we have to resolve algebraic operations following the exponent rules.
[(x)³/₅ ] / [(x)³/₁₀]
Using the quotient rule that indicates that: the exponent result will be the subtraction of these exponents, we have:
x⁽³/⁵ ⁻³/¹⁰⁾
(x)⁽⁶⁻³⁾/¹⁰
(x)³/¹⁰
As we have a fractional exponent, you must convert the exponent to root:
[tex]\sqrt[10]{}[/tex](x³)
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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15. Given the following relation {(2, 1), (-4,5), (1,7), (2, -3), (-1,2)), determine if it is a function.
We get that the relation { ( 2 , 1) , ( - 4 , 5 ) , ( 1 , 7 ) , ( 2 , - 3 ) , ( - 1, 2 ) } is a function.
We are given a relation as:
{ ( 2 , 1 ) , ( - 4 , 5 ) , ( 1 , 7 ) , ( 2 , - 3 ) , ( - 1, 2 ) }
We need to find that whether it is a function or not.
A relation is a set that shows a relationship between two values. A function is from a set X to a set Y assigns to each element of X exactly one element of Y.
Here, we can see that it is a function as one value of x only has one image in the set y.
Therefore, we get that the relation { ( 2 , 1) , ( - 4 , 5 ) , ( 1 , 7 ) , ( 2 , - 3 ) , ( - 1, 2 ) } is a function.
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Simplify the expression where possible
Is the answer 6^-9 or -54
The given expression can be rewritten as [tex]6 ^{-9}=\frac{1}{6^9}[/tex].
Power RulesThere are different power rules, as presented below:
Multiplication with the same base: you should repeat the base and add the exponents.Division with the same base: you should repeat the base and subtract the exponents.Power. For this rule, you should repeat the base and multiply the exponents.Zero Exponent. When you have an exponent equals to zero, the result must be 1.For solving this exercise, you should identify the power rules you will apply. For this question, you can apply the following rule:
"Power - repeat the base and multiply the exponents."
Lilke the base is 6 and the exponents are 3 and -3, then you can rewrite the expression as:
[tex](6^3) ^{-3}=6 ^{-9}=\frac{1}{6^9}[/tex]
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400 students were surveyed about their favorite school lunch. Exactly how many students chose pizza as their favorite school lunch based upon the data in the circle graph above?
The students chose pizza as their favorite school lunch based upon the data will be 130 students.
How to illustrate the information?Let the assumed fraction for those who choose pizza be 3/10.
From the information, 400 students were surveyed about their favorite school lunch.
Therefore, the students chose pizza as their favorite school lunch based upon the data will be:
= Fraction for pizza × Total students
= 3/10 × 400
= 120 students
Note that an overview was given as the graph wasn't found.
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hi, can anyone help me with this problem?