Mackenzie can find the amount of flour used by using subtraction. She should subtract the flour left in the bag from 10 pounds.
Subtraction is one of the four basic mathematical operations.
It is used to calculate the amount left after a quantity is reduced.
When two variables are subtracted we use the following notation '-' .
Let us consider two variables x and y such that x is subtracted from y then mathematically it is denoted by y - x .
Mackenzie used some flour to bake bread. To calculate the amount she used from 10 pound bag , first she will have to find the amount of flour left in the bag.
Let a pounds of flour is left (a<10).
So to calculate the amount of flour used by her we simply subtract a from 10 pound.
Hence flour left is (10 - a) pounds.
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Suppose you invest $ 500 in a savings account that pays 3.5 % annual interest. How much will be in the account after five years?
Amount $593.84 will be in the account after five years.
According to the question we have been given that the
amount invested initially = $500
annual interest rate = 0.035
Time = 5 years.
The formula for the future value is given as
[tex]FV = a(1 + r)^{t}[/tex] (1)
where , FV = future value
a = amount invested initially
r = annual interest rate
t = time
putting the required values in equation (1) we get
[tex]FV = 500 (1 + 0.035)^{5} \\FV = 500 ( 1.035)^{5}[/tex]
FV = 500*1.188
FV = $ 593.84
Thus, $593.84 will be the amount in the account after five years.
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f(x)=10 x-10 . Find each value.
(f ⁰ f⁻¹)(-10)
The inverse function returns the original value for which the output of a function was given.
The value of f(x) = 10x - 10 is -110.
What is the inverse formula?The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.
An inverse in mathematics is a function that serves to "undo" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f1.
Lett the function be F(x) = 10x - 10
To differentiate with respect to X
F⁻¹(x) = 10
F( f⁻¹(x)) = F(10)
F( f⁻¹(x)) = -10x -10
Substitute the value of X = 10, then we get
F( f⁻¹(x)) = -10(10)-10
simplifying the above equation, we get
F( f⁻¹(x)) = -100-10
F( f⁻¹(x)) = -110
Therefore, the value of (f ⁰ f⁻¹)(d) = -110.
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Marta paid $53 for 4 tickets to see a ballet. each ticket cost the same amount. what was the cost each ticket for the ballet?
The cost of each ticket for the ballet is $13.25.
What is cost price?The cost price or simply the cost in retail systems represents the particular value that corresponds to the unit price paid. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.
There are numerous ways to calculate cost pricing, however it all relies on the kind of query we are asking. For instance,
If a selling price and profit are provided, then,
Cost price = Selling price (SP) − profit
If a selling price and loss are provided, then,
Cost price =Selling price + loss
In the given question,
The total amount that Marta paid is $53
=> amount = $53
and total number of tickets = 4
Now, the cost of each ticket = Total amount / number of tickets
= $53 / 4
= $ 13.25
Hence, the cost each ticket for the ballet is $13.25.
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Marie can type 25 labels in 10 mins. How many can
she type
in one hour?
Step-by-step explanation:
her ratio is therefore 25/10, which can be also written as 5/2, because ratios are just a special form of fractions.
to find how many labels she can type in 1 hour, we need to find the rehashing between 10 minutes and 1 hour.
1 hour = 60 minutes.
60 minutes = 6 × 10 minutes.
so, to find the equivalent ratio based on 1 hour, we need to multiply the denominator (bottom part) by 6.
and to keep the ratio value we need to multiply the numerator (top part) by the same number :
25/10 × 6/6 = 150/60
and since the ratio is always telling us how many labels can be typed per unit of time, we see,
she can type 150 labels in 1 hour (60 minutes)
14. “-4 times a number plus 29”
Answer:
It depends on what that number is but -4+29 is equal to 29-4; making the answer to -4+29=5.
Step-by-step explanation:
help help help guys HELP
Slope can be described as rise/ run, change in the dependent variables relative to the change in the independent variables and Δy / Δx.
How to find the accurate expression of the slope?The slope of a line is a number that describes both the direction and the steepness of the line.
The slope of a line is the change in y coordinate with respect to the change in x coordinate.
Therefore, slopes can be described as follows:
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Use the properties of logarithms to evaluate each expression.
log₄48- 1/2 log₄9
Using the properties of logarithm the value of the expression is [tex]log_{4} 48 - \frac{1}{2}log_{4} 9 = 2[/tex]
A logarithm is the power to which a number must be raised in order to get some other number.
According to the question we have been given the expression as
= [tex]log_{4} 48 - \frac{1}{2}log_{4} 9[/tex]
The properties of logarithm that we are going to use are :
[tex]log(\frac{x}{y} ) = logx - logy[/tex] and [tex]log_{a} a = 1[/tex]
Also we can see that the base are same so we can use the property of logarithm in the given equation and we know that √2304 = 48. Thus replacing 48 by √2304.
Now solving this step by step using the properties of logarithm we get
[tex]=log_{4} \sqrt{2304} - \frac{1}{2} log_{4} 9 \\=\frac{1}{2} log_{4} 2304 - \frac{1}{2} log_{4} 9\\= \frac{1}{2} [log_{4} 2304 - log_{4} 9]\\= \frac{1}{2} [log_{4} (2304/9)]\\= \frac{1}{2} log_{4} 256\\= \frac{1}{2} log_{4} (4^{4} )\\= 2 * log_{4} 4\\= 2*1\\= 2[/tex]
Hence using the properties of logarithm the value of the expression is
[tex]log_{4} 48 - \frac{1}{2}log_{4} 9 = 2[/tex]
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Interest Suppose you deposit $ 2000 in a savings account that pays interest at an annual rate of 4 % . If no money is added or withdrawn from the account, answer the following questions.
d. How many years will it take for the account to contain $ 3000 ?
It will take 10.3 years for the account to contain $3000.
The formula to be used is given as follows :
A(t) = a ( 1 + r )^t (1)
where, A(t) = future value
a = principal amount or amount initially deposited.
r = annual interest rate
t = time
According to the question we have been given that
a = $2000
r = 0.04
A(t) = $3000
putting the required values in equation (1) we get
3000 = 2000(1+0.04)^t
1.5 = (1.04)^t
Taking log both sides we get
log(1.5) = t log(1.04)
0.176 = t *0.017
t = 10.3 years.
Thus it takes 10.3 years for the account to contain $3000.
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You are driving a car when a deer suddenly darts across the road in front of you. Your brain registers the emergency and sends a signal to your foot to hit the brake. The car travels a reaction distance D , in feet, during this time, where D is a function of the speed r , in miles per hour, that the car is traveling when you see the deer, given by D(r)=11 r+5/10 . Find the inverse and explain what it represents. Is the inverse a function?
The inverse of the given equation is r = (10D - 5)/11 which represents the reaction speed of the car in terms of the reaction distance.
The car travels a distance of D feet, where D is a function of the speed r miles/hour given by D(r) = (11r + 5)/10
D = (11r + 5)/10
⇒ 10D = 11r +5 (multiply by 10 on both sides)
⇒ 10D - 5 = 11r (subtracting 5 on both sides)
⇒ (10D - 5)/11 = r (dividing by 11 on both sides)
Therefore, the inverse of the given equation is r = (10D - 5)/11.
Inverse represents the speed of the car (miles/hour) in terms of the reaction distance D.
The inverse is also a function, which represents the reaction speed of the car in terms of the reaction distance.
Therefore. the inverse of the given equation is r = (10D - 5)/11 which represents the reaction speed of the car in terms of the reaction distance.
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Which of the following expressions are equivalent to
The given expression is equivalent to [tex]\frac{l}{m}[/tex]. The correct option is C. None of the above
From the question, we are to determine the expression that is equivalent to the given expression
The given expression is
[tex]- \frac{l}{-m}[/tex]
This expression can be written as
[tex]\frac{-l}{-m}[/tex]
Multiplying the numerator and the denominator by -1
[tex]\frac{-l \times -1 }{-m \times -1 }[/tex]
= [tex]\frac{l}{m}[/tex]
Hence, the given expression is equivalent to [tex]\frac{l}{m}[/tex]. The correct option is C. None of the above
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convert 3100 fluid ounces to milliliters. round your answer to the nearest whole number
Answer:
91678 milliliters
Step-by-step explanation:
hope this is helpful! stay safe, and have a blessed day! :)
Use compass and straightedge moves to construct the angle bisector for angle ABC. In other words, create a ray that divides angle ABC into 2 congruent angles.
Answer:
Step-by-step explanation:
Draw a line in the middle of the compass slightly slanted like this /with an on top of the line indicating 2 congruent angles being created.
The college bookstore is having a back to school sale. T-shirts that usually sale for 34.50 are marked down to 20.7. What percent are they?
The college bookstore is 40 percent off
How to calculate the percent off ?T-shirt are usually on sale for $34.50
The price was marked down to $20.7
The price change is = 34.5 - 20.7
= 13.8
The percent off can be calculated as follows
= 13.8/34.50 × 100
= 0.4 × 100
= 40
Hence the percent off the college bookstore is 40 percent
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Can you guys help me with my math homework? I'll be asking more q's after they get answered. THX!!!
Answer:
y = 22.5x
Step-by-step explanation:
Using the scale 1:22.5
then the actual length is y = 22.5x
find the coordinates of the point on the curve y=7-3x-2x² where the gradient is 5
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex]y=7-3x-2x^2\implies \cfrac{dy}{dx}=-3-4x\implies \stackrel{\textit{setting the derivative to 5}}{5=-3-4x} \\\\\\ 8=-4x\implies \cfrac{8}{-4}=x\implies \boxed{-2=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{when x = -2, what's "y"?}}{y=-7-3(-2)-2(-2)^2}\implies y=-7+6-8\implies \boxed{y=-9} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-2~~,~~-9)~\hfill[/tex]
Samantha is following a blueprint to build an addition to her house. The kitchen countertop will be 8.75 feet long. The scale of the blueprint is 1 centimeter = 1.75 feet. What is the length of the countertop on the blueprint?
The length of the countertop on the blueprint is 5 cm.
What is defined as the scale?Scale is a ratio that reflects the relation between the size of a model and the actual dimensions of a figure or object. It aids in the representation of real-world objects on paper with relatively tiny dimensions. Scale is primarily employed in maps as well as blueprints for building construction.For the given question;
The length of kitchen countertop = 8.75 feet.
The scale used in blueprint is 1 centimeter = 1.75 feet.
Thus, use the unitary method.
1.75 feet -----> 1 cm.
Divide both side by 1.75.
1 feet ------>1/1.75 cm
Multiply both side by 8.75.
8.75 feet ---> 8.75/1.75 cm
8.75 feet ------> 5 cm.
Therefore, the the length of a countertop for the blueprint is found as 5 cm.
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What do you notice about the decimal forms of the rates?
Answer: The question is not clear.
Step-by-step explanation:
pls help me its math gr8
simplify only its in algebra and solution to
1)9+2+9x+2 5)6x2-x1
2)9x2+3x-2
3)8x2+5x+1
4)6x2+x+1
simplify answers to each algebra equation
1) 9x + 13
2) 3x - 16
3) 5x + 17
4) x + 13
The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division.
on solving the equation we get the solution of algebra as
9x +13
3x-16
5x+17
x+13
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Find the inverse of each function. Determine if the inverse is a function.
y=2 x-3
The inverse of the function will be y = x/2 + 3/2. Yes, inverse is a function as well.
What is an inverse of a function?Functions that "undo" one another are known as inverse functions. In other words, f(g(x)) = g(f(x)) = x if g(x) is the inverse of f(x). We have a great approach we can use to achieve this given an equation for which we wish to get the inverse.
Not all functions have their opposite. It is simple to see that f(x) will never take on the same value again if f(x) has an inverse. We give this asset a unique name.
If each member of the range corresponds to precisely one element of the domain, a function is said to be one-to-one (f(x)).
Given,
We have a function,
y=2 x-3
Add 3 to each side.
⇒ y + 3 = 2x
Divide by 2 and then either
⇒ x = y/2 + 3/2 or y/2 + 3/2
Just change the labels now, x to y.
⇒ y = x/2 + 3/2
So, the inverse of given function is y = x/2 + 3/2
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If x= -2, the value of the expression 3x² - 5x +1/x is
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{3x^2 - 5x + 1}{x}}\\\\\mathsf{= \dfrac{3(-2)^2 - 5(-2) + 1}{-2}}\\\\\mathsf{= \dfrac{(3)(4) - (5)(-2)+1}{-2}}\\\\\mathsf{= \dfrac{12 - (5)(-2)+1}{-2}}\\\\\mathsf{= \dfrac{12 - (-10) + 1}{-2}}\\\\\mathsf{= \dfrac{12 + 10 + 1}{-2}}\\\\\mathsf{= \dfrac{22 + 1}{-2}}\\\\\mathsf{= \dfrac{23}{-2}}\\\\\mathsf{-11 \dfrac{1}{2}}\\\\\\\\\huge\text{Thus, your answer should be: \boxed{\mathsf{-11\dfrac{1}{2}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Identify all rays and lines in the picture below.
According to this definition given below, we identify all lines and rays as follows, EA, EB, EC, and ED are rays, and ED and BE are, Line.
A line is, it is actually difficult to give a good mathematical definition. Roughly, we can say that a line is an infinitely thin, infinitely long collection of points extending in two opposite directions. When we draw lines in geometry, we use an arrow at each end to show that it extends infinitely.
A line can be named either using two points on the line (for example, AB←→ ) or simply by a letter, usually lowercase (for example, line m ).
A line segment has two endpoints. It contains these endpoints and all the points of the line between them. You can measure the length of a segment, but not of a line.
___
A segment is named by its two endpoints, for example, AB.
A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.
A ray is named using its endpoint first, and then any other point on the ray (for example, BA−→− ).
according to this definition, EA EB EC ED are rays, and ED, and BE are Line
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Nayeli went to the grocery store and bought bottles of soda and bottles of juice. each bottle of soda has 25 grams of sugar and each bottle of juice has 15 grams of sugar. nayeli purchased 5 more bottles of soda than bottles of juice and they all collectively contain 205 grams of sugar. write a system of equations that could be used to determine the number of bottles of soda purchased and the number of bottles of juice purchased. define the variables that you use to write the system.
The system of equations are:
25s + 15j = 205
s - j = 5
Where:
s = number of soda bought
j = number of juice bottles bought
What are the system of equations?In order to determine the number of bottles of soda and juice bought, two sets of equations would need to be formed based on the information provided in the question. The equations would be solved simultaneously.
Grams of sugar in the soda bottle + grams of sugar in the juice bottle = total grams of sugar
difference in the number of bottles bought
25s + 15j = 205
s - j = 5
The methods that can be used to solve the simultaneous equations :
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Solve. Check for extraneous solutions. 3 √x=6
No extraneous solution to the equation
The equation given is
3[tex]\sqrt{x}[/tex] = 6
Now we have to find the value of x.
[tex]\sqrt{x}[/tex] = 2
[tex](\sqrt{x} )^{2}[/tex] = [tex]2^{2}[/tex]
x = 4
To find whether it is an extraneous solution or not put the value of x in the given equation.
3[tex]\sqrt{4}[/tex] = 6
3 × 2 = 6
6 = 6
Therefore we get to know that there is no extraneous solution.
x = 4 is the solution of the equation.
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the sum of three is 131 the second of three numbers is seven more than twice the first the third number is 12 less then the first what equation can be used to solos this problem
Answer:
4x - 5 = 131 where x is the first number.
Step-by-step explanation:
Let the first number be x.
Seconder number = 2x + 7.
Third number = x - 12.
So, the equation is :-
x + 2x + 7 + x - 12 = 131
4x - 5 = 131
4x = 136
x = 34
First number = 34, second = 2(34) + 7 = 75 and third number = 34-12 = 22.
Evaluate each logarithm.
log₅(-25)
log₅(-25) is undefined
Logarithms are another notation for exponents in mathematics. The logarithm of a number whose base is equal to another number.A logarithm is the reciprocal of a power. For example, if 10² = 100 then log₁₀ 100 = 2. The natural logarithm is called the base e logarithm. The natural logarithm is represented by ln or loge. where 'e' represents Euler's constant, which is approximately equal to 2.71828. For example, the natural logarithm of 78 is written ln 78. The natural logarithm determines how much "e" must be multiplied to get the desired output.Since the logarithmic function y = logₐ(x) is the inverse of the exponential function,
As the base is positive so x must also be positive
The logarithm of the real base of negative numbers is undefined.
Hence, log₅(-25) is undefined
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PLSSS HELP ILL GIVE U 100 POINTS
Solve each equation.
log 9- log x+1=6
After solving the given equation log9-log x+1=6, the value of x=(-9log+5)/log.
What is an equation?A mathematical statement made up of two expressions joined by an equal sign is called an equation.An equation is 3x - 5 = 16.We obtain the value of the variable x as x = 7 after solving this equation.So,
Given equation: log9-log x+1=6Then,
log9-logx+1=69log-logx+1=6(9log-logx+1)+(-9log-1)=6+(-9log-1)x=(-9log+5)/logTherefore, after solving the given equation log9-log x+1=6, the value of x=(-9log+5)/log.
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Castel and Huong each improved their yards by planting grass sod and ornamental grass. They bought their supplies from the same store. Castel spent $144 on 6 ft²
of grass sod and 9 bunches of ornamental grass. Huong spent $151 on 9 ft' of grass sod and 7 bunches of ornamental grass. What is the cost of one ft' of grass sod
and the cost of one bunch of ornamental grass?
The cost of one ft' of grass sod is $ [Select]
and the cost of one bunch of ornamental grass is $ [Select]
The cost of one ft' of grass sod is $9 and the cost of one bunch of ornamental grass is $10.
How to illustrate the information?Based on the information, the appropriate equation will be:
6g + 9y = 144
9g + 7y = 151
where g = grass sod
o = ornamental grass
Multiply equation I by 9
Multiply equation ii by 6
54g + 81y = 1296
54g + 42y = 906
Subtract
39y = 390
y = 390/39
y = 10
From 9g + 7y = 151
9g + 7(10) = 151
9g = 151 - 70
9g = 81
g = 81/9
g = 9
Therefore, the cost of one ft' of grass sod is $9 and the cost of one bunch of ornamental grass is $10.
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pls help in the screen shot
Using proportions, it is found that the conservationist would expect there to be 310 trouts in the lake.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the measures using a rule of three, that can be either direct or inverse, deriving from proportional relationships.
Direct relations, which are the most usual, are when both variable behave similarly(both increase or both decrease), while for inverse relations, they behave differently.
For this problem, we have that from the fact that out of the 26 trout, 13 were tagged, the proportion of tagged trouts is:
p = 13/26 = 0.5.
Hence, if 155 trouts were tagged, the expected amount is given by:
0.5n = 155
n = 155/0.5
n = 155 x 2
n = 310.
The conservationist would expect there to be 310 trouts in the lake.
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Solve each equation by factoring. Check your answers.
x²-8 x+15=0
The factors of equation are 5 and 3.
Rewriting the equation -
x² - 8x + 15 = 0
ax² + bx + c = 0
Factorizing the equation such that -
Sum of factors is equal to middle expression (b) (8x in this case)Product of factors is equal to the numeral values (a and c) (15 in this case)The suitable factors that can be used for solving the expression are 5 and 3.
x² - 5x - 3x + 15 = 0
x(x - 5) -3 (x - 5) = 0
(x - 5) (x - 3) = 0
(x - 5)= 0
x = 5
(x - 3) = 0
x = 3
Hence, the two factors of expression are 5 and 3.
To check the factors, we will keep each value of x to see if Left Hand Side is equal to Right Hand Side or not
When x = 5
x² - 8x + 15 = 0
5² - 8×5 + 15 = 0
25 - 40 + 15 = 0
-15 + 15 = 0
0 = 0
When x = 3
x² - 8x + 15 = 0
3² - 8×3 + 15 = 0
9 - 24 + 15 = 0
- 15 + 15 = 0
0 = 0
Since for both factors Left Hand Side is equal to Right Hand Side, thus, 5 and 3 are correct factors of the equation.
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