Solve each equation. Check for extraneous solutions. 2+√x+5 =4
There is no solution for the equation 2 + √x + 5 = 4 for x ∈ R.
An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.
A formula known as an equation uses the equals sign (=) to express how two expressions are equal.
Consider the equation,
2 + √x + 5 = 4
√x + 7 = 4
Subtracting 7 from each side of the equation.
√x + 7 - 7 = 4 - 7
√x = - 3
Since √f(x) cannot be negative for x ∈ R.
Hence, there is no solution for x ∈ R of the equation.
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Find the inverse of each function. Is the inverse a function?
y=5-2 x²
In mathematics, an inverse function is one that "reverses" another function. The inverse of the function y = 5 - 2x² is f ⁻¹(x) = √2(−x+5)/2, −√2(−x+5)/2
What is meant by inverse function?The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f exists bijective.
An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.
Interchange the variables.
x = 5 − 2y²x = 5 - 2y²
Solving for y
y = √2(−x+5)²y = 2(-x+5)²
y = −√2(−x+5)²y = -2(-x+5)²
Replace y with f ⁻¹(x)
f ⁻¹(x)=√2(−x+5)²,−√2(−x+5)² f ⁻¹(x)=2(-x+5)²,-2(-x+5)²
The inverse of the function y = 5 - 2x² is f ⁻¹(x) = √2(−x+5)/2, −√2(−x+5)/2.
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help, please, begging you
Pilar paid $2.40 for 2 cans of dog food at the pet store. leo visited the same pet store and spent $3.60 on 3 cans of dog food. write an equation to represent the proportional relationship between cans of dog food, x, and total cost, y.
Answer:
y = 1.2x
Step-by-step explanation:
The equation that represents the proportional relationship between cans of dog food, x, and total cost, y is
y = 1.2x
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 4 is an equation.
We have,
Pilar:
Cost of 2 cans of dog food = $2,40
We can write this as an equation:
2 = 2.40 ____(1)
Leo:
Cost of 3 cans of dog food = $3.60
We can write this as an equation:
3 = 3.60 ____(2)
From (1) and (2) we get,
The cost of dog food y is proportional to 1.2 of the cans of dog food x.
y = 1.2x
Thus,
The equation that represents the proportional relationship between cans of dog food, x, and total cost, y is
y = 1.2x
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Given f(x) = x + 9, write the new function if the y-intercept is decreased by three unit.
Answer:
f(x) = x + 6
Step-by-step explanation:
if the y-intercept is decreased by 3 units in the slope formula where b is the y-intercept, then the answer is x + 6
GIVING AWAY 45 POINTS TO THE FIRST PERSON THAT ANSWERS
Subtract (−2)−(−1) using the number line.
Select the location on the number line to plot the difference.
6x-3y=21
what would be the answer and how would i solve this
Answer:
x= 7+y/2
The slope is 2
Step-by-step explanation:
Draw a scatter plot and find the line of best fit for each set of data. (3,100),(5,150),(7,195),(9,244),(11,296),(13,346),(15,396)
The scatter plot is shown in attached images and the line of best fit for the data set is y=24.6607x+24.7637.
The given data set is (3,100),(5,150),(7,195),(9,244),(11,296),(13,346),(15,396).
Plot the points on a coordinate plane.
Calculate the mean of the x -values and the y -values.
[tex]\begin{aligned}\bar{X}&=\frac{3+5+7+9+11+13+15}{7}\\ &=\frac{63}{7} \text{ or } 9\\ \bar{Y}&=\frac{100+150+195+244+296+346+396}{7}\\ &=\frac{1727}{7}\text{ or }246.71\end[/tex]
Now, we will calculate the [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})[/tex] and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}[/tex], we get
[tex]\sum_{i=1}^{n}(x_{i}-\bar{X})^{2}=112[/tex]
and [tex]\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})=2762[/tex]
Calculate the slope.
[tex]\begin{aligned}m&=\frac{\sum_{i=1}^{n}(x_{i}-\bar{X})(y_{i}-\bar{Y})}{\sum_{i=1}^{n}(x_{i}-\bar{X})}\\ &=\frac{2762}{112}\\ &=24.6607\end[/tex]
Calculate the y -intercept.
Use the formula to compute the y -intercept.
[tex]\begin{aligned}b&=\bar{Y}-m\bar{X}\\ &=246.71-(24.6607\times 9)\\ &=246.71-221.9463\\ &=24.7637\end[/tex]
Use the slope and y -intercept to form to find the equation of the line of best fit.
The slope of the line is 24.6607 and the y -intercept is 24.7637 .
Therefore, the equation is y=24.6607x+24.7637.
Draw the line on the scatter plot.
Hence, the scatter plot is shown in attached image and the line of best fit for given data set (3,100),(5,150),(7,195),(9,244),(11,296),(13,346),(15,396) is y=24.6607x+24.7637.
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The formula for the Ideal Gas Law is P V=n R T , where P is the pressure in kilopascals ( kPA), V is the volume in liters (L), T is the temperature in Kelvin (K), n is the number of moles of gas, and R=8.314 is the universal gas constant.
a. Write an equation to find the volume in terms of P, n, R , and T .
The equation to find the volume in terms of P, n, R , and T is:
[tex]V=\frac{n R T}{P}[/tex]
What is Ideal Gas Law?The ideal gas law is the general gas equation. It is a good approximation to find behavior of gases under different conditions. This law says that the product of pressure in the atmosphere and volume is equal to product of moles and temperature. We generally use an equation to define these relations.
Equation of ideal gas law
P V=n R T
where,
P = pressure measured in atmosphere
V = volume measured in liters
n = number of moles present in gas
T = temperature
R = gas constant
Ideal gas equation shows several direct and indirect variations between the different elements , such as in the equation pressure (P) shows direct variation with n and T , and inverse variation with volume (V).
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Suppose the cost of an item is c. First, the cost is discounted by 30%. Then sales tax of 6.5% is added to the sales price. Write an algebraic expression for the final cost of the item using the variable c.
The Algebraic expression for the final cost of the item using the variable c is 0.7455c
The cost of the item is c
Algebraic expression after discounting the cost by 30%
c - 30%of c
c- 0.3c
0.7c
Now, Algebraic expression after the application of 6.5% of sales tax
0.7c + 6.5%of 0.7c
0.7c +0.065(.7c)
0.7c +0.0455c
0.74.55c
Hence, 0.7455c is the algebraic expression for the final cost of the item using the variable c.
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.
We learned how to express an unknown number using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables.
Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
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Please explain thank u
Answer:
x = 6
Step-by-step explanation:
multiply by 6 the whole equation to eliminate fractions and convert the coefficients and independent numbers to integers:
[tex]4x-1=3x+5[/tex]
[tex]4x-3x=5+1[/tex]
[tex]x=6[/tex]
Hope this helps
Answer:
[tex]x = 6[/tex]
Step-by-step explanation:
In the equation:
[tex] \frac{2}{3} x - \frac{1}{6} = \frac{1}{2} x + \frac{5}{6} [/tex]
Multiply both sides of the equation by the common denominator which is 6
[tex] \frac{2 \times 6}{3} x - \frac{1 \times 6}{6 } = \frac{1 \times 6}{2} x + \frac{5 \times 6}{6} [/tex]
[tex] ⟹ \frac{12}{3} x - \frac{6}{6} = \frac{6}{2} x + \frac{30}{6} [/tex]
Reduce the fraction
[tex]4x - 1 = 3x + 5[/tex]
Now, collect like terms to find the value of x
[tex]4x - 3x = 5 + 1[/tex]
Therefore:
[tex]x = 6[/tex]
I hope this helpsIsabel has 13 rings and 6 bracelets she chooses a ring and a bracelet at random
how many possible combinations of ring and bracelet does she have
The number of possible combinations of ring and bracelet she has is 78
How to determine how many possible combinations of ring and bracelet does she have?The given parameters are
Rings = 13
Braceletes = 6
The number of possible combinations of ring and bracelet she has is calculated by multiplying the number of rings and the number of bracelets
This is represented as
Possible combination = Rings x Braceletes
Substitute the known values in the above equation
So, we have
Possible combination = 13 * 6
Evaluate the product in the above equation
So, we have
Possible combination = 78
This means that she has 78 possible combinations of ring and bracelet
Hence, the number of possible combinations of ring and bracelet she has is 78
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The slope of line a is 5. The slope of line b is 1/5 . Which statement is true
The lines are parallel.
The lines are neither perpendicular nor parallel.
The lines are perpendicular.
The statement is true that the lines are neither perpendicular nor parallel.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
Slope tells how vertical a line is thus more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.
The Slope of parallel lines are same, similarly Slopes of perpendicular lines are negative reciprocal of each other.
Parallel lines have the same slope beacuse the slope is like a measure of steepness and since parallel lines are of the same steepness, thus, are of the same slope.
If there are two lines perpendicular to each other, then their slopes are negative reciprocal of each other meaning if one line's slope is 'a', then its perpendicular line's slope would be -1/a
We have been given that the slope of line a is 5 and the slope of line b is 1/5.
The statement is true that the lines are neither perpendicular nor parallel.
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Find the original price of a pair of shoes if the sale price 50 is after a 20 discount.
Answer:
70
Step-by-step explanation:
as the discount is 20 thus the original price would be 70
Each row of the table shows a different speed-distance-time relationship.
A 3-column table with 2 rows. Column 1 is labeled Speed (meters per hour) with entries 35, 27. Column 2 is labeled Distance (meters) with entries A, 81. Column 3 is labeled Time (hours) with entries 4, and B.
Use the drop-down menus to correctly complete the table.
A =
B =
Based on the given values in the table that shows different speed-distance-time relationships, the value of A is 140 meters and the value of B is 3 hours.
How to find distance travelled and time taken?To find the distance, the formula is:
= Speed x time
The distance of A is:
= 35 x 4
= 140 meters
To find the time taken, the formula is:
= Distance / speed
The time in B is:
= 81 / 27
= 3 hours
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The total cost (in cents) of x+2 markers is x³+5 x²+2 x-8
a. Write an expression that models the cost of each marker.
An expression that models the cost of each marker, when the cost of x + 2 markers is x³ + 5 x² + 2 x - 8, is x² + 3 x - 4
Given,
Total number of markers = x + 2
The total cost of markers = x³ + 5 x² + 2 x - 8
An expression to model the cost of each marker can be found by dividing the total cost of markers by the total number of markers.
This implies, the expression can be given as :
(x³ + 5 x² + 2 x - 8) / (x + 2)
x² + 3 x - 4
_______________
x + 2 | x³ + 5 x² + 2 x - 8
x³ + 2 x²
________________
3 x² + 2 x
3 x² + 6 x
________________
- 4 x - 8
- 4 x - 8
_________________
0
The quotient of this division is the expression that the cost of each marker.
Therefore, An expression that models the cost of each marker when the cost of x + 2 markers is taken into account. x³ + 5 x² + 2 x - 8, is x² + 3 x - 4
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PLSS HELP ILL GIVE U A STAR, PLSSSSS
6 mechanics can perform a deluxe service on 3 cars in a day. How many days will it take 2 of the mechanics to perform this service on 5 cars
Answer:
It would take 5 mechanics to repair 22 cars in 5 hours
Step-by-step explanation:
2 garage mechanics take 3 hours to repair 6 cars.
to repair 1 car, 1 garage mechanics take = (2×3)/6 = 1 hour
So In 1 hour, 1 car can be repaired by 1 mechanic
22 cars can be repaired in 1 hour by = 22/1 = 22 mechanics
22 cars can be repaired in 5 hours by = 22/5 = 4.4 = 5 mechanics
(4.4 mechanics are not possible. There should be 5 mechanics)
A scientific report says that the proportion of the population that is left-handed is
0.10 with a margin of error of 0.02.
a. Is 0.07 a plausible estimate for the proportion of the population that is
left-handed? Explain your reasoning.
b. Is 0.087 a plausible estimate for the proportion of the population that is
left-handed? Explain your reasoning.
c. Is 0.128 a plausible estimate for the proportion of the population that is
left-handed? Explain your reasoning.
A) 0.10 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is
left-handed.
B) 0.10 is part of this interval and as such we can say that it is a plausible estimate for the proportion of the population that is
left-handed.
C) 0.10 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is
left-handed.
How to Interpret Confidence Interval?
We are given that;
Population that is left-handed = 0.10
Margin of error =0.02.
A) Confidence interval = 0.07 ± 0.02
CL = (0.05, 0.09)
0.10 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is
left-handed.
b) Confidence interval = 0.087 ± 0.02
CL = (0.067, 0.107)
0.10 is part of this interval and as such we can say that it is a plausible estimate for the proportion of the population that is
left-handed.
c) Confidence interval = 0.128 ± 0.02
CL = (0.108, 0.148)
0.1 is not part of this interval and as such we can say that it is not a plausible estimate for the proportion of the population that is
left-handed.
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Write each equation in logarithmic form.
243=3⁵
The logarithmic form of the equation is [tex]log_{3}243=5[/tex] .
In mathematics, the logarithmic function is the inverse of power. Then the function is given as f(x) = log x The logarithm base is a. This can be read as the logarithmic base a of x. The two most common bases used in logarithmic functions are base 10 and base e. The logarithm function has several properties that allow the logarithm to be simplified when the input is in the form of products, quotients, or values raised to powers.We have given an equation 243 = 3⁵ .
Taking log on both sides , we get
[tex]log(243) =log3^5[/tex] ..(1)
Applying the property of logarithm which is given by [tex]loga^b=bloga[/tex] in equation (1) ,we get
[tex]log(243) =5log3[/tex]
On rearranging the above equation , we get
[tex]\frac{log243}{log3} =5[/tex] ..(2)
Applying the property of logarithm which is given by [tex]log_xy=\frac{log_ay}{log_ax}[/tex]\
[tex]\frac{log243}{log3}[/tex] can be written as [tex]log_{3}243[/tex] using property
Putting in equation (2) , we get
[tex]log_{3}243=5[/tex]
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Ravi made $378 for 18 hours of work.
At the same rate, how many hours would he have to work to make $252?
Answer:
12 hours
Step-by-step explanation:
First, figure out her hourly rate
378 ÷ 18 = 21Next, divide 252 by the hourly rate to figure out how many hours he will have to work
252 ÷ 21 = 12Multiply the hourly rate by number of hours worked to check your answer
21 × 12 = 252At a rate of $21 per hour, he has to work for 12 hours to make $252.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Ravi made $378 for 18 hours of work.
So, Ravi's unit rate or earnings per hour is $(378/18).
= $21.
Now, In one hour he makes $21.
Therefore, To make $252 he has to work (252/21) hours.
= 12 hours.
So, Ravi has to work for 12 hours to make $252.
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Please help! What is the domain of the function shown in the graph below?
Answer:
[-2,infinitysymbol)
Step-by-step explanation:
If you have a graph to look at, the domain is like you are walking up and down the x-axis (which is actually not up/down but left/right) and you're stating where this graph exists.
If you walked all the way over to -10 and looked up or down, the graph just doesn't exist over there.
The graph exists from -2, including -2, so use the SQUARE bracket [.
On the right side there's an arrow on the graph so it keeps going forever. Thats infinitysymbol.
Always wrap a parenthesis ), around the infinity symbol.
Interval notation uses the [SQUARE] brackets or (parenthesis) and even though it looks like a point, its not. It means
[FromHere, ToHere) and answers the question, where is the graph?
4 1/2 ÷ (-1 3/7) =
Dividing mixed numbers with negatives
Albert uses a grid to multiply 27 by 13. Albert then multiplies two different numbers.
It should be noted that when Albert uses a grid to multiply 27 by 13, the product that will be gotten will be 351.
What isn't a product?
It should be noted that in mathematics, a product or an expression that specifies factors to be multiplied is the outcome of multiplication.
The multiplicand, multiplier, and product are the components of a multiplication sentence. The first number is the multiplicand, the second number is the multiplier, and the result is the product.
It should be noted that based on the information, we want to multiply 27 and 13. This will be illustrated thus:
= 27 × 13
= 351
Therefore, when when Albert uses a grid to multiply 27 by 13, the product that will be gotten will be 351.
Note that the information is incomplete and was solved based on the available information given.
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Decribe and correct the error in determining whether the relation is a function.
Answer:
It is not a function because the number 4 (input) is being used more then once
Round 1.553 to the nearest hundredth.
this is bc im lazy but still help me plsss
Answer:
1.55 is the correct answer
Answer:
If you like to round 1.553 to the nearest hundredth, leaving only two numbers after the decimal point, then ask your teacher for help instead of letting yourself down. The result you'll get is 1.55
Step-by-step explanation:
Number Rounded to Nearest 100th
1.553 1.55
1.554 1.55
1.555 1.56
1.556 1.56
1.557 1.56
1.558 1.56
1.559 1.56
1.56 1.56
1.561 1.56
1.562 1.56
A standard die is rolled. Find the probability that the number rolled is less than 2
======================================================
Explanation:
E = event space = {1}
The event space is the set of things we want to happen. There's only one outcome and it's the "1" (since it's smaller than 2)
S = sample space = {1,2,3,4,5,6}
There are 6 items in the sample space.
Divide the two counts to get the fraction 1/6 which is the probability of rolling a result less than 2. In other words, the probability of landing on "1" is 1/6 since there's one face with that label out of 6 faces total.
Side note: 1/6 = 0.1667 = 16.67% approximately
A local hamburger shop sold a combined total of 437 hamburger and cheeseburgers on Thursday. There were 63 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Thursday?
A fast food restaurant estimates the cost of making hamburgers to be $2.05 per hamburger plus an ade
If $13,025 represents the total cost of making a hamburgers, which equation can be used to find the numb
O 13,025 = 2.05 + 2,000x
O 13,025 = 2.05€ + 2,000
O 13,025x = 2.05 + 2,000
O 13,025 (2.05 + 2,000)
Based on the total cost of making hamburgers, and the cost per hamburger the equation to find the number of hamburgers made is 13,025 = 2.05x + 2,000
How to find the number of hamburgers?The cost of a single hamburger is $2.05 and this is in addition to a fixed cost of $2,000 for fixed costs.
This means that the number of hamburgers x, can be found by the formula:
Total cost of hamburgers = Cost per hamburger x Number of hamburgers + Fixed costs
Using x and the given figures gives:
13,025 = 2.05x + 2,000
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In the equation b = a -2, which variable is the independent variable and which is the dependent variable ? Explain
In the equation b = a -2, which variable is the independent variable and which is the dependent variable ? Explain.
In the given equation b=a-2, a is an independent variable and b is an dependent variable.
Independent variable is variable whose values are unaffected by changes is referred to as an independent variable.
The dependent variable is defined as the variable whose evaluation of the independent variable determines the quality of the dependent variable.
For example, y=x+5
Here, According to changes in the evaluation of the variable "x," the estimation of the variable "y" also varies. The variable "y" is referred to as an dependent variable and the "x" is referred to as an independent variable.
Therefore, In the equation b=a-2, "a" is an independent variable and "b" is an dependent variable.
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The locations of a house, market, and library from a right triangle as shown in the diagram
There are √34 miles between the house and the library
How to determine how many miles is the house from the library?The given parameters are
Distance between house and market, x = 3 miles
Distance between market and library, y = 5 miles
The number of miles between the house and the library is calculated as
Distance = √x² + y²
Substitute the known values in the above equation
So, we have
Distance = √3² + 5²
Evaluate the exponents in the above equation
So, we have
Distance = √9 + 25
Evaluate the sum in the above equation
So, we have
Distance = √34
Hence, there are √34 miles between the house and the library
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