Without calculating you would that x=-2 is an extraneous solution because an absolute value inequality usually two possible solutions.
Solution of absolute value inequalities
An absolute value inequality is an expression with absolute functions as well as inequality signs. This type of inequality usually have two solutions.
The given equation
|4x + 20| = 6x
The solution to the absolute value inequality above is calculated as follows;
4x + 20 = 6x ------ (1)
-4x - 20 = 6x ------ (2)
from equation (1) above, the value of x is calculated as follows;
2x = 20
x = 20/2 = 10
from equation (1) above, the value of x is calculated as follows;
-10x = 20
-x = 20/10
-x = 2
x = -2
Thus, without calculating you would that x=-2 is an extraneous solution because an absolute value inequality usually two possible solutions.
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Solve each equation. log₇(2 x-3)²=2
The solution of the given logarithmic equation is 16.189.
What are the various properties of the logarithm?
Out of several properties of logarithms, some of the main properties are given below:
Product Rule
log (ab) = log a + log b
Change of base
log ₇ x = log x / log 7
Power Rule
log a² = 2 log a
Quotient Rule
log (a / b) = log a - log b
Solving the given equation log₇(2x - 3)² = 2
We are given a logarithmic expression: log₇(2x - 3)² = 2
Using properties of the logarithm, we have
log (2x - 3)² / log 7 = 2
log (2x - 3)² = 2 × log 7
2 log (2x - 3) = 1.6901
log (2x - 3) = 3.3802
Using exponential on both sides,
e^[log (2x - 3)] = e^(3.3802)
2x - 3 = 29.3766
2x = 32.3766
x = 16.189
Hence, the solution of the given equation is 16.189.
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The question is in the picture attached below. Pls answer, will give 50 points.
The required factorized expression is given as 3x²y + 12xy² + 3xy = 3xy(x + 4y + 3).
An incomplete equation is given we have to determine the missing terms.
The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.
Here,
The given equation,
_x²y +_y² + 9_ = 3x_(_+ 4y + _).
So, factorized expression is given as 3x²y + 12xy² + 3xy = 3xy(x + 4y + 3).
Thus, yhe required factorized expression is given as 3x²y + 12xy² + 3xy = 3xy(x + 4y + 3).
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PleSw help is it true or false
Answer:
It's True
Step-by-step explanation:
They both pass through the point 'U'ehich means they intersect.
Solve the equation
9x²29x28 = 0
Give your answers to 2 decimal places when appropriate.
Answer:
9x²29x28 = 0
The answer is 211932=0
9x2 - 29x - 28 = 0
The answer is 29x=−10
Step-by-step explanation:
Simplify. 4√162 +3 4√32
The question focuses on indices. Start by factorization of 162 and 32. Simplifying 32 yields 2^5 and 162 gives 3^4×2. Simplify the two expressions using the factors. Use the indices rule implying: b√a^c =a^(c⁄b)
∜162+3∜32
162= 81×2=3^4 ×2
32 = 2^5 = 2^4 ×2
∜(2×3^4 )+3∜(2^4×2)=∜(3^4 ) ∜2+3∜2^4 ∜2
3^(4⁄4)× ∜2+3×2^(4⁄4)×∜2 = 3×∜2+3×2∜2
3∜2+6∜2 = ∜2×(3+6) = 9∜2
= 9∜2
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What is the solution to the system of equations?
Y=2/3+3
y
x = -2
The solution to the given system of equations will be x = -2, y = 5/3. That is (-2, 5/3)
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The given system of equation is;
y = 2/3 x + 3 ----------- (1)
x= -2 ----------- (2)
The value of x has been given in the second equation.
Now, we need to determine the value of y
From the second equation, we have that;
x = -2
Now Substitute the value of x into the first equation,
y = 2/3 x + 3
y = 2/3 (-2) + 3
y = -4/3 + 3
y = 5/3
Hence, the solution to the given system of equations will be x = -2, y = 5/3. That is (-2, 5/3)
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Use the Venn diagram shown to list the set An C in roster form.
U
5
A 3
1
6
9
13
2
11
8
7
4
10
14
12
B
O A. (2, 3, 4, 6, 8, 9, 10, 11, 12, 13}
OB. {11}
O C. {4, 11, 12}
O D. (11, 13)
Answer:
Not Available
Step-by-step explanation:
Use the Venn diagram shown to list the set An C in roster form.
U
5
A 3
1
6
9
13
2
11
8
7
4
10
14
12
B
O A. (2, 3, 4, 6, 8, 9, 10, 11, 12, 13}
Germaine is saving money to buy a $367 mountain bike. He plans to save $45 every week from his paycheck until he has enough money. So far, he has saved $62. How many weeks will it take Germaine to get the mountain bike?
It will take Germaine to get the mountain bike 6.77 weeks (approximately)
let X represent the number of weeks it will take to save enough money
Money to buy a mountain bike = $367
He planned to save money every week from his paycheck = $45
So far, He had saved money already to buy bike = $62
now the required amount to buy a mountain bike is
$367-$62 = $305
Number of weeks Germaine will take to get the mountain bike is
X = 305/45
X = 6.77 weeks (approx)
It will take Germaine to get the mountain bike 6.77 weeks (approximately).
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3ax + 2b/c = 4d
Solve for x
The depth of a local river averages 16 ft, which is represented as |−16|. In January, it measured 4 ft deep, or |−4|, and in July, it was 18 ft, or |−18|. What is the difference between depths in January and July?
22 feet
14 feet
10 feet
2 feet
Answer:14 ft
Step-by-step explanation:hope it helps, brainliest? i could really use it
Greta wrote a total of 8 pages over 2 hours. After spending 3 hours writing this week, how many pages
will Greta have written in total?
The number of 12 pages written by Great in 3 hours.
What exactly is the unitary method?The unitary method is used to determine the value from one unit provided a multiple.Furthermore, once the value of a single unit has been determined, we can multiply a certain number by the number of units required. This methodology is normally used to demonstrate ratio and proportion concepts.For the given question;
Time take by Greta to write total of 8 pages is 2 hours.
Use unitary method for solving;
2 hours --------> 8 pages.
Divide both side by 2.
1 hour -------> 4 pages.
Now, fore finding the number of pages written in 3 hours.
Multiply each side by 3.
3 hours ---------> 12 pages.
Thus, the number of pages written by Great in 3 hours are 12 pages.
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Etsuko practices origami. The square papers she used have a side length of either 7.5 cm or 25.4 cm. Etsuko says the length of the larger paper is 32.9 cm greater than the length of the smaller paper
To find how many centimeters greater the length of the larger paper is than the length of the smaller paper, the lesser number of centimeters needs to be subtracted from the greater number of centimeters which gives the result that is 17.9cm. Etsuko is incorrect because 25.4 is greater than 7.5cm.
How much greater is the side length of the paper?The mathematical operation that would be used to determine how much greater the larger paper is compared to the smaller paper is subtraction. Subtraction is the process used to determine the difference between two or more numbers. The sign that is used to represent subtraction is -.
To subtract the numbers, the length of the longer paper would be subtracted from the shorter paper.
Difference in the length of the papers = 25.4 - 7.5 = 17.9cm
Etsuko is wrong because instead of subtracting the lengths, she added the lengths. Addition is used to determine the sum of two or more numbers.
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Answer:
It's easy,
To find how many centimeters greater the length of the larger paper is than the length of the smaller paper, the lesser number of centimeters needs to be subtracted from the greater number of centimeters, which gives a result that is between 7.5 and 25.4. Etsuko is not correct because 25.4 cm is 17.9 cm more than 7.5 cm.
Step-by-step explanation:
*Wish you luck on the test*
URGENT!!Given the function f(x) = 4x − 1 and the linear function g(x), which function has a greater slope? linear function increasing through 2 comma 3 and 3 comma 7 f(x) has a greater slope. g(x) has a greater slope. The slopes of f(x) and g(x) are the same. The slope of g(x) is undefined. WILL MARK BRAINLIEST!
The slopes of the linear function f(x) = 4x-1 is 4 and of the given linear function g(x) has also slope 4 . The option that the slopes of f(x) and g(x) are same is correct.
What is slope of a linear function?The slope of a linear function is the measure of steepness of the line traced by given linear function.
If a linear function is given by line y = mx +c then the slope is m
If a linear function passes through two given points (x₁, y₁) and (x₂, y₂), then its slope is (y₂ - y₁)/(x₂ - x₁)
Given the function f(x) = 4x -1 then comparing it to the form f(x) = mx + c
Slope of f(x) = m = 4
If it is given that g(x) is increasing through (2,3) and (3,7)
Then the slope of g(x) = (7- 3)/(3-2) = 4/1 = 4
Therefore, Slopes of both f(x) ang g(x) is 4.
Thus, the slopes of f(x) and g(x) are the same.
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Answer:
The answer is they are the same. Just took the test Your welcome!
Step-by-step explanation:
A 99-inch candle burns down in 12 hours. At what rate does the candle burn, in inches per hour?
Hello There!
The answer you are looking for is **8.25**.
Explanation:
If you do 8.25*12, you will get 99.
```Fact checking:
8.25*2= 16.50
8.25*4= 33.00
8.25*6= 49.50
8.25*8= 66.00
8.25*10= 82.50
and finally 8.25*12= 99.00
Since it is in inches- it would be 8 1/4in. or 20.955cm.
Hope this helps :)
Ukiah
Answer: 0.121212121
Step-by-step explanation: [tex]\frac{99}{1}[/tex]=[tex]\frac{12}{x}[/tex]
Cross multiply
99x= 12
divide both sides by 99
[tex]\frac{99x}{99} =\frac{12}{99}[/tex]
99 cancel 99 leaving x =[tex]\frac{12}{99}[/tex]=[tex]\frac{4}{33}[/tex]
in decimal
x= 0.121212121
whats are equivalents to 9y +5y +4y
A chemist is heating water so it can dissolve a larger amount of sodium chloride. The water's temperature increases 7°C each minute from an initial temperature of 21°C. How long will it take for the water to reach 49°C?
If water's temperature increases 7°C each minute from an initial temperature of 21°C. Then the time taken by the water to reach 49 degree Celsius is 4 minutes.
What is temperature?Temperature defines the atmosphere hotness. And it is expressed in different scales as well as in different parameters like Celsius etc. It is measured through the device known as thermometer.
According to the question, larger amount of sodium chloride is dissolved in the heating water. And the given data states that the water temperature increases 7 degree Celsius every minute.
Initial temperature of water is 21 degree Celsius.
Let us assume, water reaches at 49° C after 'x' minutes.
As per question, every minute temperature increases as 7°C. So, the expression can be written as: (21 + 7x)°C
⇒ 21 + 7x = 49
⇒x = 4 minutes
Hence, the time taken to reach 49° C is 4 minutes.
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/A and /B are vertical angles. If mA = (4x − 4)° and m/B = (5x – 29)°,
-
then find the measure of /A.
the measure of angle A is 96° when A and B are vertical angles.
We are given the two vertical angles as:
A = (4x − 4)° and B = (5x – 29)°
We know that, vertical angles are equal to each other.
So, we get that:
4 x - 4 = 5 x - 29
5 x - 4 x = 29 - 4
x = 25
A = 4 x - 4
A = 4 ( 25 ) - 4
A = 100 - 4
A = 96°
Therefore, the measure of angle A is 96° when A and B are vertical angles.
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(8 + 3²) x 3 quick asking 4 a friend
What is Point slope Form of
(2, 9); m= -2
Point-slope: y - 9= -2(x - 2)
Slope-intercept form (Just in case you need it): y = -2x + 13
The difference of two numbers is 29. The largest number is 3 more than twice the smallest number. What are the two numbers?
Group of answer choices
26 and 55
25 and 54
27 and 56
28 and 57
Answer:
x-x=29 answer is equal to 28and
Factor each expression completely. x²+4 x+4
The factoring of the expression x²+ 4x+4 is (x+2)²
To solve this exercise, we have to follow the rules of factoring:
x²+ 4x + 4
1. Looking for the a and b number that state the following equations:
a + b = 4a * b = 4Analyzing that (a*b) is a positive number, it means that (a) and (b) have the same signs.
The number could be:
a = 2
b = 2
Confirming:
a + b = 2 + 2 = 4
a * b = 2 * 2 = 4
2. Rewriting the factored expression (x+a)(x+b) with the obtained values, we get:
(x+2) (x+2)
3. Rewriting as the square of a binomial, we get:
(x+2)²
What is factoring?Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.
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The point J(4, – 4) is reflected over the y-axis. What are the coordinates of the resulting point, J'?
The coordinate of the resulting point J' is (-4, -4).
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the Coordinates.
The point is given as;
⇒ J (4, -4)
Now, The rule of the reflection of a point across the y-axis is equal to
(x, y) ⇒ (-x, y)
Hence, The coordinate of the resulting point J' after reflection over the y - axis of point J (4, -4) is,
(4, -4) ⇒ (-4, -4)
Hence, The coordinate of the resulting point J' is (-4, -4).
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Three pins are inserted into a cork mat at points c, e, and d. the three pins are collinear. how much string is needed to reach from the pin at e to the pin at d and then to the pin at c? leave your answer as a decimal to the nearest tenth.
Answer:2.7 - 1.1 = 1.6
What happens to the value of the expression 5/x+5 as x decreases
What happens to the value of this expression 5/x + 5 as x decreases from a large positive number to a small positive number is that: A. It increases.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
What is quotient?Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number. As a general rule, the smaller the divisor (denominator) of an expression, the larger would be the quotient.
Evaluating the given expression, we have:
When x = 3;
5/3 + 5 = 6.7
When x = 2;
5/2 + 5 = 7.5.
When x = 3;
5/1 + 5 = 10.
In conclusion, as x decreases from a large positive number to a small positive number in this expression 5/x + 5, its value would increase.
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Complete Question:
What happens to the value of the expression 5/x + 5 as x decreases from a large positive number to a small positive number? Choose 1 answer:
A. It increases.
B. It decreases.
C. It stays the same.
first person to answer gets brainliest
Given the dimensions of the shape, the length of PR can be found to be 19.8 units.
How to find the length of PR?The given triangle is an equilateral triangle which means that all the sides are equal.
That then means that:
PR = QR
So we can solve as:
2n + 9 = 7n - 18
Solving for n gives:
7n - 2n = 18 + 9
5n = 27
n = 5.4
The length of PR is therefore:
= 2n + 9
= 2 (5.4) + 9
= 19.8 units
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Classify each number as rational or irrational:
Help asap
[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\textsf{\textbf{Rational} and \textbf{Irrational} numbers}[/tex]
[tex].\qquad\bullet\textsf{\textbf{Rational} numbers can be written in fraction form, p/q.}\\.\qquad\bullet\textsf{\textbf{Rationals} can be \textbf{terminating} fractions.}[/tex]
[tex]\therefore[/tex]
[tex].\qquad\bullet\textsf{\textbf{Irrational} numbers \textbf{cannot} be written \textbf{as fractions.}}[/tex]
[tex]\textsf{These are the \textbf{rationals:}}[/tex]
[tex]\boldsymbol{\dfrac{11}{3}}[/tex]
[tex]\boldsymbol{0.01045}[/tex]
[tex]\boldsymbol{\sqrt{\dfrac{16}{81}} }[/tex]
[tex]\boldsymbol{6.25}[/tex]
[tex]\boldsymbol{0.\overline{42}\Leftarrow it's\:a\:terminating\:fraction}[/tex]
[tex]\textsf{These are the \textbf{irrationals:}}[/tex]
[tex]\boldsymbol{\sqrt{48}}[/tex]
[tex]\boldsymbol{16\pi}[/tex]
[tex]\boldsymbol{\sqrt{\dfrac{3}{16}} }[/tex]
[tex]\textsf{We come to the conclusion that there are more rationals than irrationals. \ddot\smile}[/tex] [tex]\ddot\smile[/tex]
[tex]\Large\overbrace{\underbrace{\boldsymbol{\rm{Reflection\:-RoSe}}}}^\star_\star[/tex]
A piece of ribbon of length 1m 10cm was cut off from a length 5m. What length remained?.
The length of ribbon that remained is 3m and 90 cm which is calculated by subtracting the cut length from the total length of the ribbon.
An arithmetic operation called subtraction simulates the process of removing items from a collection.
Subtraction can mean eliminating or lowering physical and abstract quantities utilizing a variety of things, such as negative integers, fractions, irrational numbers, vectors, decimals, functions, and matrices, however it is typically linked with natural numbers in mathematics.
The total length of the ribbon is is 5 meters or 500 centimeters. The length of the piece of ribbon that was cut is 1 m 10 cm=110 cm.
Length of the ribbon that remained is calculated by subtracting the total length form the cut off length 500-110 = 390 centimeters.
390 centimeters= 3 meters and 90 centimeters.
So the length that remained is 3 meters and 90 centimeters.
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Recycling Center A processes aluminum at a rate of 100 pounds per hour, while Recycling Center B processes aluminum at a rate of 2 tons per week. Assuming that both centers operate all day every day, which center processes aluminum faster, and why?
1: Recycling Center A processes aluminum faster; Recycling Center B’s rate is about 12 pounds per hour.
2: Recycling Center A processes aluminum faster; Recycling Center B’s rate is about 24 pounds per hour.
3: Recycling Center B processes aluminum faster; its rate is about 120 pounds per hour.
4: Recycling Center B processes aluminum faster; its rate is about 240 pounds per hour.
We need to know about unitary method to solve the given question. Option () is correct, Recycling Center A processes aluminium faster; Recycling Center B's rate is about 24 pounds per hour.
Unitary method is a method to find out the value for a single quantity and then derive the value for the asked quantity. Here is this question we know Center A processes aluminium at a rate of 100 pounds per hour and center B processes 2 tons per week, we need to know who processes aluminium faster. To find the answer we need to first find how much aluminium center B processes per hour, to find that we need to use unitary method.
1 ton=2000 pounds
so, 2tons=2x2000=4000 pounds
Thus Center B processes 4000 pounds per week
A day has 24 hours, a week has 7 days, we know that the centers operate all day every day so number of hours in a week is
7x24=168 hours
Center B processes 4000 pounds in 168 hours
Center B processes 4000/168 pounds in one hour
Center B processes about 24 pounds in one hour
Therefore, we can see that Center A processes aluminium faster and Center B's rate is about 24 pounds per hour, thus option (2) is right.
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choose all the values that are equivalent to -(5/3)
1. -5/3 2. 5/-3 3. 5/3 4. -5/-3 5. - (-5/3)
Fractions represent the parts of a whole or collection of objects. the equivalent fractions to -(5/3) are -5/3, 5/-3.
What is Fraction?Fractions represent the parts of a whole or collection of objects.
-(5/3) is a fraction, Actually it a improper fraction with negative sign.
The equivalent fractions are obtained by multiplying same sign or same number in numerator and denominator.
-(5/3) is equivalent to -5/3
-(5/3) is equivalent to 5/-3
-(5/3) is not equivalent to 5/-3
-(5/3) is not equivalent to -5/-3 because when negative and negative are multiplied the result will be positive but to be equivalent fraction it should be negative.
-(5/3) is not equivalent to -(-5/3) because when negative and negative are multiplied the result will be positive but to be equivalent fraction it should be negative.
Therefore the equivalent fractions to -(5/3) are -5/3, 5/-3.
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mai bought some party supplies from an online store.the shop charges a 7.95 shipping fee or 6.25%of the total purchase.whichever is greater.suppose Mai's total purchase is 128.how much shipping will she pay?
The required amount of shipping paid by Mai is 8.
What is percent?In mathematics, a percent is a number or ratio expressed as a fraction of 100. It is often denoted using percentage sign "%".
Now it is given that,
Amount of shipping fee = 7.95
percentage of shipping fee = 6.25% of the total purchase
Total amount purchased = 128
Thus, amount of shipping for this purchase is given as,
Amount of shipping = 6.25% of 128
Solving,
Amount of shipping = 0.0625*128 = 8
Since the shop charges shipping fees of whichever is greater
and 7.95 < 8
Thus, amount of shipping paid by Mai = 8
Thus, the required amount of shipping paid by Mai is 8.
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