No extraneous solution to the equation.
The equation is
[tex](x + 5)^{1/2}[/tex] - [tex](5 - 2x)^{1/4}[/tex] = 0
To know whether the equation is an extraneous solution we first need to find the value of x.
So we have,
[tex](x + 5)^{1/2} = (5 - 2x)^{1/4}[/tex]
Multiply both sides with the power of 4, then we have
[tex]((x+ 5)^{1/2})^{4}[/tex] = [tex]((5 - 2x)^{1/4} )^{4}[/tex]
[tex](x+ 5)^{2}[/tex] = 5 - 2x
[tex]x^{2}[/tex] + 10x + 25 = 5-2x
[tex]x^{2}[/tex] + 12x + 20= 0
[tex]x^{2}[/tex] + 10x + 2x + 20 = 0
x(x + 10 ) + 2(x + 10) = 0
(x + 10)(x+2) = 0
x = -10, -2
Now we have to put the value of x in the equation
x = -10
[tex](-10 + 5 )^{1/2}[/tex]-[tex](5 - 2 * -10)^{1/4}[/tex] = 0
[tex](-5)^{1/2}[/tex] - [tex]25^{1/4}[/tex]= 0
[tex](-5)^{1/2}[/tex] - [tex]5^{1/2}[/tex] = 0
Which has not possible as we don't have negative number in the square root.
x = -2
[tex](-2 + 5)^{1/2}[/tex] -[tex](5-2*-2)^{1/4}[/tex]=0
[tex]3^{1/2}[/tex]- [tex]9^{1/4}[/tex]=0
[tex]3^{1/2}[/tex]- [tex]3^{1/2}[/tex]=0
0 = 0
Therefore there is no extraneous solution to the equation
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Find the solution(s) to the system of equations. Select all that apply. y=x²-5 y=x-3
Answer:
x = 2, y = -1
x = -1, y = -4
Step-by-step explanation:
Both equations are equal to y, so just set x - 3 = x^2 - 5 and solve.
This diagram is a straightedge and compass construction. A is the center of one circle, and B is the center of the other. A rhombus is a quadrilateral with 4 congruent sides
Answer:
Step-by-step explanation:
Answer:
This diagram is a straight edge and compass construction . A is the centerof one circle , and B is the centre of the other . A rhombus is a quadrilateral with 4 congruent sides
Step-by-step explanation:
Need help ez question
Answer:
x = 0.25
Step-by-step explanation:
[tex]9\sqrt{x} =5-2x[/tex]
[tex]81x = 25 - 20x + 4x^{2}[/tex]
[tex]0=4x^{2} -101x+25[/tex]
[tex]0 = 4x^{2} -1x-100x+25[/tex]
[tex]0=x(4x-1)-25(4x-1)\\0=(x-25)(4x-1)[/tex]
[tex]x=25,\frac{1}{4}[/tex]
[tex]2*25+9\sqrt{25} =5\\50+9*5=5\\50+45=5\\95=5[/tex]
[tex]2*\frac{1}{4}+9\sqrt{\frac{1}{4} } =5 \\0.5+9*\frac{1}{2} =5\\0.5+4.5=5\\5=5[/tex]
Answer:
[tex]x=\dfrac{1}{4}[/tex]
Step-by-step explanation:
Given equation:
[tex]2x+9\sqrt{x}=5[/tex]
Subtract 2x from both sides to isolate the square root:
[tex]\implies 2x+9\sqrt{x}-2x=5-2x[/tex]
[tex]\implies 9\sqrt{x}=5-2x[/tex]
Square both sides to eliminate the square root:
[tex]\implies (9\sqrt{x})^2=(5-2x)^2[/tex]
[tex]\implies 81x=(5-2x)(5-2x)[/tex]
[tex]\implies 81x=25-20x+4x^2[/tex]
Subtract 81x from both sides:
[tex]\implies 81x-81x=25-20x+4x^2-81x[/tex]
[tex]\implies 0=25-101x+4x^2[/tex]
[tex]\implies4x^2-101x+25=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:
[tex]\implies ac=4 \cdot 25=100[/tex]
[tex]\implies b=-101[/tex]
Therefore, the two numbers are -1 and -100 as:
[tex]\implies -1 \cdot -100=100=a[/tex]
[tex]\implies -1+(-100)=-101 =b[/tex]
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies4x^2-x-100x+25=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(4x-1)-25(4x-1)=0[/tex]
Factor out the common term (4x - 1):
[tex]\implies (x-25)(4x-1)=0[/tex]
Apply the zero-product property:
[tex](x-25)=0 \implies x=25[/tex]
[tex](4x-1)=0 \implies x=\dfrac{1}{4}[/tex]
Input each solution into the original equation to check its validity:
[tex]\begin{aligned}x=25 \implies 2(25)+9\sqrt{25}&=5\\50+9(5)&=5\\50+45&=5\\95 & \neq 5\end{aligned}[/tex]
Therefore, x = 25 is not a valid solution.
[tex]\begin{aligned}x=\dfrac{1}{4}\implies 2\left(\dfrac{1}{4}\right)+9\sqrt{\dfrac{1}{4}}&=5\\\dfrac{1}{2}+9(\dfrac{1}{2})&=5\\\dfrac{1}{2}+\dfrac{9}{2}&=5\\\dfrac{10}{2}&=5\\5 & = 5\end{aligned}[/tex]
Therefore x = ¹/₄ is a valid solution.
Therefore, the only valid solution to the equation is x = ¹/₄.
What is the factored form of 2 x³+5 x²-12 x ?
(F) x(2 x-3)(x+4) (H) x(2 x+4)(x-3) (G) (2 x²-3)(x+4) (I) (2 x-4)(x+3)
After solving, the factors of equation 2x³+5x²-12x are:
(F) x(2x-3)(x+4)What basically is an equation?An equation is a mathematical statement composed of two representations joined by an equal sign.An example of an equation is 3x - 5 = 16. After attempting to solve this equation, we get the value for the variable x as x = 7.So,
Given the equation: 2x³+5x²-12x
Then,
2x³+5x²-12xx[2x²+5x-12]x[2x²+x( - )-12]x[2x²+x(8-3)-12]x[2x²+8x-3x-12]x[2x(x+4)-3(x+4)]Factors are: x(2x-3)(x+4)
Therefore, after solving, the factors of equation 2x³+5x²-12x are:
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How would I find the internal and external volume of something like this?
The figure consists of dodecahedrons having different edge length, e.
The external volume, [tex] V_{e}[/tex], is given by the formula;
[tex]V_e = \frac{15 + 7 \cdot \sqrt{5} }{4} \cdot {e_e}^{3} [/tex]The internal volume, [tex] V_{i}[/tex], is given by the formula;
[tex] V_i = \frac{15 + 7 \cdot \sqrt{5} }{4} \cdot {e_i}^{3} [/tex]What is the volume of a dodecahedron?The given figures consists of solids that are pentagonal faced.
The number of faces of the solid = 12
The shape of the solids are known as a dodecahedron
The formula for the external volume, [tex] V_{r}[/tex], is given as follows;
[tex]V_e = \frac{15 + 7 \cdot \sqrt{5} }{4} \cdot {e_e}^{3} [/tex]
Where;
[tex] e_{e}[/tex] = The length of the edges on the outside of the dodecahedron.
Given that the length of the edges on the inside are measured to be [tex] e_{i}[/tex], the internal volume is given by the formula;
[tex] V_i = \frac{15 + 7 \cdot \sqrt{5} }{4} \cdot {e_i}^{3} [/tex]
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Please help. Can you also please put the explanation?
Answer: she spent 40 minutes answering the phone calls
Step-by-step explanation:
Its 40 minutes because she spends 20 minutes delivering flowers and she worked at the hospital for 60 minutes that day. So, if you take away the 20 minutes for the 60 minutes, she spent she will only have 40 minutes left to answer calls.
Marsha pays $20 each month for a car wash membership. Which of the following represents the total amount subtracted from her account after 6 months of having the membership?
Evaluate the expression 2x² - 4 when x = -3.
Answer: 32
Step-by-step explanation: 2(-3)2. -4
I’m really stuck on my homework. I’ll give brainliest to anyone willing to help me questions 22-33. Thank you!
A rental car agency charges $170 per week plus $0.25 per mile to rent a car. How many miles can you travel in one week for $330?
Find the sum of the first 46 terms of the following series, to the nearest integer
12, 15, 18
Answer: 3657
Step-by-step explanation:
18-15=3
15-12=3
3 ==> rate of change per term
3*46=138
138-3=135
135+12=147 ==> 46th term
Now find the average of the first and 46th term of the sequence:
(147+12)/2=
159/2=79.5
Now multiply the average by 46 to find the sum of the sequence.
79.5*46=
159*23=3657 ==> sum of 46 terms
What is the equation of a line that passes through the point (2,−2) and is perpendicular to y=x4−3 ?
The equation of a line perpendicular to y = 4x - 3 that passes through the point (2,-2) is y = -1/3x - 3/2
How to find the equation of the perpendicular line?The equation of the line is given as
y = 4x - 3
Rewrite the equation as
y = 4x - 3
A linear equation is represented as
y = mx + c
Where
Slope = m
So, we have
m = 4
The slopes of perpendicular lines are opposite reciprocals
This means that
m2 = -1/m1
So, we have
m = -1/4
Evaluate
m = -1/4
The equation of the perpendicular line is then calculated as
y = m(x - x1) + y1
Where
(x1, y1) = (2, -2)
This gives
y = -1/4(x - 2) - 2
Evaluate
y = -1/3x + 1/2 - 2
Evaluate the sum and the difference
y = -1/3x - 3/2
So, the equation of a line perpendicular to y = 4x - 3 that passes through the point (2,-2) is y = -1/3x - 3/2
Hence, the required equation of a line perpendicular to y = 4x - 3 that passes through the point (2,-2) is y = -1/3x - 3/2
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can someone please explain how to find the quotient of 405/27 fraction using long division? :)
The quotient of 405/27 fraction using division is 15.
How to calculate the fraction?It should be noted that the information is simply to divide the numbers.
In this case, the numerator is 405 and the denominator is 27
Therefore, the quotient based on the information illustrated will be:
= 405 / 27
= 15
Therefore, the quotient is 15.
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Number 15. Find MN please! I do give brainliest!
Answer:
MN = 5
Step-by-step explanation:
From inspection of the given diagram:
[tex]\textsf{MN = $2.5x$}[/tex][tex]\textsf{NR = $x$}[/tex][tex]\textsf{MNR = $5x - 3$}[/tex]Therefore:
[tex]\implies \sf MN+NR=MNR[/tex]
[tex]\implies 2.5x+x=5x-3[/tex]
[tex]\implies 3.5x=5x-3[/tex]
Add 3 to both sides:
[tex]\implies 3.5x+3=5x-3+3[/tex]
[tex]\implies 3.5x+3=5x[/tex]
Subtract 3.5x from both sides:
[tex]\implies 3.5x+3-3.5x=5x-3.5x[/tex]
[tex]\implies 3=1.5x[/tex]
[tex]\implies 1.5x=3[/tex]
Divide both sides by 1.5:
[tex]\implies 1.5x \div 1.5=3 \div 1.5[/tex]
[tex]\implies x=2[/tex]
Substitute the found value of x into the expression for MN:
[tex]\implies \textsf{MN}=2.5(2)[/tex]
[tex]\implies \textsf{MN}=5[/tex]
In advertising, the decay factor describes how an advertisement loses its effectiveness over time. In math, would you expect a decay factor to increase or decrease the value of y as x increases?
When the value of x will increase then decay factor will decrease the value of y.
Given that the decay factor describes how an advertisement loses its effectiveness over time.
Exponential decay will tell us the process of reducing an amount by a consistent percentage of rate over a particular period of time. Exponential decay is the reciprocal of exponential growth when a quantity decreases by the same factor in equal intervals of time, the constant coefficient of the exponential decay function is less than 1. This can be expressed as (1 - r) and is called the decay factor.
According to the definition of the decay factor, its say that when the value of x increases then the decay factor of the value of y will decrease.
Hence, the value of x will increase then decay factor will decrease the value of y.
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A highway agent sampled cars going from one state to a neighboring state. In his report, he indicated that of the 93 cars sampled,
36 cars were driven by women, 56 cars were sport-utility vehicles, 47 cars had two or more passengers, 28 cars were driven by
women in sport-utility vehicles, 27 cars were driven by women and had two or more passengers, 22 cars were sport-utility vehicles
and had two or more passengers, and 16 cars were driven by women in sport-utility vehicles and had two or more passengers.
After his supervisor reads the report, she explains to the agent that he made a mistake. Explain how his supervisor knew that the
agent's report contained an error.
Select the correct choice below and fill in the answer box to complete your choice.
(Type a whole number.)
OA. The agent's last four statements indicate that at least
cars were driven by women. This contradicts the agent's first
statement, which says that only 36 such cars were seen.
OB. The agent's first three statements indicate that at least
or more passengers. This contradicts the agent's seventh
OC. The agent's last four statements indicate that at least cars were sport-utility vehicles. This contradicts the agent's
second statement, which says that only 56 such cars were seen.
cars were driven by women in sport-utility vehicles and had two
statement, which says that only 16 such cars were seen.
Does the table represent an exponential function
x1234
y 39 27 81
Ono
Oyes
Answer:
No.
Step-by-step explanation:
Is the equation y=x+1 / x²+1 in simplest form? Explain how you can tell.
According to the question, the equation [tex]\frac{x+1}{x^{2} +1}[/tex] is the algebraic equation as well as polynomial equation. Using square root principles, the equation can be re-write.
The factors of the denominator term is not possible and it cannot be simplified. And the simplification is possible with the concept of complex number.
What is polynomial expression?
Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.
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Select the locations on the number line to plot the points −2 , −11 , and −17 .
Number Line :
In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length. A number line can be extended infinitely in any direction and is usually represented horizontally.
or
A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.
On a number line, a number on the left is always less than a number on the right. Similarly, a number on the right is always greater than a number on the left.
The Number Line app helps students visualize number sequences and illustrate strategies for counting, comparing, adding, subtracting, multiplying, and dividing. Choose number lines labeled with whole numbers, fractions, decimals, or negative numbers. Or use a custom number line, with or without tick marks, and set your own interval.
Show intervals between points on the line using forward or backward jumps above and below the line. Jumps can also be labeled with their values or left blank. Add custom tick marks to the number line to show equivalence or compare number values.
Basic Number Line Skills:
1. Find the dot marked on a number (and name the dot)
2. Place a dot at the desired location
3. Find the desired number below the number line’s tick mark*
-17 -11 -2 0
-----|-----------------|----------|----------------|-----------------------------------------------Number line
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Rate my art HONESTLY
It’s Queen Elizabeth II pointillism
Any tips on how to fix her neck are appreciated
I would say avoid adding any more detail to the eyes and facial features. normally pointillism uses alot more dots and makes them most concentrated in darker areas. i would recommend trying to add shadows to most of it or adding more detail to the hat. Ii think her neck looks ok but there isn't really a way to get rid of the diagonal that you made.
Answer:
I think its great! I think add more hair to the side of head there. other than that it resembles her quite nicely!
Step-by-step explanation:
Vertical 1.
3+ 12, an incomplete mathematical sentence.
Addition 3+ 12, an incomplete mathematical sentence. 1.3+ 12=13.3
Addition is a mathematical procedure that is used to add numbers. The sum of the given numbers is the result of adding the given numbers. For instance, if we add 2 and 3, (2 + 3), the result is 5. We used the addition function on two numbers, 2 and 3, to produce the sum, 5
Symbol for Addition
Different symbols are used in mathematics. One of the most used arithmetic symbols is the addition symbol. We read about adding two numbers, 2 and 3, in the definition of addition above. If we look at the addition pattern (2 + 3 = 5), the symbol (+) joins and completes the two integers.
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I need help. 2(x + 6) = 2x + 12
My friend Yoy decided to buy some vreels and totts. Altogether, he
planned to buy 10 items.
Write an equation in standard form showing the relationship between
vreels (x) and totts (y).
Answer:
x + y = 10
Step-by-step explanation:
Solve the following proportion by cross multiplying: ( x + 2 ) / 6 = ( x - 4 ) / 3
The following proportion by cross multiplying:
( x + 2 ) / 6 = ( x - 4 ) / 3 is -19
Given:
( x + 2 ) / 6 = ( x - 4 ) / 3
( x + 2 )=2(x-4)
x+2=2x-8
x=-10
If the ratio between the first and second amounts is identical to the ratio between the second and third, the three quantities are said to be in continuing proportion. Similarly, the ratio between the first and second amounts in a continuous proportion will be equal to the ratio between the third and fourth.
Consider the following two ratios: a:b and c:d. We shall convert the means of the two specified ratio terms to a single term/number in order to get the ongoing proportion.
This is the LCM of means in general, and for the given ratio, the LCM of b & c is bc. As a result of multiplying the first ratio by c and the second ratio b.
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A trapezoid has sides of length 19.5 centimeters, 16.9 centimeters, 19.5 centimeters, and 18
centimeters. What is the perimeter?
centimeters
the answer is correct because you gave text evidence
To rationalize the denominator of 4√4/25, by what number would you multiply the numerator and denominator of the fraction?
Rationalization is multiplying a surd by another similar surd to obtain a rational number. In mathematics, a surd is an expression involving a square, cube, or another kind of root symbol. The surd used for multiplication is called the rationalization factor (RF). Rationalize the denominator to make it easier to perform calculations with rational numbers. Rationalizing a denominator with a fraction removes all root terms, such as square roots and cube roots, from the denominator.
[tex]\frac{4}{\sqrt{\frac{4}{25}}}[/tex]
[tex]\begin{aligned}&\frac{4}{\frac{\sqrt{4}}{\sqrt{25}}}\\&\frac{\frac{4}{\sqrt{2^2}}}{\sqrt{5^2}}\end{aligned}[/tex]
[tex]\frac{4}{\frac{\sqrt{2^2}}{\sqrt{5^2}}}[/tex]
[tex]\frac{4}{\frac{2}{5}}[/tex]
[tex]\begin{aligned}&4 \div \frac{2}{5} \\&4\left(\frac{5}{2}\right) \\&\frac{4 \cdot 5}{2} \\&2 \cdot 5\end{aligned}[/tex]
[tex]10[/tex]
And if the question is like this,
[tex]$\frac{4 \cdot \sqrt{4}}{25}$$\frac{4 \cdot \sqrt{2^2}}{25}$$\frac{8}{25}$[/tex]
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If lindley requests an extension to file her individual tax return in a timely manner, the latest she could pay her tax due without penalty is::_________
If Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is April 15th.
What is an individual tax return?A person or married couple must submit an official form known as an individual tax return to a federal, state, or local taxing authority in order to record any taxable income they received within a certain time period, typically the previous year.
This document is used to determine how much tax was paid in excess of what was required during that time period.
In this case, if Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is April 15th.
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If Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is:
April 15th.
October 15th.
August 15th.
November 15th.
None of the choices are correct.
Put the correct number in each box
1/7=4/? = ?/56
The table shows the total distance that Myra runs over different time periods.
A 2-column table with 5 rows titled Time and Distance Ran by Myra. The first column is labeled Time (minutes) with entries 0, 2, 4, 6, 8. The second column is labeled Distance (miles) with entries 0.0, 0.4, 0.8, 1.2, 1.6.
Which describes Myra’s distance as time increases?
increasing
decreasing
zero
constant
The option that describes Myra’s distance as time increases is increasing.
What is the change in Myra's distance?
Looking at the table provided, it can be seen that as time passes, the distance ran by Myra increases. It can be seen that distance increases from 0.4miles to 0.8 miles when time increases from 2 seconds to 4 seconds.
Change in distance run per time = change in distance / change in time
(0.4 - 0) / (2 - 0)
0.4 / 2 = 0.2
Myra's distance increases by 0.2 per second. This means that Myra is running at a constant speed. Thus, the rate of the increase in the distance run by Myra is a constant 0.2 per second.
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Answer:
the answer is increasing
The number line shows the distance in meters of two birds, A and B, from a worm located at point X:
Part A: Expression for the distance in meters between given two birds using subtraction = 2.5 - (-2.5)
Part B: The distance between two birds using additive inverse 2.5- (-2.5) =5 meters
What is an expression and additive inverse?An expression is an combination of numbers and mathematical operations such as addition, subtraction, division and multiplication with equating any two terms.
Additive inverse : Additive inverse of an number a is the number that when adds to a gives zero .
Let b be additive inverse of a, then a + b =0
Then, b = -a
Given two birds A and B are at points x= -2.5 and y = 2.5 respectively
Therefore, the expression for the distance in between given two birds
= y - x = 2.5- (-2.5)
We an clearly see that -2.5 is additive inverse of 2.5
Distance between the two birds = 2.5 -(-2.5) =2.5 +2.5 = 5 meters
Therefore, the expression for distance between the two birds A and B is 2.5-(-2.5) and the distance is 5 meters.
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