The correct answer of the question is {-1+√61}/ 10 or {-1-√61}/ 10 .
The given quadratic equation is 5 x²+x=3
First, we have to convert the equation in the form
ax² + bx + c = 0, then apply the quadratic formula i.e.
x = {-b±√(b²- 4ac)}/ 2a .
Now,
5 x²+x=3
⇒ 5 x²+ x - 3 = 0
Here, a = 5, b = 1 and c = -3
Now, applying quadratic formula
{-b±√(b²- 4ac)}/ 2a
= {-1±√(1²- 4 × 5 × -3)}/ (2 × 5)
= {-1±√(1 + 60)}/ 10
= {-1±√61}/ 10
= {-1+√61}/ 10 or {-1-√61}/ 10
Therefore the final answer to the given equation is is {-1+√61}/ 10 or {-1-√61}/ 10 .
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Tristan wants to build a square garden in his backyard that will cover an area of 75ft(squared). If Tristan has 32 feet of material for the perimeter of the garden, does he have enough? Explain
The 32 feet of the material for the perimeter of the garden is not enough as the perimeter of the garden is 34.64 feet.
We are given that:
Area of a square garden = 75 feet²
Let the side of the square garden be x
x² = 75
x = √ 75
x = 5 √3 feet
Perimeter of the square garden = 4 × x feet
Perimeter = 4 × 5 √ 3 feet
Perimeter = 20 √ 3 feet
P = 34.64 feet.
Now, Tristan only has 32 feet of material.
So, the material is not enough.
Therefore, we get that, the 32 feet of the material for the perimeter of the garden is not enough as the perimeter of the garden is 34.64 feet.
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What is the solution of √x+2=x ?
After the solution, the value of x for the equation √x+2 = x is 2.
What, accurately, is an equation?An equation is a mathematical statement composed of two representations joined by an equal sign.An example of an equation would be 3x - 5 = 16.After solving this equation, we get the value for the variable x as x = 7.So,
Given the equation: √x+2 = x
Then,
To get a quadratic, square it:
x+2=x²x²-x-2=0Quadratic formula:
x=1/2(1±√1+8)x=1/2(1±3)x=-1, 2However, when we square in our work, we must ensure that we haven't accidentally introduced extra roots.
In this case, -1 is not a solution to the original equation, whereas 2 is.
Therefore, after the solution, the value of x for the equation √x+2 = x is 2.
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A scientist captures a sample of fish from 100 different locations along the
Yellowstone river and measures the proportion of fish affected by copper toxicity for
each sample. Describe how the scientist could use the data to estimate the
proportion of fish affected by copper toxicity in the entire population along this
portion of the river.
It should be noted that the scientist could use the data to estimate the proportion of fish affected by copper toxicity in the entire population along this portion of the river by dividing the number of fishes affected by the fishes collected
How to illustrate the information?Let the number of fish collected in sample be represented as N.
Let the number of fish affected in it be represented by X.
Therefore, the proportion will be;
= X/N
Therefore, this can be used by the scientist to estimate the proportion of fish affected by copper toxicity in the entire population.
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Hi i need the explanation for this question in the photo asap!!!!!!
The prices of two different brands of hot
chocolate are shown below.
What is the difference in price between the two
brands when buying 800 g of hot chocolate?
Give your answer in pounds (£).
Brand A
HOT
CHOCOLATE
£2.85
160 g
Brand B
HOT
CHOCOLATE
£3.40
200 g
The difference in price between the two brands when buying 800 g of hot chocolate is 0.
What is arithmetic operation?
A field of mathematics known as arithmetic operations deals with the study of numbers and the operations on those numbers that are relevant to all other branches of mathematics. The basic operations included in it are addition, subtraction, multiplication, and division.
For brand A
For 160g of hot chocolate is $2.85
For 1g of hot chocolate is 2.85/160
For 800g of hot chocolate is [tex]\frac{2.85}{160} \times 800[/tex]
= 2.85 [tex]\times[/tex] 5
= $14
For brand B
For 200g of hot chocolate is $3.40
For 1g of hot chocolate is 3.40/200
For 800g of hot chocolate is [tex]\frac{3.40}{200} \times 800[/tex]
= 3.40 [tex]\times[/tex] 4
= $14
Difference of brand A and brand B of hot chocolate of 800g is $14 - $14 = 0.
Therefore, the difference in price between the two brands when buying 800 g of hot chocolate is 0.
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9 - 3x + x - 15 combining like terms
Hey there!
9 - 3x + x - 15
= 9 - 3x + 1x - 15
COMBINE the LIKE TERMS
= (9 - 15) + (-3x + 1x)
= (-3x + 1x) + (9 - 15)
= (-3x + x) + (9 - 15)
= -3x - x + 9 - 15
= -2x - 6
Therefore, your answer should be:
-2x - 6
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Which one of the following points lies on the line 3y=2x-1?
The graph given below y = -x + 2 have a negative slope and a positive y intercept. The point (2, 1) lies on the line 3y = 2x - 1
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. 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 graph given below have a negative slope and a positive y intercept. The graph is given by y = -x + 2
Given the equation
3y = 2x - 1
When x = 2:
3y = 2(2) - 1
y = 1
Therefore, The point (2, 1) lies on the given line 3y = 2x - 1
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which trinomials are perfect square trinomials? select each correct answer. m2 10m 100 m squared plus 10 m plus 100 m2 36m 60 m squared plus 36 m plus 60 m2 10m 25 m squared plus 10 m plus 25 m2 24m 144 m squared plus 24 m plus 144 skip to navigation
Answer:
You can use the definition of perfect square trinomials to find which of the given trinomials are perfect squares.
The trinomials which are perfect squares are:
Option B:
Option D:
What are perfect squares trinomials?
They are those expressions which are found by squaring binomial expressions.
How to find which of the given trinomials are perfect square trinomials?
Since the given trinomials are with degree 2, thus, if they are perfect square, the binomial which was used to make them must be linear.
Let the binomial term was am + b(a linear expression is always writable in this form where a and b are constants and m is a variable), then we will obtain:
Checking all options:
Option A:
Comparing it with the standard form we obtained, we have:
Option B:
Comparing it with the standard form we obtained, we have:
Thus, this trinomial is perfect squares trinomial.
Option C:
Comparing it with the standard form we obtained, we have:
Option D:
Comparing it with the standard form we obtained, we have:
Thus, this trinomial is perfect squares trinomial.
Thus,
The trinomials which are perfect squares are:
Option B:
Option D:
Step-by-step explanation:
Use a table to solve each equation. Round to the nearest hundredth.
5²x=56
[tex]5^{2x}[/tex] = 56 => x = 1.252, 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]5^{2x}[/tex] = 56
Taking logarithm on both sides:
=>log([tex]5^{2x}[/tex]) = log (56)
As [tex]log_b(a)^m = m (log_b(a))[/tex],
=> 2x ( log 5) = log (56)
=> 2x = [tex]\frac{log56}{log5}[/tex]
=> 2x = [tex]\frac{1.748}{0.698}[/tex]
=> 2x = 2.504
=> x= 1.252
Hence, [tex]5^{2x}[/tex] = 56 => x = 1.252, by properties of logarithm.
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Write each expression in simplest form. ∛125 x⁶ - ∛27 x⁶
The simplified expression after solving the given equation is 2 [tex]x^{6}[/tex] .
The given expression is,
[tex]\sqrt[3]{125}[/tex] x⁶ - [tex]\sqrt[3]{27}[/tex] x⁶ equation 1
Name the given expression as equation 1.
To simplify the given expression first we need to solve step wise,
[tex]\sqrt[3]{125}[/tex] = [tex]\sqrt[3]{25.25.25}[/tex] = 5
[tex]\sqrt[3]{27}[/tex] = [tex]\sqrt[3]{3.3.3}[/tex] = 3
Now, we need to substitute the above solved values in equation 1 and after substituting them we can write as follows:
[tex]\sqrt[3]{125}[/tex] x⁶ - [tex]\sqrt[3]{27}[/tex] x⁶ = 5[tex]x^{6}[/tex] - 3[tex]x^{6}[/tex]
On further simplifying, we will get
[tex]\sqrt[3]{125}[/tex] x⁶ - [tex]\sqrt[3]{27}[/tex] x⁶ = 2[tex]x^{6}[/tex]
Thus we can write that the simplified expression after solving the given equation is 2 [tex]x^{6}[/tex] .
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Which temperature is hottest?
-32°C
-34°C
33°C
31°C
Answer:
Step-by-step explanation:
33
Dilate (9, 9) using a scale factor of 1/3
after dilating the point ( 9 , 9 ), we get the point as ( 3 , 3 ) with the scale factor as 1 / 3.
We are given a point:
( 9 , 9 )
We have the scale factor as:
1 / 3
We need to dilate the point using the scale factor.
So, we get that:
( 9 × 1 / 3 , 9 × 1 / 3 )
= ( 3 , 3 )
Therefore, after dilating the point ( 9 , 9 ), we get the point as ( 3 , 3 ) with the scale factor as 1 / 3.
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Use long division to convert 11/20 to a decimal.
It should be noted that converting 11/20 to a decimal through division will gives 0.55.
How to illustrate the information?This can be illustrated as follows. It should be noted that the quotient is the value obtained by dividing one value by another. The quotient is 11.
The divisor is the value that divides. It should be noted that in this case, this is illustrated as 20.
It should be noted that 11 is the numerator and 20 is the denominator.
Therefore, it should be noted that converting 11/20 to a decimal through division will gives 0.55.
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Find a value of 3x-2 when x =4
If x=4, then substitute x for 4, multiply by 3 since 3 was being multiplied by x, then subtract 2, which gets you 10
Finn and Gabby are selling raffle tickets for a school fundraiser. If Gabby sold 17 fewer raffle tickets than Finn did, which of the following represents the relationship between f, the number of tickets Finn sold and g, the number of tickets Gabby sold?
A. f + g = 17
B. f - g = 17
C. fg = 17
D. f/g = 17
Answer:
B. f - g = 17
plot the point in a coordinate plane then determine whether AB and CD are congruent A(-2, 1), B(2, 1), C(3, 2), D(3, -2).
For the given points, As the distance of AB and CD is same, So AB and CD are congruent.
What are congruent lines?If and only if their lengths are identical, any two line segments are congruent. The length of the line segment AB is identical to the length of the line segment CD in the aforementioned representations. Consequently, the two line segments AB and CD are similar.
length of AB = √(2+2)² + (1-1)² = 2
length of CD = √(3-3)² + (2+2)² = 2
As the value of AB = CD So, we can say that AB and CD are congruent.
Graph is attached at the end.
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PLEASE ANSWER PLEASEEEEEEEEEEEEEEEEEEEEE
32 meters
18 meters
8 meters
6 meters
Answer:
18 meters
Step-by-step explanation:
24 is dilated by 3/4
Which means 24 * 3/4 or 24 * .75
i t h i n k
PLEASE HELP IMMEDIATELY
Answer: 55 degrees
Step-by-step explanation: If the Whole is 180 and you subtract 125 degrees you are left with 55.
earle bailey has 20 songs to choose from but can play only 7 in the next half‑hour on siriusxm classic vinyl. how many different (ordered) playlists are possible? (use decimal notation. give your answer as an exact number.)
The answer is 77520.
What is meant by decimal notation?Decimal notation is an alternative way to represent fractional values in mathematics. This indicates that base 10 is being used for the fractional representation. Both the fractions and decimals can be transformed. For instance, the decimal representation of the fraction 5/10 is 0.5.Any value between 1.0 and 10.0 that can be expressed as a decimal number and multiplied by a power of 10 is considered standard form. If you look closely, you will see that 1.23 is a decimal between 1.0 and 10.0, and as a result, we have the standard form of 123,000,000 as 1.23 108.Because they represent a portion of a whole number, decimals are equivalent. The distinction is that fractions and decimals are written using different notations. We can visually estimate how much of a full number we are working with thanks to decimal notation.How many different (ordered) playlists are possible?
Number of possible playlists = 77520
Explanation:
Total number of songs = 20
Songs in the playlist = 7
So, we need to select 7 songs out of 20. This can be done using combinations.
n = 20 , r=7
C( n , r ) = ?
C( n , r ) = C (20 , 7)
= 20! / ( 7! (20-7)!)
= 20! / ( 7! × 13! )
= 77520
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the first 5 terms are -16,-7,2,11,20 what is the eighth number in this sequence
Answer:
29
Step-by-step explanation:
to get from -16 to -7 you have to add 9
to get from -7 to 2 you have to add 9
to get from 2 to 11 you have to add 9
and the same thing for 11 to 20
Answer: The answer
is 29 because the pattern of the number is 999999
Step-by-step explanation:
if there are "n" packets of Jelly tots. The chocolates are three more than 4 times the Jelly Tots Write down an algebraic expression for the number of chocolates.
Answer:
3+(4x)
Step-by-step explanation:
The algebraic expression will be written as:
x=jelly tots
The number of chocolates=3+(4×x)
=3+(4x)
The algebraic expression for the number of chocolates is 4n + 3 where n is number of packets of Jelly Tots.
Let's use variables to represent the number of Jelly Tots and chocolates:
Let "n" be the number of packets of Jelly Tots.
Now, the number of chocolates is three more than 4 times the number of Jelly Tots.
So, represent the number of chocolates as:
Number of chocolates = 4 * n + 3
4 * n represents 4 times the number of Jelly Tots.
Multiplying the number of Jelly Tots by 4 gives us the chocolates without the additional 3.
- +3 represents the additional chocolates.
Thus, the algebraic expression is 4n + 3.
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which answer choice repsents the quotient of 98,673 divided by 222
Answer: I can't see the answer choices but 98,673 divided by 222 is 444.5
hope this helps :)
Helppp MEEEEE PLSSSSSS ⁉️⁉️❓❓❓❓❓❓
A) a
B) 0
C) 1
D)2
E)c
======================================================
Explanation:
The general quadratic ax^2+bx+c = 0 has these properties
sum of the roots = -b/aproduct of the roots = c/aFor more information, check out Vieta's formulas.
If we flip the bx term to -bx, thereby getting ax^2-bx+c = 0, then we have these properties
sum of the roots = b/aproduct of the roots = c/aWe're told the sum and product of the roots are the same
b/a = c/a
b = c
Example:
The equation x^2-10x+10=0 has the sum of the roots equal to 10, and the product of the roots is also 10. You can use the quadratic formula to confirm this.
Answer:
12
Step-by-step explanation:
good right? if not then your question was wrong
Use the properties of exponential and logarithmic functions to solve each system. Check your answers.
y=2 x⁺⁴
y-4x⁻¹=0
The solved logarithmic functions are log y = log 2 + 4 log x and log y = 2 log 2 - log x for y = 2x⁺⁴ and y - 4x⁻¹ = 0 respectively.
What is a logarithmic and exponential function?
Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet, e. For example log 10 = 1 and e^2.
Solving the given expressions: y = 2x⁺⁴, y - 4x⁻¹ = 0
Applying given properties of logarithmic and exponential function;
log a + log b = log (ab)
4 log x = log x⁴
e^(log x) = 1
e^(x + y) = (e^x) × (e^y)
Take expression y = 2x⁺⁴
Applying log on both sides, we get,
log y = log (2x⁺⁴)
log y = log 2 + log x⁺⁴
log y = log 2 + 4 log x
To Check Results,
Taking exponential,
y = e^[log 2 + 4 log x]
y = e^(log 2) × e^[4 log (x)]
y = 2 × e^(log x⁴)
y = 2x⁴
Thus, the answer is verified.
Take expression y - 4x⁻¹ = 0
Applying log on both sides, we get,
log y = log (4x⁻¹)
log y = log 4 + log x⁻¹
log y = 2 log 2 - log x
To Check Results,
Taking exponential,
y = e^[2 log 2 - log x]
y = e^(2 log 2) × e^[-log (x)]
y = e^(log 4) × e^(log x⁻¹)
y = 4x⁻¹
y - 4 x⁻¹ = 0
Thus, the answer is verified.
Hence, the solved expression is log y = log 2 + 4 log x and log y = 2 log 2 - log x for y = 2x⁺⁴ and y - 4x⁻¹ = 0 respectively.
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For what positive integers n are the domain and range of y=n√x the set of real numbers? Assume that x is a real number.
The domain and range will be a set of all real numbers for all the odd positive integers.
In its simplest form the domain is all the values that go into a function, that is the values for which function is defined and the range is all the values that come out that is the result obtained by putting all the domain valuesWe can write given equation as y² =n²x
if we Put even value of n then we get function similar to y²=x which does not match with the given question
If we put the odd value of n then we get function similar to y³ = x which match with the given question.
Hence the domain and range will be a set of all real numbers for all the odd positive integers.
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Ray QS bisects Angle PQR and m of Angle RQS = 71 °
Find m of Angle PQS and m of Angle PQR
The measure of the ∠PQS will be 71° , and the measure of the ∠PQR will be 142°.
What is an angle bisector ?
The angle bisector is the line or line segment that divides the angle into two identical portions.
Given that line, QS is bisecting the angle PQR into two angles RQS and PQS.
We know that the angle bisector bisects the two angles into two equal halves , i.e.,
∠ PQS = ∠ RQS
So ; the measure of ∠ PQS will be :
∠ PQS = 71°
So , if we want to calculate the measure of ∠PQR then it can be represented as the sum of two angles.
∠ PQR = ∠PQS + ∠RQS
or
∠PQR = 71° + 71°
or
PQR = 142°
Therefore, the measure of the ∠PQS will be 71° , and the measure of the ∠PQR will be 142°.
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Which statement about the ordered pairs (-9, 3) and (2, -4) is true for the equation 6x=14? 2
Both ordered pairs are solutions.
(-9, 3) is a solution to the equation.
Neither ordered pair is a solution.
(2, 4) is a solution to the equation.
Answer:
neither ordered pair is a solution
Step-by-step explanation:
to determine if the pairs are a solution, substitute the x- coordinate into the left side of the equation and if equal to the right side then they are a solution.
(- 9, 3 ) with x = - 9
6(- 9) = - 54 ≠ 14 ← not a solution
(2, - 4 ) with x = 2
6(2) = 12 ≠ 14 ← not a solution
6x^2-5xy-6y^2
factor it
Step-by-step explanation:
Answer:
(3x + 2y) (2x - 3y)
Step-by-step explanation:
Check it using the FOIL method - first times first, outer times outer, inner times inner, last times last
Pls help this assignment is due today! I will give brainliest!
Answer:
Step-by-step explanation:
The slope is defined as the ratio of the “rise” divided by the “run” between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line.
The inclination of a straight line is the angle that the line makes with the positive direction of the x-axis. The tangent of the angle that a line makes with the positive direction of the x-axis is called the slope or gradient of the line. The slope of a line is generally denoted by m.
Given two points (x1, y1) and (x2, y2) on a line, the slope m of the line is y = (y2 – y1)/(x2 – x1)
The slope-intercept form of a line is given by y = mx + b gives the slope of line m and the y-intercept of line b. The inclination of the line with the horizontal axis is called the slope of the line. The point at which the curve cuts or crosses the y – axis is called the y-intercept.
estimate 1624 divided by 23 using compatible numbers
The estimate of the quotient 1624 divided by 23 using compatible numbers is 81
How to estimate the quotient of the numbers using compatible numbersThe quotient of numbers is the result of dividing the numbers
The statement is given as
1624 divided by 23 using compatible numbers
The expression can be represented as:
1624 ÷ 23
Using compatible numbers, 1624 can be estimated as 1620, while 23 can be estimated as 200:
So, the expression becomes
1624 ÷ 23 = 1620 ÷ 20
Next, we divide the estimated numbers
So, we have
1624 ÷ 23 = 81
Hence, the estimate of the quotient 1624 divided by 23 using compatible numbers is 81
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