Answer:
[tex]\large\boxed{x=\dfrac{-9\pm\sqrt{41}}{2}}[/tex]
Step-by-step explanation:
[tex]\text{The quadratic formula of}[/tex]
[tex]ax^2+bx+c=0[/tex]
[tex]\text{If}\ b^2-4a<0,\ \text{then the equation has no solution}\\\\\text{If}\ b^2-4ac=0,\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}\\\\\text{If}\ b^2-4ac>0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\=========================================[/tex]
[tex]\text{We have}\ x^2+9x+10=0\\\\a=1,\ b=9,\ c=10\\\\\text{substitute:}\\\\b^2-4ac=9^2-4(1)(10)=81-40=41>0\qquad _{\text{two solutions}}\\\\\sqrt{b^2-4ac}=\sqrt{41}\\\\x=\dfrac{-9\pm\sqrt{41}}{2(1)}=\dfrac{-9\pm\sqrt{41}}{2}[/tex]
Answer:
The solution of given quadratic equation = [-9 ± √41]/2Step-by-step explanation:
Points to remember
solution of a quadratic equation ax² + bx + c = 0
x = [-b ± √(b² - 4ac)]/2a
It is given that, x² + 9x + 10 = 0.
To find the solution
Here a = 1, b= 9 and c = 10
x = [-b ± √(b² - 4ac)]/2a
= [-9 ± √(9² - 4*1*10)]/2*1
= [-9 ± √(81 - 40)]/2
= [-9 ± √(41)]/2
= [-9 ± √41]/2
Therefore the solution of given quadratic equation = [-9 ± √41]/2
The ordered pairs show (height in inches, men’s shoe size). (70, 9.5) (67, 8) (69, 9) (72, 11.5) (68, 7.5) (60, 6) (71, 11) Use the regression calculator to generate the regression equation used to make predictions. What is the approximate height of a man who wears a size 7 shoe? Round to the nearest whole number. inches
Answer:
64
Step-by-step explanation:
Just completed this for edge.
Regression equation : Y = 0.44352X - 21.29443
Approximate height of man who wears size 7 shoe = 64 inches
What is regression?
Regression can be defined as a measurement that is used to quantify how the change in one variable will affect another variable. Regression is used to find the cause and effect between two variables.
Given, ordered pairs
(height in inches, men’s shoe size).
(70, 9.5)
(67, 8)
(69, 9)
(72, 11.5)
(68, 7.5)
(60, 6)
(71, 11)
Using regression calculator
Regression equation
Y = 0.44352X - 21.29443
Approximate height of a man who wears a size 7 shoe
7 = 0.44352X - 21.29443
0.44352X = 28.29443
X = 28.29443/0.44352
X = 63.7951614 ≈ 64
Approximate height = 64 inches
Hence, Y = 0.44352X - 21.29443 is the regression equation,
64 inches is the approximate height of the man wearing size 7 shoe
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What is the range of y=log^2(x-6)
Answer:
[tex]y\geq 0[/tex] or [tex][0, \infty)[/tex]
Step-by-step explanation:
By definition the function
[tex]y = log (x)[/tex] has a domain of [tex]x> 0[/tex].
Since the function is not defined for the values of x negative or equal to zero.
The range of this function is all the real numbers.
Since [tex]y <0[/tex] when [tex]0 <x <1[/tex] and [tex]y\geq0[/tex] when [tex]1\leq x<\infty.[/tex]
In this case we have the function [tex]y = log ^ 2 (x-6)[/tex]
Therefore since the log function is squared then its range is now [tex]y\geq 0[/tex]
Answer:
Ans: All real numbers
Step-by-step explanation:
Can someone help me please
A: 8,250
B: 22
Step-by-step explanation:
A: 15 * 250 = 3,750 + 4,500 = 8,250
B: 10,000 - 4,500 = 5,500/250 = 22. 22 * 250 + 4,500 = 10,000
Solve each system by substitution
x - y=4
x+2y=-2
Answer:
x = 2 and y = -2Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x-y=4&\text{add}\ y\ \text{to both sides}\\x+2y=-2\end{array}\right\\\\\left\{\begin{array}{ccc}x=4+y&(1)\\x+2y=-2&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\(4+y)+2y=-2\qquad\text{combine like terms}\\\\4+(y+2y)=-2\qquad\text{subtract 4 from both sides}\\\\3y=-6\qquad\text{divide both sides by 3}\\\\y=-2\\\\\text{put the value of}\ y\ \text{to (1):}\\\\x=4+(-2)\\\\x=2[/tex]
Two more than the quotient of a number 9 is 8
Answer:
Equation: x/9 + 2 = 8
Solution: x = 54
Step-by-step explanation:
I'd imagine the question is asking "two more than the quotient of a number and 9 is 8." Let's break this down:
- two more than means we're going to be adding two to the following quantity in the sentence.
- the quotient of a number and 9 we can interpret as a division expression. We don't know what "a number is," so we can give it a label (I'll pick n), and we can now write it is x/9. Taken with that last bullet point, our expression becomes x/9 + 2.
- Finally, we're told that the result of this expression is 8, so we can write the compete equation as x/9 + 2 = 8.
Now, if we want to solve this:
We can start by subtracting 2 from either side, giving us
x/9 = 6
And multiplying either side by 9 gives us the solution
x = 54.
HEEEELLLP!!!!
What is the frequency of the function f(x)? f(x)=2cos(x)−4
The frequency is 1 /period = 1 / [ 2 pi ]
Final answer:
The frequency of the function f(x) = 2cos(x) - 4 is 1/(2π), meaning the function completes one full cycle every 2π units along the x-axis.
Explanation:
The frequency of a function in mathematics describes how often the function repeats its pattern over a certain interval. In the case of the function f(x) = 2cos(x) - 4, the frequency is determined by the coefficient of x inside the cosine function. The standard form of the cosine function is cos(bx), where the frequency is |b|/(2π), because a sine or cosine function oscillates between +1 and -1 every 2π radians, as denoted in Figure 16.10.
In this instance, b = 1 since there is no coefficient multiplying x inside the cosine. Therefore, the frequency of the function f(x) is |1|/(2π), which simplifies to 1/(2π). This frequency means that the function completes one full cycle every 2π units along the x-axis.
Inverse of the function Y = 3x^5 -4
The inverse of the function [tex]y = 3x^5 - 4[/tex] is [tex]y = \sqrt[5]{\frac{x + 4}{3}}[/tex]
How to determine the inverse of the function
From the question, we have the following parameters that can be used in our computation:
[tex]y = 3x^5 - 4[/tex]
Swap the variabls x and y
So, we have
[tex]x = 3y^5 - 4[/tex]
Add 4 to both sides
This gives
[tex]3y^5 = x + 4[/tex]
Divide through by 3
[tex]y^5 = \frac{x + 4}{3}[/tex]
Take the 5th root of both sides
[tex]y = \sqrt[5]{\frac{x + 4}{3}}[/tex]
hence, the inverse of the function is [tex]y = \sqrt[5]{\frac{x + 4}{3}}[/tex]
PLEASE HELP PRECALCULUS
SEE ATTACHMENT
Answer:
1+6i
Step-by-step explanation:
Given:
f(x)=x^4 - 2x^3 + 38x^2 - 2 + 37
zero of f(x) = 1-6i
another zero of function = ?
Conjugate Zero theorem:
As per conjugate zero theorem, if a function f(x) has real coefficients and one of zero is a complex number then the conjugate of that complex number will also be a zero of that function i.e. complex zeroes will occur in complex conjugate pairs.
conjugate of 1-6i is 1+6i
hence another zero of f(x) will be 1+6i !
In 18 years time Halley will be five times as old as she was two years ago. Write this information in the form of an equation involving Halley's present age, a years How old is Halley now?
To solve any questions relating to ages, I find it easier to make a table, like in the picture below.
See picture for answer and clear diagram.
-----------------------------------------------------------------
Notes/Explanations + answer in written form
Let's say that Halley's age now is: x
That means that her age in 18 years is: x + 18
It also means that her age 2 years ago is: x - 2
In the question, we are told that when Halley is 18 years older than her current age, she will be 5 times the age she was when she was 2 years younger than her current age
That means:
Halley's current age + 18 years = 5 times (Halley's current age - 2 years)
So we get this equation (which we solve to get the answer) :
x + 18 = 5 * (x -2) ( expand the brackets)
x + 18 = 5x - 10 (subtract x from both sides)
18 = 4x - 10 (add 10 to both sides)
28 = 4x (now divide both sides by 4)
7 = x
Therefore, Halley's current age is 7 years
-------------------------------------------------
Note: equation is: x + 18 = 5 * (x -2)
Which represents the solution(s) of the system of equations, y = x2 – 6x + 8 and y = –x + 4? Determine the solution set by graphing.
- The answer is simply ( 1, 3 ) and ( 4, 0 ), Nishishi~
- Ouma
Answer:
c on edge nuity
Step-by-step explanation:
Polly spent 77/100 of a dollar to buy some mints how can you express 77/100 as a money amount
$ 0.77 or 77 cents
because 77 out 100 is written in decimal form as .77
Hello there!
Answer:
Your answer would be $0.77
Step-by-step explanation:
The reason why $0.77 would be the correct answer is because that represents something that is lower than a dollar, more so you would know it as "cents."
When you look at the question, it says, "77/100 of a dollar." What that means is that there is 77 of a dollar, and a dollar is equivalent to one whole.
The denominator "100" represents a whole, so that means that there is 77 out of a whole.
When you know currencies, cents are lower than a whole, therefore would be represented as a decimal.
77/100 is equivalent to 0.77.
As a money amount, it would be $0.77.
$0.77 should be the CORRECT answer.
plz help i'm having troubled understanding how to do this
Answer:
1/2 - 2/6 = 1/6
Step-by-step explanation:
to answer two that are different simply take the lesser up or higher down example: 1/2-2/4 this would be zero because 2 x 1/2 = 2/4
1/2-2/6= 0.16
hope this helps
What expression is equivalent to 9^-2
1÷81 because you square it
9^ -2 = 1/9^2 = 1/81
Solve each equation by completing the square 6x2+12x-27=-9
Answer:
the answer to this question is x=3\4
Answer:
1 and 2
Step-by-step explanation:
look this solution :
Solve this quadratic equation using the quadratic formula. 2x 2 - 10x + 7 = 0
Answer:X=11/10
Step-by-step explanation:
2x2-10x+7=0
4-10x+7=0
11-10x=0
-10x= -11
Divide both side by -10
-10x/-10. -11/-10
Answer= 11/10
Answer:
x₁ = 5 + √11
2
x₂ = 5 - √11
2
Step-by-step explanation:
quadratic formula is given by
x = -b ±√b² - 4ac
2a
a = 2, b = -10, c = 7
x = -(-10) ± √-10² - 4*2*7
2*2
x = 10 ± √100 - 56
4
x = 10 ± √44 = 2(5 ± √11) = 5 ± √11
4 4 2
x₁ = 5 + √11
2
x₂ = 5 - √11
2
Describe the end behavior of the following function:
F(x)=x^5-x^3+x^2
Answer:
Step-by-step explanation:
Keep in mind that this is a polynomial and all odd-powered polynomials start low (read that as "in Quadrant III") and end high ("Quadrant I"). So yes, the fourth answer choice, D, is the correct one.
(D) The graph of the function starts with low and high ends.
Function:A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.Initially, functions represented the idealized relationship between two changing quantities. A planet's position, for instance, depends on time. In the past, the idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity).Solution -Remember that this is a polynomial and that all odd-powered polynomials have a low starting point (read it as "in Quadrant III") and a high ending point ("Quadrant I").
Therefore, the correct answer is (D) the graph of the function starts with low and high ends.
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lf f(x) = 5x, what is f^-1(x)?
Answer: [tex]f^{-1}(x)=\frac{x}{5}[/tex]
Step-by-step explanation:
By definition the domain of an inverse function [tex]f^-1(x)[/tex] is the range of f(x) and the range of the inverse function is equal to the domain of the principal function f(x).
If you have a function [tex]f(x)=5x[/tex], then to find the inverse function, follow these steps:
1. Make [tex]y=f(x)[/tex]
[tex]f(x)=y=5x[/tex]
[tex]y=5x[/tex]
2. Solve for the variable "x":
[tex]x=\frac{y}{5}[/tex]
3. Exchange the variable "x" with the variable "y":
[tex]y=\frac{x}{5}[/tex]
4. Exchange "y" with[tex]f^{-1}(x)[/tex]. Then the inverse function is:
[tex]f^{-1}(x)=\frac{x}{5}[/tex]
What is the range of the given function?
(-2,0,) (-4, -3,) (2, -9,) (0,5,) (-5,7)
x = -5, -4, -2, 0, 2
y = -9, -3, 0, 5, 7
x = -9, -5, -4,-3, -2, 0, 2, 5, 7
y = -9, -5, -4, -3, -2,0, 2, 5, 7
Answer:
C. y = -9, -3, 0, 5, 7
Step-by-step explanation:
The given function is represented by the set of ordered pairs
{(-2,0,) (-4, -3,) (2, -9,) (0,5,) (-5,7)}
The range of this function is the set of all the y-values.
The set of the y-values are:
{-9,-3,0,5,7}
Therefore the range is y = -9, -3, 0, 5, 7
The correct option is C
Find the f(-1) of f(x)=5x+12
Answer:
f(- 1) = 7
Step-by-step explanation:
To evaluate f(- 1) substitute x = - 1 into f(x)
f(- 1) = 5(- 1) + 12 = - 5 + 12 = 7
For this case we have a function of the form[tex]y = f (x)[/tex], where:
[tex]f (x) = 5x + 12[/tex]
We must find the value of the function when x = -1.
That is, [tex]f (-1)[/tex]:
[tex]f (-1) = 5 (-1) +12\\f (-1) = - 5 + 12[/tex]
Different signs are subtracted and the sign of the major is placed:
[tex]f (-1) = 7[/tex]
Answer:
[tex]f (-1) = 7[/tex]
What is the final step in solving the inequality –2(5 – 4x) < 6x-4
Answer:
Final step: Division Property of Inequality
Step-by-step explanation:
–2(5 – 4x) < 6x-4
-10 + 4x < 6x - 4 : Distributive property
4x < 6x + 6 : Addition Property of Inequality (Add 10 to both sides)
-2x < 6 : Subtraction Property of Inequality (Subtract 6x from both sides)
x > - 3 : Division Property of Inequality (Divide both sides by -2, flip the symbol sign)
Answer
I don't see the options here so the final step is Division Property of Inequality
estimate a 15% tip on a dinner bill of $61.72 by first roundong the bill amount to the nearest ten dollars.
Answer:
$71
Step-by-step explanation:
First
61.72 times .15= 9.258
Second
61.72+9.258= 70.978
Which is greater, the amount the average person spends in a month on coffee or the amount the average person spends in a month on gasoline?
Answer:
The correct answer is the amount the average person spends in a month on gasoline.
Step-by-step explanation:
When comparing the amounts spent on the purchase of two items, we must need to see the price difference between the products first, then we will see the consumption of those products. Here the two items that are being compared have different purchase prices. A cup of Coffee is far cheaper than purchasing a tank of gasoline. If coffee is purchased on daily basis, even then the amount spent on purchasing coffee would be much lesser than the amount spent on buying the gasoline. For example, the cup of coffee costs $1 and a tank of gasoline costs $50. If coffee is purchased daily, then monthly amount spent on it will be $30, and if gasoline is purchased twice in a month, the amount spent on it will be $100. So an average person spends more amount on gasoline than on purchasing coffee.
Simplify to create an equivalent expression. -k-(-8k+7)
Answer:
7k -7
Step-by-step explanation:
-k-(-8k+7)
Distribute the minus sign to all terms in the parentheses
-k--8k-7
Ad negative negative is a positive
-k + 8k -7
Combine like terms
7k -7
Answer:
The answer is 7k-7
Step-by-step explanation:
Hope this helps!!!
PLZZZZ HELP GIVE ALL POINTS I HAVE
Answer:
1/4
Step-by-step explanation:
Answer is
16
8
36
Explanation..multiply each by 4
What is : x=29-3(9-4)
Please show work
Answer:
Step-by-step explanation:
29-3(5)
29-15
14
X=14
5a - 5b is it monomial binomial trinomial
Binomial
A monomial is just one term. A binomial is two monomials added or subtracted together. A trinomial is three monomials added or subtracted together.
Answer:
It is a binomial because it has two terms
Find the center and radius of the circle whose diameter has an endpoint at (-3, -4) and the origin.
The center of the circle is (-1.5, -2) and the radius is 3.205.
Explanation:To find the center and radius of the circle, we can use the formula for the distance between two points in a coordinate plane. The two points given are (-3, -4) and the origin (0, 0), which represents the diameter of the circle. The center of the circle is the midpoint of the diameter, which can be found by taking the average of the x-coordinates and the y-coordinates. So, the center is ( (-3+0)/2 , (-4+0)/2 ) = (-1.5, -2). The radius of the circle is half the length of the diameter, which can be found using the distance formula as the distance between the center and one of the endpoints of the diameter. So, the radius is the distance between (-1.5, -2) and (-3, -4), which is √((-3-(-1.5))² + (-4-(-2))²) = √(2.5² + 2²) = √(6.25 + 4) = √10.25 = 3.205.
Determine which answer choice matches the dot plot you drew?
Answer:
C
Step-by-step explanation:
Given data are :
{1,2,2,2,2,4,4,5,6,6,8,8,8,10}
1 appears only once so there will be 1 point above number 1 in the dot plot.
Then choice B or C or D are possible choices.
2 appears 4 times so there will be 4 points above number 4 in the dot plot.
Then choice B or C or D are possible choices.
4 appears 2 times so there will be 2 points above number 2 in the dot plot.
Then choice C or D are possible choices.
5 appears once once so there will be 1 point above number 5 in the dot plot.
Only choice that satisfies those results is C.
Hence correct answer is C.
I need help please?!!!
Answer:
Yes
Step-by-step explanation:
3 x - 2 y = 10
( - 2 , - 8 )
We know that coordinates are put in the form ( x , y ) and from that we can work out that x = -2 and y = -8
Now we just substitute x = -2 and y = -8 into 3 x - 2 y = 10
3 x - 2 y = 10
{ 3 × ( - 2 ) } - { 2 × ( - 8 ) } = 10
{ - 6 } - { - 16 } = 10
- 6 + 16 = 10 True
Answer:
yes
Step-by-step explanation:
To determine if the ordered pair is a solution to the equation.
Substitute the x and y values into the left side of the equation and if equal to the right side then the pair are a solution
3x - 2y = 3(- 2) - 2(- 8) = - 6 + 16 = 10
Hence (- 2, - 8) is a solution to the equation
Find the measure of one exterior angle of the following polygon:
Nonagon
Answer:
40°
Step-by-step explanation:
1. Shape of a nonagon: 9 (root non-)
2. Total exterior angle: 360° (constant for all polygons)
3. Given that this polygon is regular, the one exterior angle of an nonagon is 360°/9 = 40°.
Answer:
40°Step-by-step explanation:
An exterior angle and an interior angle are supplementary angles.
Two Angles are Supplementary when they add up to 180°.
Therefore the measure of exterior angle is equal to different between 180° and an interior angle.
Method 1:
You can use the formula of the measure of interior angle of the regular polygon with n-sides:
[tex]\alpha=\dfrac{180^o(n-2)}{n}[/tex]
We have a nonagon. Therefore n = 9. Substitute:
[tex]\alpha=\dfrac{180^o(9-2)}{9}=(20^o)(7)=140^o[/tex]
[tex]180^o-140^o=40^o[/tex]
Method 2:
Look at the picture.
[tex]\alpha=\dfrac{360^o}{9}=40^o[/tex]
[tex]2\beta[/tex] - it's an interior angle
We know: The sum of measures of these three angles of any triangle is equal to 180°.
Therefore:
[tex]\alpha+2\beta=180^o\to2\beta=180^o-\alpha[/tex]
Substitute:
[tex]2\beta=180^o-40^o=140^o[/tex]
[tex]\theta[/tex] - it's a exterior angle
[tex]2\beta+\theta=180^o\to\theta=180^o-2\beta[/tex]
substitute:
[tex]\theta=180^o-140^o=40^o[/tex]