is x 2 = y a function?

ANSWER

[tex]x = \frac{ 5 - 3\sqrt{ 5} }{2} \: or \: x = \frac{ 5 +3 \sqrt{ 5} }{2} [/tex]

EXPLANATION

The given equation is

[tex] {x}^{2} - 5x - 5 = 0[/tex]

The solution is given by the formula

[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

where a=1, b=-5, c=-5

We substitute into the formula to get;

[tex]x = \frac{ - - 5 \pm \sqrt{ {( - 5)}^{2} - 4(1)( - 5)} }{2(1)} [/tex]

We simplify to get,

[tex]x = \frac{ 5 \pm \sqrt{ 45} }{2} [/tex]

The solutions are:

[tex]x = \frac{ 5 - 3\sqrt{ 5} }{2} \: or \: x = \frac{ 5 +3 \sqrt{ 5} }{2} [/tex]

The equation has no complex roots.

Answer:

x =  [5 + 3√5]/2   or x =  [5  -3√5]/2

Step-by-step explanation:

Points to remember

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

To find the solutions of given equation

It is given  x² - 5x - 5 = 0

here a = 1, b = -5 and c = -5

x = [-b ± √(b² - 4ac)]/2a

 =  [--5 ± √((-5)² - 4*1*-5)]/2*1

 = [5 ± √(25 + 20)]/2

 =  [5 ± √(45)]/2

 =  [5 ± 3√5]/2

x =  [5 + 3√5]/2   or x =  [5  -3√5]/2

Answer:

8,640 ft^2

Step-by-step explanation:

There are 144 square inches per square foot, therefore 144x60=8,640 ft^2

Hi! Let's go over the meanings of each term to find our answer.

Domain of an exponential parent function - the set of all real values of x that will give real values for y in the given function

Range of an exponential parent function - the set of all real values of y that you can get by plugging real numbers into x in the same function

Now we have our answers! All we had to do was go over the meanings, or definitions.

Hope this helps!

- Kylie

Answer:

The domain of exponential parent function is all real values and range is real positive numbers [tex]y>0[/tex].

Step-by-step explanation:

We are asked to find the domain and range of exponential parent function.

We know that an exponential parent function is in form [tex]f(x)=b^x[/tex], where b is the base of function.

We can see from parent exponential function that as x approaches to very large values of x, the value of y increases with no bounds.

As x approaches negative infinity, y approaches to zero.

We know that the domain of a parent exponential function is all real values of x that is [tex](-\infty,\infty)[/tex] in interval notation.

The range of a parent exponential function is positive real numbers that is [tex]y>0[/tex].

[tex]\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \qquad y=-\cfrac{3}{4}x+6[/tex]

Answer:

-15

Step-by-step explanation:

Note that it says x = -9. Plug in -9 for all x inside the expression and solve.

(x² + 9)/(x + 3) = (-9² + 9)/(-9 + 3)

Solve. First, solve the parenthesis, then divide:

(-9² + 9) = (81 + 9) = 90

(-9 + 3) = (3 - 9) = -6

Divide:

(90)/(-6) = -15

-15 is your answer.

~

Answer:

D y= -2 (x-8)2 -3

Step-by-step explanation:

The equation of the new parabola will be y = -2(x + 2)² + 1. Then the correct option is A.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation of the parabola is given below.

y = -2(x - 3)² + 4

If this parabola is shifted 5 units to the left and 3 units down. Then replace x with x + 5 and subtract 3 from the equation.

Then the equation of the new parabola will be given as,

y = -2(x + 5 - 3)² + 4 - 3

y = -2(x + 2)² + 1

The condition of the new parabola will be y = - 2(x + 2)² + 1. Then, at that point, the right choice is A.

More about the equation of the parabola link is given below.

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Answer:

It is an identity, the proof is in the explanation

Step-by-step explanation:

csc(A)-cot(A)=tan(A/2)

I'm going to start with right hand side

tan(A/2)=(1-cos(a))/(sin(a))                half angle identity

tan(A/2)=1/sin(a)-cos(a)/sin(a)         separate fraction

tan(A/2)=csc(a)-cot(a)                     reciprocal and quotient identities

Step-by-step answer with explanations:

Recall that a coordinate pair such as (5,-1) has two components.

The first (5, -1) means that the point is situated at x=5.

The second (5, -1) means that the point is situated at y=-1.

Now, a horizontal line through (5,-1) means that ALL points on the line have y-coordinate equal to -1, so that any point with y=-1 will lie on this horizontal line.  An example would be (-2,-1).

A vertical line through (5, -1) means that ALL points on the line have x-coordinate equal to 5, so that any point with x=5 will lie on this vertical line.  An example would be (5,4).

Answer:

its D

Step-by-step explanation:

ur welcome =)

Answer: 317.93

Step-by-step explanation:

317.93371 when rounded off to nearest hundred, we get 317.93.

Rounding off is the method by which a decimal integer is reduced to its nearest closer value of the next number . After the decimal point, if the value is greater than 5 we increment the numerical value by 1 and if the value is less than 5 we keep the numerical value intact.

The given value is 317.93371 .

Rounding off to nearest hundred means that we will get the rounded off value up to two decimal places.

We can see that the third decimal place is 3 which means that the second decimal place of the number will be kept intact.

Rounded off value is -  317.93 .

Thus, 317.93371 when rounded off to nearest hundred, we get 317.93.

To learn more about rounding off, refer -

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Answer:364.6

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

7(1–k)

= 1(7) -k(7)  -------------> distributive property

= 7–7k

Answer:

14.4 in

Step-by-step explanation:

2160/ 150= 14.4

Answer:

You MUST use parentheses around denominator 8+x, or ANY denominator that consist of more than a single number of variable. 

Also, don't use lower case and upper case interchangeably. 

In algebra, x and X are different, as are y and Y. 

f(x) = y = 3x/(8+x) 

Switch x and y, solve for y: 

x = 3y/(8+y) 

x(8+y) = 3y 

8x+xy = 3y 

8x = 3y−xy 

8x = y(3−x) 

y = f⁻¹(x) = 8x/(3−x)

I hope this helps, love 

Step-by-step explanation:

False.

This is not a function because for something to be a function each x value can only have one y value. In this case two of the points have a value of 1 and their y are different, making them NOT a function

(1, 3)

(1, 2)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Undefined

Step-by-step explanation:

You can deduce the solution in two ways: if the slope of m is zero, it is horizontal. So, n is vertical because it must be perpendicular to n. Vertical lines have undefined slope.

Alternatively, if the slope of line m is k, the slope of a perpendicular line n is -1/k. So, if k=0, you can't compute -1/0.

To find the percentage of the monthly budget that housing represents in a circle graph, divide the housing cost ($175) by the total monthly expenses ($500) and multiply by 100. This calculation shows that housing accounts for 35% of the monthly budget.

When representing a monthly budget on a circle graph, or pie chart, you need to find out what percentage of the total budget each category represents. In this case, a young single person spends $150 on food, $175 on housing, and $175 on other items. To find the percentage that represents housing, we first need to calculate the total amount of monthly expenses which are $150 for food, $175 for housing, and $175 for other items, adding up to a total of $500.

Next, we calculate the percentage that the housing expense represents by dividing the housing cost by the total expenses and then multiplying by 100 to get a percentage:

Therefore, housing represents 35% of the total monthly budget on the circle graph.

Answer:

[tex]e^{ln(12)}=12[/tex]

Step-by-step explanation:

I suppose your intended expression is;

[tex]e^{ln(12)}[/tex]

The exponential function, e, and the natural logarithm function, ln, are inverses of each other;

[tex]e^{lnx}=x\\\\lne^{x}=x[/tex]

Therefore, our expression becomes;

[tex]e^{ln(12)}=12[/tex]

                              108

                              /     \

                            12     9

                           /  \      /  \

                         4   3    3   3

                        / \

                      2   2

             2y                     5

             / \                     /  \

           2   y                 1    5

<Hope this helps!>

Step-by-step explanation:

all work is pictured and shown

Answer: 1 day, 21 hours, and 40 minutes

Step-by-step explanation: To make it less confusing, you can convert all of the days into hours (24 hours in a day)...

126 hours and 20 minutes-80 hours and 40 minutes

7580 minutes-4840 minutes=2740 minutes

We can convert 2740 minutes back into hours and days now...

1 day, 21 hours, and 40 minutes

Or....

Step-by-step explanation: Or you can just subtract, start with minutes and go up from there...

20-40 would be in the negatives and time can’t be negative, so you need to borrow from the hours. So hours is now at 5 and minutes is at 20+40 which is 80. And 80-40=40

We now have...

5 days, 5 hours, and 40 minutes-3 days and 8 hours.

Now we can do the hours...

5-8 also is negative, so we need to borrow from the days. Days is now at 4. There are 24 hours in a day so 24+5=29. Now we can subtract 29-8=21

Now we have 4 days, 21 hours, and 40 minutes

And 4-3 is 1, which means we have 1 day,

21 hours, and 40 minutes as our answer!

The difference between the given time frames 5 days 6 hours 20 minutes and 3 days 8 hours 40 minutes after performing the subtraction operation is 1 day, 13 hours, and 40 minutes.

The question is about an arithmetic operation involved in time. This arithmetic operation is subtraction. Given the time frames are 5 days 6 hours 20 minutes and 3 days 8 hours 40 minutes. Let's subtract the smaller time frame from the larger one.

So, the difference between 5 days 6 hours 20 minutes and 3 days 8 hours 40 minutes is 1 day, 13 hours, and 40 minutes.

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Final answer:

A system of equations will have the solution (2,0) if, when substituting x=2 and y=0, both equations are satisfied. This can be a linear equation where the y-intercept is set to be the negative double of the slope, or a conic section represented by a quadratic equation that intersects the x-axis at x=2.

Explanation:

Systems of equations that will have a solution of (2,0) must satisfy the condition that when x=2 and y=0, both equations are true. Considering the information provided about quadratic and differential equations, to find a system with the solution (2,0), one can set up a system of any two equations and test if the point (2,0) satisfies them. For instance, any linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept, will have a solution of (2,0) if b is set to -2m. Similarly, a second-order differential equation can be constructed with known solutions, including the point (2,0).

A system with a linear equation y = mx - 2m, where m can be any value.

A homogeneous linear differential equation with boundary conditions that result in the point (2,0) being a solution.

A conic section represented by a quadratic equation that intersects the x-axis at x=2.

For example, the quadratic equation ax² +2hxy+by² = 0, can be factored into two linear factors with no constant term, which means it represents two lines intersecting at the origin. If one of these lines passes through the point (2,0), it would confirm that our solution fits this system as well.

Hello There!

There are 32.5 kilograms in 32,500 grams.

STEPS

Write the number of grams

Divide by 1,000 because a kilogram is 1,000 grams

Answer: infinite solutions

Step-by-step explanation:

If the left side equals the right side, then every value you input for the variable will make a TRUE statement --> which means there are infinite solutions.

For example: x + 1 = x + 1

Any value you choose for "x" will result in a true statement.

This is because they are the same line, which is another way of showing that they have infinite solutions.

The linear equation is an identity, which means that it has infinite solutions.

We define an identity as an equation where we have the exact same expression in both sides of the equation.

For example, in:

f(x) = f(x).

Where f(x) is a function.

A easier example can be:

x + 5 = x + 5

Notice that we have the exact same thing in both sides, this is what Jilana gets when solving her linear equation.

This means that for any given value of x, the equation will be true. So, x can be any real value, which means that there are infinite solutions for the equation.

If you want to learn more about linear equations, you can read:

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Answer:

0.16

Step-by-step explanation:

81 is 1 standard deviation below the mean.  According to the empirical rule, 68% of data lies within 1 standard deviation of the mean; here the equivalent statement would be that half of that, or 34%, lies within 1 standard deviation below the mean.  Half of the area under the standard normal curve, less this 0.34, is the probability that the random variable is below 1 standard deviation beneath the mean.  That comes to 0.16.

On a calculator, you might enter the command normalcdf(-100,81,85,4); on my old TI-83 Plus I get 0.1587, which rounds off to 0.16.

Final answer:

The z-score of -1 corresponds to a probability of approximately 0.1587, therefore P(x < 81) is approximately 0.1587, or 15.87%.

Explanation:

To find the probability that a normally distributed random variable x is less than 81, P(x < 81), when the mean μ is 85 and the standard deviation σ is 4, we need to use the properties of the normal distribution.

First, we convert the raw score of 81 into a z-score. The formula for calculating a z-score is:

[tex]z = (x - μ) / σ[/tex]

For x = 81, the z-score would be:

z = (81 - 85) / 4

z = -1

Next, we use a standard normal distribution table, a calculator, or software to find the probability that correlates with this z-score. The table lists probabilities to the left of z-scores.

The z-score of -1 corresponds to a probability of approximately 0.1587, therefore P(x < 81) is approximately 0.1587, or 15.87%.

Answer:

The correct option is C.

Step-by-step explanation:

In a right triangle, the hypotenuse has endpoints XY as shown in the given graph.

Since XY is hypotenuse and Z is third vertex in the triangle, therefore XZ and YZ must be perpendicular at point Z.

The coordinates of X are (-4,2), so draw a vertical line x=-4 and a horizontal line y=2.

The coordinates of Y are (-1,-3), so draw a vertical line x=-1 and a horizontal line y=-3.

From the below figure it is clear that the vertcal and horizontal lines intersect each other at [tex]Z_1[/tex] and [tex]Z_2[/tex].

It is given that Z is located in the second quadrant with integer coordinates, therefore the only possible location of Z is

[tex]Z=Z_2(-1,2)[/tex]

Since the length of YZ₂ is 5 units and Z=Z₂, therefore the length of YZ is 5 units.

Hence the correct option is C.

Answer:

Kate’s photo get 14 likes

Step-by-step explanation:

Let

x ----> Kate's likes

y ---> Ali's likes

we know that

y=42 likes ----> equation A

y=3x ----> equation B

Solve by substitution

Substitute equation A in equation B and solve for x

42=3x

Divide by 3 both sides

x=42/3

x=14 likes

Kate's photo got 14 likes.

The student is dealing with a basic algebra problem that involves setting up and solving an equation. To find out how many likes Kate's photo got, we can let x represent the number of likes on Kate's photo. Given that Ali's photo got 42 likes, which is three times as many as Kate's photo, we can write the equation as:

3x = 42

To find x, we divide both sides of the equation by 3:

x = 42 / 3

x = 14

Therefore, Kate's photo got 14 likes.

Answer:

15 litres

Step-by-step explanation:

129.6 m² needs 8L

1m² needs 8/129.6L

243m² needs (8/129.6)×243 = 15L

To calculate the amount of paint required for a 243m² area, determine the coverage rate from the given data (16.2 m² per litre) and then divide the desired area by the coverage rate. We find that 15 litres of paint are necessary to cover 243m².

To find out how much paint is required to paint an area of 243m² when 8 litres of paint can cover 129.6 m², we need to calculate the paint coverage ratio and then apply it to the desired area.

First, we calculate the coverage rate of the paint:

Next, we use this rate to determine the amount of paint needed for 243m²:

Therefore, 15 litres of paint are required to paint an area of 243m².

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Answer:

P(A|B) = 0.30

Step-by-step explanation:

P(A) = 0.30

P(B) = 0.60

To Find:

P(A|B) = ?

P(A|B) means probability of occurring of event A when event B has occurred.

P(A|B) = P(A∩B)/P(B)

We know that for independent events;

P(A∩B) = P(A).P(B)

So, we have:

P(A|B) = P(A).P(B)/P(B)

P(A|B) = P(A)

So, probability of occurrence of an independent event does not depend on the probability of a different event.

Answer:

Both the lines would have the same slope since they are parallel. The lines would not however have the same y-intercept.

Step-by-step explanation:

This is because in order for lines to be parallel the lines must have the same slope, otherwise they would meet at some point. They would not have the same y-intercept because if both the y-intercept and the slope were the same it would be the same line.

Answer:

Both lines are parallel, so they have the same slope. However, the y-intercepts of the lines are not the same. For the lines to be parallel, the slopes of the lines must be the same. If both the y-intercept and slope are the same, they are the same line, so they do not have the same y-intercept.

Answer:

x = [tex]\frac{C-By}{A}[/tex]

Step-by-step explanation:

Given

Ax + By = C ( isolate the term in x by subtracting By from both sides )

Ax = C - By ( divide both sides by A )

x = [tex]\frac{C-By}{A}[/tex]

Answer:

Step-by-step explanation:

Solve Ax+By=C for x.:

Ax= - By+C

case 1 : A≠0       x = (- B/A)y+C/A

case 2 : A=0

you have : 0x = - By+C

B=0 :  ox = C     C = 0  infinity of x      C≠0  no solutions

Answer:

it is :119.5714

Step-by-step explanation:

15 3/14+24 1/14+12 2/7+12 2/7+10 1/7+10 1/7+35 3/7=

step by step now:

15 3/14+24 1/14+12 4/14+12 4/14+10 2/14+10 2/14+35 6/14=118 22/14=118+1.5714=119.5714

Final answer:

The sum of the given mixed numbers is 119 and 2/7 after adding the whole numbers separately and then the fractions.

Explanation:

To calculate the sum of the given numbers, we start by adding the whole numbers and the fractions separately. All the fractions have a common denominator, which simplifies the process. Let's proceed with the calculation:

Adding the whole numbers: 15 + 24 + 12 + 12 + 10 + 10 + 35 = 118.

Adding the fractions: 3/14 + 1/14 = 4/14, simplifies to 2/7 because 4/14 is dividable by 2. Then, we add 2/7 + 2/7 + 1/7 + 1/7 + 3/7 = 9/7. But 9/7 is more than 1, so we rewrite 9/7 as 1 whole and 2/7.

Now let's combine the sums of whole numbers and fractions: 118 + 1 = 119.

Thus, the total sum is 119 and 2/7.