for the literal equation x^2+m=y, express x in terms of y and m

Answers

Answer 1

We have the equation of y as a function of x:

[tex]y(x)=x^2+m[/tex]

To find x(y) we just need to solve for x, first by subtracting m from both sides

[tex]y-m=x^2[/tex]

Now, we just have to take the square root on both sides

Taking the square root of a number it's actually raising it to the 1/2 power:

[tex]\sqrt[]{a}=a^{\frac{1}{2}}[/tex]

Now, when we proceed to raise the square root of a number to two, we can arrange it like this:

[tex](a^{\frac{1}{2}})^2=a^{\frac{2}{2}}=a^1=a[/tex]

When we take the square root of a number that is raised to two the result will be the number without any power, like this:

[tex]\sqrt[]{a^2}=a[/tex]

Then:

[tex]\sqrt[]{x^2}=x=\sqrt[]{y-m}[/tex]


Related Questions

PLEASE ANSWER QUESTION 2(1.) The members of the gardening group plan to build a walkway through the garden as formed by the hypotenuse of each of the four triangles in the drawing. That way, the gardeners will be able to access all sections of the garden. Calculate the length of the entire walkway to the nearest hundredth of a yard. answer: 10 yards(2.)Is the value you just wrote for the total length of the walkway a rational or irrational number? Explain.

Answers

We need to compute the hypotenuse of 4 right triangles.

The Pythagorean theorem states:

[tex]c^2=a^2+b^2[/tex]

where a and b are the legs and c is the hypotenuse of the right triangle.

In one of the triangles, the length of the legs are: 6 and 8 yards. Then the length of the hypotenuse is:

[tex]\begin{gathered} c^2_1=6^2+8^2 \\ c^2_1=36+64 \\ c_1=\sqrt[]{100} \\ c_1=10yd_{} \end{gathered}[/tex]

In another triangle, the length of the legs are: 12 and 8 yards. Then the length of the hypotenuse is:

[tex]\begin{gathered} c^2_2=12^2+8^2 \\ c^2_2=144+64 \\ c_2=\sqrt[]{208} \\ c_2=4\sqrt[]{13}\text{ yd} \end{gathered}[/tex]

In the triangle whose hypotenuse (c3) is 15 yd and one of its legs is 12 yd, the unknown is one of the legs, b, which can be computed as follows:

[tex]\begin{gathered} 15^2=12^2+b^2 \\ 225=144+b^2 \\ 225-144=b^2 \\ \sqrt[]{81}=b \\ 9=b \end{gathered}[/tex]

The last triangle has legs of 9 yd and 6 yd. Its hypotenuse is:

[tex]\begin{gathered} c^2_4=9^2+6^2 \\ c^2_4=81+36 \\ c_4=\sqrt[]{117} \\ c_4=3\sqrt[]{13} \end{gathered}[/tex]

Finally, the length of the walkway is:

[tex]\begin{gathered} c_1+c_2+c_3+c_4=10+4\sqrt[]{13}+15+3\sqrt[]{13}= \\ =(10+25)+(4\sqrt[]{13}+3\sqrt[]{13})= \\ =35+7\sqrt[]{13} \end{gathered}[/tex]

This value is irrational because it includes and square root

wpn Learning. UIC 3. Solve by elimination. x + 2y = -7 x - 5y = 7 A. (-7,0) B. (-3, -2) C. (-2,-3) D. (0, -7)

Answers

x+2y=-7 ------> equation 1

x-5y=7 -------->equation 2

Change the signs in equation 2

x+2y=-7 ------> equation 1

-x+5y=-7 -------->equation 2

Add equation 1 and 2

x+2y=-7 ------> equation 1

-x+5y=-7 -------->equation 2

_________

7y=-14

y=-14/7

y=-2

Now substitute y=-2 in equation 1,

x+2(-2)=-7

x-4=-7

x=-7+4

x=-3

(x,y)=(-3,-2)

Option B is the correct answer.

E Xº = MLLEN = 50° yº = LN = ܘ L +7cm → N

Answers

In this case, we have an isosceles triangle, in this kind of figures the height (segment that goes from the vertex E to the base) bisects the upper angle, then the angle

[tex]m=\frac{50}{2}=25[/tex]

Then, the measure of the upper angle of the triangle formed to the left equals 25°, the height of the triangle forms a right angle with the base of the triangle, then the measure of the angle on the right (next to y°) equals 90°. The sum of the internal angles of a triangle always equals 180°, then we can formulate the following expression:

x° + 25° + 90° = 180°

x° + 115° = 180°

x° + 115° - 115° = 180° - 115°

x° = 65°

Then x° equals 65°

As mentioned, the height forms a right angle with the base of the triangle, then the measure of the angle y° equals 90°

The length of the side LN equals twice the length of the base of the left triangle, then we get:

LN = 2*7 = 14

Then, the length of LN equals 14 cm


Juan's office had already recycled 24 kilograms this year before starting the new recycling
plan, and the new plan will have the office recycling 1 kilogram of paper each week. After
16 weeks, how many kilograms of paper will Juan's office have recycled?
kilograms

Answers

Answer:

40kg

24+16=40kg

I need help to find the area of each sector. I will send the exercise

Answers

The area of the circular sector is given by:

[tex]\begin{gathered} A=\frac{r^2\theta}{2} \\ where\colon \\ r=radius=17mi \\ \theta=angle=\frac{2\pi}{3} \\ \end{gathered}[/tex]

Therefore:

[tex]\begin{gathered} A=\frac{(17^2)\frac{2\pi}{3}}{2} \\ A=\frac{289\pi}{3}\approx302.64 \end{gathered}[/tex]

The scores of individual students on the American College Testing (ACT) composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 5.9. What is the probability that the mean score of an SRS of 40 students chosen from all those taking the test is 21 or higher? Round your percentage to 2 decimals.

Answers

Given data

*The given mean is

[tex]\mu=18.6[/tex]

*The given standard deviation is

[tex]\sigma=5.9[/tex]

The value of the z score is calculated as

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Substitute the values in the above expression as

[tex]\begin{gathered} z=\frac{21-18.6}{5.9} \\ =0.41 \end{gathered}[/tex]

The probability that the mean score of an SRS of 40 students chosen from all those taking the test is 21 or higher is given as

[tex]\begin{gathered} P(Z\ge21)=P(X\ge0.41) \\ =1-P(X<0.41) \end{gathered}[/tex]

The corresponding probability is evaluated by the table.

Substitute the values in the above expression as

[tex]\begin{gathered} P(Z\ge21)=1-0.6591 \\ =0.34 \end{gathered}[/tex]

Instructions: Find the missing side. Round your answer to the nearest tenth. х 38° 30 X =

Answers

Let us call the third angle in the triangle y

y = 180 - 90-38 = 52 degrees ( sum of angles in a triangle is 180 degrees)

using trigonometric ratio

[tex]\sin \text{ 52=}\frac{\text{opposite}}{\text{hypothenuse}}[/tex]

opposite = x

hypothenuse = 30

[tex]\begin{gathered} \sin 52\text{ =}\frac{x}{30} \\ x=\text{ 23.64032261} \end{gathered}[/tex]

To the nearest tenth x = 23.6

The survey found that women's Heights are normally distributed with a mean of 63.9 in and standard deviation 2.2 in the survey also found that men's Heights are normally distributed with mean 67.6 in. and standard deviation 3.5 in considered and executed jet that seats 6 with a doorway height of 56.4 in. a)what percentage of adult men can fit through the door without bending?b) what's a doorway height would allow 40% of men to fit without bending

Answers

Let's begin by listing out the information given to us:

Mean for women (w) = 63.9 in

standard deviation for women (sd) = 2.2 in

Mean for men (m) = 67.6 in

standard deviation for men (sd) = 3.5 in

Graph the line that passes through the point: (-1,-4) and who's slope is -2

Answers

The equation of the line is y = -2x -6.

We have,

The line passes through the point (-1, -4)

The slope of the line is -2.

The equation of the line when it passes through the point [tex](x_{1} ,y_{1} )[/tex] and has slope m is given by

[tex]y -y_{1} =m(x -x_{1} )[/tex]

Now, putting these values in the general equation of the line, we get,

y - (-4) = -2[ x -(-1) ]

y +4 = -2 [ x +1 ]

y +4 = -2x -2

y +2x = -2 -4

y +2x = -6

y = -2x -6

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It is a Algebra problemSuppose an object is thrown upward with an initial velocity of 48 feet per second from a height of 120 feet. The height of the object t seconds after it is thrown is given by h(t)=-16t²+48t+120. Find the average velocity in the first two seconds after the object is thrown.

Answers

Answer

Average velocity in the first 2 seconds = 16 ft/s

Explanation

The average value of a function over an interval [a, b] is given as

[tex]\text{Average value of the function = }\frac{1}{b-a}\int ^b_af(x)dx[/tex]

The integral is evaluated over the same interval [a, b]

Since we are asked to find the average velocity over the first 2 seconds, we need to first obtain the funcion for th object's velocity.

Velocity = (dh/dt)

h(t)= -16t² + 48t + 120

Velocity = (dh/dt) = -32t + 48

So, we can then find the average velocity over the first 2 seconds, that is, [0, 2]

[tex]\begin{gathered} \text{Average value of the function = }\frac{1}{b-a}\int ^b_af(t)dt \\ a=0,b=2,f(t)=-32t+48 \\ \text{Average Velocity = }\frac{1}{2-0}\int ^2_0(-32t+48)dt \\ =\frac{1}{2}\lbrack-16t^2+48t\rbrack^{2_{}}_0 \\ =\frac{1}{2}\lbrack-16(2^2)+48(2)\rbrack_{} \\ =0.5\lbrack-16(4)+96\rbrack \\ =0.5\lbrack-64+96\rbrack \\ =0.5\lbrack32\rbrack \\ =16\text{ ft/s} \end{gathered}[/tex]

Hope this Helps!!!

Match each ratio of the volumes of two solids to the pair of solids it represents. 3 : 1 2r : 3h h : 4r 4r : h 4r : 3h 4 : 1

Answers

Solution

[tex]\begin{gathered} \text{ Volume of a cylinder }=\pi r^2h \\ \\ \text{ Volume of a cone =}\frac{1}{3}\pi r^2h \\ \\ \text{ Volume of a sphere }=\frac{4}{3}\pi r^3 \\ \\ \text{ Volume of hemisphere }=\frac{2}{3}\pi r^3 \end{gathered}[/tex]

For 1.

[tex]\frac{\text{ Volume of a cylinder}}{\text{ Volume of a cone}}=\frac{\pi r^2h}{\frac{1}{3}\pi r^2h}=\frac{1}{\frac{1}{3}}=\frac{3}{1}=3:1[/tex]

For 2.

[tex]\frac{\text{ Volume of a sphere}}{\text{ Volume of a cylinder}}=\frac{\frac{4}{3}\pi r^3}{\pi r^2h}=\frac{4r}{3h}=4r:3h[/tex]

For 3.

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The question is in the image. Answer question 20 only.

Answers

To convert radians to degrees we use the formula:

[tex]\theta\cdot\frac{180}{\pi}[/tex]

In this case the angle is 12 radians, then we have:

[tex]12\cdot\frac{180\degree}{\pi}=687.55[/tex]

Therefore, the angle in degrees is 687.55°

Thaddeus models the number of hours of daylight in his townas

Answers

We have the following function

[tex]D(t)=2.5\sin\frac{\pi t}{6}+12[/tex]

The maximum and minimum of that function happens when sin(x) = 1 or sin(x) = -1, respectively.

Then let's find the maximum, that happens when the sin value is 1

[tex]\begin{gathered} \begin{equation*} D(t)=2.5\sin\frac{\pi t}{6}+12 \end{equation*} \\ \\ D(t)=2.5\cdot1+12 \\ \\ D(t)=2.5+12 \\ \\ D(t)=14.5 \end{gathered}[/tex]

And the minimum, when sin value is -1

[tex]\begin{gathered} \begin{equation*} D(t)=2.5\sin\frac{\pi t}{6}+12 \end{equation*} \\ \\ D(t)=2.5\cdot(-1)+12 \\ \\ D(t)=-2.5+12 \\ \\ D(t)=9.5 \end{gathered}[/tex]

Then the least: 9.5 hours; greatest: 14.5 hours.

Peyton go shopping she finds two shirts one cost $24.97 the other cost $13.75 she needs to know if she has enough money to buy both shirt using mental math she rounds $24.97 to $25 and add that to $13.75 to get $38.75 how does Peyton need to say to find the exact a total of 2 shirts

Answers

We know that Peyton wants to buy two shirts.

• First shirt cost $24.97.

,

• Second shirt cost $13.75.

To do the mental math is ok to round $24.97 to $25, and them sum with $13.75.

However, to get the exact number, Peyton needs to subtract 3 pennies from the last amount $38.75, becuase she rounded before.

Therefore, to find the exact amount she needs to subtract 3 pennies.

please help me with this question and explain it so I can understand. thank you!

Answers

We can solve this question using trigonometric functions. Here, we use the tangent of the angle of elevation to find the height of the tree.

[tex]\begin{gathered} \tan 40^o=\frac{h}{35} \\ 0.839=\frac{h}{35} \\ 0.839\times35=h \\ 29.36=h \end{gathered}[/tex]

Thus, the height of the tree is 29 feet (to the nearest foot).

4-Which turkey is the better deal? * Sarah Lee Turkey $6.58 per lb O Butterball Turkey $11.16 for 2 lbs 4b-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 or .00, so if answer is 43 cents, its 0.43 or.43, if there is a dollar amount like 1.50, do not add zeros in front).

Answers

We will determine the best deal as follows:

We divide 11.16 by 2 to obtain the value per Lb, and we get that for each Lb the price is $ 5.58.

So, the best deal is Butterball Turkey at a price of $5.58 per Lb.

Which statement(s) can be interpreted from the equation for an automobile cost, C(t)= 28,000(0.73) *where C(t) represents the costand t represents the time in years?Select all correct statements.A. $28,000 represents the initial cost of an automobile that appreciates 73% per year over the course of t years.B. The equation is an exponential decay equation.OC. The equation is an exponential growth equation.D. $28,000 represents the initial cost of an automobile that depreciates 27% per year over the course of t years.E. The equation is neither exponential decay nor exponential growthF. $28,000 represents the initial cost of an automobile that appreciates 27% per year over the course of years.OG $28,000 represents the initial cost of an automobile that depreciates 73% per year over the course of t years.

Answers

1) Since the value in the bracket is below 1, that indicates it is a decay exponential equation if it is greater than one, it is a growth equation

Therefore option b is correct.

2) Also, since the value in the bracket is 0.73 this implies the automobile that depreciates 27% per year over the course of t years.

Therefore option d is also correct.

ity is net ranges $% per ment plus a one time.

Answers

Answer

a) The equation that represents the amount to be paid to xinfinity for using the internet for m months is

f(m) = 75m + 50

b) If Jose uses the xinfinity internet for 10 months, then he has paid the company $800.

Explanation

If the amount paid in total fir using the xinfinity internet for m months onths is f(m),

And xinfinity internet charges a $75 per month fee plus a one-time activation fee of $50.

a) So, if one really does use the xinfinity internet for m months, the total charge is

f(m) = (75 × m) + 50

f(m) = 75m + 50

b) If Jose uses the xinfinity internet for 10 months, we cam calculate how much he pays the xinfinity.

m = 10 months

f(m = 10) = 75 (10) + 50

= 750 + 50

= 800 dollars.

If Jose uses the xinfinity internet for 10 months, then he has paid the company $800.

Hope this Helps!!!is f(m),

And

Mia is painting a fence that is 1625 meters long In the morning she painted 245 meter of the fence how can Mia figure out how much more she has left to paint

Answers

If Mia is painting a fence that is 1625 meters long In the morning she painted 245 meter of the fence then she  1380 more she has left to paint

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given,

Mia is painting a fence that is 1625 meters long

Morning she painted 245 meter of the fence

We need to find how much more she has left to paint

To find this we need to subtract 245 from 1625

1625-245

1380

Hence 1380 more she has left to paint

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Let F(x) = f(f(x)) and G(x) = (F(x)) ^ 2 . You also know that f(3) = 2 , f(2)=3, f^ prime (2)=7 , f^ prime (3)=11

Answers

From the information given,

F(x) = f(f(x)

G(x) = (F(x))^2

F'(x) = f'(f(x)) * f'(x)

F'(3) = f'(f(3)) * f'(3)

f'(f(3)) = f'(2) = 7

f'(3) = 11

F'(3) = 7 * 11

F'(3) = 77

G'(x) = 2F(x) * F'(x) = 2f(f(x) * F'(x)

G'(3) = 2F(3) * F'(3) = 2f(f(3) * F'(3)

Given,

f(f(3) = f(2) = 3

G'(3) = 2 * 3 * 77

G'(3) = 462

Every day the ocean has two low tides and two high tides. Function g represents the height, in feet, of the water level in a cove relative to theaverage sea level. Let t represent the number of hours elapsed since the water height was equal to the average sea level after a low tide.s(e) = ssin(}t)Plot the points where s(4) is equal to the average sea level.

Answers

We can see from the question that we have the sine function, which is modeling the water level in a cove relative to the average sea level, and this function is given by:

[tex]g(t)=4sin(\frac{\pi}{6}t)[/tex]

And we need to find the points where g(t) is equal to the average sea level.

1. To find it, we need to analyze the given function as follows:

2. Then we can say that the function has:

• An amplitude (the value from the ,midline of the function, in this case, x = 0,).

,

• The period of the function is given by:

[tex]\begin{gathered} \text{ Period=}\frac{2\pi}{B} \\ \\ \text{ Period=}\frac{2\pi}{\frac{\pi}{6}}=2\pi(\frac{6}{\pi})=12 \\ \\ \text{ Period=}12 \end{gathered}[/tex]

3. These values can be seen as follows:

4. To find the points where g(t) is equal to the average sea level, we can see that the average sea level is represented by the midline, x = 0, and from the graph, we can see that these points are points on the x-axis, and they are (6, 0), and (12, 0) for the given graph:

A car traveled a distance of 195 miles in 390 minutes.What is the cars average rate in miles per minutes?A) 2 miles per minute b) 40 miles per minute c) 0.5 miles per minute d) 390 miles per minute

Answers

Given data

Distance = 195 miles

Time = 390 minutes

[tex]\begin{gathered} \text{Average sp}eed\text{ = }\frac{Dis\tan ce}{\text{Time}} \\ =\text{ }\frac{195}{390} \\ =0.5\text{ miles per minute} \end{gathered}[/tex]

A pizza restaurant has found that the probability that a customer will order thin crust is 0.4. In a random sample of 5 customers who order a pizza, find the probability that at least three of them want thin crust.

Answers

In this type of exercises, the probability of x successes on n reapeted trials in an experiment is given by the next formula:

[tex]P=\text{nCx}\cdot p^x\cdot(1-p)^{n-x}[/tex]

Here the nCx indicates the number of different combinations of x objects selected from a set of n objects. With the given data we can solve it easily:

p = 0.4

n = 5

x = 3

[tex]\begin{gathered} P=5\text{C3}\cdot0.4^3\cdot(1-0.4)^{5-3} \\ P=10\cdot0.064\cdot0.36 \\ P=0.2304 \end{gathered}[/tex]

Write 62° 21´ 47´´ as a decimal to the nearest thousandth. 62.413°62.366°62.363°62.373°

Answers

The given number is °:

[tex]62\degree21^{\prime}47^{\doubleprime}[/tex]

To write it as a decimal, start by placing the integer part the same, now to find the decimal part, let's take the minutes 21' and divide it by 60 (because there are 60 minutes in 1°):

[tex]\frac{21^{\prime}}{60}=0.35[/tex]

Now, let's divide the seconds 47" by 3600 (because there are 3600 seconds in 1°):

[tex]\frac{47^{\doubleprime}}{3600}=0.013[/tex]

Thus, the number is:

[tex]62\degree+0.35\degree+0.013\degree=62.363\degree[/tex]

there are 7 Red 3 blue and 5 green marbles in a bag what is the probability that the first three chosen will not be red?

Answers

Determine the total number of marble in the bag.

[tex]\begin{gathered} n(T)=7+3+5 \\ =15 \end{gathered}[/tex]

Determine the probability for first three marbles be red.

[tex]\begin{gathered} P(R=3)=\frac{^7C_3^{}}{^{15}C_3} \\ =\frac{35}{455} \\ =\frac{7}{91} \end{gathered}[/tex]

The probability for first three marble is not to be red is equal to one minus the probability for the first three marble be red.

[tex]\begin{gathered} P(R\ne3)=1-P(R=3) \\ =1-\frac{7}{91} \\ =\frac{91-7}{91} \\ =\frac{84}{91} \\ =\frac{12}{13} \end{gathered}[/tex]

So answer is 12/13.

Which of the following are true about a one-to-one function? Select all that apply.1. It graph will pass the horizontal line test2. It will always have an inverse 3. It’s graph is symmetric about the y-axis 4. It will always have either a local or maximum but not both 5. The graph will pass through point (1,1).

Answers

SOLUTION

Recall the definition of a one-to-one function

one to one function or one to one mapping states that each element of one set, say Set (A) is mapped with a unique element of another set, say, Set (B), where A and B are two different sets

There, the correct answers are

1. It graph will pass the horizontal line test

2. It will always have an inverse

A rectangle has a width of 50 centimeters and a perimeter of 208 centimeters. What is the rectangle's length?The length is cm.

Answers

The perimeter of a plane figure is the distance around it.

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(length + width)

From the information given,

Perimeter = 208 cm, Width = 50 cm

Therefore,

208 = 2(length + 50)

By dividing both sides of the equation by 2, it becomes

104 = length + 50

length = 104 - 50

length = 54 cm

Length of rectangle is 54 cm

The table shows the diameters in volume certain balls used for different sports. A bowling ball has an approximate volume of 5200 cm³ what is the best estimate for the diameter of a bowling ball

Answers

From the table, the value V = 5200 cm³ is between x = 21 cm and x = 22 cm.

Computing the average of the volumes associated to these x-values, we get:

V = (4,849.1 + 5,575.3)/2

V = 5212.2

which is near V = 5200 cm³. Then, the x-value related to V = 5200 cm³ is approximately the average between x = 21 and x = 22, that is:

x = (21 + 22)/2

x = 21.5 cm

Drake prepared 50 kilograms of dough in 5 hours. How many hours did Drake work if he prepared 70 kilogramsof dough at the same rate

Answers

We will determine how many hours he took to prepare 70 Kg as follows:

[tex]h=\frac{70\cdot5}{50}\Rightarrow h=7[/tex]

It took him 7 hours.

Here is a linear equation: y=1/4x+5/41. Are (1, 1.5) and (12,4) solutions to the equation?A. Both (1, 1.5) and (12,4) are solutions to the equation.B. Neither (1, 1.5) and (12,4) are solutions to the equation.C. (1, 1.5) is a solution but (12,4) is not.D. (12,4) is a solution to the equation but (1, 1.5) is not.Explain your reasoning.3. Find the x-intercept of the graph of the equationExplain or show your reasoning.

Answers

To find if any given point is a solution for the linear equation, simply plug in the x and y values given and check if the equality stands, as following:

[tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ (1,1.5) \\ \rightarrow1.5=\frac{1}{4}(1)+\frac{5}{4}\rightarrow1.5=\frac{6}{4}\rightarrow1.5=1.5✅ \end{gathered}[/tex][tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ (12,4) \\ \rightarrow4=\frac{1}{4}(12)+\frac{5}{4}\rightarrow4=3+\frac{5}{4}\rightarrow4=4.25✘ \end{gathered}[/tex]

Thereby the answer is:

C. (1, 1.5) is a solution but (12, 4) is not

Now, to find the x-intercept just make y = 0 and clear x, as following:

[tex]\begin{gathered} y=\frac{1}{4}x+\frac{5}{4} \\ \rightarrow0=\frac{1}{4}x+\frac{5}{4}\rightarrow0=\frac{x+5}{4}\rightarrow0=x+5\rightarrow-5=x \\ \rightarrow x=-5 \end{gathered}[/tex]

Therefore, the x-intercept is -5

Other Questions
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