Mathematics College

Solve each system by graphing.

Answers

Answer 1

9514 1404 393

Answer:

(x, y) = (4, -3)

Step-by-step explanation:

The solution is the point on the graph where the lines intersect:

(x, y) = (4, -3)

Related Questions

help with 1 b please. using ln.

Answers

Answer:

[tex]\displaystyle \frac{dy}{dx} = \frac{1}{(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra I

Terms/CoefficientsFactoringExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]

Algebra II

Natural logarithms ln and Euler's number eLogarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]

Calculus

Differentiation

DerivativesDerivative NotationImplicit Differentiation

Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

*Note:

You can simply just use the Quotient and Chain Rule to find the derivative instead of using ln.

Step 1: Define

Identify

[tex]\displaystyle y = \sqrt{\frac{x}{2 - x}}[/tex]

Step 2: Rewrite

[Function] Exponential Rule [Root Rewrite]: [tex]\displaystyle y = \bigg( \frac{x}{2 - x} \bigg)^\bigg{\frac{1}{2}}[/tex][Equality Property] ln both sides: [tex]\displaystyle lny = ln \bigg[ \bigg( \frac{x}{2 - x} \bigg)^\bigg{\frac{1}{2}} \bigg][/tex]Logarithmic Property [Exponential]: [tex]\displaystyle lny = \frac{1}{2}ln \bigg( \frac{x}{2 - x} \bigg)[/tex]

Step 3: Differentiate

Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx}[lny] = \frac{dy}{dx} \bigg[ \frac{1}{2}ln \bigg( \frac{x}{2 - x} \bigg) \bigg][/tex]Logarithmic Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{1}{2} \bigg( \frac{1}{\frac{x}{2 - x}} \bigg) \frac{dy}{dx} \bigg[ \frac{x}{2 - x} \bigg][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{1}{2} \bigg( \frac{1}{\frac{x}{2 - x}} \bigg) \bigg[ \frac{2}{(x - 2)^2} \bigg][/tex]Simplify: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{-1}{x(x - 2)}[/tex]Isolate [tex]\displaystyle \frac{dy}{dx}[/tex]: [tex]\displaystyle \frac{dy}{dx} = \frac{-y}{x(x - 2)}[/tex]Substitute in y [Derivative]: [tex]\displaystyle \frac{dy}{dx} = \frac{-\sqrt{\frac{x}{2 - x}}}{x(x - 2)}[/tex]Rationalize: [tex]\displaystyle \frac{dy}{dx} = \frac{-\frac{x}{2 - x}}{x(x - 2)\sqrt{\frac{x}{2 - x}}}[/tex]Rewrite: [tex]\displaystyle \frac{dy}{dx} = \frac{-x}{x(x - 2)(2 - x)\sqrt{\frac{x}{2 - x}}}[/tex]Factor: [tex]\displaystyle \frac{dy}{dx} = \frac{-x}{-x(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{1}{(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Book: College Calculus 10e

Use the information below to complete the problem: p(x)=1/x+1 and q(x)=1/x-1 Perform the operation and show that it results in another rational expression. p(x) + q(x)

Answers

Answer:

hope u will understand...if u like this answer plz mark as brainlist

Answer:

[tex]\displaystyle p(x) + q(x) = \frac{2x}{(x+1)(x-1)}[/tex]

The result is indeed another rational expression.

Step-by-step explanation:

We are given the two functions:

[tex]\displaystyle p(x) = \frac{1}{x+1}\text{ and } q(x) = \frac{1}{x-1}[/tex]

And we want to perform the operation:

[tex]\displaystyle p(x) + q(x)[/tex]

And show that the result is another rational expression.

Add:

[tex]\displaystyle = \frac{1}{x+1} + \frac{1}{x-1}[/tex]

To combine the fractions, we will need a common denominator. So, we can multiply the first fraction by (x - 1) and the second by (x + 1):

[tex]\displaystyle = \frac{1}{x+1}\left(\frac{x-1}{x-1}\right) + \frac{1}{x-1}\left(\frac{x+1}{x+1}\right)[/tex]

Simplify:

[tex]=\displaystyle \frac{x-1}{(x+1)(x-1)} + \frac{x+1}{(x+1)(x-1)}[/tex]

Add:

[tex]\displaystyle = \frac{(x-1)+(x+1)}{(x+1)(x-1)}[/tex]

Simplify. Hence:

[tex]\displaystyle p(x) + q(x) = \frac{2x}{(x+1)(x-1)}[/tex]

The result is indeed another rational expression.

please help! 50 points!

Answers

Answer:

a) forming a bell

b) 5

c) 4.7

d) mean

is the correct answer

pls mark me as brainliest

Which statement is true about the ratios of squares to
cicles in the tables? PLS HURRY!!!!

Answers

Answer:

show us a screenshot or image

or type it out, copy paste

Step-by-step explanation:

A manufacturer of industrial solvent guarantees its customers that each drum of solvent they ship out contains at least 100 lbs of solvent. Suppose the amount of solvent in each drum is normally distributed with a mean of 101.8 pounds and a standard deviation of 3.76 pounds.

Required:
a. What is the probability that a drum meets the guarantee? Give your answer to four decimal places.
b. What would the standard deviation need to be so that the probability a drum meets the guarantee is 0.99?

Answers

Answer:

The answer is "0.6368 and 0.773".

Step-by-step explanation:

The manufacturer of organic compounds guarantees that its clients have at least 100 lbs. of solvent in every fluid drum they deliver. [tex]X\ is\ N(101.8, 3.76)\\\\P(X>100) =P(Z> \frac{100-101.8}{3.76}=P(Z>-0.47))[/tex]

For point a:

Therefore the Probability =0.6368

For point b:

[tex]P(Z\geq \frac{100-101.8}{\sigma})=0.99\\\\P(Z\geq \frac{-1.8}{\sigma})=0.99\\\\1-P(Z< \frac{-1.8}{\sigma})=0.99\\\\P(Z< \frac{-1.8}{\sigma})=0.01\\\\z-value =0.01\\\\area=-2.33\\\\ \frac{-1.8}{\sigma}=-2.33\\\\ \sigma= \frac{-1.8}{-2.33}=0.773[/tex]

Write a quadratic equation having the given numbers as solutions. -7 and -5
The quadratic equation is ___ =0.

Answers

Answer:

x²+12x+35

Step-by-step explanation:

in factored form it would just be

(x+7)(x+5)=0

expand this

x²+12x+35=0

inveres laplace transform (3s-14)/s^2-4s+8

Answers

Complete the square in the denominator.

[tex]s^2 - 4s + 8 = (s^2 - 4s + 4) + 4 = (s-2)^2 + 4[/tex]

Rewrite the given transform as

[tex]\dfrac{3s-14}{s^2-4s+8} = \dfrac{3(s-2) - 8}{(s-2)^2+4} = 3\times\dfrac{s-2}{(s-2)^2+2^2} - 4\times\dfrac{2}{(s-2)^2+2^2}[/tex]

Now take the inverse transform:

[tex]L^{-1}_t\left\{3\times\dfrac{s-2}{(s-2)^2+2^2} - 4\times\dfrac{2}{(s-2)^2+2^2}\right\} \\\\ 3L^{-1}_t\left\{\dfrac{s-2}{(s-2)^2+2^2}\right\} - 4L^{-1}_t\left\{\dfrac{2}{(s-2)^2+2^2}\right\} \\\\ 3e^{2t} L^{-1}_t\left\{\dfrac s{s^2+2^2}\right\} - 4e^{2t} L^{-1}_t\left\{\dfrac{2}{s^2+2^2}\right\} \\\\ \boxed{3e^{2t} \cos(2t) - 4e^{2t} \sin(2t)}[/tex]

Any number that CAN be divided by 2 without having remainder is considered an _______ number

Answers

Step-by-step explanation:

Any number that can be divided by 2 without having remainder is considered an even number.

I hope it helped U

stay safe stay happy

The following 3 points are on a parabola defining the edge of a ski.
(-4, 1), (-2, 0.94), (0,1)

The general form for the equation of a parabola is:
Ax^2 + Bx + C= y

Required:
a. Use the x- and y-values of 1 of the points to build a linear equation with 3 variables: A, B, and C.
b. Record your equation here. Repeat this process with 1 of the other 2 points to build a 2nd linear equation.
c. Record your equation here. Repeat this process with the other point to build a 3rd equation.
d. Record your equation here. Build a matrix equation that represents this system of equations.
e. Record your matrix equation here. Use a graphing calculator or other graphing utility to find the inverse of the coefficient matrix.
f. Record your result here. Use the inverse matrix to solve the system of equations. Record the equation of the parabola here.

Answers

a. The linear equation for the first point (-4,1) is 16A-4B+C=1

b. The linear equation for the second point (-2, 0.94) is 4A-2B+C=0.94

c. The linear equation for the third point (0,1) is 0A+0B+C=1

d. The matrix equation looks like this:

[tex]\left[\begin{array}{ccc}16&-4&1\\4&-2&1\\0&0&1\end{array}\right]*\left[\begin{array}{c}A\\B\\C\end{array}\right]=\left[\begin{array}{c}1\\0.94\\1\end{array}\right][/tex]

e. The inverse of the coefficient matrix looks like this:

[tex]A^{-1}=\left[\begin{array}{ccc}\frac{1}{8}&-\frac{1}{4}&\frac{1}{8}\\\frac{1}{4}&-1&\frac{3}{4}\\0&0&1\end{array}\right][/tex]

f. The equation of the parabola is: [tex]\frac{3}{200}x^{2}+\frac{3}{50}x+1=y[/tex]

a. In order to build a linear equation from the given points, we need to substitute them into the general form of the equation.

Let's take the first point (-4,1). When substituting it into the general form of the quadratic equation we end up with:

[tex](-4)^{2}A+(-4)B+C=1[/tex]

which yields:

[tex]16A-4B+C=1[/tex]

b. Let's take the second point (-2,0.94). When substituting it into the general form of the quadratic equation we end up with:

[tex](-2)^{2}A+(-2)B+C=0.94[/tex]

which yields:

[tex]4A-2B+C=0.94[/tex]

c. Let's take the third point (0,1). When substituting it into the general form of the quadratic equation we end up with:

[tex](0)^{2}A+(0)B+C=1[/tex]

which yields:

[tex]0A+0B+C=1[/tex]

d. A matrix equation consists on three matrices. The first matrix contains the coefficients (this is the numbers on the left side of the linear equations). Make sure to write them in the right order, this is, the numbers next to the A's should go on the first column, the numbers next to the B's should go on the second column and the numbers next to the C's should go on the third column.

The equations are the following:

16A-4B+C=1

4A-2B+C=0.94

0A+0B+C=1

So the coefficient matrix looks like this:

[tex]\left[\begin{array}{ccc}16&-4&1\\4&-2&1\\0&0&1\end{array}\right][/tex]

Next we have the matrix that has the variables, in this case our variables are the letters A, B and C. So the matrix looks like this:

[tex]\left[\begin{array}{c}A\\B\\C\end{array}\right][/tex]

and finally the matrix with the answers to the equations, in this case 1, 0.94 and 1:

[tex]\left[\begin{array}{c}1\\0.94\\1\end{array}\right][/tex]

so if we put it all together we end up with the following matrix equation:

[tex]\left[\begin{array}{ccc}16&-4&1\\4&-2&1\\0&0&1\end{array}\right]*\left[\begin{array}{c}A\\B\\C\end{array}\right]=\left[\begin{array}{c}1\\0.94\\1\end{array}\right][/tex]

e. When inputing the coefficient matrix in our graphing calculator we end up with the following inverse matrix:

[tex]A^{-1}=\left[\begin{array}{ccc}\frac{1}{8}&-\frac{1}{4}&\frac{1}{8}\\\frac{1}{4}&-1&\frac{3}{4}\\0&0&1\end{array}\right][/tex]

Inputing matrices and calculating their inverses depends on the model of a calculator you are using. You can refer to the user's manual on how to do that.

f. Our matrix equation has the following general form:

AX=B

where:

A=Coefficient matrix

X=Variables matrix

B= Answers matrix

In order to solve this type of equations, we can make use of the inverse of the coefficient matrix to end up with an equation that looks like this:

[tex]X=A^{-1}B[/tex]

Be careful with the order in which you are doing the multiplication, if A and B change places, then the multiplication will not work and you will not get the answer you need. So when solving this equation we get:

[tex]\left[\begin{array}{c}A\\B\\C\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{8}&-\frac{1}{4}&\frac{1}{8}\\\frac{1}{4}&-1&\frac{3}{4}\\0&0&1\end{array}\right]*\left[\begin{array}{c}1\\\frac{47}{50}\\1\end{array}\right][/tex]

(Notice that I changed 0.94 for the fraction 47/50 you can get this number by dividing 94/100 and simplifying the fraction)

So, in order to do the multiplication, we need to multiply each row of the coefficient matrix by the answer matrix and add the results. Like this:

[tex]\frac{1}{8}*1+(-\frac{1}{4})(\frac{47}{50})+\frac{1}{8}*1[/tex]

[tex]\frac{1}{8}-\frac{47}{200}+\frac{1}{8}=\frac{3}{200}[/tex]

So the first number for the answer matrix is [tex]\frac{3}{200}[/tex]

[tex]\frac{1}{4}*1+(-1)(\frac{47}{50})+\frac{3}{4}*1[/tex]

[tex]\frac{1}{4}-\frac{47}{50}+\frac{3}{4}=\frac{3}{50}[/tex]

So the second number for the answer matrix is [tex]\frac{3}{50}[/tex]

[tex]0*1+0(\frac{47}{50})+1*1[/tex]

[tex]0+0+1=1[/tex]

So the third number for the answer matrix is 1

In the end, the matrix equation has the following answer.

[tex]\left[\begin{array}{c}A\\B\\C\end{array}\right]=\left[\begin{array}{c}\frac{3}{200}\\\frac{3}{50}\\1\end{array}\right][/tex]

which means that:

[tex]A=\frac{3}{200}[/tex]

[tex]B=\frac{3}{50}[/tex]

and C=1

so, when substituting these answers in the general form of the equation of the parabola we get:

[tex]Ax^{2}+Bx+C=y[/tex]

[tex]\frac{3}{200}x^{2}+\frac{3}{50}x+1=y[/tex]

For further information, you can go to the following link:

https://brainly.com/question/12628757?referrer=searchResults

13
R
S
12
What's the length of QR?
A) 1
B) 17.7
C) 6.7
OD) 5

Answers

Answer:

Step-by-step explanation:

This is a right triangle, so we can use the Pythagorean theorem

a^2+b^2 = c^2

where a and b are the legs and c is the hypotenuse

QR^2 + 12^2 = 13^2

QR^2 +144 =169

QR^2 = 169-144

QR^2 =25

Take the square root of each side

QR = sqrt(25)

QR =5

Answer as soon as you can. a. 162 comes just after b. What comes just before 182. lies in between 99 and 101. c.

Answers

Answer:

a. 161

b. 181

c. 100

Step-by-step explanation:

a. 162 comes just after 161 (160, 161, 162, 163...)

b. 181 comes just before 182 (180, 181, 182, 183...)

c. 100 is between 99 and 101 (98, 99, 100, 101, 102...)

If 8x+5(3+x)-a=15+5x, then a = ?

Answers

Answer:

a = 8x

if you want to find x also, then x = a/8

Step-by-step explanation:

Nine Increased by the product of a number and 4 is greater than or equal to -15

Use the variable y for the unknown number

Answers

Answer:

9+4y ≥ -15

y ≥ -6

Step-by-step explanation:

Nine Increased by the product of a number

9+4y

is greater than or equal to -15

9+4y ≥ -15

Subtract 9 from each side

9-9+4y ≥ -15-9

4y ≥ -24

Divide by 4

4y/4 ≥ -24/4

y ≥ -6

PLEAZE HELPPPPPPPSPPSPAP

Answers

Answer:

Step-by-step explanation:

345ftyfthftyft.plk,k,

Answer:

Hello,

Anwser is C

Step-by-step explanation:

[tex]y=log_9(12x)\\\\9^y=12x\\\\9^x=12y\ inverting \ x \ and \ y \\\\y=\dfrac{9^x}{12} \\[/tex]

What does si mean in temperature

Answers

Answer:

The kelvin (abbreviation K), also called the degree Kelvin (abbreviation, o K), is the SI unit of temperature. One Kelvin is 1/273.16 (3.6609 x 10 -3 ) of the thermodynamic temperature of the triple point of pure water (H 2 O). The ampere (abbreviation, A) is the SI unit of electric current.

Answer:

kelvin is si unit of tempreature

Difference between 5429 and 5907 to the greatest place.

Answers

answer- u have to subtract the great no. from the smaller one

Given numbers are 5429 and 5907..

To find the difference we should subtract..

5907

- 5429

-------------

478

_______

#Answered by: Cutest Ghost

Help me please thanks guys

Answers

Answer:

B, D, F

Step-by-step explanation:

In a rational exponent, the numerator is an exponent, and the denominator becomes the index of the root.

[tex]a^{\frac{m}{n}} = \sqrt[n] {a^m}[/tex]

Answer: B, D, F

Terrell loves to listen to music, so he buys a subscription to a music-streaming service. He pays $4.99 each month. How much does the streaming service cost per year?

Answers

Answer:
$59.88

Solving Steps:
So $4.99 each month. There are 12 months in a year so you have to times $4.99x12. This is $59.88 which is the answer.

Please help me to find out the answer

Answers

9514 1404 393

Answer:

44.66 in

Step-by-step explanation:

The side opposite the marked angle is given, and the side adjacent to it is the one wanted. The relevant trig relation is ...

Tan = Opposite/Adjacent

Solving for the Adjacent side, we find ...

Adjacent = Opposite/Tan

PQ = (29 in)/tan(33°) ≈ 44.66 in

PLEASE HELP

Solve the equation for y. Identify the slope and y-intercept then graph the equation.

-3y=3x-9

Y=
M=
B=

Please Include a picture of the graph and show your work if you can

Answers

9514 1404 393

Answer:

y = -x +3

m = -1

b = 3

Step-by-step explanation:

To solve the given equation for y, divide by the coefficient of y.

(-3y)/(-3) = (3x -9)/(-3)

y = -x +3

The slope is the x-coefficient, M = -1.

The y-intercept is the added constant, B = 3.

Both equations are graphed in the attachment. Texture has been added to the original so you can see the graphs are the same line.

For the given annual rate of change, find the corresponding growth or decay factor. + 300%

Answers

Answer:

50% growth would would be (1 + .5)^ n

and 100% growth would be (1+ 1)^n

I assume that the answer would be (1+3)^n

for 300% growth the factor would be 3

Step-by-step explanation:

Chad has a win loss ratio 5:5 across his games what percentage of games did he win

Answers

Answer:

Step-by-step explanation:

50%

Answer:

50%

Step-by-step explanation:

Win % = wins / total * 100%

Win% = (5/(5 + 5)) * 100

Win% = 5/10 * 100 = 50%

Need the answer please, soon as possible

Answers

9514 1404 393

Answer:

(d) 27.4%

Step-by-step explanation:

The desired percentage is ...

(juniors for Kato)/(total juniors) × 100%

= 129/(129 +194 +147) × 100%

= (129/470) × 100% ≈ 27.4%

About 27.4% of juniors voted for Kato.

Casey's phone service charges a flat monthly fee of $30 for the first 1000 minutes of calls and $0.40 per minute over 1000. Determine Casey's monthly charge if he makes 1,100 minutes of calls?

Answers

Answer:

Casey's monthly charge for making 1,100 minutes of calls is $70.

Step-by-step explanation:

We can write a piecewise function to model the situation.

Since Casey's phone service only charges a monthly fee of $30 for the first 1000 minutes, we can write that for calling t minutes:

[tex]\displaystyle C(t) = 30\text{ if } t\leq 1000[/tex]

In other words, the total cost is only $30 is the total minutes of call is less than 1000 minutes.

However, if the total minutes of calls is greater than 1000, then its $0.40 per minute on top of the 30. Thus:

[tex]\displaystyle C(t) = 30 + 0.4(t-1000)\text{ if } t>1000[/tex]

All together, our piecewise function will be:

[tex]\displaystyle C(t) = \begin{cases} 30 & t\leq 1000 \\ 30 + 0.4(t-1000) & t>1000\end{cases}[/tex]

We want to determine Caseys monthly charge if he makes 1,100 minutes of calls. So, t = 1100. Since 1100 > 1000, we will use the second equation. This yields:

[tex]C(1100)= 30+0.4((1100)-1000)[/tex]

Evaluate:

[tex]\displaystyle C(1100) = 30+0.4(100) = 30+40=\$70[/tex]

Casey's monthly charge for using 1,100 minutes of call is $70.

The firm had 15 billion VND of earnings before interest and tax (EBIT), corporate tax is 20%. The market price of stock is 60.000đ. Knowing that net income will be held 40% before using it for dividend. How much of the net income can be divided for shareholders?