5x-2y=10
4y+20=10x

Solving systemd

Answer:

The slope of the line would be y=x-1

Step-by-step explanation:

y=x-1

Subsite

3=4-1

3=3  True,

Thus y=x-1

Answer:Many

Step-by-step explanation:

As the unknown cancels itself out, it could be absolutely any number. So there are many solutions.

Answer: [tex]\Large\boxed{f(-9)=-189}[/tex]

Step-by-step explanation:

f(x) = -3x² - 6x

Requirements of the question

Find the value of f(-9)

Substitute values into the given function

f(x) = -3x² - 6x

f(9) = -3 (-9)² - 6 (-9)

Simplify the exponent

f(9) = -3 (81) - 6 (-9)

Simplify by multiplication

f(-9) = (-243) - (-54)

Simplify by subtraction

[tex]\Large\boxed{f(-9)=-189}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The value of k if (x+1) is a factor of f(x) is -4

The polynomial function is given as:

f(x)=x^3-kx^2+x+6

(x+1) is a factor of f(x)

So, we start by setting x + 1 to 0

x + 1 = 0

Solve for x

x = -1

Substitute x = -1 in f(x)=x^3-kx^2+x+6 and set the equation to 0

(-1)^3-k(-1)^2+(-1)+6 = 0

Evaluate the exponents

-1 - k - 1 + 6 = 0

Evaluate the like terms

k + 4 = 0

Solve for k

k = -4

Hence, the value of k if (x+1) is a factor of f(x) is -4

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Answer:

3024

Step-by-step explanation:

Each chosen member (out of 9 members) will occupy a different position

out of these four (president , vice-president , secretary , treasurer).

So, here we have to calculate the Number of Permutations of 9 members Taken 4 at a Time :

= 9P4

= 9 × 8 × 7 × 6

= 3024

Answer:

when x=-7

Step-by-step explanation:

if u are solving a function like this, u must not have a division by zero so if we put x=-7 in the function we hav a division by zero

Step-by-step explanation:

4.6 hrs is 46over 10 which is

13 over 5 or 2 and 3over 5

Answer:

C. 109x

Step-by-step explanation:

We know that there are 109 students in the fourth grade, who each have x cupcakes. In order to find the total amount of cupcakes, we could add all of the cupcakes together to get:

x + x + x + x + .... x

109 times because there are 109 students.

This can be simplified to become 109x.  

Answer:

3/4

Step-by-step explanation:

multiply each fraction by 100 or you could find the LCM

Answer:

Lose 12y yards.

Lose 5.2x yards.

What is the net yardage for these four plays?

is the que correct

Answer:

19.8x - 11.1y

Step-by-step explanation:

Given information:

"Gain" means to add the value.

"Lose" means to subtract the value.

Therefore, net yardage is:

⇒ 25x + 0.9y - 12y - 5.2x

Collect like terms:

⇒ 25x - 5.2x + 0.9y - 12y

Factor out the common variables x and y:

⇒ x(25 - 5.2) + y(0.9 - 12)

Carry out the operations in the parentheses:

⇒ x(19.8) + y(-11.1)

Therefore, the net yardage is  19.8x - 11.1y

The parts of algebraic expressions related to polynomials are variables and coefficients.

The parts of algebraic expressions are;

Polynomials are algebraic expressions composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, and multiplication

Polynomials consists of variables and coefficients. The variables in polynomials are also called indeterminates. The coefficients also multiply this variables.

Thus, the parts of algebraic expressions related to polynomials are variables and coefficients.

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Answer:

Step-by-step explanation:

I gotcha my dude.......

x-5 and 2x+3

The correct option is (A) P(X) × P(Y) = P(X ∩ Y)

What is probability and example?

 We are given to consider a situation in which X and Y are two events such that

P(X) = 4/5, P(Y) = 1/4, P(X ∩ Y) = 1/5

We are to select the statement that best describes the events X and Y

We know that

any two events A and B are said to be independent if

P(A) × P(B) = P (A ∩ B)

We have, for events X and Y,

P(X) × P(Y) = 4/5 × 1/4 = 1/5 = P (X ∩ Y)

P(X) × P(Y) = P(X ∩ Y)

Thus, X and Y are independent because P(X) × P(Y) = P(X ∩ Y)

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The complete question is -

Consider a situation in which P(X) = 4/5 and P(Y) = 1/4. If P(X and Y) is = 1/5, which best describes the events?

They are independent because P(X) x P(Y) = P(X and Y).

They are independent because P(X) + P(Y) = P(X and Y).

They are dependent because P(X) x P(Y) = P(X and Y).

They are dependent because P(X) + P(Y) = P(X and Y).

Answer: a

Step-by-step explanation:

just took the test

Answer: Look into step by step

Step-by-step explanation:

1. Multiply the second equation by 2; 6x - 2y = -2 then add to first equation

7x = -7 so x = -1, substitute x = -1 into the first equation -1 + 2y = -5 so y = -2

2. Multiply the first equation by 3; 3x + 6y = 6 then subtract it by second equation

y = 2, substitute y = 2 into first equation, x + 4 = 2, x = -2

3. Multiply the first equation by 2; 2x + 6y = 14 then subtract it by second equation

2y = 3 so y = 1.5, substitute y = 1.5 into the first equation x + 4.5 = 7, x = 2.5

I chose this method as it is easy

Answer:

Step-by-step explanation:

0= x2 – 2x – 3

a = 1, b = -2 and c = -3.

Answer:

A on edge

Step-by-step explanation:

Give me the brainiest please

Equation (A) C= 1.46n shows the relationship between the total cost of gasoline, c, and the number of gallons purchased, n.

To find the right equation:

Therefore, equation (A) C= 1.46n shows the relationship between the total cost of gasoline, c, and the number of gallons purchased, n.

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The complete question is given below:
The total cost of gasoline varies directly with the number of gallons purchased. Kathy pays $23.36 for 16 gallons of gasoline. Which equation

shows the relationship between the total cost of gasoline, c, and the number of gallons purchased, n?

A.C= 1.46n

B. n = 1.46c

C.C = 23.361

D. n = 23.36c

Answer:

[tex]\dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1[/tex]

Step-by-step explanation:

Given equation:

[tex]4x^2-9y^2-8x+36y-68=0[/tex]

This is an equation for a horizontal hyperbola.

To complete the square for a hyperbola

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side.

[tex]\implies 4x^2-8x-9y^2+36y=68[/tex]

Factor out the coefficient of the x² term and the y² term.

[tex]\implies 4(x^2-2x)-9(y^2-4y)=68[/tex]

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

[tex]\implies 4\left(x^2-2x+\left(\dfrac{-2}{2}\right)^2\right)-9\left(y^2-4y+\left(\dfrac{-4}{2}\right)^2\right)=68+4\left(\dfrac{-2}{2}\right)^2-9\left(\dfrac{-4}{2}\right)^2[/tex]

[tex]\implies 4\left(x^2-2x+1\right)-9\left(y^2-4y+4\right)=36[/tex]

Factor the two perfect trinomials on the left side:

[tex]\implies 4(x-1)^2-9(y-2)^2=36[/tex]

Divide both sides by the number of the right side so the right side equals 1:

[tex]\implies \dfrac{4(x-1)^2}{36}-\dfrac{9(y-2)^2}{36}=\dfrac{36}{36}[/tex]

Simplify:

[tex]\implies \dfrac{(x-1)^2}{9}-\dfrac{(y-2)^2}{4}=1[/tex]

Therefore, this is the standard equation for a horizontal hyperbola with:

The smallest possible value of m according to the task is; 1/1540.

Since it follows from the task content that the product of 1540 and m is a square number and the smallest possible small number is; 1.

The equation which holds true is; 1540 × m = 1

Consequently, m = 1/1540.

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The age of the pottery bowl to the nearest year is 4307 years. Using exponential decay or growth formula, the required value is calculated.

The formula for the exponential growth/decay is

[tex]N=N_0e^-^k^t[/tex]

Where,

N - the total amount after time t

N₀ - the initial amount

k - growth or decay rate

t - time

It is given that,

A student in Greece discovers a pottery bowl that contains 65% of its original amount of C-14.

⇒ N(t) = 0.65N₀

But we have k = 0.0001.

Then,

[tex]N(t)=N_0e^-^k^t[/tex]

0.65 N₀ = N₀ [tex]e^{-(0.0001)t}[/tex]

⇒ 0.65 = [tex]e^{-(0.0001)t}[/tex]

⇒ ln [tex]e^{-(0.0001)t}[/tex] = ln 0.65

⇒ -(0.0001)t = -0.4307

⇒ t = 0.4037/0.0001

∴ t = 4307 years.

Thus, the age of the pottery bowl is 4307 years.

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The solution to the product of 8 and three-seventh is 2 2/7. According to Laura, she made mistake in step 2 by adding 8 and 3 instead of multiplying

Multiplication of fractions and integers

Fractions are written as a ratio of two integers. For instance a/b is a fraction where a and b are integers.

Given the following equation

Multiply 3/7 and 8

This is expressed mathematically as;

3/7 * 8

Step 1: Swap to have;

8 * 3/7

Step 2: Group the numerator

(8*2)/7

Step 3; Simplify

16/7

Step 4; Convert to mixed fraction

16/7=  2 2/7

The solution to the product of 8 and three-seventh is 2 2/7. According to Laura, she made mistake in step 2 by adding 8 and 3 instead of multiplying

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Answer:

Graph b

Step-by-step explanation:

y = |x| is a "v"at x = 0

y = |x-1| is a "v" shifted to the right by 1 unit

The correct transformation of f(x) to get 4f(x+2) is by a vertical shift by 4 and 2 units in the x direction.

Given a function f(x) and other function 4f(x+2).

We are required to choose a transformation that will give 4f(x+2) from a function f(x).

Function is like a relationship between two or more variables that are expressed in equal to form. The values which we enter in a function is known as domain and the value that we get as a result are known as range.

So, we have to reach 4f(x+2) from f(x).

The value of function is usually expressed on y axis and variable x on x axis.

To increase the value of x by 2 we have to stretch it in x direction.To find the 4 times value of function we have to stretch the y axis to 4 units.

Hence the correct transformation of f(x) to get 4f(x+2) is by a vertical shift by 4 and 2 units in the x direction.

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The distance on map exists 32 cm and actual area exists 37.5 km².

Given: Scale of the map exists at 1:250000.

(a) Distance between two cities = 80 km

= 80000 m

= 8000000 cm

Distance on map = 8000000 [tex]*[/tex] 1/ 250000

= 32 cm

(b) Area of map = 6 cm²

Actual area = [tex]6(250000)^2[/tex] cm²

[tex]= 6 * 625 * 10^8[/tex] cm²

[tex]= 3750 * 10^8/ 10^{10}[/tex]

= 37.5 km²

Therefore, the distance on map exists 32 cm and actual area exists 37.5 km².

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Let [tex]A(t)[/tex] = amount of salt (in pounds) in the tank at time [tex]t[/tex] (in minutes). Then [tex]A(0) = 11[/tex].

Salt flows in at a rate

[tex]\left(0.6\dfrac{\rm lb}{\rm gal}\right) \left(3\dfrac{\rm gal}{\rm min}\right) = \dfrac95 \dfrac{\rm lb}{\rm min}[/tex]

and flows out at a rate

[tex]\left(\dfrac{A(t)\,\rm lb}{75\,\rm gal + \left(3\frac{\rm gal}{\rm min} - 3.25\frac{\rm gal}{\rm min}\right)t}\right) \left(3.25\dfrac{\rm gal}{\rm min}\right) = \dfrac{13A(t)}{300-t} \dfrac{\rm lb}{\rm min}[/tex]

where 4 quarts = 1 gallon so 13 quarts = 3.25 gallon.

Then the net rate of salt flow is given by the differential equation

[tex]\dfrac{dA}{dt} = \dfrac95 - \dfrac{13A}{300-t}[/tex]

which I'll solve with the integrating factor method.

[tex]\dfrac{dA}{dt} + \dfrac{13}{300-t} A = \dfrac95[/tex]

[tex]-\dfrac1{(300-t)^{13}} \dfrac{dA}{dt} - \dfrac{13}{(300-t)^{14}} A = -\dfrac9{5(300-t)^{13}}[/tex]

[tex]\dfrac d{dt} \left(-\dfrac1{(300-t)^{13}} A\right) = -\dfrac9{5(300-t)^{13}}[/tex]

Integrate both sides. By the fundamental theorem of calculus,

[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac1{(300-t)^{13}} A\bigg|_{t=0} - \frac95 \int_0^t \frac{du}{(300-u)^{13}} [/tex]

[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = -\dfrac{11}{300^{13}} - \frac95 \times \dfrac1{12} \left(\frac1{(300-t)^{12}} - \frac1{300^{12}}\right) [/tex]

[tex]\displaystyle -\dfrac1{(300-t)^{13}} A = \dfrac{34}{300^{13}} - \frac3{20}\frac1{(300-t)^{12}}[/tex]

[tex]\displaystyle A = \frac3{20} (300-t) - \dfrac{34}{300^{13}}(300-t)^{13}[/tex]

[tex]\displaystyle A = 45 \left(1 - \frac t{300}\right) - 34 \left(1 - \frac t{300}\right)^{13}[/tex]

After 1 hour = 60 minutes, the tank will contain

[tex]A(60) = 45 \left(1 - \dfrac {60}{300}\right) - 34 \left(1 - \dfrac {60}{300}\right)^{13} = 45\left(\dfrac45\right) - 34 \left(\dfrac45\right)^{13} \approx 34.131[/tex]

pounds of salt.

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. Hence:

Rate of the machine = 3 pounds / 20 seconds = 0.15 pound per second

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

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Answer:

I think it's A (parallel)

Answer:

A. its parallel

Step-by-step explanation:

all angles are equal... two sides are perpendicular and two are parallel