Evaluate the equation

Answer:

An equation has an equal sign between two expressions, while an inequality has a ≤ or ≥ sign.

Answer:

your laptop is nice really

Answer:

y = -5x -10

Step-by-step explanation:

plug the given values into the line equation: y = mx + b

where m is the slope and b is the y-intercept.

f(0) is the y-intercept (the point on the graph where x = 0)

The linear function with the properties f(0) = -10, Slope of -5 is f(X)=-5x-10.

To find the linear function with the given properties, we need to use the slope-intercept form of a linear function, which is:

y = mx + b

where:

y is the output (the value of the function)

x is the input (the independent variable)

m is the slope of the line

b is the y-intercept (the value of the function when x = 0)

We are given that f(0) = -10, which means when x is 0, the function value (y) is -10. This gives us the y-intercept (b = -10).

We are also given that the slope (m) is -5.

So, the linear function is f(x) = -5x - 10.

Hence, the linear function is f(x) = -5x - 10.

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Answer:

x (y+1)

xy+1x

xy+x is theanswer.

I hope this will help you.

stay safe

Answer:

The distance between two points (a, b) and (c, d) is given by:

[tex]d = \sqrt{(a - c)^2 + (b - d)^2}[/tex]

So the distance between the point (6, 5) and the line y = 5x - 10 can be thought as the distance between the point (6, 5) and the point (x, 5x - 10)

Where:

(x, 5x - 10) denotes all the points in the line y = 5x – 10

That distance is given by:

[tex]d = \sqrt{(x - 6)^2 + (5x - 10 - 5)^2} = \sqrt{(x - 6)^2 + (5x - 15)^2}[/tex]

Now we want to minimize this.

Because the distance is a positive quantity, we can try to minimize d^2 insted, so we have:

[tex]d^2 = (\sqrt{(x - 6)^2 + (5x - 15)^2})^2 = (x - 6)^2 + (5x - 15)^2}\\\\d^2 = x^2 - 2*x*6 + 36 + 25*x^2 - 2*15*x + (-15)^2\\\\d^2 = 26*x^2 - 42*x + 261[/tex]

Notice that this is a quadratic equation with a positive leading coefficient, which means that the arms of the graph will open upwards, then the minimum will be at the vertex of the parabola.

Remember that for a parabola:

y = a*x^2 + bx + c

the x-value of the vertex is:

x = -b/2a

Then for our parabola:

d^2 = 26*x^2 - 42*x + 261

The vertex is at:

x = -(-42)/(2*26) = 0.808

Then we just need to evaluate the distance equation in that value of x to get the shortest distance:

[tex]d = \sqrt{(0.808 - 6)^2 + (5*0.808 - 15)^2} = 12.129[/tex]

The shortest distance between the point A and the line is 12.129 units.

Answer:

x = 24.8

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

Sin theta = opp / hypotenuse

sin 75 = 24 /x

x sin 75 = 24

x = 24/ sin 75

x=24.84662

Rounding to the nearest tenth

x = 24.8

Answer:

3 planters can be filled, with 288,156 gallons left over.

Step-by-step explanation:

Given that a dump truck with 1500 gallons of soil arrives on campus to fill in the new planters on the quad, and each planter needs 2 cubic yards of soil, to determine how many planters can be filled the following calculation must be performed:

1 cubic yard = 201.974 gallons

2 cubic yards = 403.948 gallons

1500 / 403.948 = X

3.71 = X

1500 - (403.948 x 3) = 288.156

Therefore, 3 planters can be filled, with 288,156 gallons left over.

Answer:

Step-by-step explanation:

I assume that you mean 4⅛ batches, not 41/8 batches.

4⅛ batches × (¾ stick)/batch = 33/8 batches × (¾ stick)/batch

= 99/32 sticks

= 3 and 3/32 sticks

Answer:

It will take them both 24 minutes to mow the lawn if they are working together.

Step-by-step explanation:

Given that Sam can mow a lawn in 40 minutes, and Melissa can mow the same lawn in 80 minutes, to determine how long does it take for both Sam and Melissa to mow the lawn if they are working together, the following calculation must be performed:

1/40 + 1/60 = 1 / X

3X + 2X = 120

X = 120/5

X = 24

Thus, it will take them both 24 minutes to mow the lawn if they are working together.

the discrete compounding formula is f = p * (1 + r) ^ n

f is the future value

p is the present value

r is the interest rate per time period

n is then number of time periods

in your problem, you are given:

f = what you want to find

p = 5000

r = 30% per year / 100 = .3 per year (percent / 100 = rate).

n = 3 years

if you compound annually, the formula becomes:

f = 5000 * (1 + .3) ^ 3 = 10985

if you compound quarterly, the formula becomes:

f = 5000 * (1 + .3 / 4) ^ (3 * 4) = 11908.898

if you compound monthly, the formula becomes:

f = 5000 * (1 + .3 / 12) ^ (3 * 12) = 12162.67658

if you compound continuously, a different formula is used.

that formula is f = p * e ^ (r * n)

f is the future value

p is the present value

e is the scientific constant of 2.718281828.......

r is the interest rate per time period

n is the number of time periods.

with this formula, you leave the time periods in terms of years.

it will make no difference what time periods and compounding periods you use, the answer will be the same.

most of the time you will just give it the interest rate per year and the number of years.

the reason is as follows:

r * n = .3 * 3 = .9 when giving it rate and time in terms of years.

r * n = .3 / 4 * 3 * 4 = .9 when giving it rate and time in terms of quarters.

r * n = .3 / 12 * 3 * 12 = .9 when giving it rate and time in terms of months.

in your problem, the formula becomes f = 5000 * e ^ (.3 * 3) = 12298.01556.

the more compounding periods per year, the higher the future value.

the highest is when you compound continuously.

this is apparent from the data.

Answer:

-10x -10y=20

-10x - 20=10y

-10x - 20/10=y

-10x - 2=y

y=-10x-2

-7x -7y=14

-7x - 14 = 7y

-7x - 14/7=y

-7x - 2=y

y=-7x-2

Answer:

A square is 4 even sides.

the circumference around the square area is 1600 meters. This means that each side is 400 meters.

Square meters is the area of the square.

400 x 400 = 160000 m^2

To get to Hectares, you divide the squared measurement by 10,000.

Answer:

160000m^2 = 16ha

Step-by-step explanation:

Bit of a nit pick first the word is perimeter not circumference circumference only applies to circles. 1600/4=400 (divide by 4 because a square has 4 sides) 400^2=160000 (A=L*H the length and height are the same so you square it) 160000/10000=16 (1 hectare = 10000m^2), Hope this helps. :)

Answer:

[tex]\displaystyle 64[/tex]

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Rule [Variable Direct Substitution Exponential]:                                         [tex]\displaystyle \lim_{x \to c} x^n = c^n[/tex]

Limit Property [Multiplied Constant]:                                                                     [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \lim_{x \to 0} f(x) = 4[/tex]

Step 2: Solve

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

Unit: Limits

Book: College Calculus 10e

Answer: C. 64

Step-by-step explanation:

Edge 100%

Answer:

x = 76.9

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp side / adj side

tan 70 = x/28

28 tan 70 = x

x=76.92936

Rounding to the nearest tenth

x = 76.9

Answer:

76.9

Step-by-step explanation:

SOH: Sin(θ) = Opposite / Hypotenuse

CAH: Cos(θ) = Adjacent / Hypotenuse

TOA: Tan(θ) = Opposite / Adjacent

Tan 70 = [tex]\frac{x}{28}[/tex]

(28) tan 70 = x

76.929 = x

• 2xy + x ² y' = 0

This DE is exact, since

∂(2xy)/∂y = 2x

∂(x ²)/∂x = 2x

are the same. Then there is a solution of the form f(x, y) = C such that

∂f/∂x = 2xy   ==>   f(x, y) = x ² y + g(y)

∂f/∂y = x ² = x ² + dg/dy   ==>   dg/dy = 0   ==>   g(y) = C

==>   f(x, y) = x ² y = C

• sin(x) cos(y) + cos(x) sin(y) y' = 0

is also exact because

∂(sin(x) cos(y))/∂y = -sin(x) sin(y)

∂(cos(x) sin(y))/∂x = -sin(x) sin(y)

Then

∂f/∂x = sin(x) cos(y)   ==>   f(x, y) = -cos(x) cos(y) + g(y)

∂f/∂y = cos(x) sin(y) = cos(x) sin(y) + dg/dy   ==>   dg/dy = 0   ==>   g(y) = C

==>   f(x, y) = -cos(x) cos(y) = C

• x ² + y ² - 2xyy' = 0

is not exact:

∂(x ² + y ²)/∂x = 2x

∂(-2xy)/∂y = -2x

So we look for an integrating factor µ(x, y) such that

µ (x ² + y ²) - 2µxyy' = 0

becomes exact, which would require that these be equal:

∂(µ (x ² + y ²))/∂y = (x ² + y ²) ∂µ/∂y + 2µy

∂(-2µxy)/∂x = -2xy ∂µ/∂x - 2µy

Observe that if µ(x, y) = µ(x), then ∂µ/∂y = 0 and ∂µ/∂x = dµ/dx, so we would have

2µy = -2xy dµ/dx - 2µy

==>   -2xy dµ/dx = 4µy

==>   dµ/µ = -2/x dx

Integrating both sides gives

∫ dµ/µ = ∫ -2/x dx   ==>   ln|µ| = -2 ln|x|   ==>   µ = 1/x ²

So in the modified DE, we have

(1 + y ²/x ²) - 2y/x y' = 0

which is now exact and ready to solve, since

∂(1 + y ²/x ²)/∂y = 2y/x ²

∂(-2y/x)/∂x = 2y/x ²

We get

∂f/∂x = 1 + y ²/x ²   ==>   f(x, y) = x - y ²/x + g(y)

∂f/∂y = -2y/x = -2y/x + dg/dy   ==>   dg/dy = 0   ==>   g(y) = C

==>   f(x, y) = x - y ²/x = C

• exp(2x) (2 cos(y) - sin(y) y' ) = 0

is exact, since

∂(2 exp(2x) cos(y))/∂y = -2 exp(2x) sin(y)

∂(-exp(2x) sin(y))/∂x = -2 exp(2x) sin(y)

Then

∂f/∂x = 2 exp(2x) cos(y)   ==>   f(x, y) = exp(2x) cos(y) + g(y)

∂f/∂y = -exp(2x) sin(y) = -exp(2x) sin(y) + dg/dy   ==>   dg/dy = 0   ==>   g(y) = C

==>   f(x, y) = exp(2x) cos(y) = C

Given that y = 0 when x = 0, we find that

C = exp(0) cos(0) = 1

so that the particular solution is

exp(2x) cos(y) = 1

Answer:

13.5

Step-by-step explanation:

We can use a ratio to solve

2        3

---- = ------

11        3+x

Using cross products

2(3+x) = 3*11

Distribute

6+2x = 33

Subtract 6

6+2x-6 = 33-6

2x = 27

Divide by 2

2x/2 = 27/2

x = 13.5

Now we have to,

→ solve for x

Then use a ratio to solve,

→ 2/11 = 3/3+x

Now see the further steps,

→ 2(3+x) = 3 × 11

→ 6+2x = 33

→ 2x = 33-6

→ 2x = 27

→ x = 27/2

→ x = 13.5

Hence, 13.5 is value of x.

[tex] \Large \mathbb{SOLUTION:} [/tex]

[tex] \begin{array}{l} \dfrac{1 + \sin 2A}{1 - \sin 2A} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2} \\ \\ \dfrac{1 + 2\sin A\cos A}{1 - 2\sin A\cos A} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2} \\ \\ \because \sin 2A = 2\sin A\cos A\ (\text{Double Angle Identity}) \\ \\ \text{Divide both numerator and denominator of} \\ \text{LHS by }\cos^2 A. \\ \\ \dfrac{\frac{1 + 2\sin A\cos A}{\cos^2 A}}{\frac{1 - 2\sin A\cos A}{\cos^2 A}} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2} \\ \\ \dfrac{\frac{1}{\cos^2 A} + \frac{2\sin A\cos A}{\cos^2 A}}{\frac{1}{\cos^2 A} - \frac{2\sin A\cos A}{\cos^2 A}} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2}\\ \\ \dfrac{\sec^2 A + 2\tan A} {\sec^2 A- 2\tan A} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2} \\ \\ \dfrac{1 + \tan^2 A + 2\tan A} {1 + \tan^2 A - 2\tan A} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2} \\ \\ \because \sec^2 A = 1 + \tan^2 A\ (\text{Pythagorean Identity}) \\ \\ \text{Rearranging, we get} \\ \\ \dfrac{\tan^2 A + 2\tan A + 1} {\tan^2 A - 2\tan A + 1} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2} \\ \\ \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2} = \dfrac{(1 + \tan A)^2}{(1 - \tan A)^2}\\ \\ \text{LHS} = \text{RHS}_{\boxed{\:}}\end{array} [/tex]

what we know?:

* scale factor of 1/4

* the point (4, -8)

all we have to do is put 4/4 (because we are dilating by 1/4)

4/4= 1

same for the other one: -8/4= -2

FINAL ANSWER: (1, -2)

Answer:

???

Step-by-step explanation:

Answer:

The zeroes are -6, 1/2 and 2.

Step-by-step explanation:

f(x) = 2x3 + 7x2 - 28x + 12 = 0

From the first and last coefficient 2 and 12, one guess for a zero is x = 2.

So substituting x = 2:

f(2) = 16+ 28 - 56 + 12 = 0

So x = 2 is a zero and x - 2 is a factor of f(x)

Performing long division:

x - 2)2x3 + 7x2 - 28x + 12( 2x2 + 11x - 6 <------- Quotient

       2x3  - 4x2

                 11x2 - 28x

                 11x2 - 22x

                          - 6x + 12

                           -6x + 12

                            .............

Now we solve

2x2 + 11x - 6 = 0

(2x - 1)(x + 6) = 0

2x - 1 = 0 or x + 6 = 0, so:

x = 1/2,  x = -6.

Answer: -6, 1/2, 2.

Step-by-step explanation:

{(x) = 2x3 + 7x2 - 28x + 12 = 0

From the first and last coefficient 2 and 12, one

guess for a zero is x=2.

So substituting x=2:

{(2) = 16+ 28 - 56 + 12 = 0

So x = 2 is a zero and x - 2 is a factor of f(x)

Performing long division:

X - 2)2x3 + 7x2 - 28x + 12(2x2 + 11x - 6 <

Quotient

Answer:

1436.8

Step-by-step explanation:

4/3×π×7³

= 1372π/3

≈ 1436.8

Answered by GAUTHMATH

Answer: 1436

Step-by-step explanation:

Answer:

:D 7x+6 / x+3

Answer:

x+2

Step-by-step explanation:

To divide polynomials, one of the methods is to factor.

Take the numerator: x^2 + 5x + 6.

Factoring this numerator gives (x+3)(x+2)

Now, the question becomes (x+3)(x+2) / (x+3)

x+3 cancels out, leaving x+2 as the final answer.

Hope this helps!

(if you have other questions, leave them in the comment, and If I know how to do them, I will answer) :)

Answer: (3,0) and (-12,0)

Step-by-step explanation:

The x-intercepts of the graph of f(x) = x² + 5x - 36 are (-9,0) and (4,0).

Option B is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

To find the x-intercepts of the function f(x) = x^2 + 5x - 36,

we need to set y = f(x) to 0 and solve for x.

So, we have:

x² + 5x - 36 = 0

We can factor the left side of the equation:

(x + 9)(x - 4) = 0

Using the zero product property, we get:

x + 9 = 0 or x - 4 = 0

Solving for x, we get:

x = -9 or x = 4

Therefore,

The x-intercepts of the graph of f(x) = x² + 5x - 36 are (-9,0) and (4,0).

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Answer:

1364

Step-by-step explanation:

1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364

a1+a2 = a3, a2+a3=a4 etcetera..

1+3 =4

3+4 =7

4+7=11

.

.

a13+a14 = a15

521+843 = 1364

so, 1364 is the answer

Answer:

Step-by-step explanation:

We have two sides; the Adjacent and the Hypotnuse

Meaning we will use Cos

Cos = A/H

Cos X = 16/19

Use the inverse of Cos to find the angle

X = cos-1 (16/19)

X = 0.45499141546

X = 0.45

Answer:

Step-by-step explanation:

6 is the thousands place

0 (right next to it) is the 10 thousands place

9 is the hundred thousands place. There is only 1 nine present so the answer is unique.