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The equation of the line in slope intercept form is y = - 1 / 2 x - 5

The equation of the line in point slope form is (y + 4) = - 1 / 2 (x + 2)

The equation in a slope intercept form is represented as follows:

y = mx + b

where

Therefore, let's find the equation of the line L in slope intercept form.

The line L is perpendicular to y = 2x

Hence,

m₁m₂ = -1

2m₂ = -1

m₂ = -1 / 2

Therefore,

y = - 1 / 2 x + b

let's find b using (-2, -4)

-4 = - 1 / 2 (-2) + b

b = -4 - 1

b = -5

Hence, the equation of the line in slope intercept form is as follows:

y = - 1 / 2 x - 5

The equation of the line in point slope form is represented as follows:

(y - y₁) = m(x - x₁)

where

Therefore, using (-2, -4),

(y + 4) = - 1 / 2 (x + 2)

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Answer:

80 square units

Step-by-step explanation:

The figure given can be decomposed to have two trapezoids of equal dimensions and a rectangle.

Area of the figure = (2*area of a trapezoid) + (area of a rectangle)

Area of the 2 trapezoids:

Area of the two trapezoid = 2(½(a + b)*h)

Where,

a = 2 + 6 + 2 = 10 units

b = 6 units

h = 2 units

Plug in the values:

Area of the two trapezoid = 2(½(10 + 6)*2)

= 2(½(16)*2)

Area = 32 units²

Area of the rectangle:

Area = length × width

Length = 8 units

Width = 6 units

Area = 8 × 6 = 48 units²

✔️Area of the figure = 32 + 48 = 80 units²

Answer:

When multiplying exponents of the same base, add the exponents. When dividing exponents of the same base, subtract the exponents. When raising a power to a power, multiply the powers.

Step-by-step explanation:

Answer:

your right

Step-by-step explanation:

Answer:

p = 3

Step-by-step explanation:

48 = 16p

divide both sides by 16

3 = p

Answer:

[tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{e^\big{arctan(3e^{4x})}}{2} + C[/tex]

General Formulas and Concepts:

Calculus

Differentiation

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

Basic Power Rule:

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

Integration

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx[/tex]

Step 2: Integrate Pt. 1

Step 3: integrate Pt. 2

Set variables for u-substitution.

Step 4: Integrate Pt. 3

Step 5: Integrate Pt. 4

Set variables for u-substitution #2.

Step 6: Integrate Pt. 5

Step 7: Integrate Pt. 6

Set variables for u-substitution #3.

See attachment for rest of work (would not fit entire answer in answering box).

The set of actors with at least a return of $7.50 are {H, J, K}

The actors that would be included in this set include actors that earn an amount equal to $7.50 or an amount greater than $7.50.

A set can be described as a collection of objects whose elements are fixed and cannot be changed. Thus, elements in this set would include those who earn more than or equal to $7.50.

To write a set in a roster form, the elements in the set are written in a row within curly brackets or braces - { }. The elements in the set are then separated by commas.

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Answer:

x=9

Step-by-step explanation:

Substitution and solving

[tex]2x+3y=36\\2x+3(6)=36\\2x+18=36\\2x+18-18=36-18\\36/2=2x/2\\x=9[/tex]

Answer:

9.42

Step-by-step explanation:

C= 2 times pie times radius

Answer:

410.941

Step-by-step explanation:

Answer:

a number question's answer is a power 2. and is c power 1

Answer:

75% decrease

Step-by-step explanation:

https://www.calculatorsoup.com/calculators/algebra/percentage-decrease-calculator.php?v_1=80&v_2=20&action=solve

Based on the fact that Kamama wants her hexagons to be congruent, the transformations that she can use are:

In order to have congruent shapes, there are three transformations that can be used.

Firstly, it is important to note that congruent shapes have the same size and the same shape. They are identical except for their orientation which may be different.

A reflection would create a congruent shape that would have the same size and angles but the orientation should be different. This is the same as a rotation. A translation will often result in congruent shapes that also have the same orientation. This means that Kanama can use any of these transformations.

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Step-by-step explanation:

In the general scenario we find thaf x exceeds y by 12. If they vary directly it means even though the values x and y change they will always have the constant different 12

x=y+12

:. x=18+12

x=30

I HOPE THIS HELPS

Answer:

9/2π cm/s

Step-by-step explanation:

Volume of the spherical balloon V= 4/3πr³

Rate of change of volume dV/dt = dV/dr * dr/dt

dV/dr = 3(4/3πr²)

dV/dr = 4πr²

dV/dr = 4π(2)²

dV/dr = 16π

If V = 72cm²/s

72 = 16π*dr/dt

dr/dt = 72/16π

dr/dt = 9/2π cm/s

Hence the radius is changing at  9/2π cm/s

we can rewrite:

(-1.5)²*(3.2)⁵ = 3.76⁵

The new base of the expression is 3.76

Here we have the expression:

(-1.5)²*(3.2)⁵

And we want to write this as a single expression with a power of 5.

First we can rewrite:

(-1.5)² = x⁵

x = (-1.5)^(2/5)

Then the new base of the expression will be:

x*3.2

(-1.5)^(2/5)*3.2 = 3.76

Then we can rewrite:

(-1.5)²*(3.2)⁵ = 3.76⁵

The new base of the expression is 3.76

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According to the given statement the interest that we earn is

=  $74,059 . 64

The present value of an annuity seems to be the current worth of future annuity payments based on a predetermined rate of return, as well as discount rate. The higher the discount rate, the smaller the annuity's present value.

monthly payment is 150

at the age = 30

interest rate = 4

till age of = 65

At age 65, the annuity would be worth $137,059.64.

We only need to determine the amount of interest. = ?

 for monthly payments, we need to take n, which equals 12 points now total interest. determined by future value. Substitute minus p m t multiplied by n multiplied by t for all values now.

the amount of interest   =  deposited amount x year x no of year invested

                                       = 150 x 12x(65-30)

           present value     = 63000

At age 65, the annuity would be worth $137,059.64.

We know that the interest is  = balance - capital

                                                 = 137,059.64 - 63000

                                                 = $74,059 . 64

According to the given statement the interest that we earn is

=  $74,059 . 64

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Answer:

0.0437

Step-by-step explanation:

I can't really explain this one

Answer:

.0437

Step-by-step explanation:

the 4 is in the hundreds spot, the 37 is in the thousands and ten thousandths

Answer:

8 numbers

Step-by-step explanation:

447

477

474

774

744

747

777

444

Answer:

B

Step-by-step explanation:

For every 1 liter of water, 0.07 kilograms of salt must be added. They are asking for 0.5 liters of water, which is half of 1 liter. So therefore, they need half of 0.07 kilograms of salt, which is 0.035 kilograms

Answer:

0.035 kg.

Step-by-step explanation:

0.5 liter is 1/2 liter

0.07kilograms / 2 = 0.035kg

Answer:

B.

Step-by-step explanation:

0.32 > 0.304 > 0.03

Work and answers are provided in the screenshot attached! :)

Answer:

In Explanation.

Step-by-step explanation:

In situations like this, you want to first find the equations of the individual lines.

Let's start with the left one.

It has a negative slope of 2 while it has a y-intercept of 1

y=-2x+1

is the equation.

The other line has a slope of 3/2.

The y-intercept is not visible, so we need to use point slope form.

I chose (2,-3)

y+3=3/2(x-2)

Simplify.

y=3x/2-3-3

y=3x/2-6

so we have

y=-2x+1

and

y=[tex]\frac{3x}{2}[/tex]-6

Since both lines are solid, the signs are ≥ or ≤

The shadings intersect above both lines so the individual shadings also have to be above the line.

That means the equation is less than the "y".

y≥-2x+1

y≥[tex]\frac{3x}{2}[/tex]-6

Answer:

102 cm ²

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: i think u got it write its that one

Step-by-step explanation:

Answer:

The 25% discount on AED 4000 will be: 1000 AED

Step-by-step explanation:

Given

In order to determine a 25% discount on the amount AED 4000, all we need means is to multiply 25/100 or (0.25) by 4000.

i.e

Discount amount = 25% of 4000

                             = 25/100 × 4000

                             = 0.25 × 4000

                             = 1000 AED

Thus, the 25% discount on AED 4000 will be: 1000 AED

The equation's line that is steeper is y = 3x + 7

From the question, we are to determine which of the given equations' line is steeper

The given equations are

y = 3x + 7

and

y = (1/2)x + 9

First, we will compare the equations to the form of an equation of a straight line

The equation of a straight line is of the form

y = mx + c

Where m is the slope

and c is the y intercept

Thus,

The slope of the equation, y = 3x + 7, is 3

and

The slope of the equation, y = (1/2)x + 9, is 1/2

NOTE: The higher the slope of a line, the steeper the line

Hence, the equation's line that is steeper is y = 3x + 7

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