Write an equation of the line passing through (4,-2) that is parallel to the line -3x minus 4y =5

G=P-2M/2

Step-by-step explanation:

P=2G+2M

p - 2M = 2G

G=P - 2M/2

Answer:62.3

Step-by-step explanation:

We must apply some transformations to the function:

(1) A reflection across the y-axis is given by the transformation:

(2) A translation down 2 units is given by the transformation:

Plotting the function f(x), we get the following graph:

given the equation:

y = 5/4x - 3

to complete the table for the values of x and y using intergers

fristly,

when x = -4

y = 5/4(-4) - 3

y = -5 - 3

y = -8

when x = 0

y = 5/4(0) - 3

y = 0 - 3

y = -3

when = 4

y = 5/4(4) - 3

y = 5 - 3

y = 2

when x = 8

y = 5/4(8) - 3

y = 5(2) - 3

y = 10 - 3

y = 7

so completing the table:

y = 5/4x - 3

x y

-4 -8

0 -3

4 2

8 7

Answer:  x = -3/2

Step-by-step explanation:

Equation:

x -2x + -3 = 1x

Combine Like Terms:

x  - 2x + -3 = 1x

-x - 3 = 1x

+x        +x

[tex]-3 = 2x[/tex]

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

-3/2 = x

Given the following question:

Let l be the length of the rectangle and w its width.

From this, we have:

I) w - l = 5

II) l*w = 33

From I, we have w = 5 + l

Applying this to equation II, we have: l(5+l) = 33

l^2 + 5l - 33 = 0

The positive root of this equation is l = [sqrt(157) - 5]/2 = 3.8 yd (rounded to the nearest tenth)

Applying this to equation I, we have: w - 3.8 = 5, which implies w = 5 + 3.8 = 8.8 yd

The net present value of the project of the company Alpha Industries is $494,918.

Given,

The initial cost of the project = $7.9 million

Cost of debt = 5.58 percent

Cost of equity = 11.25 percent

The debt-equity ratio= .59

Tax rate = 40 percent.

Let us assume

Equity be $x, then

Total = $1.59x

Respective weights =  Pretax cost of debt × (1 - tax rate)

=5.58% × (1 - 0.4)

Respective weights = 3.348%

WACC = Respective costs × Respective weights

WACC = (x ÷ 1.59x × 11.25%) + (0.59x ÷ 1.59x × 3.348)

WACC = 8.318%

The present value of annuity = Annuity × (1 - (1 + interest rate)^ - time period] ÷ Rate

=1.63 × [1 - (1.08317811321)^-7]÷ 0.08317811321

= $1.63 × 5.150256501

The present value of annuity = $8,394,918.10

The net present value = The present value of  cash inflows - The present value of cash outflows

= $8,394,918.10 - $7,900,000

The net present value of the the project = $494,918

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Using the simple interest formula, the value of time (t) is 103 years.

So, the simple interest rate formula:

We need to find the value of time (t), then the formula will become:

Insert the values as follows:

Rounding off: t = 103 years

Therefore, using the simple interest formula, the value of time (t) is 103 years.

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The inequality comparison

What is Inequality?

Inequality of wealth in major cities Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income.

Given, numbers are

11 and -9

an inequality to show all  numbers: from (11) to (–9) inclusive

-9 ≤ x ≤  11

Hence, inequality to compare the numbers

11 and -9 is  -9 ≤ x ≤  11

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If you want to save $500 in two years, you need to save $20.58 per month with a 1.25% interest compounded monthly.

The monthly savings can be determined using an online finance calculator as follows:

N (# of periods) = 24 months (2 x 12)

I/Y (Interest per year) = 1.25%

PV (Present Value) = $0

FV (Future Value) = $500

Results:

Monthly Savings = $20.58

Sum of all periodic savings = $494.04

Total Interest = $5.96

Thus, the investor needs to save $500 in two years to save $20.58 monthly.

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Let the unknown number be "x"

We will write an algebraic equation from the word problem given. Then we will solve for "x".

Given,

Sum of number (x) and 4 times the reciprocal is 13/3

We can convert it into an algebraic equation:

Now, let's solve for the unknow, x,

The numbers are

The Solution.

To obtain the maximum value of T, we differentiate with respect to x and equate to zero.

To get the maximum value of P, we shall substitute 350 for T in the given function.

The correct answer is T = 350 degrees Fahrenheit , and P = 96 percent.

First, let's clear y to get the slope-intercept form:

This way, we can conclude that the y-intercept is 4. This is the first point we have to graph:

Therefore, it has exactly one solution.

Given

The formula

The final answer

Answer:

[tex]{ \tt{ = 2f + 6f}}[/tex]

- Factorise out f as the common factor;

[tex]{ \tt{ = f(2 + 6)}} \\ = 8f[/tex]

The value of -5 ( -10-2(-3)) to the 2nd power is -6480.

It should be noted that an exponent simply means the number through which another number can be multiplied by itself.

Based on the information given, it should be noted that PEDMAS will be used. This implies:

P = parentheses

E = Exponents

D = division

M = multiplication

A = addition

S = subtraction

-5 ( -10-2(-3)² will be illustrated thus:

It's important to calculate the value in the parentheses first according to PEDMAS.

= -5 [(-12(-3)]²

= -5 (36)²

= -5 × 1296

= -6480

The value is -6480.

In this case, the concept of PEDMAS is used to get the value.

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The length of the rod that he could use to complete the triangle is 12 inches. This is solved based on the principle of Pythagorean Triples.

Pythagorean triples are a collection of three positive numbers that fit into the Pythagorean theorem formula, which is written as a² + b² = c², where a, b, and c are positive integers. In this case, 'c' is the 'hypotenuse,' or the triangle's longest side, while 'a' and 'b' are the other two legs of the right-angled triangle.

Pythagorean triples are denoted as (a,b, c). The most well-known Pythagorean triple example is (3, 4, 5). We can see that the numbers 3, 4, and 5 meet the equation a² + b² = c².

To prove that the length of the rod that should be used to complete the triangle is 12. Let's subject the values to the Principles of Pythagorean Triples.

Given:

9,

let's assume that 15 is the longest side.

Thus,

If we are correct,

9² + 12² should equal 15²

9² = 81

12² = 144

15² = 225

81 + 144 =225

Hence the length of the rod that must be used to complete the triangle is 12 inches.

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Gabe, you are doing great. Now you need to solve for x:

3x + 6x + x = 180

10x = 180

dividing by 10 at both sides:

10x/10 = 180/10

x = 18 That is the answer you have.

Finally, you need to multiply the ratio for the value of x, you just calculated:

Side 1 = 3 * 18

Side 2 = 6 * 18

Side 3 = 1 * 18

Consider x as Takao's fourth score.

Then, to achieve an 87 average, we have:

Answer:

c. 85

SOLUTION

For the four points to form a rectangle, the length of the diagonals will be equal.

This means that we have to find the distance between the point BD and AC. If

BD = AC, then the four points would form a rectangle.

Now let's find AC

So, since BD = AC, the four points A, B, C and D would form a rectangle.

Equation:

The vertex is given by the following formula:

where the vertex is (h, k). Thus, in our equation k = -1 and h = 5, and the vertex

is (5, -1).

Additionally, the focus is given by (h+p, k). In our case:

Then, the focus is:

Simplifying:

The directrix is x = h - p:

Finally, the axis of symmetry is y = -1.

Given

A(11,9)

B(11,3)

C(5,3)

D(5,9)

In the coordinate system (x,y), x determines the horizontal position, and y determines the vertical position. Having a translation of 9 units left, and 1 unit down, means that each coordinate system will be translated as (x-9 , y-1).

Therefore, the coordinates of the post image are A'(2,8), B'(2,2), C'(-4,2), D'(-4,8).

Answer:

Explanation:

Experimental probability = number of favorable outcomes/number of total outcomes

From the information given,

number of favorable outcomes = 54

number of total outcomes = 120

The experimental probability that the coin will land on heads on the next toss = 54/120

Dividing the numerator and denominator by 6,

The experimental probability that the coin will land on heads on the next toss = 9/20

Given that:

- The probability that an individual is left-handed is 12%.

- There are 30 students in the class.

You need to use this Binomial Distribution Formula, in order to find the probability of finding exactly 4 left-handed students :

Where "n" is the number being sampled, "x" is the number of successes desired, and "p" is the probability of getting a success in one trial.

In this case:

Therefore, by substituting values into the formula and evaluating, you get:

Hence, the answer is:

The surface area of the triangular prism will be 217.95 cm²

When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.

It is given that,

Base side, a = 7 sm

Base side, b = 6 cm

Base side, c = 7 cm

Height, h = 9 cm

The surface area of a triangle prism: The formula for a triangular prism's surface area is,

A=bh+(b₁+b₂+b₃) units²

where b is the base of a triangular face, h is the height of a triangular face, b₁ is the side of the triangular base, b₂ is the side of the triangular base, and l is the prism's length.

The surface area of the triangular prism will be,

[tex]\rm A = ah + bh + ch + \dfrca{1}{2} \sqrt{-a^4 +2(ab)^2 +2(ac)^2 -b^4+2(bc)^2 -c^4}[/tex]

Substitute the given values,

[tex]\rm A = 7 \times 9 + 6 \times 9 + 7 \times 9 + \dfrac{1}{2} \times \sqrt{-7^4 + 2(7 \times 6)^2 +2 (7\times 7)^2 -6^4 + 2(6 \times 7)^2 - 7^4} \\\\ A = 217.94 \ cm^2[/tex]

Thus, the surface area of the triangular prism will be 217.95 cm².

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Answer:

Step-by-step explanation:

-4

1) In this question, there's not much information so let's think of a rule

2) We can sketch this out:

We could even write a function that describes this, which "W" stands for Water Level and "t":

3) So if the level of water is decreasing by 4 feet each and every water level from now on is negative.