find the equation of the line that is parallel y= 2x+10 and passes through the point (6,-4)

Answer:

y = -4x - 14

Step-by-step explanation:

plug (x, y) in to the y = mx+ b formula, and plug -4 in as m

Aril's cumulative donation exceeds Dita's cumulative donation in the 5th month. At that time, Aril has donated 4,656.25 kr and Dita has donated 4,400 kr.

To solve the problem, we can start by setting up the equation for the cumulative donation for each person. Let A be Aril's cumulative donation in kr and let D be Dita's cumulative donation in kr. Then we have:

A(n) = 150(2.5)⁽ⁿ⁻¹⁾ where n is the number of months

D(n) = 300 + 400(n-1) where n is the number of months

We want to find the smallest value of n such that A(n) > D(n). Substituting in the equations above, we get:

150(2.5)⁽ⁿ⁻¹⁾  > 300 + 400(n-1)

Simplifying, we get:

(2.5)⁽ⁿ⁻¹⁾ > 2 + 8/15(n-1

We can solve this inequality by trial and error or by using logarithms. Using logarithms, we get:

(n-1)log(2.5) > log(2 + 8/15(n-1))

(n-1) > log(2 + 8/15(n-1))/log(2.5)

Using trial and error or a calculator, we can find that the smallest integer n that satisfies this inequality is 6. Therefore, Aril's cumulative donation exceeds Dita's cumulative donation in the 6th month.

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Complete question:

Aril and Dita are wealthy Norwegian business owners who make monthly donations to international disaster relief.

• Aril donated 150 Norwegian kroner (kr) the first month, and the cumulative number of Norwegian kroner she has donated increases by a factor of 2.5 each month.

• Dita donated 300 kr the first month, and the cumulative number of Norwegian kroner she has donated increases by 400 kr each month.

They started making donations at the same time, and they both make their monthly donations at the beginning of each month.

What is the first month in which Aril's cumulative donation exceeds Dita's cumulative donation?

Answer:

The Forth Answer

Step-by-step explanation:

I Think That Is correct

Answer:

$5.29 per pair of socks

Step-by-step explanation:

26.45/5=5.29

Answer:-3

x=-5-1

x=-6

x+3

=-6+3

=-3

The solution to the variables are p = 45 and k = 26.3

Proportional equation 1

The equation is given as

2 : 9 = 10 : p

Multiply both sides of the first ratio by 5

So, we have the following representation

5 * 2 : 9 * 5 = 10 : p

Evaluate the products

10 : 45 = 10 : p

By comparison, we have:

p = 45

Proportional equation 2

Here, we have

2.45 : 7 = 9.2 : k

Express as fractions

7/2.45 = k/9.2

So, we have

k = 7/2.45 * 9.2

Evaluate

k = 26.3

Hence, the value of k is 26.3

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Answer:

y = 43, z = 16

Step-by-step explanation:

congruent essentially means they're the same. If you mentally map one triangle onto the other, you'll see that 43, the hypotenuse, lines up with y, and 16 lines up with z.

Elise was wrong, To ensure congruency of any given triangle the congruency rules will be followed

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

Side -  Side - Side = SSS

Side - Angle - Side = SAS

Angle - Side - Angle = ASA

Angle - Angle - Side = AAS

Hypotenuse and one leg = HL

The problem did not specify other information about other sides and this makes the method wrong since it does not follow the congruency rules.

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The unit 2-vector in the direction of fastest descent is (4/5, -3/5), and the slope of the path in this direction is -16/5.

(a) To descend fastest, you should move in the direction of the negative gradient vector of the function f(x,y) = 2x^2 + 3y^2 - 15 at the point (3,1).

The gradient of f(x,y) is given by ∇f(x,y) = <4x, 6y>. Therefore, at (3,1), the gradient is ∇f(3,1) = <12, 6>.

To move in the direction of the negative gradient, we take the opposite direction, which is <−12/√180, −6/√180>, or simplified, <-2√5/3, -√5/3>.

(b) Moving in the direction of the negative gradient vector, the slope of our path is equal to the directional derivative of f(x,y) in the direction of the negative gradient vector.

The directional derivative of f(x,y) in the direction of a unit vector u is given by D_uf(x,y) = ∇f(x,y) · u, where · denotes the dot product.

In this case, the unit vector in the direction of the negative gradient is <-2√5/3, -√5/3>, so the slope of our path is

D_uf(3,1) = ∇f(3,1) · <-2√5/3, -√5/3> = <12, 6> · <-2√5/3, -√5/3>

= (-24√5 - 18)/3 = -8√5 - 6.

Therefore, the slope of our path is -8√5 - 6.

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Answer:

{ -4 , 2 , 4 } and { 5 , 0 , -4 }

Step-by-step explanation:

Given the solution to an inequality expression as x > -5. The values of x are the values that are greater than -5.

The values greater than -5 are the values that falls towards the positive sides of the number line but greater than -5. The numbers are -4, -3, -2, -1, 0 ,1 ,2, 3, 4, 5, 6....

From the given numbers, the correct set of numbers will be  { -4 , 2 , 4 } and { 5 , 0 , -4 } since the values are within the range of listed values

5x+6y is the answer i jope this helps you

The first thing he has to do is take that "minus" sign through the parentheses containing the second polynomial. Some students find it helpful to put a " 1 " in front of the parentheses, to help them keep track of the minus sign. Here's what the subtraction looks like, when working horizontally.

The distance between two points is the number of units between them

The possible value of x is -66

The given parameters are:

\(\mathbf{S = (-6,8)}\)

\(\mathbf{T = (x,-3)}\)

\(\mathbf{ST = 61}\)

Distance ST is calculated using:

\(\mathbf{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}\)

So, we have:

\(\mathbf{d = \sqrt{(-6 - x)^2 + (8 - -3)^2}}\)

\(\mathbf{d = \sqrt{(-6 - x)^2 + (8 +3)^2}}\)

\(\mathbf{d = \sqrt{(-6 - x)^2 + 11^2}}\)

Substitute 61 for d

\(\mathbf{ \sqrt{(-6 - x)^2 + 11^2} = 61}\)

Square both sides

\(\mathbf{ (-6 - x)^2 + 11^2 = 61^2}\)

\(\mathbf{ (-6 - x)^2 + 121 = 3721}\)

Subtract 121 from both sides

\(\mathbf{ (-6 - x)^2 = 3721 - 121}\)

\(\mathbf{ (-6 - x)^2 = 3600}\)

Take square roots of both sides

\(\mathbf{ -6 - x = 60}\)

Add 6 to both sides

\(\mathbf{ - x = 60 + 6}\)

\(\mathbf{ - x = 66}\)

Multiply both sides by -1

\(\mathbf{ x = -66}\)

Hence, the possible value of x is -66

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The number 1473 represents the slope, indicating that the cost per class at Michigan State University is $1473.

The number 5495 represents the y-intercept, representing the base cost for room and board regardless of the number of classes.

In the equation T = 1473c + 5495, the coefficient 1473 represents the slope.

Interpretation of the slope: The slope indicates the rate of change or cost per class. In this case, it suggests that for every additional class (c) taken at Michigan State University, the total cost (T) for the semester increases by $1473. The slope represents the linear relationship between the number of classes and the total cost.

The number 5495 represents the y-intercept in the equation.

Interpretation of the y-intercept: The y-intercept indicates the starting point or the total cost (T) when the number of classes (c) is zero. In this situation, the y-intercept of 5495 suggests that even if a student takes no classes, they would still have to pay a one-time fee for room and board amounting to $5495 for the semester.

Therefore, the slope provides insight into how the total cost changes with the number of classes taken, while the y-intercept represents the baseline cost that includes the one-time fee for room and board, regardless of the number of classes.

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Answer:

3/2

Step-by-step explanation:

Since the lines goes through the point (0,0)

We have a point (2,3)

The slope is y/x = 3/2

Answer:

I think its a student loan

Step-by-step explanation:

Answer:

studint loan

Step-by-step explanation:

dont have explination for this one

Answer:

Step-by-step explanation:

Bob's deal : 11/10= 1.1 dollars per bagel

Danny's bagel=3/4=0.75 dollars per bagel

Danny's deal is better the price is lower

2- fraction : 11/10>3/4

1.1>0.75 the lower the price the better

3- Danny's deal is better because the price of 10 bagels=7.5 dollars

Answer:

1.)  20 yrs --> $1,045.63

    30 yrs --> $1,204.08

2. See the attachment

3. See the attachment

Step-by-step explanation:

Please find the attachment for detail

Answer:

Each boy recieved $25.25 each

Step-by-step explanation:

First, you add up all the money the 3 boys spent.

15+15+15=45

Then you add the sum of the equation to the amount all the boys had afterward.

45+30.75=75.75

Finally, you divide that product to 3 boys.

75.75/3=25.25

Therfore the answer is $25.25 each.      

The equation that is false is the one in option B,

\((x^{3/5})^{1/2} = \sqrt[3]{x^{10}}\)

An equation is false if the thing in the left side is different than the thing in the right side.

Now, remember the exponent rules:

\((x^a)^b = x^{a*b}\\\\x^{1/n} = \sqrt[n]{x}\)

Now let's go to the second option, the expanding the thing we have in the left side we will get:

\((x^{3/5})^{1/2} = x^{3/5*1/2} = x^{3/10} = \sqrt[10]{x^3}\)

Now, this is different of the thing we can see in option B, so we conclude that B is the false equation.

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Answer:

Step-by-step explanation:

You would divide 244.40 by 26%

You would get  63.544.... Now times the 63.544 to the remainder of the 26 from 100...which is 74.  63.544 times 74 equals 4702.256.

Now add the 244.40 to that and u get the answer of 4946.656.

Answer:

Good Luck

Step-by-step explanation:

Let the regular price be "x".

According to the problem, the sofa is being sold for 26% of the regular price, which means the sale price is:

Sale price = 0.26x

The problem also states that the sale price is $244.40, so we can write:

0.26x = 244.40

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides by 0.26:

x = 244.40 ÷ 0.26

x = 940

Therefore, the regular price of the sofa is $940.

Answer:

-6.25

Step-by-step explanation:

The answer is -6.25.

Answer:

390 in 6.5 minutes

60*6.5

Answer:

none

Step-by-step explanation:

if you try to get n to one side they would cancel each other out so there is no solution

Answer:

Step-by-step explanation:

-5n=3-5n

+3=+3-5n

-2n=6

/2=/2

n=3

Answer:

x ≈ 18.6

Step-by-step explanation:

using the tangent ratio in the right triangle

tan37° = \(\frac{opposite}{adjacent}\) = \(\frac{14}{x}\) ( multiply both sides by x )

x × tan37° = 14 ( divide both sides by tan37° )

x = \(\frac{14}{tan37}\) ≈ 18.6 ( to the nearest tenth )

Answer:

49 square metres

Step-by-step explanation:

The area of a square is the length of the side times itself.

The area is 7 x 7 = 49

Answer:

mean=6+8+8+9+9+10divided 6 =

Answer:

1.

Step-by-step explanation:

The mean score is (8+6+9+9+8+8)/ 6

= 48/8

= 8.

Deviations from the mean are 0 , -2, 1, 1, 0, 0

Squares of these deviations  are 0, 4, 1, 1, 0, 0

So the variance =  (0 + 4 + 1 + 1 + 0 + 0)/ 6 =  1

Standard deviation = √1 = 1.

Based on the number of cookies that Fatima was able to package in a certain amount of time, the relationship between the cookies and the time it takes to package them is a single cookie is packaged in 12 seconds.

To find the amount of time it takes to package the cookies, the formula is:

= Number of minutes /  Number of cookies

= 4 / 20

= 1/5

= 0.20 minutes  

When converted to minutes, this is:

= 0.20 x 60 seconds per minute

= 12 seconds

In conclusion, it takes 12 seconds to package a cookie on average.

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Answer:

Step-by-step explanation:

2x = 6 + 3y

2x - 6 = 3y

Find the y-intercept when x = 0:

0 - 6 = 3y

-6 = 3y

-2 = y

Find the x-intercept when y = 0:

2x - 6 = 0

2x = 6

x = 3