Write an equation of a the line passing through the point (2,-9) that is perpendicular to the line y=x+6
An equation of the line is…..

ANSWER

Infinitely many solutions (0 = 0)

EXPLANATION

We have the two equations and we are to solve them simultaneously.

We have:

y = 5x + 2 ___(1)

10y - 50x = 20 ___(2)

Put (1) in (2):

We have that:

10(5x + 2) - 50x = 20

50x + 20 - 50x = 20

=> 50x - 50x = 20 - 20

=> 0 = 0

This kind of solution implies that there are infinitely many solutions to this equation.

Answer:

Proportion: 22.80/2=x/3

x= 34.20

Step-by-step explanation:

First find what the value of one scarf is:

22.80/2=11.40

Then multiple by 3 to get $34.20

Answer:

Proportion : 1 scarf = $11.40

Cost of 3 scarves = $34.20

Step-by-step explanation:

GIVEN: 2 SCARVES = 22.80

LET X = # OF SCARVES

2X=22.80

X=$11.40

$11.40(3) = cost of 3 scarves

$34.20 = cost of 3 scarves

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} (2x - 4) -( \frac{{x}^{2} - 4x + 5) }{2 \sqrt{x} } )}{x } [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ {x}^{2} - 4x + 5 }{ \sqrt{x} } [/tex]

We know, division rule of differentiation :

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{u}{v} [/tex]

then,

[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{v\frac{du}{dx} - u \frac{dv}{dx} }{(v) {}^{2} } [/tex]

So, let's do the same in given equation :

[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} \frac{d}{dx}(x {}^{2} - 4x + 5) - ( {x}^{2} - 4x + 5) \frac{d}{dx}( \sqrt{x} ) }{( \sqrt{x} ) {}^{2} } [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ \sqrt{x} (2x - 4) -( {x}^{2} - 4x + 5) \frac{1}{2 \sqrt{x} } }{x } [/tex]

[ This is the required Answer, but you can simplify it however you want according to the choices given ]

[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{x \bigg( \frac{\sqrt{x} (2x - 4)}{x} -( {x}^{2} - 4x + 5) \frac{1}{2x \sqrt{x} } \bigg)}{x } [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{\sqrt{x} (2x - 4)}{x} -( {x}^{2} - 4x + 5) \frac{1}{2x \sqrt{x} } [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{(2x - 4)}{ \sqrt{ x}} - \frac{( {x}^{2} - 4x + 5) }{2 \sqrt{x {}^{3} } }[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

in this case we have that it is growth formula, so we have that r= 0.05 and a =5500. Therefore the formula is

we only need to replace t by 20 and calculate

so after 20 years we hace $14593.13 in our bank account

1. The pairs of measurements that could have the dimensions of Rectangle B include:

A. 6cm by 1.5cm

D. 18cm by 4.5cm

E. 80cm by 20cm

2. Rectangle A is a scaled copy of rectangle B as the scale factor is 3:2.

Rectangle C isn't a scales factor of rectangle B since they have different ratio.

1. It should be noted that from the information, Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A.

Therefore, it should be noted that the ratio will be:

= 12 / 3

= 4 / 1

= 4:1

Therefore, the values that will give same ratio will be:

6cm by 1.5cm = 6/1.5 = 4:1

18cm by 4.5cm = 18/4.5 = 4:1

80cm by 20cm = 80/20 = 4:1

In conclusion, the correct options are A, D, and E.

2. Rectangle A is 12 long and 8 wide. The ratio will be:

= 12/8 = 3/2 = 3:2.

Rectangle B is 15 long and 10 wide. The ratio will be:

= 15/10 = 3/2 = 3:2

Rectangle C is 30 long and 15 wide. The ratio will be:

= 30/15 = 2:1

Therefore, rectangle A and B have same scale.

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Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all pairs of measurements that could have the dimensions of Rectangle B.

A. 6cm by 1.5cm

B. 10cm by 2cm

C. 13cm by 4cm

D. 18cm by 4.5cm

E. 80cm by 20cm

the value of  P(E and F) is equal to 0.175 when E and F are independent events with P(E) = 0.25 and P(F) = 0.7.

We are given the two events:

E and F

We are also given that these events are independent events and:

P (E) = 0.25

P (F) = 0.7

We need to find:

P (E and F)

We know, that when two events are independent events that is they don't relate to each other, then P(E and F) is given by:

P(E and F) = P (E) × P (F)

P(E and F) = 0.25 × 0.7

P(E and F) = 0.175

Therefore, we get that, the value of  P(E and F) is equal to 0.175 when E and F are independent events with P(E) = 0.25 and P(F) = 0.7.

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According to the exterior angle theorem, an external angle's measure is equal to the sum of its remote interior angle's two measurements. The opposite interior angles are another name for the remote interior angles. Where can I determine a triangle's outer angle? In a triangle, how can I determine the interior and outside angles?

Take the total of two interior angles of a triangle that are known and deduct it from 180 to find the internal angle of the triangle.

Simple addition of the triangle's two opposite internal angles will yield the triangle's external angle. 180° minus the inside angle equals each exterior angle. Using this formula requires the knowledge of the corresponding internal angle. Exterior angle = Total.

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Answer:

213

Step-by-step explanation:

First we decide how many ounces 12 has in 32 (2.6)

Then we multiply 2.6 to 80 calories and get 213 calories

Answer:

[tex]7 {x}^{2} + 49 = 0 \\ 7( {x}^{2} + 7) = 0 \\ \frac{7( ({x}^{2} + 7) }{7} = \frac{0}{7} \\ {x}^{2} + 7 = 0 \\ {x}^{2} = - 7[/tex]

NOTE THERE IS NO SOLUTION FOR THE GIVEN EQUATION SINCE THE SQUARE OF ANY NUMBER CANNOT GIVE A NEGATIVE NUMBER.

THE SQUARE OF ANY NUMBER WHETHER IT'S POSITIVE OR NEGATIVE ALWAYS GIVES A POSITIVE NUMBER.

GOODLUCK!!

Answer:

x = 8, y = 4

This can also be written as an ordered pair: (8, 4)

Step-by-step explanation:

First, set up a system of equations:

x + y = 12, $2x + $6y = $40

The first equation shows that there are a total of 12 tickets, and the other shows that the total of money for all the tickets adds to $40.

Then, solve by elimination by subtracting twice the first equation from the second to isolate y:

  2x + 6y = 40

- (2x + 2y = 24)

  0   + 4y = 16

And now we can solve for y:

4y = 16

y = 4

Then, put this back into the original equation to solve for x:

x + y = 12

x + 4 = 12

x = 8

The next two terms in the sequence,  -13, 8, -5, 3,-2 is 1 and -1.

The mathematical operations that would be used to determine the next two terms are addition and subtraction. Addition is used to determine the sum of two or more numbers. Subtraction is used to determine the difference between two or more numbers.

The first step is to determine the relationship between the numbers in the sequence. Looking at the numbers, it can be seen that the the difference between the first number and the second number gives the third number.

-13 + 8 = -5

-5 + 3 = -2

3 - 2 = 1

-2 + 1 = -1

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Answer:

24 ajsndkalxndma skwma wjlslaos ndnajala

The value of x in the equation x⁵ + 64x² = 0 is x = 0 or  x = -8 after taking common.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

It is given that the polynomial equation is:

x⁵ + 64x² = 0

x²(x³ + 64) = 0

x² = 0    or  x³ + 64 = 0

x = 0   or    x³ = -64

x = 0 or    x = -8

Thus, the value of x in the equation x⁵ + 64x² = 0 is x = 0 or  x = -8 after taking common.

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Answer:

y = 25x + 865

so the monthly rent in 2021 is 1,140

do you need an explanation or is this fine?

Answer:

A is 729,2187,6561 and it would be geometric

B is 46,55,64 and is arithmetic

C is 32,36,40 and is arithmetic

y = -2x + 12 is the linear equation of the line that passes through the coordinates of points (1, 10) and (2, 8).

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

The slope of a line is expressed as change in y over change in x.

Slope m = (y₂-y₁)/(x₂-x₁)

Given the data in the question;

Point 1 ( 1, 10 )

Point 2 ( 2, 8 )

First, we determine the slope of the line.

Slope m = (y₂-y₁)/(x₂-x₁)

Slope m = ( 8 - 10 )/( 2 - 1 )

Slope m = (-2)/( 1 )

Slope m = -2

Now, determine the y-intercept b, by substituting the slope and the coordinates of one point into the equation of line formula.

y = mx + b

10 = -2(1) + b

Solve for b

10 = -2 + b

b = 10 + 2

b = 12

Now that we have the slope m and y-intercept b, plug these into y = mx + b to determine the equation of the line.

y = mx + b

y = -2(x) + 12

y = -2x + 12

Therefore, the equation of the line that goes through the given points is y = -2x + 12.

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Popular Problems Algebra Solve for h A=1/2h(b+B)

A = 1/2h (b+B)

h=2Ab+B

Explanation

Popular Problems Algebra Solve for h A=1/2h(b+B)

A= 1/2 h(b+B)

Rewrite the equation as

1/2⋅(h(b+B))=A.

1/2⋅(h(b+B))=A

Multiply both sides of the equation by 2.

2(1/2⋅(h(b+B)))=2A

hb+hB=2A

Factor h out of hb+hB.

h(b+B)=2A

Divide each term in h(b+B)=2A by b+B and simplify.

h=2Ab+B

How is algebra solved?

A General Rule for Equation Solving

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Brian likes the feeling of owning his own car. He takes good care of it and doesn't like changing cars often is whom a car loan would be a better option than a car lease and is denoted as option B.

This is referred to as the total money borrowed which is used in the purchase of a car while on the other hand car lease involves the vehicle being made available to be driven for  certain period of time or limit.

Since Brian likes the feeling of owning his own car and doesn't change cars often, then the car loan is best for him as it becomes his after the money or amount to be repaid is completed.

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The approximate percentage of buyers who paid between $1925 and $2075 is; 68%

The approximate percentage of buyers who paid between $1925 and $2000 is; 34%

We are given;

Mean = $2000

Standard Deviation = $75

1) We want to find the approximate percentage of buyers who paid between $1925 and $2075

The formula that is used to calculate the z-score of a a normal distribution is;

z = (x' - μ)/σ

where;

z is z-score

x' is sample mean

μ is population mean

σ is standard deviation

For a payment of 1925;

z = (1925 - 2000)/75 = -1

For a payment of2075;

z = (1925 - 2000)/75 = 1

Thus, this is 1 standard deviation from the mean.

Thus, this is a percentage of 68%

2) We want to find the approximate percentage of buyers who paid between $1925 and $2000?

For a payment of 1925;

z = (1925 - 2000)/75 = -1

For a payment of 2000;

z = (2000 - 2000)/75 = 0

This translates to a percentage of (1/2) * 68% = 34%

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Missing options are;

1) What is the approximate percentage of buyers who paid between $1925 and $2075?

2) What is the approximate percentage of buyers who paid between $1925 and $2000?

Solution:

Given that a sight-seeing ship is stopped in the water for an hour, miles from the shore. Then the captain heads the ship back to the shore at a constant rate. The ship docks at shore for awhile, then returns to the open sea.

This implies that that:

Answer:

Explanation:

A die has 6 faces numbered 1 to 6.

The sample space when a die is rolled is:

Thus, the number of odd number outcomes when a die is rolled is:

The rule of probability is

Since the die has 6 numbers, then

The total = 6

Since there are 5 numbers without 3, then

A = 5

Substitute them in the rule above

The answer is 5/6

The 2000th digit after the decimal point is 5. See the explanation below.

First, we divide the fraction to get the decimal number.

2/13 = 0.15384615384

Paying close attention, you'd notice that after the 6th number forms the decimal point, the number forms a loop that repeats again. That is:

0.153846 153846 154...

Hence, to detect the 2000th number,

we divide 2000/6

we are left with 2

(that is 333 x 6 = 1998)

Hence we count two from the decimal and that gives us the 2000th digit.

That is: 5

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Full Question:

[tex]When $\dfrac{2}{13}$ is written as a decimal, what is the $2000^\text{th}$ digit after the decimal point?[/tex]

It should be emphasized that a connection is proportional if its graph is a line that passes through its origin.

If the graph of a connection is a line passing through the origin, the connection is proportionate. If it is not a line or ray that fails to achieve this, the ratio is not proportional.

The equation for the proportionality constant is K = y/x. This is the same equation used to get the slope of a straight line with respect to the origin.

If the graph of a connection is a line or ray that goes through the origin, the relationship is proportional. If the line or ray does not pass through the origin, it is not proportional.

Additionally, if anything is not linear, it is not proportional.

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The amount of direct materials cost in the unfinished job would be $97600.

The price of direct materials is directly related to the unit of production and is immediately identifiable. For instance, the price of glass is a direct material expense in the production of light bulbs. The primary component needed for the production of commodities or products was material. Costs of raw materials or components used directly in the production of goods are referred to as direct material costs. For instance, if Company A manufactures toys, the cost of the plastic used to build the toys would be an example of a direct material cost.

Given Data

Work in Process inventory account was credited for $120,500.

charged with $9,600 of applied overhead cost.

Direct material cost = Work in progress - Overhead cost - Direct labor

Direct labor = 9600 ×[tex]\frac{100}{75}[/tex]

Direct labor = 12800

Direct material cost =  120000 - 9600-12800

Direct material cost = 97600

The amount of direct materials cost in the unfinished job would be $97600.

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Explanation

We are given the following equation:

We are required to determine the solution of the given equation.

This is achieved thus:

The only solution to this equation involves complex numbers. So, there is no real solution.

Hence, the answer is:

The coordinates of the point of intersection are (-6, -7)

The graph represents the given parameter

On the graph, we can see that there are two lines with the following properties:

The above properties means that:

From the graph, we can see that the lines A and the other line meet at a point

The point where these lines meet is referred to as the point of intersection

The coordinates of this point are (-6, -7)

Hence, the coordinates of the point where line a & tne line that has an undefined slope intersect are (-6, -7)

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NSWER

EXPLANATION

In a isometry the distances between points are conserved, so the image of segment PQ has to have the same length as segment PQ.

When we have a translation defined by a vector the x-coordinate of the vector tells the horizontal translation and the y-coordinate the vertical translation.

For this problem, if the vector is <3, 5>, we have to translate each point 3 units to the right and 5 units up.

The endpoints of the image segment are Q'(1, 3) and P'(-1, 1)

====================================================

Work Shown:

(2.50 dollars)/(8 juice boxes) = (x dollars)/(24 juice boxes)

2.50/8 = x/24

2.50*24 = 8x

60 = 8x

8x = 60

x = 60/8

x = 7.50

----------------

Another approach:

She paid $2.50 for 8 juice boxes. The unit price is 2.50/8 = 0.3125 dollars per juice box. Multiply this by 24 to get 24*0.3125 = 7.50

----------------

Yet another method:

We know the cost for 8 juice boxes is $2.50

We want to know the cost for 24 juice boxes.

The jump from 8 to 24 is "times 3". So we'll multiply the $2.50 cost by 3 to get 3*2.50 = 7.50

We can think of it like this

[tex]\frac{2.50 \ \text{dollars}}{8 \ \text{juice boxes}}=\frac{3*2.50 \ \text{dollars}}{3*8 \ \text{juice boxes}}=\frac{7.50 \ \text{dollars}}{24 \ \text{juice boxes}}[/tex]