46 x 2 in standard algorithm

The equation of the required perpendicular line is x + 3y = 24.

What is the slope relation for two perpendicular lines?
For two perpendicular lines on a plane, the product of their slopes always equals (-1).
What is the equation of line with slope 'm' and passing through the point (x₁, y₁)?
The standard equation of the line with slope 'm' and passing through the point (x₁, y₁) is y - y₁ = m(x - x₁).

Given, the required line is perpendicular to line given by y = 3x + 5 with slope, m₁ as 3, on analysis with standard equation of line; also the line passes through the point (9, 5) i.e. (x₁, y₁).
Let the slope of the required line be = m₂
As per statement established in the literature above, we have:
Slope of two perpendicular lines = -1
∴m₁ × m₂ = -1 ⇒ 3m₂ = -1 ⇒ m₂ = (-1)/3
Again, equation of the required perpendicular line is:
y - 5 = [(-1)/3][x - 9] ⇒ 3y - 15 = 9 - x ⇒ x + 3y = 24
Thus, the equation of the required perpendicular line is x + 3y = 24.

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If  a triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers. No it is not a right triangle.

We would be making use of converse of Pythagoras' theorem to determine whether the triangle is a right triangle.

In a situation were we have a right triangle the square on longest side will be the same with the sum of square of other sides

Longest side

45²  =  2025

Other side

30 ² + 35 ²

900 + 1,225

= 2125

Hence,

2025 ≠ 2125

Based on the above it is  not a right triangle because the longest side did not equate the other side.

Therefore it is not a right triangle.

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As 2125 ≠ 2025 therefore it didn't meet the requirements of Pythagoras' theorem, it is not a right-angle triangle.

This type of question makes a right-angled triangle that can be solved by Pythagoras's theorem.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

Given, A triangle has sides with lengths of 30 kilometers, 35 kilometers, and 45 kilometers.

∴ 30² + 35² = 45².

900 + 1225 = 2025.

2125 ≠ 2025.

It is not a right-angle triangle because it didn't satisfy the property of Pythagoras's theorem.

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Answer:

r = 23.7

Step-by-step explanation:

17 = r - 6.7 ( add 6.7 to both sides )

23.7 = r

Answer:

  73 : 27

Step-by-step explanation:

You want the ratio of students that have a pet to students that don't have a pet, given that 73% of students have a pet.

If 73% of students have a pet, then the remaining 100% -73% = 27% of students do not have a pet.

The ratio of students who have a pet to students who don't have a pet is then ...

  (have a pet) : (don't have a pet) = 73% : 27% = 73 : 27

According to a recent survey, 73% of elementary school students have a pet, making the ratio of students with pets to those without pets 73:27.

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

You want the ratio of students that have a pet to students that don't have a pet, given that 73% of students have a pet.

If 73% of students have a pet, then the remaining 100% -73% = 27% of students do not have a pet.

The ratio of students who have a pet to students who don't have a pet is then,(have a pet) : (don't have a pet) = 73% : 27% = 73 : 27

A recent survey found that 73% of elementary school students own a pet, making the proportion of students who own pets to those who don't stand at 73:27.

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Answer:

The equation in slope-intercept form is:

[tex]y=\frac{1}{3}x+3[/tex]

So the second option is the correct one.

Step-by-step explanation:

Step 1: Identify the gradient

The perpendicular line's equation is given as:

[tex]y=-3x+4[/tex]

This equation is in the form of:

[tex]y=mx+b[/tex]

Upon comparing the [tex]x[/tex] components of both equations, we get[tex]-3x=mx\\\text{Remove the}~ x~ \text{from both sides:}\\-3=m\\m=-3[/tex]

So, the gradient of this 'reference' equation is -3.

The equation we need to find is perpendicular to this 'reference' equation.

So, its gradient should be the negative reciprocal of the gradient of the 'reference' equation.

The negative reciprocal of -3 is:

[tex]-\frac{1}{(-3)}\\=\frac{1}{3}[/tex]

So, the gradient of our equation is [tex]\frac{1}{3}[/tex].

Step 2: Create the equation:

The equation crosses the x-axis at -9, which means its y-coordinate is 0 (at x-axis, y=0) ,so its coordinate is [tex](-9,0)[/tex].

The formula for an equation is:

[tex]y-y_{1}=m(x-x_{1})[/tex]

The coordinate [tex](x_{1},y_{1})[/tex] is [tex](-9,0)[/tex], and the gradient ([tex]m[/tex]) is [tex]\frac{1}{3}[/tex].

Substitute the values into the equation:

[tex]y-y_{1}=m(x-x_{1})\\y-0=\frac{1}{3}(x-(-9))\\\\\text{Simplify}\\y=\frac{1}{3}(x+9)[/tex]

[tex]\text{Simplify further}\\y=\frac{1}{3}x+3[/tex]

Since, the slope-intercept form is:

[tex]y=mx+b[/tex]

We already have our equation in the slope-intercept form.

Answer:  The slope is [tex]\frac{2}{3}[/tex].

Step-by-step explanation:

[tex]Slope = \frac{y_{2} -y_{1} }{x_{2}-x_{1} } =\frac{-8-(-6)}{-2-1} =\frac{-2}{-3} =\frac{2}{3}[/tex]

Answer:

the subtraction property of equality

Step-by-step explanation:

trust

Answer:

Subtraction

Step-by-step explanation:

The probability that you will be satisfied with 3 or more of the purchased products is 0.916

Given that,

The chance of being pleased with an internet purchase is 0.555. if you purchase 8 items online

Solution -

let  X denote the no of success of

Purchased product online

X ~ B(n,p)

n = 8

P= 0. 555

a = 1 - 0 .555 = 0.445

P ( X = x) = [tex]nc_{x} b^{x} a^{n-x}[/tex]

P ( X = x)= [tex]8c_{x} (0.555^{x} )(0.445)^{8-x[/tex]

P ( X>=3)= [tex]\lim_{3 \to 8} 8c_{x} (0.555^{x} )(0.445)^{8-x[/tex]

P ( X>=3)) = 0.91614

                 =0.916

Therefore we can conclude the probability that you will be satisfied with 3 or more of the purchased products is 0.916

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Based on the center of the regular decagon, we can find that the perimeter of the decagon would be 98.9 units.

When given the midpoint of a decagon and the measurement of the radius, the perimeter can be found by the formula:

= 10 x ( ( 2 x Radius of the decagon) / (1 + √5)))

Given a radius of 16 units, the perimeter of this decagon is:

= 10 x ( (2 x  16) / (1 + √5)))

= 10 x ( (32 / (1 + √5)))

= 98.9 units

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Perimeter of Decagon with radius and midpoint given is 100 units.

Polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides.

Given polygon is a decagon. A decagon is a polygon which have ten sides with same length with centre o.

The radius of the decagon is 16.

When radius and midpoint is given the perimeter can be given by formula

Perimeter= 10 x ( ( 2 x Radius of the decagon) / (1 + √5)))

=10×((2×16) / (1 + √5)))

=10×((32) / (1 + √5)

=320/1+√5

=320/1+2.2

=320/3.2

=100 units.

Hence perimeter of Decagon with radius and midpoint given is 100 units.

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Here is the graph for you!!

Answer:

[tex]\frac{1}{2}[/tex] y +3

Step-by-step explanation:

You want to combine like terms

[tex]\frac{2}{5}[/tex] y and [tex]\frac{-9}{10}[/tex] y are like terms because they both have a variable y

-4 and + 7 are like terms because they are both constants.  (numbers without letters)

We combine these

[tex]\frac{4}{10}[/tex] means the same as [tex]\frac{2}{5}[/tex]  I just multiplied the numerator (top) and the denominator (bottom) by 2.  I did this so that I could add it to [tex]\frac{-9}{10}[/tex]

[tex]\frac{4}{10}[/tex]y - [tex]\frac{9}{10}[/tex]y  = [tex]\frac{-5}{10}[/tex] y (4-9 = -5)  or [tex]\frac{-1}{2}[/tex] y simplified

-4 + 7 = 3

Answer:

Yes.

Step-by-step explanation:

Replace x with 2 and y with 1 and see if the equation is true

x - 4y = -2

2 - 4(1) = -2

2 - 4 = -2

-2 = -2

The statement is true so the point is on the line.

The true statements about the constraints in this situation are:

In order to determine the true statements, we would substitute the value of x and y into the given linear equation and then evaluate. From the information provided, the constraints in this situation are modeled or represented by this linear equation:

2x + 0.50y = 120

Where:

When x = 40 and y = 60, we have:

2x + 0.50y = 120

2(40) + 0.50(60) = 120

80 + 30 = 120

110 ≠ 120 (Not a solution).

When x = 30 and y = 120, we have:

2x + 0.50y = 120

2(30) + 0.50(120) = 120

60 + 60 = 120

120 = 120 (True solution).

Therefore, if we buy 30 pounds of beans we can buy with 120 pounds of rice.

When x = 0 and y = 240, we have:

2x + 0.50y = 120

2(0) + 0.50(240) = 120

0 + 120 = 120

120 = 120 (True solution).

Therefore, if we buy no beans we can buy 240 pounds of rice.

When x = 0 - 5 and y = 240 + 20, we have:

2x + 0.50y = 120

2(0 - 5) + 0.50(240 + 20) = 120

-10 + 130 = 120

120 = 120 (True solution).

Therefore, if we buy 20 more pounds of rice, we would have to buy 5 less pounds of beans.

When x = 0 + 10 and y = 240 - 60, we have:

2x + 0.50y = 120

2(0 + 10) + 0.50(240 - 60) = 120

20 + 90 = 120

110 = 120 (Not a solution).

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the unit price for 1 lb of turky is $0.99

The cost of 14 lb of turkey = $13.86

let the cost of 1 lb of turkey = y

The unit price is the cost for 1lb of turkey:

14 lb = 13.86

1 lb = y

cross multiply:

14(y) = 1(13.86)

14y = 13.86

divide both sides by 14:

14y/14 = 13.86/14

y = 0.99

Hence, the unit price for 1 lb of turky is $0.99

Average speed of the group for the two day event is 0.105 miles\min.

The average is defined as the mean value that is equal to the ratio of the total sum of the number of a given set of values to the total number of values present in that set.

Time taken on day 1 in minutes = 9x60 + 44

                                                   = 540 + 44 = 584 minutes.

Time taken on day 2 in minutes = 2x60 + 55

                                                   = 120 + 55 = 157 minutes

Now we will be applying speed-distance formula we get,

Speed= Distance/time

On day 1,

[tex]Speed_{1}[/tex]= 28/584 = 0.0479 miles/min

On day 2,

[tex]Speed_{2}[/tex]= 10/175 = 0.0571 miles/min

Thus,the average speed is:

Average = [tex]Speed_{1} + Speed_{2}[/tex] = 0.0479 + 0.0571= 0.105 miles/min

Hence,the average speed is 0.105 miles/min

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The y-intercept of the function y = 3.5x - 7 is ( 0, - 7 ).

A function is an association between inputs in which each input has a unique link to one or more outputs. Each function has a range, codomain, and domain.

Consider the function,

y = 3.5x - 7

The equation of a straight line is expressed in the slope-intercept form (a linear function). It takes the formula y = mx + b, where m is the slope, b is the y-intercept, and y and x serve as variables.

The value of y at x = 0 can be used to determine the y-intercept. The graph's intersection with the y-axis occurs at this location.

Then,

y = 3.5x - 7

y = 3.5( 0 ) - 7

y = - 7

The y-intercept of the function is ( 0, - 7).

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We are asked to find an equivalent amount to 100 USD in french francs. Acording to the table, on tuesday, a dollar costs 4.3450 french francs, then we can find how many francs we got by multiplying 100 USD and 4.345, then we get:

Francs = 100×4.3450 = 434.50

Then, the answer is 434.5 french francs

486lb of grass seed is required to cover the field on the right.

The area of Rectangle is length times of width

Let us find the areas of two rectangle larger and smaller.

Area of the larger rectangle:

60×90=5400 square feet.

Now divide the larger square area by the smaller square area:

Area of the smaller rectangle

40×50=200 square feet.

Now divide larger rectangle with smaller

5400/200 =27

27 is the ratio of the difference

27×18=486 lb.

Hence 486lb of grass seed is required to cover the field on the right.

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The image of triangles are given .

a.

b. Find the ratio,

c.Hence the triangles are similar .

The correct option is A.

The possible values of x that satisfies the given dimensions and the condition that the volume must be no more than 280 cubic feet is x = [1,5]

The dimensions of the aquarium is: 2x ft , (x -1) ft, and (x + 2) ft. Since the volume must be no more than 280 ft³, it means:

V = 2x (x - 1) (x + 2) ≤ 280

Divide both sides by 2:

x (x - 1) (x + 2) ≤ 140

x³ + x² - 2x - 140 ≤ 0

(x - 5) (x² + 6x + 28) ≤ 0

Since x² + 6x + 28 is always greater than zero then x that satisfies the above inequality is:

x - 5  ≤ 0

or x  ≤ 5

Using the interval notation, x = (-∞, 5]

However, remember that the dimension is always a positive number.

Hence,

x - 1 ≥ 0

or x  ≥ 1

Therefore, the solution is [1, 5]

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Answer:

The answer would be 1.3, and the three is repeating.

Step-by-step explanation:

First, make 4 2/15 into a improper fraction.

4 2/15= 62/15

Now, when we divide fraction, use the rule Keep, Change, Flip.

Keep the 62/15.

Change the division sign into a multiplication sign.

To make the 3.1 into a fraction, put a one over it.

3.1/1

Now, flip the fraction.

3.1/1= 1/3.1

Your equation will look like this:

62/15x1/3.1

Multiply across.

62/46.5

Now simplify.

The answer would be 1.3, and the three is repeating.

To give an entity the desired position, orientation, or shape starting from the current position, orientation, or shape, geometric transformations are required. Scaling, rotation, translation, and shear are the fundamental transformations. Projections and mappings are two additional crucial categories of transformation.

Y =- X is what kind of a transformation?

Y = X's reflection:

The x-coordinate and the y-coordinate switch positions when a point is reflected across the line y = x. Y = -x reflection: The x-coordinate and the y-coordinate switch places when you reflect a point across the line y = -x, and they are negated (the signs are changed).

The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. The cross-sectional reflection of point (x, y)

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By the distribution,6.3 minutes is the time limit that 75.8% of college students go over when looking for a parking space in the library parking lot.

Given that,

Finding a parking spot in the library parking lot takes college students an average of 7.0 minutes, with a standard deviation of 1 minute, according to a normal distribution.

Find the window of opportunity that 75.8% of college students miss when looking for a place in the library parking lot.

The following formula calculates the z-score of a measure X of a normally distributed variable with mean μ and standard deviationσ:

Z=(X-μ)/σ

The z-score calculates how far the measure deviates from the mean by standard deviation.

The p-value for this z-score, which is the percentile of X, can be obtained by looking at the z-score table.

The cut-off time is the 100th percentile minus 75.8th percentile, or X, for Z = -0.7, so:

Z=(X-μ)/σ

-0.7=(X-7)/1

-0.7=X-7

X=-0.7+7

X=6.3

Therefore, 6.3 minutes is the time limit that 75.8% of college students go over when looking for a parking space in the library parking lot.

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The value of ∠CBD is  68° and the value of ∠ABC is 22°

Given

Angle CBD = 4x + 52

Angle ABC = 8x − 10

If BA is perpendicular to BD, then ∠BAD = 90°

∠BAD = ∠CBD + ∠ABC

On substituting this values into the formula:

4x + 52 +  8x − 10 = 90

12x + 42 = 90

Add -42 to both sides

12x + 42 - 42 = 90 -42

12x = 48

x = 48/12

x = 4°

Here,

∠CBD = 4x + 52

∠CBD = 4 x 4 + 52 = 16 + 52 = 68°

Then,

∠ABC = 8x − 10

∠ABC = 8 x 4 − 10 = 32 - 10 = 22°

That is,

The value of ∠CBD is  68° and the value of ∠ABC is 22°

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Answer:

68 degrees

Step-by-step explanation:

got it right on khan academy

Answer:

30

Step-by-step explanation:

it doesn't seem to be correct question

x=3

As the y-values of a function are the values that the function takes, the largest y-value of a function is called the maximum value of the function

Answer:

C)

Step-by-step explanation:

elimination is not substitution.

therefore, A and B are out.

D does not work, because in the described way the x terms don't get different signs, and the addition does not eliminate any variable.

C brings both y terms to the same absolute value, and their signs are different, so the addition will eliminate the y terms leaving us with one equation in x that we can solve :

15x + 12y = 21

8x - 12y = 12

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

23x 0 = 33

23x = 33

x = 33/23

Answer:

a is the right answer for you