Find the slope of a line perpendicular to the line whose equation is x + y = 3. Fully
simplify your answer.

Answer:

y = 2;

x = 2√2

.

Step-by-step explanation:

Use trigonometry:

[tex] \tan(45°) = \frac{y}{2} [/tex]

Use the property of proportion to find x (cross-multiply):

[tex]y = 2 \times \tan(45°) = 2 \times 1 = 2[/tex]

Use the Pythagorean theorem to find x:

[tex] {x}^{2} = {y}^{2} + {2}^{2} [/tex]

[tex] {x}^{2} = {2}^{2} + {2}^{2} = 4 + 4 = 8[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{8} = \sqrt{4 \times 2} = 2 \sqrt{2} [/tex]

Answer:

based on the information provided, Madelyn has a total of 26 dogs in her animal rescue. Of these, there are 13 smaller dogs who consume a total of 19.5 cups of food per day (1.5 cups per dog), and there are 13 larger dogs who consume a total of 39 cups of food per day (3 cups per dog).

Step-by-step explanation:

We know that the total number of cups of food consumed by the dogs is 39. We can use this information to create an equation:

1.5s + 3l = 39

We also know that Madelyn has a total number of dogs, which we can represent as:

s + l = total number of dogs

However, we cannot solve for s and l with only one equation. We need another equation to help us solve for both variables.

From the information provided, we know that each smaller dog gets 1.5 cups of food per day and each larger dog gets 3 cups of food per day. Therefore, the total amount of food consumed in one day can also be represented as:

1.5s + 3l = total cups of food consumed in one day

Since we know that the total cups of food consumed in one day is equal to 39, we can substitute this value into the equation:

1.5s + 3l = 39

1.5s + 3l = 39

2s + 4l = 52

Now we have two equations with two variables:

s + l = total number of dogs

2s + 4l = 52

We can use substitution or elimination to solve for s and l. Using substitution:

s + l = total number of dogs

s = total number of dogs - l

2(total number of dogs - l) + 4l = 52

2total number of dogs - 2l + 4l = 52

2total number of dogs + 2l = 52

total number of dogs + l = 26

Now we have two equations:

s + l = total number of dogs

total number of dogs + l = 26

We can use substitution again:

s + l = total number of dogs

s = total number of dogs - l

(total number of dogs - l) + l = 26

total number of dogs = 26

Therefore, Madelyn has a total of 26 dogs. We can now solve for the number of smaller and larger dogs using one of the previous equations:

s + l = total number of dogs

s + (26 - s) = 26

s = 13

Therefore, Madelyn has 13 smaller dogs and 13 larger dogs.

For given Sample Space, the probability that the next born child is a boy, given that the first 6 children born were girls, is 0.5 i.e. A.

What exactly is a sample space?

A sample space is the collection of all potential results of an experiment or random process in probability theory. It is a key idea that allows us to define and assess event probability.

Consider the following experiment: rolling a six-sided die. This experiment's sample space is the set of all potential results of rolling the dice, which are 1, 2, 3, 4, 5, 6. Each member of the sample space indicates a possible experiment outcome.

Now,

The probability of a baby being a boy or a girl is 0.5 each, and each birth is an independent event, meaning that the outcome of one birth does not affect the outcome of the others. Therefore, the probability of having 6 girls in a row is (0.5)⁶ = 0.015625, or approximately 1.5625%.

Now, we want to find the probability that the next born child is a boy, given that the first 6 children born were girls.

Using the conditional probability formula:

P(boy | 6 girls) = P(boy and 6 girls) / P(6 girls)

The probability of having 6 girls and a boy is the same as the probability of having 7 children in a row, with the last one being a boy. The probability of having 7 children in a row, with any gender, is (0.5)⁷ = 0.0078125, or approximately 0.78125%.

Therefore,

P(boy | 6 girls) = (0.5)⁷ / (0.5)⁶ = 0.5

So the probability that the next born child is a boy, given that the first 6 children born were girls, is 0.5.

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A boat's distance from the coast is measured from station A, where the angle is [tex]50[/tex] degrees, and the shore lies [tex]868[/tex] feet away.

A scalar number known as distance measures "how so much ground an item has traversed" while moving. A vector quantity called displacement describes how far an item is out of place.

A segment's or a room's dimensions are examples of things that may be measured in terms of length. Distance is the separation between two things, like two major cities or 2 points. There will never be a zero sign for either length or distance.

Let Ø be the third angle in the triangle.  Ø=180°-70°-60°=180°-130°=50°

Since we now have an angle and its opposite side, the Law of Sines can be used to find the lengths of other sides.  Let [tex]X[/tex] be the distance from the boat to station A, then

590/sin(Ø)=X/sin(°70)

X=590[sin(70°)/sin(50°)]=868 ft

Distance boat to shore=868sin(70°)[tex]=868 ft[/tex]

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The least possible number of games that Jennifer won is three. This is because when the total number of games won is 300.

A situation where two or more decisions makers (players) have to make decisions based on the probabilities of each outcome.

To find this number, we must first calculate the total number of games played. Since Jennifer won 30%, Grace won 25%, and Janet won 45%, the total number of games played can be determined by multiplying the total percentage by the number of players.

30% + 25% + 45% = 100%

100%  x  3 players = 300 games played

To find out how many games Jennifer won, we must multiply 30% by the total number of games played.

30% x 300 games = 90 games

Since Jennifer won 90 games, Grace won 25% of 300 games, which is 75 games, and Janet won 45% of 300 games, which is 135 games, the total number of games won is 300.

Therefore, the least possible number of games that Jennifer won is three. This is because when the total number of games won is 300, the least possible number of games that one player can win is three.

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Answer: The dimensions on the map are 10 cm by 15 cm, so the area on the map is 10 cm × 15 cm = 150 cm^2.

Since the scale is 1 cm = 50 m, every 1 cm on the map corresponds to an actual distance of 50 m. Therefore, the actual dimensions of the park are 10 cm × 50 m/cm = 500 m by 15 cm × 50 m/cm = 750 m.

The actual area of the park is the product of the actual dimensions, so the actual area is 500 m × 750 m = 375000 square meters.

Step-by-step explanation:

Answer: then get help

Step-by-step explanation:

Answer:

A) 4 x (one-half x 6) ÷ 3

Step-by-step explanation:

Hope it helps:)

Answer:32

Step-by-step explanation:

subtract each seperately

first the numbers with x

-2 - -10 becomes -2 + 10 which is 8x

now the constants

then -6 - -2 becomes -6 + 2 which is -4

so its 8x - 4

youre welcome b

Answer: Let x be the percentage discount given to Scott. Then we can write:

Discounted price for Libby = Original price - 20% of the original price

Discounted price for Scott = Original price - x% of the original price

We know that Libby paid $600 and Scott paid $630 for the same watch, so we can set up the following equation:

Original price - 20% of original price = $600

Original price - x% of original price = $630

Simplifying each equation, we get:

0.8 * Original price = $600

(1 - x/100) * Original price = $630

Dividing the second equation by the first, we get:

(1 - x/100) / 0.8 = 630/600

Simplifying the right-hand side, we get:

(1 - x/100) / 0.8 = 21/20

Multiplying both sides by 0.8, we get:

1 - x/100 = (21/20) * 0.8

Simplifying the right-hand side, we get:

1 - x/100 = 0.84

Subtracting 1 from both sides, we get:

-x/100 = -0.16

Multiplying both sides by -100, we get:

x = 16

Therefore, Scott was given a 16% discount on the original price of the watch.

Step-by-step explanation:

Step-by-step explanation:

Numbers:

[tex]1 \frac{5}{8} [/tex]

[tex] - 2.35[/tex]

[tex] - 4.3[/tex]

[tex] - \frac{3}{5} = - 0.6[/tex]

.

From the least to the greatest:

[tex] - 4.3[/tex]

[tex] - 2.35[/tex]

[tex] - 0.6[/tex]

[tex]1 \frac{5}{8} [/tex]

(A)  the annual rate of change between 1992 and 2006 was 0.0804

(B) r = 0.0804 * 100% = 8.04%

(C) value in 2009 = $11,650

What is the rate of change?

The rate of change is a mathematical concept that measures how much one quantity changes with respect to a change in another quantity. It is the ratio of the change in the output value of a function to the change in the input value of the function. It describes how fast or slow a variable is changing over time or distance.

A) The initial value is $44,000 and the final value is $15,000. The time elapsed is 2006 - 1992 = 14 years.

Using the formula for an annual rate of change (r):

final value = initial value * [tex](1 - r)^t[/tex]

where t is the number of years and r is the annual rate of change expressed as a decimal.

Substituting the given values, we get:

$15,000 = $44,000 * (1 - r)¹⁴

Solving for r, we get:

r = 0.0804

So, the annual rate of change between 1992 and 2006 was 0.0804 or approximately 0.0804.

B) To express the rate of change in percentage form, we need to multiply by 100 and add a percent sign:

r = 0.0804 * 100% = 8.04%

C) Assuming the car value continues to drop by the same percentage, we can use the same formula as before to find the value in the year 2009. The time elapsed from 2006 to 2009 is 3 years.

Substituting the known values, we get:

value in 2009 = $15,000 * (1 - 0.0804)³

value in 2009 = $11,628.40

Rounding to the nearest $50, we get:

value in 2009 = $11,650

Hence, (A)  the annual rate of change between 1992 and 2006 was 0.0804

(B) r = 0.0804 * 100% = 8.04%

(C) value in 2009 = $11,650

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The function of the sequence is T(n) = n² + n and it is quadratic

The domain of the graph is [0, 18]

From the question, we have the following parameters that can be used in our computation:

Step          Cells

1                 2

2                6

3                12

From the table, we have

T(n) = n * (n + 1)

This gives

T(n) = n² + n

Hence, the function is T(n) = n² + n

The sequence T(n) = n² + n is a quadratic sequence

This is the set of the x values

From the graph, we have

x = 0 to 18

So, we have

Domain = [0, 18]

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Answer:

1/3

Step-by-step explanation:

We can first find 7/9 of 3/7 by multiplying 7/9 and 3/7:

[tex]\frac{7}{9}*\frac{3}{7}=\frac{21}{63}[/tex]

Now, we can simplify the fraction by finding the GCF of the numerator and 63.

The GCF shared by 21 and 63 is 21, as 21 is the highest number that both the numerator (21) and the denominator (63) are evenly divisible by.  Thus, we divide both the numerator and denominator by 21 to simplify the fraction fully and bring it to lowest terms:

[tex]\frac{21/21}{63/21}=\frac{1}{3}[/tex]

Answer:

C) y = 5x - 7

Step-by-step explanation:

Slope- intercept form: y =mx +b

Here, m is the slope and b is the y intercept.

    Substitute m = 5 and (-1 , -12) in the above equation and find the value of b.

         -12 = 5*(-1) + b

        -12 = -5 + b

   -12 + 5 = b

            b = -7

Equation in slope intercept form:

               [tex]\boxed{\bf y = 5x -7}[/tex]

The proof for the above question are given above accordingly.

10) Since OA ⊥ OC; and

OB ⊥ OD (Given)
Thus,

∠AOC = 90°;  perpendicular bisector theorem

∠BOD = 90°; perpendicular bisector theorem

Therefore,

90° Less ∠1 = ∠BOC; and

90° less ∠3 = ∠BOC,

Thus,

∠1≅∠3 - subtraction theorem of congruence

11)

Since ∠A is complimentary to ∠ ADB; Given.....1

and ∠C is complimentary to ∠CDB - Given. .....2
Where DB  bisects ∠ADC, thus,

∠DBC = 90° ----Line bisector theorem .......3
∠BDC = 90° -----Line bisector theorem........4

From 1 and 2 above, we know that:

∠A + ∠ADB = 90°
∠C + ∠CDB = 90°, thus,


Since

∠A + ∠ADB + ∠DBA = 180° - Sum of Angles in a triangle; and

∠C + CDB + ∠BDC = 180° - Sum of angles in a triangle, we can state that

∠A ≅∠C.

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According to the solution we have come to find that, As the metal lid was heated, it expanded so that it was not as tight. The correct answer is (G) As the metal lid was heated, it expanded so that it was not as tight.

what is heat?

Heat is a form of energy that is transferred between objects or systems as a result of a temperature difference. It is the energy that flows from a body of higher temperature to a body of lower temperature until they reach a state of thermal equilibrium. Heat can be transferred through three different mechanisms: conduction, convection, and radiation.

Conduction involves the transfer of heat through direct contact between two objects that are at different temperatures. Convection involves the transfer of heat through the movement of fluids, such as air or water, due to differences in temperature. Radiation involves the transfer of heat through the emission and absorption of electromagnetic waves, such as infrared radiation.

The correct answer is (G) As the metal lid was heated, it expanded so that it was not as tight.

When the metal lid was placed in hot water, the heat caused it to expand. This expansion allowed the lid to loosen from the glass jar, making it easier to turn. This is because metals generally expand when heated and contract when cooled. The expansion of the metal lid due to heat causes it to become slightly larger than before, thereby loosening its grip on the jar. As a result, the lid can be turned with less force, and it comes off easily.

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Scenario A: Cannot be determined

Scenario B: Linear

Scenario C: Cannot be determined

The calculated areas are the same for regular polygon and equal to 43.5 units squared.

The area of polygon is given by the formula:

A = (1/2)ap,

where A is the area, an is the apothem (the distance from the centre of the polygon to the midpoint of any side), and p is the polygon's perimeter, is the formula for calculating the area of a regular polygon.

The apothem of the equilateral triangle can be found using the formula:

a = s / (2 tan(π/n))

Substituting the value of s = 10 we have, and n = 3 side.

a = 10/ / (2 tan(π/3))

a ≈ 2.9 units

The perimeter of the triangle is given as:

p = 3 x 10 = 30 units

Now, the area of the triangle is given as:

A = (1/2)ap

A = (1/2)(2.9)(30) = 43.5 sq. units.

Hence, the calculated areas are the same and equal to 43.5 units squared.

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Answer:

Step-by-step explanation:

Bianca’s answer.

The apothem, rounded to the nearest tenth, is

✔ 2.9 units.

The perimeter of the equilateral triangle is

✔ 30 units.

Therefore, the area of the equilateral triangle is

✔ 1/2(2.9)(30) , or approximately 43.5 units2.

The calculated areas are

✔ the same, despite using different formulas

.

The steps to verify the identity cos(-Θ)/(1 + sin(-Θ)) = sec(Θ) + tan(Θ) are:

Start with the left-hand side of the identity: cos(-Θ)/(1 + sin(-Θ))

Use the fact that cos(-Θ) = cos(Θ) and sin(-Θ) = -sin(Θ) to rewrite the expression as: cos(Θ)/(1 - sin(Θ))

Multiply the numerator and denominator by (1 + sin(Θ)) to get: cos(Θ)(1 + sin(Θ))/((1 - sin²(Θ)))

Use the Pythagorean identity sin²(Θ) + cos²(Θ) = 1 to simplify the denominator to cos²(Θ): cos(Θ)(1 + sin(Θ))/(cos²(Θ))

Rewrite the expression using the definitions of secant and tangent: cos(Θ)/cos(Θ) + sin(Θ)/cos(Θ) = sec(Θ) + tan(Θ)

Simplify the expression to arrive at the right-hand side of the identity: sec(Θ) + tan(Θ)

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Image transcribed:

1. Put the steps in order to verify the identity.

cos(-Θ)/1 + sin(-Θ) = sec Θ + tan Θ

↑↓ (cos Θ/1 - sin Θ) (1+ sin Θ/1 + sin Θ)

↑↓ (cos Θ + sin Θ cos Θ) / (1-sin² Ө)

↑↓ cos Θ + sin Θ cos Θ)/ cos² Θ

↑↓ cos Θ/(1- sin Θ)

↑↓ 1/cos Θ + sin Θ/ cos Θ

↑↓ sec Θ +tan Θ

The probability that a record player will break down during the guarantee period is 26.4%.

Cumulative distribution shows the probability of a randomly-selected value falling below or equal to a certain value.

To find the probability that a record player will break down during the guarantee period, we need to calculate the probability of the record player breaking down within two years, which is given by the cumulative distribution function of the normal distribution.

This function uses the mean and standard deviation of the distribution, so for the Radio Shack record player, the probability of breaking down within two years is given by the cumulative distribution function

P(X ≤ 2) = CDF(X; 3.3, 0.8)

To find this probability, we can use a normal distribution calculator to find the cumulative probability of X ≤ 2.

The cumulative probability of X ≤ 2 for a normal distribution with a mean of 3.3 and standard deviation of 0.8 is 2.64.

Therefore, the probability that a Radio Shack record player will break down during the guarantee period is 2.64.

This indicates that there is a 26.4% chance that a Radio Shack record player will break down before the end of the two-year guarantee period.

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Answer:

[tex]x = ± \frac{5 \sqrt{3} }{3} [/tex]

Step-by-step explanation:

[tex](x + 3)(x - 3) = 16 - 2 {x}^{2} [/tex]

Use the quick multiplication formula:

[tex] {x}^{2} - 9 = 16 - 2 {x}^{2} [/tex]

[tex] {x}^{2} + 2 {x}^{2} = 16 + 9[/tex]

[tex]3 {x}^{2} = 25[/tex]

Divide both parts by 3 to make x the subject:

[tex] {x}^{2} = ±8 \frac{1}{3} [/tex]

[tex]x = ± \frac{5 \sqrt{3} }{3} [/tex]

According to the question, the total cost to complete the company taxes is $135.

We can use the following equation to describe the problem:

Total cost = Fixed cost + Hourly rate * Number of hours

In this case, the fixed cost is $100 to complete the company taxes, and the accountant charges an additional $35 per hour to complete the taxes. Let's say it takes the accountant "h" hours to complete the taxes. Plugging in these values, we get:

Total cost = $100 + $35/h * h

Simplifying the equation, we get:

Total cost = $100 + $35

Total cost = $135

Therefore, the total cost to complete the company taxes is $135.

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The calculated values of the angles 1 and 2 are <1 = 95.9 and <2 = 56.8

from the question, we have the following parameters that can be used in our computation:

The triangle

The adjacent angle of 117.5 is

Angle = 180 - 117.5

Angle = 62.5

The third angle in the big triangle is

Angle = 180 - 62.5 - 39.1

Angle = 78.4

So, the measure of angle 2 is calculated as

<2 = 180 - 21.6 - (180 - 78.4)

<2 = 56.8

Also, the measure of angle 1 is calculated as

<1 = 39.1 + <2

<1 = 39.1 + 56.8

<1 = 95.9

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Answer: 9cm

Step-by-step explanation: i hope this this helps!

The following statements are true about parallelograms: diagonals bisect each other, opposite sides are congruent, opposite angles are congruent and opposite angles are supplementary.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are supplementary to the transversal on the same side. 360 degrees is the total of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.

The properties of a parallelogram are shared by the shapes of a square and a rectangle.

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The textile factory does not have enough dye to dye 5 rolls of fabric using 4 buckets of dye which is certain feet long.

Calculating the amount of dye needed to color one roll of fabric and comparing it to the total amount of dye available will help us decide whether the textile mill can dye 5 rolls of cloth with 4 buckets of dye.

We are aware that a single roll of fabric is 1,067 feet long and need for a 43-liter dye bucket. We divide the dye's volume by the fabric's length to get how much dye is needed per foot of fabric:

0.0403 litres per foot or 43 litres divided by 1,067 feet

Consequently, the factory needs 0.0403 litres of dye to colour one foot of fabric.

Considering there are 4 buckets and each bucket holds 43 litres of colour, the total amount of dye accessible is:

4 buckets at a rate of 43 litres each equal 172 litres.

The factory must dye a total of: to dye 5 rolls of fabric.

5,335 feet are equal to 5 rolls at 1,067 feet each.

We calculate the required amount of dye per foot by the total length of fabric to see if the factory has enough dye to colour this length of fabric:

5,335 feet * 0.0403 litres per foot = 215.1 litres

The manufacturer cannot colour 5 rolls of fabric with 4 buckets of dye because the whole amount of dye needed (215.1 litres) is more than the total amount of dye available (172 litres).

In conclusion, there isn't enough dye in the textile plant to colour 5 rolls of fabric using 4 buckets of dye.

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Answer:

x = 2,5

Step-by-step explanation:

3(3 - 2x) = 2x - 11

Multiply every term inside the bracket by the term on the outside:

9 - 6x = 2x - 11

Collect like terms and add them together (also, when moving the terms to the other side, the sign changes to the opposite)

-6x - 2x = -11 - 9

-8x = -20 / : (-8)

x = 2,5