The legs of a right triangle have lengths of 3 and 4. What is the length, to the nearest tenth, of the altitude to the hypotenuse?

Answer:

Plan B is correct answer.

Step-by-step explanation:

Raise the price by 10 percent each week until the price reaches $8.00.

Week 1. Starting price $5

[tex]0.1\times5=0.5[/tex]

price becomes = [tex]5+0.5=5.5[/tex]

Week 2.

[tex]0.1\times5.5=0.55[/tex]

Price becomes = [tex]5.5+0.55=6.05[/tex]

Week 3.

[tex]0.1\times6.05=0.605[/tex]

Price become = [tex]6.05+0.605=6.655[/tex]

Week 4.

[tex]0.1\times6.655=0.6655[/tex]

Price becomes = [tex]6.655+0.6655=7.320[/tex]

Week 5.

[tex]0.1\times7.320=0.732[/tex]

Price becomes = [tex]7.320+0.732=8.052[/tex]

So, we can see that in 5 weeks the price becomes $8 from $5. Therefore, plan B is the best plan.

The equation of velocity of sound in air is v = 20 √(273 + t). In this problem, we need to find the temperature when the velocity is 329 meters/s. You need to measure the time it takes a sound to travel a measured distance in order to measure its speed in air.

Given:

Velocity of sound in air equation = v = 20 √(273 + t)

Velocity = 329 m/s

To solve:

V = 20 √(273 + t)

329 = 20 * sqrt(273 + t)

16.45 = sqrt(273 + t)

273 + t = 16.45^2

t- 16.45^2-273

t = -2.4 degrees Celsius

So, the temperature when the velocity is 329 meters per second is -2.4 degrees Celsius.

Answer:

Term

Step-by-step explanation:

hope this helps

First, we construct an equation based on the problem: x+(4x)+(5x)=30. Solving this gives us x=3 inches. Thus, the first piece is 3 inches, the second piece is 12 inches and the third piece is 15 inches.

In this problem, a 30 inch board is being divided into three pieces. If the first piece is designated as x, then the second piece would be 4 times as long which is 4x, and the third piece would be 5 times as long which is 5x. If all these pieces add up to the total length of the board which is 30 inches so we can construct the equation: x+(4x)+(5x)=30.

To solve, we combine like terms to get 10x = 30. Divide both sides by 10 to isolate x, so x=3 inches. Thus, the first piece is 3 inches, the second piece is 4 times the first piece which is 12 inches, and the third piece is 5 times the first piece which is 15 inches.

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Answer:

[tex]x=2+-i \sqrt{6}[/tex]

Step-by-step explanation:

[tex]x^2 + 4x + 10[/tex]

To find out the solution we set the expression =0 and solve for x

[tex]x^2 + 4x + 10=0[/tex]

Apply quadratic formula to solve for x

[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]

a=1, b=4, c=10 plug in the values in the formula

[tex]x=\frac{-4+-\sqrt{4^2-4(1)(10)}}{2a}[/tex]

[tex]x=\frac{-4+-\sqrt{-24}}{2(1)}[/tex]

The value of square root (-1) is 'i'

[tex]x=\frac{-4+-2i\sqrt{6}}{2}[/tex]

Divide each term by 2

[tex]x=2+-i\sqrt{6}[/tex]

Answer:

y=-2x+5

Step-by-step explanation:

Final answer:

Calculating the overall percentage of defective products from the given data, we find that 150 out of 1000 products are defective, leading to an overall defect rate of 15%.

Explanation:

The question asks us to calculate the overall percentage of defective products based on the given scenarios. Firstly, it's mentioned that 75% of 1000 products are shipped on time, which means 750 are shipped on time and 250 are initially defective.

Since clients complain that 10% of the products are defective and 5% of the products are shipped late or are defective, we need to consider these percentages in our calculations.

To find the number of defective products, we can assume the 10% complaint rate on the entire batch of products which would lead to 100 out of 1000 products being defective. This is the initial estimated number of defective products.

To address the 5% of the products that are both shipped late and are defective, we consider this as an additional defect rate on top of the existing one, which would be another 50 products.

Total defects would then be the sum of defects from the complaints about defects and the defects because of shipping delay, which amounts to 100 + 50 = 150 defective products. To find the overall percentage, we divide 150 by 1000 and multiply by 100, giving us an overall defect rate of 15%.

The required amount of drug for each time a day is given as 425 mg.

A measurement unit is a unit to measure certain quantities.

For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.

To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.

Given that,

The weight of the person is 80 pounds.

The amount of dose of drug per day is 25 mg/kg

Then, the amount of drug for each time a day is 12.5 mg/kg.

The weight of the person in kilogram can be calculated as follows,

1 pound = 0.45 kg

Then, 80 pounds = 0.45 × 80

                             = 34 kg

Now, the amount of drug to be taken each time is 34 × 12.5 = 425mg.

Hence, the amount of drug that should be administered to the person each time is 425 mg.

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(x^2)/a^2+(y^2)/b^2=1

a>b

a=6, a^2=36

foci=(a^2-b^2)^(1/2)

4=(36-b^2)^(1/2)

16=36-b^2

b^2=36-16

b^2=20

b=2(5)^(1/2) or (20)^(1/2)

1=(x^2/36)+(y^2/20)

The base of parallelogram is 15 inches.

A parallelogram is a two-pair quadrilateral with parallel sides. A parallelogram has opposite sides that are the same length and have opposite angles that are the same size. Additionally, the interior angles on the same transversal side are supplemental. 360 degrees is the sum of all the interior angles.

Given area  of a parallelogram is 60  square inches

area of parallelogram is given by product of base and height,

Area = b × h

where b = base and  h = height

height = 4 inches

Area = b × h

60 = b × 4

b = 60/4 = 15 inches

Hence the base is 15 inches.

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Answer:

Yes, the relation is a function.

Step-by-step explanation:

We have been given the table

x         y  

-1         -2

2          3

3         1

6         -2

We know that a relation is a function if every x value has a unique y value.

For the given relation all the x values have a single and unique y values. For example -1 has value -2, 2 has a value 3, 3 has a value 1 and 6 has a value -2.

Thus, the given relation is a function.

Final answer:

By applying the theorem that an inscribed angle is half the measure of its intercepted arc, we can solve the given equation to find that the value of x is 1.

Explanation:

The problem involves the relationship between an inscribed angle and its intercepted arc in a circle, which is a fundamental concept in circle geometry. According to the theorem that states an inscribed angle is half the measure of its intercepted arc, we can set up an equation to find the variable x.

Given that angle C measures (3x + 5)° and arc AB measures (16x)°, the relationship between them can be expressed as:

Angle C = ½ × measure of arc AB

(3x + 5)° = ½ × (16x)°

Solving this equation for x gives:

3x + 5 = 8x

5 = 5x

x = 1

Therefore, the value of x is 1.

Answer:  The correct option is (A) 2 + 0.2 + 0.02 + 0.002 +  .  .  .

Step-by-step explanation:  We are given to select the correct geometric series that converges.

We know that

a geometric series converges if the modulus of its common ratio is less than 1.

Option (A) : 2 + 0.2 + 0.02 + 0.002 +  .  .  .

Here, first term, a= 2  and the common ratio is given by

[tex]r=\dfrac{0.2}{2}=\dfrac{0.02}{0.2}=\dfrac{0.002}{0.02}=~.~.~.~=0.1\\\\\Rightarrow |r|=|0.1|=0.1<1[/tex]

So, this geometric series will converge.

Option (A) is correct.

Option (B) : 2 + 4 + 8 + 16 +  .  .  .

Here, first term, a= 2  and the common ratio is given by

[tex]r=\dfrac{4}{2}=\dfrac{8}{4}=\dfrac{16}{8}=~.~.~.~=2\\\\\Rightarrow |r|=|2|=2>1.[/tex]

So, this geometric series will not converge.

Option (B) is incorrect.

Option (C) : 2 - 20 + 200 - 2000 +  .  .  .

Here, first term, a= 2  and the common ratio is given by

[tex]r=\dfrac{-20}{2}=\dfrac{200}{-20}=\dfrac{-2000}{200}=~.~.~.~=-10\\\\\Rightarrow |r|=|-10|=10>1.[/tex]

So, this geometric series will not converge.

Option (C) is incorrect.

Option (D) : 2 +2 + 2 + 2 +  .  .  .

Here, first term, a= 2  and the common ratio is given by

[tex]r=\dfrac{2}{2}=\dfrac{2}{2}=\dfrac{2}{2}=~.~.~.~=1\\\\\Rightarrow |r|=|1|=1.[/tex]

So, this geometric series will not converge.

Option (D) is incorrect.

Thus, the correct option is (A).

The geometric series that converges is 2+0.2+0.02+0.002+ ...:

Thus, option (A) is correct.

In a geometric series, the terms are multiplied by a constant ratio to obtain the next term.

If the absolute value of the common ratio is less than 1, the series converges.

A. 2 + 0.2 + 0.02 + 0.002 + ...:

In this series, the common ratio is 0.1 (each term is divided by 10).

Since the absolute value of the common ratio is less than 1, this series converges.

B. 2 + 4 + 8 + 16 + ...:

In this series, the common ratio is 2 (each term is multiplied by 2).

Since the common ratio is greater than 1, this series diverges.

C. 2 - 20 + 200 - 2000 + ...:

In this series, the terms alternate in sign, but the absolute value of the common ratio is 10.

Since the absolute value of the common ratio is greater than 1, this series diverges.

D. 2 + 2 + 2 + 2 + ...:

In this series, the common ratio is 1 (each term is the same).

Since the common ratio is equal to 1, this series neither converges nor diverges. It is a divergent series.

Therefore, the geometric series that converges is 2 + 0.2 + 0.02 + 0.002 + ...

Thus, option (A) is correct.

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The value of x for which l is parallel to m would be; 31.

An equation is an expression that shows the relationship between two or more numbers and variables.

First angle 105 is the vertical opposite angle with the other angle.

The angles are corresponding angles which are equal when the lines are parallel.

Therefore,

3x - 18 + 105 = 180

3x + 87 = 180

3x = 180 - 87

3x = 93

x = 93/3

x = 31

Hence, the value of x for which l is parallel to m would be; 31.

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The angles of triangle PQR are ordered from largest to smallest as <>R,

The question involves applying the principles of geometry to compare lengths of sides in a triangle, and thereby determine the relative magnitude of angles in triangle PQR. According to the triangle inequality theorem, the largest angle in a triangle is opposite the longest side, and the smallest angle is opposite the shortest side. Given that the side lengths are represented as PQ = 3x + 2, QR = x, and RP = x + 2, we can compare the expressions to conclude which side is longest and which is shortest, assuming all values of x are positive since they represent lengths.

Firstly, it is obvious that QR (x) is the shortest side since it is just x without any additional positive value. Secondly, between RP (x + 2) and PQ (3x + 2), PQ will always be longer than RP for all positive x because it has a larger coefficient in front of x. Hence, the angle opposite PQ (angle R) will be the largest angle, and the angle opposite QR (angle P) will be the smallest. The angle at Q will be between the other two angles in terms of their measurements since PQ is longer than RP but both are longer than QR.

To summarize, the angles of Triangle PQR ordered from largest to smallest are: ∠R, ∠Q, and ∠P.