the long leg of a right triangle is 71 feet longer than the short leg. the hypotenuse is 85 feet long. how long are the legs of the right triangle?

Spanish 45 and french 42.5. When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common.

When attempting to solve a Venn diagram with three circles, it is best to start by entering the number of items that the three sets of data have in common. After that, input how many items are still there in each pair of sets' overlapping zone.

The quantity of each set's leftover pieces should be entered. Lastly, locate any missing numbers using any known totals.

Using a Venn diagram to determine probabilities: The Venn diagram's subset's components should be identified. Figure out the subset's frequency. Work out the larger set's overall frequency.  

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Answer: We can start by using algebra to represent the given information. Let's call the number we're trying to find "x".

We know that:

quotient = (3x)/5

quotient + 4 <= 34

We can simplify the first equation:

(3x)/5 + 4 <= 34

We can then solve this inequality for x:

(3x)/5 + 4 <= 34

3x/5 <= 30

3x <= 150

x <= 50

So the quotient of three times a number and five is no more than 34 if that number is less than or equal to 50.

Step-by-step explanation:

An artist connects stained glass pieces with lead strips and cut the strips so that FH = 28 in and JG = 14 in.  

Now, According to the question:

A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.

Here, we have

FH ≅ GH

FH = EG = 28in

If diagonals bisect each other then, an artist connects stained glass pieces with lead strips

1/2(EG) = JG

1/2 (28) = JG

14 = JG

Hence, an artist connects stained glass pieces with lead strips and cut the strips so that FH = 28 in and JG = 14 in.  

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Used the distributive property a(b+c)=ab+ac, the value of x is x>1/2

Solving inequality using distribution property includes change of inequality signs when multiplied or divided by negative number but, not in the equation.

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

Curran:

-4(x-6)< 22

Used the distributive property a(b+c)=ab+ac

-4x+24<22

Then subtracted 24 from bot the sides

-4x<22-24

-4x< -2

Divide both sides by -4 ( inequality changes because of dividing by negative number)

x>1/2

Anjani:

-4(x-6)< 22

Divide both sides by -4

x-6> -22/4

add 6 on both sides

x> -22/4 + 6

x> -11/2 + 6

x> 1/2

Solving inequality using distribution property includes change of inequality signs when multiplied or divided by negative number but, not in the equation.

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People celebrate Pi Day on March 14th at 1:59 because this date and time is an easy way to remember the mathematical constant pi (π).

Pi, which is represented by the Greek letter π, is an irrational number that starts with 3.14 and continues for an infinite amount of digits. The numerical value of pi is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.1415926535897932384626433832795. The date and time of March 14th, 1:59 is a way to represent the first four digits of pi (3.14). People celebrate Pi Day by eating pie, making pi-related crafts, and sharing facts about pi. People celebrate Pi Day on March 14th at 1:59 because this date and time is an easy way to remember the mathematical constant pi (π).

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The number of days before she mows the lawn and washes her window on the same day is 60 days.

The day she would mow the lawn and wash her window on the same day would be the least common multiple of 12 and 20.

A multiple of a number is the product of an integer and that number. A common multiple is a multiple that two or more numbers share. The least common multiple is the smallest multiple that two or more numbers share.

Multiple of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 120

Multiple of 20 = 20, 40, 60, 80, 100, 120, 140, 160, 180, 200

Least common multiple = 60

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The simplification of the given expression after addition would be = 163.241.

Addition is the combination of two or more given values and it's one of the major arithmetic operations in mathematics.

The given expression is a s follows;

127.98+35.261 = 163.241

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The Centers for Disease Control and Prevention (CDC) states that the average height for men and women in the United States is around 5 feet, 9 inches and 5 feet, 4 inches, respectively.

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Answer:

I think 9/10 but I am not sure

Answer:

Step-by-step explanation:

35

(a) The area of the space shuttle is:2.07x10⁻⁹km²

(b) $11.0321 is the cost of the patch.

Area of the patch of the space shuttle = 21.9cm²

a) 1 cm=0.00001 km

1cm²=(0.00001 km)²=10⁻¹⁰km²

21.9cm²=21.9x10⁻¹⁰km²=21.9x10⁻⁹km²

the patch's area =21.9x10⁻⁹km²

b) 1 cm = 0.393701 inch

1cm²=0.1550inch²

21.9cm²=21.9x0.1550inch²=3.3945inch²

The cost of patching area = 3.3945inch²

The cost of patching is are: 3.3945inch²

3.25inch²x3.3945inch²=11.0321

the cost of the patch to the nearest cent=11.0321

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The measurement of indicated angle is 20 degree.

Here opposite angles are congruent .

Therefore the indicated angle is 20 degree.

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Answer:

is try ur hardest

Step-by-step explanation:

The side length of AC is 6 units for the shown triangle. The correct answer would be an option (C).

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

The right triangle is given in the question, as shown.

AD = 4 cm and BD = 5

In ΔACD and ΔABC

∠ACD = ∠ABC

∠ACD = ∠BAC = 90°

∠CAD = ∠ACD (remaining)

So ΔACD and ΔABC are similar

Hence

AD / AC = AC/ BC

Apply the cross-multiplication operation, and we get

AC² = AD × BC

AC² = 4 × 9

AC² = 36

AC = 6 cm

So, the side length of AC is 6 units.

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The person being called is a function of the phone number, as for each phone number, there is only one person associated with the number.

A relation represents a function when each input value is mapped to a single output value.

The input and output variables for this problem are given as follows:

Each phone number is mapped to a single person, meaning that the relation is in fact a function.

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Marlon's height is 42.52 inches.

Since the heights of four-year-old's are normally distributed with a mean of 40 inches and a standard deviation of 3 inches, we can use the z-score formula to find Marlon's height.

z = (x - mean) / standard deviation

where x is Marlon's height, mean is the population mean of 40 inches, and standard deviation is the population standard deviation of 3 inches.

We know that Marlon's height is taller than 70% of boys his age, so we can find his z-score using the cumulative standard normal distribution table, which tells us the proportion of the population that is less than a given value.

A z-score of 0.84 corresponds to a cumulative probability of 0.70.

So we can substitute this value into the z-score formula:

0.84 = (x - 40) / 3

Solving for x, we get:

x = 40 + (3 * 0.84) = 40 + 2.52 = 42.52 inches

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The surface area of the pyramid is 5,685 ft².

To find the surface area of the pyramid, we need to find the area of the base and the area of the four triangular faces. Since the base is a rectangle, we can find its area by multiplying the length and width:

length, l = 25 ft

width,w = 22 ft

Area = l x w

Area = 25 ft x 22 ft

Area = 550 ft².

To find the area of each triangular face, we first need to find the slant height of the pyramid, which can be found by using the Pythagorean theorem on the net dimensions. The slant height is the square root of

Net dimensions of the pyramid:

length, l = 74.8 ft

width, w = 70.4 ft

h = [tex]\sqrt{l ^{2} +w^{2} }[/tex]

h = [tex]\sqrt{(74.8^{2} + 70.4^{2} ) }[/tex]

h = 102.7 ft.

Now, we can use the formula for the area of a triangle:

Area = (1/2) x base x height,

where,

base,b = the length of the rectangular base (25 ft)

height = the slant height (102.7  ft).

So, the area of each triangular face is:

A = (1/2) x 25 ft x 102.7  ft

A = 1283.75 ft².

Since there are four triangular faces, the total area of all the triangular faces is:

A= 4 x 1283.75 ft²

A = 5,135 ft².

To find the surface area of the pyramid, we add the area of the base to the area of the triangular faces:

SA= 550 ft² +  5,135 ft² = 5,685 ft².

Hence, the surface area of the pyramid is 5,685 ft².

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The simple interest earned on a deposit of $2800 after 5 years at a 2% annual rate is $280.

It is the interest calculated on the principal at a given rate for a time period.

We have,

P = $2800

T = 5 years

R = 2%

Now,

The formula for simple interest.

SI = PRT/100

Now,

SI = (2800 x 2 x 5) / 100

SI = 28 x 10

SI = $280

Thus,

Simple interest is $280.

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Answer: i think y =  x + 5

Step-by-step explanation:

When it's a quarter full, the shipping container holds a volume of 350 cubic feet.

Bassically, we want to find one quarter (1/4) of the volume of the rectangular prims.

The dimensions are 20ft by 8ft by (8ft + 9in)

Let's rewrite that last part only using feet.

Remember that 12 in = 1ft

Then:

9 in = (9/12)ft = 0.75 ft

Then we can rewrite the dimensions as:

20ft by 8ft by 8.75 ft

The volume is the product between these numbers, and we want one fourt of the volume, so we need to find:

V = (1/4)*(20ft)*(8 ft)*(8 .75 ft) = 350ft³

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The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900[tex]e^{\frac{-t}{400}}[/tex]

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

[tex]\int p(t)dt = \int\frac{1}{400}dt[/tex][tex]\int p(t)dt = \frac{1}{400}t[/tex]

[tex]\mu=e^{\int p(t)dt}[/tex]

[tex]\mu=e^{\frac{t}{400}}[/tex]

So, S(t) = [tex]\frac{\int\mu q(t)dt+C}{\mu}[/tex]

S(t) = [tex]\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}[/tex]

S(t) = [tex]e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)[/tex]

S(t) = [tex]e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)[/tex]

S(t) = [tex]e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)[/tex]

Now solving the bracket

S(t) = 4000 + [tex]e^{\frac{-t}{400}}[/tex]C.....(1)

At S(0) = 100

100 = 4000 + [tex]e^{\frac{-0}{400}}[/tex] C

100 = 4000 + [tex]e^{0}[/tex] C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900[tex]e^{\frac{-t}{400}}[/tex]

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

The solution set to the inequality as represented in another way is {x | x ∈ ≤ 4.5}. The second option is correct from the photo.

The set builder form is the representation of components of a set by a statement or an expression. The represented element(s) will be written using a variable, accompanied by a vertical line or colon, then the general attribute of the same represented element. This approach avoids listing the elements as seen in the roster method or the listing method.

From the given sets in roster form:

{-5,-4, -3, -2, -1, 0, 1, 2, 3, 4.5}

The same set above can be denoted by x, where x represents all the elements in the set and can be written as:

= {x | x ∈ ≤ 4.5}

This is read as x is an element of x such that x represent all the values from negative infinity to 4.5.

Therefore, we can conclude that the second option is correct from the photo.

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Answer:

A ratio in words compares a whole to a part. For example, the ratio of apples to oranges in a basket is "three to one." This can also be written as "3:1" or "3/1."

Another example: is the ratio of students to teachers in a class is "twenty to one." This can also be written as "20:1" or "20/1."

Step-by-step explanation:

The lateral area for the prism is equal to 54 square inches. (Correct choice: B)

Herein we have the case of a prism with five faces, two triangles and three rectangles. The lateral area for the prism is the sume of the areas of the three rectangular faces, whose formula is described below:

Rectangle

A = w · l

Where:

Finally, we proceed to determine the lateral area of the prism:

A = 3 · (3 in) · (6 in)

A = 54 in²

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Answer:

cotθ=√21/2

Step-by-step explanation:

we have,

sinθ= 2/5= perpendicular/hypotenuse

here,

perpendicular=2

hypotenuse = 5

Now using Pythagorean theorem,

h^2 = p^2+ b^2

(5)^2 = 2^2 +b^2

b= √21

so,

cotθ= base/perpendicular = √21 /2

Hope you like the explanation.

Answer:

The maximum total cost for tickets is $320 + $160 = $480.

Step-by-step explanation:

The maximum number of people that can go on the field trip is 100, so the maximum number of students is 100 - (100/5) = 80 students.

The maximum number of adult chaperones is 1 adult chaperone for every 4 students, so the maximum number of chaperones is 80/4 = 20 chaperones.

The total cost for student tickets is $4 x 80 = $320.

The total cost for adult chaperone tickets is $8 x 20 = $160.

The maximum total cost for tickets is $320 + $160 = $480.

Answer:

the maximum amount for the equation is 320+160=480

The time taken by the submarine to make the descent when the equation of descent is given is 0.677 hours.

Submarine's descent can be represented by the equation, y = -3100 x

where,  

y is elevation

x is time in hours

We need to determine how long it will take this submarine to travel 2,100 feet below the surface of the ocean.

Since the submarine to make the descent to the seafloor 2,100 feet below the surface

So, y = - 2100

y = - 3100x gives

- 2100 = - -3100 x

Divide both sides by -3100,

x = 2100/3100 = 0.677 hours

As a result, the submarine will need 0.677 hours to complete the descent.

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6.93 × 10⁷ dogs were household pets in the U. S. In 2012.

To find the total number of dogs as household pets in the U.S. in 2012, we need to multiply the number of households by the average number of dogs per household.

Number of households = 4.33 × 10⁷

The average number of dogs per household = 1.6

Total number of dogs = (4.33 x 10⁷) × (1.6) = 6.93 × 10⁷

Therefore, approximately 6.93 × 10⁷ dogs were household pets in the U.S. in 2012.

Hence, the correct answer is D.

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