Using the Pythagorean theorem decided if the values 10 11 2 could be a right triangle

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

In simplifying this is simple.

Answer:

x=96

Step-by-step explanation:

Answer:

$0.64 per cup

Step-by-step explanation:

There are 16 cups in 1 gallon, so the number of cups in 2 gallons is:

1 gallon: 16 cups

2 gallon = 2 x 1 gallon = 2 x 16 cups = 32 cups

So we need to find the price of each cup:

1 cup = ($20.48 / 32 cups) = $0.64 per cup.

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

We have,

To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.

The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.

Let's calculate the number of half-lives required to reach 150mg:

Initial amount of aspirin = 625mg

Final amount of aspirin = 150mg

625mg / 150mg = 4.17

This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.

Since each half-life is 6 hours, we can calculate the total time it will take:

Total time = Number of half-lives * Half-life duration

Total time = 4.17 x 6 hours

Total time ≈ 25 hours and 1 minute

Therefore,

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

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Answer:

18.285 in.²

Step-by-step explanation:

3 in. × 4 in. = 12 in.²

A = πr²

A = 12.57 in.²

12.57 in.² ÷ 2 = 6.285 in.²

6.285 in.² + 12 in.²

18.285 in.²

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)

where s = half the perimeter,

s = (a + b + c)/2.

given data:

In ΔHIJ,

semi -perimeter s = (i + j + h) / 2

s = (33 + 61 + 39) / 2

s = 66.5

Now,

s - h = 66.5 - 33 = 33.5

s - i = 66.5 - 61 = 5.5

s - j = 66.5 - 39 = 27.5

area of ΔHIJ = √s(s - h)(s - i)(s - j)

area of ΔHIJ = √66.5*33.5*5.5*27.5

area of ΔHIJ = √336947.1875

area of ΔHIJ = 580.47

Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.

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Answer:

x + 9

Step-by-step explanation:

The sum of x and 9,

x + 9

Answer:

n/2[2a+(n-1)d]

12/2[2(-5)+(12-1)6]

66-10=56×6=336

336 is the 12th term

In a geometric sequence, each term is obtained by multiplying the previous term by a constant factor called the common ratio (denoted by \(\displaystyle\sf r\)). In the given sequence, the common ratio is \(\displaystyle\sf r=-2\).

To determine if the sequence converges or diverges, we look at the absolute value of the common ratio (\(\displaystyle\sf |r|\)). If the absolute value of the common ratio is less than 1 (\(\displaystyle\sf |r|<1\)), the sequence converges. If the absolute value of the common ratio is greater than or equal to 1 (\(\displaystyle\sf |r|\geq 1\)), the sequence diverges.

In this case, the absolute value of the common ratio is \(\displaystyle\sf |-2|=2\), which is greater than 1. Therefore, the sequence diverges.

Answer:

Step-by-step explanation:

The common ratio in a geometric sequence is calculated by dividing any term by its preceding term. In this case:

-2.5 ÷ 5 = -0.5

1.25 ÷ -2.5 = -0.5

-0.625 ÷ 1.25 = -0.5

We can observe that the common ratio between each term is -0.5.

A geometric sequence converges if the absolute value of the common ratio is between -1 and 1. In this case, the absolute value of the common ratio (-0.5) is less than 1. Therefore, the geometric sequence converges.

In a converging geometric sequence, as more terms are added, the values approach a certain limiting value. In this case, since the common ratio is negative, the terms alternate between positive and negative values. As the sequence progresses, the absolute values of the terms decrease, approaching zero.

Hence, the geometric sequence 5, -2.5, 1.25, -0.625, ... converges.

The resultant force acting on the block is 47.6N.

The acceleration of the block will be 23.8 m/s².

The speed of the block after 5 seconds of movement is 119 m/s.

In this question, we need to make use of Newton's second law, hence:

resultant force = mass × acceleration

So, for question a. The value of the resultant force  will be obtained by adding the two forces together:

resultant force = F₁ + F₂

                       = 25N + 22.6N

                        = 47.6N

b.  Its acceleration will be:

acceleration = resultant force / mass

                  = 47.6N / 2kg

                  = 23.8 m/s²

c. The speed of the block after 5 seconds of movement will be:

Velocity  (v) = u + at

velocity = initial velocity + acceleration x time

Based on the block was initially at rest, the initial velocity is 0.

Hence:

V = acceleration x time

    = 23.8 m/s² x 5s

     = 119 m/s

Hence the speed of the block after 5 seconds of movement will be: 119 m/s.

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See full text below

The block in the figure is at rest when the forces begin to act.

F₁ = 25N

F, = 22.6 N

m = 2kg

to. Find the value of the resultant force.

b. Determine its acceleration.

C. Calculate the speed of the block after 5 seconds of movement.

It takes the toy car 2.43 seconds to fall to the bottom floor,  answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.

An equation is a mathematical statement that asserts that two expressions are equal. An equation consists of two sides, the left-hand side and the right-hand side, separated by an equal sign (=).

For example, 2x + 5 = 11 is an equation, where the left-hand side is 2x + 5 and the right-hand side is 11. This equation asserts that the expression 2x + 5 is equal to 11, and the value of x can be determined by solving for x.

Equations can be simple or complex, and they can involve one or more variables. They can also be linear or nonlinear, depending on the nature of the expressions involved.

Solving an equation involves finding the values of the variables that make the equation true. This may involve applying algebraic operations and simplification techniques to isolate the variable on one side of the equation.

Equations are used in many areas of mathematics, science, engineering, and economics, and they provide a powerful tool for modeling and analyzing real-world situations. They are also used extensively in computer programming and cryptography, where they play a critical role in the development of algorithms and data encryption methods.

We have the equation \(h = 94 - 16t^2\), where h is the height of the toy car in feet and t is the time in seconds.

When the toy car reaches the bottom floor, its height will be h = 0. So we can set the equation equal to 0 and solve for t:

\(0 = 94 - 16t^216t^2 = 94t^2 = 94/16\)

\(t = \sqrt{(94/16)} = \sqrt{(23.5/4)} = 2.43 seconds\) (rounded to two decimal places)

Therefore, it takes the toy car 2.43 seconds to fall to the bottom floor.

The closest answer choice is B. 9/4 seconds, which is equal to 2.25 seconds.

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Answer:

A number. :) lol

Step-by-step explanation:

The correct answers are Options: B and C as both  are applicable in this case.

The terminal point determined by theta can not be in quadrant 3 since tan theta is greater than zero in this quadrant.

In addition, if tan theta =-12/5 then csc theta = ±13/12 since the terminal point determined by theta can be in quadrant 2 where sine theta and consequently csc theta would be positive or in quadrant 4 where csc theta would be negative.

In conclusion, we chose Options: B and C as correct answers as both  are applicable in this case.

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Corrected Question

The statement "tan theta=-12/5 , csc theta = -13/5 , and the terminal point determined by theta is in quadrant 3":

A. cannot be true because tan theta must be less than 1.

B. cannot be true because tan theta is greater than zero in quadrant 3.

C. cannot be true because if tan theta = -12/5 , then csc theta = +/- 13/12

D. cannot be true because 12^2 + 5^2 ≠ 1

Answer:

the answer is 9 ft 12in here is a simple formula to find how many inches are In a yard

1 yard = 24 inches and half of 24 equals 12

Answer:

10 mins

Step-by-step explanation:

Proportion:

21/6=35/x

x=(35*6)/21

x=10

Hope this helps plz hit the crown :D

Answer:

10 mintes

Step-by-step explanation:

Mika would need 10 minutes to eat 35 hot dogs.

Mika can eat 21 hot dogs in 6 minutes. So Mika eats 21 hot dogs/6 minutes

So Mika eats 35 hot dogs/m minutes. The proportion is set up like this:

21/6 = 35/m Then, cross-multiply:

6·35 = 21m

m = 210/21

m = 10 minutes

The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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Using the binomial distribution, it is found that there is a 0.4295 = 42.95% probability that at least 4 of them say job applicants should follow up within two weeks.

For each manager, there are only two possible outcomes. Either they say job applicants should follow up within two weeks, or they do not say it. The opinion of a manager is independent of any other manager, which means that the binomial distribution is used to solve this question.

Binomial probability distribution  

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)  

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

The probability that at least 4 of them say job applicants should follow up within two weeks is \(P(X \geq 4)\), which is given by:

\(P(X \geq 4) = 1 - P(X < 4)\)

In which:

\(P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)\)

Then:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{8,0}.(0.41)^{0}.(0.59)^{8} = 0.0147\)

\(P(X = 1) = C_{8,1}.(0.41)^{1}.(0.59)^{7} = 0.0816\)

\(P(X = 2) = C_{8,2}.(0.41)^{2}.(0.59)^{6} = 0.1985\)

\(P(X = 3) = C_{8,3}.(0.41)^{3}.(0.59)^{5} = 0.2759\)

\(P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0147 + 0.0816 + 0.1985 + 0.2759 = 0.5707\)

\(P(X \geq 4) = 1 - P(X < 4) = 1 - 0.5705 = 0.4295\)

0.4295 = 42.95% probability that at least 4 of them say job applicants should follow up within two weeks.

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Answer:

We know that:

Over a half-mile stretch of road, there are 7 evenly spaced street signs.

If we assume that there is a sign right at the beginning and another right at the end, then the distance between each sign will be equal to the total distance divided by the total number of signs minus one because the distance is measured in pairs of consecutive signs, if we have 7 signs, then we will have 6 pairs of consecutive ones ( 1st and 2nd, 2nd and 3rd, 3rd and 4th, ...)

(0.5mi)/6 = 0.83... mi

So, rounding to the second decimal after the decimal point, the distance between each sign is 0.83 miles.

C. Unique solution. The system of linear equations have a unique solution because the equations are consistent and have the same number of variables and equations.

The given system of linear equations is x+2y=3 and 2x+4y=15. To determine whether the system of linear equations have no solution, infinitely many solution or unique solutions, we need to solve the system of equations. Firstly, we expand and simplify both equations to get x+2y=3 and 2x+4y=15. Then, we compare the coefficients of the equations to determine if the system of equations is consistent, inconsistent or dependent. Since the equations are consistent and have the same number of variables and equations, we can solve the system of equations. By isolating the variables and using the substitution method, we can solve the system of equations to get x=3 and y=3. This means that the system of linear equations have a unique solution.

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Answer:

-12

Step-by-step explanation:

n*2 + 5n + 2

-2 × 2 + 5(-2) + 2

-4 + -10 + 2

= -12

Answer: 37-07

Step-by-step explanation:

The only true statement about the domain of the given function is:

B. f(x) is negative for all x < -5

The domain of a function is defined as the set of values that we can possibly plug into our function. This set is the x values in a function such as f(x).

Now, we are given the function as:

f(x) = \(\frac{2}{x^{2} } + 3x - 10\)

When x < -5, we have:

f(-4) = \(\frac{2}{(-4)^{2} } + 3(-4) - 10\)

f(-4) = -21.875

This suggests that for all values below x = -5 will result in negative values

When x > 2

f(3) = \(\frac{2}{3^{2} } + 3(3) - 10\)

f(3) = -0.78

Thus, it will get positive for higher values but it can also be negative as seen here.

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Answer:

5 & -4

4 & -3

3 & -2

2 & -1

Step-by-step explanation:

5 + (-4) = 1

4 + (-3) = 1

3 + (-2) = 1

2 + (-1) = 1

Matching of the functions domain and range are as follows:

f(x)   = 4-4x ;

Domain:{0,1,3,5,6}

Range;{-20,-16,-8,0,4}

f(x) = 5x - 3

Domain:{-2,-1,0,3,4}

Range:{-13,-8,-3,12,4}

f(x) = -10x

Domain:{-4,-2,0,2,4}

Range:{-40,-20,0,20,40}

f(x) = (3/x) + 1.5

Domain:{-3,-2,-1,2,6}

Range:{0.5,0,-1.5,3,2}.

1) The function f(x) = 4 - 4x

Take Domain:{0,1,3,5,6}

If, we take x=0 and put in the function then we get

f(x)=4-0

f(x)=4

put x=1

f(x) = 4 - 4 =0

put x=3 then we get

f(x)=4-12=--8

put x=5 them we get

f(x)=4-20=-16

put x=6 then we get

f(x)=4-24=-20

Therefore ,range:[-20,-16,-8,0,4}

2) The function f(x)=5x-3

Take domain{-2,-1,0,3,4}

Now, put x=-2 in the function then we get

f(x) = -13

now put x=-1 then we get

f(x)=-5-3=-8

Put x=0 then we get

f(x)=0-3=-3

Put x=3 then we get

f(x)=15-3=12

Put x=4 then we get

f(x)=20-3=17

Therefore , range:{-13,-8,-3,12,17}

3) The function f(x)=-10x

Take domain:{-4,-2,0,2,4}

Put x=-4 in the function then we get

f(x)=40

Put x= -2 then we get

f(x)=20

Put x=0 then we get

f(x)=0

Put x=2 then we get

f(x)=-20

Put x=4 then we get

f(x)=-40

Therefore , range :{-40,-20,0,20,40}

4) The function f(x)= (3/x) + 1.5

Take domain:{-3,-2,-1,2,6}

Put x= -3 in the taken function then we get

f(x)=-1+1.5=0.5

put x=-2 then  we get

f(x)= -1.5+1.5=0

Put x=-1 then we get

f(x)=-3+1.5=-1.5

Put x= 2 then we get

f(x)=1.5+1.5=3

Put x= 6 then we get

f(x)=0.5+1.5=2

Therefore, range : {0.5,0,-1.5,3,2}.

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Answer:

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.........

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Answer:

0.04

Step-by-step explanation:

Standard deviations== square root of variance define as spread.

Standard deviations square = variance

[0.2]^2= 0.04

We can draw the following picture:

the area A is given by

therefore, the area is 135 ft^2. Which corresponds to option C.