Test Pythagorean Theorem
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Unit Test: Pythagorean Theorem
UNIT TEST:
Pythagorean Theorem
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ABCD is a right triangle. The length of the hypotenuse is 18 centimeters. The length of one of the legs is 14 centimeters.
What is the length of the other leg?
Enter your answer, as a decimal rounded to the nearest tenth, in the box

Answer:

1,2 and 4

Step-by-step explanation:

Answer:

(a)

(b)Discrete

(c)Ratio Scale and Discrete Variable

(d) Experimental Method

Step-by-step explanation:

The psychologist wants to evaluate the claim that omega-3 fatty acids can help improve memory in normal adult humans.

(a)In the study, the participants in the two groups were given fish extracts containing Omega-3 (500 mg) and no Omega-3 (0 mg).

The memory test involves measuring the number of items each participant remembers from the past three weeks of news.

Therefore:

(b) The dependent variable is discrete since the number of news items remembered can only be whole numbers.

(c)The independent variable is in milligrams of Omega-3 where the placebo is 0 mg. This is a ratio scale since it has an absolute zero.

Since the dosage is given in multiples of 50mg, it is a discrete variable.

(d)Since the psychologist seeks to manipulate the conditions of the study by introducing Omega-3 to some of the participants and placebo to other participants, it is an experimental distribution.

Answer:

3.5÷5

Step-by-step explanation:

It's asking what problem can be solved by doing 3.5 ÷ 5

the problem is 3.5 ÷ 5

Ten times to get the required amount of 100ml of milk for her recipe.

Avery needs to measure 100ml of milk for her recipe but she only has a 10ml measuring cup.

Therefore, she needs to determine how many times she will need to fill her 10ml measuring cup to get the required amount of milk.

To calculate this, we can divide the required amount of milk by the capacity of the measuring cup. In this case, we divide 100ml by 10ml to get:

100ml ÷ 10ml = 10

This means that A very will need to fill her 10ml measuring cup 10 times to get the required amount of milk for her recipe.

Another way to think about it is to consider that 100ml is ten times the capacity of the 10ml measuring cup. Therefore, Avery will need to fill the measuring cup ten times to get the required amount of milk.

In summary, Avery will need to fill her 10ml measuring cup ten times to get the required amount of 100ml of milk for her recipe. t

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Answer:

  y = negative 2 cosine (2 (x + pi)) minus 1

Step-by-step explanation:

The amplitude of the trig function will be half the difference of the minimum and maximum, so is ...

  A = (1 -(-3))/2 = 2

The coefficient of x is 2π divided by the period, so is ...

  B = (2π)/π = 2

The vertical offset is the average of the maximum and minimum:

  C = (1 +(-3))/2 = -1

Since the extreme negative value is at x=0, this can be the opposite of the cosine function:

  y = -A·cos(Bx) +C

The answer choices have a horizontal offset of pi, which does nothing, since the period is pi.

  y = -2cos(2(x+π)) -1

Answer:

C on E2020.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Constants in an equation represents numbers. They are not attached to any variable. Given the equation y = 3x + 2, you will see that the term that is standing alone without  a variable here is 2. This shows that the constant used in the equation is 2

Answer:

The longest segment is approximately 19.13cm

Step-by-step explanation:

Given

\(l = 14cm\)

\(w = 11cm\)

\(h = 7cm\)

Required

The length of the longest segment (d)

This is calculated using:

\(d = \sqrt{l^2 +w^2 + h^2\)

So, we have:

\(d = \sqrt{14^2 +11^2 +7^2\)

Using a calculator, the equation becomes

\(d = \sqrt{366\)

Take square roots

\(d = 19.13cm\)

We are asked to find the perimeter of the figure shown below:

We are going to add all the sides in the figure, and noticing that all those sides marked with a single tick measure 3 in and all those sides marked with a double tick measure 5 in. We count a total of four sides of length 5 in, and also four sides of length 3 in. Then the perimeter becomes:

Perimeter: 4 x 5 in + 4 x 3 in = 20 in + 12 in = 32 in.

The perimeter of the figure is : 32 in.

Answer:

The length of rectangle seven more than triple the width. If the perimeter 126 inches, find the dimensions The width inches. The length inches.

Answer:

130 degrees

Step-by-step explanation:

DE+DA=130

The missing values in the quantitative reasoning given are : -2, 13 and 9

Given the rule :

We can deduce that :

For the left circle :

circle = -6 - (-4) = -6 + 4 = -2

For the right circle :

circle = 11 - (-2) = 11 + 2 = 13

For the left square :

square = 13 + (-4)

square = 13 -4 = 9

Therefore, the missing values are : -2, 13 and 9

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Answer:

(-1,-6)

Step-by-step explanation:

Answer:

The answer would be (-1,-6)

Step-by-step explanation:

(13 + x)/2 = 6

13+x= 12

x = -1

~~~~~~~~~~~~~~~

(-2 + y ) / 2 = -4

-2 + y = -8

y = -6

Answer:

BD = 4

Step-by-step explanation:

∆BAD is congruent to ∆CAD based on the AAS Congruence Theorem.

Therefore:

BD = CD

3x + 1 = 5x - 1 (substitution)

Collect like terms

3x - 5x = -1 - 1

-2x = -2

Divide both sides by -2

x = -2/-2

x = 1

✔️BD = 3x + 1

Plug in the value of x

BD = 3(1) + 1

BD = 3 + 1

BD = 4

Answer:

28 potatoes

Step-by-step explanation:

1 Potato = 2 Samosas

So...You would do this equation

56 divided by 2 = ?

STEPS IN THE DIVIDING

2 goes into 5 (2 times)

Subtract. 5 - 4 = 1

Bring down the 6 and you got 16

2 goes into 16 evenly (8 times)

You got your answer!!!

28!

Answer:

f(x) has a greater slope.

Step-by-step explanation:

The slope of the image line

= difference in y coordinates / difference in x coordinates

= (7-3) / (3-2)

= 4.

The  slope of f(x) = 6x + 1 is  6.

The function f(x) has a greater slope because the slope of the f(x) is 6, and g(x) is 4.

What is mean by straight line?

A straight line is a combination of endless points joined on both sides of the point.

Given that;

The function, f(x) = 6x + 1

And the function g(x) is a linear function which passes through the points (2 , 3) and (3, 7).

Since, The slope 'm' of any straight line is given by:

m = (y₂ - y₁) / (x₂ - x₁)

And, m = d/dx (f(x))

So, The slope of function f (x) will be;

f(x) = 6x + 1

M = d/dx (f(x))

M = d/dx (6x + 1)

M = 6

And, Slope of linear function which passes through the points (2 , 3) and (3, 7) is;

m = (7 - 3) / (3 - 2)

m = 4/1

m = 4

Thus, The function f(x) has a greater slope because the slope of the f(x) is 6, and g(x) is 4.

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The only possible solution is x = 2. Therefore, the three consecutive integers that form the sides of the right triangle are 2, 3, and 4.

Since they are consecutive integers, let's assume that the hypotenuse, which is the longest side of the right triangle, is x+2, as it is three units longer than the shortest side.

In a right triangle, the hypotenuse's square is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem. We can thus write:

\((x+2)^2 = x^2 + (x+1)^2\)

Expanding the squares, we get:

\(x^2 + 4x + 4 = x^2 + x^2 + 2x + 1\)

Simplifying and rearranging terms, we get:

\(2x^2 - 2x - 3 = 0\)

We can solve this quadratic equation by using the quadratic formula:

x = (-b ± \(\sqrt{b^2 - 4ac}\)) / 2a

where a = 2, b = -2, and c = -3.

Plugging in these values, we get:

x = (-(-2) ± \(\sqrt{((-2)^2 - 4(2)(-3)))\) / 2(2)

x = (2 ± \(\sqrt{(4 + 24))\) / 4

x = (2 ± \(\sqrt28}\) / 4

x = (2 ± \(2\sqrt{7}\)) / 4

x = 1/2 ± \(\sqrt{7}\)/2

The only option is x = 2, since x must be an integer. As a result, the numbers 2, 3, and 4 are the three consecutive integers that make up the sides of the right triangle.

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Answer:

corresponding angels

hope it's helps you

After a small search, I've found that we want to find the inverses of both functions. We will find that E(x) does not have an inverse function, and the inverse function of T(x) is h(x) = x/6 - 1/6

Here we have a piecewise function:

T(x) = 6(x-3) + 25  if x > 3

E(x) = 25    if 0 ≤ x ≤ 3

First, remember that two functions f(x) and g(x) are inverses if:

f(g(x)) = x

g(f(x)) = x

From that definition we can see that E(x) does not have an inverse, because for any function g(x), we will have:

E(g(x)) = 25

So E(x) can't meet the condition.

Now let's analyze the function T(x)

T(x) = 6(x-3) + 25  

We can rewrite it as:

T(x) = 6x - 6×3 + 25

T(x) = 6x + 1

Note that T(x) is a linear equation, so the inverse will also be a linear equation. Let's assume that the inverse is h(x) = ax + b

We will have:

T(h(x)) = 6×h(x) + 1 = 6(ax + b) + 1  

Now, if these are inverses, we have:

6(ax + b) + 1 = x

6ax + 6b + 1 = x

Then we must have:

6b + 1 = 0

6ax = x

From the first equation, we can get:

6b + 1 = 0

6b = -1

b = -1/6

From the second equation we have:

6ax = x

6a = 1

a = 1/6

Then:

h(x) = x/6 - 1/6

And this is the inverse function of T(x)

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Answer:

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    63-(9*j)=0

Step by step solution :

STEP

1

:

Pulling out like terms

1.1     Pull out like factors :

  63 - 9j  =   -9 • (j - 7)

Equation at the end of step

1

:

STEP

2

:

Equations which are never true:

2.1      Solve :    -9   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

2.2      Solve  :    j-7 = 0

Add  7  to both sides of the equation :

                     j = 7

solved

j = 7

Answer:

132.2 ft

Step-by-step explanation:

This is a right angle problem where 32 is the angle and 200 feet is the leg unederneath. To solve for the height we use tangent since we have the adjacent side and we are solving for the opposite side.

Steps:

1. tan32 = x/200

2. (tan32)200=x

3. x=132.2 ft

Answer:

13, 9, 0.75, 1/2, -0.75, -5, -7

-7, -5, -0.75, 1/2, 0.75, 9, 13

Step-by-step explanation:

Answer: 13, 9, 1/2, 0.75, -0.75, -5 , -7

the anwer to your question is very ieasy it's b

Answer:

ig

Step-by-step explanation:

The resulting equation after multiplying the first equation by 2 and subtracting the second equation is:

-5y = -375

1. Given equations:

  - x + 3y = 350    (Equation 1)

  - 2x + 4y = 625   (Equation 2)

2. Multiply Equation 1 by 2:

  - 2(x + 3y) = 2(350)

  - 2x + 6y = 700    (Equation 3)

3. Subtract Equation 2 from Equation 3:

  - (2x + 6y) - (2x + 4y) = 700 - 625

  - 2x - 2x + 6y - 4y = 75

  - 2y = 75

4. Simplify Equation 4:

  -2y = 75

5. To isolate the variable y, divide both sides of Equation 5 by -2:

  y = 75 / -2

  y = -37.5

6. Therefore, the resulting equation is:

  -5y = -375

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Answer:

it is 6

Step-by-step explanation:

11-5=6 that's how

Answer:

In step 2, 5-7= -2 instead of +2

Step-by-step explanation:

Answer:

3+5=8

=8-7

8-7=1

=1

Step-by-step explanation:

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Answer:

60%

Step-by-step explanation:

first you make a fraction. 30 ore girls and thats your numerator. the denominator is 50. make it a whole 100 on the denominator. what you do to the bottom fraction you do to the top. we multiple by 2, so 30 is now 60. 60/100. reduce it to its lowest 3/5. divide 3 by 5. its .6. which is 60%

Answer:

60%

Step-by-step explanation:

The probability that less than 75% of the sample students have iPhones is approximately 0.2478.

What is probability?

This is a binomial probability problem, where each student either has an iPhone or does not have an iPhone, and the probability of success (having an iPhone) is 0.789.

Let X be the number of students in the sample who have an iPhone. We want to find P(X < 0.75 * 50) = P(X < 37.5)

Using the binomial probability formula, we have:

P(X < 37.5) = Σ P(X = k), for k = 0, 1, 2, ..., 37

However, this is a tedious calculation. Instead, we can use a normal approximation to the binomial distribution, since n * p = 50 * 0.789 = 39.45 > 10 and n * (1 - p) = 50 * 0.211 = 10.55 > 10.

Using the normal approximation, we can standardize the random variable X:

Z = (X - μ) / σ

where μ = n * p = 39.45 and σ = √(n * p * (1 - p)) = √(50 * 0.789 * 0.211) = 2.88.

Then, we have:

P(X < 37.5) = P(Z < (37.5 - 39.45) / 2.88) = P(Z < -0.68)

Using a standard normal table or calculator, we find that P(Z < -0.68) is approximately 0.2478.

Therefore, the probability that less than 75% of the sample students have iPhones is approximately 0.2478.

Binomial probability is a type of probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure. It assumes that the probability of success in each trial is constant, and the trials are independent of each other. The binomial distribution is characterized by two parameters: the number of trials and the probability of success in each trial.

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