Q 9-1 Pythagorean Theorem and Trig

A girl is 20 ft. east of her school and her bike is 21 ft. south of the school. How far is she from her bike? Round to the nearest hundredth.

Answer: The first three odd prime numbers are 3, 5, and 7. A number is a multiple of two but not three of these prime numbers if it is divisible by two of them, but not the third.

To find the number of numbers between 1000 and 2000 that are multiples of two but not three of the first three odd prime numbers, we can count the number of multiples of each pair of prime numbers and subtract the number of multiples of all three prime numbers.

There are 200 multiples of 3 and 5 between 1000 and 2000 (200 numbers for each, for a total of 200 * 2 = 400). There are 133 multiples of 3 and 7 between 1000 and 2000 (133 numbers for each, for a total of 133 * 2 = 266). There are 80 multiples of 5 and 7 between 1000 and 2000 (80 numbers for each, for a total of 80 * 2 = 160). There are no multiples of all three prime numbers between 1000 and 2000.

Thus, the total number of numbers between 1000 and 2000 that are multiples of two but not three of the first three odd prime numbers is 400 + 266 + 160 = 826.

Step-by-step explanation:

In either the Hay Bale Toss or Pie Eating Contest, the graph's range of 0-19 will be extended by 20.

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices.

In either the Hay Bale Toss or Pie Eating Contest, the graph's range of 0-19 will be extended by 20. 20 students attended the fair, total. Group age = 0 to 16

This age range is located in the histogram's first interval, which is 0–19. The graph for the pie eating competition would remain the same if all 20 pupils had participated in the hay bale toss, with the bar representing 0–19 rising from 40 to 60.

The graph of the Hay Bale Toss would remain same if all 20 pupils had participated in the Pie Eating Contest, increasing the bar of 0-19 from 20 to 40.

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Answer:

u can use formula whole root ,( x2-x1)²+(y2-y1)²

hope it helps...

Answer:

7.8 (1.d.p) or √61

Step-by-step explanation:

To solve this question we must use Pythagoras (a²+b²=c²)

Imagine that the line given is the hypotenuse (the longest side of a right-angled triangle) of a right-angled triangle and the other sides as a line from B going to the right, and a line from A going downwards (making the final vertexes for the triangle at coordinates: (3,2), which is B,  (9,7), which is A, (9,2), which is the vertex the 2 imaginary lines we added, created) So now we use Pythagoras to find the length of the hypotenuse:

9-3=6 (subtracting the xs of vertexes A and B to find the length of the imaginary line we extended from B) and

7-2=5 (subtracting the ys of vertexes A and B to find the length of the imaginary line we extended from A)

Now to put them into Pythagoras's formula:

6²+5²=c² ⇒ 36+25=c² ⇒ √36+25=c ⇒ √61 = c ⇒ c = 7.8102....

Which can be rounded to 7.8 (as the third digit, the 1, rounds down.

Answer:

1. D (x-5)^2-(y-2/2)^2=1

2. A

3. C No. The car travels counterclockwise in a circle at the origin with radius 2.

Step-by-step explanation:

Answer:

0.00525

Step-by-step explanation:

The value that would be put for rate (r) is, 0.069

Simple interest is often a predetermined percentage of the principal amount borrowed or lent paid or received over a specific time period.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

The present value monthly payment formula is as follows,

M = (Pr(1 + r)ⁿ)/(1 - r) - 1

Where,

P is the Present Value.

r is the interest rate.

n is the number of times compounded.

Now that we know the interest rate is 6.9%, we can put that in our text., r = 6.9/100 = 0.069

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Answer:

4

Step-by-step explanation:

The amplitude of the sin graph is 4. Sin graphs are written as [tex]y=A sin(B(x-D))+C[/tex] where A is the amplitude. In the equation above 4 is multiplied in front of sin, which shows it is the amplitude. Since 4 is the amplitude the graph will have a range of [-4,4].

Answer:

10 units ^2

Step-by-step explanation:

Area 1:

A = lw

   = 2 * 5 = 10

Answer

x=a 1/2+i / a 1/2

Step-by-step explanation:

Answer:

x ≈ 47.0°

Step-by-step explanation:

using the cosine ratio in the right triangle.

cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{15}{22}[/tex] , then

x = [tex]cos^{-1}[/tex] ( [tex]\frac{15}{22}[/tex] ) ≈ 47.0° ( to the nearest tenth )

Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.

While the denominator of a percentage is always 100, a proportion is the relationship or equivalence between two ratios or fractions. Both proportion and percentage can be expressed as fractions.

A percentage is an equation in which two ratios are made equal to one another.

Out of a possible 100, the percentage is given.

Because 32 ounces is the difference between 128 and 96, making it 1/3 of 96, we can divide $4.80 by 3 to get $1.60, then add $1.60 to $4.80 to get $6.40.

Response is $6.40, a proportion is the relationship or equivalence between two ratios or fractions.

The complete question is,

It cost $4.80 for a 96-ounce bottle of orange juice. How much should be charged for a 128-ounce container in order to equalize the unit rates of the two sizes? Describe your thought process.

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The system of equations is inconsistent for any value of k.

If we subtract the first equation from the second one, we get 0 = 12x, which is inconsistent no matter what value k is. This means that the system of equations has no solution and is therefore inconsistent.

The system of equations KX + 3y = K + 2 and 12x + Ky = K is inconsistent for any value of k. This is because when we subtract the first equation from the second one, we get 0 = 12x, which is an inconsistent equation no matter what value k is. This means that the system of equations has no solution and is therefore inconsistent. No matter what value we assign to k, the equations cannot be solved simultaneously and so the system of equations is inconsistent.

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Answer:

Step-by-step explanation:

5. The problem gives us that the dollar value of the quarters we have is v, and the number of quarters we have is n. So basically, for example, if n was 8 then v would be 2 because there are 4 quarters in every dollar, so 8 quarters would be 2 dollars. Thus, to find how many dollars in the amount of quarters you have, you must divide by 4. Therefore, the equation would be v = 1/4n.

6. To be honest, I don't know what number 6 is asking. It's asking for Output $, but to find the output, you must have an input, but the problem doesn't give you one. It might be cropped out so, if the problem gives you an input (in this case, n quarters), you divide it by 4 and that will be your answer to 6. (ie. the problem gives you 12 as the input. Answer would be 3 because 12 quarters = 3 dollars).

If it doesn't give you the input, then I believe it would be 0.25 because each quarter is 0.25 of a dollar. I believe it should have an input number though, because it doesn't make any sense to me.

7. The independent variable is the thing you are changing, or the input. Since the number of the quarters is the input and not the VALUE of the quarters, it is false.

Answer:

Length of AC = 4.5

Length of DB = 4.5

Slope of AC = [tex]-\frac{1}{2}[/tex]

Slope of DB = 2

Classification: Square

Hope this helps!

Answer:

Hey there! So the square root of 38 can be simplified by breaking it down into simpler parts. We can use a technique called prime factorization. We need to find the largest perfect square that is a factor of 38 and extract it from the square root. So, we can express 38 as 219 and that means we have 2^2=4 as the largest perfect square. Therefore, we can simplify the square root of 38 as 2sqrt(19).

It can't be simplified anymore, but it gives us a more manageable form. Let me know if you have any more questions, I'm happy to help!

________________________________________________________

A perfect square is a number that can be written in the form of n^2 (n raised to the power of 2) for some whole number n. For example 4, 9, 16, 25 and 36 are perfect squares. A way to determine if a number is a perfect square is by taking the square root of that number, if the result is a whole number it's a perfect square. Also, you can check it by finding the prime factorization of the number, if each of the prime factors appears in even power, it's a perfect square.

There are a few techniques that can make simplifying square roots quicker and easier:

Recognizing perfect squares (as described above) and extracting them from the square root

Using prime factorization to simplify the square root

Recognizing when the square root can be written as a rational number (a fraction of two integers)

Another way to approach is to factorise the radicand and combine any pairs of identical factors out from the square root.

Please let me know if you have any other questions on this topic or any other topic I could help with.

√38 is the simplest representation of the square root of 38.

The square root of a number is a value that, when multiplied by itself, gives the original number.

In the case of √38, we are looking for a number that, when multiplied by itself, equals 38.

Since 6 multiplied by itself is 36 and 7 multiplied by itself is 49, we can conclude that the square root of 38 lies between 6 and 7.

We cannot find a whole number that satisfies the equation √38 = x, where x is an integer.

Therefore, we express the square root of 38 as an irrational number, meaning it cannot be expressed as a simple fraction or a terminating or repeating decimal.

Hence, √38 is the simplest representation of the square root of 38.

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Answer:

C. Total Points = 10 • Months + 100

Answer:

0.2 out of 1

Step-by-step explanation:

Lets say you have $100

20% of that is 20

10% of that is 10

Answer:

I think its 5?

Step-by-step explanation:

Im not rlly 100% sure but i think all u have to do is just divide 100 by 20

The easiest way to find this is to use the library's catalog. Depending on the integrated library system (or ILS) the library subscribes to, the process might be slightly different. Generally, you can use a catalog system on a computer to search by title, author, subject, and more.

Answer:

A

Step-by-step explanation:

The two equations represents two lines that have the same slope, and so they are parallel.

this means that the two lines have no points in common

Answer:

A

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

No

The given problem has been proved below using the rules of Congruence.

The given problem can be solved easily if we apply the basic rules of Congruence on the question properly as they are required. Congruence is when two given figures have the same shape and size.

Given that,

3AB=7AD

3AC=7AE

So, by re-arranging them we get the same ratio that is,

AB/AD=7/3

AC/AE=7/3

Hence, we can conclude that,

AB/AD=AC/AE

Also, we can show that ∠BAC and ∠DAE by the property of vertical angles.

But ∠BAC ≌ ∠DAE is also true by the vertical angle theorem in this diagram.

So, SAS property ∆ABC~∆ADE is proved in the end.

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Answer:

You have to draw a graph.

Step-by-step explanation:

Multiply all of your sides together to figure out the area then plot the points.

The answer of this problem is -0.6. I'm also gonna leave the solution to show you that it's correct.

Answer:

Step-by-step explanation:

f(x)= 12x2+5 should be written as  f(x) = 12x^2 + 5; the " ^ " symbol signifies exponentiation and is mandatory.

Here's how we find the inverse function.

1.  Apply the horizontal line test.  if a horizontal line intersects the graph in more than one place, the function is not one-to-one and does not have an inverse for all x.  However, if we focus on only [0, infinity), this part of the graph does have an inverse, which we can find as follows:

2.  Replace 'f(x)' with 'y:  y = 12x^2 + 5

3.  Interchange x and y:  x = 12y^2 + 5

                                                              x - 5

4.  Solve for y:  12y^2 = x - 5;   y^2 = ------------

                                                                12

                          x - 5

               y = √(----------)

                             12

Answer:

11.5

Step-by-step explanation:

Answer:(-2,-2)

Step-by-step explanation:

The radical has a value of 0 when x = -2. At that point, the function value is ...

 f(-2) = √(-(-2)-2) -2 = √(0) -2

 f(-2) = -2

The term given to us is 4 , this is a constant number therefore this cannot be regarded as a polynomial.

An expression is said to be a polynomial if it also contains a variable along with constants which are joined with each other through various mathematical operations. These expressions usually have more than one terms.

A polynomial can be of various degrees such as one degree , two degree based upon that they are known as linear , quadratic , cubic polynomial etc. Unlike terms are polynomial terms in which the variables are different and also the same variables with different powers. Contrary terms are two or more terms that are not synonymous.

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Answer:

About 20%

Step-by-step explanation:

The probability of a point on the un-shaded region will be given by;

Area of the shaded region/total area  

Considering that the circles are of the same size, then the length of the square is 2d

Area of the square = 4d²

Area of the shaded = (4d² -4π(d/2)²

= 4d² -πd², but π = 22/7

= 6/7d²

Probability = (6/7d² ÷ 4d²) × 100%

= (6/28 d²) × 100%

= 21.42 %

So your answer is B. 20%

Don't thank me this was easy.