Question 7(Multiple Choice Worth 2 points)
(Pythagorean Theorem LC)
Determine which set of side measurements could be used to form a right triangle.
O5, 12, 13
07, 15, 20
O 5, 8, 14
O 6, 7, 8

Speed

1500 m/sec

Time 20 seconds

Given speed and time, you can calculate distance.

Distance = Time * Speed

Distance = 1500 * 20

Distance = 15000 * 2

Distance travelled by the sonar = 30,000 meters

Since its bouncing off the ocean floor and returning, divide by 2 to find one way distance.

Depth 15,000 meters

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

Answer:

[tex]y+5=-\frac{2}{3}(x-5)[/tex]

Step-by-step explanation:

The slope of the line is [tex]\frac{-1-(-5)}{-1-5}=-\frac{2}{3}[/tex].

Using the point [tex](5,-5)[/tex], the equation is [tex]y+5=-\frac{2}{3}(x-5)[/tex].

Answer:

-11 in top left, 5 in top right, -12 in bottom left, and -2 in bottom right.

Step-by-step explanation:

4C is the matrix C with all its elements multiplied by 4. Same logic applies for 3D. Then subtract each element of 3D from its counterpart of 4C which gives you the final answer. A big shortcut however if you have a TI-84 Plus Graphing Calculator is to use second x^-1 for matrices to edit the matrices and do matrix operations.

Answer:

  7x -(12¾)

Step-by-step explanation:

You want the algebraic expression for "12¾ less than the product of 7 and a number x".

The product of 7 and x is represented as ...

  7x

If you want 12¾ less than that, then you subtract 12¾.

  7x -12¾ . . . . . . . the desired expression

__

Additional comment

A "product" is what we call the result of multiplication. The operation of multiplication can be indicated several ways. If there is no ambiguity, the most common way to show multiplication is to write the values next to each other without any symbol.

  7x . . . . 7 times x

Sometimes, it is helpful to put the values in parentheses:

  (7)(x)

A multiplication symbol can be used, if desired.

  7·x

  (7)×(x)

When showing multiplication using the symbol ×, care must be taken to differentiate it from the symbol x, especially if confusing these symbols will give a different result than desired. (Sometimes, when the symbol × is unavailable, an 'x' is used instead.)

Occasionally, you will see a dot on the baseline used as a multiplication symbol. Likewise, you may see a centered dot intended as a decimal point.

  7.x . . . . . 7 times x

  7·3x . . . . 7 and 3 tenths times x (maybe)

When different numbers are involved, the use of a baseline dot for multiplication, and a centered dot for a decimal point can be confusing.

  7.3.x . . . . could be (7)(3)(x) or (7.3)(x)

  7·3.x . . . . could be (7)(3)(x) or (7.3)(x)

In general, a notation should be chosen so as to reduce any ambiguity to a minimum and communicate in a way that the audience understands.

When a mixed number is involved, as above, it can be useful to enclose it in parentheses, so it is not confused with the product of an integer and a fraction. The font used to express the fraction can be chosen to help reduce the ambiguity.

Answer:12,-8

Step-by-step explanation:

3 to the right 1 down

Answer:

TRUEEEEEEEEEEEEEEEEEE

Step-by-step explanation:

At the district competition for 5th grade jump-roper of the year, the mean number of jumps, rounded to the nearest hundredth is 242.83 and the median number of jumps is 265

The mean can be calculated as follows:

Observations (the number of jumps each student without pausing was counted); There were 24 observations

Mean is calculated by adding all of the observations together.

Mean = (203 + 245 + 237 + 233 + 90 + 100 + 100 + 277 + 265 + 264 + 265 + 285 + 288 + 291 + 291 + 290 + 300 + 224 + 200 + 257 + 290 + 279 + 266 + 288)/24

Mean = 5828/24

Mean = 242.83

to figure out the median;

The observations must first be put into either ascending or descending order.

Ordered in descending order

90, 100, 100, 200, 203, 224, 233, 237, 245, 257, 265, 265, 265, 266, 277, 279, 285, 288, 288, 290, 290, 291, 291, 300

Given that there have been 24 observations (an even number).

The middle number, 265 and 265 at the midway of items 12 and 13, is used to calculate the median.

The average of these figures is then determined.

Median = 1/2 (265 + 265)

Median = 265

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The required length of the ladder using the Pythagorean theorem is (D) 5 ft.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The hypotenuse (third side) of a right-angled triangle, for instance, can be determined using the formula c² = a² + b², where 'c' stands for the hypotenuse and 'a' and 'b' are the two legs.

So, the length of the ladder will be:

Pythagorean theorem: c² = a² + b²

Now, substitute the values and calculate as follows:

c² = a² + b²

c² = 4² + 3²

c² = 16 + 9

c² = 25

c = √25

c = 5ft

Therefore, the required length of the ladder using the Pythagorean theorem is (D) 5 ft.

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The value of the number will be;

⇒ 5/2

A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.

Given that;

The rational number is,

⇒ 2.5

Now,

Since, The rational number is,

⇒ 2.5

Hence, We get;

⇒ 2.5 = 25/10

          = 5/2

Thus, The value of the number = 5/2

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The answer would be (C) 20.

Answer:

The 2nd quartile, also known as the median, is the middle value of a dataset, or the value that separates the lower half of the data from the upper half. In a box-and-whisker plot, the 2nd quartile is represented by the line in the middle of the box.

In the given box-and-whisker plot, the 2nd quartile is 12.5, which is the middle value of the data set. This can be determined by looking at the scale on the x-axis and finding the value that is in the middle of the box.

Option B, 12.5, is the correct answer.

Step-by-step explanation:

The reduced fraction of 0.245 is 49/200.

What is the greatest common factor (GCF)?

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4. Since four is the largest, we refer to the GCF of 12, 20, and 24 as four. Frequently, GCF is used to identify common denominators.

We have,

0.245

Write 0.245 as  

0.245 / 1

Multiply both the numerator and denominator by 10 for each digit after the decimal point.

0.245/1

=   0.245 x 1000 / 1 x 1000

=  245 / 1000

In order to reduce the fraction find the Greatest Common Factor (GCF) for 245 and 1000. Keep in mind a factor is just a number that divides into another number without any remainder.

The factors of 245 are: 1  5  7  35  49  245

The factors of 1000 are: 1  2  4  5  8  10  20  25  40  50  100  125  200  250  500  1000

The Greatest Common Factor (GCF) for both 245 and 1000 is: 5

Now to reduce the fraction we divide both the numerator and denominator by the GCF value.

245/ 1000

= 245 ÷ 5 /1000 ÷ 5

=  49 / 200

The decimal part is: 0.245 = 245/1000

Full simple fraction breakdown: 245/1000

= 49/200

Hence, the reduced fraction of 0.245 is 49/200.

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Answer:

No solution.

Step-by-step explanation:

You would multiply -2 to the 2nd equation and you would get -8x+2y=-2 and you would add that to 8x-2y=2 and when you would add all of them would eliminate or cross each other out, showing no solution.

Answer:

6/49  

Step-by-step explanation:

-2/7  *   -3/7   = (-2 * -3) / (7*7) =  6/49

Answer:

not enough information

Answer:

y= -1/2x+2

Start at -5 then go up 1 then right 3

Step-by-step explanation:

If the tubing size delivers 15 drops per gtt/ml, then the drip rate is 7 gtt/min.

This easy calculation can be used to determine the IV drip rate: Total Volume (mL)/Time (min) x Drop Factor (gtt/mL) equals IV Drip Rate (gtt/min) When given the volume to be injected, the drip rate, and the drop factor, this equation can also be rearranged to determine the amount of time needed for an infusion.

Based on how many drops (gtt) are given to the patient each minute, the rate of an intravenous infusion is described as having an IV drip rate. The amount that needs to be infused in total, the type of tubing used (microdrip vs. macrodrip), and the length of time the infusion is scheduled to run all have an impact on this.

We will use the drip rate formula

Total Volume(mL)/Time (min) x Drop Factor(gtt/mL) = IV Drip Rate (gtt/min)

18 hours = 18 × 60min

              = 1080 mins

IV Drip Rate = 500/1080 × 15

                    = 7 gtt/ min

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All the statements are true.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

Y = mx + b, where m is the slope and b is the y-intercept, is the slope equation utilizing the equation of a line.

A. The triangles drawn between each pair of points are similar.

B. The ratio of y2-y1/x2-x1  will be the same for Tavion and Jess.

C. Both students should find a slope of .

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Answer:

2/-5

Step-by-step explanation:

The measure of all the angles from 1 to 20 is obtained from the concepts related to transversal lines.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

Given, AB || CD and EF || GH.

m∠5 = 63° and m∠8 = 80°.

Now from all the concepts of vertically opposite angles are equal,

pair of alternate angles are equal, the sum of all the sides of interior angles in a triangle is 180°, pair of linear angles is 180°, measure of an exterior angle in a triangle is the sum of two opposite interior angles we obtain that,

m∠1 = 37°, m∠2 = 63°, m∠3 = 80°, m∠4 = 37°, m∠5 = 63°, m∠6 = 80°,

m∠7 = 100°, m∠11, = 63°, m∠12 = 80°, m∠13 = 47°. m∠14 = 63°, m∠15 = 80°,

m∠16 = 47°, m∠17 = 110°, m∠18 = 70°, m∠19 = 110°, m∠20 = 70°.

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s is an eigenvalue of A.

Eigenvalues are a unique collection of scalar values connected to a set of linear equations that are most likely seen in matrix equations. The characteristic roots are another name for the eigenvectors. It is a non-zero vector that, after applying linear transformations, can only be altered by its scalar component.

A =[tex]\left[\begin{array}{ccc}a_{11} &a_{12} &\\a_{21} &a_{22} &\\&\end{array}\right][/tex][tex]\left[\begin{array}{ccc}f1\\f2&\\\end{array}\right][/tex]

[tex]f_{1} = a_{11} + a_{12}[/tex]

[tex]f_{2} = a_{21} + a_{22}[/tex]

We see that if (A - sI) is unique, then s is an eigenvalue of A. ( I is the identity matrix). Keep in mind that if every column in A adds up to s, then the total of the resultant vector is zero when s is subtracted from one item.

We know that the image of a matrix is the span of its column vectors. Since all the column vectors are members of the above-mentioned subspace, the image of the transformation is contained in this subspace. Thus, the rank of our n x n matrix is less than n. Thus, (A - sI) is singular.

Thus, s is an eigenvalue of A.

Transposition preserves eigenvalues (this is actually a profound statement, in a way). If A has columns adding to s, then A^T has rows adding to s. Let v be the column vector of 1's.

A^T * v = s * v.

Thus, s is an eigenvalue of A^T

Thus, s is an eigenvalue of A.

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The measure of three angles of triangle are 45°, 55° and 80°.

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Let the smallest angle of triangle be x.

One angle the triangle measures 10° greater the smallest angle, that is x+10°

The third angle measures 10° less than twice the smallest angle.

The third angle is 2x-10°

Now, x+2x-10°x+10°=180°

⇒ 4x=180°

⇒ x=45°

So, 2x-10°=80° and x+10°=55°

Therefore, the measure of three angles of triangle are 45°, 55° and 80°.

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The total carbon dioxide that the country would emit over the course of the 6 year period is 661,505 kilotons.

The formula that can be used to determine the emission each year is:

Emission in the first year x(1 - rate of decrease)^number of years

Emission in the first year = 120,000

Emission in the second year = 120,000 x (1 - 0.034)^1 = 115,920

Emission in the third year = 120,000 x (1 - 0.034)^2 = 111,978.72

Emission in the fourth year = 120,000 x (1 - 0.034)^3 = 108,171.44

Emission in the fifth year = 120,000 x (1 - 0.034)^4 = 104,493.61

Emission in the sixth year = 120,000 x (1 - 0.034)^5 = 100,940.83

Sum of emissions from the first year to the sixth year = 661,505

This illustrates the concept of exponential decrease.

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From the explanations, we can say that for the research experiment;

A Her results were not typical. She should have called on females fewer than 10 times since most of the data is centered around 10.

Since the teacher is conduction the experiment to see if she  was more likely to call on boys or girls in class, it means that there may have been some bias in the research.

The reason for the purposed bias comes from the  she is also a female. However,  it is not only just about genders only but which student was closer and as such if the teacher is female it’s more likely for a female student to be closer to her eye view whereas the boys may be in the back as usual and so 23 shows a typical expectation.

Now, looking at the options, we can say that the correct one is certainly.

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Answer: 2 / (x + 2)

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The sale price of the shirt can be found by calculating 30% of the original price, which in this case would be $22.40 x 0.30 = $6.72. Thus, the sale price of the shirt would be $22.40 - $6.72 = $15.68.

The counter example for the system of equation is given by x + y = 1 ,

-x - y = 1 has the result 0 = 2 but ( 0, 2 ) is not the solution of the equation. It proves statement is false.

As given in the question,

Form the given system of equations , using elimination method to get the solution of the equation which shows the result 0 = 2 is as follow:

a. x + y = 1

- x - y = -1

0 = 0

Not the required result.

b. x + y = 1

  x - y = 1

 2x = 2

Not a required result.

c. x + y = 1

  - x - y = 1

     0 = 2

Required result.

Analyze : substitute x = 0 and y = 2 in any one equation

0 + 2 = 1

or -0 -2 = 1

Both the equations proves that statement is false.

d. x + y = -1

  -x -y = -1

   0 = -2

Not a required result.

Therefore, the system of equation of option c.  x + y = 1 , -x - y = 1 has the result 0 = 2 and proves it is the false statement.

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Answer:

  35.8

Step-by-step explanation:

It looks like you want the value of ...

  [tex]\dfrac{22}{7.8-\left|-3\dfrac{2}{5}\right|}\times(-3)^2-9\dfrac{1}{5}[/tex]

Simplifying and writing the numbers as decimal values, we have ...

  [tex]\dfrac{22}{7.8 -3.4}\times9-9.2=\dfrac{22}{4.4}\times9-9.2=5\times9-9.2\\\\=45-9.2=\boxed{35.8}[/tex]