MATHEMATICS HIGH SCHOOL

Systems of Equations:a boat traveled 210 miles downstream and back. the trip downstream took 10 hours. the trip back took 70 hours. what is the speed of the boat in still water? what is the speed of the current?


Need to show step by step. Thanks in advance.

Answers

Answer 1
Answer: v_b-the\ speed\ of\ the\ boat\nv_c-the\ speed\ of\ the\ current\n\nv_b+v_c=(210)/(10)=21\ (mph)\n\nv_b-v_c=(210)/(70)=3\ (mph)\n\n +\left\{\begin{array}{ccc}v_b+v_c=21\nv_b-v_c=3\end{array}\right\n-----------\n.\ \ \ \ \ \ 2v_b=24\ \ \ \ /:2\n.\ \ \ \ \ \ \ \ \ v_b=12\ (mph)\n\n12+v_c=21\nv_c=21-12\nv_c=9\ (mph)

Answer:\nthe\ speed\ of\ the\ both\ is\ 12mph\nthe\ speed\ of\ the\ current\ is\ 9mph

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A boater travels 532 miles. Assuming the boat averages 6.3 miles per gallon, how many gallons of gasoline(to the nearest then of gallon) were used? plz show work

Could someone help me do this :D

Answers

y = side

Perimeter = 8y

The diagram shows three squares that are joined at vertices to form a right triangle. Which statement is true? A. The sum of the areas of Square N and Square L is equal to the area of Square K.
B. The sum of the areas of Square N and Square L is greater than the area of Square K.
C. The sum of the areas of Square N and Square K is equal to the area of Square L.
D. The sum of the areas of Square N and Square K is less than the area of Square L.

Answers

The sum of the areas of Square N and Square L is equal to the area of Square K and this can be determined by using the Pythagorean theorem.

Given :

The diagram shows three squares that are joined at vertices to form a right triangle.

The following steps can be used in order to determine which statement is true:

Step 1 - The Pythagorean theorem can be used in order to determine which statement is true.

Step 2 - According to the Pythagorean theorem, the sum of the square of the shorter sides is equal to the square of the longer side.

Step 3 - So, from the above steps, it can be concluded that the sum of the areas of Square N and Square L is equal to the area of Square K.

Therefore, the correct statement is given by option A).

For more information, refer to the link given below:

brainly.com/question/25277954

answer:

a) the sum of the areas of square n and square l is equal to the area of square k.

step-by-step explanation:

https://quiz izz.com/admin/quiz/5ecffa4789713d001cea9223/2019-8th-grade-staar

good luck :)

i hope this helps

have a nice day!

Can someone help me it’s geometry :(

Answers

Answer:

Step-by-step explanation:

3) ∠JKN =∠ MKL Vertical angles theorem  - Vertically opposite angles are equal

4) ΔJKN ≅ΔMKL     AAS congruency

5) ∠J ≅ ∠ M    CPCTC

Answer:

The vertical angles theorem

Step-by-step explanation:

The correct answer is the vertical angles theorem, which states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent

2+3i divided by 3-3i ( a+bi form)

Answers

(2+3i):(3-3i)=(2+3i)/(3-3i)\cdot(3+3i)/(3+3i)=((2+3i)(3+3i))/((3-3i)(3+3i))=(6+6i+9i-9)/(3^2-(3i)^2)=(-3+15i)/(9+9)\n\n=(-3+15i)/(18)=-(3)/(18)+(15i)/(18)=-(1)/(6)+(5)/(6)i

How to i find the missing 2 angles

Answers

Answer:

therefore, x is 71 degrees

Step-by-step explanation:

we know that the exterior angle is 142 degrees.

we also know that we have to find x, which is labeled two times as an interior triangle (in the same triangle), so they must be the same degree.

there are different ways to solve this but the easiest way is this:

exterior angle = opposite interior angle 1 + opposite interior angle 2

142 degrees = x + x

142 degrees = 2x

142/2 = x

x = 71

therefore, x is 71 degrees

Solve equation 2x^{2}−5x−7 = 0 by using the quadratic formula. Then write 2x^{2}−5x−7 in form of a(x−r_{1})(x−r_{2}).

Answers

2x^2+2x-7x-7=2x(x+1)-7(x+1)=(2x-7)(x+1)=\n \n=2(x-3.5)(x+1)\n \n2x^2-5x-7=0\ \ \ \Leftrightarrow\ \ \ 2(x-3.5)(x+1)=0\n \nx-3.5=0\ \ \vee\ \ \ x+1=0\n \n.\ \ \ \ \ \ \ x=3.5\ \ \ \ \ \ \ \ \ \ \ x=-1
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