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Given:

The vertices of a right triangle are:

[tex](-3,4),(3,4),(3,-4)[/tex]

To find:

The length of the hypotenuse of the given right triangle.

Solution:

Let the vertices of the right triangle are [tex]A(-3,4),B(3,4),C(3,-4)[/tex].

The distance formula is:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using distance formula, we get

[tex]AB=\sqrt{(3-(-3))^2+(4-4)^2}[/tex]

[tex]AB=\sqrt{(3+3)^2+(0)^2}[/tex]

[tex]AB=\sqrt{(6)^2+0}[/tex]

[tex]AB=\sqrt{36}[/tex]

[tex]AB=6[/tex]

Similarly,

[tex]BC=\sqrt{(3-3)^2+(-4-4)^2}[/tex]

[tex]BC=\sqrt{(0)^2+(-8)^2}[/tex]

[tex]BC=\sqrt{64}[/tex]

[tex]BC=8[/tex]

And,

[tex]AC=\sqrt{(3-(-3))^2+(-4-4)^2}[/tex]

[tex]AC=\sqrt{(6)^2+(-8)^2}[/tex]

[tex]AC=\sqrt{36+64}[/tex]

[tex]AC=\sqrt{100}[/tex]

[tex]AC=10[/tex]

Now, taking sum of squares of two smaller sides, we get

[tex]AB^2+BC^2=6^2+8^2[/tex]

[tex]AB^2+BC^2=36+64[/tex]

[tex]AB^2+BC^2=100[/tex]

[tex]AB^2+BC^2=AC^2[/tex]

By the definition of the Pythagoras theorem, AC is the hypotenuse of the given triangle.

Therefore, the length of the hypotenuse is 10 units.

You can download answer here

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Answer:

288mm^2

Step-by-step explanation:

Formula: A=2(wl+hl+hw)

Answer: 2·(14·6+3·6+3·14)

2 • (84 + 3•6 + 3•14)

2 • (84 + 18 + 3•14)

2 • (84 + 18 + 42)

2 • 144 =

288mm^2

Press answer 2 on the question of the image you inserted

Answer:

25/28

Step-by-step explanation:

5/4 x 5/7 = 25/28

Answer:

25/28

Step-by-step explanation:

Answer:

y=-2x +1

Step-by-step explanation:

hope this helps

Answer: x = -4

Step-by-step explanation:

-4 + 4 = 0

if  y = 0 then X will be -4

Answer:

hello

Step-by-step explanation:

answer is x=-4

because if we add

4-4=0

x+4=0

-4+4=0

Answer:

LS is parallel to MN

Step-by-step explanation:

LS and MN are the only lines to have the parallel symbol (the 2 arrows)

Answer:

438.4

Step-by-step explanation:

100% + 37% = 137% = 1.37

320 x 1.37 = 438.4

so the answer that I got is 438.4

I really hope this helps

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

x = 42

Step-by-step explanation:

[tex]\frac{x}{6} = 7[/tex]

Multiply both side of the equation by 6.

[tex]6(\frac{x}{6} ) = 7 * 6[/tex]

∴ x = 42

So, the answer is D.

Hope this helps

Answer:

30 (ft^2/gal)

Step-by-step explanation:

The "unit rate" in this problem is (number of square feet covered) / (1 gallon paint).

Here we have the unit rate

120 ft^2

---------------- = (30 ft^2)/gal or 30 (ft^2/gal)

 4 gallons

150+10=160

160p+200=1200

-200 -200

160p= 1000

1000/160= 6.25

Answer:

whats (2x)x(76) x is 50 btw im new

Step-by-step explanation:

Answer:

5m+6

Step-by-step explanation:

Hello There!

We can simplify the given expression using distributive property

We can distribute the 2 to the m and - 3

2 * m = 2m

2 * -3 = -6

Now lets distribute the 3 to the m and the 4

3 * m = 3m

3 * 4 = 12

we´re left with

2m - 6 + 3m +12

our final step would be to combine like terms

2m + 3m = 5m

-6 + 12 = 6

so the simplified version would be

5m+6

Answer:

324

Step-by-step explanation:

divide 752 by 2 to get 376

then subtract 52 from 376 to get 324

Answer:

∠B = 78°

Step-by-step explanation:

∠C = 1/2 arc AB = 1/2(120°) = 60°   because it is an inscribed angle

∠B = 180° - 42° - 60° = 78°

The measure of  ∠ B is  78°.

An inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle.

The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

According to the question

m ∠ A= 42º.

mAB = 120°

By  inscribed angle theorem :

mAB = 2 m∠C

120° = 2 m∠C

m∠C = 60°

now,

according to the sum of angle of triangle

m ∠ B + m∠C + m ∠ A = 180°    

m ∠ B +60° + 42º= 180°  

m ∠ B = 78°

Hence, the measure of  ∠ B is  78°.

To know more about inscribed angle theorem here:

https://brainly.com/question/5436956

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Answer:

9

Step-by-step explanation:

l l means absolute value

the absolute value of any negative number is the same number but positive

so the absolute value of -9 is positive 9

Answer:

9

Step-by-step explanation:

Absolute value (or the lines) makes everything inside of it positive, so |-9| = 9

Answer:

simplified its 5:4 for juniors to freshmen's

Step-by-step explanation:

Answer:

5 : 4

Step-by-step explanation:

Ratio of juniors to freshmen = 15 : 12

15 = 3 * 5

12 = 3 * 4

GCF = 3

15 : 12 = 15÷3 : 12÷ 3

         = 5 : 4

Answer:

The population would be 1 million in 2024.

Step-by-step explanation:

In order to find the answer you can use the population growth formula:

A= P*e^rt

A=Population after time=1,000,000

P= Starting population=705,000

e= Euler number that is equal to 2.718

r= rate of growth=0.0151

t= time

Now, you can replace the values on the formula and solve for t:

1,000,000 = 705,000*e^0.0151t

1,000,000/705,000 = e^0.0151t

ln(1,000/705) = ln(e^0.0151t)

ln(1000/705) = 0.0151t

t = [ln(1000/705)]/0.0151

t = 23.14 years

According to this, the answer is that the population would be 1 million in 2024.

Answer:

2.5

Step-by-step explanation:

graham crackers  each student receive = total number of crackers / total number of students

20 / 8 = 2.5

Answer:

p ≥ 5

4s + 10p ≤ 100

Step-by-step explanation:

Here, we want to write a system of inequalities

Let the number of bags of soil be s and the number of plants be p

She wants to buy at least 5 plants

mathematically, when something is at least 5, it means greater than or equal to 5

In inequality, we have this as;

p ≥ 5

Secondly, she wants to spend not more than $100; she can spend less but cannot spend more

We have this as;

The number of bags she can buy at $4 per bag is 4 * s = 4s

the number of plants at $10 per one will be;

10 * p = 10p

Adding both should give a cost less than or equal to 100

We have this as;

4s + 10p ≤ 100

So, we have the system of inequalities as;

p ≥ 5

4s + 10p ≤ 100

Answer:

3.5/1.5 or 14/6

Step-by-step explanation:

equivalent

Answer: = 5 (a-5b)(a+b)

Step-by-step explanation:

= 5a² - 25b²​

= 5 (a²-5b²)

= 5 (a-5b)(a+b)

Answer:

volume = wide x length x deep

            = 3{1/3} ft x 2{1/2} ft x 3{3/4}ft

             = 10/3ft  x 5/2ft    x 15/4ft

             = (10 x 5 x 15)/(3 x 2 x 4) ft^3

              = 125/4 ft^3

               = 31{1/4} ft^3

Step-by-step explanation:

Answer:

We can assume that the number of 3-pointers he made in his last game was 10 3-pointers

Step-by-step explanation:

In the question, we have;

The 3-point percentage rate for Stephen Curry = 43.5 successful made out of 100 attempts

The 3-point percentage rate for LeBron James = 34.5 successful made out of 100 attempts

The 3-point percentage rate for James Harden = 36.4 successful made out of 100 attempts

Whereby Steph Curry attempted 25 3-pointers in the last game he played and where 'x' represents the number of 3-pointers we can assume he made, we have;

x = 43.5% of 25

[tex]\therefore x = \dfrac{43.5}{100} \times 25 = 10.875[/tex]

Given that 'x' can only have whole number values, and the 3-point percentage is calculated using a larger number of attempts than 25, we can assume he made 10 3-pointers in his last game

The 3-pointers the Stephen Curry made in last game is 10, if he attempted 25 3-pointers.

It is given that the four players from the NBA and their career 3-point percentages are listed below in the table

It is required to find the number of 3 pointers he made if Steph Curry attempted 25 3-pointers in his last game.

It is defined as the ratio or number presented as fraction of 100, the symbol of percentage is %.

We have in the question that:

The 3-point percentage rate for Stephen Curry is 43.5% out of 100 attempts.

We know that,

[tex]\rm 3-point \ percentage = \frac{Number \ of \ 3-pointers}{Number \ of \ 3-pointers \ attempts} \\[/tex]

3 - point percentage for Stephen Curry = 43.5%

Number of 3-pointers he attempts = 25

Putting these values in the above formula, we get:

[tex]\rm 43.5 \%=\frac{Number \ of \ 3-pointers}{25} \\\\\rm \frac{43.5}{100} \times25 = Number \ of \ 3-pointers\\\\\rm Or \ number \ of \ 3-pointers = 10.875[/tex]

But the number of 3-pointers can be a whole number, so we can assume that the 3-pointers is 10.

Thus, the 3-pointers the Stephen Curry made in last game is 10, if he attempted 25 3-pointers.

Learn more about three pointer here:

https://brainly.com/question/519034

Answer:

4,128 books

Step-by-step explanation:

Let

x = number of books

Fixed cost = $44,376

Variable cost = $8.25 per book

Total cost = fixed cost + variable cost

Total cost = 44,376 + 8.25x

Selling price of book = $19 per book

Total revenue = 19x

How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Total cost = Total revenue

44,376 + 8.25x = 19x

44,376 = 19x - 8.25x

44,376 = 10.75x

x =44,376/10.75

x = 4,128 books

The publisher must produce and sell 4,128 books so that the production costs will equal the money from sales

Answer:

RO = 39.5

Step-by-step explanation:

RO/9 = 57/13

13RO = 513

RO = 513/13

RO = 39.46

Answer:

39.5

Step-by-step explanation:

[tex]\frac{KN}{NM} =\frac{RO}{RQ} \\\\\frac{9}{13} =\frac{x}{57} \\\\13x=513\\x=39.5[/tex]