On the grid below draw a right triangle
with vertices at P(2, 4), Q(7, 9), and
R(10,6). what is the lengths of the three sides to the nearest tenth.

Answer:

range 18

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

1. The range of a data set is the difference between the largest and smallest number. In this case, the largest number is 28, and the smallest number is 10.

Therefore, the range is 18.

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[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]

[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]

[tex] \tt \:\int \: \frac{ x + 2 }{( {x}^{2} + 3x + 3) \sqrt{x + 1}} \: dx \\ [/tex]

First, let's take I as ⇨ [tex]\tt \:\int \: \frac{ x + 2 }{( {x}^{2} + 3x + 3) \sqrt{x + 1}} \: dx \\ [/tex].

[tex]\tt \:I = \int \: \frac{ x + 2 }{( {x}^{2} + 3x + 3) \sqrt{x +1}} \: dx \\\tt \: I =\int \: \frac{ x + 2 }{( {x}^{2} + 2x + 1 + x + 2) \sqrt{x + 1}} \: dx \\ \tt \:I =\int \: \frac{ x + 2 }{( ({x + 1}^{2}) + x + 2) \sqrt{x + 1}}[/tex]

Let, x + 1 = m² => dx = 2mdm.

[tex]\tt \:I =\int \: \frac{ {m}^{2} + 1}{ {m}^{4} + {m}^{2} + 1 \cdot \: m} 2mdm \\ \tt \:I =\int \: \frac{ {m}^{2} + 1}{ {m}^{4} + {m}^{2} + 1 \cdot \: \bcancel{ m}} 2 \bcancel{m}dm \\ \tt \: I = \: \int \: \frac{ {m}^{2} + 1}{ {m}^{4} + {m}^{2} + 1 } 2dm[/tex]

Now, divide the numerator & denominator by m²....we'll get it as...

[tex]\tt \:I =2\int \: \frac{ 1 + \frac{1}{ {m}^{2} } }{ {m}^{2} + 1 + \frac{1}{ {m}^{2} } } \: dm \\\tt \: I =2\int \: \frac{ 1 + \frac{1}{ {m}^{2} } }{( {m}^{2} + \frac{1}{ {m}^{2} } - 2) + 3} \: dm \\\tt \: I =2\int \: \frac{ (1 + \frac{1}{ {m}^{2} }) \: dm }{ ({m} - \frac{1}{ m } ) ^{2} + 3} [/tex]

Now, let m - 1/m be t => (1 + 1/m²) dm = dt

[tex]\tt \:I =2\int \: \frac{ dt}{ {t}^{2} + 3 } \\ \tt \:I = 2\int \: \frac{ dt}{ {t}^{2} + ( \sqrt{3}) ^{2} }[/tex]

We know, [tex]\tt \:\int \: \frac{dx}{ {x}^{2} + a ^{2} } = \frac{1}{a} tan ^{ - 1} (\frac{x}{a} ) + c[/tex]...therefore...

[tex]\tt \:I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{t}{ \sqrt{3} } ) + c \: \rightarrow \boxed{ \tt \: eq. \: 1}[/tex]

Now, substitute the value of 't' in eq. 1..we'll get..

[tex]\tt \:I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{m - \frac{1}{m} }{ \sqrt{3} } ) + c \: \rightarrow \boxed{ \tt \: eq. \: 2}[/tex]

Now, substitute the value of 'm' in eq. 2...we'll get...

[tex] \tt \: I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{ \sqrt{x + 1} - \frac{1}{ \sqrt{x - 1} } }{ \sqrt{3} } ) + c \\ \tt \:I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{x + 1 - 1}{ \sqrt{3} \sqrt{x - 1} } ) + c \\ \boxed{\boxed{ \bf \: I = \frac{2}{ \sqrt{3} } {tan}^{ - 1} ( \frac{x }{ \sqrt{3 (x - 1} )} ) + c }}[/tex]

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ℓu¢αzz ッ

Answer:

greatest velocity 6

Step-by-step explanation:

v=12t-6t2

dv/dt=0

12-12t=0

t=1

v at t=1=12-6=6

Answer:

Step-by-step explanation:

Kites have one pair of congruent angles.

In this case it is B and D:

Find the measure of B and D:

Find the measure of angle C:

The smallest angle is C

Answer:

0.25 hours, or 15 minutes

Step-by-step explanation:

Ok, so the rate is 32 miles per hour, so it would take about 1/4 of a hour to go 8 miles (8/32= 0.25)

Answer:

64 miles per hour

Step-by-step explanation:

512 divided by 8 equals 64

Answer:

jkb jhb n

Step-by-step explanation:

Answer:

Step-by-step explanation:

first put 6:4

6 is 3 by 2

4 is 2 by 2

the 2 in 4 and 6 is gone

so we will have in the 6 3 left and in the 4 2 left

so what is 3 by 2

→ You will pay $ 89.7.

The tip value is based on the bill value. Hence, to find the total payment you have to multiply 78 by 1.15 (this includes the tip, 1.15).

[tex]\Large \text {$Total = 78 \times 1.15 = 89.7 $}[/tex]

Or you can first find how many 15% is from $78:

[tex]\Large \text {$0.15 \times 78 = 11.7$}[/tex]

And then add this to $78:

[tex]\Large \text {$78 +11.7 = 89.7$}[/tex]

→ See more on:

https://brainly.com/question/12901165

Answer:

$89.70

Step-by-step explanation:

15/100=0.15

78 * 0.15 =89.70

Answer:

Step-by-step explanation:

[tex](\dfrac{1}{2}a-\dfrac{2}{3}b)(\dfrac{3}{5}a+\dfrac{2}{3}b)=\dfrac{1}{2}a*(\dfrac{3}{5}a+\dfrac{2}{3}b) - \dfrac{2}{3}b*(\dfrac{3}{5}a+\dfrac{2}{3}b) \\\\\\= \dfrac{1}{2}a*\dfrac{3}{5}a + (\dfrac{1}{2}a*\dfrac{2}{3}b) - \dfrac{2}{3}b*\dfrac{3}{5}a- \dfrac{2}{3}b*\dfrac{2}{3}b\\\\\\=\dfrac{3}{10}a^{2} + \dfrac{1}{3}ab - \dfrac{2}{5}ab -\dfrac{4}{9}b^{2}\\\\=\dfrac{3}{10}a^{2} +\dfrac{1*5}{3*5}ab-\dfrac{2*3}{5*3}-\dfrac{4}{9}b^{2}\\\\\\[/tex]

[tex]=\dfrac{3}{10}a^{2}+\dfrac{5}{15}ab-\dfrac{6}{15}ab -\dfrac{4}{9}b^{2}\\\\=\dfrac{3}{10}a^{2}-\dfrac{1}{15}-\dfrac{4}{9}b^{2}[/tex]

Answer:

carltzy Poland in ngayon

y=-2x(squared)+3x-7

the 2x is squared

hope that helped

sorry po di ko ma intindihan

Step-by-step explanation:

sorry po

Answer:

4 groups of 3

Step-by-step explanation:

Answer:

-6 is the same as Subtracting 6, C.

Hope this helps!

Step-by-step explanation:

For example,

5 - 6

5 is positive, +5

and 6 is negative, -6

Answer:

easy subtracting 6 :))

Step-by-step explanation:

can i get brainliest uwu^_^

Answer:

a)-30

b)-60

c)98

d)-54

Step-by-step explanation:

320/-4

-180/3

-14X-7

6X-9

Answer:

It is 16over 3or 5.333333333333

Step-by-step explanation:

1/3*16=16/3

16/3=5.33333333333333

none of these i guess

Answer:

the answer is the third one 3

Answer:

x equals 375

Step-by-step explanation:

75+0.70x=0.90x

Answer: y = .15x + 1250

y = weekly salary

x = sales

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

m(x) = 4x+15; m(x) = 7

7= 4x+15

7-4x=15

-4x=15-7

-4x=8 / :(-4)

x= -2

Answer:

(3,-1)

Step-by-step explanation:

Answer:

if x is the number

4/9x - 7=5

4/9x= 7+5

4/9x= 12

x= 12×9/4

x= 108/4

x=27

Answer:

1. 4.5

2. The scale factor is 3/4

Step-by-step explanation:

Answer: B

Step-by-step explanation: