solve the inequality

Answer:

The triangles are congruent

Step-by-step explanation:

Given

[tex]P(5,-4), Q(-3, 7), R(0, 2), X(-2,-1), Y(9, 7), Z(3, 2)[/tex]

Required

Determine if PQR = XYZ

To do this, we make use of distance formula.

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

For PQ:

[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (-3,7)[/tex]

So:

[tex]PQ = \sqrt{(-3-5)^2+(7-(-4))^2}[/tex]

[tex]PQ = \sqrt{(-8)^2+(7+4)^2}[/tex]

[tex]PQ = \sqrt{(-8)^2+(11)^2}[/tex]

[tex]PQ = \sqrt{64+121}[/tex]

[tex]PQ = \sqrt{185}[/tex]

For XY:

[tex](x_1,y_1) = (-2,-1)[/tex]

[tex](x_2,y_2) = (9,7)[/tex]

So:

[tex]XY = \sqrt{(9-(-2))^2+(7-(-1))^2}[/tex]

[tex]XY = \sqrt{(9+2)^2+(7+1)^2}[/tex]

[tex]XY = \sqrt{(11)^2+(8)^2}[/tex]

[tex]XY = \sqrt{121+64}[/tex]

[tex]XY = \sqrt{185}[/tex]

For QR:

[tex](x_1,y_1) = (-3,7)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]

So:

[tex]QR = \sqrt{(0-(-3))^2 + (2-7)^2}[/tex]

[tex]QR = \sqrt{(0+3)^2 + (-5)^2}[/tex]

[tex]QR = \sqrt{(3)^2 + 25}[/tex]

[tex]QR = \sqrt{9 + 25}[/tex]

[tex]QR = \sqrt{34}[/tex]

For YZ:

[tex](x_1,y_1) = (9,7)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]

So:

[tex]YZ = \sqrt{(3-9)^2+(2-7)^2}[/tex]

[tex]YZ = \sqrt{(-6)^2+(-5)^2}[/tex]

[tex]YZ = \sqrt{36+25}[/tex]

[tex]YZ = \sqrt{61}[/tex]

For PR:

[tex](x_1,y_1) = (5,-4)[/tex] and [tex](x_2,y_2) = (0,2)[/tex]

So:

[tex]PR = \sqrt{(0-5)^2+(2-(-4))^2}[/tex]

[tex]PR = \sqrt{(-5)^2+(2+4)^2}[/tex]

[tex]PR = \sqrt{(-5)^2+(6)^2}[/tex]

[tex]PR = \sqrt{25+36}[/tex]

[tex]PR = \sqrt{61}[/tex]

For XZ:

[tex](x_1,y_1) = (-2,-1)[/tex] and [tex](x_2,y_2) = (3,2)[/tex]

So:

[tex]XZ = \sqrt{(3-(-2))^2+(2-(-1))^2}[/tex]

[tex]XZ = \sqrt{(3+2)^2+(2+1)^2}[/tex]

[tex]XZ = \sqrt{5^2+3^2}[/tex]

[tex]XZ = \sqrt{34}[/tex]

From the calculations above:

[tex]PQ = XY = \sqrt{185[/tex]

[tex]QR = XZ = \sqrt{34[/tex]

[tex]PR = YZ = \sqrt{61[/tex]

Hence, the triangles are congruent base on SSS (Sides- Sides-Sides)

Answer:

you're scale is 1.6666667

Step-by-step explanation:

because if you do 30 decided by 18 it gives u 1.6666667

Answer:

The slope of this equation is 11/2. The point is (1/2, 0)

Step-by-step explanation:

I hope this is the right answer, good luck!

We are given:                                                                                                        

Density of glass in g/cm³ = 2.5

Finding the density in kg/m³:                                                                              

In converting 2.5 g/cm³ to kg/m³, we will first convert the g to kg

Converting the g to kg:

2.5 g/cm³ * 1

Since 1kg = 1000g, 1kg/1000g = 1

2.5 g/cm³ * 1kg / 1000g

the g in the numerator and the denominator will cancel out and we will get:

2.5 kg / 1000 cm³

Converting the cm³ to m³:

We know that 1 m³ = 10⁶ cm³

So, 10⁶ cm³ / 1 m³ = 1

Multiplying the density by 1

2.5 kg / 10³ cm³   *   1

2.5 kg / 10³ cm³   *   10⁶ cm³ / 1 m³

the cm³ in the numerator and the denominator will cancel out

2.5 * 10⁶ kg / 10³ m³

2.5 * 10³ * 10³ kg / 10³ m³

2.5 * 10³ kg / m³

2500 kg/m³

Answer:

11/4

29/6

32/5

Step-by-step explanation:

Answer: 11/4, 29/6, 32/5

Step-by-step explanation:

This is going to help trust me

X=22

14 plus 8 gives you x

[tex]\frac{x}{20} =\frac{14}{8} \\x=\frac{14}{8} \times 20=35[/tex]Answer:

35

Step-by-step explanation:

Answer:

-19.9y-5.3

Step-by-step explanation:

Answer:

6. 225 feet in 3 minutes = 75 feet in 1 minute (slower)

   360 feet in 5 minutes = 72 feet in 1 minute

7. $4 for 5 ounces = $0.80 for 1 ounce (most expensive)

   $14 for 20 ounces = $0.70 for 1 ounce

8. 72 people in 6 hours = 12 people in 1 hour

    117 people in 9 hours = 13 people in 1 hour (greater rate per hour)

Answer:

A = 369 feet in 5 minutes B = $4 for 5 ounces C = 117 people in 9 hours

9x9x9x9divide by 4x4x4

Answer:

4⁹ / 4³ = 4⁶ = 4096

Step-by-step explanation:

You can solve this by realising that exponents (the 9 and the 3 in this case), simply tell you how many times to multiply the numbers together.

What you're see there then can also be expressed as:

[tex]\frac{4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4}{4 \times 4 \times 4}[/tex]

Because the numerator and denominator are all multiples of the same number repeatedly, you can simply eliminate the bottom three fours from the top and bottom, giving you:

[tex]\frac{4 \times 4 \times 4 \times 4 \times 4 \times 4 \times (4 \times 4 \times 4)}{(4 \times 4 \times 4)}\\\\= 4 \times 4 \times 4 \times 4 \times 4 \times 4[/tex]

[tex]4 \times 4 \times 4 \times 4 \times 4 \times 4[/tex]

A simpler way to look at it is to understand that when the same number is being raised to different bases, and then multiplied or divided, you can simply add or subtract the exponents.  For example, speaking very generically:

[tex]x^a \times x^b = x^{a + b}[/tex]

and

[tex]x^a \div x^b = x^{a - b}[/tex]

In this case then, we can simply say:

[tex]\frac{4^9}{4^3} = 4^{9 - 3} = 4^6[/tex]

So when simplified, the expression is equal to 4⁶, or 4096.

Answer:

88%

Step-by-step explanation:

25*4=100. this means we have to multiply 22*4, which gets us 88%

Answer:

0.88%

Step-by-step explanation:

25 divided by 22

Answer:

First, we can write a fraction as a/b

Where a is the numerator, and b is the denominator.

A proper fraction is a fraction where the numerator is smaller than the denominator.

Using only the given numbers (only once per fraction), some examples of proper fractions are:

3/5

3/8

5/8

3/85

3/58

5/83

5/38

8/35

8/53

You can see that in all of them the denominator is larger than the numerator.

The improper fractions are those where the numerator is equal or larger than the denominator.

The 9 examples using the given numbers are:

5/3

8/5

8/3

35/8

38/5

53/8

58/3

83/5

85/3

Answer:

y= -3/2

Step-by-step explanation:

Answer:

174

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

yes what that guy said is right

Answer:

SOOOOOO

Step-by-step explanation:

YOU MAKE  IT 1/5 + -2/3

INTOOO

3/15+-10/15

THENNNN

YOU ADD THEMMM

AND UU GETTTT

-7/15

SOOO THAT UR ANSWER ITSS A THE FIRST ONE

-7/15

Answer: B.12 years

Step-by-step explanation:

Answer:

1.48 miles

Step-by-step explanation:

If the trail is 14.8 miles and Rita has hiked 1/10 of it. Then just multiply 14.8 by 1/10.

14.8 * 1/10 = 1.48 miles.

Answer:

1.48

Step-by-step explanation:

I know the answer is correct

Answer:

llll, Vl, Vll

Step-by-step explanation:

Answer: 36÷4=9

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The relation given as represented by the table of values is definitely not a function. This is because, 1 domain value (x-value), is having two range values (y-values), 2 and 5, that are assigned to it.

A function cannot have two y-values assigned to one x-values.

Answer:

3 plus 3

Step-by-step explanation: its in the parenthesis

Answer:

You have to add 3 and 3 first. That has to be done first.

Answer:

( x^2 - 6 )^2

Step-by-step explanation:

*solution* ( x^2 - 6 )^2

Answer:

???

Step-by-step explanation:

wheres y

Answer:

the equation to find slope is (y2-y1)/(x2-x1)

A: (-4,1) (0,3) (for all of these except for the last one, i included the y-intercept as one of the points)

3-1/0-(-4)

2/4

m=1/2

y= 1/2x +3

B: (0,-1) (3,1)

3-0/1-(-1)

m=3/2

y=  3/2x -1

C: (0,-3) ( 6,-1)

-1 -(-3) / 6-0

2/6

m= 1/3

y = 1/3x -3

D: (3,-3) (6,0)

0 -(-3) / 6-3

3/3

1

m= 1

y -y1 = m (x - x1)  (this is point-slope form, plugging in the slope and a point on the line, and then solving it will give you slope-intercept form)

y - 0 = 1(x -6)

y = 1x -6

Step-by-step explanation:

I hope this helped :)

Answer:

13 away

i used my fingers

Answer:

12

Step-by-step explanation:

-8_-7_-6_-5_-4_-3_-2_-1_0_1_2_3_4

Just count he bottom lines

Answer:

njnjfsdnjfe

Step-by-step explanation:

Answer:

we cant see

Step-by-step explanation:

Answer:

 [tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]

Step-by-step explanation:

Explanation

Given function f(r) = r² log r  ....(i)

Apply derivatives formula

              [tex]\frac{d}{dx} UV = U^{l} V + V^{l} U[/tex]

             [tex]\frac{d}{dx}x^{n} = nx^{n-1}[/tex]

            [tex]\frac{d}{dx}log x = \frac{1}{x}[/tex]

Differentiating equation (i) with respective to 'r' , we get

                [tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )\frac{d}{dr} (\frac{1}{r } )+ log(\frac{1}{r} ) 2 r[/tex]

                [tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )(\frac{-1}{r^{2} } )+ log(\frac{1}{r} ) 2 r[/tex]

Final answer:-                

               [tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]