consider this right triangle with given measures what is the unknown length

3x - 2 ≤ -20

Add 2 to both sides:

3x ≤ -18

Divide both sides by 3:

x ≤ -6

Answer:

1. [tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 1}}}}}[/tex]

2. [tex] \boxed{ \bold{ \huge{ \boxed{ \sf{n = - 5}}}}}[/tex]

Step-by-step explanation:

1. [tex] \sf{ \frac{6}{x + 1} = \frac{3}{x} }[/tex]

Do cross multiplication

[tex] \dashrightarrow{ \sf{6x = 3(x + 1)}}[/tex]

Distribute 3 through the parentheses

[tex] \dashrightarrow{ \sf{6x = 3x + 3}}[/tex]

Move 3x to left hand side and change it's sign

[tex] \dashrightarrow{ \sf{6x - 3x = 3}}[/tex]

Collect like terms

[tex] \dashrightarrow{ \sf{3x = 3}}[/tex]

Divide both sides by 3

[tex] \dashrightarrow{ \sf{ \frac{3x}{3} = \frac{3}{3} }}[/tex]

Calculate

[tex] \dashrightarrow{ \sf{x = 1}}[/tex]

The value of x is 1

---------------------------------------------------------------------

2. [tex] \sf{ \frac{2}{6} = \frac{2n + 8}{n - 1}} [/tex]

Do cross multiplication

[tex] \dashrightarrow{ \sf{2(n - 1) = 6(2n + 8)}}[/tex]

Distribute 2 through the parentheses

Similarly, distribute 6 through the parentheses

[tex] \dashrightarrow{ \sf{2n - 2 = 12n + 48}}[/tex]

Move 12n to left hand side and change it's sign

Similarly, move 48 to right hand side and change it's sign

[tex] \dashrightarrow{ \sf{2n - 12n = 48 + 2}}[/tex]

Collect like terms

[tex] \dashrightarrow{ \sf{ - 10n = 48 + 2}}[/tex]

Add the numbers : 48 and 2

[tex] \dashrightarrow{ \sf{ - 10n = 50}}[/tex]

Divide both sides by -10

[tex] \dashrightarrow{ \sf{ \frac{ - 10n}{ - 10} = \frac{50}{ - 10} }}[/tex]

Calculate

[tex] \dashrightarrow{ \sf{n = - 5}}[/tex]

The value of n is -5 .

Hope I helped!

Best regards! :D

Answer:

Quadrant 3 and Quadrant 4

Step-by-step explanation:

If the point is negative, then it will definetely be on the left side of the graph. The two quadrants on the left side are 3 and 4. Hope this helps!

Answer:

10

Step-by-step explanation:

Begin with x3 + y3 = 4 . Differentiate both sides of the equation, getting

D ( x3 + y3 ) = D ( 4 ) ,

D ( x3 ) + D ( y3 ) = D ( 4 ) ,

(Remember to use the chain rule on D ( y3 ) .)

3x2 + 3y2 y' = 0 ,

so that (Now solve for y' .)

3y2 y' = - 3x2 ,

.

Answer:

Rocket can hold maximum 4.5 gallons of water.

Step-by-step explanation:

Volume of the rocket = Volume of the cone on the top + Volume of the cylinder at the bottom

Volume of the cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]

Here r = radius of the circular base

h = height of the cone

Volume = [tex]\frac{1}{3}\pi (4)^{2}(14)[/tex]

             = [tex]\frac{224\pi }{3}[/tex] cubic inch

Volume of the cylinder = [tex]\pi r^{2}h[/tex]

Here r = radius of the base

h = height of the cylinder

Volume = [tex]\pi (4)^{2}(16)[/tex]

             = 256π cubic inches

Volume of the rocket = [tex]\frac{224\pi }{3}+256\pi[/tex]

                                   = [tex]\frac{992\pi }{3}[/tex]

                                   = 1038.82 cubic inches

Since 231 cubic inches volume of a rocket can hold water = 1 gallon

Therefore, 1038.82 cubic inches space can hold water

= [tex]\frac{1038.82}{231}[/tex]

= 4.497

≈ 4.5 gallons

Rocket can hold 4.5 gallons of water.

Answer:

7, 14, 8, 16, 10, 20, 14, 28, 22...

7 times 2 is 14, 8 times 2 is 16, 10 times 2 is 20, and so on.

hope this helps

Answer: x=2

hope this helps!

Answer:

Midpoint of a Line Segment

Step-by-step explanation:

Add both "x" coordinates, divide by 2.

Add both "y" coordinates, divide by 2.

Answer:

$61.434

Step-by-step explanation:

Teniendo en cuenta que el enunciado señala que la pantalla de tv cuesta el doble de la bicicleta, debes multiplicar el valor de la bicicleta por 2 para encontrar su precio:

Precio pantalla de tv=$8.562*2=$17.124

Además, el enunciado señala que el refrigerador cuesta $1.500 más que el doble de la tv, por lo cual para encontrar su precio debes multiplicar el valor de la tv por 2 y sumarle $1500:

Precio del refrigerador=($17.124*2)+$1.500

Precio del refrigerador=$34.248+$1.500

Precio del refrigerador=$35.748

Finalmente, el gasto total es igual a la suma de los precios de la bicicleta, la tv y el refrigerador:

$8.562+$17.124+$35.748=$61.434

De acuerdo a esto, la respuesta es que Sebastian gastó $61.434.

Answer:

just multiply the absolute values and make them positive or negative

Step-by-step explanation:

for example:

2×2=4

-2×2=-4

Answer:

just multiply the absolute values and make them positive or negative

Step-by-step explanation:

for example:

2×2=4

-2×2=-4

Answer:The quotient of -100 and -5  is the same as the quotient of 100/5 because if you divide a negative number by a negative number, you will get a positive number and the same way if you divide a positive number by a positive number you will get a positive number.

Step-by-step explanation:

-100/-5 = 20

100/5 = 20

Answer:

Rotation of 90° (x, y) → ( ‐ y,  x )

Rotation of 180° (x, y) → ( ‐ x,  ‐ y )

Rotation of 270° (x, y) → ( y,  ‐ x )

idk 360...

Answer:

y=(7/5)x + 34/5

Step-by-step explanation:

All straight lines generally follow the equation format of: y=mx+c

Where m is the slope/gradient of the line, and c is a constant, the y-intercept, the y value when x=0.

To start, we need to find the slope, which we do by dividing the rise of the line by the run, that is the difference between the y value of two points divided by the different between the x value of two points.

We can use the two given points on the graph: (-7,-3) and (-2,4).

The rise is 7 because 4-(-3)=7, and the run is 5 because -2-(-7)=5.

Therefore the slope is 7/5.

so our equation so far is:

y=(7/5)x + c, (It is positive because the line is 'going upwards'.)

Now to find the c, we can just substitute in a pair of coordinates, we can use (-2,4):

4= (7/5)(-2) + c

4 = -14/5 + c

4 + 14/5 = c

c= 34/5

Therefore our full equation is:

y=(7/5)x + 34/5

Hope this helped!

Answer:

1- r=.5

2- x=.5

Step-by-step explanation:

sorry my handwriting is bad

Answer:

the shaded area= s²-2πr²

Step-by-step explanation:

you have 2 circles

Area of circle=πr²

2 circles=πr²+πr²=2πr²

the area of square=s*s=s²

the shaded area= s²-2πr²

Answer:5

Step-by-step explanation:

w(n)=4-1

=5

Answer:

he last ratio is written incorrectly.

Mandy reversed the input and output in the numerator and denominator.

The correct ratio is 50/10.

The relationship is proportional.

Answer:

67,900

Step-by-step explanation:

Move the decimal place 4 spaces to the right.

Answer:

it is for sure 67,900 :)

Step-by-step explanation:

Answer:

house 3 floors

Step-by-step explanation:

i'm totally guessing i'm most likely wrong

Answer:

98.8 km/h

Step-by-step explanation:

Given that:

Distance traveled towards east, [tex]D_1[/tex] = 567.6 km

Time taken towards east, [tex]t_1[/tex] = 2.3 hours

After turning back:

Distance traveled towards west, [tex]D_2[/tex] = 221.8 km

Time taken towards west, [tex]t_2[/tex] = 1.2 hours

To find:

Average Velocity during the trip in km/h = ?

Solution:

First of all, let us consider the image attached in the answer area:

Let the black panther runs to point I from G and the turns back to point H.

GI = 567.6 km

IH = 221.8 km

Formula for Average Velocity is given as:[tex]\text{Average Velocity= }\dfrac{\text{Displacement}}{\text{Total Time Taken}}[/tex]

Here, Displacement will be GI - IH = [tex]D_1-D_2[/tex] =567.6 - 221.8 = 345.8 km

Total time taken = t_1+t_2 = 2.3 + 1.2 = 3.5 hours

[tex]\text{Average Velocity= }\dfrac{345.8}{3.5} = \bold{98.8\ km/h }[/tex]

The answer is:

Average Velocity = 98.8 km/h

Answer:

Below.

Step-by-step explanation:

If the angle is x degrees then its complement is 90-x degrees.

So 90-x = 4x - 10

90 + 10 = 4x + x

5x = 100

x = 20.

and the complement is 90-20 = 70.

Answer:

y=-7

Step-by-step explanation:

when you multiply a negative by a negative, it turns into a positive. -4 x -7 will equal 28, so y=-7, hope this helps

Answer:

7/25

Step-by-step explanation:

0.56 move two times to get rid of the point that will give you 56/100 divide by an digit that can go equally in both of them to the lowest form start from 2

Answer:

40. neither

41. Perpendicular

42. Parallel

43.  y= -4x+1

44. 2x-y=5

45. y=-3/2x-2

46.  -1/4x+y=5

Step-by-step explanation:

Answer: 30

Step-by-step explanation:

*Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ..., 30

* Multiples of 6: 6, 12, 18, 24, 30

* Multiples of 15: 15, 30