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The measure of z in its simplest form is 3√11

We solve the triangle using pythagoras' theorem.

Pythagoras' theorem states that in any right angled triangle with sides a, b and hypotenuse side, c which is the longest side, the square of the hypotenuse side equal the sum of the squares of the other two sides.

So, according to Pythagoras' theorem,

c² = a² + b²

Since we have three right angled triangles, in the smallest right angled triangle, we have

z² = y² + 3²  (1)

In the next larger right angled triangle, we have

x² = y² + 27² (2)

In the largest right angled triangle, we have

(3 + 27)² = z² + x²

30² = z² + x² (3)

Substituting (2) into (3), we have

30² = z² + x²

30² = z² + y² + 27²

30² - 27² = z² + y²

900 - 729 = z² + y²

171 = z² + y²

z² = 171 - y² (4)

Equating (1) and (4), we have

y² + 3² = 171 - y²

y² + 9 = 171 - y²

y² + y² = 171 + 9

2y² = 180

y² = 180/2

y² = 90

Substituting y² into (1), we have

z² = y² + 3²

z² = 90 + 9

z² = 99

z = √99

z = 3√11

So, the measure of z is 3√11

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Answer: first answer 3, 2nd answer 10.

Step-by-step explanation:

I just did the question on acellus

Answer:

Step-by-step explanation:

apply the indices law

Answer:

y + 3 = 10/11(x + 3)

Step-by-step explanation:

Given the points (-3, -3) and (8, 7), we can use these coordinates to solve for the slope of the line using the formula:

[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

Let (x1, y1) = (-3, -3)

(x2, y2) = (8, 7)

Substitute these values into the slope formula:

[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{7 - (-3)}{8 - (-3)} = \frac{10}{11}[/tex]

Thus, slope (m) = 10/11.

Next, using the slope (m) = 10/11, and one of the given points (-3, -3), we'll substitute these values into the point-slope form:

y - y1 = m(x - x1)

Let (x1, y1) = (-3, -3)

m = 10/11

y - y1 = m(x - x1)

y - (-3) = 10/11[x - (-3)]

Simplify:

y + 3 = 10/11(x + 3) this is the point-slope form.

Answer:

(A) 5cm and 8cm

Step-by-step explanation:

Look to find out the triangle side you here to add and find outnth sum.

Answer:

okay 1. nice name what your middle?

2. why would someone with a name like that have a hamster

3. a pencil is nothing compared to a vehicle like a tesla

4. AK 47 Mac 11 Glocks N 9’s

it will take exactly 217.2529865 pencils to replace the alternator on a Tesla

Answer:

x = 12

Step-by-step explanation:

Answer:

284 scratched cups

Step-by-step explanation:

it's in the picture

9514 1404 393

Answer:

   B.  3x+y=4

Step-by-step explanation:

The constant on the right is positive, so the signs of the coefficients match the signs of the respective intercepts. The graph shows both x- and y-intercepts are positive, so the equation will have positive coefficients everywhere. The appropriate choice is ...

  3x +y = 4

Answer:

yes because....

Step-by-step explanation:

6 + 11 > 13

Answer:

22.5

Step-by-step explanation:

8hrs=220

1hr=220÷8

1hr=22.5

According to the question,

The worker makes,

then,

Per hour, worker will make,

→ [tex]1 \ hour = \frac{220}{8}[/tex]

By applying division, we get

→ [tex]1 \ hour = 22.5[/tex]  

Thus the solution above is appropriate.

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Answer

-10

Step-by-step explanation:

-8w-7=9

add 7 to both sides

-8w=16

divide by negative 8 on both sides

w=-2

w-8=-10

On simplifying,

-8w - 7 = 9

-8w = 16

w = -2

then,

= w - 8

= -2 - 8

= -10.

Answer:

$38 for 2 sweaters

Step-by-step explanation:

$38 for 2 sweaters  ---> $38/2 = $19

$72 for 3 sweaters

$96 for 4 sweaters

$120 for 5 sweaters

Answer:

[tex]2x + 7 = 3x - 7 \\ 3x - 2x = 7 + 7 = 14 \\ x = 14 \\ 2x + 7 + 12y + 1 = 180 \\ 12y + 36 = 180 \\ 12y = 180 - 36 = 144 \\ y = 144 \div 12 = 12[/tex]

Answer:

x = 4.4

Step-by-step explanation:

The ratios of corresponding sides are in proportion , that is

[tex]\frac{x}{11}[/tex] = [tex]\frac{4}{10}[/tex] ( cross- multiply )

10x = 44 ( divide both sides by 10 )

x = 4.4

Answer:

no

0-9 is nine

coz zero have no value to subtaract 9 from zero

Answer:

16

Step-by-step explanation:

i use tally marks

Answer:

16 girls.

Step-by-step explanation:

There are two ways,

The Relationship between each ratio is multiplying by 4.

Or cross multiply;

12×4=48

48÷3=16

Hope you're having a splendiferous day or evening.

3.5 to 2.167

2.80

Step-by-step explanation:

[tex]\\ \sf\longmapsto \dfrac{x}{3}+9>14[/tex]

[tex]\\ \sf\longmapsto \dfrac{x}{3}>5[/tex]

[tex]\\ \sf\longmapsto x>3(5)[/tex]

[tex]\\ \sf\longmapsto x>15[/tex]

Answer:

the answer is x>15

Step-by-step explanation:

Answer:

C = 25.13cm

C = π d = π · 8 ≈ 25.13274cm

Answer:

the answer is 4cm circumference

Answer is 68.9 m/min.

Let's convert the units. To do this, we need to cancel the original units to get the units we want. We achieve this the following way :-

[tex]2.57 \frac{mi}{hr} \times \frac{1069.34 \: m}{1 \: mi} \times \frac{1 \: hr}{60 \: min} [/tex]

[tex] =>68.9 \: \frac{m}{min} [/tex]

Therefore, 2.57 mi/hr is the same as 68.9 m/min .

✍️ By Benjemin ☺️

Answer:

(− ∞ , 1 /3 )  ∪  ( 5 , ∞ )

Step-by-step explanation:

Answer:

[tex] - 3 < z < 6[/tex]

Step-by-step explanation:

[tex]z + 6 > 3 \\ 2z < 12[/tex]

1.

[tex]z + 6 > 3 \\ z + 6 - 6 > 3 - 6 \\ z > - 3[/tex]

2.

[tex]2z < 12 \\ \frac{2z}{2} < \frac{12}{2} \\ z < 6[/tex]

answer

[tex] - 3 < z < 6[/tex]

Answer:

Radius = 6

Step-by-step explanation:

The volume of a cone is V= pi*r^2*h/3

In this case, h=18 in.

Volume= 216pi in^3

So all you need to do is plug in and solve.

216pi = pi*r^2 *6

36=r^2

r=6

Radius of cone is 6 in.

A cone is a shape created by connecting all the points of a circular base (which does not contain the apex) to a common point known as the apex or vertex using a series of line segments or lines.

Given that;

Volume of cone =  216π in³

Height = 18 in

Since we know that,

The volume of a cone is V= πr²h/3

Therefore plug the values,

⇒216π = πr²(18)/3

⇒    36 = r²

⇒       r = 6 in

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Answer: 0.8333

Step-by-step explanation: