The diagram shows a triangle ABC in which AB= 6 cm, BC=8 cm and ABC = 90°.
Calculate the length of AC.

The answer should be 12. please help with explanation and calculation!!!

Answer:

3

Step-by-step explanation:

Express the numbers as a product of their primes.

42 = 2 × 3 + 7

30 = 2 × 3 × 5

45 = 3 × 3 × 5

Identify the prime factors common to all 3 numbers.

common prime factor = 3 , thus

GCF = 3

Answer: 3

Step-by-step explanation: The factors of 30 are 1. 2. 3. 5. 6. 10, 15, 30

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The factors of 45 are 1, 3, 5, 9, 15, 45

As you can see they all share the factors of 1 and 3. Since 3 is the greatest number of the factors all of them share it is the greatest common factor.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{4\times \dfrac{2}{3}}[/tex]

[tex]\huge\textbf{Simplifying it:}[/tex]

[tex]\mathbf{4\times \dfrac{2}{3}}[/tex]

[tex]\mathbf{= \dfrac{4}{1}\times\dfrac{2}{3}}[/tex]

[tex]\mathbf{= \dfrac{8}{3}}[/tex]

[tex]\rightarrow\large\text{Finding out what is equal to: }\rm{\dfrac{8}{3}}\leftarrow[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]\huge\text{Option A.}[/tex]

[tex]\mathbf{6\times \dfrac{2}{3}}[/tex]

[tex]\mathbf{= \dfrac{6}{1}\times\dfrac{1}{3}}[/tex]

[tex]\mathbf{= \dfrac{6\times1}{1\times3}}[/tex]

[tex]\mathbf{= \dfrac{6}{3}}[/tex]

[tex]\mathbf{= 2}[/tex]

~~~~~

[tex]\rm{\bf 2 \neq \dfrac{8}{3}}[/tex]

~~~~~~

[tex]\huge\text{Option B.}[/tex]

[tex]\mathbf{10\times \dfrac{1}{3}}[/tex]

[tex]\mathbf{= \dfrac{10}{1}\times\dfrac{1}{3}}[/tex]

[tex]\mathbf{= \dfrac{10\times1}{1\times 3}}[/tex]

[tex]\mathbf{= \dfrac{10}{3}}[/tex]

~~~~~~

[tex]\rm{\bf \dfrac{10}{3} \neq \dfrac{8}{3}}[/tex]

~~~~~~

[tex]\huge\text{Option C.}[/tex]

[tex]\mathbf{2\times\dfrac{1}{3}}[/tex]

[tex]\mathbf{= \dfrac{2}{1}\times\dfrac{1}{3}}[/tex]

[tex]\mathbf{= \dfrac{2\times1}{1\times3}}[/tex]

[tex]\mathbf{= \dfrac{2}{3}}[/tex]

~~~~~

[tex]\rm{\bf \dfrac{2}{3} \neq \dfrac{8}{3}}[/tex]

~~~~~

[tex]\huge\text{Option D.}[/tex]

[tex]\mathbf{8\times\dfrac{1}{3}}[/tex]

[tex]\mathbf{= \dfrac{8}{1}\times\dfrac{1}{3}}[/tex]

[tex]\mathbf{= \dfrac{8\times1}{1\times3}}[/tex]

[tex]\mathbf{= \dfrac{8}{3}}[/tex]

~~~~~

[tex]\rm{\dfrac{8}{3} = \dfrac{8}{3}}\large\checkmark[/tex]

~~~~~

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{Option\ D. 8\times \dfrac{1}{3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

11.25cm^2

Step-by-step explanation:

given the area of the rectangle as 40cm^2, we can get the width of the rectangle.

Area =Length x width

40cm^2 = 8cm x width

we can divide both sides 8 to be left with the width

40/8 = 5cm

so the width is 5cm which is equal to the height of the triangle.

Area of BDC = 1/2 x base x height

BDC = 1/2 x 4.5 x 5

=11.25cm^2

Answer:

Step-by-step explanation:

radius of circle is 12

also there is 2 right angles in the triangle if you wanted to solve this problem yourself

but here's the answer:

arc angle of the triangle inside the sircle is double the angle closest to x.

(the pointy area of the triangle is half the angle length of the arc)

i can add more though:

Answer:

The answer is 37

Step-by-step explanatio

Answer:

96

Step-by-step explanation:

80*120=9600 divided by 100

Answer:

[tex]x = \frac{ 5 \ + \ \sqrt{31}}{2} \ , \ x = \frac{ 5 \ - \ \sqrt{31}}{2}[/tex]

Step-by-step explanation:

[tex]2x^2 - 10x - 3 = 0 \\\\a = 2 \ , b = - 10 \ , \ c = - 3 \\\\x = \frac{-b^2\ \pm \ \sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{10 \ \pm \sqrt{(-10)^2 - ( 4 \times 2 \times -3)} }{2 \times 2}\\\\x = \frac{10 \ \pm \sqrt{(100 - ( -24 )} }{4}\\\\x = \frac{10 \ \pm \sqrt{(100 + 24 } }{4}\\\\x = \frac{ 10 \ \pm \sqrt{124}}{4}\\\\x = \frac{ 10 \ \pm \sqrt{4 \times 31}}{4}\\\\x = \frac{ 10 \ \pm \sqrt{2^2 \times 31}}{4}\\\\x = \frac{ 10 \ \pm2 \sqrt{31}}{4}\\\\x = \frac{ 5 \ \pm\sqrt{31}}{2}\\\\[/tex]

[tex]x = \frac{ 5 \ + \ \sqrt{31}}{2} \ , \ x = \frac{ 5 \ - \ \sqrt{31}}{2}[/tex]

Answer:

12) A

the values are each devided by three then multiplied by 4

13) C

values are 4 times as big as in the right figure

14) and 15) two thirds of the value in the left figure. the rotation is just to disorient you a lil :D just keep the 90° angle as a reference point

x is option A

and y is option C

Answer:

x = - 10

Step-by-step explanation:

Expand the equation first then simplify it

Answer:

5a) -8 .     Plan : addition/negative?

5b) -30 .   Plan: subtraction/negative?

Step-by-step explanation:

Im not so sure about what "Plan" means, hopefully you know..

5a)

-15 + 7 = 7 - 15 = -8

5b) -10 +(-20) = -10 - 20 = -30

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Below

Step-by-step explanation:

So lets start with the first one:

-15+7

We are going to add these together, and will get -8.

Next we have:

-10+(-20)

When there is both a subtraction or negative sign, and a plus sign, the plus sign is removed.

So we can think of this as:

-10-20

And since the -10 is negative, and we are subtracting it, it is going to get more engative:

-10-20=-30

This is the solution answer.

I do not know what the answer to the plan is, i dont understand what plan means.

Answer:

It will take the train 1.2375 minutes to pass the tunnel

Step-by-step explanation:

Mathematically, we know that ;

time = distance/ speed

The distance here is the length of the train which is 132 m ; we can convert this to km by dividing by 1000

We have this as 132/1000 = 0.132 km

So, we have the time as;

0.132 km/6.4 km/hr = 0.020625 hr

Mathematically, we know that 60 minutes make an hour;

so we have

0.020625 * 60 = 1.2375 minutes

Answer:

c

Step-by-step explanation:

Answer:

x is greater than or equal to 3

So it is the first answer.

Answer:

x = 30

Step-by-step explanation:

If two triangle are similar then the measure of their corresponding sides are

proportional.

   [tex]\frac{JL}{PQ} = \frac{JK}{PR}\\\\\frac{20}{x} = \frac{24}{36}\\\\x \times 24 = 20 \times 36[/tex]                              [tex][ \ cross \ multiply \ ][/tex]

   [tex]x = \frac{20 \times 36}{24}\\\\x = 5 \times 6 = 30[/tex]

Answer:

-23

Step-by-step explanation:

Answer:

-23

Step-by-step explanation:

When you do positive-negative you subtract the 2 numbers then take the sign of the number that had the highest absolute value.

25-2=23

The absolute value of -25 is 25

(|-25| = 25)

And the absolute value of 2 is 2

(|2| = 2)

25 > 2

So it would be -23

Answer:

( x − 3 ) ( x + 5 )

Step-by-step explanation:

HAVE A NICE DAY

Answer:

B

Step-by-step explanation:

; factor the left side of the equation

; (x−3) (x+5) = 0

set factors equal to 0

x − 3 = 0

or

x + 5 = 0

; so, x = 3  or  x = −5

Answer:

397

Step-by-step explanation:

Sea 'p (x)' el número que no es divisible por 4, 6, 9, 11 y 12 de manera que cuando se divide por estos números da un resto igual, tenemos;

Por teorema del resto, tenemos;

p (x) = (x - a) · Q (x) + R

Dónde;

p (x) = El número, que se divide

Q (x) = El cociente

(x - a) = El divisor

R = El resto

Dado que el número más pequeño es 4, el resto, 0 <R <4

Para el número entero más pequeño arriba (x - a) · Q (x), tenemos;

R = 1

Observamos que el mínimo común múltiplo de 4, 6, 9, 11 y 12 = 396, por lo tanto, podemos tener;

(x - a) · Q (x) = 396

R = 1, dar;

p (x) = 396 + 1 = 397

Por lo tanto;

El número que no es divisible por 4, 6, 9, 11 y 12, de manera que cuando se divide por estos números da residuos iguales, p (x) = 397

Answer:

subtract 8 from both sides

Step-by-step explanation:

Answer:

Step-by-step explanation:

Straight line equation is in the form of:

Lets verify the options:

Step-by-step explanation:

x2+1/x2=27

x2+1=27x2

1=26x2

x2 = 1/26

x = √(1/26)

x3+1/x3 = (√(1/26))^3 + 1 / (√(1/26))^3

x3+1/x3 = 134

Please find attached photograph for your answer

Answer:

101°

Step-by-step explanation:

In the rightmost triangle the missing angle is:

180° - 51° - 90° = 39° .     90° comes from the other angle in the straight horizontal line, because there is a 90° on the other side

In the leftmost triangle, the missing angle is:

180° - 90° - 50° = 40° .         50° comes from 180° - 130°

In the straight line

ABC = 180° - 40° - 39° = 101°

Answer = 101°

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer: 3 7/12

Step-by-step explanation:

1. Solving the whole number

4-1=3

2. Solving the fraction parts

3/4 - 1/6=

Find the LCM. The LCM is 12 so we rewrite the factions like this:

9/12-2/12=7/12

3. Add.

3+ 7/12= 3 7/12

Hey there!

4 3/4 - 1 1/6

= 19/4 - 7/6

= (19 × 6) - (7 × 4) / 4 × 6

19 × 6 = 114

7 × 4 = 28

= 114 - 28 / 4 × 6

4 × 6 = 24

114 - 28 / 24

114 - 28 = 86

= 86/24

= 3 7/12

Answer: 86/24 OR 3 7/12

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

On a number line, -2 appears to the right of -5, and therefore -2 is warmer than -5.  (Answer A)

The difference between -2 and -5 is -2 - (-5) = 5 - 2 = 3 degrees C  (Answer B)

In other words, -2 is 3 degrees C warmer than -5 degrees C.

Answer:

Step-by-step explanation:

Hope this helps u!!

Answer:

C =(x-3)(x-2)/x

or

x²-5x+6/x

Step-by-step explanation:

2x^2 - 4x - 6/x + 2 * x^2 - 4/2x^2 + 2x

Factorizing the given factors

1) 2x^2 - 4x - 6

= 2x^2 - 6x+2x - 6

= 2x(x-3) +2(x-3)

= (x-3)(2x+2)

2) x^2 - 4

= (x+2) (x-2)

3) 2x^2 + 2x

= 2x( x+1)

Putting the factors

(x-3)(2x+2)/x + 2   *  (x+2) (x-2)/2x( x+1)

= (x-3)(2x+2) (x-2)/2x( x+1)

= 2(x-3)(x+1) (x-2)/2x( x+1)

=(x-3)(x-2)/x

Now multiply

(x-3)(x-2) =x²-5x+6

Then the answer becomes  x²-5x+6/x

Answer:

A

Step-by-step explanation:

the middle angle has to be equal to make the entire angle equal

Answer:

63 is the range of the following test scores.

Step-by-step explanation:

1. The largest number is 95.

2. The smallest number is 32.

3. The range is the difference between the largest and the smallest number.

4. Subtract 95 - 32 which equals 63.

5. 63 is the range of the following test scores.

Well there are no choices listed so it's going to be hard to say which; we'll write an expression for all of them and then give a few instances.

A parabola with a minimum forms a CUP, concave-up positive, meaning the coefficient a on x² must be positive, a>0.  

The general form with vertex (p,q) is

y = a(x-p)² + q

So for us, all our parabolas are of the form

y = a(x- -3)² + 9

y = a(x² + 6x + 9) + 9

y = ax² + 6ax + 9(a+1)

That's the general form for a parabola with vertex (-3,9); a>0 assure the parabola has a minimum at the vertex.

Some instances:

a=1 gives

Answer: y = x²+6x+18

a=4 gives

y = 4x² + 24x + 45

Other positive as give other possible answers; without the choices it's impossible to know which one they're seeking.

Answer:

Step-by-step explanation:

Io