Find the value of x in the triangle shown below.

1. x = 3
2. x = √20
3. x = 2
4. x = √36

Answer:

short side = 4

Step-by-step explanation:

area = 1/2BH

18 = 1/2(x - 1)(x + 4)

18 = 1/2(x² + 4x - x - 4)

multiply both sides of the equation by 2:

36 = x² + 3x - 4

x² + 3x - 40 = 0

(x + 8)(x - 5) = 0

x = 5

short side = 5 - 1 = 4

The shortest length of the right angled triangle is 4 cm.

where

b = base

h = height

Therefore,

area = 18 cm²

18 = [tex]\frac{1}{2}[/tex] × (x - 1)(x + 4)

36 = (x - 1)(x + 4)

x² + 4x - x - 4 = 36

x² + 3x - 4 = 36

x² + 3x - 4 - 36 = 0

x² + 3x - 40 = 0

x² - 5x + 8x - 40 = 0

x(x - 5) + 8(x - 5) = 0

(x + 8)(x - 5) = 0

x = -8 or 5

we can only use positive numbers.

Therefore,

x = 5

The shortest sides is definitely one of the 2 legs . The hypotenuse of a triangle is the longest side.

Therefore,

h = x - 1 = 5 - 1 = 4 cm

b = x + 4 = 5 + 4 = 9 cm

learn more on right angled triangle here: https://brainly.com/question/2292567?referrer=searchResults

Answer:

-2/3

Step-by-step explanation:

8^(x+2) =8^-2x

since the base are the same we deal with the exponent

x+2=-2x

x= -2/3

Answer:

The answer is B $23.

Step-by-step explanation:

You take 391 and divide it by 17

391/17=23

Hope this helps!

Answer:

4080cm²

Step-by-step explanation:

Answer:

Tommy would have to pull at least 40.0000000..... something to beat Artie but the closest whole number is 41 becouse it has to be over 200

Step-by-step explanation:

200 /= 60 + 20 +25 + 55 + x

200/= 160 + x - 160 both sides

40 = x

Answer: try C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

It's c because you multiply 3 1/8 by 3 and 3 1/4 by 4 and 3 1/2 by 1.

Answer:

the answer to the questions are c,b,a

Answer:

Interest is $25

Step-by-step explanation:

Formula to find interest:

I = Prt

Given:

P = 100

r = 5% or 0.05

t = 5

Work:

I = Prt

I = 100(0.05)(5)

I = 5(5)

I = 25

Answer:

1.) Right triangle

2.) Not right triangle

3.) Not right triangle

4.) Not right triangle

5.) Right triangle

6.) Right triangle

Step-by-step explanation:

The ones that are a right triangle have at least one angle that has an L shape

Answer:

8

Step-by-step explanation:

sqrt8*sqrt8 = sqrt8^2 = 8

Step-by-step explanation:

i don't have a step by step explanation so here you go the answer

Answer:

Step-by-step explanation:

First of all you have to put the zeros into factor form.

y1 = (x + 2)(x - 5)

Notice that the x changes sigh. You say that the zeros are -2 and  5. To get y1 to go to zero, you must make x the opposite sign of what you are given.

Now you have to expand the factored form to get the standard form

y = x^2 + 2x - 5x - 10

y = x^2 - 3x - 10

That's not the right answer.

f(0) = 30 but you have - 10 at the end so you have to multiply the factored form by - 3

-3(f(x)) = -3(x + 2)(x - 5)

-3(f(x)) = -3(x^2 - 3x - 10)

f(x) = -3x^2 + 9x + 30    

f(0) = -3(0)^2 + 9(0) + 30

f(0) = 30

The quadratic still has roots of (x +2)(x - 5) but that 3 makes the y intercept = 30.

See the graph below.

Answer:

Area of the shaded region = 450.52 square inch

Step-by-step explanation:

Area of the shaded region = Area of the circle - Area of the right triangle inscribed in the semicircle

By applying Pythagoras theorem in the given right triangle,

(Hypotenuse)² = (leg 1)² + (leg 2)²

                        = (21)² + (20)²

Hypotenuse = [tex]\sqrt{441+400}[/tex]

                     = [tex]\sqrt{841}[/tex]

                     = 29

Since, hypotenuse of the right triangle is the diameter of the circle.

Therefore, radius of the circle = [tex]\frac{29}{2}[/tex]

                                                  = 14.5 in.

Area of the circle = πr²

                             = π(14.5)²

                             = 660.519

                             ≈ 660.52 in²

Area of the right triangle = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                         = [tex]\frac{1}{2}(21)(20)[/tex]

                                         = 210 in²

Area of the shaded region = 660.52 - 210

                                            = 450.52 square inch

Answer:

The length of the other two sides are: 43.09 and 32.60

Step-by-step explanation:

Let the given side of the triangle be b(= 40), and the angles be;

A = [tex]72^{o}[/tex], B = [tex]62^{o}[/tex]and C = [tex]46^{o}[/tex].

Applying the Sine rule,

[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex] = [tex]\frac{c}{Sin C}[/tex]

So that,

[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex]

[tex]\frac{a}{Sin 72}[/tex] = [tex]\frac{40}{Sin62}[/tex]

a = [tex]\frac{0.9511*40}{0.8829}[/tex]

  = 43.0898

a = 43.09

Also,

[tex]\frac{b}{SinB}[/tex] = [tex]\frac{c}{Sin C}[/tex]

[tex]\frac{40}{Sin62}[/tex] = [tex]\frac{c}{Sin46}[/tex]

c = [tex]\frac{0.7193*40}{0.8829}[/tex]

  = 32.5881

c = 32.60

The length of the other two sides are: 43.09 and 32.60

-2

Divide each term (-4x = 8 by -4)

Cancel the common factor of -4

x = 8/-4

THEN DIVIDE

x=-2

Answer:

None of the choices are correct

Step-by-step explanation:

This is because it should be going down if it was subtracting but no answer says that so

Answer:

10x=180-80

x=100/10=10

:.x=10

9.

8x+2=7x+14 corresponding angle of parallelogram are equal

8x-7x=14-2

x=12

10.

4x+4=5x+1 corresponding sides of parallelogram are equal

4-1=5x-4x

x=3

11.

4+3x=19corresponding sides of parallelogram are equal

3x=19-4

x=15/3

x=5

Answer:

angle Q is 68°

angle R is 112°

Answer:

3/5

Step-by-step explanation:

subtract the fractions then turn the decimal into a fraction.

Answer:

63.76

Step-by-step explanation:

85.95-30% 60.16

60.16+6% 63.76

Hello!

Here we are given a composite shape, meaning that we can divide this shape up into ways that we are given formulas to solve for legs and such.

I can see here that this can be divided into a triangle and a rectangle using a horizontal line.

The leg lengths of this triangle would be 9, because it is congruent to the bottom side of the rectangle, and 7, because it is the left side minus the right side.

This would also make a right triangle, meaning we could solve for the hypotenuse utilizing the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

[tex]6^2+7^2=c^2[/tex]

[tex]36+49=c^2[/tex]

[tex]c^2=85[/tex]

[tex]c=\sqrt{85}[/tex]

Which is in simplest radical form.

Hope this helps!