solve for x in the equation

Exact Answer:     x = 16/3

Approximate Answer:      x = 5.333

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Work Shown:

base = 3x-1

height = x

area of triangle = (base*height)/2

40 = x*(3x-1)/2

40*2 = 3x^2 - x

80 = 3x^2 - x

0 = 3x^2 - x - 80

3x^2 - x - 80 = 0

Now apply the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-1)\pm\sqrt{(-1)^2-4(3)(-80)}}{2(3)}\\\\x = \frac{1\pm\sqrt{961}}{6}\\\\x = \frac{1\pm31}{6}\\\\x = \frac{1+31}{6} \ \text{ or } \ x = \frac{1-31}{6}\\\\x = \frac{32}{6} \ \text{ or } \ x = \frac{-30}{6}\\\\x = \frac{16}{3} \ \text{ or } \ x = -5\\\\x \approx 5.333 \ \text{ or } \ x = -5\\\\[/tex]

A negative height doesn't make sense, so we ignore x = -5

The only solution is x = 16/3 which approximates to x = 5.333

Answer:

11.1

Step-by-step explanation:

Use the Pythagorean theorem to find the unknown side.

[tex]a^{2} +b^{2} =c^{2} \\AB^{2} +BC^{2} =AC^{2} \\AB^{2} +19^{2} =22^{2} \\\\AB^{2}=22^{2}-19^{2\\AB=\sqrt{123} \\AB=11.1[/tex]

Answer:

38, 26

Step-by-step explanation:

(x+78) + (x-12) +x = 180

3x + 66 =180

3x = 114

x = 38

P = 38-12=26

Answer:

AB = 7

Step-by-step explanation:

The polygon pictured is a hexagon, which means that it has 6 equal side lengths. The perimeter is 42. AB is the length of one side.

Perimeter = 6 x length of one side

If you plug everything you know in the equation, you would get...

42 = 6 x length of one side

42 ÷ 6 = 7

So, 7 is the length of AB, since in a hexagon, all sides are the same length.

The length of side AB  is 7.

A regular polygon is a closed shape that has straight sides of equal length and interior angles of equal measure.

This means that all of the sides and angles of a regular polygon are congruent (i.e., have the same size).

We have,

The given polygon is a hexagon since it has 6 faces.

Now,

The six faces are equal in length.

So,

6 faces length = 42

Now,

Each face = x

And,

6x = 42

x = 42/6

x = 7

Thus,

The length of AB  is 7.

Learn more about regular polygons here:

https://brainly.com/question/24328525

#SPJ

Answer:

1/2

Step-by-step explanation:

Answer:

Option. A

Step-by-step explanation:

Have a great day!

Answer: A

Step-by-step explanation: there's 8 spaces on the spinner

Answer 8.1

Step-by-step explanation:

3 x 9 x 0.3 = 8.1

Answer:

B

Step-by-step explanation:

The hl theorem says that if we have two right triangles that have a congruent hypotenuse and a congruent leg, the two triangles are congruent

in this case the exercise says the two leg are congruent, so we have to say that the two hypotenuse are congruent

So

JB congruent to FC

do u want us to draw it 4 u ? cuz I can

Answer:

[tex]11^2 *11^10 \\13^6 *13^4\\14^9 * 14^10\\2^4*2^4\\7^8*7^6\\3^3*3^9[/tex]

Step-by-step explanation:

Please Mark Brainliest for helping

if i understand the question it's 25

Step-by-step explanation:

6/21 equal 10/10+x

info x is GJ

6x=150

x=25

i used the similarity in trangle formula because he sayed that FG is parelel to HJ

Answer:

No

Step-by-step explanation:

this is my opinion so No

Answer:

A. (x − p) (x + p) = x² - p²

B. (x – 5) (x + 7) = x² + 2x - 35

C. (x + p) (x + p) = x² + 2px + p²

Step-by-step explanation:

To find - Multiply and match each of the following  expressions.

A. (x − p) (x + p)

B. (x – 5) (x + 7)

C.(x + p) (x + p)

Proof -

A.)

The expression is - (x − p) (x + p)

Now,

(x − p) (x + p) = x(x + p) - p(x + p)

                     = x(x) + x(p) - p(x) - p(p)

                     = x² + xp - px - p²

                     = x² - p²

⇒(x − p) (x + p) = x² - p²

B.)

The expression is - (x – 5) (x + 7)

Now,

(x − 5) (x + 7) = x(x + 7) - 5(x + 7)

                     = x(x) + x(7) - 5(x) - 5(7)

                     = x² + 7x - 5x - 35

                     = x² + 2x - 35

⇒(x − 5) (x + 7) = x² + 2x - 35

C.)

The expression is - (x + p) (x + p)

Now,

(x + p) (x + p) = x(x + p) + p(x + p)

                     = x(x) + x(p) + p(x) + p(p)

                     = x² + xp + px + p²

                     = x² + 2px + p²

⇒(x + p) (x + p) = x² + 2px + p²

Answer:

x= 23.33

Step-by-step explanation:

7=x+2x-5-58

combine like terms

7=3x-63

add 63 to both sides

70=3x

divide by 3

x=23.33

Answer:

Im sorry i dont understand what you mean by sentence but there are 6 boys

Step-by-step explanation:

Answer:

= 5^-8 . 5^-10

= 5^(-8 ) + (-10)

=5^-18

Answer:

5^-18

Step-by-step explanation:

[tex](5^{-8})(5^{-10}) = 5^{-8-10} = 5^{-18}[/tex]

Answer:

y = √61

Step-by-step explanation:

the steps are in the pic above, stay outta drugs and pass ur tests.

Answer:

c=-18 d=2

Step-by-step explanation:

[ 6 8 -11 15 ]-[c+2 3 -5 d-4 ]=[ 22 5 -6 17]

The equation tells that when the two matrices are subtracted we get the resultant matrix.

Each element of the first matrix corresponds to each element of the second matrix

From above

6- (c+2)= 22

6- c-2= 22

4-c= 22

-c= 22-4

-c= 18

c= -18

And

15-( d-4)= 17

15- d+4= 17

19-d= 17

-d= 17-19

-d= -2

d= 2

Answer:

D

Step-by-step explanation:

c= -18

d= 2

Answer:

$49,057.50

Step-by-step explanation:

To find how much a percent is of a number you multiply that number and that percent then add the two

SO.... 46,500x5.5% is 2557.50 and then you add the 2 so 46,500 + 2557.50= 49,057.50 hope this helps

Answer:

113.1 in

Step-by-step explanation:

C = πd

d = 36

C = 36π = 113.1 in

The required equation of the hyperbola is expressed as

[tex]\frac{x^2}{10}- \frac{y^2}{15}=1 \\[/tex]

The standard form for calculating the equation of a parabola along the x-axis is expressed as:

[tex]\frac{(x-k)^2}{a^2}-\frac{(y-h)^2}{b^2} = 1 \ ............. 1[/tex] where:

(h, k) is the center

(k±c, h) are the foci

[tex]x=h\pm\frac{a^2}{c}[/tex] is the directrix

From the question given, we can see that foci = (±5, 0)

k±c, h = ±5, 0

k = 0

h = 0

c = 5

From the directrix,

[tex]x=h\pm\frac{a^2}{c}\\x =0\pm\frac{a^2}{5}\\\pm2 = \pm\frac{a^2}{5}\\a^2 = 10\\[/tex]

Also, we need to know that;

a²+b² = c²

10 + b² = 5²

b² = 25 - 10

b² = 15

Substituting the gotten values into the equation of a hyperbola;

[tex]\frac{(x-0)^2}{10}- \frac{(y-0)^2}{15} =1\\\frac{x^2}{10}- \frac{y^2}{15} =1\\[/tex]

This gives the required equation of the hyperbola

Learn more on the equation of hyperbola here: https://brainly.com/question/20409089

Answer:

The answers are between C and D

Step-by-step explanation:

It can't be A or B because they create a horizontal hyperbola, when the directrices are vertical.

Answer:

D

Step-by-step explanation:

Using the tangent ratio in the right triangle

tanθ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{7}{4}[/tex] , then

θ = [tex]tan^{-1}[/tex] ([tex]\frac{7}{4}[/tex] ) ≈ 60° ( to the nearest degree )

Answer:

The answer should be 18.

Answer:

there are seven variable terms

Step-by-step explanation:

variables are letters (a, b, c, etc.)

i hope this helps :)

Answer:

The answer is 4 because are all separate variables (also  combines into one variable)

Step-by-step explanation:

Answer:

Let the three consecutive numbers be x,x+1,x+2 . The numbers are: 23,24,and25 and the smallest one is 23

Step-by-step explanation:

Answer: (x-1) + (x) + (x+1) = 72; smallest number is 23.

Step-by-step explanation:

The numbers are consecutive, meaning they sit next to each other on a number line. For example 4, 5, 6.

Because they are three consecutive numbers, their average will be the value of the middle one. For example the average of 4, 5, 6 is 5.

Knowing this, we can divide 72 by three to get the value of the middle number.

72/3 = 24, so the middle number is 24.

The numbers that fall either side of 24 on the number line are 23 and 25, so the three consecutive numbers are 23, 24, 25.

You can also set up and solve the equation: (x-1) + (x) + (x+1) = 72 because the numbers are consecutive.

To solve, combine like terms. The (-1) and (+1) cancel out and the equation becomes 3x = 72.

72/3 = 24, so x = 24, and the smallest term, (x-1) = 23.

Answer:

1.   5 in.

2.   12 in.

3.   3.5 in.

4.   30 ft

5.   4 m

6.   32 mm

7.   53.41 m

8.   18.85 ft

9.   87.96 in

10.  56.56 mm

11.   20.57 in

12.  25.71 yd

Step-by-step explanation: