What is the positive solution to this equation?
4x2 + 12 x= 135

Answer:

24.5 unit²

Step-by-step explanation:

Area of ∆

= ½ | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |

= ½ | (-1)(3 -(-4)) + 6(-4 -3) + (-1)(3 - 3) |

= ½ | -7 - 42 |

= ½ | - 49 |

= ½ (49)

= 24.5 unit²

Method 2:

Let the vertices are A, B and C. Using distance formula:

AB = √(-1-6)² + (3-3)² = 7

BC = √(-6-1)² + (-4-3)² = 7√2

AC = √(-1-(-1))² + (4-(-3))² = 7

Semi-perimeter = (7+7+7√2)/2

= (14+7√2)/2

Using herons formula:

Area = √s(s - a)(s - b)(s - c)

here,

s = semi-perimeter = (14 + 7√2)/2

s - a = S - AB = (14+7√2)/2 - 7 = (7 + √2)/2

s - b = (14+7√2)/2 - 7√2 = (14 - 7√2)/2

s - c = (14+7√2)/2 - 7 = (7 + √2)/2

Hence, on solving for area using herons formula, area = 49/2 = 24.5 unit²

Answer:

24.5

Step-by-step explanation:

To find the area with the coordinates provided:

(-1,3), (6,3), (-1,-4)

First we count the units that are inside the triangle which is area.

[tex]\frac{49}{2}[/tex]

So we know that there are [tex]\frac{49}{2}[/tex] units and then we divide 49 by 2 which gets you 24.5.

49 ÷ 2 = 24.5

The answer is 24.5 units.

Answer:

x = 2, y = 3

Step-by-step explanation:

Log x + log y = log 6         Log xy = Log 6            xy = 6

y = 6/x

Log(x-1)+2 Log y=2 Log 3

Log(x-1) = 2 Log 3 - 2 Log y = Log 3² - Log y² = Log 9 - Log y² = Log (9 / y²)

x - 1 = 9/y²

x - 1 = 9 / (6/x)² = 9 /(36/x²) = x²/4

4x - 4 = x²

x² -4x + 4 = 0

(x-2)² = 0

x = 2

y = 6/x = 3

Answer:

i believe the answer is A 90

Step-by-step explanation:

Answer:

B

A=2

B=6

Step-by-step explanation:

The expression that shows how much farther Adam can see to the horizon should be considered as the d = 400 - 256 and d = 256 - 400.

Since

Pam's eye–level height is 256 feet above sea level and Adam's eye–level height is 400 feet above sea level.

So here the expression be like The expression that shows how much farther Adam can see to the horizon should be considered as the d = 400 - 256 and d = 256 - 400.

Learn more about an expression here: https://brainly.com/question/4700495

Answer: $67.15

Step-by-step explanation:

Answer:

first blank 8, 2nd blank 12

Step-by-step explanation:

plug X into the equation to find y

y = -4(-2) = 8

y = -4(3) = -12

Answer:

There are 10 two point questions and 16 five point questions.

Step-by-step explanation:

Answer:

Step-by-step explanation:

2.50   for water

1.25     for protein bar   interesting that is exactly half of the water

22.50   exactly was spent

I couldn't come up a slick equation, so I just applied some logic and used brute forced (trail and error) to solve the problem.

2.5Water + 1.25Protein =   22.5  

      8W     +           2P    =   22.5

      6W     +           6P    =   22.5

      4W     +          10P    =   22.5

      2W     +          14P    =   22.5

There are the possible combinations of both protein bars AND water, since he bought both.  He could have also bought 10 water or 18 protein bars, but that is not part of the combination.

Answer:

point estimate: .73

margin of error: .02

Step-by-step explanation:

correct on edg

Answer:

Then, the polynomial [tex]x^{2}+11\cdot x + 30[/tex] is equal to the product of the binomials [tex](x+5)[/tex] and [tex](x+6)[/tex].

Step-by-step explanation:

The polynomial [tex]x^{2}+11\cdot x + 30[/tex] is a polynomial of the form [tex]x^{2} - (r_{1}+r_{2})\cdot x + r_{1}\cdot r_{2} = (x-r_{1})\cdot (x-r_{2})[/tex], where [tex]r_{1}[/tex] and [tex]r_{2}[/tex] are the roots of the polynomial. Then, we find the following system of equations:

[tex]-r_{1}-r_{2} = 11[/tex] (1)

[tex]r_{1}\cdot r_{2} = 30[/tex] (2)

After some algebraic handling, the solution of this system is [tex]r_{1} = -5[/tex] and [tex]r_{2} = -6[/tex].

Then, the polynomial [tex]x^{2}+11\cdot x + 30[/tex] is equal to the product of the binomials [tex](x+5)[/tex] and [tex](x+6)[/tex].

Answer:

[tex]2^x-4=32\quad :\quad x=\frac{2\ln \left(6\right)}{\ln \left(2\right)}\quad \left(\mathrm{Decimal}:\quad x=5.16992\dots \right)\\\\2^x-4=32 \\\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\\2^x-4+4=32+4\\\mathrm{Simplify}\\2^x=36\\\\apply exponential rule\\x\ln \left(2\right)=\ln \left(36\right)\\x\ln \left(2\right)=\ln \left(36\right)\\x=\frac{2\ln \left(6\right)}{\ln \left(2\right)}[/tex]

hope it helps:)

Answer:

x=29

Step-by-step explanation:

3x+15+2x+20=180

3x+2x+15+20=180

5x+35=180

5x=180-35

5x=145

x=145/5

x=29

Step-by-step explanation:

-3. 2

-2. 1

-7. 6

i did my best.

Answer:x=-7

Step-by-step explanation:

Step-by-step explanation:

I'm not sure it's probably x=-2

Answer:

(x-6)(x+2) D

Step-by-step explanation:

first you need to see which two numbers add up to -4 and multiply to -12 which is -6 and 2

Answer:

Both A and B are possible.

Step-by-step explanation:

It's both!

This is a might tricky. First you have to find the altitude. You have to determine if this is a real triangle.

Sin(22) = opposite / hypotenuse. The hypotenuse = 111. The angle is 22

opposite = hypotenuse * sin(22)

opposite = 111 * sin(22)

opposite = 41.58  and this is the altitude.

What have you learned?

Since 42 is larger than 41.58 you have 2 solutions to the triangle. One of the angles is acute, and the other one is obtuse. They are supplementary angles.

Sin(C) / c = Sin(A) / a

Sin(C) = c * Sin(22) / 42

Sin(C) = 111*sin(22)/ 42

Sin(C) = .99003

Sin(C) = 81.9

So that's your first answer. The second answer comes from Finding the supplement to this angle

supplement + 81.9 = 180

supplement = 180 - 81.9

supplement = 98.1

Answer:

Step-by-step explanation:

Each part is equal to 65/(1+4)=$13

Since Stephanie only got 1 part, she got $13.

Answer:

13/25

Step-by-step explanation:

if you put it in decimal the fraction is greater

Answer:

13/25 is larger then 50%

Step-by-step explanation:

13/25=52%

50%=12.5/25

Answer:

Uriel's stick is LONGER by 7/24 feet

Step-by-step explanation:

Uriel's hiking stick is 3 2/3 feet long, and Nat's is 3 3/8 feet long. Whose walking stick is longer and by how much?

The above question is solved as

Uriel's stick - Nat's stick

= 3 2/3 feet - 3 3/8 feet

= 7/24 feet

Hence, Uriel's stick is LONGER by 7/24 feet

Answer:

The second and third one

Step-by-step explanation:

According to the statement, numbers between 4 and 5 is 4.1 - 4.9

But it is doubled so it is 8.2 - 9.8

These numbers are greater than 8 and less than 9

These numbers are also greater than 9 and less than 10

Answer:

it will take 4 months

Step-by-step explanation:

Answer: 14 pages a day

Step-by-step explanation:

98 / 7 = 14

Answer: 14 pages read per day.

Step-by-step explanation:

98/7= 14

Hope this helps!

Answer: The answer is 133.4 degrees.

Sorry if it’s wrong, and hopes this is helps.

The measure of the angle ∠G to the nearest tenth will be 31.6°.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The length of the perpendicular is 28.2 units and the length of the base is 45.8 units, Then the measure of the angle ∠G is calculated as,

tan G = Perpendicular / Base

Substitute the value, then the angle is given as,

tan G = 28.2 / 45.8

tan G = 0.6157

G = 31.6°

The measure of the angle ∠G to the nearest tenth will be 31.6°.

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

#SPJ2

The figure that shows a reflection of pre-image ABC over the y-axis is the third figure.

From the complete information, the triangle ABC is reflected over the y axis.

The vertices of the triangle are A(1, 1), B(3, 4) and C(3, 1). The vertices of the images are A(1, 1) = A'(-1, 1). B(3, 4) = B(-3, 4) ans C(3, 1) = C'(-3, 1).

In conclusion, the figure that shows a reflection of pre-image ABC over the y-axis is the third figure.

Learn more about reflection on:

https://brainly.com/question/3643476

Answer:

Ecuación estándar de un círculo

(x−2)2+(y−2)2=25

Forma general de la ecuación de un círculo

x2−4x+y2−4y−17=0

Ecuaciones paramétricas de un círculo

x=5cosθ+2y=5sinθ+2

Step-by-step explanation:

Ecuación Estándar de un Círculo

La ecuación estándar de un círculo con el centro en (x_0, y_0) y radio r es

(x^2-x_0) + (y^2-y_0)=r^2

Ecuaciones Paramétricas de un Círculo

Las ecuaciones paramétricas de un círculo con el centro en (x_0, y_0) y radio r son

x=r cos \theta + x_0\\y=r sin \theta + y_0

Ecuación General de un Círculo

La ecuación general de un círculo con el centro en (x_0, y_0) y radio r es

x^2+ax+y^2+by+c=0,

donde

a=-2x_0\\b=-2y_0\\c=x^2_0+y^2_0-r^2