which statement is true?

Answer:

Perimeter of ΔABC: [tex]\frac{27}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] units

Area of ΔABC: [tex]\frac{81}{8}*\sqrt3 + \frac{243}{8}[/tex] units

Skills required: HS Geo, Special Triangles

Step-by-step explanation:

1) The best option is to break down this triangle. Let's draw an altitude from Point B down to Segment AC. The point from the altitude that intersects AC is Point D. BD is the height of our triangle, AC is the base.

2) Angle A is 60 degrees, and since Angle BDA is 90 degrees, Angle ABD is 30 degrees. We can use the 30-60-90 degree right triangle property for the triangle BDA.

AB is 9 units, and it is opposite the 90 degree angle. This means that [tex]2x=9, x = \frac{9}{2}[/tex] ==> This then means that AD, the segment opposite the 30 degree angle in this triangle is [tex]\frac{9}{2}[/tex] units. Segment BD (the height) is [tex]\frac{9}{2} * \sqrt3[/tex].

3) Angle C is 45 degrees, and Angle BDC is 90 degrees, which means that Angle CBD is 45 degrees. We can use the 45-45-90 degree right triangle property for the triangle BCD.

BD is [tex]\frac{9}{2} * \sqrt3[/tex], which means DC is the same. BC, which is the hypotenuse is BD multiplied by square-root-2, which is [tex]\frac{9}{2} * \sqrt6[/tex].

4) Area is [tex]\frac{1}{2}*b*h[/tex], the base (b) is AC (which is [tex]\frac{9}{2}+\frac{9}{2}*\sqrt3[/tex]), the height is BD ([tex]\frac{9}{2}*\sqrt3[/tex]). When multiple you will get [tex]\frac{81}{4}*\sqrt3 + \frac{243}{4}[/tex], then this multiplied by 1/2 is

[tex]\frac{81}{8}*\sqrt3 + \frac{243}{8}[/tex] <--> this is the area!

5) Perimeter is just the sum of all side: 9 + [tex]\frac{9}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] = [tex]\frac{27}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] unit

Answer:

beyond the words of a constitution or statute to consider the broader societal implications of their decisions.

Step-by-step explanation:

[tex]\frac{-8(7-\sqrt{2)} }{47}[/tex]

Answer:

A wheel completes a rotation when it moves 360 degrees. The descriptions of the graph are: The Ferris wheel will rotate 4 times.

Step-by-step explanation:

but what graph

The Ferris wheel makes 4 rotations.

The maximum points on the graph represent when the Ferris wheel is at the top, and the minimum points on the graph represent when the Ferris wheel is at the bottom

Answer:

381.(3) [km.]

Step-by-step explanation:

if according to the condition distance=286 [km] per 3 hours, then it is possible to make up the equation:

[tex]\frac{286}{3}=\frac{d}{4};[/tex]

and to calculate required distance 'd':

[tex]d=\frac{286*4}{3}=381.(3)[km].[/tex]

Answer:

75

Step-by-step explanation:

First divide 2/5 to get 0.4. Then divide 30 by 0.4 to get the answer. A simple way to think about it is how many 0.4 grams are in 30 gram tube.

Answer:

12

Step-by-step explanation:

1/12x1/x

1x=12x1

x=12

Answer:

12 twelfths make a whole.

Step-by-step explanation:

when the numerator and the denominator of a fraction are the same, they always equal one. 12/12 would simply to one, just like 3/3 or 200/200.

I hope this helps

Answer:

You accedently put Mathematics I think you meant Social Studies haha

Step-by-step explanation:

Answer:

Step-by-step explanation:

When you have four terms and 3rd degree equation (the highest power is 3) you will want to try to "factor by grouping"

Group together two terms, watch out for the negative signs!

x^3 + 2x^2-5x-10=0

(x^3 + 2x^2) - (5x+10)=0

Find a common factor in each group and factor it out. You're hoping that what is left in the parenthesis is the same in both cases.

x^2(x+2)-5(x+2)=0

Now you can factor out that (x+2) because it is both terms.

x^2(x + 2) - 5(x + 2)=0

~~~~ ~~~~

Pull these out.

What will be left is the x^2 and the - 5 (dont lose that - in front of the 5)

(x + 2)(x^2 - 5) = 0

If all you have to do is factor, then you're done. It is factored. But if you have to "solve" also, then put x+2=0 and x^2-5=0 and solve.

x = -2 and x = +- sqrt5

Answers:

There are infinitely many other possible answers.

===================================================

Explanation:

The [tex]\frac{3}{3}[/tex] simplifies to 1. Dividing any nonzero number over itself always leads to 1.

So the equation [tex]y = \frac{3}{3}x+6[/tex] simplifies to [tex]y = x+6[/tex]

To determine y, we add 6 to x.

Pick 3 random values you want for x.

Let's say we picked x = 0

y = x+6

y = 0+6

y = 6

So x = 0 leads to y = 6

-----------

If you tried something like x = 2, then,

y = x+6

y = 2+6

y = 8

So (2,8) is another point on the line

-----------

Lastly, let's try a negative number. Let's go for x = -10

y = x+6

y = -10+6

y = -4

The input x = -10 gives the output y = -4

There isn't any restriction on x, so you can use any number you want. Therefore, there are infinitely many possible answers.

Answer:

Pronator??

Step-by-step explanation:

Answer:

94.6-18.8=75.8

75.8 is the answer

Step-by-step explanation:

Hope this helps

May i get braineist pls?

Answer:

95% of Grade 6 pupils graduated

Answer:

95% of Grade 6 Pupils Graduated

Step-by-step explanation:

Express the Statement Mathematically:

Add Percentage

By Division

Then, Multiply

Answer:

None of these

Step-by-step explanation:

None of these are correct because you would need to multiply 5 x 10 to a certain power. 5.55621 x 10 to the 8th power would do it.

Answer: I believe D is correct

Step-by-step explanation:

Answer:

  A) 1: linear; 2: exponential (see equations in part B)

  B) the value of 2 will be almost 15% greater

Step-by-step explanation:

As is often the case with multi-part questions, later parts of the question answer earlier parts. The equations shown in Part B are linear for Option 1 and exponential for Option 2.

The table values for Option 1 have a common difference of (1200 -1100) = 100.

The table values for Option 2 have a common ratio of (1210/1100) = 1.10.

Linear functions produce sequential values with a common difference (the slope of the function). Option 1 is linear.

Exponential functions produce sequential values with a common ratio (the growth factor). Option 2 is exponential.

__

The investment values after 7 years will be ...

  Option 1: f(7) = 100(7) +1000 = 1700

  Option 2: g(7) = 1000(1.1^7) ≈ 1948.72

The value of Option 2 will be about $248.72 higher, or 14.6% higher than the value of Option 1. Whether that is significant or not is in the eye of the beholder. Many people might consider that to be significantly better performance. (It would take another 2 1/2 years for Option 1 to have that value.)

Yes?? i dont understand the question that much

Step-by-step explanation:

Hello there, you are asking us to distribute [tex]\frac{2}{3}(x-66)[/tex], which can also be phrased as [tex](x\cdot\frac{2}{3})-(66\cdot\frac{2}{3})[/tex], complete what's in the parenthesis, and we get [tex]\frac{2}{3} x-44[/tex] as our answer,

Definition- Distribute Property - The distributive property is one of the most frequently used properties in math. In general, this term refers to the distributive property of multiplication which states that the Definition: The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

[tex]35m>-30\\\\\implies \dfrac{35m}{35}>-\dfrac{30}{35}\\\\\implies m>-\dfrac{6}{7}[/tex]

Answer:

22.5

Step-by-step explanation:

Answer:

Enter a value for a so that the system of equations shown has infinitely many solutions.

y = −5x + 9y =    ax + 9

Step-by-step explanation:

Step-by-step explanation:

the solutions for a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -4

c = k

x = (4 ± sqrt(16 - 4k))/2 = 2 ± sqrt(4 - k)

x1 = 2 + sqrt(4 - k)

x2 = 2 - sqrt (4 - k)

x1 = 2 + x2

2 + sqrt(4 - k) = 2 + 2 - sqrt(4 - k)

2×sqrt(4 - k) = 2

sqrt(4 - k) = 1

4 - k = 1

k = 4 - 1 = 3

x1 = 3

x2 = 1

Answer:

The roots are 1 and 3.

k = 3.

Step- by-step explanation:

We use the facts that if α and β are the roots of ax^2 + bx + c = o then α+ β = -b/a and  α β = c/a.

The roots are written as  α and α+2, then:

α + α + 2 = -(-4)

2α + 2 = 4

α + 1 = 2

α = 1

also

α (α + 2) = k

Substituting for α:

1(1 + 2) = k

k = 3.

The roots are 1 and 1 + 2 = 3.

Answer:

check online for more information

Answer:

Check online for more informations.

Answer:

n = 11

Step-by-step explanation:

n+5=2n-6

you add 6 on both sides and you get

n+11=2n

you then subtract n on both sides and get

11=n

Step-by-step explanation:

n+5 = 2n - 6 -> Original equation

5 = n - 6 -> Take n away from both sides

11 = n -> Add 6 to both sides

n = 11 -> Final answer

*Remember, we are trying to get n by using inverse operations.

Answer:

you can do a trial and improvement

Step-by-step explanation:

Answer:

Step-by-step explanation:

Garage A = 7+3t

Garage B = 4+4t

Garage A = 7+6

Garage B = 4+8

B = Cheaper

Answer:

A = 3t + 7, B = 4t + 4, B is cheaper

Step-by-step explanation:

A = 3(2) + 7 = 6 + 7 = 13

B = 4(2) + 4 = 8 + 4 = 12

Answer: 49

Step-by-step explanation:

Answer: See below

Step-by-step explanation:

Isolate x for x-2y+2z=9

3x=9+2y

[tex]x=\frac{9+2y}{3}[/tex]....(1)

Substitute (1) into the 2nd equation

[tex]\begin{bmatrix}-\frac{9+2y}{3}+3y=-4\\ 2\cdot \frac{9+2y}{3}-5y+3z=16\end{bmatrix}[/tex]

[tex]\frac{3\left(-9+7y\right)}{3}=3\left(-4\right)[/tex]

7y=-3

y=-3/7

Substitute y=-3/7

[tex]\begin{bmatrix}3z+\frac{18-11\left(-\frac{3}{7}\right)}{3}=16\end{bmatrix}[/tex]

[tex]\begin{bmatrix}3z+\frac{53}{7}=16\end{bmatrix}[/tex]

Isolate z by substituting it

[tex]3z+\frac{53}{7}=16[/tex]

[tex]\frac{3z}{3}=\frac{\frac{59}{7}}{3}[/tex]

[tex]z=\frac{59}{21}[/tex]

For x =9+2y/3 substitute z=59/21 and y=-3/7

[tex]x=\frac{9+2\left(-\frac{3}{7}\right)}{3}[/tex]

[tex]x=\frac{19}{7}[/tex]

[tex]x=\frac{19}{7},\:z=\frac{59}{21},\:y=-\frac{3}{7}[/tex]

Answer:

(1, - 1, 3 )

Step-by-step explanation:

x - 2y + 2z = 9 → (1)

- x + 3y = - 4 → (2)

2x - 5y + 3z = 16 → (3)

Add (1) and (2) term by term to eliminate x

y + 2z = 5 → (4)

Multiply (2) by 2

- 2x + 6y = - 8 → (5)

Add (3) and (5) term by term to eliminate x

y + 3z = 8 → (6)

Subtract (6) from (4) term by term to eliminate y

- z = - 3 ( multiply both sides by - 1 )

z = 3

Substitute z = 3 into (4)

y + 2(3) = 5

y + 6 = 5 ( subtract 6 from both sides )

y = - 1

Substitute y = - 1, z = 3 into (1) and solve for x

x - 2(- 1) + 2(3) = 9

x + 2 + 6 = 9

x + 8 = 9 ( subtract 8 from both sides )

x = 1

solution is (1, - 1, 3 )

Answer:

x = 22

Step-by-step explanation:

4x + 28 = 116 (corresponding angles are equal when two lines are parallel)

4x = 88

x = 22

Corresponding angles must be equal

[tex]\\ \tt\hookrightarrow 4x+28=116[/tex]

[tex]\\ \tt\hookrightarrow 4x=116-28[/tex]

[tex]\\ \tt\hookrightarrow 4x=88[/tex]

[tex]\\ \tt\hookrightarrow x=22[/tex]