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3 years ago

Solve by using addition method x-2y=-3 , -2x+4y=6

1 answer:

8 0

X - 2y = -3....multiply by 2
-2x + 4y = 6
----------------
2x - 2y = -6 (result of multiplying by 2)
-2x + 4y = 6
----------------add
0 = 0

This system of equations has infinite solutions

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The figure shows the layout of a symmetrical pool in a water park. What is the area of this pool rounded to the tens place? Use

k0ka [10]

Answer:

$2489ft^{2}$

Step-by-step explanation:

The pool are is divided into 4 separated shapes: 2 circular sections and 2 isosceles triangles. Basically, to calculate the whole area, we need to find the area of each section. Due to its symmetry, both triangles are equal, and both circular sections are also the same, so it would be enough to calculate 1 circular section and 1 triangle, then multiply it by 2.

<h3>Area of each triangle:</h3>

From the figure, we know that <em>b = 20ft </em>and <em>h = 25ft. </em>So, the area would be:

$A_{t}=\frac{b.h}{2}=\frac{(20ft)(25ft)}{2}=250ft^{2}$

<h3>Area of each circular section:</h3>

From the figure, we know that $\alpha =2.21 radians$ and the radius is $R=30ft$ . So, the are would be calculated with this formula:

$A_{cs}=\frac{\pi R^{2}\alpha}{360\°}$

Replacing all values:

$A_{cs}=\frac{(3.14)(30ft)^{2}(2.21radians)}{6.28radians}$

Remember that $360\°=6.28radians$

Therefore, $A_{cs}=994.5ft^{2}$

Now, the total are of the figure is:

$A_{total}=2A_{t}+2A{cs}=2(250ft^{2} )+2(994.5ft^{2})\\A_{total}=500ft^{2} + 1989ft^{2}=2489ft^{2}$

Therefore the area of the symmetrical pool is $2489ft^{2}$

3 0

2 years ago

Depending on the car and the additional features, a convertible sports car can cost between $19,028 and $370,790. Write two ineq

liraira [26]

Cost of Car= C

$19,028 <span>≥</span><span> C ≤ $370,790
</span>
The cost of the sports car is greater than or equal to $19, 028 and less than or equal to $370,790.

6 0

3 years ago

PLEASE HELP!!

erik [133]

$2.=c.\\\\2\sin4x\cos4x=2\sin(2\cdot4x)=2\sin8x\\\\Used:\\\sin2\alpha=2\sin\alpha\cos\alpha$

$1.=b.\\\\\csc x-\sin x=\dfrac{1}{\sin x}-\dfrac{\sin^2x}{\sin x}=\dfrac{1-\sin^2x}{\sin x}=\dfrac{\cos^2x}{\sin x}\\\\=\dfrac{\cos x\cos x}{\sin x}=\cos x\cdot\dfrac{\cos x}{\sin x}=\cos x\cot x\\\\Used:\\\csc x=\dfrac{1}{\sin x}\\\\\sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\\\\\cot x=\dfrac{\cos x}{\sin x}$

$3.=a.\\\\\dfrac{\sin x-1}{\sin x+1}=\dfrac{\sin x-1}{\sin x+1}\cdot\dfrac{\sin x+1}{\sin x+1}=\dfrac{\sin^2x-1^2}{(\sin x+1)^2}=\dfrac{\sin^2x-1}{(\sin x+1)^2}\\\\=\dfrac{-(1-\sin^2x)}{(\sin x+1)^2}=\dfrac{-\cos^2x}{(\sin x+1)^2}\\\\Used:\\(a-b)(a+b)=a^2-b^2\\\\\sin^2x+\cos^2x=1\to \cos^2x=1-\sin^2x$

8 0

3 years ago

Which is an equivalent expression for 21a+35?

ki77a [65]

Answer:

7(3a + 5)

Step-by-step explanation:

Rewrite 21 as 7 · 3

Rewrite 35 as 7 · 5

Therefore,

⇒ 21a + 35 = 7 · 3a + 7 · 5

Factor out common term 7:

⇒ 7 · 3a + 7 · 5 = 7(3a + 5)

5 0

2 years ago

Katie is reading a 200-page book that is divided into 5 chapters. The bar graph shows the number of pages in each

Lunna [17]

Answer:

I don't see any bar graph, can you add it please?

Step-by-step explanation:

Thanks

6 0

3 years ago