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2 years ago

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The town council wants to know if the residents support beautification of the downtown area. What is the best design for this st

udy? Question 16 options: Observational study Experiment Census Sample survey

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Natasha_Volkova [10]2 years ago

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Experimental census sample survey

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What is the solution to the linear equation? 2.8y + 6 + 0.2y = 5y – 14 y = –10 y = –1 y = 1 y = 10

svp [43]

2.8y + 6 + 0.2y = 5y – 14

Simplify the left side:

3y +6 = 5y-14

Subtract 3y from both sides:

6 = 2y -14

Add 14 to each side:

2y =20

Divide both sides by 2:

y = 20 / 2

y = 10

5 0

2 years ago

Read 2 more answers

Which expressions are equivalent to 5 x minus 15? Select three options. 5 (x + 15) 5 (x minus 3) 4 x + 3 y minus 15 minus 3 y +

Aleksandr [31]

Answer:

B) 5 (x minus 3)

C) 4 x + 3 y minus 15 minus 3 y + x

E) Negative 20 minus 3 x + 5 + 8 x

tep-by-step explanation:

5x minus 15

5x - 15

5(x - 3)

4 x + 3 y minus 15 minus 3 y + x

4x + 3y - 15 - 3y + x

5x - 15

Negative 20 minus 3 x + 5 + 8 x

-20 - 3x + 5 + 8x

5x - 15

6 0

2 years ago

Read 2 more answers

Frank needs to fill juice cups for his little sister's birthday party. There are 35 juice cups and each juice cup holds 12 fluid

skelet666 [1.2K]

128 oz. in one gallon. 35 cups of 12 oz. equals 420 oz. 420 divided by 128 equals 3.28 so youll need 4 bottles. D.

4 0

2 years ago

For the diagram below figure b is a reflection of y=2x of the line y =x

Scilla [17]

The equation of the line would be y = (1/2)x.

To find the equation of a line that is reflected through the line y = x, we just switch the x and y. Then, solve for y.

y = 2x
x = 2y
0.5x = y

5 0

2 years ago

Find the equation of the plane through the point (2,5,7) that is parallel to the line r=(3i+2j−2k)+t(i+2j+9k) and perpendicular

insens350 [35]

The plane we want to find has general equation

$a(x-2)+b(y-5)+c(z-7)=0$

with $a,b,c$ not equal to 0, and has normal vector

$\vec n=a\,\vec\imath+b\,\vec\jmath+c\,\vec k$

$\vec n$ is perpendicular to both the normal vector of the other plane, which is $4\,\vec\imath+5\,\vec\jmath+6\,\vec k$ , as well as the tangent vector to the line $\vec r(t)$ , which is $\vec\imath+2\,\vec\jmath+9\,\vec k$ .

This means the dot product of $\vec n$ with either vector is 0, giving us

$\begin{cases}4a+5b+6c=0\\a+2b+9c=0\end{cases}$

Suppose we fix $c=1$ . Then the system reduces to

$\begin{cases}4a+5b=-6\\a+2b=-9\end{cases}$

and we get

$(4a+5b)-4(a+2b)=-6-4(-9)\implies-3b=30\implies b=-10$

$a+2(-10)=-9\implies a=11$

Then one equation for the plane could be

$\boxed{11(x-2)-10(y-5)+(z-7)=0}$

or in standard form,

$\boxed{11x-10y+z=-21}$

The solution is unique up to non-zero scalar multiplication, which is to say that any equation $(11x-10y+z)k=-21k$ would be a valid answer. For example, suppose we instead let $c=2$ ; then we would have found $a=22$ and $b=-20$ , but clearly dividing both sides of the equation

$22(x-2)-20(y-5)+2(z-7)=0$

by 2 gives the same equation as before.

7 0

2 years ago