Collect like terms: $x^(2)$ $x^(2) +6x-2x-12$

Answers

Answer 1

Answer: theonly like erms are the x terms
6x-2x=4x

x^2+4x-12

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Find the distance from the point $(6, 4)$ to the line $y=x+4$ .

Answers

Answer:

$\large \boxed{3√(2)}$

Step-by-step explanation:

1. Express the line in standard form.

ax + by + c = 0

$\begin{array}{rcl}y & = & x + 4\n-x + y - 4 & = & 0\n\end{array}$

2. Calculate the distance

The formula for the distance d from a point (x, y) and the line is:

$d = \frac{|ax + by + c|}{\sqrt{a^(2) + b^(2)}}$

Insert the values: a = -1; b = 1; c = -4; x = 6; y = 4

$\begin{array}{rcl}d &= &\frac{|(-1)(6) + 1*4 + (-4)|}{\sqrt{(-1)^(2) + 1^(2)}}\n\n& = & (|-6 + 4 - 4|)/(√(1 + 1))\n\n& = & (|-6|)/(√(2))\n\n& = &(6)/(√(2))\n\n& = & (3*√(2)*√(2))/(√(2))\n\n& = & \mathbf{3{√(2)}}\end{array}\n\text{The distance from the point to the line is $\large \boxed{\mathbf{3√(2)}}$}$

Hey!

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First, we need to find the second coordinate.

$\text{We know that the slope is 1 and the y-intercept is 4.}\n\text{We use}~(1 - 4)/(x - 6) = 1~\text{to solve for x.}\n\text{We can simplify this to}~(-3)/(x-6)\n\text{Now we know that whatever x subtracts to 6 we get -3 to get a slope of 1.}\n\text{After solving we can use 3 for x.}\n\text{We subsitute for x and end of getting}~(-3)/(-3)~\text{which equals 1.}\n\text{The second point is (3, 4)}$

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Second, we need to find the distance between both points.

$d = √((3 - 6)^2 + (1 - 4)^2) \nd = √((-3)^2 + (-3)^2) \nd = √(9+9) \nd = √(18) \n\text{We can simplify this using what we know about radicals.}\nd = 3√(2)$

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Hence, the answer is $3√(2)$ !

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Hope This Helped! Good Luck!

I need help please and thank you

Answers

Answer:

Step-by-step explanation:

each face is 9 cm squared because 3 times 3 is 9

9 times 6 is 54

squared units for area and surface area

Answer: C) 54 sq cm

Step-by-step explanation:

All of the sides in the example are 3 cm each, and there are 6 sides to a cube. 3^2*6 (3 squared times 6) = 54. Because we squared 3, the answer would be C)54 sq cm.

Julio walks 3 1/2miles in 1 1/4hours

Answers

So, you have to turn the fractions into decimals so..
3 1/2 = 3.5
1 1/4 = 1.25
Then divide and you'll get 2.8.

What is an equation of the line that is perpendicular to y-3 =-4(x+2)

Answers

Answer:

$y - 3 = (1)/(4)(x+2)$ or choose any line with slope 1/4

Step-by-step explanation:

The slope of this line is -4. The slope of the line perpendicular to this line will be the negative reciprocal or 1/4.

Write the equation using the slope m=1/4 and the point slope form.

$y-y_1=m(x-x_1)\ny-3=(1)/(4)(x+2)$

This is the equation of the line that is perpendicular and passes through the same point (-2,3) as the equation listed.

Answer:

$y=(1)/(4) x+c$ where $c$ can be any number.

Step-by-step explanation:

First we need to clear for y:

$y-3 =-4(x+2)\ny=-4(x+2)+3\ny=-4x-8+3\ny=-4x-5$

and now we have an equation of the form:

$y=mx+b$

where m is the slope and b is the y-intercept.

in this case $m=-4$ and $b=-5$

to find and equation perpendicular to this line, the following must be true: $m*m_(1)=-1$

where m is the slope of the original line that i just mentioned, and $m_(1)$ is the slope of the new line. Substituting $m=-4$

$-4*m_(1)=-1$

clearing for $m_(1)$

$m_(1)=(-1)/(-4) \nm_(1)=(1)/(4)$

thus, the new perpendicular line must have the form:

$y=m_(1)x+c\ny=(1)/(4)x+c$

where the y-intecept $c$ can be any number, some examples are:

$y=(1)/(4)x+3\ny=(1)/(4)x-8$

and so on, the important thing to be a perpendicular line is that the slopes are related to the equation $m*m_(1)=-1$ .

What is this simbol
$√(?)$

Answers

That symbol is radical sign

Square root of a number

30 girls who tried out for the lacrosse team Euclid middle school 12 were selected of the 40 boys Who tried out 16 were selected are the ratios of the number of students on the team to the number of students trying out the same for both boys and girls

Answers

Answer:

Yes, the ratio of the number of students on the team to the number of students trying out is same for both girls and boys.

The ratio is: 2:5

Step-by-step explanation:

It is given that:

Out of 30 girls who tried out for the lacrosse team Euclid middle school 12 were selected.

This means that the ratio of the number of girls on the team to the number of girls trying out is:

12/30=2/5

Also, 40 boys Who tried out 16 were selected .

This means that the ratio of the number of boys on the team to the number of boys trying out is:

16/40=2/5

Hence, we get that the ratio is same for boys and girls i.e. 2:5

12/30=2/5
16/40=2/5
The ratio is the same because they both simplify to 2/5

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