What is the area, in square centimeters, of the isosceles trapezoid below?

In my carpenter shop I make 3 legged stools and 4 legged chairs. I looked at my days output and counted 55 legs and 16 seats. Ho

Stells [14]

$x-number\ of\ stools\\y-number\ of\ chairs\\\\ \left \{ {{y+x=16} \atop {3x+4y=55}} \right. \\\\From\ first\ equation:\\\\y=16-x\\\\Substract\ to\ second\ equation:\\\\3x+4(16-x)=55\\3x+64-4x=55\\3x-4x=55-64\\-x=-9\\x=9\\\\y=16-9=7\\\\ \left \{ {{y=7} \atop {x=9}} \right.$

7 0

3 years ago

What is the equation of a circle centered at the origin with radius 20?

Colt1911 [192]

We know that
the equation of a circle is
(x-h)²+(y-k)²=r²
where
(h,k)-----> is the center
r--------> is the radius

is the center is the point (0,0) and radius r=20
then
(h,k) is (0,0)

(x-0)²+(y-0)²=20²---------> (x)²+(y)²=400

the answer is
the option D.) x2 + y2 = 400

3 0

3 years ago

What is the domain of the function shown in the table?

ASHA 777 [7]

Answer:

{ -2,-1,0,1}

Step-by-step explanation:

The domain are the values for the input

Domain { -2,-1,0,1}

3 0

2 years ago

Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options.

Elanso [62]

Answer:

2 and 5

Step-by-step explanation:

The slope-intercept form of a line is y=mx-b where m is slope and b is y-intercept.

The point-slope form of a line is y-y1=m(x-x1) where m is the slope and (x1,y1) is a point on the line.

The standard form a line is ax+by=c.

So anyways parallel lines have the same slope.

So if we are looking for a line parallel to 3x-4y=7 then we need to know the slope of this line so we can find the slope of our parallel line.

3x-4y=7

Goal: Put into slope-intercept form

3x-4y=7

Subtract 3x on both sides:

-4y=-3x+7

Divide both sides by -4:

$y=\frac{-3}{-4}x+\frac{7}{-4}$

Simplify:

$y=\frac{3}{4}x+\frac{-7}{4}$

So the slope of this line is 3/4. So our line that is parallel to this one will have this same slope.

So we know our line should be in the form of $y=\frac{3}{4}x+b$ .

To find b we will use the point that is suppose to be on our new line here which is (x,y)=(-4,-2).

So plugging this in to solve for b now:

$-2=\frac{3}{4}(-4)+b$

$-2=-3+b$

$3-2=b$

$b=1$

so the equation of our line in slope-intercept form is $y=\frac{3}{4}x+1$

So that isn't option 1 because the slope is different. That was the only option that was in slope-intercept form.

The standard form of a line is ax+by=c and we have 2 options that look like that.

So let's rearrange the line that we just found into that form.

$y=\frac{3}{4}x+1$

Clear the fractions because we only want integer coefficients by multiplying both sides by 4.

This gives us:

$4y=3x+4$

Subtract 3x on both sides:

$-3x+4y=4$

I don't see this option either.

Multiply both sides by -1:

$3x-4y=-4$

I do see this as a option. So far the only option that works is 2.

Let's look at point slope form now.

We had the point that our line went through was (x1,y1)=(-4,-2) and the slope,m, was 3/4 (we found this earlier).

y-y1=m(x-x1)

Plug in like so:

y-(-2)=3/4(x-(-4))

y+2=3/4 (x+4)

So option 5 looks good too.

7 0

3 years ago

Read 2 more answers

if I have a question on my work that says solve the equation how could I solve this one, (7,-6): m = -4 ..... im not really sure

Nimfa-mama [501]

Answer:

y= -4x+22

Step-by-step explanation:

slope= -4

-6=-4(7)+b

-4x7=-28

-6=-28+b

28-6=22

so the equation would be y= -4x+22

b=y-intercept

mx=slope multiplied by x

6 0

3 years ago