The least. Common multiple for 8 19 and 23

Vilka [71]

Comment
|First of all, the triangles are equal by ASA the way the diagram has been marked.

B and E are both right angles.
Side BC = Side DE
<BCA =< EDA

So triangle BCA = triangle EDA

Now to the letters.
x = y - 1 Add 1 to both sides.
x + 1 = y (1)
3x - 2 = 2y + 1 Subtract 1 from both sides.
3x -2 - 1 = 2y
3x - 3 = 2y Divide by 2
3x/2 - 3/2 = 2y/2
1.5x - 1.5 = y (2)

Step One
Since (1) and (2) both have y isolated on their respective right sides, they can be equated.

1.5x - 1.5 = x + 1 Take an x from both sides.
0.5x - 1.5 = x - x + 1
0.5x - 1.5 = 1 Add 1.5 to both sides.
0.5x = 1 + 1.5
0.5x = 2.5 Divide 0.5 on both sides.
0.5x/0.5 = 2.5/0.5

x = 5

Now we need a y value.
x = y - 1
5 = y - 1 Add 1 to both sides.
5 + 1 = y - 1 + 1
6 = y

So the 2 sides and the 2 angles are equal when
x = 5
y = 6

C Answer <<<<<<

4 0

3 years ago

Cheeseburgers to go has advertised for counter help. If you take the job, you will be working 18 hours a week for $75.20 per wee

julsineya [31]

Divide the weekly amount by the number of hours worked:

75.20 / 18 = 4.177

Rounded to the nearest cent = $4.18 per hour.

4 0

3 years ago

Read 2 more answers

Find a and b if the point p(6,0) and Q(3,2) lie on the graph of ax+ by=12

tiny-mole [99]

to get the equation of any straight line we only need two points off of it, hmmm let's use P and Q here and then let's set the equation in standard form, that is

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$(\stackrel{x_1}{6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{6}}}\implies \cfrac{2}{-3}\implies -\cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{6})$

$\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-0)~~ = ~~3\left( -\cfrac{2}{3}(x-6) \right)}\implies 3y=-2(x-6) \\\\\\ 3y=-2x+12 \implies \stackrel{a}{2} x+\stackrel{b}{3} y=12$

5 0

2 years ago

Which points lie on the line whose equation is 8x - 2y + 7 = -9? Select all that apply.

Anestetic [448]

Answer:

A.(-2, 0)

C. (-1.4)

Step-by-step explanation:

we know that

If a point lie on the line, then the point must satisfy the equation of the line (makes the equation true)

we have

$8x-2y+7=-9$

subtract 7 both sides

$8x-2y=-9-7$

$8x-2y=-16$

divide by 2 both sides

$4x-y=-8$

Substitute the value of x and the value of y of each point in the linear equation and analyze the result

Verify each point

case A) we have

(-2, 0)

For x=-2, y=0

substitute

$4(-2)-(0)=-8$

$-8=-8$ ---> is true

so

the point lie on the line

case B) we have

(1, 3)

For x=1, y=3

substitute

$4(1)-(3)=-8$

$1=-8$ ---> is not true

so

the point not lie on the line

case C) we have

(-1, 4)

For x=-1, y=4

substitute

$4(-1)-(4)=-8$

$-8=-8$ ---> is true

so

the point lie on the line

case D) we have

(1, -4)

For x=1, y=-4

substitute

$4(1)-(-4)=-8$

$8=-8$ ---> is not true

so

the point not lie on the line

case E) we have

(0, -1)

For x=0, y=-1

substitute

$4(0)-(-1)=-8$

$1=-8$ ---> is not true

so

the point not lie on the line

7 0

3 years ago

An artist creates a cone-shaped sculpture for an art exhibit. If the sculpture is 5 feet long and has a base with a circumferen

Semenov [28]

the volume of the sculpture is $Volume = 64.11ft^3$ .

Step-by-step explanation:

Here we have , An artist creates a cone-shaped sculpture for an art exhibit. If the sculpture is 5 feet long and has a base with a circumference of 21.980 feet, We need to find the volume of the sculpture . Let's find out:

We know that

⇒ $Circumference = 2\pi r$