hectictar

y   =   3x + 10

3x + 2y   =   16

                                       Since  y = 3x + 10  we can replace  y  with  3x + 10

3x + 2(3x + 10)  =  16

                                       Distribute  2  to the terms in parenthesees

3x  +  6x + 20   =   16

                                       Combine  3x  and  6x  to get  9x

9x  +  20   =   16

                              Subtract  20  from both sides of the equation

9x   =   -4

                              Divide both sides of the equation by  9

x   =   -4/9

Now that we know  x  we can plug this back into the first equation to find  y

y   =   3x + 10   =   3(-4/9) + 10   =   -4/3 + 10   =   26/3

So the solution to the system of equations is  (-4/9, 26/3)

The most he can spend on the album is $12.93

Is this a multiple choice question? If so, what are the choices?

The sum of the prices of the albums must be less than or equal to $25

m + 9.99 + 1.29 + 0.79   ≤   25

                                                   Simplify the left side of the inequality

m + 12.07   ≤   25

                                                   Subtract  12.07  from both sides of the inequality

m  ≤   25 - 12.07

m  ≤  12.93

f(1) = 5

f(2) = 3

f(3) = 1

Let  y = f(f(x))

When  x = 2,    y  =  f(f(2))  =  f(3)  =  1

When  x = 3,    y  =  f(f(3))  =  f(1)  =  5

So the points  (2, 1)  and  (3, 5)  must be on the graph of  y = f(f(x))

ab + cd   =   2 * 1  +  3 * 5   =   2 + 15   =   17

volume  =  area of base * height

First let's work on finding the area of the base. The shape of the base can be broken up into two rectangles, one with length 6 cm and width 4 cm, and the other with length 14 cm and width 12 cm. So the area of the base is the sum of the areas of these two recangles.

area of base   =   (6 cm)(4 cm)  +  (14 cm)(12 cm)

area of base   =   24 cm²  +  168 cm²

area of base   =   192 cm²

Now that we know the area of the base, we can find the volume

volume   =   area of base * height

volume   =   ( 192 cm² )( 2 cm )

volume   =   384  cm³

First we can draw AC to create right triangle ACE

Since AB = 10 and CD bisects AB at the point E, we can see that AE = 5

Since CD = 10 the radius of the circle is 10, which means AC = 10

Now we have a right triangle where two of the sides are known.

We can use the Pythagorean theorem to find the length of the unknown side.

AE² + CE²  =  AC²

5²  +  CE²   =   10²

CE²   =   10²  -  5²

CE²   =   100 - 25

CE²   =   75

CE   =   √[ 75 ]

CE   =   5√3

radius of circle  =  distance between  (-3, 4)  and  (9, -3)

radius of circle   =   \(\sqrt{(-3-9)^2+(4--3)^2}\)

radius of circle   =   \(\sqrt{193}\)

area of circle   =   pi * ( radius )2

area of circle   =   \(\pi\cdot(\sqrt{193})^2\)

area of circle   =   \(193\pi\)

Here's a diagram with all the angles labeled with letters so that it is easier to talk about.

9)

m∠E   =   55°   because it is the other base angle of an isosceles triangle.

m∠D   =   180°  -  55°  -  55°   =   70°   because the sum of the interior angles in a triangle is  180°

m∠C   =   m∠D   =   70°     because they are vertical angles and vertical angles are congruent.

m∠B   =   m∠C   =   70°     because they are base angles of an isosceles triangle.

m∠A   =   180° - 70° - 70°   =   40°

And so...back to the main question...

m∠2  =  m∠A   =   40°       And so...

40  =   7x - 2

Solve the above equation for  x  to get the final answer.

10)

m∠I   =   76°     because they are base angles of an isosceles triangle.

m∠H  =   180° - 76° - 76°   =   28°       because the sum of the interior angles in a triangle is  180°

m∠G  =  90° - m∠H   =   90° - 28°   =   62°       because the sum of  ∠G  and  ∠H  is  90°

m∠F   =   m∠G   =   62°       because they are base angles of an isosceles triangle

And so....back to the main question...

m∠2   =   m∠F   =   62°

62   =   x + 74

x   =   -12

That is really cool!!

One way to color in something is to do an inequality like this:

\(x^{2}+\left(y-20\right)^{2}\le60\left\{y\ge21.8\right\}\)

(Changed the equal sign to a  ≤  for your hat  )

area   =   area of rectangle  +  area of square

area, in square meters   =   12 * 6   +   4 * 4

area, in square meters   =   72  +  16

area, in square meters   =   88

perimeter, in meters   =   12 + 6 + 4 + 4 + 4 + 4 + 4 + 6

perimeter, in meters   =   44