Answer:
m∠J = 45° , m∠I = 45° and m∠M = 90°
And the ΔJIM is an isosceles right angled triangle.
Step-by-step explanation:
(a). In ΔJIM,
∠J = 2x + 15,
∠I = 5x - 30, and
∠M = 6x
Now, using angle sum property of a triangle that sum of all the angles in a triangle is 180°
⇒ ∠J + ∠I + ∠M = 180°
⇒ 2x + 15 + 5x - 30 + 6x = 180°
⇒ 13x -15 = 180°
⇒ 13x = 195
⇒ x = 15
Therefore, m∠J = 45° , ∠I = 45° and m ∠M = 90°
(b). Now, ΔJIM is a right angled triangle right angled at M.
Also, ∠J = ∠I = 45°
So, JM = IM ( because in a triangle sides opposite to equal angles are equal)
So, ΔJIM is an isosceles triangle because its two sides are equal.
Hence, ΔJIM is a right angled isosceles triangle right angled at M.
Because of the added insulation to control the temperature inside,the cost of heating and cooling went down
Answer:
33 copies were paperback and 12 were hardcover.
Step-by-step explanation:
Let h represent the number of hardcover copies and p represent the number of paperback copies.
We know that the total number of copies was 45; this gives us the equation
h+p = 45
We know that each hardcover copy is 7 ounces; this gives us the expression 7h.
We also know that each paperback copy is 5 ounces; this gives us the expression 5p.
We know that the total weight was 249 ounces; this gives us the equation
7h+5p = 249
Together we have the system

We will use elimination to solve this. First we will make the coefficients of the variable p the same; to do this, we will multiply the top equation by 5:

To eliminate p, we will subtract the equations:

Divide both sides by -2:
-2h/-2 = -24/-2
h = 12
There were 12 hardcover copies sold.
Substitute this into our first equation:
12+p=45
Subtract 12 from each side:
12+p-12 = 45-12
p = 33
There were 33 paperback copies sold.
Answer:
212
Step-by-step explanation:
volume of new figure = sum of the two individual figures
volume of one cuboid=l*b*h
volume of first cuboid=92
volume of second cuboid=120
sum of two figures=212
hope this helps
plzz mark me brainliest