Answer:
-5 < x < 9
Step-by-step explanation:
By Hinge theorem,
"If two sides of a triangle are congruent to the two sides of another triangle, and the included angle of one triangle is larger than the included angle of the second, then the 3rd side of triangle one will be larger than the third side of the second"
23 > 21
Therefore, 42° > (3x + 15)°
42° - 15° > 3x
27 > 3x
9 > x
And (3x + 15) > 0
3x > -15
x > -5
Therefore, range for x will be,
-5 < x < 9
Answer:
1) 15a - 15c + 3
2) -7n + 31 + 13m + 7p or 13m - 7n + 7p + 31
3) 44x + 6y + 3
4) 9m - 6n + 23
Step-by-step explanation:
1. Add like terms. 6a + 9a=15a. -8c - 7c=-15c
2. Add like terms. You can rearrange them in descending order based off of exponents and variables.
3. Multiply what's in parentheses first (distribute the 6). It should end up being (6y + 42x). Then you add like terms and put in descending order.
4. Distribute the (-3) to what in the parentheses. It should end up being (-6n + 15 - 3m). Then you add like terms and put the expression in descending order.
Answer:
Step-by-step explanation:
Because CB = 6 cm, we can find CD
Use Triangle CDB.
<BCD = <BCA - <ACD
<BCD = ?
<BCA = 90
<ACD = 60
<BCD = 90 - 60
<BCD = 30
Cos 30 = CD / CB
CD = Cos(30) * BC
CD = 5.196 cm
<A = 90 - ACD
<ACD = 60
<A = 90 - 60
<A = 30
Sin(<A) = CB / AB
AB = CB / sin(<A)
AB = 6 / 0.5
AB = 12
Area =1/2 CD * AB
Area = 1/2 * 5.196 * 12
Area = 31.18
Answer:
M = 1170 g
Step-by-step explanation:
Mass = density × volume
M = p x v
M = 78 x 15
M = 1170 g
First, we need to find the least common denominator. The LCD for 7/8 and 1/3 would be 24. 7*3/8*3 = 21/24. 1*8/3*8 = 8/24. So, how many 8/24 will go into 21/24? 8 goes into 21 two times, and we are left with a remainder of 5. The answer is: Karen can make 2 and 1/24 servings of 1/3 cups of ice cream.
