Answer:
(12, 48 )
Step-by-step explanation:
Given the 2 equations
y = 5x - 12 → (1)
y = 3x + 12 → (2)
Substitute y = 5x - 12 into (2)
5x - 12 = 3x + 12 ( subtract 3x from both sides )
2x - 12 = 12 ( add 12 to both sides )
2x = 24 ( divide both sides by 2 )
x = 12
Substitute x = 12 into either of the 2 equations and evaluate for y
Substituting into (2)
y = 3(12) + 12 = 36 + 12 = 48
solution is (12, 48 )
1) surface of a rectangular prism=2(length x width)+2(length x height)+2(width x height)
Therefore:
148 cm²=2(5 cm x 4 cm)+2(5 cm x h)+2(4 cm x h)=
148 cm²=40 cm²+10 cm h+8 cm h
18 cm h=148 cm²-40 cm²
18 cm h=108 cm²
h=108 cm² / 18 cm=6 cm.
answer: height=6 cm
2)
Volume of a rectangular prism= length x width x height
therefore:
34 cm³=(1.7 cm)(0.5 cm) h
0.85 cm² h=34 cm³
h=34 cm³/0.85 cm²
h=40 cm.
answer: height=40 cm
3)
volume of a cylinder: πr²h
therefore.
118.79 ft³=πr²(5 ft)
r=√(118.79 ft³/5π ft)≈2.75 ft
answer: radius=2.75 ft
4)
Surface area of the pyramid with square base=4(A side)+A base
A side=(1/2)(8ft)(12 ft)=48 ft²
A base=(8 ft)(8 ft)=64 ft²
surface area=4(48 ft²)+64 ft²=256 ft²
Answer: the surface area of this pyramid would be 256 ft².
5)
surface of a cone=πrs+πr²
therefore:
radius=diameter/2=6.2 ft/2=3.1 ft
63.3 ft²=π(3.1 ft) s+π(3.1 ft)²
3.1π ft s=33.109 ft²
s=33.109 ft² /3.1π ft
s≈3.4 ft
Answer: the slant height would be 3.4 ft.
6)
volume of a square pyramid=(area of base x heigth)/3
therefore:
area of base=(6 ft)(6 ft)=36 ft²
126.97 ft³=36 ft² h /3
h=126.97 ft³/12 ft²=10.58 ft
answer: the height would be 10.58 ft.
7)
volume of a cone =(base x height)/3
base of a cone=πr²
therefore:
199.23 cm³=πr²(9 cm)/3
r=√(199.23 cm³ / 3π cm)≈4.6 cm
answer: the radius would be 4.6 cm.
Answer:
the second one
Step-by-step explanation:
i did it in my head and double checked :)
Answer:
True expressions:
- The constants, -3 and -8, are like terms.
- The terms 3 p and p are like terms.
- The terms in the expression are p squared, negative 3, 3 p, negative 8, p, p cubed.
- The expression contains six terms.
- Like terms have the same variables raised to the same powers.
Step-by-step explanation:
The expression is:
p² - 3 + 3p - 8 + p + p³
False expressions:
- The terms p squared, 3 p, p, and p cubed have variables, so they are like terms. (They don't have the same exponents)
- The terms p squared and p cubed are like terms. (They don't have the same exponents)
- The expression contains seven terms. (It contains 6 terms)
You would first need to find a common denominator for 3/8 and 1/3 the common denominator would be 24 because 8 times three is 24 and 3 times 8 is 24. After you find your common denominator your fraction becomes 9/24 + 8/24. This gives you 17/24.
