solve the system of equations
-6y +11x=-36
-4y+7x=-24
–6y + 11x = –36 multiply both sides x4 –24 + 44x = –144
–4y + 7x = –24 multiply both sides x6 –24 + 42x = –144
subtract 2x = 0
x = 0
–6y + 11x = –36
–6y +(11)(0) = –36
–6y = –36
y = 6
check answer
–4y + 7x = –24
Does –4(6) + 7(0) = –24 ?
–24 + 0 = –24 True
.
Brianna spends a total of $24.25 on 3 drinks and 4 bags of popcorn. Chloe spends a total of $37.00 on 9 drinks and 1 bag of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations determine and state the price of a bag of popcorn to the nearest cent.
3D + 4P = 24.25 mult both sides x3 9D + 12P = 72.75
9D + P = 37.00 9D + P = 37.00
subtract 11P = 35.75
P = 3.25
A rectangular garden has an area of 24 square meters. The width is 8 meters less than twice the length. Find the dimensions of the garden
A = length x width
24 = L x (2L – 8)
2L2 – 8L = 24
2L2 – 8L – 24 = 0
(2L + 4)(L – 6) = 0
L = –2 disregard neg
L = 6
W = (2 • 6) – 8
W = 4
In a circle, a 90° sector has area 64π ft2. What is the radius of the circle?
Entire circle = (4)(64 π) = 256 π
A = π r2 = 256 π
divide both sides by π r2 = 256
r = 16
If Celestia can type 50 words every five seconds,
how many seconds does it take to type 18 words?
( 50 wd ) / (5 sec) = 10 wd/sec
(18 wd) / (10 wd/sec) = 1.8 sec
C is the center of the circle. Find arc DGE.
A circle is 360o all the way around.
So, arc DGE = 360o – 115o = 245o.
The diameter of a sphere is 12cm. What is the volume of the sphere, in cubic centimeters?Use 3.14 for π\piπ . Round your answer to the nearest tenth.
Volume sphere = (4/3) π r3
V = (4/3) (3.14) (63)
V = (4/3) (3.14) (216)
V = 904.32 rounds to 904.3
