Answer: (3, -2)
Step-by-step explanation: graphed both of em on desmos and thats the intersection.
Answer:
Vertical intercepts: (-2,pi/2) and (-10,pi/2)
Horizontal intercepts: (4,0) and (-4,0)
Step-by-step explanation:
I took the test and got it right.
Answer:
6.75
Step-by-step explanation:
h=hat, s=scarf
5h + 1s = $47 (equation 1)
2h + 2s = $40 (equation 2)
multiply equation 1 by 2 , we get: 10h + 2s = $94 (equation 3)
equation 3 minus equation 2, we get:
8h = $54 ⇒ h = $6.75 ⇔ 1 hat cost $6.75
substitute h = $6.75 into equation 2 to find s,
2($6.75) + 2s = $40
$13.5 + 2s = $40
2s = $26.5
s = $13.25 ⇔ 1 scarf cost $13.25
Answer:
A) 3 in
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Geometry</u>
- Surface Area of a Sphere: SA = 4πr²
- Diameter: d = 2r
Step-by-step explanation:
<u>Step 1: Define</u>
SA = 23 in²
<u>Step 2: Find </u><em><u>r</u></em>
- Substitute [SAS]: 23 in² = 4πr²
- Isolate <em>r </em>term: 23 in²/(4π) = r²
- Isolate <em>r</em>: √[23 in²/(4π)] = r
- Rewrite: r = √[23 in²/(4π)]
- Evaluate: r = 1.35288 in
<u>Step 3: Find </u><em><u>d</u></em>
- Substitute [D]: d = 2(1.35288 in)
- Multiply: d = 2.70576 in
- Round: d ≈ 3 in
Answer:
<u><em>(-1,1)</em></u>
Step-by-step explanation:
We can solve this by either graphing and finding ther point the lines intersect, or mathematically, I'll do both.
<u>Graphing:</u>
<u>Mathematically:</u>
−2x + 4y = 6
y = 2x + 3
See the attached graph. The lines intersect at (-1,1)
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I'll rearrange the first equation (to make it easier for me):
−2x + 4y = 6
4y = 2x + 6
y = (1/2)x + 1.5
Now lets substitute the second equation into the first so that we can eliminate y:
y = 2x + 3
[(1/2)x + 1.5] = 2x + 3
- (3/2)x = (3/2)
x = -1
If x = -1:
y = 2(-1) + 3
y = 1
The solution is x = -1 and y = 1, or (-1,1)
=================
Both approaches give us (-1,1), the solution to the system of equations. It is the only point that satisfies both equations.
