Answer:
The desired equation is y = (-8/3)x + 26/3.
Step-by-step explanation:
Moving from (1,6) to (4, -2) involves an increase of 3 in x and a decrease of 8 in y. Thus, the slope of the line thru these two points is m = rise / run = -8/3.
Using the slope-intercept form of the eq'n of a straight line and inserting the data given (slope = m = -8/3, x = 4, y = -2), we get:
y = mx + b => -2 = (-8/3)(4) + b, or -2 = -32/3 + b
Multiply all terms by 3 to clear out the fraction:
-6 = -32 + 3b.
Then 26 = 3b, and b = 26/3.
The desired equation is y = (-8/3)x + 26/3.
Answer:
x=5.2
Step-by-step explanation:
8x−14=7.7x+3x
Step 1: Simplify both sides of the equation.
8x−14=7.7x+3x
8x+−14=7.7x+3x
8x−14=(7.7x+3x)(Combine Like Terms)
8x−14=10.7x
8x−14=10.7x
Step 2: Subtract 10.7x from both sides.
8x−14−10.7x=10.7x−10.7x
−2.7x−14=0
Step 3: Add 14 to both sides.
−2.7x−14+14=0+14
−2.7x=14
Step 4: Divide both sides by -2.7.
−2.7x
/−2.7 =
14
/−2.7
x=−5.185185 or 5.2
Answer: $48
Step-by-step explanation:
From the question, we are told that in Michigan, the sales tax rate is 6% and that an item costs $50.88 including tax.
Let the cost of the item before tax be x. This means that x plus 6% of x equals to $50.88. This can be mathematically expressed as:
x + (6% of x) = $50.88
x + (6/100 × x) = $50.88
x + (0.06 × x) = $50.88
x + 0.06x = $50.88
1.06x = $50.88
When then divide by the coefficient of x
1.06x/1.06 = #50.88/1.06
x = $48
The price before the tax is $48
Answer:
c = 9/16
Step-by-step explanation:
<h3>step1</h3>
(a-b)²
a² - 2ab + b²
here a = x
b = ?
so
x² - (2)(x)(?) + ?²
Now we can see that -(2x)? = -3x/2
-2x? = -3x/2
cancel -x on both sides
2? = 3/2
? = 3/2 * (2)
? = 3/4
so b = 3/4
<h3>step2</h3>
(x² - 3x + 9/16) = (x-3/4)²
so from the expression we can see that C = 9/16
Answer:
If the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder, then its volume is
Use following formulas to determine volumes of sphere and cylinder:
wher R is sphere's radius, r - radius of cylinder's base and h - height of cylinder.
Then
Answer 1: correct choice is C.
If both the sphere and the cylinder are dilated by a scale factor of 2, then all dimensions of the sphere and the cylinder are dilated by a scale factor of 2. So
R'=2R, r'=2r, h'=2h.
Write the new fask volume:
Then
Answer 2: correct choice is D.
Step-by-step explanation:
