Answer:
x=4
Step-by-step explanation:
-7x=-28
-7 -7
x=4
Divide both sides by -7. A negative divided by a negative will give you a positive. So the answer would be x=4.
Answer:
x=4
you divide both sides by -7 to get the x by itself. -28 divided by -7 is 4.
Question 3 options:
A)
29.32 and 3.97
B)
32.27 and 4.57
C)
27.48 and 5.20
D)
No Solution
The closest choice is ...
C) 27.48 and 5.20
Using the equation ...
y = ax² + bx + c
You can substitute the first three points to get linear equations in a, b, and c.
10 = a(-3)² +b(-3) +c = 9a -3b +c
4 = a(0)² + b(0) +c = c
-1 = a(3)² + b(3) +c = 9a +3b +c
The second equation tells us c=4. Subtracting the first equation from the last, we get ...
(9a +3b +c) -(9a -3b +c) = (-1) -(10)
6b = -11
b = -11/6
Then we can find "a" from the first equation:
10 = 9a -3(-11/6) +4
1/2 = 9a . . . . subtract 19/2
1/18 = a . . . . . divide by 9
The model is ...
y = (1/18)x² -(11/6)x +4 . . . . . . . . [call this "model A"]
y = (x² -33x +72)/18
Solving this for y = -4, we have ...
-4 = (x² -33x +72)/18
x² -33x +144 = 0 . . . . . . multiply by 18, add 72
(x -16.5)² -128.25 = 0 . . . . put in vertex form
x = 16.5 ±√128.25 ≈ {5.17525, 27.8248}
___
The closest values to these among the choices offered are those of choice C. It appears that the coefficients of model A were rounded to 3 decimal places (or so) before the predicted x-values were computed.
Answer:
Step-by-step explanation:
The original price of the wind chimes at the home improvement store is $w.
A customer signed up for a free membership card and received a 5% discount off the price. The value of the discount is
5/100 × w = 0.05w
The discounted price would be
w - 0.05w = 0.95w
Sales tax of 6% was applied after the discount. The amount of sales tax applied would be
6/100 × 0.95w = 0.057w
The algebraic expression to represent the final price of the wind chime is
0.95w + 0.057w
= 1.007w
How do you identify the center and radius of a circle?
How do you define the radian measure of an angle?
How are arc length and area of a sector related to proportionality?
Answer:
How do you derive the equation of a circle?
you can reverse the circle formula
How do you identify the center and radius of a circle?
You can identify the center because it is the middle of the circle and the radius can be draw from the center to the round part.
How do you define the radian measure of an angle?
it is the ratio of the length of the arc the angle forms÷the radius of the circle
How are arc length and area of a sector related to proportionality?
sector x radian
area = (r^2 x)/2
arc length = r x
they are not propotional
because Area / arc length = r/2 , (it's not a constant)
High Hopes
Barrii
Answer and Step-by-step explanation:
Let x and y be two positive integers and their sum is 14:
X + y = 14
And the sum of square of this number is:
f = x2 + y2
= x2+ (14 – x)2
Differentiate with respect to x, we get:
F’(x) = [ x2 + (14 – x)2]’ = 0
2x + 2(14-x)(-1) = 0
2x +( 28 – 2x)(-1) = 0
2x – 28 +2x = 0
2x + 2x = 28
4x = 28
X = 7
Hence, y = 14 – x = 14 -7 = 7
Now taking second derivative test:
F”(x) > 0
For x = y = 7,f reaches its maximum value:
(7)2 + (7)2 = 49 + 49
= 98
F at endpoints x Є [ 0, 14]
F(0) = 02 + (14 – 0)2
= 196
F(14) = (14)2 + (14 – 14)2
= 196
Hence the sum of squares of these numbers is minimum when x = y = 7
And maximum when numbers are 0 and 14.
To find two positive integers such that their sum is 14, and the sum of their squares is minimized, we need to consider all possible pairs of positive integers and calculate their sums of squares. The pair (6, 8) has the minimum sum of squares of 100. To find two positive integers such that their sum is 14, and the sum of their squares is maximized, the pairs (1, 13) and (2, 12) both have the maximum sum of squares of 170. Since we need to find two positive integers, the pair (1, 13) is the answer.
To find two positive integers such that their sum is 14 and the sum of their squares is minimized, we need to consider all possible pairs of positive integers that add up to 14 and calculate their sums of squares. Let's list all the pairs:
From the list, we can see that the pair (6, 8) has the minimum sum of squares, which is 100.
Similarly, to find two positive integers such that their sum is 14 and the sum of their squares is maximized, we need to again consider all possible pairs and calculate their sums of squares. Let's list the pairs:
From the list, we can see that the pair (1, 13) and the pair (2, 12) both have the maximum sum of squares, which is 170. Since we need to find two positive integers, the pair (1, 13) is the answer.
#SPJ11
What percent of the carbon-14 had been lost from the pollen?
(half-life of carbon-14 = 5730)
Answer:4 34/100
Step-by-step explanation:
31=100%
14=?
14*100/31
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