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Doss [256]
2 years ago
10

Solve the equation. Graph the solution(s) if possible. ∣x−3∣+4=9

Mathematics
1 answer:
Mazyrski [523]2 years ago
3 0

Answer:

x=8

x=-2

Step-by-step explanation:

∣x−3∣+4=9

= ∣x−3∣=5

<u>Positive term: (x-3)</u>

  (x-3) = 5

Rearrange and Add up

  x = 8

<u>Negative term: -(x-3)</u>

Multiply

     -x+3 = 5  

Rearrange and Add up

     -x = 2  

Multiply both sides by (-1)

     x = -2

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Simplify the product using the distributive property. (-4h +2)(3h +7)
Alekssandra [29.7K]

Answer:

  A.  -12h² - 22h + 14

Step-by-step explanation:

(-4h +2)(3h +7) = -4h(3h +7) +2(3h +7) . . . . . . . (a +b)c = ac +bc

  = (-4h)(3h) + (-4h)(7) + (2)(3h) + (2)(7) . . . . . . . a(b +c) = ab +ac . . . (twice)

  = -12h² -28h +6h +14

  = -12h² -22h +14 . . . . . . . . collect terms

3 0
3 years ago
Can a triangle be drawn with side lengths 8.4 inches, 9.2 inches, and 17 inches?
sasho [114]

Answer:

yes

Step-by-step explanation:

based on the triangle inequality theorem, add the two smallest numbers together (8.4,9.2) to get 17.6 which is bigger than 17

3 0
3 years ago
How can properties of operations help to generate equivalent expressions that can be used in solving problems ?
svet-max [94.6K]
I’m not the best at math, but ⬇️

For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y
6 0
4 years ago
: A new bear population that begins with 150 bears in 2000 decreases at a rate of 20% per year.
d1i1m1o1n [39]

Answer:

2 bears in 2020.

Step-by-step explanation:

We have been given that a new bear population that begins with 150 bears in 2000 decreases at a rate of 20% per year.

We will use exponential decay formula to solve our given problem as:

y=a\cdot (1-r)^x, where,

y = Final quantity,

a = Initial value,

r = Decay rate in decimal form,

x = Time

20\%=\frac{20}{100}=0.20    

Upon substituting our given values in above formula, we will get:

y=150(1-0.20)^x

y=150(0.80)^x, where x corresponds to year 2000.

To find the population in 2020, we will substitute x=20 in our equation as:

y=150(0.80)^{20}

y=150(0.011529215046)

y=1.7293822569    

y\approx 2

Therefore, 2 bears are there predicted to be in 2020.

Since population is decreasing so population is best described as exponential decay.

8 0
3 years ago
If f(1) = 10 and f '(x) ≥ 3 for 1 ≤ x ≤ 6, how small can f(6) possibly be?
Natalka [10]

Answer:

f'( x ) =  \frac{f(b) - f(a)}{b - a}  \\  = \frac{f(6) -f(a)}{6 - 1} \\  3\leqslant \frac{f(6) - 10}{5} \\  15\leqslant f(6) - 10 \\ f(6) \geqslant 15 + 10 \\ f(6) \geqslant 25

6 0
3 years ago
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