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vampirchik [111]
3 years ago
6

Given 2x+7=27 and 3x+1=28, does 2x+7=3x+1? Explain

Mathematics
2 answers:
serious [3.7K]3 years ago
7 0
No, in 2x+7=27, x=10. In 3x+1=28 x =9, so it doesn't.
GarryVolchara [31]3 years ago
5 0
2x+7=27 is x=10 in 3x+1=28 the answer is x=9 the answers are the the same
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Enter the correct answer in the box. What are the solutions of this quadratic equation? X^2+164=16x Substitute the values of a a
saw5 [17]

Answer:

x = 8 - 10i or 8 + 10i

Step-by-step explanation:

Our equation is given as:

x² + 164 = 16x

x² - 16x + 164 = 0

We solve using Almighty formula

x = -b ± √b² - 4ac/2a

Where : ax² + bx + c

For our Equation

a = 1, b = -16, c = 164

Hence,

x = -(-16) ± √-16² - 4 × 1 × 164/2 × 1

x = 16 ± √256 - 656/2

x = 16 ± √-400/2

Finding the roots

x = 16/2 ± √-400/2

x = 8 ± 20i/2

x = 8 ± 10i

Therefore, the value of x

= 8 - 10i or 8 + 10i

4 0
2 years ago
Suppose `h\left(t\right)=-5t^{2}+10t+3`is an expression giving the height of a diver above the water (in meters), t seconds afte
prisoha [69]

Answer:

Step-by-step explanation:

a) The height of the springboard above the water should be h(0) : Read, the height at t = 0

h(0) = -5(0) + 10(0) + 3

h(0) = 0 + 0 + 3

h(0) = 3

a) 3 meters

b)  The time it takes the diver to hit water should be, the positive 0 solution for t.  Remember, in a quadratic equation,  there are two values for t where a parabola crosses the horizontal axis, which in this case would be t.  Just by looking at the function, h(t) = -5t2 + 10t + 3 , one should be able to see that it cannot be factored easily, so it requires the Quadratic Formula to find the zeros ; x = -b ±√(b2-4ac)  / 2a

Substitute t for x, and use the coefficients for a, b, c:

t  =  (-10 ± √((102 - 4(-5)(3)))/2(-5)

t = (-10 ±√(100 + 60))/-10

t = (-10 ±√160)/-10) ; Now factor the 160 to simplify:

t = (-10 ±√(10*16))/-10

t = (-10 ±4√10)/-10 ; Factor out leading coefficient of -2 from the numerator:

t = -2(5 ± 2√10)/-10

t = (5 ± 2√10)/5

Using a calculator to find the zeros, and disregarding the negative zero (because t starts at 0):

t ≈ 2.265

b) approx. 2.265 seconds for diver to hit water.

c) To find this, set the function equal to 3 to find what other value for t would be equal to 3 (we know one is 0).

-5tt + 10t + 3 = 3

-5t2 + 10t = 0 ; factor out t

t(-5t + 10) = 0

We know t = 0:

We also know that -5t + 10 = 0

-5t = -10

t = 2

c) 2 seconds. This is the time that diver would equal height of t=0 which is where he started, and where he equals the height of the springboard.

d and e) The peak of the dive (parabola), is determined using the formula h = -b/2a (Derived from the Quadratic Formula) to find the y value (in this case, the h value, answering e) and then using that result in the function to find the x value (in this case, the t value answering d) of the point where the parabola (dive path) reaches a maximum(height), or minimum(in upward opening parabolas).

h = -10/2(-5)

h = -10/-10

h = 1

h(1) = -5(1)2 + 10(1) + 3

h(1) = -5 + 10 + 3

h(1) = 8

d) At t = 1 second, diver will have reached peak of dive.

e) At t = 1 second, diver will have reached a maximum height of 8 meters.

5 0
2 years ago
A biologist took a count of the number of migrating waterfowl at a particular lake, and recounted the lake's population of water
taurus [48]

Quadratic function ( in standard form ):

y = a x² + b x + c

x = 0:

635 = 0 + 0 + c

c = 635

x = 1:

644 = a + b + 635

a + b = 9

x = 2:

719 = 4 a + 2 b + 635

4 a + 2 b = 84

and now we have a system:

a + b = 9   /  * ( - 2 )

4 a + 2 b = 84

-------------------------

- 2 a + 2 b = - 18

+

 4 a + 2 b  = 84

-------------------------

  2 a = 66

 a = 33;   b = - 24;

 Function is:

 f ( x ) = 33 x² - 24 x + 635

f ( 8 ) = 33 * 64 - 24 * 8 + 635 = 2,112 - 192 + 635 = 2,555

 Answer: The number of waterfowl on week 8 would be 2,555.

 

8 0
3 years ago
Please need help, Will give brainiest!!!!
timurjin [86]
I'd say its D but im not quite sure, its what makes most sense to me.
6 0
3 years ago
A "child has six blocks, three of which are red and three of which are green". How many patterns can shemake by placing them all
makvit [3.9K]

Answer: There are 20 ways and 1680 ways respectively.

Step-by-step explanation:

Since we have given that

Total number of blocks = 6

Number of red blocks = 3

Number of green blocks = 3

So, Number of patterns she can make by placing them all in a line is given by

\dfrac{6!}{3!\times 3!}\\\\=20

If there are 3 white blocks

so, total number of white blocks becomes 9

So, Number of total pattern she can make by placing all nine blocks in a line is given by

\dfrac{9!}{3!\times 3!\times 3!}\\\\=1680\ ways

Hence, there are 20 ways and 1680 ways respectively.

6 0
3 years ago
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