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erma4kov [3.2K]
3 years ago
7

Help help help help help help help

Mathematics
1 answer:
neonofarm [45]3 years ago
3 0

Answer:

D= -16.8

Step-by-step explanation:

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The vertex of the parabola below is at the point (1.-3). Which of the equations below could be the one for this parabola?
Ilia_Sergeevich [38]

Answer: Choice D. y = (x-1)^2 - 3

The vertex is (h,k) = (1,-3). So h = 1 and k = -3.

We have a = 1 as the leading coefficient.

Plug those values into the equation below

y = a(x-h)^2 + k

y = 1(x - 1)^2 + (-3)

y = (x - 1)^2 - 3

3 0
3 years ago
Read 2 more answers
Tim drove 217 miles in 3.5 hours. Emily drove 244 miles in 4 hours. Who drove faster?
Naya [18.7K]

Answer:

Tim

Step-by-step explanation:

Tim drove 62 miles per hour you get this by dividing 217 by 3.5 and then you divide Emily's. 244/4 and you get 61

8 0
2 years ago
Pls Help I’m stuckThere are 89 students in the Oakwood Middle School band. The number of boys in the band is 5 more than twice t
Rasek [7]

Answer:

42

Step-by-step explanation:

5 more than 2 times the girls

89=5+2x

x=42

4 0
2 years ago
HELP 40 POINTS
Tom [10]
Answer: the function g(x) has the smallest minimum y-value.


Explanation:


1) The function f(x) = 3x² + 12x + 16 is a parabola.


The vertex of the parabola is the minimum or maximum on the parabola.


If the parabola open down then the vertex is a maximum, and if the parabola open upward the vertex is a minimum.


The sign of the coefficient of the quadratic term tells whether the parabola opens upward or downward.


When such coefficient is positive, the parabola opens upward (so it has a minimum); when the coefficient is negative the parabola opens downward (so it has a maximum).


Here the coefficient is positive (3), which tells that the vertex of the parabola is a miimum.


Then, finding the minimum value of the function is done by finding the vertex.

I will change the form of the function to the vertex form by completing squares:

Given: 3x² + 12x + 16

Group: (3x² + 12x) + 16
Common factor: 3 [x² + 4x ] + 16
Complete squares: 3[ ( x² + 4x + 4) - 4] + 16
Factor the trinomial: 3 [(x + 2)² - 4] + 16
Distributive property: 3 (x + 2)² - 12 + 16
Combine like terms: 3 (x + 2)² + 4

That is the vertex form: A(x - h)² + k, whch means that the vertex is (h,k) = (-2, 4).


Then the minimum value is 4 (when x = - 2).


2) The othe function is <span>g(x)= 2 *sin(x-pi)
</span>

The sine function goes from -1 to + 1, so the minimum value of sin(x - pi) is - 1.


When you multiply by 2, you just increased the amplitude of the function and obtain the new minimum value is 2 (-1) = - 2


Comparing the two minima, you have 4 vs - 2, and so the function g(x) has the smallest minimum y-value.

7 0
3 years ago
After writing part of his novel, Thomas is now writing 16 pages per week. After 4 weeks, he has written 85 pages. Assume the rel
d1i1m1o1n [39]

The initial value is 21 and rate of change is 16 pages per week

<em><u>Solution:</u></em>

Given that After writing part of his novel, Thomas is now writing 16 pages per week

After 4 weeks, he has written 85 pages.

Given that assume the relationship to be linear

Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + c

y = mx + c

where "y" is the number of pages written after 4 weeks

x = 4 weeks and m = 16 pages

Therefore,

85 = 16(4) + c

85 = 64 + c

c = 85 - 64

c = 21

Therefore, initial value is 21 and rate of change is 16 pages per week

7 0
3 years ago
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