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labwork [276]
3 years ago
13

What is the next number in the sequence? 2, -1.25, -4.5, -7.75, ...

Mathematics
1 answer:
MAXImum [283]3 years ago
8 0
You subtract 3.25 each time so -11
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The equation for a parabola has the form y = ax^2 + bz + c, where a, b, and c are constants and aメ0. Find an equation for the pa
vova2212 [387]

Answer:

a = 2, b = -9, c = 3

Step-by-step explanation:

Replacing x, y values of the points in the equation y = a*x^2 + b*x +c give the following:  

(-1,14)

14 = a*(-1)^2 + b*(-1) + c  

(2,-7)

-7 = a*2^2 + b*2 + c  

(5, 8)  

8 = a*5^2 + b*5 + c  

Rearranging:

a - b + c = 14  

4*a + 2*b + c = -7

25*a + 5*b + c = 8

This is a linear system of equations with 3 equations and 3 unknows. In matrix notation the system is A*x = b whith:

A =

1    -1  1

4    2  1

25  5  1

x =

a  

b

c

b =

14

-7

8

Solving A*x = b gives x = Inv(A)*b, where Inv(A) is the inverse matrix of A. From calculation software (I used Excel) you get:

inv(A) =  

0.055555556 -0.111111111   0.055555556

-0.388888889 0.444444444   -0.055555556

0.555555556 0.555555556 -0.111111111

inv(A)*b

2

-9

3

So, a = 2, b = -9, c = 3

5 0
3 years ago
PLEASE HELP VERY URGENT
worty [1.4K]

Answer:

A. square root of a^2 + b^2 for both answers

Step-by-step explanation:

The first problem, we are given

a^2 + b^2 = c^2

What we do is solve for c.

sqrt(a^2 + b^2) = c

c = sqrt(a^2 + b^2)

For problem 2,

WE can apply the Pythagorean theorem because we have a right triangle.

The equations is

a^2 + b^2 = c^2 like the first problem

Solving gets us

sqrt(a^2 + b^2) = c

c = sqrt(a^2 + b^2)

3 0
2 years ago
I need help pls!! Question in the picture!!
SIZIF [17.4K]

Answer:

ABD=180  and EHF=90

Step-by-step explanation:

8 0
3 years ago
Suppose x=18,y=24, and z=30 in the figure, which is not drawn to scale. Determine the following values. Enter exact answers (as
sammy [17]

Answer:

See explanation

Step-by-step explanation:

cos(θ)= 18/30 = 3/5

sin(θ)= 24/30 = 4/5

tan(θ)= 24/18 = 4/3

cos(ϕ)= 24/30 = 4/5

sin(ϕ)= 18/30 = 3/5

tan(ϕ)= 18/24 = 3/4

3 0
3 years ago
A grasshopper jumps off a tree stump. The height, in feet, of the grasshopper above the ground after t seconds is modeled by the
klasskru [66]

Answer:

Hence, Grasshopper will land on the ground after 1.5 sec.

Step-by-step explanation:

It s given that:

The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function:

h(t)=-t^2+\dfrac{4}{3}t+\dfrac{1}{4}

Now we are asked to find:

In how many seconds will the grasshopper land on the ground?

i.e. we have to find the value of t such that h(t)=0

i.e.

-t^2+\dfrac{4}{3}t+\dfrac{1}{4}=0

i.e. we need to find the roots of the given quadratic equation.

On solving the quadratic equation or plotting it's graph we could observe that the point where h(t)=0 are:

t=-\dfrac{1}{6},t=\dfrac{3}{2}

As time can't be negative hence we will consider:

t=\dfrac{3}{2}=1.5sec

Hence, grasshopper will land on the ground after 1.5 sec.

4 0
3 years ago
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