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dimulka [17.4K]
2 years ago
10

9

Mathematics
1 answer:
stiks02 [169]2 years ago
8 0

Answer:QB = 1/2 QE

QC = CF

DE = 2AB

Step-by-step explanation: hope it works

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Consider the function f(x) defined by the finite set f(x)={(−2,5),(0,4),(1,−3)}. Graph the function f(x) and the transformation
Lelu [443]

let's calculate it step by step.

I'll assume that the function we look for is quadratic, because we only got 3 points

I plotted the 3 points for checking the equation later, and some intuited insight. see screenshot 1

let's write the general form of quadratic equations:

f(x) = a*x² + b*x + c

our goal is to correctly determine a, b and c

since we know from the 2nd point that

f(0) = a*0² + b*0 + c = 4

we can say

<em><u>c = 4</u></em>

this one comes almost for free

now to the next point, the 3rd one

f(1) = a*1² + b*1 + 4 = -3

we can write it as

a + b + 4 = -3

we can rearrange that to

<em><u>a = -b -7</u></em>

lastly, to the first point

f(-2) = a*(-2)² + b*(-2) + 4 = 5

simplified to

4a -2b + 4 = 5

since sort of defined a, let's plug it into our newest equation

4*(-b-7) -2b +4 = 5

we just swapped a for what its equal to.

now we just got numbers and b's

simplify it to

-4b -28 -2b +4 = 5

-6b -24 = 5

-6b = 29

<em><u>b = -29/6</u></em>

now we use the exact value of b to plug it into the rather simple equation from earlier. into this one

a = -b -7

a = -(-29/6) -7

a = 29/6 -42/6

<em><u>a= -13/6</u></em>

now that we got a, b and c we can write the whole equation

<em><u>f(x) = -13/6*x² -29/6*x +4</u></em>

see the graphic check in screenshot 2

second part of the problem:

if we want to move the whole graph 4 units down, we effectivly just cancel the +4 part

g(x) = f(x) -4 = f(x) = -13/6*x² -29/6*x +4 -4

<em><u>g(x) = -13/6*x² -29/6*x</u></em>

see screenshot 3 for the graph

5 0
2 years ago
Explain why y = 3x IS an exponential function and y = x3 is NOT an exponential function.
arlik [135]
Because y=3x has a coefficient of 3 and y=x3 does not have a coefficient because the variable is the first terms. therefore it is not an exponential function.
8 0
3 years ago
John and Andrew have £3.40 between them. John has £1.20 more than Andrew. John has £u and Andrew £v
Dahasolnce [82]
In the given question, there are several information's of immense importance and they can be used to find the necessary answers. It is already given that John and Andrew have 3.40 pound together. It is also given that John has 1.20 pound more than Andrew. It is also assumed that John has"u" pound and Andrew has "v" pounds.
Then we can write the two equations as
u + v = 3.40
u = v + 1.20
To find the values of u and v, we can replace the u in the first equation with the value of u in the second equation. Then
u + v = 3.40
(v + 1.20) + v = 3.40
2v + 1.20 = 3.40
2v = 3.40 - 1.20
2v = 2.2
v = 2.2/2
  = 1.1
Now we replace the value of v in the first equation to find the value of u.
 u + v = 3.40
u + 1.1 = 3.40
u = 3.40 - 1.1
u = 2.3
6 0
3 years ago
What is the quadratic equation of the curve of best fit shown below
Kisachek [45]
First off, we know that the y-interecept is 2, so there is going to be a plus two in the final equation. Now with the two answers input the number 8 to see which will output 6.

6 = 1/12(8)^(2) + 2
6 = 1/12(64) + 2
6 = 64/12 + 2
6 = 16/3 + 6/3
6 does not equal 22/3

6 = 1/16(8)^(2) + 2
6 = 1/12(64) + 2
6 = 64/16 + 2
6 = 4 + 2
6 = 6
This means that y = 1/16 x^2 + 2 is the correct answer. I hope that helps!
4 0
3 years ago
Al, Tom and Joe share €3000.
agasfer [191]

Answer:

Tom's share = €800

Step-by-step explanation:

Given that:

Amount shared by Al, Tom and Joe = €3000

Ratio of Al's share to Tom's share = 5 : 4

Joe's share = 1.5(Tom's share) = 1.5(4) = 6

Therefore,

Ratio of Al, Tom and Joe = 5 : 4 : 6

Let,

x be the number of times of amount each get.

5x + 4x + 6x = 3000

15x = 3000

Dividing both sides by 15

\frac{15x}{15}=\frac{3000}{15}\\x=200

Tom's share = 4x = 4(200) = €800

Hence,

Tom's share = €800

5 0
3 years ago
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