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3 years ago

Is the relation represented in this table a function? Helppp

Mathematics

1 answer:

k0ka [10]3 years ago

6 0

The answer is no because the numbers are repeated

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1. Find the vertex of the following: y = (x - 4)(x - 10) *

horsena [70]

Answer:

1. (7,-9)

2. (4,0) and (10,0)

3. (3,0) and (-3,0)

4. (0,-9)

5. (-1,-32)

Step-by-step explanation:

To find the vertex use the formula

$\frac{-b}{2a}$

First make the equation into a quadratic equation.

$(x-4)(x-10)\\x^{2} -10x-4x+40\\x^{2} -14x+40$

Now it is in the form

$ax^{2} +bx+c=0$

Now we can substitute the values

$\frac{-(-14)}{2(1)} \\\frac{14}{2} \\7$

Now we have 7 as our x value for the vertex we can substitute for y,

$x^{2} -14x+40=y\\(7)^{2} -14(7)+40=y\\49-98+4=y\\y=-9$

So the vertex for 1 is (7,-9)

To find the intercepts for 2 & 3, they basically already give it to you. You just need to find a value for x for x-4 that will equal it to 0 and another for x for x-10 that will equal it to 0.

$x-4=0\\x=4\\\\x-10=0\\x=10$

4 is slightly different but start the same,

$(x-3)(x+3)\\x^{2}+3x-3x-9\\x^{2}-9$

Here, c (9) just shows the graph move down 9, so the y intercept = 9.

5 is the same process as 1,

$2(x-3)(x+5)\\2(x^{2}+5x-3x-15)\\2(x^{2}+2x-15)\\2x^{2}+4x-30$

Vertex,

$\frac{-(4)}{2(2)} \\\frac{-4}{4} \\-1$

Substitute,

$2x^{2}+4x-30\\2(-1)^{2}+4(-1)-30\\2-4-30\\-32$

So the vertex is (-1,-32)

8 0

3 years ago

The sum of three consecutive terms in an arithmetic sequence is 27, and their product is 585. find the three terms.

sammy [17]

$\text{the three consecutive terms in an arithmetic sequence}\\a;\ a+d;\ a+2d\\\\\text{system of equals}\\\\ \left\{\begin{array}{ccc}a+a+d+a+2d=27\\a(a+d)(a+2d)=585\end{array}\right\\ \left\{\begin{array}{ccc}3a+3d=27&|:3\\a(a+d)(a+2d)=585\end{array}\right\\ \left\{\begin{array}{ccc}a+d=9&\to d=9-a\\a(a+d)(a+2d)=585\end{array}\right\\$
$\text{substitute to the second equation}\\\\a(a+9-a)(a+2(9-a))=585\\\\a(9)(a+18-2a)=585\\9a(18-a)=585\ \ \ |:9\\a(18-a)=65\\18a-a^2=65\ \ \ |\text{change the signs}\\a^2-18a=-65\\a^2-2a\cdot9=-65\ \ \ |+9^2\\\underbrace{a^2-2a\cdot9+9^2}_{(a-b)^2=a^2-2ab+b^2}=-65+9^2\\(a-9)^2=16\to a-9\pm\sqrt{16}\\a-9=-4\ \vee\ a-9=4\ \ \ |+9\\a=5\ \vee\ a=13\\\\d=9-5=4\ \vee\ d=9-13=-4$
$Answer:\ a=5;\ a+d=9; a+2d=13\ vee\ a=13;\ a+d=9;\ a+2d=5$

5 0

3 years ago

What is 4848/40404 written as an improper fraction +34422222222 wiil mark brainliset if right

ruslelena [56]

Answer:

675/12

Step-by-step explanation:

3 0

3 years ago

Cot theta= 0 what is the value

lana [24]

The Answer:a=02.718282

3 0

3 years ago

Show work pls !!!!!!!!!!!

-Dominant- [34]

Answer:

Step-by-step explanation:

$\frac{32}{24} = \frac{ab}{27} \\ ab = 32 \times 27 \div 24 \\ ab = 36$

7 0

3 years ago