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3 years ago

Function: y=x^2−4x−12

Mathematics

1 answer:

Sati [7]3 years ago

4 0

Answer:

Below in bold.

Step-by-step explanation:

y=x^2−4x−12

Factored form: y = (x - 6)(x + 2)

x-intercepts: (-2, 0) and (6, 0).

Axis of symmetry is found by converting to vertex form:

y = x^2−4x−12

y = (x - 2)^2 - 4 - 12

y = (x - 2)^2 - 16.

So axis of symmetry is x = 2.

Vertex is at (2, -16)

Domain is all Real Numbers.

Range is y ≥ -16.

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Step2247 [10]

Answer:

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3 years ago

If the first number is increased by 7 and the second number is reduced by 6 times, the sum of these numbers is 29.

Marta_Voda [28]

Answer:

First number = 20

Second number = 12

Explanation:

Let the 1st number be x

Let the 2nd number be y

=====================

Condition 1

$\sf \rightarrow x + 7 + \dfrac{y}{6} = 29$

$\rightarrow \sf x=-\dfrac{y}{6}+22$

=====================

Condition 2

$\rightarrow \sf 2y - (x - 5) = 9$

$\rightarrow \sf x = 2y -4$

=====================

Substitute equations

$\rightarrow \sf -\dfrac{y}{6}+22 = 2y-4$

$\rightarrow \sf y=12$

=====================

Find value of 1st number

$\rightarrow \sf x = 2y - 4$

$\sf \rightarrow x = 2(12) - 4$

$\rightarrow \sf x = 20$

7 0

2 years ago

Richard is given one of four pieces of equal-sized fabric. After using some of his fabric for a project, he has 5/6 of a square

ValentinkaMS [17]

Answer:

Richard used $2\frac{1}{12}\ yd ^2$ of fabric for his project.

Step-by-step explanation:

Given:

Total amount of fabric = $11\frac23\ yd^2$

Now To convert a mixed fraction to an improper fraction, Multiply the whole number part by the fraction's denominator, Add that to the numerator,Then write the result on top of the denominator.

$11\frac23\ yd^2$ can be Rewritten as $\frac{35}{3}\ yd^2$

Number of pieces fabric was cut = 4

Richard is given one of four pieces of equal-sized fabric.

Amount of fabric Richard was given = $\frac14 \times \frac{35}{3}=\frac{35}{12}\ yd^2$

Amount of fabric left with Richard = $\frac56 \ yd^2$

We need to find the amount of fabric Richards used for his project.

Solution:

Now we can say that;

amount of fabric Richards used for his project is equal to Amount of fabric Richard was given minus Amount of fabric left with Richard.

framing in equation form we get;

amount of fabric Richards used for his project = $\frac{35}{12}-\frac56$

Now we will make the denominator common using LCM we get;

amount of fabric Richards used for his project = $\frac{35}{12}-\frac{5\times2}{6\times2} = \frac{35}{12}-\frac{10}{12}$

Now Denominator is same so we will solve the numerator.

amount of fabric Richards used for his project = $\frac{35-10}{12}= \frac{25}{12}\ yds^2$

$\frac{25}{12}\ yds^2$ can be rewritten as $2\frac{1}{12}\ yd ^2$

Hence Richard used $2\frac{1}{12}\ yd ^2$ of fabric for his project.

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3 years ago

Ben starts with a certain number of fruit chew packages.He puts 27 packages into each of 85 cases.He has 3 packages left.How man

Ganezh [65]

He would have started with a total of 2,278 packages of fruit chew packages.
First, you would multiply the 27 packages by the 85 cases wich is 2,275, then you would add the three leftover packages to the total making it 2,278.
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4 years ago

Describe differences between recursive and explicit functions. Explain situations in which using a recursive or an explicit func

Misha Larkins [42]

Explanation:

An <em>explicit function</em> returns a value based only on the arguments given.

y = f(x)

A <em>recursive function</em> returns a value based on the arguments given and on other values of the function.

y = f(x, f(g(x))

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3 years ago