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3 years ago

Let f(x) = |x|, ????????(x) = f(x − 3), and h(x) = f(x + 2), where x can be any real number.

Mathematics

1 answer:

ra1l [238]3 years ago

5 0

Answer:

g(x)= |x-3|

h(x) = |x+2|

Step-by-step explanation:

1. Let g(x)=f(x-3), we can write the function in terms of |x| as:

g(x)= |x-3|

2. Let h(x)=f(x+2), the function can be rewrite in terms of |x| as:

h(x) = |x+2|

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How to solve for y.

NARA [144]

25, 65, and y make a right triangle. use a^2 + b^2 =c^2.
so...
y^2 + 25^2 = 65^2
y^2 + 625 = 4225
y^2 = 3600 take the square root of both sides
y=60

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3 years ago

What is the definition of csc θ ?

Greeley [361]

Csc is the inverse of sin. This means the formula in regards to a triangle for csc is h/o, unlike o/h for sin. csc can also be knows as 1/sin.

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4 years ago

(08.07 HC)

andreev551 [17]

Answer:

$\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}$

$\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

C) See attachment.

Step-by-step explanation:

Given function:

$f(x)=2x^2-x-10$

To factor a <u>quadratic</u> in the form $ax^2+bx+c$ <em> , </em>find two numbers that multiply to $ac$ and sum to $b$ :

$\implies ac=2 \cdot -10=-20$

$\implies b=-1$

Therefore, the two numbers are -5 and 4.

Rewrite $b$ as the sum of these two numbers:

$\implies f(x)=2x^2-5x+4x-10$

Factor the first two terms and the last two terms separately:

$\implies f(x)=x(2x-5)+2(2x-5)$

Factor out the common term (2x - 5):

$\implies f(x)=(x+2)(2x-5)$

The x-intercepts are when the curve crosses the x-axis, so when y = 0:

$\implies (x+2)(2x-5)=0$

Therefore:

$\implies (x+2)=0 \implies x=-2$

$\implies (2x-5)=0 \implies x=\dfrac{5}{2}$

So the x-intercepts are:

$x=-2, \:\:x=\dfrac{5}{2}$

The x-value of the vertex is:

$\implies x=\dfrac{-b}{2a}$

Therefore, the x-value of the vertex of the given function is:

$\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}$

To find the y-value of the vertex, substitute the found value of x into the function:

$\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}$

Therefore, the vertex of the function is:

$\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)$

Plot the x-intercepts found in Part A.

Plot the vertex found in Part B.

As the <u>leading coefficient</u> of the function is positive, the parabola will open upwards. This is confirmed as the vertex is a minimum point.

The axis of symmetry is the <u>x-value</u> of the <u>vertex</u>. Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is <u>symmetrical</u>.

Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).

5 0

2 years ago

What is the answer 0,12km² a m² show work

seraphim [82]

Answer:

120 000 m^2

Step-by-step explanation:

I ASSUME you're being asked to convert from km^2 to m^2.

For this you need to identify the conversion rate, which is 1 000 000 m^2 / 1 km ^2. Multiply by the thing you're converting from and cancel the units.

(1 000 000 m^2 / 1 km ^2) x 0,12 km^2 = 120 000 m^2 (the km^2 cancels out, leaving you only with your target unit of m^2)

8 0

2 years ago

Read 2 more answers

What is the solution of the equation 3x − 7 = 4x?<br> -7<br> -1<br> 1<br> 7

gogolik [260]

The solution of this equation is -7.
3x - 7 = 4x
3x - 7 - 4x = 0
3x - 4x - 7 = 0
-x - 7 = 0
-x = 7
x = -7

8 0

3 years ago

Read 2 more answers