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4 years ago

Suppose that the function f is defined. , for all real numbers, as follows.

Mathematics

1 answer:

aivan3 [116]4 years ago

5 0

Answer: The values of......

$f(-5)=\frac{9}{4}\\ \\ f(-2)= -1\\ \\ f(4)=0$

Step-by-step explanation:

Given function is: $\left \{ {{f(x)= \frac{1}{4}x^2 -4, if x\neq -2} \atop {=-1, if x=-2}} \right.$

For $f(-5),$ the value of $x$ is -5, which is not equal to -2.

So, $f(-5)= \frac{1}{4}(-5)^2 -4 = \frac{1}{4}(25)-4 =\frac{25}{4}-4=\frac{25-16}{4}=\frac{9}{4}$

For $f(-2),$ the value of $x$ is -2.

So, $f(-2)= -1$

For $f(4),$ the value of $x$ is 4, which is not equal to -2.

So, $f(4)=\frac{1}{4}(4)^2 -4 =\frac{1}{4}(16)-4 =4-4=0$

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Square root of 576 with process

klio [65]

Step-by-step explanation:

here you go:

√24•24= 24

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6 0

3 years ago

Read 2 more answers

Todd earned some money doing chores. He spent one-fourth of his money see a movie. Then he spent $6.00 on popcorn and drinks. Wh

Vsevolod [243]

Answer: Todd earned $40 mowing the neighbor's lawn.

Step-by-step explanation:

Let x represent the amount of money that Todd earned, mowing his neighbor's lawn.

He spent one-fourth of his money see a movie. It means that the amount spent in seeing a movie is x/4

Then he spent $6.00 on popcorn and drinks. It means that the total amount spent is

x/4 + 6

The amount left would be

x - (x/4 + 6) = x - x/4 - 6

When he went home, he had $24.00 left. It means that

x - x/4 - 6 = 24

x - x/4 = 24 + 6

x - x/4 = 30

Cross multiplying by 4, it becomes

4x - x = 120

3x = 120

x = 120/3

x = $40

7 0

3 years ago

DochEvi [55]

Answer:

12pi cm

Step-by-step explanation:

The Perimeter of the full shape is the sum of the lengths of the edges of the parts. For convenience in referencing them, we'll call the large curve " $curve_{big}$ " and the three smaller curves " $curve_1$ " " $curve_2$ " " $curve_3$ " in order from left to right.

Thus, the Perimeter of the full shape can be written as an equation:

$P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)$ Since all of those edge lengths are curves, and the question states that all of the curves are made from parts of circles, then we need to know how to find the length of the edge of a circle.

Parts of a circle

Since values in the diagram are diameters, use the formula for the Perimeter of a circle $P=\pi d$ (where d is the diameter).

Let's call the diameters of each of our curves " $d_{big}$ " " $d_1$ " " $d_2$ " " $d_3$ ", with the subscripts denoting which curve we're referring to.

Note that for each curve, the curve only represents half of a circle. So, to find the length of each curve, we'll need half of the full perimeter of each circle.

So for instance: $Length(curve_{big})=\frac{1}{2} \pi d_{big}$

Substituting back into the main equation above:

$P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)$ $P_{overall}=\frac{1}{2} \pi d_{big} + \frac{1}{2} \pi d_{1} + \frac{1}{2} \pi d_{2} + \frac{1}{2} \pi d_{3}$

Note that all terms have common factors of "one-half" and "pi" in them. These can be factored out:

$P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})$

The diameter for the large Curve, is the sum of the three small diameters, so $d_{big}=12cm$ , and $d_{1}=d_{2}=d_{3}=4cm$

Substituting and simplifying (in terms of pi):

$P_{overall}=\frac{1}{2} \pi ( (12cm) + (4cm) + (4cm) + (4cm) )\\P_{overall}=\frac{1}{2} \pi ( 24cm)\\P_{overall}=12 \pi cm$

Additional Understanding

Interesting for this problem, since the diameters of the 3 small curves formed the diameter of the large curve $d_{1} + d_{2} + d_{3} =d_{big}$ , one could make a different substitution into one of our formulas above:

$P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})$

$P_{overall}=\frac{1}{2} \pi (d_{big} + (d_{big}))$

$P_{overall}=\frac{1}{2} \pi (2d_{big})$

$P_{overall}=\pi d_{big}$

Notice that $\pi d_{big}$ is just the full perimeter of a circle with the big diameter.

So, if one imagined starting with a full circle with the big diameter, even though the bottom half of the circle was turned into a bunch of smaller half circles, since they were in a line along the diameter of the large circle, the full perimeter of the new shape didn't change.

The number of smaller circles doesn't need to be 3 either... as long as it goes the full distance across, right along the diameter.

7 0

2 years ago

Tavon has a gift card for $115 that loses $2.50 for each 30-day period it is not used. He has another gift card for $95 that lo

Amiraneli [1.4K]

The question is incomplete:

Tavon has a gift card for $115 that loses $2.50 for each 30-day period it is not used. He has another gift card for $95 that loses $2 for each 30-day period it is not used.

Write and solve an equation for the number of 30-day periods until the value of the gift cards will be equal.

Answer:

115-2.5x=95-2x

The value of the gift cards will be equal after 40 30-day periods.

Step-by-step explanation:

From the information given, you can write the following equation:

115-2.5x=95-2x, where x is the number of 30-day periods the gift card is not used.

Now, you can solve for x:

115-95=-2x+2.5x

20=0.5x

x=20/0.5

x=40

According to this, the answer is that the value of the gift cards will be equal after 40 30-day periods.

5 0

3 years ago

Write the equation of the line in fully simplified slope-intercept form.

Ostrovityanka [42]

Y = 3x - 1
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5 0

3 years ago