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3 years ago

The graph of y=f(x) is given above. For what value of x is y=f(x-4) undefined?

Mathematics

1 answer:

cricket20 [7]3 years ago

8 0

Answer: Choice D) 5

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Notice the hole at (1,2). This means x = 1 and y = 2
y = f(x)
y = f(1) after we replace x with 1
y = 2

If we go from f(x) to f(x-4), then we shift the xy axis four units to the left. The curve will stay still though it will move relative to the xy axis. The xy axis moves four units to the left, so it appears that the curve moved 4 units to the right.

Add 4 to the x coordinate:
x = 1 ---> x+4 = 1+4 = 5
The y coordinate stays the same. No vertical shifting is done.

So we go from (1,2) to (5,2)
(1,2) is a hole on y = f(x)
(5,2) is a hole on y = f(x-4)

This is why the answer is x = 5

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A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a single-strand electric f

likoan [24]

Step-by-step explanation:

Let x be the length and y be the width of the rectangular plot.

The plot is bounded on one side by a river and on the other three sides by a single-strand electric fence. It means,

x+2y = 1500

x = 1500 - 2y ....(1)

We know that the area of a rectangular plot is given by :

A = xy ....(2)

Put the value of x from equation (1) in (2)

$A=(1500-2y)y\\\\A=1500y-2y^2$ .....(3)

For largest area, differentiate above area equation wrt y.

$\dfrac{dA}{dy}=\dfrac{d}{dy}(1500y-2y^2)\\\\=1500-4y\\\\\text{Put}\ \dfrac{dA}{dy}=0\\\\1500-4y=0\\\\y=\dfrac{1500}{4}\\\\=375$

Put the value of y in equation (1).

x = 1500-2(375)

= 750 m

Put the value of y in equation (3).

$A =1500(375)-2(375)^2\\A=281250\ m^2$

Hence, the largest area is 281250 m² and its dimensions are 750 m and 375 m.

3 0

3 years ago

Which expression is equivalent to −4(2x − 8)−2x ?

Vesnalui [34]

C. -10x+32

Explanation: Solve the problem
( -4(2x-8)-2x )

5 0

2 years ago

Which of the following is a solution of the equation -5x + 2 = -13: answers: x=-9, x=75 x=3 x=-3

slamgirl [31]

Answer:

x= 3

Step-by-step explanation:

1. -5(3) + 2 = -13

2. -15 + 2 = -13 A positive times a negative will always equal a negative

3. -13 = -13 Whenever you add anything to a negative number, the

number becomes smaller

Ex: -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, ...........

Although the number itself becomes smaller, its value

becomes bigger

Hope this helps.

7 0

3 years ago

A line passes through the points (2,4) and (5,6) .

Alenkinab [10]

Answer:

Option B and D are correct.

Step-by-step explanation:

Given: A line passes through the points (2,4) and (5,6).

* Case 1:

If a line passes through the points (2, 4) and (5, 6)

Point slope intercept form:

for any two points $(x_1,y_1)$ and $(x_2, y_2)$

then the general form $y -y_1=m(x-x_1)$ for linear equations where m is the slope given by:

$m =\frac{y_2-y_1}{x_2-x_1}$

First calculate slope for the points (2, 4) and (5, 6);

$m = \frac{y_2-y_1}{x_2-x_1} =\frac{6-4}{5-2} = \frac{2}{3}$

then, by point slope intercept form;

$y-4=\frac{2}{3}(x-2)$

* Case 2:

If a line passes through the points (5, 6) and (2, 4)

First calculate slope for the points (5, 6) and (2, 4);

$m = \frac{y_2-y_1}{x_2-x_1} =\frac{4-6}{2-5} = \frac{-2}{-3}= \frac{2}{3}$

then, by point slope intercept form;

$y-6=\frac{2}{3}(x-5)$

Yes, the only equation of line from the given options which describes the given line are;

$y-4=\frac{2}{3}(x-2)$ and $y-6=\frac{2}{3}(x-5)$

8 0

4 years ago

A blackjack is a 10-point card and an ace for a value of 21. Use your answers to parts (a), (b), and (c) to determine the probab

kondor19780726 [428]

Answer:

Results:

0.1432

0.0045

0.0905

0.0483

Step-by-step explanation:

Step a:

P(A or 10, A or 10) = 20/52 * 19/51 = 5/13 / 19/51 = 95/663 = 0.1432

Step b:

P(A A) = 4/52 * 3/51 = 1/13 * 1/17 = 1/221 = 0.0045

Step c:

P(10 10) = 16/52 * 15/51 = 4/13 * 5/17 = 20/221 = 0.0905

Step d:

P(A 10 or 10 A) = 2 * 4/52 * 16/51 = 2/13 * 16/51 = 32/663 = 0.0483

As well we get the probability by subtracting a, b and c:

P(blackjack): 0.1432 - 0.0905 - 0.0045 = 0.0482

7 0

4 years ago