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3 years ago

If f(x)=-5x-1 and g (x)= √x-6 what is (f º g)(7)

Mathematics

1 answer:

Lyrx [107]3 years ago

8 0

$(fog)(7) = -6$

Step-by-step explanation:

The function composition is achieved by putting the second function in first function in place of independent variable.

Given functions are:

$f(x) = -5x-1\\g(x) =\sqrt{x-6}$

In order to find (fog)(x) we will put function g in function f in place of x

$(fog)(x) = -5(g(x)) -1\\= -5\sqrt{x-6}-1$

Since we have to find (fog)(7)

Putting 7 in place of x

$= -5\sqrt{7-6} - 1\\=-5\sqrt{1}-1\\= -5(1) -1\\= -5-1\\=-6$

Hence,

$(fog)(7) = -6$

Keywords: Functions, composition

Learn more about functions at:

#LearnwithBrainly

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An equation for 10/50=12/60

VashaNatasha [74]

Answer:

Infinitely Many Solutions

Step-by-step explanation:

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3 years ago

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Dafna1 [17]

Answer:

6/0

Step-by-step explanation:

Step 1: Label your x and y's

(0,-11) (0, 5)

x1 y1 x2 y2

Step 2: Plug in your x1, x2, y1, and y2 into the slope formula

The slope formula is y1 -y2/ x1 - x2

-5-(-11)/ 0 = 6/0

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3 years ago

2. Solve the equation by completing the square. Show your work.

scoundrel [369]

Answer:

x = 5 or 25

Step-by-step explanation:

I think the method I am about to explain is slightly quicker and easier than the method in your question. This works for any 'complete the square' question.

We begin with x² - 30x = - 125.

First, we are going to factorise the left-hand side of the equation by dividing the 'b' value (-30) by 2 (you'll see why this works in a minute):

(x - 15)²

We want these brackets to multiply out to give x² - 30x, so that they equal the left-hand side of the equation. Unfortunately, if we multiply them out, we get:

(x - 15)(x - 15) =

x² - 30x + 225

There is an unwanted term (the + 225, from 15²)! We only want x² - 30x, so we have to remove this term by subtracting it from the left side of the equation. To do this, let's set up the original equation again:

(x² - 30x + 225) - 225 = - 125

Note: The reason why we don't have to subtract it from both sides is because the original equation is x² - 30x = - 125, and so we must make sure the left hand side is still equal to x² - 30x.

So now we know that (x - 15)² multiplies out to give x² - 30x +225, we can write this as (x - 15)² in our equation:

(x² - 30x + 225) - 225 = - 125

is the same as:

(x - 15)² - 225 = - 125

Now add 225 to both sides of the equation:

(x - 15)² = - 125 + 225 = 100

(x -15)² = 100

The next step is to square root both sides. Be careful here, and remember that √100 can either be 10 or -10, as (-10)² = 100. To indicate both results, write ±10 ("plus or minus 10").

√(x - 15)² = √100

x - 15 = ±10

Because, there are two possible values for the right-hand side of the equation, we need to separate our equation into two equations:

1. x - 15 = 10

and

2. x - 15 = -10

Now we solve these two simple linear equations for x:

1. x = 10 + 15 <- add 15 to both sides

x = 25 This is our first solution.

2. x = -10 + 15 <- add 15 to both sides again

x = 5 This is our other solution.

So our two solutions are x = 5 and x = 25!

I have attached the quick version of the working out for this question - that is what you would be expected to write down in a test.

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4 years ago

I need the answer ASAP! Please help me!

masha68 [24]

Answer:

Please check the explanation.

Step-by-step explanation:

Determining the length of BC

From the diagram, it is clear that

The point B is located at (-8, 10) and point C is located at (8, 10)

Since points A and C are located on a horizontal straight line. Thus, the length of BC can be determined by counting the x-axis units from reaching x = -8 to x = 8. i.e. 8-(-8) = 8+8 = 16

Thus, the length of BC = 16 units

Determining the length of CD

Given

C (8, 10)

D (2, -2)

The distance between C(8, 10) and D(2, -2)

$\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$CD=\sqrt{\left(2-8\right)^2+\left(-2-10\right)^2}$

$=\sqrt{6^2+12^2}$

$=\sqrt{36+144}$

$=\sqrt{180}$

$=\sqrt{36\times 5}$

$=6\sqrt{5}$

Thus, the length of CD $=6\sqrt{5}$ units

Determining the length of ED

Given

E (-8, -4)

D (2, -2)

The distance between E(-8, -4) and D(2, -2)

$ED=\sqrt{\left(2-\left(-8\right)\right)^2+\left(-2-\left(-4\right)\right)^2}$

$=\sqrt{10^2+2^2}$

$=\sqrt{100+4}$

$=\sqrt{104}$

$=\sqrt{26\times \:4}$

$=2\sqrt{26}$

Thus, the length of ED $=2\sqrt{26}$ units

Determining the length of EB

From the diagram, it is clear that

The point E is located at (-8, -4) and the point B is located at (-8, 10)

Since points E and B are located on a vertical straight line. Thus, the length of EB can be determined by counting the y-axis units from reaching y = -4 to y = 10. i.e. 10-(-4) = 10+4 = 14

Thus, the length of EB = 14 units

4 0

3 years ago

I need some help with the question

vagabundo [1.1K]

To solve this you first need to turn your mixed numbers into improper fractions. to do this for $9 \frac{4}{5}$ you multiply the denominator (5) by the whole number (9) to get 45 and then add that to the numerator (4) to get your new fraction $\frac{49}{5}$ .

You repeat this process with $3\frac{1}{2}$ to get $\frac{7}{2}$ .

Now that you have two fractions you can multiply by the opposite reciprocal. To do this you flip the second fraction and change the division sign to a multiplication sign like so $\frac{49}{5} * \frac{2}{7}$

Then, you just multiply the fractions by multiplying the numerators to get 98 and multiplying the denominators to get 35.

Now, to simplify $\frac{98}{35} * \frac{2}{7}$ you first divide both the numerator and denominator by 7 to get $\frac{14}{5} * \frac{2}{7}$ .

Finally, you can take 10 out of the numerator to make $2\frac{4}{5} * \frac{2}{7}$

8 0

4 years ago