If f(x)=3/x-3, what is (f•f)(x)?

Answer:

(x + 7)(x - 3)

Step-by-step explanation:

To factor the quadratic

Consider the factors of the constant term (- 21) which sum to give the coefficient of the x- term (+ 4 )

The factors are + 7 and - 3 since

+ 7 × - 3 = - 21 and + 7 - 3 = + 4, hence

x² + 4x - 21 = (x + 7)(x - 3)

The quadratic equation x^2 + 4x - 21 is factored into (x - 3)(x + 7) where these two factors multiply to -21 and add up to 4.

To completely factor the equation x^2 + 4x - 21, we look for two numbers that multiply to -21 (the c term) and add up to 4 (the b term). The numbers that satisfy these conditions are 7 and -3.

Therefore, the factored form of the equation x^2 + 4x - 21 is: (x - 3)(x + 7) as (x - 3) * (x + 7) gives x^2 + 4x - 21.

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Answer:

[tex]\frac{3x}{5(x+2)}[/tex]

Step-by-step explanation:

Multiply the fractions by multiplying the numerators.

[tex]\frac{6x^2}{x(x-3)} * \frac{(x-3)}{10(x+2)} \\\\\frac{6x^2(x-3)}{10x(x-3)(x+2)} \\\\ \frac{6x}{10(x+2)} \\\\\frac{3x}{5(x+2)}[/tex]

Answer:

x=4±9i

Step-by-step explanation:

Solve the equation for x by finding a, b, and c of the quadratic then use the qaudratic formula

Answer:

[tex]x=4-9i[/tex] or  [tex]x=4+9i[/tex]

Step-by-step explanation:

The given equation is

[tex]x^2-8x+97=0[/tex]

By comparing to [tex]ax^2+bx+c=0[/tex], we have a=1,b=-8 and c= 97.

The quadratic formula is;

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

We substitute the values to obtain;

[tex]x=\frac{--8\pm\sqrt{(-8)^2-4(1)(97)} }{2(1)}[/tex]

[tex]x=\frac{8\pm\sqrt{-324} }{2}[/tex]

[tex]x=\frac{8\pm18i }{2}[/tex]

[tex]x=4\pm9i[/tex]

Therefore [tex]x=4-9i[/tex] or  [tex]x=4+9i[/tex]

Answer:

Neither

Step-by-step explanation:

Check if it's arithmetic:

-8, -3, 6, 11, -22

+5  +6   +5  -33

Nope

Check if geometric:

-8, -3, 6, 11, -22

*3/8  *-2 *11/6 *-2

Nope

So it's neither

Answer:

i need more details

Step-by-step explanation:

[tex] \frac{x + 1}{x - 1} > 0 \\ [/tex]

multiply both sides by the x-1 to get rid of the fraction.

[tex]x + 1 > 0 \\ because \: x - 1 \times 0 = 0[/tex]

subtract 1 from each side

x>-1

The solution is

x<−1

x>1

See the image

Answer:

[tex]\large\boxed{C=87.92\ in}[/tex]

Step-by-step explanation:

The formula of an area of a circle:

[tex]A=\pi r^2[/tex]

r - radius

We have A = 615.44 in². Substitute:

[tex]615.44=\pi r^2[/tex]

[tex]\pi\approx3.14[/tex]

[tex]3.14r^2=615.44[/tex]          divide both sides by 3.14

[tex]r^2=196\to r=\sqrt{196}\\\\r=14\ in[/tex]

The formula of a circumference of the circle:

[tex]C=2\pi r[/tex]

Substitute:

[tex]C=2\pi\cdot14=28\pi\approx28\cdot3.14=87.92\ in[/tex]

Answer:

Yes, y varies directly with x, and the equation is [tex]y=1.6x[/tex].

Step-by-step explanation:

To check where there is a direct relationship between x and y, we need to check whether all the x,y pairs we have fit some rule:

[tex]y=k\times x[/tex].

For the first pair (x=4, y=6.4),

[tex]6.4=k\times 4[/tex]

Therefore [tex]k = 1.6[/tex].

For the second pair (x=7, y=11.2),

[tex]11.2=k\times 7[/tex]

Therefore [tex]k = 1.6[/tex].

For the third pair (x=10, y=16),

[tex]16=k\times 10[/tex]

Therefore [tex]k = 1.6[/tex].

For the second pair (x=13, y=20.8),

[tex]20.8=k\times 13[/tex]

Therefore [tex]k = 1.6[/tex].

So x does directly vary with y, and we have found out that [tex]k=1.6[/tex].

Answer:   [tex]\bold{\dfrac{y}{x}=1.6\quad \text{which is also equivalent to}\quad y=1.6x}[/tex]

Step-by-step explanation:

[tex]\begin {array}{c|c||l}x&y&\dfrac{y}{x}=k\\--&--&-----\\4&6.4&\dfrac{6.4}{4}=1.6\\\\11.2&7&\dfrac{11.2}{7}=1.6\\\\10&16&\dfrac{16}{10}=1.6\\\\13&20.8&\dfrac{20.8}{13}=1.6\\\end{array}\\[/tex]

Since the k-value is the same for every value in the table, we can conclude that y varies directly with x and the constant of variation k = 1.6  

Answer:

3

Step-by-step explanation:

We are given the following expression and we are to evaluate it when the value of [tex] y [/tex] is [tex] - 3 [/tex]:

[tex] 2 y + 7 - 4 y - 1 0 [/tex]

Given that [tex] y = 3 [/tex], we will substitute this value of [tex] y [/tex] in the given expression to get:

[tex] 2 y + 7 - 4 y - 1 0 [/tex]

[tex] - 2 y - 3 [/tex]

[tex] - 2 (-3) - 3 [/tex]

[tex] 3 [/tex]

Answer:

.5 or 1/2

Step-by-step explanation:

type the problem in you calculator

The circumference of the circle is found using the formula C = 2 PI r

Circumference = 2 *PI * 15.5 = 31pi

The angle is 90 degrees, which is 1/4 of a complete circle ( 360 degrees).

The arc length would be 1/4 of the circumference:

Arc length = 31pi / 4 = 7.75PI

Answer:

0.964

Step-by-step explanation:

It's easier to approach this problem if you find the prob. that z is less than -1.8 and then subtract your result from 1.00.

The prob. that z is less than -1.8 can be found using any calculator with probability and statistic functions.

The prob. that z is less than -1.8 = normcdf(-100,-8) = 0.036.  Here "cdf" stands for "cumulative probability density function)," -100 is far to the left of z = -1.8, and the result (0.036) is the area under the standard normal probability density curve to the left of z = -1.8.

Finally, subtract this 0.036 from 1.000, obtaining 0.964.  This is the probability that z is greater than -1.8.

Answer:

Step-by-step explanation:

3.14159 is irrational because it's a repeating decimal; it cannot be expressed as the ratio of two integers.  All the others can be expressed in that way.

Answer:

B. would be your answer

Answer:   c) -1372

Step-by-step explanation:

[tex]\sqrt[3]{2x} +6=-8\\\\\sqrt[3]{2x} =-14\\\\(\sqrt[3]{2x})^3 =(-14)^3\\\\2x=-2744\\\\\boxed{x=-1372}[/tex]

Answer:

c = 5

Step-by-step explanation:

This is the classic problem that the ancients (particularly the Egyptians) used extensively. When the Nile over flowed in spring, the land had to be reclaimed and  surveyed in the early summer for planting. The 3-4-5 triangle was used to determine right angles for surveying purposes.

Formula

c^2 = a^2 + b^2

Givens

a = 3

b = 4

c = ?

Solution

c^2 = 3*3 + 4*4

c^2 = 9 + 16

c^2 = 25

Take the square root of both sides

To take the square root on your calculator, find the √ on the key pad. Some calculators give it a key and some have the symbol on the body of the calculator. If has its own key do it like this.

√

25

=

The answer should come up as five. If the √ is on the body of the calculator, then

2nd F

√

25

=

The same 5 will come up.

Answer

c = 5

The hypotenuse c of a right triangle with legs a = 3 and b = 4 can be found using the Pythagorean theorem, yielding c = 5

To solve for c, the hypotenuse of a right triangle when given the legs a and b, we utilize the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This is expressed as a² + b² = c².

To solve for c when a = 3 and b = 4, we substitute these values into the theorem to get 3² + 4² = c², which simplifies to 9 + 16 = c². When we combine the values we get 25 = c². Finally, we take the square root of both sides to solve for c, resulting in c = 5.

ANSWER

[tex]{f}^{ - 1}( f(x)) = f( {f}^{ - 1} ( x)) = x[/tex]

EXPLANATION

The given functions are;

[tex]f(x) = \frac{1}{2} x[/tex]

[tex] {f}^{ - 1} (x) = 2x[/tex]

[tex]f( {f}^{ - 1} (x)) = f(2x)[/tex]

[tex]f( {f}^{ - 1} (x)) = \frac{1}{2} \times 2x = x[/tex]

Also,

[tex] {f}^{ - 1}( f(x)) = {f}^{ - 1} ( \frac{1}{2} x)[/tex]

[tex]{f}^{ - 1}( f(x)) = 2 \times \frac{1}{2} x = x[/tex]

In general,

[tex]{f}^{ - 1}( f(x)) = f( {f}^{ - 1} ( x)) = x[/tex]

Answer:

1/5

Step-by-step explanation:

Answer:

The missing value is [tex]18.41\°[/tex]

Step-by-step explanation:

Let

x-----> the angle (missing value)

we know that

[tex]sin(x)=\frac{6}{19}[/tex]

therefore

[tex]x=arcsin(\frac{6}{19})=18.41\°[/tex]

Answer:

8 units²

Step-by-step explanation:

The area (A) of a triangle is calculated using the formula

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = LK = 7 - 3 = 4 units

and h = J → x- axis = 4 - 0 = 4, hence

A = [tex]\frac{1}{2}[/tex] × 4 × 4 = 8 units²

Answer: Option a.

Step-by-step explanation:

1. Multiply the numerator and the denominator of the expression shown in the image, by the conjugate of the denominator ( [tex]\sqrt{x}-\sqrt{7}[/tex]), as you can see below:

[tex]\frac{(\sqrt{x})(\sqrt{x}-\sqrt{7})}{(\sqrt{x}+\sqrt{7})(\sqrt{x}-\sqrt{7})}[/tex]

2. By definition, you know that:

[tex](a+b)(a-b)=a^2-b^2[/tex]

3. Therefore, you obtain the following result:

[tex]\frac{(\sqrt{x})^2-\sqrt{7x}}{(\sqrt{x})^2-(\sqrt{7})^2}=\frac{x-\sqrt{7x}}{x-7}[/tex]

Then, the answer is option a.

The answer is:

a. [tex]\frac{x-\sqrt{7x}}{x-7}[/tex]

Rationalizing involves eliminating or the roots of both numerator and denominators, there are severals ways to do it but one of the most common methods is using the conjugate term.

We must remember that:

[tex](a-b)(a+b)=a^{2}-b^{2}[/tex]

So, for the given expression:

[tex]\frac{\sqrt{x}}{\sqrt{x}+\sqrt{7}}[/tex]

The conjugate is:

[tex]\sqrt{x}-\sqrt{7}[/tex]

The, we need to multiply both numerator and denominator (in order to not affect the expression) by the conjugate expression in order to eliminate the radicals in the denominator:

[tex]\frac{\sqrt{x}}{\sqrt{x}+\sqrt{7}}*\frac{\sqrt{x}-\sqrt{7}}{\sqrt{x}-\sqrt{7}}=\frac{(\sqrt{x})*(\sqrt{x}-\sqrt{7})}{(\sqrt{x}+\sqrt{7})*(\sqrt{x}-\sqrt{7})}[/tex]

[tex]\frac{(\sqrt{x})*(\sqrt{x}-\sqrt{7})}{(\sqrt{x}+\sqrt{7})*(\sqrt{x}-\sqrt{7})}=\frac{(\sqrt{x})^{2}-(\sqrt{x})*(\sqrt{7})}{(\sqrt{x})^{2}-(\sqrt{7})^{2}}[/tex]

[tex]\frac{(\sqrt{x})^{2}-(\sqrt{x})*(\sqrt{7})}{(\sqrt{x})^{2}-(\sqrt{7})^{2}}=\frac{x-\sqrt{7x}}{x-7}[/tex]

Have a nice day!

Answer:

d=4/7

Step-by-step explanation:

d=5/7*4/5

The numbers are 19 and 28.

Answer:

28 and 19

Step-by-step explanation:

let the 2 numbers be x and y, x > y, then

x + y = 47 → (1) ← sum of numbers

x - y = 9 → (2) ← difference of numbers

Adding the 2 equations to eliminate y

2x = 56 ( divide both sides by 2 )

x = 28

substitute x = 28 into (1) and solve for y

28 + y = 47 ( subtract 28 from both sides )

y = 47 - 28 = 19

The 2 numbers are 28 and 19

Answer:

There was 94 unopened packets.

Step-by-step explanation:

Divide 9425 by 100.

9425 / 100 = 94.25

That means there was 94 unopened packets.

Answer:

thirty-six inches

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

12x3 = 36

Answer:

Step-by-step explanation:

The angular coefficient is a slope.

The slope-intercept form of an equation of a line:

y = mx + b

m - slope

b - y-intercept

We have the equation y = 4 - 2x → y = -2x + 4

The slope is m = -2

Answer:

Option D.

Step-by-step explanation:

Precision refers to the the level of measurement and exactness of a measurement. The mean diference between 'precision' and 'exactness' is that  if a measuring device gives consisten measurements it's considered precise, but it's not necessarily accurate.

For example, a measurement of 2.365m is more precise than a measurement of 2.3m, given that 2.365m has more significant figures and was made with an instrument that has higher precision. This doesn't mean that the measurement is accurate, the real value could be 3m for example! ✅

Answer:

How you make predictions is by finding the ratio of the number of times an event occurs to the total number of trials.

Step-by-step explanation:

Answer: The answer to this question is 3y + 3z, You need to distribute into the parentheses.

Step-by-step explanation: Distribute the 4 outside the parentheses to each inside term. Then, move the coefficient in front of the term. Finally, rearrange to put the coefficient in front.

[tex]\bf \cfrac{32}{100}\div \cfrac{4}{4}\implies \cfrac{32}{100}\div 1\implies \cfrac{32}{100}\implies \cfrac{\underline{2\cdot 2}\cdot 2\cdot 2\cdot 2}{\underline{2\cdot 2}\cdot 5\cdot 5}\implies \cfrac{2\cdot 2\cdot 2}{5\cdot 5}\implies \cfrac{8}{25}[/tex]

Answer:

8/25

Step-by-step explanation:

you divide 32/100 by 4/4=8/25 because 8x4=32 and 4x25=100

Answer:

AC

Step-by-step explanation:

Looking at triangles ABD and ACD, they appear to be congruent. This means they have corresponding or matching parts which are equal and form each triangle.

The segment AB is the shortest segment of triangle ABD. It matches to the shortest segment in ACD. This segment is AC.

Answer:

AB <--> AC

Step-by-step explanation:

Hello! Segment AB is congruent to segment AC in ABD and ACD.

Thus, they are in correspondence to one another.

Hope this helps!