What is the solution to r/-3 = 12? A. r=-36 B. r= -4 C. r=4 D. r=36 (1 point)

The functions f(x) and g(x) so the given function can be expressed as h(x) = f(g(x) are f(x) = 8/x^2 and g(x) = x + 4

The function h(x) is given as:

h(x) = 8/(x + 4)^2

The definition of the function h(x) is

h(x) = f(g(x))

So, we have:

f(g(x)) = 8/(x + 4)^2

Let g(x) = x + 4

So, we have:

f(g(x)) = 8/(g(x))^2

Express g(x) as x

So, we have:

f(x) = 8/x^2

Hence, the functions f(x) and g(x) so the given function can be expressed as h(x) = f(g(x) are f(x) = 8/x^2 and g(x) = x + 4

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Answer:

1 solution

b=7

Step-by-step explanation:

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2b - 5 = 9

2b=14

b=7

1 solution

Explanation:

Think of a substitute teacher. They temporarily replace your original teacher. The same idea applies with replacing the variable with a number.

For example, the equation x+2 = 7 has the solution x = 5. We can check this by substituting or replacing x with 5 to say 5+2 = 7, which is indeed a true mathematical statement. This confirms the solution.

Answer:

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Answer:

5+n/9=3

Step-by-step explanation:

Here we go ~

A.) Derivative of 6x² :

[tex]\qquad \sf  \dashrightarrow \:f {}^{ \prime}(x) = \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{f(x + h) - f(x)}{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{6(x + h) {}^{2} - 6(x) {}^{2} }{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{6(x {}^{2} + 2xh + h {}^{2} ) {}^{} - 6(x) {}^{2} }{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel{6x {}^{2}} + 12xh +6 h {}^{2} {}^{} - \cancel{6x{}^{2}} }{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ 12xh +6 h {}^{2} {}^{} }{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel{ h}( 12x +6h ) {}^{} {}^{} }{ \cancel{h}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: 12x + 6h[/tex]

[tex]\qquad \sf  \dashrightarrow \: 12x + 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: f {}^{ \prime} (x) = 12x[/tex]

B.) The derivative of f(x) = 2x² -7x + 8 :

[tex]\qquad \sf  \dashrightarrow \:f {}^{ \prime}(x) = \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{f(x + h) - f(x)}{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ 2(x + h) {}^{2} - 7(x + h) + 8 - (2 {x}^{2} - 7x + 8)}{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ 2(x {}^{2} + 2xh + {h}^{2} ) {}^{} - \cancel{7x} + 7h+ \cancel8 - 2 {x}^{2} + \cancel{7x } - \cancel 8)}{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel{ 2x {}^{2}} + 4xh + 2{h}^{2} {}^{} - 7h - \cancel{2 {x}^{2}} }{h} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: \frac{ \cancel {h}( 4x + 2{h}^{} {}^{} - 7) }{ \cancel{h} }[/tex]

[tex]\qquad \sf  \dashrightarrow \: \sf\displaystyle { \lim_{h\to0}} \sf\: \: 4x + 2{h}^{} {}^{} - 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4x - 0 - 7[/tex]

[tex]\qquad \sf  \dashrightarrow \: f {}^{ \prime} (x) = 4x - 7[/tex]

The diamonds produced by country A and B are 24,000,000 and 4,000,000 carats respectively.

Here, we are given that Country A produces about six times the amount of diamonds in carats produced in country B.

Let the diamonds produced by country B be x

Then, the diamonds produced by country A will be 6x

The total diamonds produced by the two countries = 28,000,000

Thus, we can get the following equation-

x + 6x = 28,000,000

7x = 28,000,000

x = 28,000,000/ 7

x = 4,000,000

⇒ 6x = 24,000,000

Thus, the diamonds produced by country A and B are 24,000,000 and 4,000,000 carats respectively.

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Answer:

181

Step-by-step explanation:

Sally is running laps around a track. She runs 12 laps to warm up. Then she runs 13² laps.

First write the equation. we know she alr ran 12 laps so its going to be +12

to 13^2. so the equation will be 12+13^2 then using PEMDAS we know that we have to do the exponents first so 13^2 is just 13 * 13 which is 169. so now the equation is 169+12 now just add. the answer is 181

The solution in interval form is given as (-∞, -6-√29

] or [-6+√29, ∞)

Given the quadratic inequality below;

x^2+ 12x+7<0

Using the general formula

x = -12±√12²-4(1)(7)/2(1)

x = -12±√144-28/2

x = -6±√116/2

x = -6±√29

Hence the solution in interval form is given as (-∞, -6-√29

] or [-6+√29, ∞)

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Answer:

B=30°

Step-by-step explanation:

Recall that the sum of interior angles of a triangle equals to 180°. So basically

[tex]A+B+\alpha+\beta=180^{\circ}[/tex]

[tex] \implies B + {70}^{ \circ} + {80}^{ \circ} = {180}^{ \circ} \\ \implies B = {180}^{ \circ} - {150}^{ \circ} \\ \implies B = \boxed{{30}^{ \circ} }[/tex]

Answer:

y = 2x +4

Step-by-step explanation:

Equation of a line in slope-intercept form is

y = mx + b

where m is the slope and b is the y-intercept, the point at which the line crosses the y axis (at x = 0)

Given slope is 2 we get the equation as

y = 2x + b

We have to solve for b by plugging in the x and y values for point(1,6)

Thus we get y = 6 = 2(1) + b

Or 6 = 2 + b

b= 6-2 = 4

Equation in slope-intercept form is

y = 2x +4

Hi!

Apply the Point-Slope formula:

◈Where:

◈We know that:

◈Plug in the values:

[tex]\bigstar\textsf{\textbf{Solution: \boxed{\textsf{\textbf{2x+4}}}}}[/tex]

Have a great day!

I hope this helped!

-stargazing

The value of x is 52° and the value of y is 104 ° as calculated using the chord properties of a circle.

A circle is defined as the locus of a moving point such that the distance of the point from a fixed point is always same.

In the given figure AC is the diameter of the circle.

We know that the  angle subtended by the chord is always 90°.

∴∠CBA = 90°

Now in ΔABC

∠ABC+∠BCA+ ∠CAB =180° (sum of all angles of a triangle is always 180°)

or, 90° + 38° + x° = 180°

or, 128° + x° =180°

or, x = 52°

Again in ΔDBC ,

DB=DC (radius of the circle)

∴∠DCB = ∠DBC (base angles of an isosceles triangles are equal)

∴∠DBC = 38°

Again in ΔDBC

∠DBC+∠BCD+ ∠CDB = 180° (sum of all angles of a triangle is always 180°)

or, y =  180° - 76°

or, y = 104°

Therefore the value of x is 52° and the value of y is 104 ° .

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Answer:The value of coordinates G', H', and F' are (1,6) , ( 7,3) and (4 , 0) respectively.What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.For example (5,3) here 5 will be for the x and 3 will be for the y.Another example is (9,0) here 9 is for x and 0 is for y.

Step-by-step explanation:

Answer:

y =x - 1

Step-by-step explanation:

Here, m is the slope and b is the y-intercept.

Plot any two points on the line. (5,4)  & (0,-1)

[tex]\sf \boxed{Slope =\dfrac{y_2-y_2}{x_2-x_1}}[/tex]

          [tex]\sf =\dfrac{-1-4}{0-5}\\\\=\dfrac{-5}{-5}\\\\=1[/tex]

m = 1

At y-intercept x = 0.  So, the -1 is the y-intercept.

m = 1 & b = -1

y = 1x + (-1)

The confidence interval for n = 22, X bar = 30 and σ = 7 at a 98% confidence level is 30 ± 3.472 which means the value will range between [26.528 – 33.472] respectively.

In statistics, a confidence interval is a range of values that is determined through the use of observed data, calculated at a desired confidence level that may contain the true value of the parameter being studied.

The formula used for the calculation of confidence interval is given by

Confidence level = X bar ± Z×σ/√n

where, X bar is the sample mean, Z is the confidence level value, σ is the sample standard deviation and n is the sample size.

Given that, n = 22, X bar = 30, σ = 7 and Z = 2.326 for 98%

= 30 ± 2.3263 × 7/√22

= 30 ± 3.472

= [26.528 – 33.472]

Therefore, The confidence interval for n = 22, X bar = 30 and σ = 7 at a 98% confidence level is 30 ± 3.472 which means the value will range between [26.528 – 33.472] respectively.

Hence, 30 ± 3.472 or [26.528 – 33.472] is the required answer.

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Answer:

Step-by-step explanation:

You are given the solution to a 2-step linear equation and asked to identify the properties of equality and operations that support the steps of the solution.

5(x -3) = 20 . . . . This is the Given equation we're solving.

(1/5)(5(x -3)) = (1/5)(20) . . . . Both sides are multiplied by 1/5. The Multiplication property of equality says you can do this without changing the value of the variable.

1(x -3) = 4 . . . . (1/5)(5) is replaced by 1. The Multiplicative inverse property tells you the product of a number and its multiplicative inverse is 1.

x -3 = 4 . . . . 1(x -3) is replaced by (x -3). The Multiplicative identity property tells you multiplication by 1 changes nothing. These properties of multiplication are what allow you to remove the factor of 5 from the equation.

Now, we're about to do the same thing with addition: use its properties to remove the unwanted -3.

x -3 +3 = 4 +3 . . . . 3 is added to both sides. The Addition property of equality says you can do this without changing the value of the variable.

x +0 = 7 . . . . -3+3 is replaced by 0. The Additive inverse property tells you the sum of a number and its additive inverse is zero.

x = 7 . . . . x+0 is replaced by x. The Additive identity property tells you addition of 0 changes nothing. These properties of addition are what allow you to remove the added -3 from the equation.

__

Additional comment

Clearly, for exercises like this, it is essential to know the names of these properties and what they mean. Once you understand cancelling multiplication using multiplicative inverses, and cancelling addition using additive inverses, you are on your way to solving most algebra problems.

You must always keep in mind the properties of equality that tell you the same operation must be performed on both sides of the equal sign.

Understanding these properties can also help you understand the relation between multiplication and division, addition and subtraction. Division is multiplication by the multiplicative inverse; subtraction is addition of the additive inverse.

It should be noted the difference between - 4 1/2 and 3 1/4 is - 1/14.

It should be noted that fractions are not while numbers. The number at the top is the numerator and the number down is the denominator.

In this case:

- 4 1/2 + 3 1/4

= - 4 2/4 + 3 1/4

= - 1 1/4

Therefore, it should be noted the difference between - 4 1/2 and 3 1/4 is - 1/14.

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The interest rate required to get a total amount of $3,688.86 from compound interest on a principal of $2,000.00 compounded 12 times per year over 5 years is 12.306% per year.

Given,

The total amount (A)= $3688.86

Principal (P) = $2000

time period (t) = 5 years.

compounded monthly (n) = 12

rate of interest per year = ?

we know that r=n[(A/P)¹/ⁿt  -1]

substitute the above values.

r = 12 × [(3688.86/2000)¹/⁽¹²⁾⁽⁵⁾ - 1]

r = 12 × [(1.84443)¹/⁶⁰ - 1]

r = 12 × 0.0102

r = 0.12306

Now convert r to R as a percentage.

R = r × 100

R = 0.12306 × 100

R = 12.306%

Hence the rate of interest compounded monthly is 12.306%

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The dimensions of the field is Length = 34 meters, width = 14 meters.

Let rectangle: x for width, y for length.

2 ( x + y ) = 96

x + y = 48

2 ( x + y ) + x = 110

x = 110 - 96

x = 14

x + y = 48

y = 48 - 14 = 34

Length = 34 meters, width = 14 meters.

A quadrilateral with equal angles and parallel opposing sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and breadth of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.

A closed shape with four sides that forms a 90° angle is known as a rectangle. A rectangle can have many different characteristics. The following list includes some of a rectangle's key characteristics.

A quadrilateral is a rectangle.

A rectangle's opposing sides are equal and parallel to one another.

Each vertex of a rectangle has a 90° internal angle.

360° is the total of all interior angles.

The diagonals cut each other in half.

The diagonals are all the same length.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

First of all, it's a graph of mod function, which is transformed.

So, let's proceed with taking graph of modulus initially ~

[tex]\qquad \sf  \dashrightarrow \: y = |x| [/tex]

The required can be tranformed by moving it three units left and four units down.

so, we need to add 3 to x within the function to move it left by units.

i.e

[tex]\qquad \sf  \dashrightarrow \: y = |x + 3| [/tex]

Now, to move it down by 4 units we need to subtract 4 from the whole function.

[tex]\qquad \sf  \dashrightarrow \: y = |x + 3| - 4[/tex]

So, the correct choice is : C

the required can be transformed by moving at 3 units left and 4 units down do you understand ? after that are 3 and x

y = x + 3

now to move it down by 4 units we need to subtract for from the whole function which is y is equal to x + 3 - 4

y = |x+3| - 4

the answer is c

Answer:

y = - x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - x + 5 ← is in slope- intercept form

with slope m = - 1

• Parallel lines have equal slopes , then

y = - x + c ← is the partial equation of the parallel line

to find c substitute (3, - 2 ) into the partial equation

- 2 = - 3 + c ⇒ c = - 2 + 3 = 1

y = - x + 1 ← equation of parallel line

The elevation of the trench is between 4 miles and 5 miles.

Herein we have the information of the elevation of the trench in feet and we need to determine between which integers in miles is that elevation, based on the unit conversion from feet to miles. The exact elevation in miles is found by simple rules of three:

x = 22,889 feet × (1 / 5,280 miles / feet)

x ≈ 4.335 miles

The elevation of the trench is between 4 miles and 5 miles.

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Answer:

let (5,4)=(x1,y1)

(-3,-2)=(x2,y2)

now, by using distance formula

we get distance between line segment =10 unit

therefore distance =10 units ans

Solution,

As the formula...

[tex] = \sqrt{( - 3 - 5 {)}^{2} + ( - 2 - 4 {)}^{2} } [/tex]

[tex] = \sqrt{( - 8 {)}^{2} + ( - 6 {)}^{2} } [/tex]

[tex] = \sqrt{64 + 36} [/tex]

[tex] = \sqrt{100} [/tex]

= 10 units...

☘☘☘....

The missing number (x) from the sequence → 11, 29, 11, x  is 17.

We have the mean of given set of numbers.

We have to identify the missing number.

The mean in math and statistics summarizes an entire dataset with a single number representing the data's center point or typical value. It is calculated  using the formula -

Mean (M) = ∑a[i] / n

where -  

∑a[i] = sum of the elements in a data set

n = total number of elements

According to the question - assume that the missing number is x. Then, we have -

11, 29, 11, x

Now, using the formula of mean -

M = ∑a[i] / n

17 = (11 + 29 + 11 + x)/4

68 = 51 + x

x = 68 - 51

x = 17

Therefore, the missing number is 17.

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