Given f(x)=(x-6)^2+7 find f^-1(x) then state whether f^-1(x) is a function

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x-5y=9&\text{multipy both sides by 4}\\3x+4y=2&\text{multiply both sides by 5}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}8x-20y=36\\15x+20y=10\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad23x=46\qquad\text{divide both sides by 23}\\.\qquad x=2\\\\\text{put it to the second equation}\\\\3(2)+4y=2\\6+4y=2\qquad\text{subtract 6 from both sides}\\4y=-4\qquad\text{divide both sides by 4}\\y=-1[/tex]

Part A: Scatter plot with best-fit line attached. You'll find the line to have equation (approximately)

[tex]y=51.34+3.98x[/tex]

The positive slope suggests that test scores and study time are directly are proportional.

Part B: Same as in a previous question you had posted. Pick two points on the provided line and compute the slope as best you can. For example, I might pick (2, 30) and (4, 40), which gives a slope of

[tex]\dfrac{40-30}{4-2}=5[/tex]

and assuming the line passes through (2, 30) exactly, it would have equation

[tex]y-2=5(x-30)\implies y=5x-148[/tex]

Answer:

3(x-2)÷(x-2)=3.....

Answer:

Step-by-step explanation:

[tex]3x-6\qquad\text{distributive}\\\\=(3)(x)-(3)(2)=(3)(x-2)=3(x-2)\\\\\dfrac{3x-6}{x-2}=\dfrac{3(x-2)}{x-2}\qquad\text{cancel}\ (x-2)\\\\=\dfrac{3(1)}{1}=3[/tex]

Answer:

(3x^2-5x-5)/(x^2+x) <--- answer  

Step-by-step explanation:

3x/(x+1) - 5/x = (3x^2 - 5(x+1) )/[ x(x+1) ]  

= (3x^2 - 5x - 5)/(x^2 + x)

The difference between the rational expressions 3x+1/x and 5/x is 3x - 4/x.

The difference between these two rational expressions will be obtained by subtracting the second expression from the first. To do this, we first need to simplify the expressions wherever possible. The first expression, 3x + 1/x, remains as it is. The second expression, 5/x, is a simple fraction and can't be simplified any further either.

Subtracting the second from the first, you get (3x + 1/x) - (5/x) which simplifies to 3x - 4/x. The difference between these two rational expressions is hence 3x - 4/x.

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Answer:

Part 1) The inscribed angle is the angle ∠TRS and the intercept arc is the arc LST

Part 2) The inscribed angle is the angle ∠YWX and the intercept arc is the minor arc XY

Part 3) The inscribed angle is the angle ∠YXZ and the intercept arc is the arc YBZ

Part 4) The figure does not show an inscribed angle

Step-by-step explanation:

Part 1) The figure shown a inscribed angle

The inscribed angle is the angle ∠TRS

The intercept arc is the arc LST

Remember that

The inscribed angle measures half that of the arc comprising

so

∠TRS=(1/2)[arc LST]

Part 2) The figure shown a inscribed angle

The inscribed angle is the angle ∠YWX

The intercept arc is the minor arc XY

Remember that

The inscribed angle measures half that of the arc comprising

so

∠YWX=(1/2)[minor arc XY]

Part 3) The figure shown a inscribed angle

The inscribed angle is the angle ∠YXZ

The intercept arc is the arc YBZ

Remember that

The inscribed angle measures half that of the arc comprising

so

∠YXZ=(1/2)[arc YBZ]

Part 4) The figure does not show an inscribed angle

The figure shown a interior angle ∠BAC

Answer:

4

Step-by-step explanation:

Let's call the width W and the length L.

We know the width is 3 less than the length, so:

W = L - 3

And we know the area is 28, so:

28 = WL

If we solve for L in the first equation:

L = W + 3

And substitute into the second equation:

28 = W (W + 3)

28 = W² + 3W

0 = W² + 3W - 28

0 = (W + 7) (W - 4)

W = -7, 4

Since W can't be negative, W = 4 units.

The width, in units, of the rectangle, if the area of the rectangle is 28 units, is  4 units.

The measurement that expresses the size of a region on a plane or curved surface is called an area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given:

The width of a rectangle is 3 units less than the length. The area of the rectangle is 28 units,

Write the equation as shown below,

b = l - 3   (Here, l is the length and b is the width)

l × b = 28

Solve the above equations,

l = 7 units and b = 7 - 3 = 4 units

Therefore, the width, in units, of the rectangle, if the area of the rectangle is 28 units, is  4 units.

To know more about Area:

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Answer:

14.93

Step-by-step explanation:

For this problem you need to know distance formula, which is

d=√(x2-x1)²+(y2-y1)². You'll want to plug in (0,3) and (-2, 9) and go on to plug in all of them at some point. You'll get 6.32 as the distance between (0,3) and (-2, 9), 3.61 as the distance between (-2, 9) and (-4, 6), and 5 as the distance between (-4, 6) and (0, 3). You add them up and get your answer.

Answer:

Step-by-step explanation:

[tex](a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\2x^2+12x-14=0\qquad\text{divide both sides by 2}\\\\x^2+6x-7=0\qquad\text{add 7 to both sides}\\\\x^2+2(x)(3)=7\qquad\text{add}\ 3^2=9\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=7+9\\\\(x+3)^2=16\Rightarrow x+3=\pm\sqrt{16}\\\\x+3=-4\ or\ x+3=4\qquad\text{subtract 3 from both sides}\\\\x=-7\ or\ x=1[/tex]

A)x+4x = Juice and water

x = Water

4.00 is total juice relative to water

  +

1.00 is total water

B) 4 liters

(1 liter)+4(1 liter) = Total

1 + 4 = 5

Find the length of a side of a square with an area of 169 in^2.

Answer:

D. 13 in

Step-by-step explanation:

A square has sides of equal length.

A = L^2 where:  A = area  and  L = side

L^2 = 169

L=√169

L=13 in^2.    

The length of a side of a square with an area of 169 in2 is calculated by taking the square root of the area, which is 13 inches. The correct answer is D. 13 in.

The student is asking to find the length of a side of a square given that the area of the square is 169 square inches. The formula to calculate the area of a square is side length squared, which can be written as:

Area = side × side

To find the side length, we need to take the square root of the area:

Side = √169

Upon calculation, the side length is:

Side = 13 {in}

Therefore, the correct answer is D. 13 in.

x/2 + 10 = 35 - 2x

x/2 + 2x = 35 - 10

5x/2 = 25

5x = 25.2

5x = 50

x = 50/5

x = 10

The number is 10

Let's take it step by step to find the number for the given situation:
Step 1: Define the variable.
Let's denote the number we are trying to find as \( x \).
Step 2: Set up the equation based on the given information.
The problem statement says "Half a number increased by 10 is equal to 35 less than twice the number." This gives us the equation:
\[ \frac{1}{2}x + 10 = 2x - 35 \]
Step 3: Solve the equation.
Now we'll solve for \( x \). To do this, we need to get all terms involving \( x \) on one side and the constant terms on the other. Start by subtracting \( \frac{1}{2}x \) from both sides to get rid of the \( x \) term on the left-hand side:
\[ 10 = \frac{3}{2}x - 35 \]
Now, add 35 to both sides to isolate the \( x \)-related term on the right-hand side:
\[ 10 + 35 = \frac{3}{2}x \]
\[ 45 = \frac{3}{2}x \]
Next, to solve for \( x \), multiply both sides by \( \frac{2}{3} \) to cancel out the fraction:
\[ \frac{2}{3} \cdot 45 = x \]
\[ x = 30 \]
Step 4: Verify the solution.
Plugging the value of \( x \) back into the original equation to check:
\[ \frac{1}{2} \cdot 30 + 10 = 2 \cdot 30 - 35 \]
\[ 15 + 10 = 60 - 35 \]
\[ 25 = 25 \]
The equation is true, confirming that the solution \( x = 30 \) is correct.
Therefore, the number we were trying to find is 30.

Answer:

B

Step-by-step explanation:

Using the rule of logarithms

• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Given

[tex]log_{x}[/tex] ([tex]\frac{1}{8}[/tex] ) = - [tex]\frac{3}{2}[/tex], then

[tex]\frac{1}{8}[/tex] = [tex]x^{-\frac{3}{2} }[/tex]

Square both sides

[tex]\frac{1}{64}[/tex] = [tex]x^{-3}[/tex]

[tex]4^{-3}[/tex] = [tex]x^{-3}[/tex] ⇒ x = 4 → B

Answer: Disc, Congruent, parallel

Step-by-step explanation:

The disks, congruent, and parallel choices describes the bases of a cylinder option (A), (B), and (D) are correct.

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

[tex]\rm V = \pi r^2 h[/tex]

We have given a statement:

Which of the following choices describes the bases of a cylinder:

The options given:

A) disks

B) congruent

C) similar

D) parallel​

As we know, the cylinder has two circular bases at height h between them.

The bases of a cylinder can be described as disks, congruent, and parallel.

Thus, the disks, congruent, and parallel choices describes the bases of a cylinder option (A), (B), and (D) are correct.

Learn more about the cylinder here:

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Answer:

[tex]300,000.04\ people[/tex]

Step-by-step explanation:

we know that

To find how many people live in that city multiply the population density by the area of the city

so

[tex](46\ \frac{people}{mi^{2}})(6,521.74\ mi^{2})=300,000.04\ people[/tex]

Answer: None of them are equal

Step-by-step explanation:

Answer: I hope this helps with any confusion

A) x + 4

Step-by-step explanation:

x(x + 9) + 20

x + 5

x2 + 9x + 20

x + 5

(x + 4)(x + 5)

x + 5

x + 4

[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta )=1-sin^2(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin^2(\theta )}{1-sin^2(\theta )}\implies \cfrac{sin^2(\theta )}{cos^2(\theta )}\implies \left[ \cfrac{sin(\theta )}{cos(\theta )} \right]^2\implies tan^2(\theta )[/tex]

Leo needs 6 red roses and 9 pink daisies for 3 bouquets, calculated by dividing the number of flowers needed for 5 bouquets by 5 and then multiplying by 3.

To calculate the amount of red roses and pink daisies Leo needs for 3 bouquets, we first determine the number needed for one bouquet. Since Leo needs 10 red roses and 15 pink daisies for every 5 bouquets, we divide each amount by 5 to find the number per single bouquet:

Now, we multiply the number of flowers needed per bouquet by 3 to find the total number for 3 bouquets:

Therefore, for 3 bouquets, Leo needs 6 red roses and 9 pink daisies.

Answer:

Step-by-step explanation:

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

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have m = -1 and the point (-3, 5). Substitute:

[tex]y-5=-1(x-(-3))\\\\y-5=-(x+3)[/tex]

ANSWER

See sample space below

EXPLANATION

The sample space refers to the set of all the possible outcomes.

When two fair dice are rolled, the possible by outcomes are:

{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

The total number of outcomes is 36.

Answer:

1:4

Step-by-step explanation:

24 divided by 6 is 4. and 6 divided by 6 is 1

Answer:

1:4

Step-by-step explanation:

24÷6=4 and 6÷6=1 this is all you need

Answer:

61 second I would say but what is the weight of the rock?

Answer:

Option B. 7.8 seconds

Step-by-step explanation:

Shyanne drops a rock from a hill at initial height of 975 feet above the ground level.

We have to calculate the time taken by rock to hit the ground.

As we know the formula of motion under gravity is

h = ut + [tex]\frac{1}{2}gt^{2}[/tex]

Here h = initial height = 975 feet

u = initial velocity = 0

t = time taken by the rock to hit the ground

g = 32.174 [tex]\frac{\text{Feet}}{\text{Second}^{2}}[/tex]

Now we plug in these values in the formula

975 = 0 + [tex]\frac{1}{2}(32.174)(t)^{2}[/tex]

975 = 16.087t²

t² = [tex]\frac{975}{16.087}[/tex]

t = [tex]\sqrt{60.60}[/tex]

t = 7.78 ≈ 7.8 seconds

Option B. 7.8 seconds is the answer.

Answer: (4y - 3)(3x - 2)

Step-by-step explanation: Factor the polynomial.

Hope this helps! :) ~Zane

For this case we must factor the following expression:

[tex]12xy-9x-8y + 6[/tex]

So:

We group the first two and two last terms:

[tex](12xy-9x) + (- 8y + 6) =[/tex]

we factor the maximum common denominator of each group:

[tex]3x (4y-3) -2 (4y-3) =[/tex]

We factor the polynomial by factoring the highest common denominator:

[tex](3x-2) (4y-3)[/tex]

ANswer:

[tex](3x-2) (4y-3)[/tex]

3 terms. Just count the terms (which are separated by the +/- signs)

The answer is:

The polynomial have 3 terms. (it's a trinomial).

A polynomial is an expression which consists of one or more terms (numbers or variables) being added or subtracted.

So, we are given the polynomial:

[tex]x^{2} +xy-y^{2}[/tex]

We have that there are three terms separated by differents being added and subtracted, so, the polynomial has 3 terms, and it's a trinomial.

Have a nice day!

Answer: The answer is 94

Step-by-step explanation: First you should pay attention to the main numbers and since more and many are addition word than you should add 7 + 4 which equals 11 then add 83 + 11 which would equal 94. Tell me if the answer is wrong and I would find another way to answer it.  

Final answer:

Linda sent 8 text messages, Jim sent 15 messages, and Dale sent 60 messages during the weekend.

Explanation:

The question asks to solve a word problem to find out how many text messages Linda, Dale, and Jim sent over the weekend.

Let's denote the number of messages Linda sent as L, Jim as J, and Dale as D.

The problem states that Jim sent 7 more messages than Linda, so J = L + 7.

Dale sent 4 times as many messages as Jim, so D = 4J.

Together they sent 83 messages, which gives us the equation L + J + D = 83.

Substituting the expressions for J and D in terms of L into the equation, we get L + (L + 7) + 4(L + 7) = 83.

This simplifies to 6L + 35 = 83. Solving for L gives us L = 8.

This means Linda sent 8 messages, Jim sent 15 messages (8 + 7), and Dale sent 60 messages (4 times 15).

Answer:

Nikolaus Otto was  responsible for inventing the first working four-stroke engine.

​

Step-by-step explanation:

Answer:

Step-by-step explanation:

if i had to guess i would say a

ANSWER

The midpoint is a) (m,n)

EXPLANATION

The point O has coordinate (0,0) and the point A has coordinate (2m,2n)

The x-coordinate of the midpoint is

[tex]x = \frac{0 + 2m}{2} [/tex]

[tex]x = \frac{2m}{2} [/tex]

[tex]x = m[/tex]

Also,

[tex]y = \frac{0 + 2n}{2} [/tex]

[tex]y = \frac{ 2n}{2} [/tex]

[tex]y = n[/tex]

The answer is A

Answer:

9⁹ ÷ 9⁶.

The expression 9³ is equivalent to 9⁹ ÷ 9⁶.

Step-by-step explanation

hope it

Answer:

It is correct.

Step-by-step explanation:

Orange to Apple juice = 3:1.

Work out the 'multiplier':

3 + 1 = 4.

3 parts are orange so we need 3 * the multiplier = 3*4 = 12  litres.

Answer:

No.

Step-by-step explanation:

To be prime, it has to be a number more than 1.

Answer:

No

Step-by-step explanation:

The number 1 is only divisible by itself, so it is neither prime nor composite.

Answer:

false

Step-by-step explanation:

One milliliter of water has one gram of mass, and weighs one gram in typical situations

One milliliter of water does not have a mass of 2.00 grams.

Water has a density of 1g/mL, so one milliliter of water has a mass of 1 gram.