f(x) = x 2+ 6 and g(x) = 2x - 1

g[f(x)] =

Just solve.

[tex](17-k)^3\\k=12 \\ \\ (17-12)^3 \\ \\ (5)^3 \\ \\ 125\\[/tex]

[tex]\\\\(5+2n)^5 \\ n=-2 \\ \\ (5+2(-2))^5 \\ \\ (5-4)^5 \\ \\ (1)^5 \\ \\ 1[/tex]

Answer:

(-2,-4)

Step-by-step explanation:

in this exercise I have the formula of the parable expressed as:

[tex]y=ax^{2} +bx+c[/tex]

I can write it in its "vertex form"

[tex]y=a(x-d)^{2} +e[/tex] being (d,e) the coordinates of the vertex of said parabola.

by clearing the equation I can see that [tex]d=\frac{-b}{2a}[/tex] so I substitute[tex]d=-\frac{4}{2*1} =-2[/tex]

Now taking d as the value for the x axis of the vertex coordinate, I substitute d in x, in the initial equation

[tex]y=x^{2} +4x =(-2)^{2}+4(-2)=4-8=-4[/tex]

So finally, I have the coordinates of the vertex of the parabola are (-2,-4)

Done

Answer:

She'll need 8143 cubic inches of foam and 1,809.6  square inches of fabric.

Step-by-step explanation:

Assuming you want to know how much foam and fabric she will need...

First the foam... so we need to determine the volume of that footstool.  The Volume of a cylinder is given by:

V = π * r² * h

So, we plug in the numbers:

V = π * 12² * 18 = π * 144 * 18

V = 2,592 π  = 8143 cubic inches.

Now for the fabric... we'll assume Maria wants to cover the side of the stool and the top, but not the bottom.

The side of the stool is basically a rectangle of width of 18 inches and a length of the circumference of the base of the stool.  The circumference is given by: C = 2 π * r of course, so C = 24π = 75.14 inches.

So the lateral surface of the cylinder is:

LS = 18 * 75.14 = 1,357.2 sq inches.

Then we need to calculate the area of the top... which is easy:

A = π * r²  = π * 12²  = 144 π = 452.4 sq inches

So, to cover the lateral side of the footstool and its top, she needs to use:

TA = 1,357.2 + 452.4 = 1,809.6 sq inches of fabric.

Answer:

The team needs to win 15 races today.

Step-by-step explanation:

The team has completed 45 races so far and has won 30 so far.

The current success rate is

[tex]r = \frac{30}{45} * 100\% = 66.7\%[/tex]

We need this success rate to be 75%

Then the team must win a number x of races such that

[tex]r = \frac{30 + x}{45 + x} = 0.75[/tex]

Now we solve the equation for x.

[tex]\frac{30 + x}{45 + x} = 0.75\\\\30 + x=0.75(45 +x)\\\\30 + x=0.75(45) +0.75x\\\\x- 0.75x = 33.75-30\\\\0.25x = 3.75\\\\x= \frac{3.75}{0.25}\\\\x=15[/tex]

Finally the team need to win  15 carreras today

Answer: 15 races

Proof of validity is shown below.

Answer: x = 4.69/ x = (squareroot) 22

Quadratic Equation: 17 - x² = -5

Subtract 17 from both sides

17 - x² - 17 = -5 - 17

Simplify

-x² = -22

Divide both sides by -1

-x² / -1  =  -22 / -1

Simplify

x² = 22

x = (squareroot) 22 or

x = 4.69

The solutions to the equation are x= √ 22 and x= -√ 22.

The Solving Quadratic Equation given is 17-x²=-5.

First, let's rearrange this equation in a form ax²+bx+c=0.

When rearranged, it reads as: x² - 22 = 0. Here, a=1, b=0, c=-22.

The solutions or the roots of this quadratic equation can be calculated using the quadratic formula -b ± √b² - 4ac/2a.

Substituting the values into the formula gives -0 ± √(0 - 4(1)(-22))/2(1), simplifying this gives x = ± √ 22.

Therefore, the solutions to the equation are x= √ 22 and x= -√ 22.

Learn more about Solving Quadratic Equation here:

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The probable question may be:

Solve the following quadratic equation for all values of x in simplest form !! Please answer this !!

17-x^2=-5

The equation represented by the tape diagram is: 2x + 3 = 5x

This can be solved by subtracting 2x from both sides: 3 = 3x

Dividing both sides by 3 gives the solution: x = 1

Therefore, the equation to solve is: 2x + 3 = 5x

The tape diagram represents the following equation:

2x + 3 = 5x

This can be solved by subtracting 2x from both sides:

2x + 3 - 2x = 5x - 2x

3 = 3x

Dividing both sides by 3 gives the solution:

x = 3 / 3

x = 1

Therefore, the equation to solve is:

2x + 3 = 5x

The solution is:

x = 1

The  equation to solve m is  2/3 = 1/4 + m.

The equation you wrote, 2/3 = 1/4 + m, is indeed correct based on the tape diagram you described.

Here's how to solve it:

Combine fractions:

Get both fractions on the same side of the equation. Subtract 1/4 from both sides:

m = 2/3 - 1/4

Find a common denominator:

The smallest common denominator for 3 and 4 is 12.

Multiply both sides by 12:

12m = 8 - 3

Solve for m: Combine like terms and simplify:

12m = 5

m = 5/12

Therefore, the value of m is 5/12.

Explanation:

1. The set of points 5 cm from the nearest point on a circle of radius 2 cm will be a circle with a radius 5 cm larger: a circle with a radius of 7 cm.

__

2. The set of points 6 in from the nearest point on a line will be a cylindrical shell 12 inches in diameter centered on the line.

If AB is a line segment, then the shell will have hollow hemispherical ends of radius 6 inches about the end points.

sa- is 113.04 i think

[tex]\bf \textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} r=6 \end{cases}\implies SA=4\pi (6)^2 \\\\\\ SA=144\pi \implies SA\approx 452.39 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} r=6 \end{cases}\implies V=\cfrac{4\pi (6)^3}{3} \\\\\\ V=288\pi \implies V\approx 907.78[/tex]

Answer:

Step-by-step explanation:

The first question is true. In order for a relation to be a function, it has to have only one x value for every y value. y = 3x - 5 is a straight line, so it doesn't share any x values with any y values. In other words, each x value in that graph will not be "used" more than once. Also, the function will pass the vertical line test. this means that if you draw a perfectly vertical line through the function ANYWHERE it will only go through the function at a single point.

The second question is false. There are several different types of functions that come to mind right away, besides a straight line. There's a parabola, which opens up like a "u" (at least the positive one does!), an absolute value function, a cubic function, an exponential function, a log function...

Hope that helps!

3/14

When you multiply two negative numbers together, the negatives cancel each other out and you get a positive answer. So, you can just forget about the negative signs. This leaves us with 1/6 * 9/7.

To multiply a fraction, multiply the numerators together and multiply the denominators together. So, multiply 1 * 9 to get 9, and multiply 6 * 7 to get 42. This means the answer is 9/42.

However, the numerator and denominator share a factor, and that is 3. So, you can divide the numerator and the denominator each by 3 to simplify the fraction to 3/14.

Answer:

90

Step-by-step explanation:

Answer:

The distance between points P1 = (4,2) and P2=(8,5)  is 5.

Step-by-step explanation:

Let P1 = (4,2) and P2=(8,5)

The distance between two points can be found using formula:

[tex]d(P,Q), \sqrt{(x_{2}-x_{1})^2+ (y_{2}-y_{1})^2}[/tex]

where x₁ = 4 , x₂=8, y₁= 2 and y₂ = 5

Putting values in the formula

[tex]=\sqrt{(8-4)^2+(5-2)^2} \\=\sqrt{(4)^2+(3)^2} \\=\sqrt{16+9} \\=\sqrt{25} \\=5[/tex]

So, the distance between points P1 = (4,2) and P2=(8,5)  is 5.

Final answer:

The distance between the points (4,2) and (8,5) can be found using the Pythagorean Theorem. After calculating the squares of the differences in the x and y coordinates and adding them, the square root of the sum gives a distance of 5 units.

Explanation:

The distance between two points in a two-dimensional plane can be calculated using the Pythagorean Theorem. The coordinates of the points provided are (4, 2) and (8, 5). To find the distance, we calculate the difference in the x-coordinates and the difference in the y-coordinates, and then square both values before adding them together. This gives us the distance squared.

The formula is as follows:

d² = (x2 - x1)² + (y2 - y1)²

In this scenario:

d² = (8 - 4)² + (5 - 2)²

d² = (4)² + (3)²

d² = 16 + 9

d² = 25

Finally, we take the square root of the distance squared to get the distance:

d = √25

d = 5

The distance between the points (4,2) and (8,5) is 5 units.

Answer:

Step-by-step explanation:

The total number of students is 350 + 50 + 225 + 375 = 1000.

There are 225 students in band only, as well as 50 students in both band and choir.  So there are 275 students in band out of the total of 1000, or 27.5%.

There are 350 students in choir only, as well as 50 students in both choir and band.  So there are 400 students in choir, 50 of whom are also in band.  So the probability is 50/400, or 12.5%.

The probabilities are not the same.

Since the probabilities are not the same, the probability of being in band is affected by whether or not the student is in choir.  So the events are not independent.

The answer is Perpendicular and parallel lines have their line extending in one direction only

Answer:

Perpendicular and parallel lines have their lines extending in one direction only.

Step-by-step explanation:

Answer:

$11,480

Step-by-step explanation:

1,400 x 0.9 = 1,260

1,260 x 8 = 10,080

1,400 + 10,080 = 11,480

Answer:

The building is [tex]116\ m[/tex] high

Step-by-step explanation:

we know that

Using proportion

Let

x-----> the height of the building

[tex]\frac{2}{6}=\frac{x}{348}\\ \\x=2*348/6\\ \\x=116\ m[/tex]

The quotient of 7 and 1/5 is calculated by multiplying 7 by the reciprocal of 1/5, which is 5. This yields the result 35.

To compute the division of integers and fractions, we generally 'multiply by the reciprocal'. The reciprocal of a fraction is obtained by reversing the numerator and denominator.

In this case, you are asked to obtain the quotient of 7 and 1/5. The reciprocal of 1/5 is 5/1, or simply 5. Thus, we manipulate the problem from division to multiplication:

7 ÷ (1/5) = 7 * 5 = 35.

So, the quotient of 7 and 1/5 is 35.

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The probability of a new financial establishment succeeding and making profits in either the $25,000-$50,000 range or the $50,000-$75,000 range is 18.59 percentage points higher than the probability of a new food establishment succeeding and earning up to $25,000. None of the given options (A-D) are correct.

To answer Perry’s question, we first need to calculate the success rate for the different types of businesses. The success rate can be calculated by subtracting the number of closed businesses from the number opened, and this result is divided by the number opened initially.

For food businesses, the success rate = (3193 - 1977)/3193 = 38.06%. Next, from those successful new food businesses, 945 out of 1216 make up to $25,000, hence the probability is 945/1216 * 100 = 77.67%.

For financial businesses, the success rate = (1898 - 1443)/1898 = 23.97%. Among those successful new financial businesses, 244 out of 455 are making profits in the range of $25,000 - $50,000 and 195 out of 455 are in the range of $50,000 - $75,000. The combined probability is (244+195)/455 * 100 = 96.26%.

This demonstrates that the probability of a new financial establishment succeeding and making profits in either the $25,000-$50,000 range or the $50,000-$75,000 range (96.26%) is higher than the probability of a new food establishment succeeding and making up to $25,000 (77.67%), by 18.59 percentage points.

Therefore, none of the given options (A-D) are correct.

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Answer:

Step-by-step explanation:

m=marta's rope

d=dilbert's rope

3d-10=m

m+d=120

Then you can substitute equation 1 into the second one

(3d-10)+d=120

3d-10+d=120

4d-10=120

4d=130

d=32.5

m+d=120

m+32.5=120

m=120-32.5

Answer:

8y+12

Step-by-step explanation:

Answer:

Dependent

Step-by-step explanation:

The given system of equations is inconsistent.

The given system of equations is:

-35x + 40y = 55

7x = 8y - 11

To determine if the system is consistent and independent, consistent and dependent, or inconsistent, we need to solve the system of equations and analyze the solution.

We can start by rearranging the second equation to solve for x:

7x - 8y = -11

Next, we can multiply the first equation by 7:

-245x + 280y = 385

Now, we can add the two equations together:

-245x + 280y + 7x - 8y = 385 - 11

-238x + 272y = 374

Simplifying this equation:

-119x + 136y = 187

We can see that the coefficients of x and y in this equation are not equal to the coefficients in the original equations. Hence, the lines represented by the equations do not intersect and the system is inconsistent.

Therefore, the answer is: The system is inconsistent.

Answer:

the first year 8

the second 16

the third 24

hope this helps

give me a five star plz

since AC=1/2AB=6 THEREFORE C is the midpoint ofAB

Step-by-step explanation:

Given : AB = 12 , AC = 6

To prove = AB = 2 × AC (C is mid point of AB)

Solution:

AB = 12...[1]

AC = 6.....[2]

[1] ÷ [2]

[tex]\frac{AB}{AC}=\frac{12}{6}[/tex]

[tex]\frac{AB}{AC}=\frac{2}{1}[/tex]

[tex]AB=2\times AC[/tex] (hence, proved)

Answer:

24

Step-by-step explanation:

Write a proportion.  1 serving is to ¼ apples as x servings is to 6 apples.

1 / ¼ = x / 6

Cross multiply:

¼ x = 6

Multiply both sides by 4:

x = 24

She can prepare 24 servings with 6 apples.

Hey there! :)

Given the coordinates (1, 4) & (3, 10), we must find the slope, y-intercept, and standard form.

Keep in mind that in order to find the slope, we must use the slope formula, which is : [tex]m = \frac{y_{2-y_{1} } }{x_{2}-x_{1}  }[/tex]

(1, 4) is our first set of coordinates while (3, 10) is our second set. Meaning that for 1 = x1, 4 = y1 while 3=x2, 10 = y2

Using this information, simply plug into our slope formula.

m = (10-4) / (3-1)

Simplify/

m = 6/2 --> 3

Therefore, our slope is 3.

Now, use the point-slope form to figure out what the y-intercept is.

y - y1 = m(x - x1)

Plug in using the above coordinates and our slope, which is 3.

y - 4 = 3(x - 1)

Simplify!

y - 4 = 3x - 3

Add 4 to both sides.

y = 3x + 1

This means that 1 is our y-intercept.

This is also our equation in standard form.

Hope this helped! :)

If the decimal expansion of pi would end, then it would have to be a rational number, ie pi could be written as a fraction pi = p/q with integers p and q. There are many proofs that this is not the case, but they are all a bit complicated

Pi is an irrational and transcendental number, meaning it never terminates or repeats. Its non-ending and non-repeating nature is reflected in its definition as the ratio of a circle's circumference to its diameter. Pi's transcendence ensures it cannot be expressed by any algebraic equation with rational coefficients.

Understanding the Nature of Pi ( 3.141592653589793237...)

Pi ( 3.14159...) is known to be a non-terminating, non-repeating decimal, which classifies it as an irrational number. This means that no matter how many digits you calculate, Pi will never repeat in a pattern nor end. The number has been calculated to trillions of digits without any repeating pattern emerging.

The non-ending nature of Pi arises from its definition as the ratio of a circle's circumference to its diameter. This ratio is the same for all circles, but it can never be expressed exactly by a fraction or a finite decimal.

Moreover, Ferdinand von Lindemann's proof that Pi is a transcendental number further solidifies that it cannot be the solution of any algebraic equation with rational coefficients, making Pi an essentially complex and infinite entity in mathematics.

N = 3 - Y

- You isolate the variable by dividing each side by factors that don't contain any variables what so ever.

- Ouma

Answer:

n = 3 - p

Step-by-step explanation:

Given

14n + 6p - 8n = 18 ← simplify left side

6n + 6p = 18 ( subtract 6p from both sides )

6n = 18 - 6p ( divide both sides by 6 )

n = [tex]\frac{18-6p}{6}[/tex] = [tex]\frac{18}{6}[/tex] - [tex]\frac{6p}{6}[/tex] = 3 - p

Answer:

a =4   b=8 c=-8

y-value of vertex =

ah^2 + bh + c

where h = -b/2a

h= -8/8 =-1

y-value of vertex =

4(-1)^2 + 8*-1 -8

4 -8 -8

y value of vertex = -12

Step-by-step explanation:

Answer: OPTION D

Step-by-step explanation:

To complete the table, you need to substitute the values of "x" given in the table into the quadratic equation [tex]y=x^{2}-x-6[/tex] to obtain the corresponding value of "y".

Then:

When [tex]x=-5[/tex] :

[tex]y=(-5)^{2}-(-5)-6[/tex]

[tex]y=24[/tex]

When [tex]x=-3[/tex] :

[tex]y=(-3)^{2}-(-3)-6[/tex]

[tex]y=6[/tex]

When [tex]x=-1[/tex] :

[tex]y=(-1)^{2}-(-1)-6[/tex]

[tex]y=-4[/tex]

When [tex]x=2[/tex] :

[tex]y=(2)^{2}-(2)-6[/tex]

[tex]y=-4[/tex]

The answer will be c

Answer is a) because you cut parallel with the base