Express your answer as a polynomial in standard form. f(x) = x - 1
g(x) = 3x² - 4x-12
Find: g(f(x))​

The value of n in the right triangle is 12 cm.

The shortest side of a right angle triangle is 6cm shorter than the hypotenuse.

The difference in length of the other two sides is 3cm.

The hypotenuse side is the longest side of a right triangle.

Hence,

hypotenuse side = n - 3 + 6

hypotenuse side = n + 3

Shortest side of the right triangle = n - 3

Other side = n

Therefore, using Pythagoras theorem,

(n + 3)² = (n - 3)² + n²

(n + 3)(n + 3) = (n - 3)(n - 3) + n²

n² + 3n + 3n + 9 = n² -3n -3n + 9 + n²

n² + 6n + 9 = 2n² - 6n + 9

Therefore,

2n² - n² + 9 - 9  = 6n + 6n

n² = 12n

n² - 12n = 0

n(n - 12) = 0

n = 0 and n = 12

Therefore,

n = 12

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The correct equation that is balanced using the given numbers once is;

5(-1 + (-3)) = (7 * -4) + 8

There are some properties of Algebra such as;

Commutative Property of Addition or multiplication

Associative Property of Addition or multiplication

Transitive Property

Distributive Property

Now, looking at the given numbers, one good idea is to use only a positive digit outside the bracket on the left hand side of the equation to make it easy to balance on the right hand side of the equation. Thus, for the left hand side we will try;

5(-1 + (-3))

When that is solved we will get -20

Now, to balance that on the right hand side , we will have;

(7 * -4) + 8 which also equals -20

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Answer:

x = -21

Step-by-step explanation:

The first you have to do is distribut the -8 to the -14 and x. Once you do that, you get 280 = 112 - 8x. Next, you need to subtract 112 from each side, so you get 168 = -8x. Now, you divide -8 from each side and you get -21 = x. Hope this helps!

The trigonometric expression sin(30°) + cos(60°) is equal to 1.

What is trigonometry?

Trigonometry is the study of relationships between angles and side lengths of triangles. The use of geometry in astronomical studies gave rise to the field in the Hellenistic era in the third century BC. Greek mathematicians focused on chord calculation, whereas Indian mathematicians created the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine.

There are two trigonometric ratios in the given expression,

sin(30°) and cos(60°).

Here, sin(30°) is equal to the value 1/2

i.e. sin(30°) = 1/2

And, cos(60°) is equal to the value 1/2

i.e. cos(60°) = 1/2

Adding these equations, we get

sin(30°) + cos(60°) = 1/2 + 1/2 = 2/2 = 1

therefore, on solving the given trigonometric expression we get answer value 1.

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Answer:

3 1/2

Step-by-step explanation:

each dozen needs 1/2 cup of chocolate chips so 1/2 times 7 = 3 1/2

Answer: B) 5h³- 5h² + 4h - 4

Step-by-step explanation:

First, get rid of the parenthesis by distributing the negative sign to (3h³+5h²-3h - 7).

The expression is now 8h³ + h -11 - 3h³ - 5h² + 3h + 7

Now, combine like terms. Add terms with the same exponent. Let's start with the terms with the highest exponents.

8h³ + (- 3h³) = 5h³

                     - 5h²

h + 3h.          = 4h

-11 + 7            = -4        

Rewrite the new combined terms to get 5h³- 5h² + 4h - 4

Answer:

b) 5h³-5h²+4h-4

Step-by-step explanation:

Greetings !

look at the figure i have attached above

Hope it helps !!

Answer:

3

Step-by-step explanation:

You have 3 lots of 2 1/4 to get as close to 7 7/8 without going over it. Meaning thats how many batches you can make.

Answer:

∠3 and ∠6

Step-by-step explanation:

∠3 and ∠6 because they lie inside the parallel lines (the lines going left to right) and are on opposite sides of the transversal (diagonal line)

Answer: 20.8

Step-by-step explanation:

(8*5.2)/2 so 8/2=4*5.2=20.8

Answer: 20.8 [tex]cm^{2}[/tex]

Step-by-step explanation:

The functions that are shown on the graph are:

                              f(x) = x2

                             f(x) = mx + b

     where 'm' and 'b' are real numbers.

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The correct option is A :the number of pencils and the total cost are in a proportional relationship because the cost does not increase with the number of pencils.

Given cost of one pencil is $3

Thus when we have to find the cost of three pencils we will multiply it with 3 and would be able to get the required amount that is $ 9.

Thus we can say that the number of pencil and cost has direct relationship.

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The values of the composite function are (f o g)(x) = √2x² - 8 and (f o g)(x) = 2x - 8, while their domains are x > 2 and 0 < x < oo, respectively

Lastly, the value of (g o f)(3) is -2

Composite function 1

The functions are given as

f(x) = √x

g(x) = 2x² - 8

The composite function definition is given as

(f o g)(x)

This composite function is calculated using the following composite function formula

(f o g)(x) = f(g(x))

Substitute the known values in the above equation

(f o g)(x) = √g(x)

This gives

(f o g)(x) = √2x² - 8

For the domain, we have

2x² - 8 > 0

This gives

x > 2

Composite function 2

The functions are given as

f(x) = √x

g(x) = 2x² - 8

The composite function definition is given as

(g o f)(x)

This composite function is calculated using the following composite function formula

(g o f)(x) = g(f(x))

Substitute the known values in the above equation

(g o f)(x) = 2f(x)² - 8

This gives

(g o f)(x) = 2(√x)² - 8

Evaluate

(g o f)(x) = 2x - 8

The function is a linear function

So the domain is the set of all real values

Substitute 3 for x in (g o f)(x) = 2x - 8

(g o f)(3) = 2(3) - 8

Evaluate

(g o f)(3) = -2

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Answer:

Guess it's 7.040 yards in 4 miles

Step-by-step explanation:

8.800÷5= 1.760 in 1 yard

4×1.760=7.040

prove me wrong

Answer:

In both number lines, from 0-8,800 and 0-5 there are 5 notches from the first and last, so what you first want to do is solve for the first number line. You can do this by divideing the largest number by the number of notchest on the line:

8,800/5 = 1760

So the notch after 0 will be 1760. To finish the pattern, you want to add the number you got after dividing the total, by itself, 4 more times, as shown:

1,760 + 1,760 = 3,520

3,520 + 1,760 = 5,280

5,280 + 1,760 = 7,040

7,040 + 1,760 = 8,800

Now the number line will look like this:

0, 1760, 3520, 5280, 7040, 8800

0, 1, 2, 3, 4, 5

Compared to the second number line we find that there are 7,040 yards in 4 miles!

Step-by-step explanation:

Hope it helps! =D

For a confidence interval, she would use her sample mean, hence the mean of 6.7 pounds.

In the context of this problem, we use the t-distribution instead of the z-distribution, as we have the standard deviation for her sample.

The bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the parameters are defined as follows:

From the first bullet point, we get that she should use her sample mean for the calculation of the confidence interval, that is, the mean of 6.7 pounds should be used.

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Answer:

Yes the other person is correct

Step-by-step explanation:

oop their answer got deleted

my bad

[tex]a(c - b) = d \\ \frac{a(c - b}{a} = \frac{d}{a} \\ c - b = \frac{d}{a} \\ c = \frac{d}{a} + b \\ c = \frac{d}{a} + \frac{b}{1} \times \frac{a}{a} \\ c = \frac{d}{a} + \frac{ab}{a} \\ c = \frac{d + ab}{a} [/tex]

THIRD OPTION IS THE ANSWER.

HOPETHIS HELPS

By dividing the complex number  5 / -5[tex]i}[/tex] we get the answer as :

5 / -5[tex]i}[/tex] = [tex]i}[/tex]

Steps to simplify complex number:

Given complex number , 5 / -5[tex]i}[/tex]

multiply the numerator and denominator with conjugate [tex]-i /-i[/tex]

          = [tex]5(-i)/-5i(-i)[/tex]

by again simplifying we get ,

          = [tex]-5i/-5[/tex]

-5 common from numerator and denominator is eliminated

so we get ,

         5 / -5[tex]i}[/tex] = [tex]i[/tex]

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Answer:

231+26=x

x=257 pounds

Answer:

a.25

b.26

c. Eva as her unit rate is faster than Sarah

ask me if u want me to explain

Answer:

18.75

Step-by-step explanation:

I'm not exactly sure.

I divided 30 by 2 and 45 by 2 and took both answers and added them together and then took the sum of that and divided it by 2.

From the given graph, the exchange rate is; 1 dollar = 0.9 euros

The formula to find the slope from two coordinate points is;

m = (y2 - y1)/(x2 - x1)

To get the slope, let us use points A and B;

A(0, 0) and B(1, 0.9)

Thus;

Slope = (0.9 - 0)/(1 - 0)

Slope = 0.9

Let us use points C and D to verify the slope.

Slope = (2.6 - 1.7)/(3 - 2)

Slope = 0.9

Thus, 0.9 euros costs 1 dollar

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The time (in hours) taken by the bus and the car to travel between the two towns in terms of x is 5 hours 20 minutes and 4 hours respectively and the equation in x formed is [tex]x^2 + 15x -2700=0[/tex]

Given that:-

Distance between towns A and B = 240 km

A bus takes 80 minutes longer than a car to travel between the two towns.

The car is travelling at 15 km/h faster than the bus which is travelling at x km/h.

Let the speed of the bus be s km/hr and,

The time taken by the car to travel from A to B be t hours.

Hence,

(15+x)*t = (t + 80/60)*x

15t + xt = xt + 4x/3

15t = 4x/3

t = 4x/45 hours.

Hence,

(15 + x)*(4x/45) = 240

x(x + 15)/45 = 60

[tex](x^2 + 15x) = 60*45[/tex]

[tex](x^2 + 15x) = 2700\\x^2 + 15x -2700=0\\x^2-45x+60x-2700 = 0[/tex]

x(x-45) +60(x - 45) = 0

(x - 45)(x + 60) = 0

x = 45,-60

As the time cannot be negative,

x = 45 km/hr

t = (4*45)/45

t = 4 hours (time taken by car)

Time taken by bus = 4 hours + 80 minutes = 5 hours 20 minutes

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The solution of the system of equation is [tex]e=1 , d= 3[/tex] [tex],f=3[/tex]

The area of mathematics known as algebra is used to help express issues or circumstances into mathematical expressions. We employ integers with definite or fixed values in algebra, such as 2, 7, 0.068, etc. In addition to integers, algebra uses variables like x, y, and z.

The solution is written as below:

Given: d= f

2d + 4e - 3f = 1 --------------1

and - 3d + 2e + 4f = 5----------------------2

Put the value of f as d because it is given,

thus equation becomes; 2d+ 4e - 3d= 1 ⇒ 4e- d= 1 ----3

-3d+2e +4d= 5 ⇒  2e+ d=5 ----4

Thus on solving 3 and 4 we get;

[tex]4e-d=1\\+2e+d=5\\[/tex]

We get 6e= 6 which implies e= 1

And putting this value of e in equation 3 we get,

4X1 -d=1

-d= 1-4 ⇒ -d= -3

thus d = 3

Thus [tex]e=1 , d= 3[/tex]

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Answer:

Step-by-step explanation:

4 1/7 = 29/7

6 = 42/7

What you need to add to 4 1/7 is:

6 - 4 1/7

42/7 - 29/7

13/7.

In mixed fractions, it's 1 6/7.

Hello! So...

We are given the following to simplify:

[tex]7\sqrt{28x^6} -5\sqrt{63x^6}[/tex]

_________________________________________________

To solve this, we must simply simplify.

[tex]7\sqrt{28x^6} =14\sqrt{7} x^3[/tex]

[tex]5\sqrt{63x^6}=15\sqrt{7}x^3[/tex]

[tex]=14\sqrt{7}x^3-15\sqrt{7}x^3[/tex]

Now, add the similar elements:

[tex]14\sqrt{7}x^3 -15\sqrt{7} x^3=-\sqrt{7}x^3 \\[/tex]

Now, considering we are assuming all variables are positive in this situation, we need to convert the negative into a positive solution.

[tex]=-\sqrt{7}x^3[/tex]

[tex]= x^3\sqrt{7}[/tex]

^Hence, our solution.^

______________________________________________________

Hope this helps! If so, please lmk! Thanks and good luck!

The amount of sugar that went into each pitcher was 0.375, which was taken from the 3(3/4) cups of sugar utilized for the lemonade stand.

Division allows us to divide a large number of objects into equal-sized groups. Division is represented by the symbol ÷.

We can use the distributive property to divide larger numbers by breaking them down into smaller factors.

It is implied that Lucy made her lemonade stand using 3 3/4 cups of sugar.

Further, she distributed the sugar into 6 pitchers in equal portions.

Therefore, we need to divide the total cups of sugar by 6 to get the value of sugar that went into each pitcher.

sugar went into each pitcher = 3(3/4) ÷ 6

                                                 = (9/4) ÷ 6

                                                 = 2.25 ÷ 6

                                                 = 0.375

Therefore, each pitcher of sugar contained 0.375 of the 3(3/4) cups of sugar utilized for the lemonade stand.

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Using mathematical operations, yes Mrs. Davis and her two sisters can get hair coloured under $100 including $10, and their actual cost will be $96.85.

So, the total cost of hair coloring:

Now, calculate as follows:

Therefore, using mathematical operations, yes Mrs. Davis and her two sisters can get hair coloured under $100 including $10, and their actual cost will be $96.85.

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The complete question is given below:
Could Mrs.Davis and her two sisters get their hair colored for less than $100 if they include a $10 tip explain also the cost is $28.95 for the hair coloring.