What is (f.g)(x)?

f(x)=x^3 - 4x + 2
g(x)=x^2 + 2

Answer:

It's the second option

Step-by-step explanation:

Graph for -(x+3)(x+1)

The graph of f(x) = -(x + 3)(x + 1) is the option B.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given function is,

f(x) = -(x + 3)(x + 1)

Simplifying,

f(x) = - (x² + 3x + x + 3)

f(x) = -x² - 4x - 3

This is a quadratic function, the graph of which is a parabola.

Leading coefficient is negative, so the parabola opens downward.

Options are either A or B.

x coordinate of the vertex of a parabola of equation ax² + bx + c is -b/2a.

Here x coordinate = -(-4) / (2 × -1) = -2

The vertex of first graph is (2, 1) and that of second graph is (-2, 1).

The correct option is second graph.

Hence the second graph is the graph of the given function.

Learn more about Quadratic functions here :

https://brainly.com/question/12723502

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Answer:

5/2

Step-by-step explanation:

(18/15)*(25/12)=(18*25)/(15*12)=450/180=5/2

Answer:

x> 0

Step-by-step explanation:

There is an open circle at 0 so this means it is not equal to

The line goes to the right so x is greater than

x> 0

Answer:

1)

2)

3)

4)

5)

6)

7)

Answer:

1) [tex]5^{-3}[/tex]-

Exponent rule:- [tex]a^{-b}=\frac{1}{a^b}[/tex]

[tex]5^{-3}=\frac{1}{5^3}[/tex]

[tex]=\frac{1}{5^3}[/tex]

[tex]5^3=125[/tex]

Answer:- [tex]\frac{1}{125}[/tex]

---------

2) [tex]-3^{-4}[/tex]

[tex]-(\frac{1}{3} )^{4}[/tex]

Answer:- [tex]-(\frac{1}{3}\times\frac{1}{3} \times \frac{1}{3} \times\frac{1}{3} )[/tex]

---------

3) [tex]3^{-8}\times 3^{4}[/tex]

[tex]3^{-8+4}[/tex]

Answer:- [tex]3^{-4}[/tex]

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4) [tex]7^{-3} /7^{-5}[/tex]

[tex]7^{-3-(-5)}[/tex]

[tex]7^{-3+5}[/tex]

Answer:- [tex]7^{2}[/tex]

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5) [tex](8^{10} )^{2}[/tex]

[tex]8^{10\times2}[/tex]

Answer:- [tex]8^{20}[/tex]

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6) [tex](9\times8)^{4}[/tex]

Answer:- [tex]9^{4} \times 8^{4}[/tex]

---------

7) [tex]\left(\frac{2}{7}\right)^5[/tex]

Answer:- [tex]\frac{2^{5} }{7^{5} }[/tex]

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OAmalOHopeO

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Answer:

dont understand clearly

Step-by-step explanation:

Answer:

[tex]5x^{2} - 30x[/tex]

Step-by-step explanation:

Answer:

The slope of the line is 2

Step-by-step explanation:

y=2x+1, compare it to the slope intercept form of a line, y=mx+c, the slope will be 2

Answer:

its 2

comment for more understanding

Good luck

Answer:

25/60

Step-by-step explanation:

Numerator = n

[tex]\frac{n}{2n + 10} = \frac{5}{12}[/tex]

Cross multiply:

n * 12 = (2n + 10) * 5

12n = 10n + 50

12n - 10n = 10n + 50 - 10n

2n = 50

n = 25

Fraction = [tex]\frac{25}{60}[/tex]

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

25/60

Step-by-step explanation:

Study Island:)

Answer:

x = 8, y = 3

Step-by-step explanation:

Equating corresponding x and y coordinates , then

- y = - x + 5 ( multiply through by - 1 )

y = x - 5 → (1)

2x - 5y = 1 → (2)

Substitute y = x - 5 into (2)

2x - 5(x - 5) = 1 ← distribute and simplify left side

2x - 5x + 25 = 1

- 3x + 25 = 1 ( subtract 25 from both sides )

- 3x = - 24 ( divide both sides by - 3 )

x = 8

Substitute x = 8 into (1) for corresponding value of y

y = 8 - 5 = 3

Answer:

Who is at the trail start at 9:00 a.m.? : Andy

Who runs fastest? : Caedin

When do Andy and Berta cross paths? : 9:08 am

Who is closest to the 1.5 mile mark after 6 minutes? : Berta

Step-by-step explanation:

assignment

Answer:

102

Step-by-step explanation:

x= 12

y= 30

z= 60

Hope u got it

Answer:

Hello,

a) -6

b) -39

c) 102

Step-by-step explanation:

I suppose this are sequence arithemical or geometrical

[tex]a)\\u_1=-14\\u_2=x\\u_3=-6\\u_4=y\\u_5=2\\u_6=z\\u_7=10\\\\We\ see\ that\ :\\u_3-u_1=-6-(-14)=-6+14=8\\u_5-u_3=2-(-6)=2+6=8\\u_7-u_5=10-2=8\\\\We\ may \imagine\ that\ the\ difference\ bethween\ 2\ terms\ is\ =8/2=4\\\\so\ x=-10, y=-2, z=6 \ and\ x+y+z=-10+(-2)+6=-6\\[/tex]

[tex]b)\\u_1=x\\u_2=-2\\u_3=4\\u_4=y\\u_5=16\\u_6=z\\u_7=64\\\\We\ see\ that\ :\\\\\dfrac{u_5}{u_3}=\dfrac{16}{4} =4\\\dfrac{u_8}{u_6}=\dfrac{64}{16} =4\\\dfrac{u_3}{u_2}=\dfrac{4}{-2} =-2\\\\The\ common\ factor\ is\ -2\\\\u_1=x=\dfrac{u_2}{-2} =1\\\\u_4=y=\dfrac{u_5}{-2} =-8\\\\u_6=z=\dfrac{u_7}{-2} =-32\\x+y+z=1+(-8)+(-32)=-39\\[/tex]

c)

All those numbers are divisor of 3*4*5=60

x=12, y=30, z=60

x+y+z=12+30+60=102

Answer:

a

Step-by-step explanation:

all angles of an equilaterall triangle are equal therefore 180÷3 = 60

Answer:

Step-by-step explanation:

The model for exponential growth/decay is

[tex]P(t)=a(b)^t[/tex] where a is the initial population and b is the growth/decay rate. Filling in the info you were given:

[tex]P(t)=10(1.04)^t[/tex]

Because this is a growth rate, we have 100% of the population and that population is growing by 4%, which is .04 in decimal form. If the population is not declining, we are adding to the 100% of the population we already have. That's why the growth rate is 1.04.

.96 means that the population is declining at 4% each year; and 1.4 means that the population is growing at 140% instead of the 104% that it is.

Answer:

There are 3 possible values for a.

Step-by-step explanation:

a/b=2/3

3a=2b

If b>5 and b<13

apply all possible values

b=6 -> 3a=12 ==> a=4 1st possibility

b=7 -> 3a=14 ==> a=4.something Not a possibility

b=8 -> 3a=16 ==> a=5.something Not a possibility

b=9 -> 3a=18 ==> a=6 2nd possibility

b=10 -> 3a=20 ==> a=6.something Not a possibility

b=11 -> 3a=22 ==> a=7.something Not a possibility

b=12 -> 3a=24 ==> a=8  3rd possibility

Step-by-step explanation:

you're just going to switch x and y and then solve for y

Answer:

Hello,

Step-by-step explanation:

The problem is that the inverse function is not a function but

an union of 2 functions.

[tex]y=(x+6)^2+1\ is\ the\ orignal\ function\ f(x).\\\\Inverting\ x\ and\ y\ gives: \ x=(y+6)^2+1\\\\(y+6)^2=x-1 \ nota\ bene\ x-1\geq 0 \\(y+6)^2-(x-1)=0\\\\((y+6)-\sqrt{x-1} ) * ((y+6)+\sqrt{x-1}) =0\\\\y=-6+\sqrt{x-1}-6\ or\ y=-6-\sqrt{x-1}\\[/tex]

For the fun

,[tex]f_1(x)= (x+6)^2+1=0\ if\ x<6\\f_1^{-1}(x)=-6-\sqrt{x-1} =0\ if\ x<6\\\\f_2(x)=(x+6)^2+1=0\ if\ x \geq 6\\\\f_2^{-1}(x)=-6+\sqrt{x-1} =0\ if\ x\geq 6\\[/tex]

Answer:

Neither a relation nor a function

Step-by-step explanation:

A relation in mathematics is a relationship between two or more set of values in an ordered pair, such as related x and y-values

An equation is a statement that gives declare the equality between two expressions

A function is a mapping rule that maps each element in the domain set to only one element in the range set

Therefore, the given equation in one variable, x, that asserts the equality of the expressions on the left and right hand side, is neither a relation nor a function

C.P. = $95000

S.P. = $280000

a. Profit

= S.P. - C.P.

= $280000 - $95000

= $185000

b. Let the profit% of C.P. be x.

(x/100) × $95000 = $185000

=> x/100 = $185000/$95000

=> x/100 = 37/19

=> x = (37/19) × 100

=> x = 3700/19

=> x = 194 14/19

So, profit percent of buying price is 194 14/19%.

c. Let the profit% of S.P. be x.

(x/100) × $280000 = $185000

=> x/100 = $185000/$280000

=> x/100 = 37/56

=> x = (37/56) × 100

=> x = 3700/56

=> x = 925/14

=> x = 16 1/14

So, profit percent of selling price is 16 1/14%.

d. Buying price percentage profit sounds better as far as Ella is concerned.

Answer:

circumference = 2*PI*radius

circumference = 2 * PI * 5 cm

circumference = 31.4159265358979 cm

50 km = 500,000 centimeters

rotations = 500,000  / 31.4159 cm

15,915.51  rotations

Step-by-step explanation:

Answer:

-25/9

Step-by-step explanation:

1 + (-2/3) - m

Plug in:

1 + (-2/3) - 9/2

1 + 2/3 - 9/2

1/3 - 9/2

-25/9

Hope this helped.

Answer:

4 5/6

Step-by-step explanation:

1+-2/3--m

Subtracting a negative is like adding

1-2/3 +m

1/3+m

m = 9/2

1/3 +9/2

Get a common denominator of 6

1/3 *2/2 +9/2*3/3

2/6 + 27/6

29/6

Changing to a mixed number

4 5/6

Answer:

135

Step-by-step explanation:

The sum of the interior angles of a pentagon is 540

3x+3x+2x+2x+2x = 540

12x = 540

Divide by 12

12x/12 = 540/12

x = 45

E = 3x = 3*45 = 135

Answer:

135

Step-by-step explanation:

Answer:

y = 0.4x^2 + 3.4x + 4

Step-by-step explanation:

The coordinates (-5,-3) work with this equation. Please give brainliest, I need 1 more to move on to the next tier.

Answer:

2nd option

Step-by-step explanation:

putting x = 1 in the 3rd option,

0.4+3.4+4 = 7.8

Answer:

Parthava had 100 arrows.

Step-by-step explanation:

Let's define N as the number of arrows that Parthava originally has.

He uses one-half of them in defending himself, so he used N/2 arrows

Now he uses four times the square root of the number of arrows, so now he uses:

4*√N

Then he uses 6

Then he uses 3

Then he uses the last one.

If we add all these numbers of arrows that he used, we should get the initial number of arrows that he used, then:

N/2 + 4*√N  + 6 + 3 + 1  = N

Now we have an equation that we can try to solve.

First, let's move all the terms to the same side:

N/2 + 4*√N + 6 + 3 + 1 - N  = 0

now we can simpify it:

(N/2 - N) + 4*√N + (6 + 3 + 1) = 0

-(1/2)*N + 4*√N + 10 = 0

Now we can define a new variable x = √N

Then we have: x^2 = N

now we can replace these new variables in our equation to get:

-(1/2)*x^2 + 4*x + 10 = 0

Now we just have a quadratic equation.

Remember that for a quadratic equation of the form:

0 = a*x^2 + b*x + c

The solutions were given by:

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

Then in our case, the solutions will be:

[tex]x = \frac{-4 \pm \sqrt{4^2 - 4*(-1/2)*10} }{2*(-1/2)} = \frac{-4 \pm 6 }{-1} = 4 \pm 6[/tex]

So there are two solutions:

x = 4 + 6 = 10

x = 4 - 6 = -2

And remember that x = √N

Then x should be positive, then we take x = 10 as our solution here.

then we can use the equation:

x = 10 = √N

then

10^2 = √N^2 = N

10^2 = 100 = N

Parthava had 100 arrows.

Step-by-step explanation:

Area=b×h

= (x+5)×(x+6)

=x^2+6x+5x+30

=x^2+11x+30

If u simplify u will get (x+5)(x+6) as answer.

Keep smiling and hope u are satisfied with my answer.Have a good day :)

Step-by-step explanation:

Side-Angle-Side is a rule used to prove whether a given set of triangles are congruent. The SAS rule states that: If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.

Answer:

521.25

Step-by-step explanation:

the circle is 78.75 in area and the square is 600 so 600- 78.75 = 521.25

Answer:

17. C

18.G

Step-by-step explanation:

17. According to the question, gravel is 4/13 of the total asphalt substance. One parking lot has 260 tons of asphalt. So this means there is 80 tons of gravel because 260 times 4/13=80. We need to find the tons of gravel if we made 3 parking lot. This means 3 parking lot is the same as 780. So we can just find the measure of gravel by multiplying

4/13 by 780.

[tex] \frac{4}{13} \times 780 = 240[/tex]

So there is 240 tons of gravel. C is the answer.

18. Set up system of equations.

[tex]a + b + c = 110[/tex]

The ratio of a to c is 1:7 and the ratio of b to c is 3:7. Using this information,

Using this info, we can make alternate equations

[tex]c = 7a[/tex]

[tex]b = 3a[/tex]

Subsitue this into the original equation,

[tex]a + 7a + 3a = 110[/tex]

[tex]11a = 110[/tex]

[tex]a = 10[/tex]

We need to find c, c is 7 times more than a so c is

[tex]c = 10 \times 7 = 70[/tex]

Answer:

0.026

Step-by-step explanation:

6 out of 10 steps between 0.02 and 0.03.

Answer:

3.71 yd

Step-by-step explanation:

Heron's formula:

area = 0.25 * √((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c))

so h = 0.5 * √((a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c)) / c

a = 6

b = 10

c = 14

a+b+c = 30

-a+b+c = 18

a-b+c = 10

a+b-c = 2

x = h = 0.5×sqrt(30×18×10×2)/14 = sqrt(30×18×10×2)/28 =

= sqrt(10800)/28 = sqrt(400×9×3)/28 =

= 20×3×sqrt(3)/28 = 60×sqrt(3)/28 = 15×sqrt(3)/7 =

= 3.711537 yd