If f(x) = 4x + 5 and fog(x) = 8x + 13 then find g(x).​

9514 1404 393

Answer:

  (-2, 4]

Step-by-step explanation:

  -21 ≤ -6x +3 < 15 . . . . given

  -24 ≤ -6x < 12 . . . . . . subtract 3

  4 ≥ x > -2 . . . . . . . . . . divide by -6

In interval notation, the solution is (-2, 4].

__

Interval notation uses a square bracket to indicate the "or equal to" case--where the end point is included in the interval. A graph uses a solid dot for the same purpose. When the interval does not include the end point, a round bracket (parenthesis) or an open dot are used.

Answer:

Carmen:27

Abdul:17

David=34

Step-by-step explanation:

Carmen+Abdul+David = 78

Carmen-Abdul=10

David=2Abdul

Carmen=Abdul+10

Carmen+Abdul+David = Abdul+10+Abdul+2Abdul=78

4Abdul=68

Abdul = 68/4=17

Carmen = 17+10=27

David = 2 * 17 = 34

27+17+34=78

Answer:

See below

Step-by-step explanation:

a)

[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]

[tex]\therefore x=\dfrac{4\pi }{3}[/tex]

But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution

Therefore,

[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]

This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.

Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]

b)

[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]

Once

[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]

As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]

[tex]\therefore x=-\dfrac{\pi }{6}[/tex]

c)

[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]

Therefore,

[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]

[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

The solutions are

[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

Answer:

The point estimate of the proportion of the population that would provide Yes responses is 0.28.

Step-by-step explanation:

Point estimate of the proportion of the population that would provide Yes

The sample proportion of yes responses.

In the sample:

112 yes responses in the sample of 400, so:

[tex]p = \frac{112}{400} = 0.28[/tex]

The point estimate of the proportion of the population that would provide Yes responses is 0.28.

Answer: A

Step-by-step explanation: x=-2, y=3, z=-3

Answer:

A. -2, 3, -3

Step-by-step explanation:

x = 7 - 2y + z

y = 21 + 6x + 2z = 21 + 6×(7 - 2y + z) + 2z =

= 21 + 42 - 12y + 6z + 2z = 63 - 12y + 8z

13y = 63 + 8z

y = (63 + 8z)/13

2x + 2y - 3z = 11

2×(7 - 2y + z) + 2×(63 + 8z)/13 - 3z = 11

2×(7 - 2×(63 + 8z)/13 + z) + 2×(63 + 8z)/13 - 3z = 11

14 - 4×(63 + 8z)/13 + 2z + 2×(63 + 8z)/13 - 3z = 11

-2×(63 + 8z)/13 - z = -3

-2×(63 + 8z) - 13z = -39

-126 - 16z - 13z = -39

-29z = 87

z = -3

y = (63 + 8×-3)/13 = (63 - 24)/13 = 39/13 = 3

x = 7 - 2×3 + -3 = 7 - 6 - 3 = -2

Answer:

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Step-by-step explanation:

There's a handy formula we can use to find the sum of a geometric sequence, and here it is

[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]

The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.

First lets visualize this sequence

[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]

Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.

[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]

Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.

[tex]S_n = \sum{a*r^{n-1}}[/tex]

To finish up lets plug these coefficients in and get our sum after 10 terms.

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Answer:

3/10

Step-by-step explanation:

2/5*3*4

=6/20

=3/10

Answer:

soory i dont know just report me if you angry

Answer:

n=39/5

Step-by-step explanation:

24=5(n-3)

24=5n-15

-5n= -15-24

-5n=39

n= 39/5

Answer: y = 7x + 18

Step-by-step explanation:

y = mx + b, (-2,4), m = 7

4 = 7(-2) + b

4 = -14 + b

b = 18

y = 7x + 18

Step-by-step explanation:

Sequence is

4

,

7

,

10

,

13

,

16

,

.

.

.

a

1

=

4

,

a

2

=

7

,

a

3

=

10

,

.

.

.

If it is Arithmetic sequence,

a

2

−

a

1

=

a

3

−

a

2

=

a

4

−

a

3

& so on

In the given sum,

a

2

−

a

1

=

7

−

4

=

3

a

3

−

a

2

=

10

−

7

=

3

a

4

−

a

3

=

13

−

10

=

3

Since the difference between the successive terms is same and

hence

common difference

d

=

3

Answer:

4/27

Step-by-step explanation:

total number of marbles=9

probability of red=4/9

since you returned the first marble, the total number of marbles remains the same

prob(Blue)=(3/9)=1/3

P(red then blue)=(4/9)*(1/3)

=4/27

Answer:

The exact answer is 12*√2, if you need approximately answer it is 12*1.4= 16.8

Step-by-step explanation:

√50 + √98​ ​= √(25*2)+√(49*2)= √25√2+√49*√2= 5√2+7*√2=12*√2

Answer:

2 2/3

Step-by-step explanation:

hope this helps :)

don't be afraid to ask questions

Solution :

Given information :

A sample of n = 10 adults

The mean failure was 24 and the standard deviation was 3.2

a). The formula to calculate the 95% confidence interval is given by :

[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]

Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]

                       = 2.145

Substitute the values

[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]

(26.17, 21.83)

When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]

b). The formula to calculate 95% prediction interval is given by :

    [tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]

   [tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]

   (31.13, 16.87)

Answer:

Step-by-step explanation:

(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0

Answer:

A

Step-by-step explanation:

The answer is prime! I hope this helps you out!

Answer:

23 is a prime number. Reason: Prime number are those numbers which are divisible by 1 and itself. Example: 5 is divisible by 1 and 5 only.

Answer:slope 2/3

Y-int 6

Step-by-step explanation:

Answer:AE=EC và BF=FC => EF là đường trung bình của tam giác ABC

=> EF // và bằng 1/2 AB

=> AB = 16

Step-by-step explanation:

Answer:

AB=16

Step-by-step explanation:

Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.

The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle.

AD=DB

AD+DB=AB=2EF

AB=2×8=16

Answer:

2016

Step-by-step explanation:

using USA dollars:

$42000 x .072 (7.2%) = 3024 total commission

3024 x 2/3 = 2016 brokers amount

Answer:

1/8 is less than

Step-by-step explanation:

i dont see any fractions below gona have to edit your answer

9514 1404 393

Answer:

Step-by-step explanation:

Let b represent the length of the base. Then (b+4) is the height and the area of the triangle is ...

  A = 1/2bh

  70 = 1/2(b)(b+4)

  b² +4b -140 = 0 . . . . . multiply by 2, put in standard form

  (b +14)(b -10) = 0 . . . . factor

  b = 10 . . . . the positive solution

The base of the triangle is 10 yards; the height is 14 yards.

Answer:

x = -3

Step-by-step explanation:

12 -4x-5x = 39

Combine like terms

12 - 9x = 39

Subtract 12 from each side

12-9x-12 = 39-12

-9x = 27

Divide by -9

-9x/-9 = 27/-9

x = -3

Answer:

x = -3

Step-by-step explanation:

12 - 4x - 5x = 39

Combine like terms

12 - 9x = 39

Subtract 12 from both sides

12 - 12 - 9x = 39 - 12

-9x = 27

Divide both sides by -9

-9x/-9 = 27/-9

x = -3

Answer:

279+x

Step-by-step explanation:

Emily + Yani + Joyce=3209 stickers

how many stickers does Emily have than Joyce:

(279+2x)-(x)

279+2x-x

=279+x

Observe that the x coords of the roots of a polynomial are,

[tex]x_{1,2,3,4}=\{-3,0,1,4\}[/tex]

Which can be put into form,

[tex]y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]

with data

[tex]y=a(x-(-3))(x-0)(x-1)(x-4)=ax(x+3)(x-1)(x-4)[/tex]

Now if I take any root point and insert it into the equation I won't be able to solve for y because they will always multiply to zero (ie. when I pick [tex]x=-3[/tex] the right hand side will multiply to zero,

[tex]y=-3a(-3+3)(-3-1)(-3-4)=0[/tex]

and a will be "lost" in the process.

If we observed a non-root point that we could substitute with x and y and result in a non-loss process then you could find a. But since there is no such point (I don't think you can read it of the graph) there is no other viable way to find a.

Hope this helps :)

Answer:

25.40

Step-by-step explanation:

tickets  ( 2 at 10.95 each) = 2* 10.95 = 21.90

popcorn ( 1 at 7.50)         = 7.50

Total cost before discount

21.90+7.50=29.40

subtract the discount

29.40-4.00 =25.40

Answer:

Yep! That's correct!

Step-by-step explanation:

We know that Marilyn and her sister are each getting a ticket that cost $10.95. They are also getting a $7.50 popcorn to share. Let's add those values up.

(10.95 * 2) + 7.50 {Multiply 10.95 by 2 to get 21.90.}

21.90 + 7.50 {Add 7.50 to 21.90 to get 29.40}

$29.40 (without the credit) in toal

A credit on a movie reward card functions as a discount, so what we need to do next is subtract 4 from 29.40. That will get us $25.40 as the total cost.

After doing the math, I can deduce that your answer is correct!

Answer:

4y

They would have the same value if a number was substituted for y

Step-by-step explanation:

y+y+2y =

Combine like terms

4y

These are all like terms

They would have the same value if a number was substituted for y

Let y = 5

5+5+2(5) = 5+5+10 = 20

4(5) =20

Answer:

11

Step-by-step explanation:

Hopefully you can see that this is an isosceles triangle and remembering the inequality theorem of a triangle (4,4,11 triangle cannot exist).  Iso triangle has two side the same length - as well as two angles the same.