f(x) = 3x + 2 and g(x) = x + 5
g[f(x)] =
Help please :((

Answer:

2/3

Step-by-step explanation:

Ah, I see. A 1-6 die.

Probability of one number = 1/6

2 numbers? = 2/6

6/6-2/6=4/6

4/6=2/3

[tex]\huge{\boxed{\frac{2}{3}}}[/tex]

There are [tex]4[/tex] numbers on a number cube that are greater than [tex]2[/tex]. They are [tex]3, 4, 5, 6[/tex].

Write this as a fraction. [tex]\frac{\text{4 favorable outcomes}}{\text{6 total outcomes}}[/tex]

Divide both the numerator and denominator by [tex]2[/tex] to simplify. [tex]\boxed{\frac{2}{3}}[/tex]

Answer: The direction of the rotation is counterclockwise about the origin.

Step-by-step explanation:

          [tex](x,y)[/tex] → [tex](-y, x)[/tex]

In this case, we can observe that the coordinates of the Pre-image of the Point G are:

[tex](7 ,-5)[/tex]

And the coordinates of its Image are:

[tex](5, 7)[/tex]

Then:

[tex](x,y)[/tex] → [tex](-y, x)[/tex]

[tex](7 ,-5)[/tex] → [tex](5, 7)[/tex]

Therefore, the direction of the rotation is counterclockwise about the origin.

Answer:

Please look at the different answers. I wasn't 100% sure what your expression was.

Step-by-step explanation:

If you mean 2/(5x-1) then g(x) will take the fraction into account with a constant 2 for the numerator and a variable for the denominator since that is where our variable is so g(x)=2/x.

Now h(x)=5x-1 since if you plug in 5x-1 into 2/x where x is you will get our original expression.

Now if you did mean (2/5)x-1 I would take notice of where the variable is which is in (2/5)x so g(x)=x-1 where h(x)=(2/5)x since if you plug (2/5)x in place of the x in x-1 you will get the original.

Please let me know if I didn't interpret your expression correctly.

The required functions which satisfy the condition [tex]\ h (x) = g (f (x))[/tex] are,

[tex]h (x) = \dfrac{2}{5} x[/tex]  and [tex]g (x) = x - 1[/tex].

Used the concept of composition which states that,

The composition of a function is an operation where two functions say f and g generate a new function say h in such a way that;

[tex]\ h (x) = g (f (x))[/tex]

Consider the given function as

[tex]f (x) = \dfrac{2}{5} x - 1[/tex]

It is given that [tex]\ f (x) = g (h (x))[/tex] and neither [tex]g (x)[/tex] nor [tex]h (x)[/tex] is solely x.

Let us assume that,

The function h (x) is defined as,

[tex]h (x) = \dfrac{2}{5} x[/tex]

Then we get;

[tex]\ f (x) = g (h (x))[/tex]

= [tex]h (x) - 1[/tex]

Substitute [tex]h (x) = x[/tex] in the above function for the value of function g (x),

[tex]g (x) = x - 1[/tex]

Therefore, the required functions are [tex]h (x) = \dfrac{2}{5} x[/tex]  and [tex]g (x) = x - 1[/tex].

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Answer:

[tex]cos^{-1}[\frac{6.3}{9.8}][/tex]

[tex]sin^{-1}[\frac{7.5}{9.8}][/tex]

Step-by-step explanation:

step 1

Find the measure of angle ABC using the function cosine

we know that

The function cosine of angle ABC is equal to divide the adjacent side to angle ABC by the hypotenuse of the right triangle

cos(∠ABC)=BC/AB

substitute

cos(∠ABC)=6.3/9.8

[tex]ABC=cos^{-1}[\frac{6.3}{9.8}][/tex]

step 2

Find the measure of angle ABC using the function sine

we know that

The function sine of angle ABC is equal to divide the opposite side to angle ABC by the hypotenuse of the right triangle

sin(∠ABC)=AC/AB

substitute

sin(∠ABC)=7.5/9.8

[tex]ABC=sin^{-1}[\frac{7.5}{9.8}][/tex]

Answer:

First part:

Set h(t) = 231and solve for t.

-16t²+ 152t + 9= 231

-16t² + 152t - 222= 0

Solve this quadratic equation for t. You should get 2 positive solutions. The lower value is the time to reach 231 on the way up, and the higher value is the time to reach 231 again, on the way down.

Second part:

Set h(t) = 0 and solve the resulting quadratic equation for t. You should get a negative solution (which you can discard), and a positive solution. The latter is your answer.

Answer:

6 squared cm

Step-by-step explanation:

The height of a triangle is length of the segment that is perpendicular to the base.  So that length is 2cm here.

The base and the height of the triangle should be perpendicular. So the base is 6cm

The area of a triangle is 1/2 * b * h.

1/2 * b  * h

1/2 *6   * 2

    3    *  2

        6

The answer is 6 squared cm

Answer:

Step-by-step explanation:

The formula of an area of a triangle:

[tex]A_\triangle=\dfrac{bh}{2}[/tex]

b - base

h - height

In ΔBCD we have b = 6cm, and h = 2cm.

Substitute:

[tex]A_{\triangle BCD}=\dfrac{(6)(2)}{2}=\dfrac{12}{2}=6\ cm^2[/tex]

Answer:

i think she should eat

I think ??????

Step-by-step explanation:

Answer:

x = 6 + 3√10

Step-by-step explanation:

Since this is an unfactorable expression, we need to apply the Quadratic Formula, -b ± √b² - 4ac\2a [radical wrapped around b² - 4ac]. Evaluate, then you will end up with the answer above.

I am joyous to assist you anytime.

Answer:

There is a scale factor of 1

Step-by-step explanation:

the ratio 1:1 means that there is no difference between the two triangles, and that they are congruent.

Answer:

Step-by-step explanation:

To find the zeros, set y=-4(x - 3)2 + 8 = 0.  Then -4(x - 3)^2 = -8, and:

4(x - 3)^2 = 8.  Dividing both sides by 4 yields (x - 3)^2 = 2.

Taking the square root of both sides yields x - 3 = ±2, so that

x = 3 ±2, or x = 5 and x = 1.  These are the zeros. The correct interpretatioon is A:  where the daily profit is $0.

Answer:

Interpretation: The zeros are where the daily profit is $0.00.

Zeroes are x = 1.58 and x = 4.41.

Step-by-step explanation:

Given function,

[tex]y=-4(x-3)^2+8[/tex]

For finding the zeros,

y = 0,

[tex]-4(x-3)^2+8=0[/tex]

[tex]-4(x-3)^2=-8[/tex]

[tex](x-3)^2=2[/tex]

[tex]x-3=\pm \sqrt{2}[/tex]

[tex]\implies x = 3\pm \sqrt{2}[/tex]

[tex]\implies x\approx 4.41\text{ or }x=1.58[/tex]

Hence, the zeroes of the function are x = 1.58 and x = 4.41,

∵ x represents the price of a taco and y represents daily profit,

Therefore, the zeroes are where the daily profit is $ 0.00.

Answer:

The expression is 5⁵-1 (=3124)

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]-2<\dfrac{x}{3}+1<5\qquad\text{subtract 1 from both sides}\\\\-2-1<\dfrac{x}{3}+1-1<5-1\\\\-3<\dfrac{x}{3}<4\qquad\text{multiply both sides by 3}\\\\(3)(-3)<3\!\!\!\!\diagup^1\cdot\dfrac{x}{3\!\!\!\!\diagup_1}<(3)(4)\\\\-9<x<12[/tex]

Answer:

Therefore the probability of 10 - 12 inclusive = 0.20613 + 0.21862 + 0.17004  

= 0.59479  

+ 59.5% to one place of decimals

Step-by-step explanation:

P(exactly 10) = 15C10 * (0.70)^10 * (0.30)^5  

=15! / (10! * 5!) * (0.70)^10 * (0.30)^5  

= (15*14*13*12*11) /(5*4*3*2*1) * (0.70)^10 * (0.30)^5  

= 0.20613  

P(exactly 11) = 15C11 * (0.70)^11 * (0.30)^4  

= (15*14*13*12)/(4*3*2*1) *(0.70)^11 *(0.30)^4  

= 0.21862  

P(exactly 12) = 15C12 * (0.70)^12 * (0.30)^3  

= (15*14*13)/(3*2*1) * (0.70)^12 * (0.30)^3  

= 0.17004  

Answer:

37*20 = 740/4 = 185 -> Spent on new CD's

740 - 185 = $ 555 -> Savings Account

Step-by-step explanation:

Answer:

Amount of money she spend on CDs: $185

Amount of money she is going to be in her savings account: $555

Step-by-step explanation:

She sold 37 pairs of earrings with each of them costing 20 dollars.

That means she made 20(37)=740 dollars.

She is going to use 1/4 of 740 dollars to buy new CDS. This means she is going to use 740/4 =185 dollars on CDs.

So what money is left from 740 dollars after spending 185 dollars?

740-185=555 dollars

She is going to put 555 dollars into savings.

Answer:

D

Step-by-step explanation:

From any point (x, y ) on the parabola the focus and directrix are equidistant

Here the focus = (- 6, 0) and the directrix is x = 6

Using the distance formula

[tex]\sqrt{(x+6)^2+(y-0)^2}[/tex] = | x - 6 |, that is

[tex]\sqrt{(x+6)^2+y^2}[/tex] = | x - 6 |

Squaring both sides

(x + 6)² + y² = (x - 6)² ← distribute factors on both sides

x² + 12x + 36 + y² = x² - 12x + 36

Subtract x² - 12x + 36 from both sides

24x + y² = 0 ( subtract y² from both sides )

24x = - y² ( divide both sides by 24 )

x = - [tex]\frac{1}{24}[/tex] y² → D

Answer:

16 mph

Step-by-step explanation:

You should first form equations related to this information

Given,Tamara can go 4 mph faster than her sister, Samantha

Lets take speed to ride a bike for Samantha to be=  x mph

The speed to ride a bike for Tamara will be= x+4 mph

To cover a distance of 80 miles, Samantha takes 1 hour longer than Tamara

Introduce the formula for time; time=distance/speed=D/S where D is distance in miles and S is speed in miles per hour

Here time Samantha takes to cover a distance of 80 miles is 1 hour more than that taken by Tamara, hence

Time taken by Samantha

[tex]=\frac{80}{x}[/tex]

Time taken by Tamara

[tex]=\frac{80}{4+x}[/tex]

Equation for difference in time

[tex]=\frac{80}{x} -\frac{80}{4+x} =1[/tex]

Solve the equation for difference in time to get value of x which is samantha speed

[tex]=\frac{80}{x} -\frac{80}{x+4} =1\\\\\\=80(4+x)-80(x)=x(4+x)\\\\\\=320+80x-80x=4x+x^2\\\\\\=x^2+4x-320=0[/tex]

Solve quadratic equation by the quadratic formula where a=1,b=4 and c=-320

x=(-b±√b²-4ac)÷2a

x=(-4±√4²-4×1×-320)÷2×1

[tex]x=\frac{-4+/-\sqrt{4^2-4*1*-320} }{2} \\\\\\x=(-4+/-\sqrt{1296} )/2\\\\\\x=\frac{-4+36}{2} =\frac{32}{2} =16[/tex]

Samantha speed is 16 mph

Answer:

[tex]\Huge \boxed{\frac{1}{4}}[/tex]

Step-by-step explanation:

Slope formula:

[tex]\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\displaystyle \frac{3-2}{3-(-1)}=\frac{1}{4}[/tex]

Therefore, the slope is 1/4, and the correct answer is 1/4.

Answer:

C 1/4

Step-by-step explanation:

To find the slope of the line given two points, we use the formula

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

   = (3-2)/(3--1)

   = (3-2)/(3+1)

   = 1/4

Answer:

A) 1:1

Step-by-step explanation:

Each leg is the same value and the hypotenuse is [tex]\sqrt{2}[/tex] of the value.

Answer:

Answer A:  1:1

Step-by-step explanation:

In a 45-45-90 triangle, the two legs are of equal length.

Thus, Answer A:  1:1, is the correct one.

Answer:

-6

Step-by-step explanation:

This means what value can I plug into -3x-8 so that I get output 10.

g(x)=-3x-8

g(a)=-3a-8

So we are going to solve g(a)=10 for a.

g(a)=10

-3a-8=10

Add 8 on both sides:

-3a   =18

Divide both sides by -3:

 a     =-6

Check it!

g(-6)=-3(-6)-8=18-8=10 and it's good! :)

Answer:

Henry's monthly payment is $457.5

Henry pays up for the boat at the end overall $35,960

Step-by-step explanation:

* Lets explain how to solve the problem

- Henry buys a large boat with full amount of $32,000

- He cannot pay the full amount at once

- He puts a down payment of $14,000

- He receives a loan for the rest of the payment

∵ The rest of payment = 32,000 - 14,000 = $18,000

- The loan has an interest rate of 5.5%

∴ The rate of interest = 5.5/100 = 0.055

- It is to be paid out over 4 years

∵ The amount of interest = P × r × t , where

# P is the principle amount

# r is the rate

# t is the time

∵ P = 18, 000 , r = 0.055 , t = 4

∴ The amount of interest = 18,000 × 0.055 × 4 = $3960

- The total remaining amount is the sum of the rest of payment and

 the amount of interest

∵ The rest of payment is $18,000

∵ The interest amount = $3,960

∴ The total remaining amount = 18,000 + 3,960 = $21960

- The number of monthly payments = 12 × t

∵ t = 4

∴ The number of monthly payment = 12 × 4 = 48 months

- The monthly payment = the total remaining ÷ the number of

  monthly payment

∵ The total remaining is 21960

∵ The number of monthly payment = 48

∴ The monthly payment = 21960 ÷ 48 = $457.5

* Henry's monthly payment is $457.5

- The total paying for the boat is the sum of the payment down and

  the remaining total payment

∵ The payment down is $14,000

∵ The remaining total payment is 21,960

∴ The total payment for the boat = 14,000 + 21,960 = $35,960

* Henry pays up for the boat at the end overall $35,960

Answer:

yes; 4² + 3² = 5²

Step-by-step explanation:

Pythagorean theorem.

In a right triangle the square of the hypotenuse is equal to  the sum of the squares of the other two sides. Hypotenuse is the longest side of the triangle.

4² + 3² = 5²

16 + 9 = 25

25 = 25  

Answer:

V = 942.48cm³

Step-by-step explanation:

The volume of a right circular cylinder with a radius of 5 cm and a height of 12 cm is 942.48.

Formula: V=πr2h

V=πr2h=π·52·12≈942.4778cm³

Answer:

Observe the attached image

Step-by-step explanation:

The inequality we have is:

[tex]y <2[/tex]

This means that the region represented by this inequality includes all the values below the horizontal line [tex]y = 2[/tex].

To graph this region, draw a dotted horizontal line that intersects the y axis at [tex]y = 2[/tex]. Then shade all the region that is below the horizontal line, as shown in the attached image.

Answer:

The measure of angle xba is 43°

Step-by-step explanation:

we know that

If ray ba bisects the angle xby, then the measure of angle xby is divided into two equal angles

see the attached figure to better understand the problem

so

∠xba=∠aby

∠xba+∠aby=∠xby

we have

∠xby=86°

therefore

∠xba=∠xby/2=86°/2=43°

Answer:

f(g(-1)) = -8 and g(f(1/2) = 4/19.

Step-by-step explanation:

The question specifies f(x) = x^2 + 9x and g(x) = 1/x. The question requires that there should be composite functions. This means a function in a function. Therefore, f(g(x)) means that the function g(x) is taken is an input in the function f(x). Simply replace g(x) instead of x in f(x). This gives:

f(g(x)) = (1/x)^2 + 9(1/x) = x^(-2) + 9/x.

Similar process for g(f(x)) gives:

g(f(x)) = 1/(x^2 + 9x).

Now there are two separate composite functions. Now taking inputs in the composite functions:

f(g(-1)) = (-1)^(-2) + 9/(-1) = 1 - 9 = -8.

g(f(0.5) = 1/(0.5^2 + 9(0.5)) = 1/(0.25+4.5) = 1/4.75 = 100/475 = 4/19.

Therefore f(g(-1)) = -8 and g(f(1/2) = 4/19!!!

Answer:

False

Step-by-step explanation:

A point has zero dimension, once two pints are connected then you get one dimension which is a line

B. False

A point is a fundamental concept in geometry and represents a location in space. It is considered zero-dimensional because it has no length, width, or height.

A point is often represented by a dot or a small symbol and is described by its coordinates in a coordinate system.

In a one-dimensional context, you would have a line segment or a line that consists of multiple points.

However, a single point on its own is considered to have no dimension and is therefore not classified as one-dimensional.

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Answer:

[tex]a_n=42n-621[/tex]

Step-by-step explanation:

This is arithmetic sequence so you should go to linear equations in your head.

Think of the question asking you to find the equation of line going through the points:

(14,-33) and (15,9).

First, let's find the slope.

You need to compute y's change over x's change.

The way I like to do that is line up the points vertically, subtract them, and then put 2nd difference over first.

Like this:

(  15  ,   9)

-(  14  ,  -33)

------------------

   1         42

So the slope is 42/1=42.

(The slope is our common difference.)

Now point slope form is:

y-y1=m(x-x1) where m is the slope and (x1,y1) is a point you know on the line.

So we have m=42 and (x1,y1)=(15,9).  (You could have chose the other point.)

y-9=42(x-15)

I'm going to put in slope-intercept form.  Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

y-9=42(x-15)

Solve for y by adding 9 on both sides:

y=42(x-15)+9

Distribute 42 to terms in the ( ) :

y=42x-42(15)+9

y=42x-630+9

y=42x-621

So we can which back to n now:

[tex]a_n=42n-621[/tex]

Answer:

C. Hours

Step-by-step explanation:

It wouldn't take minutes or seconds to travel 2,442 miles so A and B don't make sense.

Also, it wouldn't take days to travel in the same country, it might a day but not days.

So the only answer that would make sense would be C. Hours

Hope This Helps!!

Answer:

-140

Step-by-step explanation:

Plug in -4 for x, and -6 for y, in the expression:

-7(x - 4y) = -7((-4) - 4(-6))

Simplify. First, solve the terms within the parenthesis. Multiply:

-7((-4) (-4 * -6))

-7((-4) (+24))

-7(-4 + 24)

Solve the parenthesis. Add:

-7(20)

Fully simplify.

-7 * 20 = -140

-140 is your answer.

~

Answer:

The answer Is B.

Step-by-step explanation:

In "A" I believe japanese should be capatalized and in "C" "genji" should be capitalized but In "B" Murasaki Shikibu’s is a name so it should be capitalized.