Find the inverse function of g(x) = 2x + 4. g -1(x) = 4x + 2 g -1(x) = 2x + g -1(x) = x - 2 g -1(x) = 2x - 4

Answer:

16C14 = 120

Step-by-step explanation:

we need to find the value of the combination 16C14.

The formula used is [tex]nCr= \frac{n!}{r!(n-r)!}[/tex]

in the given question

n = 16

and r = 14

Putting values and solving:

[tex]16C14= \frac{16!}{14!(16-14)!}\\16C14= \frac{16!}{14!2!}\\16!\,\,can\,\,be\,\,written\,\,as\,\, 16*15*14!\\16C14= \frac{16*15*14!}{14!2!}\\16C14= \frac{16*15}{2*1}\\16C14= \frac{240}{2}\\16C14 = 120[/tex]

So, 16C14 = 120

Answer:

120

Step-by-step explanation:

Using the definition of n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]

where n ! = n(n - 1)(n - 2)...... × 3 × 2 × 1

16[tex]C_{14}[/tex]

= [tex]\frac{16!}{14!2!}[/tex]

= [tex]\frac{16(15)14!}{14!(2)(1)}[/tex] ← cancel 14 !

= [tex]\frac{16(15)}{2}[/tex] = [tex]\frac{240}{2}[/tex] = 120

Answer:  y < 1

Step-by-step explanation:

[tex]\begin{array}{c|c||l}\underline{x; x<-3}&\underline{y=2x+2}&\\-5&2(-5)+2=-8&\\-4&2(-4)+2=-6&\\-3&2(-3)+2=-4&\text{approaching but not including -4}\\&&&\underline{x; x=-3}&\underline{\qquad y=x\qquad}&\\-3&-3&\\&&&\\\underline{x; x>-3}&\underline{y=-x-2}&\\-3&-(-3)-2=1&\text{approaching but not including 1}\\-2&-(-2)-2=0&\\-1&-(-1)-2=-1&\end{array}[/tex]

The first function has the range of y < -4

The second function has the range of y = -3

The third function has the range of y < 1

The largest y-value is 1 and the smallest y-value is -∞, therefore the range (y-values) are from -∞ to 1 → y < 1

Answer:

y=-6

y=-4

y=-3

y=0

Step-by-step explanation:

Answer:

$16.75

Step-by-step explanation:

$25×.33=$8.25

$25-$8.25=$16.75

Answer:

x = -1

Step-by-step explanation:

x + 2.5 = 1.5

- 2.5   -2.5

x = -1

Answer:

The equation is y = 15(2)^x , the graph is X

Step-by-step explanation:

* Lets talk about the exponential graph

- The form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

 b ≠ 1, and x is any real number

- It has a constant base b

- It has a variable exponent x

- The constant a is the beginning value

* Lets solve the problem

- The sample containing 15 cells

∴ a = 15

- The cells double with each cycle ⇒ means × 2 each cycle

∴ b = 2

- x is the number of cycles

- y is the number of cells

∴ The equation is y = 15(2)^x

- From the graphs the answer could be X or Y

* To know which one substitute the values of x to find the value of y

# Figure X

∵ y = 15(2)^x

∵ x = 0

∴ y = 15(2)^0

∵ (2)^0 = 1 ⇒ any number to the power of 0 = 1 except the zero

∴ y = 15(1) = 15

∵ x = 1

∴ y = 15(2)^1 = 15(2) 30

- The graph has y = 30 when x = 1

# In the Figure Y the value of y not equal 30 at x = 1

∴ The answer is graph X

* The equation is y = 15(2)^x , the graph is X

Final answer:

The number of cells after each cycle of mitosis can be represented by an exponential growth model with the equation N = 15 × 2ⁿ. Graphically, this will be a rapidly ascending curve, starting with 15 cells at cycle 0 and doubling each cycle.

Explanation:

The question is asking us to determine the number of cells after each cycle of mitosis given an initial count of 15 cells. When a cell undergoes mitosis, it produces two genetically identical daughter cells, effectively doubling the number of cells with each cycle. To represent the number of cells after each cycle, we will need to use an exponential growth model as each cell division results in doubling the number of cells present.

The general equation representing the growth of cells through mitosis is given by N = N0 × 2ⁿ, where N is the number of cells after n cycles, N0 is the initial number of cells, and n is the number of cycles of mitosis. For the given initial condition of 15 cells (N0 = 15), the equation becomes N = 15 × 2ⁿ.

The corresponding graph to this equation would show a curve that rises sharply upward, reflecting the exponential increase in the number of cells after each cycle. The graph starts at 15 cells when n = 0 (no cycles have occurred) and doubles with each subsequent cycle.

Answer:

10°

Step-by-step explanation:

i did it in my brain maybe not the best but can help u 75°(180°-115°)+4k+5°+6k+10°=180

Answer:

k=10

Step-by-step explanation:

The measure of the exterior angle is equal to the sum of the opposite interior angles

115 = 4k+5 + (6k+10)

Combine like terms

115 = 10k +15

Subtract 15 from each side

115-15 =10k+15-15

100 = 10k

Divide by 10

100/10= 10k/10

10 =k

Answer:

[tex]\boxed{2.7 \times 10^{3}}[/tex]

Step-by-step explanation:

[tex]\dfrac{4 \times 10^{9}}{1.5 \times 10^{6}}[/tex]

1. Divide the coefficients and the exponentials separately

[tex]\dfrac{4 \times 10^{9}}{1.5 \times 10^{6}} = \dfrac{4}{1.5} \times \dfrac{10^{9}}{10^{6}}[/tex]

2. Divide the coefficients

[tex]\dfrac{4}{1.5} \approx 2.7[/tex]

3. Divide the exponential terms

Subtract the exponent in the denominator from the exponent in the numerator.

[tex]\dfrac{10^{9}}{10^{6}} = 10^{(9 - 6)} = 10 ^{3}[/tex]

4. Rejoin the new coefficient and the new exponential

[tex]\dfrac{4 \times 10^{9}}{1.5 \times 10^{6}} \approx \boxed{\mathbf{2.7 \times 10^{3}}}[/tex]

Answer:

2.7 x 10(3)

Step-by-step explanation:

Answer:

B) 2x² = 3x

Step-by-step explanation:

Answer:

Option 2 - [tex]x^2=3x[/tex]                

Step-by-step explanation:

Given : Susan wants to make 2 square flags to sell at a crafts fair. The fabric she wants to buy is 3 meters wide. she doesn't want any fabric left over.

To find : What's the least amount of fabric she should buy?

Solution :

If  she doesn't want any fabric left over.

The fabric purchased should have same area of the flags.

So, let x be the length of 1 side of the flag.

Area of the flag is

[tex]A=s^2[/tex]

[tex]A=x^2[/tex]

Area of 2 square flags is [tex]A=2x^2[/tex]

Now, Area of fabric is

[tex]A=l\times b[/tex]

[tex]A=x\times 3[/tex]

[tex]A=3x[/tex]

According to question,

Area is same so,

[tex]x^2=3x[/tex]

Therefore, Option 2 is correct.

Answer:

f(x) = x

Step-by-step explanation:

note : slope is positive 1, so the x term must be positive

also note the graph intersects the curve at y = 0, which means that they y-intercept is zero .

if we substitute this into the general equation for a line

y = mx + b, where m = +1 and b = 0,

we get y = x

or f(x) = x (in function form)

Answer: 348 kiwis.

Step-by-step explanation:

You need to analize the information provided in the exercise.

First: You know that you can put 6 trays in crates.

Second: Each one of these trays holds 58 kiwis.

Therefore, in order to calculate the number of kiwis that the crates contain when it is full, you need to multiply the total number of trays you can put in crates by the number of kiwis each tray can hold.

Then:

[tex]number\ of\ kiwis=(6)(58\ kiwis)\\\\number\ of\ kiwis=348\ kiwis[/tex]

Answer:

The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution is correct.

Step-by-step explanation:

1) The system of linear equations 6x - 5y = 8 and 12x - 10y = 16 has no solution.

Solve these linear equations simultaneously

Step 1 : Find y in terms of x from any one equation

6x - 5y = 8

y = 8 - 6x

        -5

Step 2 : Substitute y in terms of x from step 1 in the second equation.

16x - 6y = 22

16x - 6 (8 - 6x) = 22

              -5

80x - 48 + 36x = 22 x -5

94x = 43

x = 0.457

This statement is incorrect as it does have a solution.

2) The system of linear equations 7x + 2y = 6 and 14x + 4y = 16 has an infinite number of solutions.

Solve these linear equations simultaneously

Step 1 : Find y in terms of x from any one equation

7x + 2y = 6

y = 6 - 7x

        2

Step 2 : Substitute y in terms of x from step 1 in the second equation.

14x + 4y = 16

14x + 4(6 - 7x) = 16

              2

14x + 12 - 14x = 16

0 ≠ 4

This statement is not true as there are no solutions.

3) The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution.

Solve these linear equations simultaneously

Step 1 : Find x in terms of y from any one equation

8x - 3y = 10

x = 10 + 3y

        8

Step 2 : Substitute x in terms of y from step 1 in the second equation.

16x - 6y = 22

16(10 + 3y) - 6y = 22

       8

20 + 6y - 6y = 2

0 ≠ -18

This statement is true because there are no solutions

4) The system of linear equations 9x + 6y = 14 and 18x + 12y = 26 has an infinite number of solutions.

Solve these linear equations simultaneously

Step 1 : Find x in terms of y from any one equation

9x + 6y = 14

x = 14 - 6y

        9

Step 2 : Substitute x in terms of y from step 1 in the second equation.

18x + 12y = 26

18 (14 - 6y) + 12y = 26

        9

8 - 12y + 12y = 26

0 ≠ 18

This statement is incorrect because there are no solutions. It does not have infinite number of solutions.

!!

Answer:

Step-by-step explanation:

The true statement is the third one, because that system of equations has no solutions. This is because those lines are parallel, see image attached.

We can demonstrate this by solving the system:

[tex]\left \{ {{8x-3y=10} \atop {16x-6y=22}} \right.[/tex]

If we multiply the first equation by -2, we would have

[tex]\left \{ {{-16x+6y=-20} \atop {16x-6y=22}} \right\\0x+0y=2\\0=2[/tex]

When this happens, means that the system has no solution, that is, the lines that represents those linear equations, are parallel.

Therefore, the right answer is the third option.

Answer:

[tex]x=\frac{7}{5}[/tex]

Step-by-step explanation:

The question states product so we know that we're multiplying.

A number and 5, and since the unknown variable is now [tex]x[/tex] we have [tex]5x[/tex] so far.

Then we need to make it so that it is 2 more.

[tex]5x+2[/tex]

Equals 9.

[tex]5x+2=9[/tex]

Solve for the unknown number.

[tex]5x=7[/tex]

[tex]x=\frac{7}{5}[/tex]

Transforming the problem into the equation 5x + 2 = 9, where 'x' is the unknown number, we solve for 'x' by subtracting 2 from both sides and then dividing by 5, yielding 'x' = 7/5, or 1.4.

The mathematics problem described can be solved using simple algebra. The problem is stated as: two more than the product of a number and 5 equals 9. If we use the variable 'x' to represent the unknown number, then we can write the algebraic equation to represent this problem as 5x + 2 = 9. The next step would be to solve this equation to find the value of 'x'. In order to isolate 'x', you would first subtract 2 from both sides of the equation, yielding 5x = 7. To find 'x', you would then divide both sides of the equation by 5. The solution to the equation, and therefore the value of the unknown number 'x', would thus be 7/5 or 1.4.

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Answer:

The first answer :)

Step-by-step explanation:

That is because N represents the amount of hours that the other person studied.

Answer:

4 weeks and 2 days

Step-by-step explanation:

There are 7 days in one week.

To convert 30 days into weeks and days, divide 30 by 7.

The biggest number you can divide it by is 4 [without going over 30]

7 x 4 = 28.

30 - 28 = 2.

So 30 days = 4 weeks and 2 days.

I hope this helps! :)

Answer:

4 weeks and 2 days

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

Given

7x - 4 = 2x + 11 ( subtract 2x from both sides )

5x - 4 = 11 ( add 4 to both sides )

5x = 15 ( divide both sides by 5 )

x = 3

Answer:

45-2(h-1)<32

Step-by-step explanation:

This is a problem related to arithmetic progression. The formula we use is that of for nth term

[tex]a_{n}=a+(n-1)d[/tex]

Here

[tex]a=45 , d=-2 ,n=h , a_{n}=a_{h}[/tex]

[tex]a_{h}=45+(h-1)(-2)\\a_{h}=45-2(h-1)\\[/tex]

Now we have to analyse a situation when our temperature comes below 32

or

[tex]a_{h}<32[tex]

[tex]45-2(h-1)<32\\45-2h+2<32\\45-2h<32-2\\45-2h<30\\[/tex]

This is our inequality

Solving this

[tex]45-2h<30\\-2h<30-45\\-2h<-15\\h>7.5\\[/tex]

Hence in 8th hours the temperature will be below 32F

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf y+2=\cfrac{1}{2}(x-4)\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{2\left( y+2 \right)=2\left( \cfrac{1}{2}(x-4) \right)}\implies 2y+4=2(x-4) \\\\\\ 2y+4=2x-8\implies 2y=4x-12\implies -4x+2y=-12\implies 4x-2y=12[/tex]

Answer:

20 minutes

Step-by-step explanation:

Both will meet again at start point after LCM(60,80) seconds.

That is 240 seconds.

in time slower car completes one lap, faster one covers 1 +20/80 lap, that is 1.25 laps. After 20 laps faster by slower car car will be 5 laps ahead, time =20*60 = 1200s = 20 minutes

Answer:

300 teenagers

Step-by-step explanation:

Let

x -----> the number of children

y ----> the number of teenagers

z ----> the number of adults

we know that

x+y+z=1,200 ----> equation A

4x+5y+6z=5,300 ---> equation B

y/x=3/8

y=(3/8)x ----> equation C

Substitute equation C in equation A and equation B and solve for x,z

x+y+z=1,200 ----> x+(3/8)x+z=1,200 ---> (11/8)x+z=1,200 -----> equation D

4x+5y+6z=5,300 --> 4x+5(3/8)x+6z=5,300 --> (47/8)x+6z=5,300 --> equation E

Solve the system of equations D and equation E by graphing

(11/8)x+z=1,200 -----> equation D

(47/8)x+6z=5,300 --> equation E

The solution is the intersection point both graphs

The intersection point is (800,100)

see the attached figure

therefore

x=800 children

z=100 adults

Find the value of y

y=(3/8)x  ----> y=(3/8)800=300 teenagers

The smallest possible value for the sum of the squares of two numbers differing by 1 is 0.5. This is obtained by setting one number as x and the other as x + 1, and then minimizing the function f(x) = x² + (x + 1)².

The difference of two numbers is 1 implies that if we set one number as x, then the other would be x + 1. To find the smallest possible value for the sum of their squares, you need to minimize the function f(x) = x² + (x + 1)².

Completing the square, this simplifies to 2(x² + 1)². Setting the derivative of this expression, 4x(x² + 1), equal to zero and solving for x, we obtain x = 0 or x = -1. Testing these values within the function f(x), we find that the minimum value is when x = -0.5 and x + 1 = 0.5 and the sum of their squares equals 0.5.

Although one can handle an equation containing an unknown square which produces two solutions, in this problem, the meaningful solution is that the smallest possible value for the sum of their squares is 0.5.

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Answer:

36π cubic inches

Step-by-step explanation:

Volume of sphere:

V = 4/3 πr^3

Given: r = 3 in.

Plug in

V = 4/3 π (3^3)

V = 4/3 π (27)

V = 36 π

Answer

36π cubic inches

Answer with explanation:

 Radius of the Sphere (r)= 3 inches

Volume of the sphere

                  [tex]=\frac{4*\pi *r^3}{3}\\\\\rightarrow \frac{4*\pi *3^3}{3}\\\\\rightarrow 4*\pi *3^2\\\\=36\pi \text{Cubic inches}[/tex]  

→→→Option B: 36 π Cubic inches          

The probability of getting heads on a coin toss is 1/2

The probability of getting an even number rolling a number cube is 1/2 ( 3 even numbers out of 6 total numbers).

To find the probability of both happening, multiply each probability by each other:

1/2 x 1/2 = 1/4

Answer:

127%

Step-by-step explanation:

All you have to do is multiply both numerator and denominator by 100.

Hello There!

1.27 to a percent would be 127%

"Percent" means "per 100" or "over 100". So, to convert 1.27 to percent we rewrite 1.27 in terms of "per 100" or over 100.

Multiply 1.27 by 100/100. Since 100/100 = 1, we are only multiplying by 1 and not changing the value of our number.

Therefore, we have shown that

1.27 = 127%

Answer:

1.) 8 = 8

2.) -12 = -12

3.) -3y² = -3y²

4.) 6x² + 36x = 6x(x + 6)

5.) 7x - 14x² = 7x(1 - 2x)

~

Answer:

The length is 39.6 feet.

Step-by-step explanation:

Since the area is lw, we make this an equation. The width is already known, it's 26.2. So make a single variable equation: 26.2w=1037.52

dividing both sides by 26.2 gives you the answer of 39.6.

Hope this helps!

We know that - Area of a Rectangle is given by : Length × Width

Here : Length = u  and  Width = 26.2 ft

Given : Area of the Rectangle = 1037.52 ft²

[tex]:\implies[/tex]  u × 26.2 = 1037.52

[tex]\mathsf{\implies u = \dfrac{1037.52}{26.2}}[/tex]

[tex]:\implies[/tex]  u = 39.6 ft

[tex]x- 13 =25\\x=38[/tex]

Answer:

[tex]x = 38[/tex]

Step-by-step explanation:

We have the following equation

[tex]x- 13 =25[/tex]

We must solve the equation for the variable x

Add 13 on both sides of the equation

[tex]x- 13 +13 =25+ 13[/tex]

[tex]x=25+ 13[/tex]

[tex]x=38[/tex]

So the solution to the equation is [tex]x = 38[/tex]