for f(x)=4x+1 and g(x)=x^2-5, find (f-g) (x) need help guys!

Answer:

(a)[tex]e^{-0.000428 t}[/tex]

Step-by-step explanation:

We are given that

Half life of radium-226=1620 yr

The quantity left Q(t) after t years is given by

[tex]Q(t)=(\frac{1}{2})^{\frac{t}{1620}}[/tex]

a. We have to convert the given function into an exponential function using base e.

[tex]Q(t)=(\frac{1}{2})^{\frac{t}{1620}}[/tex]

=[tex]((\frac{1}{2})^t)^{\frac{1}{1620}[/tex]

=[tex]e^{ln(1/2) t/1620}[/tex]

[tex]=e^({\frac{ln(1/2)}{1620}t)[/tex]

=[tex]e^{-0.000428 t}[/tex]

(b)

[tex]Q(0)=e^{-0.000428 \times 0}[/tex]

=1

From original function

Q(0)=1

[tex]Q(1620)=(\frac{1}{2})^{\frac{t}{1620}}[/tex]

[tex]Q(1620)=\frac{1}{2}=0.5[/tex]

From exponential function

[tex]Q(1620)=e^{-0.000428 \times 1620}[/tex]

[tex]=0.499\approx 0.5[/tex]

[tex]Q(3240)=(\frac{1}{2})^{\frac{3240}{1620})=0.25[/tex]

[tex]Q(3240)=e^{-0.000428 \times 3240}[/tex]

Q(3240)=0.249=[tex]\approx 0.25[/tex]

Hence, verified.

Answer:

C

Step-by-step explanation:

The sum of the measures of the three angles of a triangle is 180 degrees.

A

50 + 40 + 90 = 180    good

B

55 + 35 + 90 = 180     good

C

45 + 40 + 90 = 175    not good

Answer: C

Answer:

12 cm

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Define

Identify variables

a = 12 cm

c = 17 cm

Step 2: Solve for b

Answer:

<ABC = 27

< BAC = 126

Step-by-step explanation:

<C = <B since it is an isosceles triangle.  We know this since AC - AB

<C = 27 so <ABC = 27

The sum of the angles of a triangle = 180

A + B+ C = 180

A + 27+27 = 180

A + 54 =180

A = 180-54

A =126

< BAC = 126

Answer:

a) No.

b) Lies between 253 and 320.

c) No.

d) Central limit theorem is not applicable here.

e) The process of estimation can always help us make the right prediction about future sales, demands, costs, profits, and so on based on the past data or any such data available and hence take the correct decision

Step-by-step explanation:

1) No I do not agree, it's just because the mean should be always within the confidence interval. in this case, the above statement doesn't satisfy the condition.  

2)The true mean values at 95% confidence interval lies between 253 and 320.  

3) No, because this is only used for the difference in mean. If there is a difference then the mean is different.  

4) Central limit theorem is not applicable here. Since the sample size is very small, it better to use t distribution rather which indicated normal data.  

in case the sample size is greater than 30, we can then apply the central limit theorem.

5) The process of estimation can always help us make the right prediction about future sales, demands, costs, profits, and so on based on the past data or any such data available and hence take the correct decision.

Answer:

x - 51 [tex]\leq[/tex] 43

x - 99 [tex]\leq[/tex] -104

75 < 69 - x

150 + x ≤ 144

Step-by-step explanation:

Answer:

Step-by-step explanation:

6,800, percentage increased by 12% (percent) of its value = 7,616  

20, percentage increased by 1,000% (percent) of its value = 220  

1,000,000, percentage increased by 0.49% (percent) of its value = 1,004,900

Answer:

7616

hope it helps

mark brainliest please

Area = side²

=> 81cm² = side ²

=> √81cm² = side

=> 9cm = side

Perimeter = 4 × side

=> Perimeter = 4 × 9cm

=> Perimeter = 36cm

Step-by-step explanation:

[tex]here \: is \: your \: solution : - \\ \\ Given :- \\ \\ = > area \: of \: square \: = 81cm {}^{2} \\ \\ = > we \: need \: to \: find \: perimeter \\ \\ for \: this \: we \: have \: to \: find \: its \: side. \\ \\ = > area \: of \: square \: = side { }^{2} \\ \\ = > side {}^{2} = 81cm {}^{2} \\ \\ = > \: side \: = \sqrt{} 81cm \\ \\ = > side = \sqrt{9 \times 9} \\ \\ = > side \: = 9 \: cm \\ \\ now \: we \: can \: find \: (perimeter) \\ \\ = > perimeter \: of \: square \: = 4 \times side \\ \\ = > perimeter = (4 \times 9 )cm \\ \\ = > perimeter \: of \: square = 36cm \\ \\ HOPE \: IT \: HELPS \: (. ❛ ᴗ ❛.)[/tex]

Answer:

the slopes are different, and the y-intercepts are also different

Step-by-step explanation:

We can rewrite the equations given in slope-intercept to easily determine the slope (m) and the y-intercept (b). Slope-intercept equation is y = mx + b

Let's rewrite each equation:

✔️5x + 2y = 2

Subtract 5x from each side

2y = -5x + 2

Divide both sides by 2

y = -5x/2 + 2/2

y = -⁵/2(x) + 1

The slope (m) = -⁵/2

y-intercept (b) = 1

✔️3x - 3y = 18

Subtract 3x from each side

-3y = -3x + 18

Divide both sides by -3

y = -3x/-3 + 18/-3

y = x - 6

Slope (m) = 1

y-intercept (b) = -6

✅Therefore, the slopes are different and the y-intercepts are also different

Step-by-step explanation:

everything can be found in the picture

Answer:

n (2n-7) (2n+7)

Step-by-step explanation:

Fyi you can use the app photo math you just take a pic of the problem and it gives you the answer and explains the steps and it is free.

Given:

Consider the below figure attached with this question.

To find:

The function that has the domain [tex]x\geq -11[/tex].

Solution:

We know that, a radical function is defined for only non negative radicand.

In option A, the function is defined if

[tex]x+11\geq 0[/tex]

[tex]x\geq -11[/tex]

The domain of this function is [tex]x\geq -11[/tex]. So, option A is correct.

In option B, the function is defined if

[tex]x-11\geq 0[/tex]

[tex]x\geq 11[/tex]

The domain of this function is [tex]x\geq 11[/tex]. So, option B is incorrect.

In option C and D, the function is defined if

[tex]x+5\geq 0[/tex]

[tex]x\geq -5[/tex]

The domains of these function are [tex]x\geq -5[/tex]. So, options C and D are incorrect.

Hence, option A is correct.

Answer:

A

Step-by-step explanation:

Answer:

192 points

Step-by-step explanation:

he earned 120 points for passing 6 levels and getting 20 points per level

he earned 72 points for racing 45 laps and getting 24 points per every 15 laps

Answer:

the mod always gives positive answers

so the answer will be

Step-by-step explanation:

x+2+4=11

x+6=11

x=11-6

x=5

answer is x is 5

Answer:

x=5,9

Step-by-step explanation:

|x+2|+4=11

|x+2| = 7

next you get two answers by adding two or subtracting two. SO the right answer should be 5 and 9. A is wrong . I DONT SEE THE OTHER ANSWER CHOICES BUT THIS IS WHAT I GOT.

Answer:

b

Step-by-step explanation:

this because both VCSs were recording on the same time hence Butch will have two copies of record and the A vcr having an Extra of what B vcr will

Answer:

I don't really know but I'm pretty sure u can fix it and answer this question

Given:

The table and the relative frequency histogram show the distribution of the number of tails and three coins are tossed.

To find:

The probability [tex]P(T=3)[/tex].

Solution:

In the given table T represents the number of tails.

From the given table it is clear that the value of probability is [tex]\dfrac{1}{8}[/tex] and [tex]T=3[/tex]. So,

[tex]P(T=3)=\dfrac{1}{8}[/tex]

Therefore, the probability [tex]P(T=3)[/tex] is equal to [tex]\dfrac{1}{8}[/tex].

Step-by-step explanation:

the answer is already as simplified as it could be

Answer:

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

2a. 1/4

2b. 2/8

2c. yes, 1/4 = 2/8 because

2 / 8 = 2 ÷ 2 / 8 ÷ 2 = 1 / 4.

2d. the total number of parts doubled in the denominator, the number of parts represented in the numerator doubled as well.

The operations of division and multiplication are made proportionally to the numerator and denominator.

Answer:

75.7m^2

Step-by-step explanation:

[tex] \frac{30}{360} \times \pi {r}^{2} \\ \frac{30}{360} \times \frac{22}{7} \times {17}^{2} \\ \frac{1}{12} \times \frac{22}{7} \times 289 \\ 75.6904761905 = 75.7[/tex]

Answer:

(5/2, 7/2)

Step-by-step explanation:

Use the midpoint formula to solve for the midpoint:

[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\\\(\frac{3+2}{2},\frac{5+2}{2})\\\\(\frac{5}{2},\frac{7}{2})[/tex]

Answer:

2.3

Step-by-step explanation:

if you mean √2.3×√2.3 then the answer is 2.3 because √2.3×√2.3= (√2.3)² and that square cuts the square root and what remains is 2.3 which is the answer.

Answer:

B. g(x)=1/2x2

Step-by-step explanation:

Function f(x):

[tex]f(x) = x^2[/tex]

At [tex]x = 2, y = f(2) = 2^2 = 4[/tex]

Function g:

Function g is a division of function f by a value. When [tex]x = 2, y = 2[/tex], that is, the value of f is divided by two, and thus, the correct answer is given by option b.

Answer: It decreases on the interval   (-infinity, 3)

This is the same as saying -infinity < x < 3, or simply x < 3

=============================================================

Work Shown:

f(x) = (3−x)^2 + 5

f(x) = (-x+3)^2 + 5

f(x) = (-1(x-3))^2 + 5

f(x) = (-1)^2*(x-3)^2 + 5

f(x) = 1(x-3)^2 + 5

The last equation is in the form y = a(x-h)^2 + k

We have a = 1, h = 3 and k = 5

The vertex is (h,k) = (3,5)

Since 'a' is positive, this means the function decreases on the left and increases on the right (forming a parabola that opens upward). See below.

So the function is decreasing when x < 3, which represents everything to the left of the vertex.

We can expand that out to -infinity < x < 3 which converts to the interval notation (-infinity, 3)

Answer:

It is a type of non-probability sampling that involves the sample being drawn from that part of the population that is close at hand

Answer:

Step-by-step explanation:

Set this up as a ratio of proportions of petrol : oil

[tex]\frac{p}{o}[/tex] and if the ratio of the mix has to be 5p to 2 oil then:

[tex]\frac{p}{o}:\frac{5}{2}[/tex]  We need to find how much oil, x, is needed to mix with 10 liters of petrol. Completing the proportion with that ratio gives us the problem in its entirety:

[tex]\frac{p}{o}:\frac{5}{2}=\frac{10}{x}[/tex] and cross multiply

5x = 20 so

x = 4 liters of oil are needed to mix with 10 liters of petrol.

Answer:

3

Step-by-step explanation:

I think its 3 because when we add 2 to x the graphic must be continue two step to right

Answer:

9:4 4:13

Step-by-step explanation:

Answer:

a) 9:4  b) 13 : 9

Step-by-step explanation:

13 = total

4 = green

13-4   ( which Is 9) = red

Ratio of red apples to green apples?

9:4

RATIO of all apples to red

13: 9