If f(x) = 3^x
+ 10 x and g(x) = 5x - 3, find ( f - g )(x).

±√5

x² = 5

x = ±√5

The solution to the equation [tex]x^2=5[/tex] is [tex]x = \pm \sqrt{5}[/tex].

In order to evaluate and solve this equation, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.

Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical equation:

[tex]x^2=5[/tex]

By taking the square root of both sides of the equation, we have:

[tex]x = \pm \sqrt{5}[/tex].

Read more on expression here: brainly.com/question/16729936

#SPJ6

Answer:

56

Step-by-step explanation:

The sum of two even consecutive integers is 114.

Let's let the first even integer be 2n, where n is some integer: it doesn't matter what n is, but if we multiply n by 2, we are certainly getting an even number. This is because any integer multiplied by 2 is even.

So, this means that the second number is 2n+2.

Their sum is 114. In other words:

[tex](2n)+(2n+2)=114[/tex]

Solve for n.

Combine like terms:

[tex]4n+2=114[/tex]

Subtract 2 from both sides:

[tex]4n=112[/tex]

Divide both sides by 4:

[tex]n=28[/tex]

So, n is 28.

This means that the first number is 28(2) or 56.

And the second number is 58.

So, the smallest integer is 56.

And we're done!

Answer:

  161.5 miles

Step-by-step explanation:

19 inches is 9.5 times 2 inches. So, the actual distance is 9.5 times 17 miles:

  9.5 × 17 miles = 161.5 miles

Answer:

Number of mugs in cartoon = 24 / 25

Step-by-step explanation:

Given:

Pints of cartoon = 4/5

Pints of mugs = 5/6

Find:

Number of mugs in cartoon

Computation:

Number of mugs in cartoon = Pints of cartoon / Pints of mugs

Number of mugs in cartoon = (4/5) / (5/6)

Number of mugs in cartoon = 24 / 25

Answer: Choice C

[tex](xy)^{1/2}[/tex] which is equivalent to [tex]\sqrt{xy}[/tex]

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

Explanation:

The exponent for the y term inside the parenthesis is 1/6 and then that expression is raised to the 3rd power. The exponents multiply to (1/6)*3 = 3/6 = 1/2

This means [tex]\left(y^{1/6}\right)^3 = y^{1/2}[/tex]

Having an exponent of 1/2 is the same as applying the square root, so,

[tex]\sqrt{x} = x^{1/2}[/tex]

Meaning,

[tex]y^{1/2}\sqrt{x} = y^{1/2}x^{1/2} = (xy)^{1/2} = \sqrt{xy}[/tex]

Answer:it got colder by more than 2 degrees

Answer:

well It would have been a change of -5ºF

Answer:

X=7

Step-by-step explanation:

(2) means time 2 so use 5 times 2 and get 10 and take away 3 you get 7 and 7 is X

to prove I am right use 7x5-3/2=16-3x2=10

hey bro I was joking at first

Answer:

f(2) = 5(2) -3

         10 - 3

f(2) = 7

Image of the correlation between Risk-Taking (R) and Relationship Happiness (HAPPY) is missing, so i have attached it.

Answer:

Option 1 - The relationship is non - significant

Step-by-step explanation:

From the image attached, we can see that under the correlations table;

For correlation between relationship happiness and risk taking;

σ(sigma) = 0.053

Similarly, for correlation between risk taking and relationship happiness;

σ(sigma) = 0.053

.

Now,σ(sigma) = 0.053 is more than the standard alpha level of 5%(0.05). Thus, we fail to reject the null hypothesis since it is non - significant.

Answer:

Step-by-step explanation:

Given two coordinates (x₁, y₁) and (x₂,y₂), the midpoint of the coordinates is expressed as M(X,Y) = [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex] where;

[tex]X = \dfrac{x_1+x_2}{2}\ and \ Y = \dfrac{y_1+y_2}{2}[/tex]

Given the midpoint (X, Y) = (1,6) and one end point to be ​(-2​,​1), to get the unknown endpoint (x,y), we will apply the formula above. from the coordinates given X = 1, Y = 6, x₁ = -2 and y₁ = 1

[tex]Given \ X = \dfrac{x_1+x_2}{2}\\1 = \dfrac{-2+x}{2}\\cross \ multiply\\2 = -2+x\\x = 2+2\\x = 4[/tex]

Similarly to get y;

[tex]Given \ Y = \dfrac{y_1+y}{2}\\6 = \dfrac{1+y}{2}\\cross \ multiply\\2*6 = 1+y\\12 = 1+y\\y = 12-1\\y = 11[/tex]

Hence the unknown endpoint (x,y) is (4,11)

Answer:

If x= - 2. then 6x - 2 = -14

If x = 6, then 6x - 2 = 34

If x= - 5. then 6x-2= -32

Step-by-step explanation:

You have to substitute the value of x in the expression.

If x = -2,

6x-2 = 6*(-2) - 2 = -12-2 = -14

Answer:

1

Step-by-step explanation:

Anything to the power is 0 is equal to 1.

Answer:

the answer is 1

Step-by-step explanation:

Answer:

$187.5

Step-by-step explanation:

25 times 7.5 is 187.7

Answer:

[tex]A=-5+9i[/tex]

Step-by-step explanation:

[tex]\left(3+4i\right)-\left(8-5i\right)\\\\\mathrm{Group\:the\:real\:part\:and\:the\:imaginary\:part\:of\:the\:complex\:number}\\\left(a+bi\right)\pm \left(c+di\right)=\left(a\:\pm \:c\right)+\left(b\:\pm \:d\right)i\\\\=\left(3-8\right)+\left(4+5\right)i\\3-8=-5\\4+5=9\\\\=-5+9i[/tex]

Answer:

1/3

Step-by-step explanation:

hope this helps  

Answer:

It is 3/8

Step-by-step explanation:

I got it right on Edge 2021.

Answer:

[tex]\dfrac{-1}{6}[/tex]

Step-by-step explanation:

Given the limit of a function expressed as [tex]\lim_{ x\to \ 0} \dfrac{sin(x)-tan(x)}{x^3}[/tex], to evaluate the following steps must be carried out.

Step 1: substitute x = 0 into the function

[tex]= \dfrac{sin(0)-tan(0)}{0^3}\\= \frac{0}{0} (indeterminate)[/tex]

Step 2: Apply  L'Hôpital's rule, by differentiating the numerator and denominator of the function

[tex]= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ sin(x)-tan(x)]}{\frac{d}{dx} (x^3)}\\= \lim_{ x\to \ 0} \dfrac{cos(x)-sec^2(x)}{3x^2}\\[/tex]

Step 3: substitute x = 0 into the resulting function

[tex]= \dfrac{cos(0)-sec^2(0)}{3(0)^2}\\= \frac{1-1}{0}\\= \frac{0}{0} (ind)[/tex]

Step 4: Apply  L'Hôpital's rule, by differentiating the numerator and denominator of the resulting function in step 2

[tex]= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ cos(x)-sec^2(x)]}{\frac{d}{dx} (3x^2)}\\= \lim_{ x\to \ 0} \dfrac{-sin(x)-2sec^2(x)tan(x)}{6x}\\[/tex]

[tex]= \dfrac{-sin(0)-2sec^2(0)tan(0)}{6(0)}\\= \frac{0}{0} (ind)[/tex]

Step 6: Apply  L'Hôpital's rule, by differentiating the numerator and denominator of the resulting function in step 4

[tex]= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ -sin(x)-2sec^2(x)tan(x)]}{\frac{d}{dx} (6x)}\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^2(x)sec^2(x)+2sec^2(x)tan(x)tan(x)]}{6}\\\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^4(x)+2sec^2(x)tan^2(x)]}{6}\\[/tex]

Step 7: substitute x = 0 into the resulting function in step 6

[tex]= \dfrac{[ -cos(0)-2(sec^4(0)+2sec^2(0)tan^2(0)]}{6}\\\\= \dfrac{-1-2(0)}{6} \\= \dfrac{-1}{6}[/tex]

Hence the limit of the function [tex]\lim_{ x\to \ 0} \dfrac{sin(x)-tan(x)}{x^3} \ is \ \dfrac{-1}{6}[/tex].

Answer:

1) we will fail to reject the null hypothesis and conclude that the population mean apartment rental rate does not exceed the level reported in 2002

2) P - value = 0.116435

Step-by-step explanation:

We are given;

Population mean; μ = $895

Sample mean; x' = $915

Population standard deviation; σ = $225

Sample standard deviation; s = $227.50

Sample size; n = 180

Let's state the hypothesis;

Null hypothesis;H0: μ ≤ $895

Alternative hypothesis;Ha: μ > $895

Now, the z-score formula is;

z = (x' - μ)/(σ/√n)

Thus, we are making use of the population standard deviation

z = (915 - 895)/(225/√180)

z = 20/16.7705

z = 1.193

From online p-value from z-score calculator attached, with α = 0.10, one tail, we have;

The P-Value is 0.116435

This is more than the significance level of 0.1, thus we will fail to reject the null hypothesis and conclude that the population mean apartment rental rate does not exceed the level reported in 2002

Answer: 943,212

Step-by-step explanation:

Suppose that you want to know the value of a given digit in a given number, where the digit is x.

Now, you should count the position of this digit, starting at the decimal point and counting to the left.

This position, a number n, will give the value of our digit as:

Value = x*10^(n-1)

in the number 893,417 the digit 9 is in the fifth place (counting from right to left).

Then the value of this 9 is:

9*10^(5 - 1) = 90,000

Now, if we want something ten times larger than this, we have:

N = 10*90,000 = 900,000

Now the 9 is in the sixth place, then we must find a number with a 9 in the sixth place, for example, 943,212.

Answer:

K(F) = 5/9 (F - 32) + 273.15

K(F)=298.15k

Step-by-step explanation:

C(F) =5/9 (F - 32) is used to convert temperature from Fahrenheit (F) to Celsius (C).

C(F) =5/9 (F - 32)

The function K(C)= C + 273.15 is used to convert temperature from Celsius (C) to the Kelvin (K) scale.

K(C)= C + 273.15

K(c) - 273= C

Equating both values of C

K(F) - 273.15=5/9 (F - 32)

K(F) = 5/9 (F - 32) + 273.15

If F = 77°F

K(F) = 5/9 (F - 32) + 273.15

K(F) = 5/9(77-32) + 273.15

K(F) = 5/9(45) +273.15

K(F) = 25+273.15

K(F)=298.15k

Answer:

K

C

F

298.15

Step-by-step explanation:

Answer:

T=112.5+0.50*b (since there was not a given number of beads)

Answer:

12(4+1) i think

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Solving for:}[/tex]

[tex]\large\textbf{4 + 12}[/tex]

[tex]\huge\textbf{Convert it to an easier way to}\\\huge\textbf{understand or keep it as it is:}[/tex]

[tex]\large\textbf{= 12 + 4}[/tex]

[tex]\huge\textbf{The answer:}[/tex]

[tex]\large\textbf{= 16}[/tex]

[tex]\huge\textbf{Now, let's see which one of your choices}\\\huge\textbf{are equivalent to your original equation.}[/tex]

[tex]\huge\textsf{Option A.}[/tex]

[tex]\large\textbf{6(8 + 6)}[/tex]

[tex]\large\textbf{= 6(8) + 6(6)}[/tex]

[tex]\large\textbf{= 48 + 36}[/tex]

[tex]\large\textbf{= 84}[/tex]

[tex]\large\textsf{OR}[/tex]

[tex]\large\textbf{6(8 + 6)}[/tex]

[tex]\large\textbf{= 6(14)}[/tex]

[tex]\large\textbf{= 84}[/tex]

[tex]\large\textbf{84 }\boxed{\neq}\large\textbf{ 16}[/tex]

[tex]\huge\textsf{Option B.}[/tex]

[tex]\large\textbf{12(4 + 1)}[/tex]

[tex]\large\textbf{= 12(4) + 12(1)}[/tex]

[tex]\large\textbf{= 48 + 12}[/tex]

[tex]\large\textbf{= 60}[/tex]

[tex]\large\textsf{OR}[/tex]

[tex]\large\textbf{12(4 + 1)}[/tex]

[tex]\large\textbf{= 12(5)}[/tex]

[tex]\large\textbf{= 60}[/tex]

[tex]\large\textbf{60 }\boxed{\neq}\large\textbf{ 16}[/tex]

[tex]\huge\textsf{Option C.}[/tex]

[tex]\large\textbf{4(44 + 3)}[/tex]

[tex]\large\textbf{= 4(44) + 4(3)}[/tex]

[tex]\large\textbf{= 176 + 12}[/tex]

[tex]\large\textbf{= 188}[/tex]

[tex]\large\textsf{OR}[/tex]

[tex]\large\textbf{4(44 + 3)}[/tex]

[tex]\large\textbf{= 4(47)}[/tex]

[tex]\large\textbf{= 188}[/tex]

[tex]\large\textbf{188 }\boxed{\neq}\large\textbf{ 16}[/tex]

[tex]\huge\textsf{Option D.}[/tex]

[tex]\large\textbf{8(6 + 4)}[/tex]

[tex]\large\textbf{= 8(6) + 8(4)}[/tex]

[tex]\large\textbf{= 48 + 32}[/tex]

[tex]\large\textbf{= 80}[/tex]

[tex]\large\textsf{OR}[/tex]

[tex]\large\textbf{8(6 + 4)}[/tex]

[tex]\large\textbf{= 8(10)}[/tex]

[tex]\large\textbf{= 80}[/tex]

[tex]\large\textbf{80 }\boxed{\neq}\large\textbf{ 16}[/tex]

[tex]\huge\text{Therefore, your answer: \boxed{\textsf{None of the above}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Liquid

Step-by-step explanation:

solids :have definite shape and definite volume.

Liquids :have definite volume and shape of the container.(or no definite shape)

Gas: has no definite volume and no definite shape.

Answer:

12^1 = 12

Step-by-step explanation:

Any number raised to the power of one equals the number itself.

Answer:

11 25/64 in ^3

Step-by-step explanation:

Volume of a cube is given by

V = s^3

s = 2 1/4 = 9/4

V = (9/4) ^3

  = 729/64

  =11 25/64 in ^3

Answer:

Area of a rectangle= L×B

=8.26cm×5.5cm

=45.43cm square

Answer:

45.43cm squared

Step-by-step explanation:

Length times breadth =

8.26cm x 5.5cm.

8.26cm x 5.5cm = 45.43cm squared.

Using an algorithm is a good way to figure out this question. There are useful websites to teach you about them :)

I'm going to assume you're asking where the point is located on a coordinate plane.

We have x = 0 and y = -4.

So, we start at (0, 0) and move down 4 units.

Best of Luck!